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+# Adapting Pre-trained 3D Models for Point Cloud Video Understanding via Cross-frame Spatio-temporal Perception
+
+Baixuan Lv $^{1*}$  Yaohua Zha $^{1,2*}$  Tao Dai $^{3\dagger}$  Xue Yuerong $^{1}$  Ke Chen $^{2}$  Shu-Tao Xia $^{1,2}$  Tsinghua University Pengcheng Laboratory Shenzhen University
+
+# Abstract
+
+Point cloud video understanding is becoming increasingly important in fields such as robotics, autonomous driving, and augmented reality, as they can accurately represent object motion and environmental changes. Despite the progress made in self-supervised learning methods for point cloud video understanding, the limited availability of 4D data and the high computational cost of training 4D-specific models remain significant obstacles. In this paper, we investigate the potential of transferring pre-trained static 3D point cloud models to the 4D domain, pointing out the limitations of static models that capture only spatial information while neglecting temporal dynamics. To address this, we propose a novel Cross-frame Spatio-temporal Adaptation (CSA) strategy by introducing the Point Tube Adapter as the embedding layer and the Geometric Constraint Temporal Adapter (GCTA) to enforce temporal consistency across frames. This strategy extracts both short-term and long-term temporal dynamics, effectively integrating them with spatial features and enriching the model's understanding of temporal changes in point cloud videos. Extensive experiments on 3D action and gesture recognition tasks demonstrate that our method achieves state-of-the-art performance, establishing its effectiveness for point cloud video understanding. Code is available at: https://github.com/LvBaixuan/Point-CSA.
+
+# 1. Introduction
+
+Four-dimensional (4D) point cloud videos offer an accurate representation of object motion, making them increasingly valuable in fields such as robotics, autonomous driving, and augmented reality. A comprehensive understanding of point cloud videos is crucial for effectively perceiving environmental changes and facilitating interactions with the real world. Consequently, the learning-based point cloud video understanding [9-11, 20, 33] has attracted significant re
+
+![](images/020e3c8aa6140894301c64f722b0043a4156f722663e8aacb25a4b6d62b7178b.jpg)  
+Figure 1. Comparison of direct transfer of static point cloud pretraining model and point cloud video pre-training model on MSR-Action dataset. Blue bars represent the performance of 4D-specific models, yellow bars indicate the results from directly transferring static point cloud pre-trained models, and orange bars depict the performance after applying our Adaptation Method.
+
+search interest in recent years.
+
+Self-supervised representation learning has become the most popular approach for current point cloud video understanding, as it learns general representations using unlabeled 4D data. Although various self-supervised methods [25-28, 46] have achieved some success in point cloud video modeling, the difficulty in collecting 4D data results in relatively small pre-training datasets, which limits the ability to learn general representations. Furthermore, the introduction of the temporal dimension in point cloud videos increases the time and computational resources required during the pre-training phase, thereby raising the costs of training 4D-specific models.
+
+Pre-trained models [4, 8, 23, 37-39, 42, 44] for 3D static point clouds have seen significant success within the community and have gained widespread adoption. Static and dynamic point clouds exhibit spatial consistency, raising the question of whether existing pre-trained models for static point clouds can be effectively leveraged for point cloud videos, thereby reducing the need for additional training of 4D-specific models. To explore this, we initially di
+
+rectly transfer existing popular pre-trained models for static point clouds to the 4D domain. However, as shown in Figure 1, the direct transfer of static point cloud pre-trained models results in significantly inferior performance compared to existing pre-training methods [25, 26, 28] specifically designed for point cloud videos. This performance gap is primarily due to the static models capturing only spatial information while neglecting critical temporal dynamics. These observations have motivated us to design an adaptation strategy that incorporates temporal awareness.
+
+The straightforward idea is to incorporate temporal information into static point clouds. Inspired by previous work [9, 11], we introduce the Point Tube Adapter as our embedding layer, replacing the embedding layer in static point cloud pre-trained models. As shown in Table 3, although this modification significantly enhances the model's ability to understand point cloud videos, there remains a gap compared to dedicated 4D models. We believe this is due to the self-attention mechanism in the frozen backbone network being unable to dynamically capture the long-range spatio-temporal correlations between patches. To this end, we propose the Geometric Constraint Temporal Adapter (GCTA), which introduces geometric constraints on neighboring points to ensure the consistency of point cloud structures across different time frames during interaction, capturing cross-temporal geometric information. This strategy enables the model to perceive structural changes in spatial regions throughout the entire video and integrates global dynamic information into the pre-trained encoder, enriching the model's understanding of temporal dynamics.
+
+The Cross-frame Spatio-temporal Adaptation (CSA) strategy not only allows the model to capture short-term structure changes but also emphasizes long-term dynamics, significantly enriching its understanding of temporal information. We evaluated our model on 3D action recognition and gesture recognition tasks. Experiments on the MSR-Action3D [18] and SHREC'17 [7] datasets demonstrate the effectiveness of our approach. The contributions of this paper include:
+
+- We explore methods for transferring spatial semantic information from static point clouds to point cloud videos. To our knowledge, this is the first exploration of applying static point cloud pre-trained models in point cloud video tasks.  
+- We propose a novel Cross-frame Spatio-temporal Adaptation (CSA) strategy by introducing the Point Tube Adapter as the embedding layer and the Geometric Constraint Temporal Adapter (GCTA) to enforce temporal consistency across frames. This strategy extracts both short-term and long-term temporal dynamics, effectively integrating them with spatial features and enriching the model's understanding of temporal changes in point cloud videos.
+
+- Extensive experiments on 3D action and gesture recognition tasks demonstrate that our method achieves state-of-the-art performance, highlighting its efficacy in point cloud video understanding.
+
+# 2. Related Work
+
+# 2.1. Static Point Cloud Pre-trained Model
+
+Recent research on pre-training methods for 3D point cloud analysis has made significant progress. These methods typically involve learning latent semantic information from point clouds through pretext tasks, followed by fine-tuning the model for specific applications to enhance performance. Existing pretext tasks can be categorized into two types: discriminative tasks [2, 5, 12, 34, 45], and generative tasks [13, 19, 30, 36, 40, 41]. Discriminative methods enable the model to distinguish similar point clouds by contrasting various views or instances. For example, techniques such as PointContrast [35] and CrossPoint [1] leverage both in-domain and cross-domain features. Generative methods learn the latent features of the data relying on autoencoders to reconstruct the original input. For example, PointBERT [37] generates discrete point tokens that contain meaningful local information derived from masked tokens. Point-MAE [23] employs an autoencoder to learn high-level latent features from unmasked patches, with the aim of reconstructing the masked point patches. ACT [8] significantly improves the performance of 3D self-supervised networks on real scanned point clouds by combining pretrained language and image models. PointGPT [4] introduces an autoregressive generation task for point clouds to pre-train Transformer models, offering high scalability.
+
+However, these pre-trained models have primarily been fine-tuned for downstream tasks associated with static point clouds. Our research aims to extend their applicability by transferring these models to the domain of point cloud video understanding.
+
+# 2.2. Point Cloud Video Understanding
+
+Point cloud videos exhibit a dual nature, being unordered in the spatial dimension while ordered in the temporal dimension. This characteristic necessitates the design of specialized methods to aggregate spatio-temporal information to perceiving both geometry and dynamics. Current approaches in this domain can be broadly classified into voxel-based [15, 43] and point-based [9-11, 20, 21, 33] techniques. Voxel-based methods, such as MinkowskiNet [6], involve voxelizing the original point clouds and then employing 4D convolution to extract features from 4D voxels. However, this voxelization process inherently results in quantization loss. In contrast, point-based methods operate directly on the raw point data. MeteorNet [20] introduces the temporal dimension and tracks motion at the point level,
+
+![](images/df570255063dd93aac7158cbde2603dc98fd2241d04947a77f32406c81c605c6.jpg)  
+Figure 2. Illustration of the proposed Cross-frame Spatio-temporal Adaptation strategy. We divide point cloud videos into point tubes. Aggregate points within the point tube to obtain local spatio-temporal embedding, and construct a cross-frame KNN graph based on the coordinates of the anchor point of the point tubes. Our proposed Geometric Constraint Temporal Adapter (GCTA) aggregates long-term changes based on the cross-frame KNN graph. During fine-tuning, the parameters of Attention and Feed Forward Network(FFN) of the pre-trained model are frozen.
+
+while PSTNet [11] constructs point tubes along the time axis to facilitate 4D point convolution. Recent advances, including P4Transformer [9], PPTr [33], and LeaF [21], have integrated transformer architectures to expand the receptive field. PST-Transformer [10] builds on P4Transformer, enhancing its ability to model spatio-temporal structures through spatial displacement encoding. To effectively learn the inherent information in point cloud videos, rather than focusing solely on downstream tasks, several methods employ self-supervised learning to enhance generalization capabilities. One approach [31] pretrains an encoder by predicting the temporal order of shuffled segments. C2P [46] introduces a complete-to-part 4D distillation method to predict representations of point cloud frames over short time windows. Additionally, several methods [26-28] utilize spatial and inter-frame contrastive learning to extract inherent geometric and dynamic features. However, these techniques often rely on clip-level or frame-level pretext tasks to learn motion information, which may be limited by inconsistencies in points across frames. MaST-Pre [25] proposes a masked prediction approach that segments continuous point clouds into point tubes for reconstruction. While this method effectively encodes relative spatio-temporal information within the point tubes, it falls short in capturing global semantics.
+
+Our approach preserves the model's strong encoding
+
+capability for spatial structures learned from static point clouds while also emphasizing the capture of short-term morphological changes and long-term dynamics.
+
+# 3. Method
+
+# 3.1. Overview
+
+The general framework of our method is shown in Figure 2. To enable the static point cloud pre-trained model to perceive dynamic information within point cloud videos, we introduce the Cross-frame Spatio-temporal Adaptation (CSA) strategy, which allows the model to comprehend point cloud videos through both short-term and long-term spatial structural changes. Initially, we incorporate point tubes during the feature embedding phase. This grouping strategy combines local points along both spatial and temporal dimensions. By integrating relative spatio-temporal information, the model effectively captures temporal dynamics along with spatial structures. Subsequently, to enhance attention to the spatial structural changes of point clouds across the entire video, we propose a Geometric Constraint Temporal Adapter(GCTA). This module facilitates feature aggregation over a global temporal range, allowing each point tube to traverse time and identify relevant features from other point tubes throughout the video. By aggregating spatial information from various frames, we in
+
+fuse global dynamic knowledge into the pre-trained model.
+
+Through this approach, we successfully adapt the static point cloud pre-trained model for point cloud video understanding tasks while keeping its parameters frozen.
+
+# 3.2. Point Tube Adapter
+
+Some widely used static point cloud pretraining methods process input point clouds using farthest point sampling (FPS) and K-Nearest Neighbors (KNN) algorithms to obtain center points and point patches. This encoding technique effectively aggregates information from local spatial neighborhoods. However, point cloud video data exhibit dynamic characteristics, necessitating a neighborhood partitioning method that can extract spatial structures while concurrently encoding temporal information.
+
+Building on previous work [9, 11], we introduce the concept of point tubes. Point cloud videos can be represented as a series of 3D point coordinates  $P \in \mathbb{R}^{L \times N \times 3}$ , where  $L$  is the length of the video and  $N$  is the number of points per frame. First, we uniformly select anchor frames within the point cloud video, obtaining anchor points using FPS within these frames and extending them to adjacent frames. Next, we search for neighbors within a spatial radius  $r_s$  around the anchor points in both the anchor frame and its adjacent frames, forming a point tube, denoted as  $T \in \mathbb{R}^{l \times k \times 3}$ , where  $l$  is the temporal length of the point tube and  $k$  is the number of points per frame in the point tube.
+
+Similarly to the embedding methods for static point clouds, we explicitly calculate the relative distances between the points in the tube and the anchor points, which aids the model in capturing local spatial structures. In addition, we incorporate relative temporal information to encode short-term local structural dynamics. The obtained spatio-temporal displacements  $(\delta_x,\delta_y,\delta_z,\delta_t)$  serve as point-level features  $F_{p}$ . The embedding of point tubes is accomplished by an extended lightweight 4D PointNet [24], which mainly consists of feature mapping functions and pooling layers. This embedding can be represented as:
+
+$$
+T _ {e} = \operatorname {m a x p o o l} [ \psi (F _ {p}) ], \tag {1}
+$$
+
+where  $\psi : \mathbb{R}^{lk \times 4} \longrightarrow \mathbb{R}^{lk \times C}$  aims to increase the dimensionality of point features to enhance feature representation capabilities. We directly input the embeddings  $T_{e}$  into the pre-trained encoder.
+
+# 3.3. Geometric Constraint Temporal Adapter
+
+The classical Transformer [29] relies on the self-attention mechanism to perceive long-range correlations among all patches globally and has achieved great success in static 3D domains. However, simply replacing point patch embeddings with point tube embeddings still makes it challenging to adapt static point cloud pre-trained models for point cloud video. The temporal scope of point tubes remains
+
+![](images/7fdd5372e234196414af714833976bcd8555f37cfc1f07611b43f1ac5326c4e0.jpg)  
+(a) Cross-frame KNN.
+
+![](images/98c7ba51ebd397422148e5d5f32eb3d8976c353c76698f62f0d15a6c341cdc68.jpg)  
+(b) Aggregation of point tube features through cross-frame KNN Graph.  
+Figure 3. Illustration of Geometric Constraint Temporal Adapter.
+
+limited by their length, capturing only short-term changes. Moreover, static point clouds only contain spatial structural information, which results in the frozen parameter static point cloud pre-trained models having a limited ability to perceive temporal relationships between point tubes.
+
+To address this issue, we propose Geometric Constraint Temporal Adapter (GCTA) to capture long-term dynamic information from point cloud videos. The structure of GCTA is shown in Figure 3. Inspired by EdgeConv [32], We construct a directed cross-frame KNN graph  $G = (T, E)$  based on the spatial distance between all point tubes, allowing each point tube to explore more relevant point tubes across the entire video without being constrained by time. Consider a point cloud video divided into  $N'$  point tubes with features denoted as  $F = \{f_1, f_2, \dots, f_{N'}\}$ , we define the edge feature between the  $i$ -th and the  $j$ -th point tube as:
+
+$$
+e _ {i j} = \phi (\operatorname {c o n c a t} \left(f _ {j} - f _ {i}, f _ {i}\right)), \tag {2}
+$$
+
+where  $\phi : \mathbb{R}^{2C} \longrightarrow \mathbb{R}^{C'}$  is a function parameterized by a set of learnable parameters. We use a symmetric operation, max pooling, to aggregate the edge features and project them into feature dimension  $C$  using  $\xi : \mathbb{R}^{C'} \longrightarrow \mathbb{R}^C$ :
+
+$$
+f _ {i} ^ {\prime} = \xi (m a x p o o l (e _ {i j})). \tag {3}
+$$
+
+GCTA explicitly combines global variation, captured by  $f_{j} - f_{i}$ , with local structural features, captured by the point tube embedding  $f_{i}$ . By aggregating point tubes distributed across different timestamps, GCTA can learn the global dynamics of spatial structures, thereby enhancing long-term
+
+<table><tr><td>Methods</td><td>Reference</td><td>8 Frames</td><td>12 Frames</td><td>16 Frames</td><td>24 Frames</td></tr><tr><td colspan="6">Supervised Learning</td></tr><tr><td>MeteorNet[20]</td><td>ICCV2019</td><td>81.14</td><td>86.53</td><td>88.21</td><td>88.50</td></tr><tr><td>PSTNet[11]</td><td>ICLR2021</td><td>83.50</td><td>87.88</td><td>89.90</td><td>91.20</td></tr><tr><td>P4Transformer[9]</td><td>CVPR2021</td><td>83.17</td><td>87.54</td><td>89.56</td><td>90.94</td></tr><tr><td>Kinet[47]</td><td>CVPR2022</td><td>83.84</td><td>88.53</td><td>91.92</td><td>93.27</td></tr><tr><td>PPTr[33]</td><td>ECCV2022</td><td>84.02</td><td>89.89</td><td>90.31</td><td>92.33</td></tr><tr><td>LeaF[21]</td><td>ICCV2023</td><td>84.50</td><td>-</td><td>91.50</td><td>93.84</td></tr><tr><td>PST-Transformer[10]</td><td>TPAMI2023</td><td>83.97</td><td>88.15</td><td>91.98</td><td>93.73</td></tr><tr><td>X4D-SceneFormer[17]</td><td>AAAI 2024</td><td>86.47</td><td>-</td><td>92.56</td><td>93.90</td></tr><tr><td colspan="6">Self-Supervised Learning (End-to-End Fine-Tuning)</td></tr><tr><td>CPR[27]</td><td>AAAI2023</td><td>86.53</td><td>91.00</td><td>92.15</td><td>93.03</td></tr><tr><td>C2P[46]</td><td>CVPR2023</td><td>87.16</td><td>-</td><td>91.89</td><td>94.76</td></tr><tr><td>PointCMP[26]</td><td>CVPR2023</td><td>89.56</td><td>91.58</td><td>92.26</td><td>93.27</td></tr><tr><td>PointCPSC[28]</td><td>ICCV2023</td><td>88.89</td><td>90.24</td><td>92.26</td><td>92.68</td></tr><tr><td>MaST-Pre[25]</td><td>ICCV2023</td><td>-</td><td>-</td><td>-</td><td>94.08</td></tr><tr><td colspan="6">Adaptation for Pre-Trained Models</td></tr><tr><td>Point-BERT+CSA</td><td>-</td><td>90.72</td><td>92.39</td><td>93.38</td><td>94.77</td></tr><tr><td>Point-MAE+CSA</td><td>-</td><td>91.41</td><td>92.04</td><td>93.73</td><td>95.12</td></tr><tr><td>PointGPT-S+CSA</td><td>-</td><td>91.41</td><td>93.08</td><td>94.08</td><td>94.42</td></tr></table>
+
+Table 1. Action recognition accuracy (%) on the MSR-Action3D.
+
+temporal perception.
+
+# 3.4. Feature Interaction
+
+In this section, we fuse local and global spatio-temporal information. The Point Tube Adapter provides the model with local spatio-temporal information, while the GCTA learns global dynamic knowledge. The global information related to spatial positions is provided by a customized position encoder (PE) implemented as a simple multilayer perceptron (MLP). The position encoders in different layers maintain the same architecture but have different parameters. The specific architecture is illustrated in the figure. The feature interaction process at the  $i$ -th layer can be represented as:
+
+$$
+\begin{array}{l} \mathcal {F} _ {i + 1} = F F N \left(\text {A t t e n t i o n} \left(\mathcal {F} _ {i}\right)\right) \tag {4} \\ + G C T A (\mathcal {F} _ {i}) + P E (\mathcal {F} _ {i}), \\ \end{array}
+$$
+
+where FFN is a feedforward neural network whose parameters, along with the attention parameters, are pre-trained on static point cloud data and frozen during the adaptation process.
+
+# 4. Experiments
+
+We evaluated the performance of our proposed Cross-frame Spatio-temporal Adapting (CSA) strategy on 3D action recognition and gesture recognition tasks. We also discuss the benefits of our adaptation strategy and architecture in
+
+Sec 4.4. We used three classic pre-trained models, Point-Bert [37], Point-MAE [23], and PointGPT-S [4], as our baseline.
+
+# 4.1. Experiment Setting
+
+We apply our CSA strategy on three baseline models: Point-BERT [37], Point-MAE [23], and PointGPT-S [4]. All three are pre-trained on ShapeNet [3] dataset for 300 epochs.
+
+To ensure a fair comparison, we use the same experimental settings for each baseline. We freeze the weights of the pre-trained static point cloud model and only update the parameters of the Point Tube Embedding module, the GCTA, and the head during downstream task training. We employ the SGD optimizer. The learning rate warms up to 0.01 in the first 10 epochs and decays at a rate of 0.1 in the 20th and 30th epochs. The model is trained for a total of 50 epochs.
+
+# 4.2.3D Action Recognition
+
+We only use the coordinates of the points, without incorporating color information. The point cloud videos are divided into multiple clips with a fixed number of frames as input. During evaluation, we average the prediction probabilities at the clip level to obtain the video-level prediction result.
+
+The experiment is conducted on the MSR-Action3D [18] dataset. MSR-Action3D consists of 567 depth videos, with 20 action categories. Each video in the MSR-Action3D dataset contains an average of 40 frames. Following pre
+
+vious work [9], we partition the dataset into 270 training videos and 297 testing videos. To evaluate the performance of our adaptation strategy under different temporal resolutions, we conduct experiments by extracting 8, 12, 16, and 24 frames, with each frame randomly sampled to 2048 points.
+
+We select an anchor frame every two frames and sample 64 anchor points from it. We set the temporal length of the point tube  $l = 3$ , the neighborhood space radius  $r_s = 0.3$  and randomly sample 32 points in the neighborhood space. The results summarized in Table 1 demonstrate that our adaptation method outperforms both supervised and self-supervised learning approaches across all temporal configurations. These results underscore the potential of transferring knowledge from static point cloud pre-trained models to point cloud video understanding. The robust spatial feature extraction capabilities inherent in these models provide valuable insights that enhance action recognition in dynamic settings. The CSA strategy effectively bridges the gap between static and dynamic representations, ensuring that the model can capitalize on both short-term and long-term temporal dynamics. The consistent improvements across varying input configurations suggest that our approach adapts flexibly to different temporal resolutions. In the experiments with 8, 12, and 16 frames, the application of our CSA to the three baseline models outperformed existing methods, demonstrating the effectiveness of this approach at low temporal resolutions.
+
+Overall, our results not only validate the effectiveness of the proposed adaptation method but also highlight the importance of leveraging existing pre-trained models to improve performance in downstream tasks.
+
+# 4.3. Gesture Recognition
+
+We conduct gesture recognition experiments on the SHREC'17 [7] dataset. SHREC'17 consists of 2800 videos in 28 classes for gesture recognition, of which  $70\%$  (2960 videos) are training data and the other  $30\%$  (840 videos) are the test set. To adapt our models, we freeze the parameters of the pre-trained models and retain the same architecture used in the action recognition tasks from the MSRAction3D dataset.
+
+As shown in Table 2, our method achieved higher recognition accuracy compared to both supervised and self-supervised methods. Notably, pre-trained models using the Cross-Frame Spatio-temporal Adaptation (CSA) strategy achieved impressive accuracies: PointGPT-S+CSA reached  $96.5\%$ , Point-BERT+CSA attained  $96.2\%$ , and Point-MAE+CSA achieved  $95.2\%$ . The high performance across various tasks reinforces the adaptability of our approach. By effectively leveraging the consistency in spatial structures between static point clouds and point cloud videos, our method successfully adapts static pre-trained
+
+models to a variety of downstream tasks. This indicates that the structural insights gained from static point clouds can be effectively transferred to dynamic contexts.
+
+<table><tr><td>Methods</td><td>Reference</td><td>Acc.(%)</td></tr><tr><td colspan="3">Supervised Learning</td></tr><tr><td>PLSTM-base [22]</td><td>CVPR2020</td><td>87.6</td></tr><tr><td>PLSTM-early [22]</td><td>CVPR2020</td><td>93.5</td></tr><tr><td>PLSTM-PSS [22]</td><td>CVPR2020</td><td>93.1</td></tr><tr><td>PLSTM-middle [22]</td><td>CVPR2020</td><td>94.7</td></tr><tr><td>PLSTM-late [22]</td><td>CVPR2020</td><td>93.5</td></tr><tr><td>Kinet [47]</td><td>CVPR2022</td><td>95.2</td></tr><tr><td colspan="3">Self-Supervised Learning (End-to-End Fine-Tuning)</td></tr><tr><td>PointCMP [26]</td><td>CVPR2023</td><td>93.3</td></tr><tr><td>MaST-Pre [25]</td><td>ICCV2023</td><td>92.4</td></tr><tr><td colspan="3">Adaptation for Pre-Trained Models</td></tr><tr><td>Point-BERT+CSA</td><td>-</td><td>96.2</td></tr><tr><td>Point-MAE+CSA</td><td>-</td><td>95.2</td></tr><tr><td>PointGPT-S+CSA</td><td>-</td><td>96.5</td></tr></table>
+
+Table 2. Gesture recognition accuracy  $(\%)$  on the SHREC'17.
+
+# 4.4. Ablation Studies
+
+To analyze the impact of each module in our proposed method on performance, we utilize Point-MAE as the baseline model and conduct ablation experiments on the MSRAction3D dataset.
+
+# 4.4.1. Architecture Design
+
+Our proposed Cross-frame Spatio-temporal Adaptation strategy enhances static point cloud pre-trained models with spatio-temporal information in three key ways: (1) Point Tube Adapter: This component aggregates local spatiotemporal neighborhood information. (2) Position Encoders: These encoders are independently learned for each layer, providing adaptive global spatial context. (3) Geometric Constraint Temporal Adapter(GCTA): This module extends the temporal field of view, enabling the model to perceive global dynamics effectively. we conduct extensive ablation studies, as shown in Table 3.
+
+We first present the performance of model A0 as the baseline (freeze the pre-trained model and only tuned the task head), achieving an accuracy of  $77.35\%$ . Model A1, which integrates Point Tube Adapter, increases the accuracy by  $6.62\%$ , highlighting the benefit of local spatio-temporal aggregation. Adding Position Encodings in model A2 further enhances accuracy to  $87.11\%$ , emphasizing the importance of adaptive global spatial context. Model A3, which combines Point Tube Adapter with the GCTA, achieves an accuracy of  $94.08\%$ , demonstrating the value of extend
+
+<table><tr><td></td><td>PTA</td><td>PE</td><td>GCTA</td><td>Acc.(%)</td></tr><tr><td>A0</td><td>×</td><td>×</td><td>×</td><td>77.35</td></tr><tr><td>A1</td><td>✓</td><td>×</td><td>×</td><td>83.97</td></tr><tr><td>A2</td><td>✓</td><td>✓</td><td>×</td><td>87.11</td></tr><tr><td>A3</td><td>✓</td><td>×</td><td>✓</td><td>94.08</td></tr><tr><td>A4(ours)</td><td>✓</td><td>✓</td><td>✓</td><td>95.12</td></tr></table>
+
+Table 3. Ablation studies on architecture designs. PTA denotes Point Tube Adapter, and PE denotes additional Position Encoders.
+
+ing the temporal field of view. Finally, our full model A4, incorporating all components, reaches an accuracy of  $95.12\%$ , confirming the effectiveness of our Cross-frame Spatio-temporal Adaptation strategy in leveraging both local and global information to improve recognition performance in dynamic point cloud scenarios.
+
+We visualize the attention distribution of the model with and without the GCTA. As shown in the Figure 4, for the same input video, the model adding the GCTA focuses more on the key frames where the action occurs, and allocates less attention to the frames that are weakly related to the motion (the first two frames). This demonstrates that the GCTA helps the model understand long-term motion.
+
+![](images/9e99cca72102df5355d0d027c0d65855ab8a1bcbc4a20c6ea8e9e0049b837e36.jpg)  
+(a) Without Geometric Constraint Temporal Adapter
+
+![](images/c1c19478334db726035c77289e3a0e6c15b9d66ff16b363492dad233f6aa938a.jpg)  
+(b) With Geometric Constraint Temporal Adapter  
+Figure 4. Visualization of the attention of model with/without the Geometric Constraint Temporal Adapter. Warmer color indicates higher attention. The model with the Geometric Constraint Temporal Adapter can correctly identify important frames and moving areas.
+
+# 4.4.2. Advantages of CSA compared to Other Tuning strategies
+
+To demonstrate the effectiveness of our Cross-frame Spatiotemporal Adaptation strategy, we conduct comprehensive comparative experiments against various tuning strategies while keeping the parameters of the pre-trained model frozen. As shown in the Figure 5, we compare our method with the vanilla adapter [14], VPT-Deep [16], and IDPT [39]. The baseline is consistent with that described in Sec 4.4.1. Our CSA outperforms other tuning strategies in terms of performance. We fully consider the spatially disordered and temporally ordered characteristics of point cloud
+
+![](images/dae291fa3b63c04987fb1f7e71cdbcb8eed7e92c3ad7c6cbc9776afe7df7f29b.jpg)  
+Figure 5. Comparison of different tuning strategies.
+
+videos, and enhance the ability of models to capture dynamics by combining spatio-temporal information. This focus on dynamics is crucial for point cloud video tasks such as action recognition and gesture detection, where temporal changes play a significant role.
+
+# 4.4.3. Receptive Field of Geometric Constraint Temporal Adapter
+
+The size of the convolutional kernel significantly influences the ability to model local structures. In the Geometric Constraint Temporal Adapter, the kernel size of EdgeConv [32] is determined by the number of neighbors  $k$  selected for each anchor point during graph construction. We investigate the impact of varying  $k$  values on spatio-temporal modeling. The kernel radius is defined as the distance between the center point of a point tube and the farthest point tube among its k-nearest neighbors. Figure 6a shows the average kernel radius corresponding to different  $k$  values. Figure 6b shows the video-level recognition accuracy under different  $k$  values.
+
+![](images/24d2e69d841479dd647312bf91ed0597795f6579e157b2cafbdecd396c948c5e.jpg)  
+(a) Kernel radius.  
+Figure 6. The effect of number of edge per point tube in the Geometric Constraint Temporal Adapter.
+
+![](images/bb763ba388302e4fc1090f984ac759b094b44d4fac9f496aaa39caaa9082bdd4.jpg)  
+(b) Accuracy.
+
+As  $k$  increases, the kernel radius also increases, indicating that a larger  $k$  allows the model to consider a broader spatial context when processing local structures. The kernel radius  $(< 0.1)$  is much smaller than the point tube spatial radius (0.3), which means that the GCTA can focus on changes in spatial structure at similar locations in different frames.
+
+In the case of  $k = 1$ , point tubes do not aggregate infor
+
+mation from others. Increasing  $k$  to 5 results in a slight decrease in accuracy to  $91.99\%$ , suggesting that too few neighbors may limit the ability to capture relevant features or even confuse its own information. The peak accuracy of  $95.12\%$  is observed at  $k = 20$ , demonstrating optimal performance when the model has access to a sufficient number of neighbors. However, as  $k$  increases to 25 and 30, the accuracy decreases by  $1.04\%$  and  $0.69\%$ , respectively, suggesting that excessive neighborhood information may introduce redundancy that negatively impacts performance.
+
+We further cut the point cloud video into slices, which limits the process of searching for spatial K-nearest neighbors within those slices. We evaluate the impact of the temporal range on the GCTA. The results shown in Table 4 indicate a clear trend: as the temporal range increases, model performance tends to improve, peaking when the full video is utilized. The model achieves the highest accuracy of  $95.12\%$  when using the full video as the slice length. This result underscores the advantage of utilizing the entire temporal span of the video, enabling the model to integrate global context and dynamics effectively.
+
+<table><tr><td>Slice Lenth</td><td>Acc.(%)</td></tr><tr><td>4</td><td>93.38</td></tr><tr><td>6</td><td>93.03</td></tr><tr><td>8</td><td>94.08</td></tr><tr><td>12</td><td>94.77</td></tr><tr><td>24(full clip)</td><td>95.12</td></tr></table>
+
+Table 4. The effect of temporal range.
+
+# 4.4.4. Location of Geometric Constraint Temporal Adapter
+
+We add the GCTA at different locations to explore how spatio-temporal information can be effectively combined with static point cloud pre-trained models. As shown in the Figure 7, we conducted experiments at 4 locations: (a) Bypass (b) Prepend (c) Post (d) Middle.
+
+The model achieves the highest accuracy of  $95.12\%$  when the GCTA is positioned at the Bypass location. This suggests that integrating spatio-temporal information in a way that allows the model to process it alongside static features leads to optimal performance. The Bypass configuration allows the model to maintain the integrity of the pretrained static features while benefiting from additional temporal dynamics. Compared to the result of placing at the Middle location, those at the Post location indicate that applying the GCTA after adding the global spatial position information still maintains a strong impact on the model's performance, suggesting that the temporal dynamics introduced at this stage enhance the overall understanding of the data. The lowest accuracy is observed at the Prepend loca
+
+![](images/88e359d88179f7419b466c1c8dc5683509051adb906b964f320c09784e636a68.jpg)
+
+![](images/d5e3dcc64c1995e2b8da52f8bd14165b50fdabce0f84cfdf80c0094fc704f54f.jpg)
+
+![](images/faffdac3e9e6a527144e69233fd425d6c0ec77ab7db34f61777b24e2aa13b4b4.jpg)  
+Figure 7. Different location of Geometric Constraint Temporal Adapter.
+
+tion. This placement disrupts the initial processing of static features, indicating that introducing temporal dynamics too early in the pipeline can hinder the model's ability to effectively leverage pre-trained static information.
+
+# 5. Conclusion
+
+In this paper, we explored transferring pre-trained static point cloud models to point cloud video tasks and identified the limitations of static models in capturing temporal dynamics. We proposed a novel Cross-frame Spatiotemporal Adaptation (CSA) strategy, integrating the Point Tube Adapter and Geometric Constraint Temporal Adapter (GCTA) to capture both short-term and long-term temporal dynamics. Our method outperforms existing approaches in 3D action and gesture recognition tasks, demonstrating its effectiveness in bridging the gap between static and dynamic point cloud representations. This work advances point cloud video understanding and offers valuable insights for future research.
+
+# Acknowledgment
+
+This work is supported in part by the National Natural Science Foundation of China, under Grant (62302309,62171248), Shenzhen Science and Technology Program (JCYJ20220818101014030, JCYJ20220818101012025), and the PCNL KEY project (PCL2023AS6-1).
+
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+# Adapting Text-to-Image Generation with Feature Difference Instruction for Generic Image Restoration
+
+Chao Wang $^{1,2*}$ , Hehe Fan $^{4}$ , Huichen Yang $^{2}$ , Sarvnaz Karimi $^{2}$ , Lina Yao $^{2,3}$ , Yi Yang $^{4\dagger}$ $^{1}$ ReLER, AAII, University of Technology Sydney  
+ $^{2}$ Data61, CSIRO  
+ $^{3}$ University of New South Wales  
+ $^{4}$ CCAI, Zhejiang University
+
+![](images/4b69f5f47df889f965d49123685c2a410717e383b68c662fe2defb26065cf788.jpg)  
+Deraining
+
+![](images/726f4fcafb771b7ea2c2f0f499f6808b13cc907f8c5896c234c16c12af67d05d.jpg)  
+Dehazing
+
+![](images/02cd9c718762293adad24f7f687733c1f83a0fe0e0baa49c206e305d9d164be7.jpg)  
+Desnowing  
+Figure 1. Our image restoration results. The proposed DiffRes introduces cross-modal understanding by leveraging multimodal vision-language models through an efficient adapter, without modifying the pre-trained diffusion model. This enables DiffRes to effectively produce clean and sharp results over 10 image restoration tasks. For simplicity, we only show several representative tasks here.
+
+![](images/91af981aa4f4fd61a0d558250aa4ed9ac0255e71ce70269961248ccfa8de3ba6.jpg)  
+Low-light Enhancement
+
+![](images/beff1d6e23afa4e796bb89d6423764d6e7cd245d91513a6af1e800ce291ba310.jpg)  
+Denoising
+
+![](images/8a6531bef0bd89815ee21ed40f5c4c54935200641f621b1de3b07ba510d490b3.jpg)  
+Motion Deblurring
+
+![](images/3ffcf2e48af0790780544ced5a906d5c5f10d469764aa2668249104eac52a0f5.jpg)  
+Mixed Degradations
+
+# Abstract
+
+Diffusion-based Text-to-Image (T2I) models have demonstrated significant potential in image restoration. However, existing models continue to grapple with challenges such as complex training and prompt design. We introduce a new perspective for improving image restoration by injecting knowledge from pretrained vision-language models into current T2I models. We empirically show that the degradation and content representations in BLIP-2 can be linearly separated, providing promising degradation guidance for image restoration. Specifically, the Feature Difference Instruction (FDI) is first extracted by Q-Formers through a simple subtraction operation based on reference image pairs. Then, we propose a multi-scale FDI adapter to decouple the degradation style and corrupted artifacts, and inject the styleflow exclusively into specific blocks through adapter-tuning, thereby preventing noise interference and eschewing the need for cumbersome weight retraining. In this way, we can train various task-specific adapters according to different degradations, achieving rich detail enhancement in the restoration results. Furthermore, the proposed FDI adapters have attractive properties of practical value, such as composability and generalization abl
+
+ity for all-in-one and mixed-degradation restoration. Extensive experiments under various settings demonstrate that our method has promising repairing quality over 10 image restoration tasks and a wide range of other applications.
+
+# 1. Introduction
+
+As a classical yet challenging Computer Vision (CV) task for many real-world applications, image restoration aims to recover high-quality images from degraded inputs by removing rain [19, 27, 63], haze [22, 64, 84], snow [10, 11, 42], low-light [36, 70, 90], etc. These traditional methods typically concentrate on specific, pre-defined weather conditions. To improve model scalability, researchers have proposed all-in-one networks [12, 31, 38, 45, 77] capable of handling different types of degradations through combined model ensembles. However, such approaches often necessitate separate training for each distinct condition or struggle with multiple degradations within a single image. Aiming at this problem, several works [21, 79, 80] have been proposed to restore images with mixed corruptions in a blind setting, i.e., both the mixing degradation types as well as the mixing mechanism are unknown. Nevertheless, these methods still
+
+![](images/c77406c80d7dd61bc744b4399d094ce3a3faa3f8e7d4573d2b1edda62b9b4ada.jpg)  
+Figure 2. Our framework employs BLIP-2 to extract features from both clean and degraded image sets. The Feature Difference Instruction (FDI) is obtained by subtracting the Q-former output of clean features from that of degraded features. FDI is not only interpretable by the LLM to provide textual descriptions of degradation, it can also be leveraged in our DiffRes as the repairing instruction in a difference-based "DA-BLIP" way.
+
+heavily rely on the complex multi-head structure design or tedious pre-training on large datasets.
+
+Meanwhile, recent advancements in large Multimodal Vision-Language Models (MVLMs) have dramatically improved the capability to process and interpret visual and textual information in tandem. These models, which leverage both vision and language modalities, are integral to a range of applications, from understanding models for image captioning [34, 39, 61, 82, 98], visual question answering [4, 13, 33, 35, 74], to generating models for text-guided image creation [20, 52, 62, 66, 69] and editing [6, 8, 49, 50, 97]. Taking into account both effectiveness and efficiency, how to stably and reliably combine the strengths of both understanding and generating models for downstream CV tasks becomes intractable.
+
+Several studies leverage pretrained MVLMs for downstream computer vision tasks. CLIPStyler [30] and InstanStyle [81] propose to use CLIP-based guidance for style transfer, aligning input image content with target styles described by text prompts. Similar to CLIPStyler, DA-CLIP [45] and MPerceiver [3] further explore acquiring Degradation-Aware (DA) hints from the pretrained CLIP model and then inject the guidance into Text-to-Image (T2I) models for image restoration. However, two problems remain: (1) Both studies heavily rely on the design of prompt generation based on input-degraded images, which leads to mutual interference between content and degradation within the visual embedding [56]; and, (2) For complex illumination-related degradations such as haze, their visual degradative effects cannot be accurately described solely through text descriptions [46].
+
+In this paper, we aim to address these challenges for a more efficient and robust restoration framework, named DiffRes. We observe that BLIP-2 can effectively capture features encompassing both semantic content and degradation attributes, which are linearly separable to some extent. Specifically, we find the feature difference between
+
+clean and degraded images from BLIP-2 can be interpreted by Large Language Models (LLMs) [17], and effectively used as degradation instructions/conditions for T2I models, guiding image restoration during the denoising process (see Figure 2). Compared to past studied that utilize CLIP-based prompts derived from the input degraded image, our reference-image-pair-based Feature Difference Instruction (FDI) is easily accessible while being able to circumvent the impact of degradation factors during the CLIP image encoding, and encapsulate more directed DA-aware information through feature-level subtraction. Combined with the input image features, FDI provides more effective and efficient guidance for high-quality restoration.
+
+Building on this, we further design an adapter tuning-based framework that leverages FDI as a core component to enhance image restoration. Our framework, DiffRes, integrates FDI within a pretrained T2I model, enabling it to precisely reconstruct images using the feature differences as restoration cues. DiffRes consists of an inversion-based T2I model for high-fidelity reconstruction, a multi-scale FDI adapter for precise restoring guidance, and a degradation classifier for mixed degradation removal. During training, the pretrained Stable Diffusion (SD) remains frozen, in which DDIM inversion projects the degraded image into the latent space of LDM to provide the content information. The adapters extract defacement-related guidance instructions from FDI, such as color, depth, illumination, and stylization, and then inject them into the reverse diffusion process in a tuning way. A multi-label classifier enables composite degradation restoration and more customized image processing. By injecting the FDI within the denoising process, DiffRes addresses both semantic content and degradation factors simultaneously. This design not only enhances restoration quality but also improves the model adaptability across various types of degradation, paving the way for a more versatile and robust restoration solution.
+
+Our contributions are threefold:
+
+- We show that the BLIP-2 feature differences between clean and degraded images have the potential to instruct image restoration, with more targeted and clear Degradation-Aware (DA) guidance.  
+- We propose Feature Difference Instruction (FDI) adapter, a more effective tuning-based method to inject the implicit DA instructions into pretrained SD in a low-cost feature addition manner.  
+- Without loss of generalizability, we conduct extensive experiments under various settings to verify the superiority of DiffRes. Results show that our method achieves state-of-the-art performance over 10 image restoration tasks.
+
+# 2. Related Work
+
+Multimodal Vision-Language Models Broadly, multimodal vision-language models can be categorized into two
+
+![](images/90e6862fb0c94e09dbf214ff6fc8bc5b06e7fcf10f42f2f7715f1c6810e6a6bd.jpg)  
+Figure 3. The overview of the proposed DiffRes. DiffRes consists of pretrained stable diffusion, an FDI adapter, and a degradation classifier. Given a degraded image input, DiffRes first utilizes inversion to obtain an accurate latent space representation  $Z_{T}$ . During the denoising process (take step  $S$  as an example), FDI is further optimized through cross-attention with image features  $A_{S}^{i}$ , which are derived from four feature extraction blocks and three downsample blocks. These blocks adjust the feature resolution to match the latent space resolution of stable diffusion  $E_{S}^{i}$ . The FDI adapter then injects the final restoration-relevant guidance  $\hat{A}_{S}^{i}$  into the encoding layers of the Denoising U-Net through direct addition. Meanwhile, the visual modulator in the adapter integrates the optimized FDI  $\hat{F}_{S}^{i}$ , promoting feature regularization  $\theta_{S}^{i}$  in the decoding layers to encourage alignment with the distribution of clean images. Note that all trainable parameters are in the FDI adapter, which can be removed at any time without affecting the original T2I model. Additionally, an optional degradation classifier is employed to enable more challenging all-in-one, mixed-degradation, and customized image restoration.
+
+distinct types: Understanding and Generating. Understanding models such as CLIP (Contrastive Language-Image Pretraining) [61], BLIP (Bootstrapped Language-Image Pretraining) [34], and BLIP-2 [35] advanced cross-modal understanding by aligning visual and linguistic representations. Leveraging these foundations, a recent study [30, 32, 45, 81, 89] explored their applications in computer vision tasks. For instance, InstantStyle [81] leverages CLIP by capturing style features through the difference in encoded features between images and text. Similarly, DEADiff [56] employs BLIP-2 to manually decouple style and content using Q-formers during training. Meanwhile, inspired by the great success of diffusion-based vision-language generation models [52, 62, 66, 69], several recent text-to-image (T2I) methods [3, 40, 53, 68] have been proposed for both supervised and zero-shot computer vision tasks such as image stylization and super-resolution.
+
+In this paper, we propose DiffRes to efficiently combine two pre-trained MVLMs, i.e., vision-language understanding model BLIP-2 [35] and vision-language generating model Stable Diffusion [66], for universal image restoration. Considering the restoration as a process of decoupling degradation style and generating corrupted content, we discover that the feature difference in BLIP-2 can be effectively applied to image restoration tasks as repairing instruction for pre-trained T2I models.
+
+Image Restoration While single degradation image restoration methods [19, 22, 27, 42, 64, 90] have received significant progress, recent studies [9, 12, 38, 45, 54] seek to use an all-in-one framework to handle different degradations simultaneously. For instance, DA-CLIP [45] utilizes an additional image controller based on the pretrained CLIP model, which learns the degradation embeddings matched to the input image through contrastive learning. However, these methods can only repair one single type of degradation every time during inference, making them inapplicable to real-world scenarios where multiple weather degradations may coexist in a single image. To solve this challenge, several methods [3, 21, 79, 80] are proposed for mixed degradations removal. For example, Han et al. propose the Blind Image Decomposition (BID) [21] setting, regarding rain and other real-world weather corruptions as superimposing and separable to a clean image. MPerceiver [3] designs a multimodal prompt-based network with a learnable degradation predictor for restoration. Luo et al. [46] further improved DA-CLIP by incorporating mixed degradation labels into the dataset and optimizing the discrepancy between degraded and clean image embeddings through a fidelity loss. However, these methods still require tedious network training or prompt optimization against input noise interference, thus impeding the real-world implementation.
+
+In contrast, through efficient reference-based adapter tuning on pre-trained T2I models, our DiffRes enables both
+
+degradation-specific or -agnostic, and single- or mixed-degraded image restoration with high flexibility. Meanwhile, benefiting from the multimodal understanding capabilities of BLIP-2 and the generative priors of pre-trained diffusion models, our method can also be extended to other image-to-image translation applications.
+
+# 3. Method
+
+# 3.1. Preliminary
+
+Our method is based on the Latent Diffusion Model (LDM), which operates in a compressed latent space to enable efficient generation. The input image is first encoded into a latent representation using a pretrained Variational Autoencoder (VAE) [28]. The model then combines a forward diffusion process that incrementally adds noise to the latent representation and a reverse denoising process that reconstructs the original data. This approach is formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {L D M}} = \mathbb {E} _ {z _ {0}, c, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} (z _ {t}, c, t) \| ^ {2} \right], \tag {1}
+$$
+
+where  $z_{t}$  is the noisy latent representation at time step  $t$ ,  $\epsilon$  represents the true Gaussian noise, and  $c$  is the conditional information provided. The network  $\epsilon_{\theta}$  is trained to estimate this noise given the condition  $c$ , guiding the reverse diffusion process to reconstruct the original latent embedding  $z_{0}$ .
+
+After the reverse process, the final denoised latent representation is passed through the VAE decoder to generate the final image in pixel space.
+
+# 3.2. Feature Difference Instruction (FDI)
+
+Given a pretrained BLIP-2 model with a pair of corrupted  $S_{noise}$  and clean image  $S_{clean}$  sets, the Feature Difference Instruction (FDI), denoted as  $F$ , can be obtained as follows:
+
+$$
+\begin{array}{l} F = \mathrm {Q} - \text {f o r m e r (E n c o d e r} (S _ {\text {n o i s y}})) \\ - \text {Q - f o r m e r} (\operatorname {E n c o d e r} \left(S _ {\text {c l e a n}}\right)). \tag {2} \\ \end{array}
+$$
+
+The Q-former, pretrained on large-scale datasets generates features with a certain degree of linear separability, and the differences between paired images can be further interpreted by LLM (see Figure 2). This leads to the potential of aligning these differences with a pretrained T2I model to address downstream CV tasks. Based on this observation, we provide customized alignment between the vision-language understanding models (e.g., BLIP-2) and generating models (e.g., stable diffusion). Instead of retraining T2I models from scratch, we use adapter-tuning methods by integrating external plugins. An overview of our method is presented in Figure 3, consisting of a pretrained inversion-based T2I model for high-fidelity reconstruction, a multiscale FDI adapter for fine-grained instruction, and an optional degradation classifier for mixed degradation removal.
+
+# 3.3. Inversion-based Reconstruction
+
+In our image-to-image restoration task, standard diffusion sampling cannot directly map an existing image to a corresponding noise state. First, we use the pretrained VAE encoder to encode the clean image into the latent space as  $z_0$ . Then, starting from  $z_0$ , we gradually add noise to a specific state  $z_t$  following DDIM inversion [72], thus enabling the restoration conditioned on our FDI. This inversion process can be expressed as:
+
+$$
+\begin{array}{l} z _ {t} = \frac {\sqrt {\alpha_ {t}}}{\sqrt {\alpha_ {t - 1}}} z _ {t - 1} + \sqrt {\alpha_ {t}} \left(\sqrt {\frac {1}{\alpha_ {t}} - 1} \right. \\ \left. - \sqrt {\frac {1}{\alpha_ {t - 1}} - 1}\right) \epsilon_ {\theta} \left(z _ {t - 1}, t - 1\right). \tag {3} \\ \end{array}
+$$
+
+Unlike previous methods [3, 65] that inject content features through extra encoding on degraded images, our inversion-based method injects the content information in a direct and accurate way. It also encourages the model to generate content in regions obscured by degradation during the sampling process. Combined with the FDI adapter, our method facilitates higher-quality restoration from perspectives of noise removal and content inpainting.
+
+# 3.4. FDI Adapter
+
+Noise Decoupling. Since FDI already contains the degradation style and spatial information, we employ an inversion-based diffusion process to inpaint the corrupted areas. Consequently, the FDI, serving as the degradation or de facto restoration guidance, should ideally retain only degradation-related information. However, in practice, when dealing with complex degraded images, such as those severely obscured by rain or haze, the FDI still suffers from certain noise interference from the corrupted unpaired regions. To mitigate this problem, we propose emphasizing the degradation-relevant features in FDI combined with a more comprehensive pixel-level image feature space. We employ cross-attention [78] to refine the input FDI  $F$  (Query) based on the multi-stage image features  $A_{S}^{i}$  (Key, Value) extracted from the adapter. In this way, the refined output FDI  $\hat{F}_S^i$  become more focused on the degradation-related parts, enhancing the accuracy of subsequent image restoration or enhancement tasks.
+
+Multi-level Guidance. After the FDI refinement, we first inject the repairing guidance into the encoding layers of the denoising U-Net. Considering for low-level CV tasks, different encoding channels focus on varying types of information [5, 93]. For example, in the style transfer field [16, 25], features at different levels typically represent different aspects of style: lower-level features capture textures and details, while higher-level features are more inclined towards
+
+overall color and abstract style. Thus, we utilize the optimized FDI  $\hat{F}_S^i$  to further generate channel-wise weights based on the classical SEBlock [24], guiding the focus of information in each encoding layer through channel attention. The channel attention process can be formulated as:
+
+$$
+D _ {S} ^ {i} ^ {'} = D _ {S} ^ {i} \cdot \sigma \left(W _ {2} \cdot \operatorname {R e L U} \left(W _ {1} \cdot \operatorname {G A P} \left(\hat {F} _ {S} ^ {i}\right)\right)\right), \tag {4}
+$$
+
+where  $\cdot$  is the dot product, GAP refers to global average pooling,  $W_{1}$  and  $W_{2}$  are the weight matrices for the fully connected layers, and  $\sigma (\cdot)$  denotes the Sigmoid function.
+
+After channel attention, the final instruction  $\hat{A}_S^i$  has the same dimension as the intermediate feature  $E_S^i$  in the denoising U-Net. Similar to the T2I-Adapter [50], we directly add  $\hat{A}_S^i$  with  $E_S^i$  at each scale  $i$  for guidance injection.
+
+Visual Modulator. For the decoding layers in U-Net, we also utilize SEBlock, which is based on the refined FDI  $\hat{F}_S^i$  and the decoding features  $D_S^i$  following the skip-connection correspondence. Furthermore, we incorporate hierarchical stylized degradation information into the generation process through AdaIN [25], aligning with the encoding process. As shown in Figure 3 (a), our adaptive instance normalization can be expressed as:
+
+$$
+\hat {D} _ {S} ^ {i} = \gamma \left(\hat {F} _ {S} ^ {i}\right) \odot \operatorname {N o r m} \left(D _ {S} ^ {i} ^ {\prime}\right) + \beta \left(\hat {F} _ {S} ^ {i}\right), \tag {5}
+$$
+
+where  $\odot$  represents the element-wise multiplication,  $\gamma (\cdot)$  and  $\beta (\cdot)$  are implemented through two convolutional layers. Note that this visual modulator is also a plug-and-play module as a part of our FDI Adapter.
+
+# 3.5. Degradation Classifier
+
+In real-world scenarios, multiple types of degradation frequently co-occur, leading to the coexistence of various distortions within a single image. For instance, an image may depict weather conditions involving both rain and fog simultaneously. To address this complexity, we additionally deploy an MLP-based multi-label classifier to identify the degradation types present in the input image, as illustrated in Figure 3 (b). This multi-label classifier enables our DiffRes model to perform both all-in-one and mixed-degradation removal with high flexibility from two perspectives. (1) Composite: Simultaneously employ multi-branch FDI adapters trained on mixed datasets with different degradation types. Each branch can be combined through direct addition with adjustable weights obtained from the classifier. In this setting, the input  $\hat{F}_S^i$  of our visual modulator is the mean value of each adapter branch. (2) Progressive: Sequentially apply different task-specific adapters. This approach also allows for flexible customization to selectively remove specific weather effects, as shown in Figure 4.
+
+![](images/4837ab8c13c49c73b6594aeca40acc43b8af1b8b006dcf717a21b6decc734880.jpg)  
+Figure 4. Illustration of composite restoration (red) and progressive restoration (blue). Both approaches can produce satisfactory results for mixed-degradation removal. Zoom in to see the details.
+
+# 4. Experimental Setup and Results
+
+Datasets. For the task-specific and task-agnostic settings, we consider 10 restoration tasks: deraining, raindrop removal, dehazing, desnowing, low-light enhancement, denoising, motion deblurring, defocus deblurring, shadow removal, and JPEG decompression. For each degradation type, we collect data from the corresponding datasets, Rain: Rain100 (L&H) [88] and Rain1400 [19]; Haze: RESIDE-6K [58]; Snow: Snow100K [42]; Raindrop: RainDrop [57]; Low-light: LOL-v1 [83] and MEF [47]; Noise: DIV2K [2], Flickr2K [75] and CBSD68 [48]; Motion blur: GoPro [51]; Defocus blur: DPDD [1]; Shadow: SRD [59]; JPEG compression: DIV2K [2], Flickr2K [75] and LIVE1 [71]. For the mixed-degradation setting, we use RainDS [60] for raindrop + rainstreak, NYU-Rain [37] and OutDoor-Rain [77] for rainstreak + haze + low-light, and BID [21] for more complex combinations. Note that during the testing stage, to ensure a fair comparison, we use the whole training set corresponding to the test set to obtain the average FDI. Details of the dataset selection under different task settings are provided in the Supp.
+
+Evaluation Metrics. Apart from the commonly used pixel-level metrics PSNR and SSIM, we also adopt a variety of widely used metrics to provide a comprehensive evaluation of the different methods. In terms of feature-level perceptual quality, we use FID [23] and LPIPS [99] as reference-based metrics to measure the distance and similarity between ground truth images and the restored images.
+
+Implementation Details. We choose the pre-trained SD V2.1-512 model with 50 sampling steps as our base model. During training, we employ the AdamW optimizer [43]  $(\beta_{1} = 0.9, \beta_{2} = 0.99)$  over 50 epochs with a learning rate of  $1 \times 10^{-5}$ . All experiments are conducted on 4 NVIDIA A100 GPUs with a batch size of 32. The total training time of one FDI adapter is approximately 8 hours
+
+Table 1. Quantitative comparison between our method with other state-of-the-art approaches on nine different degradation-specific datasets.  $\downarrow$  represents the smaller the better, and  $\uparrow$  represents the bigger the better. Best and second best performance are in red and blue, respectively.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Deraining (Rain100H)</td><td rowspan="2">Method</td><td colspan="2">Dehazing (RESIDE)</td><td rowspan="2">Method</td><td colspan="2">Desnowing (Snow100K)</td></tr><tr><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td></tr><tr><td>MPRNet [91]</td><td>30.42 / 0.891</td><td>61.59 / 0.158</td><td>DehazeFormer [73]</td><td>30.29 / 0.964</td><td>7.58 / 0.045</td><td>DesnowNet [42]</td><td>27.53 / 0.899</td><td>9.84 / 0.147</td></tr><tr><td>MAXIM [76]</td><td>30.81 / 0.903</td><td>58.72 / 0.133</td><td>MAXIM [76]</td><td>29.12 / 0.932</td><td>8.12 / 0.043</td><td>DDMSNet [96]</td><td>28.85 / 0.877</td><td>3.24 / 0.096</td></tr><tr><td>IR-SDE [44]</td><td>31.65 / 0.904</td><td>18.64 / 0.047</td><td>IR-SDE [44]</td><td>25.25 / 0.906</td><td>8.33 / 0.060</td><td>PromptIR [55]</td><td>30.91 / 0.913</td><td>3.79 / 0.100</td></tr><tr><td>DA-CLIP [45]</td><td>33.91 / 0.926</td><td>11.79 / 0.031</td><td>DA-CLIP [45]</td><td>30.16 / 0.936</td><td>5.52 / 0.030</td><td>DA-CLIP [45]</td><td>30.83 / 0.907</td><td>3.01 / 0.082</td></tr><tr><td>Ours</td><td>34.55 / 0.935</td><td>9.97 / 0.023</td><td>Ours</td><td>30.87 / 0.970</td><td>5.08 / 0.023</td><td>Ours</td><td>31.32 / 0.925</td><td>2.10 / 0.077</td></tr><tr><td rowspan="2">Method</td><td colspan="2">Randrop Remocal (RainDrop)</td><td rowspan="2">Method</td><td colspan="2">Low-light Enhancement (LOL-v1)</td><td rowspan="2">Method</td><td colspan="2">Denoising (CBSD68, sigma=50)</td></tr><tr><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td></tr><tr><td>AttGAN [57]</td><td>31.59 / 0.917</td><td>22.38 / 0.058</td><td>MIRNet [90]</td><td>24.14 / 0.830</td><td>69.18 / 0.250</td><td>Restormer [92]</td><td>26.85 / 0.753</td><td>75.12 / 0.221</td></tr><tr><td>IDT [87]</td><td>31.87 / 0.931</td><td>25.54 / 0.059</td><td>URetinex-Net [85]</td><td>19.84 / 0.824</td><td>52.38 / 0.237</td><td>Xformer [95]</td><td>29.45 / 0.848</td><td>59.33 / 0.152</td></tr><tr><td>PromptIR [55]</td><td>32.05 / 0.933</td><td>25.13 / 0.054</td><td>Retinexformer [7]</td><td>24.08 / 0.825</td><td>58.31 / 0.244</td><td>PromptIR [55]</td><td>28.82 / 0.816</td><td>65.33 / 0.177</td></tr><tr><td>DA-CLIP [45]</td><td>30.75 / 0.892</td><td>24.31 / 0.061</td><td>DA-CLIP [45]</td><td>23.75 / 0.833</td><td>34.03 / 0.083</td><td>DA-CLIP [45]</td><td>28.55 / 0.807</td><td>66.35 / 0.201</td></tr><tr><td>Ours</td><td>33.70 / 0.939</td><td>19.65 / 0.047</td><td>Ours</td><td>24.55 / 0.839</td><td>29.17 / 0.075</td><td>Ours</td><td>29.17 / 0.823</td><td>61.29 / 0.161</td></tr><tr><td rowspan="2">Method</td><td colspan="2">Motion Deblur (GoPro)</td><td rowspan="2">Method</td><td colspan="2">Defocus Deblur (DPDD)</td><td rowspan="2">Method</td><td colspan="2">JPEG Compression (LIVE1, Q=10)</td></tr><tr><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td><td>PSNR ↑ / SSIM ↑</td><td>FID ↓ / LPIPS ↓</td></tr><tr><td>DeblurGAN [29]</td><td>28.70 / 0.858</td><td>27.02 / 0.178</td><td>DRBNet [67]</td><td>25.73 / 0.791</td><td>49.04 / 0.183</td><td>FBCNN [26]</td><td>27.77 / 0.803</td><td>30.16 / 0.997</td></tr><tr><td>Restormer [92]</td><td>30.05 / 0.937</td><td>13.54 / 0.138</td><td>FocalNet [15]</td><td>26.25 / 0.810</td><td>47.83 / 0.210</td><td>Restormer [92]</td><td>27.65 / 0.805</td><td>30.52 / 0.103</td></tr><tr><td>DiffIR [86]</td><td>32.55 / 0.952</td><td>10.21 / 0.087</td><td>PromptIR [55]</td><td>25.66 / 0.791</td><td>53.64 / 0.197</td><td>PromptIR [55]</td><td>27.47 / 0.793</td><td>32.34 / 0.078</td></tr><tr><td>DA-CLIP [45]</td><td>30.88 / 0.903</td><td>6.15 / 0.058</td><td>DA-CLIP [45]</td><td>26.15 / 0.802</td><td>48.11 / 0.193</td><td>DA-CLIP [45]</td><td>27.35 / 0.790</td><td>32.97 / 0.121</td></tr><tr><td>Ours</td><td>32.58 / 0.952</td><td>6.15 / 0.055</td><td>Ours</td><td>26.22 / 0.810</td><td>44.39 / 0.188</td><td>Ours</td><td>27.77 / 0.802</td><td>30.05 / 0.081</td></tr></table>
+
+Table 2. Quantitative results on five restoration tasks with state-of-the-art all-in-one methods.  $\downarrow$  represents the smaller the better, and  $\uparrow$  represents the bigger the better. Best and second best performance are in red and blue, respectively.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Deraining (Rain100L)</td><td colspan="2">Dehazing (SOTS)</td><td colspan="2">Denoising (BSD68, average)</td><td colspan="2">Deblurring (GoPro)</td><td colspan="2">Low-light Enhance. (LOL-v1)</td><td colspan="2">Average</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td></tr><tr><td>DL [18]</td><td>21.96</td><td>0.762</td><td>20.54</td><td>0.826</td><td>23.09</td><td>0.745</td><td>19.86</td><td>0.672</td><td>19.83</td><td>0.712</td><td>21.05</td><td>0.743</td></tr><tr><td>TransWeather [77]</td><td>29.43</td><td>0.905</td><td>21.32</td><td>0.885</td><td>29.00</td><td>0.841</td><td>25.12</td><td>0.757</td><td>21.21</td><td>0.792</td><td>25.22</td><td>0.836</td></tr><tr><td>TAPE [41]</td><td>29.67</td><td>0.904</td><td>22.16</td><td>0.861</td><td>30.18</td><td>0.855</td><td>24.47</td><td>0.763</td><td>18.97</td><td>0.621</td><td>25.09</td><td>0.801</td></tr><tr><td>AirNet [31]</td><td>32.98</td><td>0.951</td><td>21.04</td><td>0.884</td><td>30.91</td><td>0.882</td><td>24.35</td><td>0.781</td><td>18.18</td><td>0.735</td><td>25.49</td><td>0.846</td></tr><tr><td>IDR [94]</td><td>35.63</td><td>0.965</td><td>25.24</td><td>0.943</td><td>31.60</td><td>0.887</td><td>27.87</td><td>0.846</td><td>21.34</td><td>0.826</td><td>28.34</td><td>0.893</td></tr><tr><td>PromptIR [55]</td><td>36.75</td><td>0.963</td><td>26.63</td><td>0.945</td><td>31.58</td><td>0.886</td><td>28.44</td><td>0.863</td><td>22.34</td><td>0.826</td><td>28.79</td><td>0.894</td></tr><tr><td>DA-CLIP [45]</td><td>35.91</td><td>0.972</td><td>26.28</td><td>0.939</td><td>31.58</td><td>0.887</td><td>28.81</td><td>0.882</td><td>22.57</td><td>0.832</td><td>29.23</td><td>0.898</td></tr><tr><td>InstructIR-5D [14]</td><td>36.84</td><td>0.973</td><td>27.10</td><td>0.956</td><td>31.40</td><td>0.883</td><td>29.40</td><td>0.886</td><td>23.00</td><td>0.836</td><td>29.55</td><td>0.907</td></tr><tr><td>Ours</td><td>37.25</td><td>0.979</td><td>27.23</td><td>0.958</td><td>32.07</td><td>0.890</td><td>29.33</td><td>0.883</td><td>23.13</td><td>0.843</td><td>29.78</td><td>0.911</td></tr></table>
+
+with 45M parameter count. We divide the sampling process into three stages and inject the restoration instructions into the denoising U-Net during the beginning stage, as adding guidance in the middle and late stages has minimal effect on the results [50]. In addition to  $\mathcal{L}_{\mathrm{LDM}}$ , we incorporate an  $\mathcal{L}_1$  reconstruction loss between the generated and GT images in the latent space. Note that during testing, since degradation types are known, the degradation classifier is not needed. During inference, our classifier gives users more customized options. Given a random inference image, DiffRes first identifies potential degradation types (choosing one or more as needed) using the classifier and then computes the FDI from any dataset of that type. They
+
+can either manually set thresholds based on predicted labels to select the most similar degradation types for composite restoration, or progressively eliminate each specified type of degradation. More details are provided in the Supp.
+
+# 4.1. Results
+
+Single-task setting. We independently train the FDI-Adapter without the degradation classifier and evaluate it on task-specific restoration. The quantitative results across different datasets are summarized in Table 1. Compared to other task-specific methods, our approach achieves the best overall performance on most tasks. Figure 5 provides a visual comparison. Compared to other CLIP-based methods,
+
+![](images/06593735ef561bb78d19c015fb864c11faa5d23cbc4cd5cf76b24768df8bb6e2.jpg)
+
+![](images/c374f9bc27442d391d03b6ff4ff567b11ef01294ad20eed80f6331bdca82fc5f.jpg)
+
+![](images/794859a674cc75e6bb2968e7beade6022e0ff0224304d9d9ec9db6712f5471b1.jpg)  
+Figure 5. Qualitative comparison of different methods on four restoration tasks. Please zoom in to see the details.
+
+![](images/d83037939281501000ed4da2fd9a92487473c88e4cf149b1a87e40107659cfca.jpg)
+
+![](images/c05dd098806eed1ce74fcc2d65adcbf3a07aea82ed5dfac8a616c7bad6a3d70d.jpg)
+
+![](images/ebd0fdd18aa0d1bb538d819813abdb7cdc00362033f21abd6b69165aaee112ba.jpg)
+
+![](images/3a4ffe5e2685510f48e7efb28dc66f2713428d7e1e5acf3cd44ecf5243a9c845.jpg)
+
+![](images/a0bd2afe937729d0f57415d6d53a54da0f56d061c04f7c3097a180448cffd439.jpg)
+
+![](images/653641fa019eba5b8feecf1955739236f4ed210903af5e14b0f7aafc398a02bb.jpg)  
+Mixed-degraded Input
+
+![](images/24162be6815fd0308e867b1cba7f0c65b022a95734cfce3f4050fd309f8bb7ad.jpg)  
+Composite Restoration Output
+
+![](images/625f1a715db8cd2012593dfd5db823ddce93833ffe13d3826c7a334284e5d209.jpg)  
+Mixed-degraded Input
+
+![](images/62a1245baf086fad18d5a8d4a8fd098b49761e28a0ed75d865da1085c0121706.jpg)  
+Composite Restoration Output
+
+![](images/937ffa44b5fa0cee301175d81870ac8ff73b1ec4f58ee12a8d1fc8d7e4f83587.jpg)  
+Mixed-degraded Input
+
+![](images/ac183078d9ce26197e622123544f696630f0286e2bb06bb34d0b1b2bc9f6f353.jpg)  
+Composite Restoration Output
+
+![](images/5dab6cce59781ec106c6d45d61975d725356f06dc941f649d8f087fe77ecc137.jpg)  
+Single LLIE Output
+
+![](images/8578d8134fc338a0eab6e5558537d01b1a6537dfbdaeddcadb7890ac89259fb7.jpg)  
+Single Deraining Output
+
+![](images/1509c5f9ece23a4eb07e4f2071b15e827e46c05008122912a7297ffcc30c4a1c.jpg)  
+Single Dehazing Output
+
+![](images/78370798e7620f317b2bd9f06aef1c2e956cc51198d0ea2acf03c8f75f4ab74c.jpg)  
+Single Deraining Output  
+Figure 6. Visual examples on hybrid-degraded images. Our method remains superior performance when input images are simultaneously corrupted by mixed degradations. Our DiffRes can also achieve customized specific degradation removal with composable adapters.
+
+![](images/68bfcb818fe0640b8fde85c3aed77d72104c8bb4a20bce4d18cc9d7d94465b3b.jpg)  
+Single Dehazing Output
+
+![](images/4a4198ac0eff746709aefe809ef6f226db0aee5a2e30690d4db868e90944d68c.jpg)  
+Single Deraining Output
+
+such as DA-CLIP [45], our approach generates sharp and visually pleasing results that closely resemble high-quality images. This demonstrates that FDI from BLIP-2 leads to better performance for downstream restoration models. Note that DiffRes is particularly suitable for noise types that the degraded image differs noticeably from the original, such as adverse weather conditions, where the noise affects the original image semantics, allowing BLIP-2 to capture it and extract degradation clues through subtraction.
+
+Multi-task setting. We evaluate our method for unified image restoration, which is trained on a mixed dataset with multiple adapters. Table 2 presents a comprehensive comparison with SOTA all-in-one methods across 5 tasks. Our method consistently outperforms these compared methods on all datasets. Compared to other all-in-one methods, our DiffRes achieves the best average performance, primarily benefiting from the complementary interactions between multiple adapters in handling various degradations. This advantage is especially obvious in challenging test inputs, which often contain elements of other degradation types (e.g., noise in low-light images).
+
+Mixed-degradation setting. During the multi-branch adapter training, each adapter independently captures the restoration specific to different degradations. Therefore, our
+
+Table 3. Quantitative comparisons on mixed-degradation images. InstructIR is manually given text instructions for progressive restoration, each time restoring one type of degradation.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Rainstreak + Raindrop (RainDS, Real-world)</td><td colspan="3">Rainstreak + Haze + Low-light (Outdoor-Rain, Test 1)</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>AirNet [31]</td><td>23.41</td><td>0.633</td><td>0.390</td><td>19.29</td><td>0.615</td><td>0.438</td></tr><tr><td>TransWeather [77]</td><td>24.13</td><td>0.655</td><td>0.378</td><td>20.77</td><td>0.631</td><td>0.386</td></tr><tr><td>PromptIR [55]</td><td>24.05</td><td>0.661</td><td>0.380</td><td>21.47</td><td>0.704</td><td>0.314</td></tr><tr><td>Restormer [92]</td><td>23.39</td><td>0.628</td><td>0.396</td><td>20.80</td><td>0.687</td><td>0.335</td></tr><tr><td>InstructIR-5D [14]</td><td>24.26</td><td>0.647</td><td>0.330</td><td>21.45</td><td>0.707</td><td>0.285</td></tr><tr><td>Ours (composite)</td><td>25.11</td><td>0.702</td><td>0.230</td><td>22.30</td><td>0.791</td><td>0.221</td></tr></table>
+
+Table 4. Cross-dataset generalization test on different training sets.  
+
+<table><tr><td>Test Set</td><td colspan="3">Deraining (GT-Rain)</td><td colspan="3">Dehazing (O-Haze)</td></tr><tr><td>FDI source</td><td>Rain800</td><td>NYU-Rain</td><td>GT-Rain</td><td>ITS</td><td>OTS</td><td>O-Haze</td></tr><tr><td>PSNR ↑</td><td>19.52</td><td>22.33</td><td>22.49</td><td>21.33</td><td>25.09</td><td>26.88</td></tr><tr><td>LPIPS ↓</td><td>0.401</td><td>0.221</td><td>0.207</td><td>0.167</td><td>0.146</td><td>0.131</td></tr></table>
+
+DiffRes also achieves single-image mixed-degradation removal with improved results. Table 3 presents quantitative results for two common real-world degradation combinations. Additionally, Figure 8 shows that, beyond composite removal, DiffRes can also perform progressive restoration through consecutive single-task FDI adapters. Further mixed-degradation results with different combinations are provided in the Supp 3.
+
+![](images/61913da65e6f94a43634edaab235d920ed0f6b7466561a8d90c5deab567e2849.jpg)  
+OutDoor-Rain Test Input
+
+![](images/d21489fc52e0e9e73cd046511c49423d966e2f1b0fb3b1d40d67bbb3644881f6.jpg)  
+Ground Truth
+
+![](images/a7901730d63c04dddb6d0b2ea5be85a3feca6d7be21efa276f7d294f05e25044.jpg)
+
+![](images/4a88bf335b555901b5414996eb3612e97da894f61b9879300c20557be19f7783.jpg)  
+FDI from Rain100H PSNR: 14.28dB
+
+![](images/1c6469de7d881e42aaa8e7b91f57d43428054a56ae859c8c971da73bf9a2e95c.jpg)  
+FDI from Rain1400 PSNR: 17.46dB
+
+![](images/3bf7bf0037fb67c6574eca0d5af5e759684e7757bc958b90687a9eed0b548f1b.jpg)  
+FDI from OutDoor-Rain PSNR: 24.30dB  
+FDI from NYU-Rain PSNR:22.20dB  
+Figure 7. Examples of cross-dataset experiments: given a test input, we apply FDI from different datasets within the same task to perform restoration. Examples are evaluated using PSNR.
+
+Cross-dataset. We observed empirically that for tasks with abundant datasets (e.g., deraining), the FDI from these datasets within the same task often demonstrates direct cross-dataset compatibility. As illustrated in Figure 7, datasets such as NYU-Rain [37] and OutDoor-Rain [77], which both emphasize depth-aware rain accumulation effects like illumination and accompanying haze, exhibit superior cross-dataset FDI performance compared to datasets that merely depict synthetic rain streaks. Table 4 further presents a generalization test of different training sets on real-world test sets. Note that this is only a preliminary, performance could improve with more advanced datasets.
+
+Cross-task. Apart from being composable, FDI from certain tasks also demonstrates cross-task compatibility (e.g., leveraging FDI from denoising datasets for image desnowing). This suggests that we can address multiple restoration tasks with fewer adapter combinations. Results for different task combinations are provided in the Supp.
+
+Progressive vs. Composite. Figure 8 compares progressive and composite restoration using three task-specific adapters. While no clear pattern emerged in the progressive restoration order, it generally outperformed composite restoration by addressing specific degradations and minimizing interference between them [46].
+
+Furthermore, our FDI mechanism can be extended to multiple applications. For example, by customizing reference image pairs, DiffRes can be applied to image-to-image translation tasks such as style transfer. This flexibility enables our method to adapt to various image transformation objectives, using a unified framework to achieve diverse translation results in image processing. Other applications are provided in Supp 3.
+
+# 4.2. Ablation Study
+
+To understand the contribution of each of the components in DiffRes, we conduct further ablation experiments with different model variants. The quantitative results are pre
+
+![](images/1b90c71520fae4ee00349de1df5812f18b859508a94e114528b3106924ad95a4.jpg)  
+Multi-degradation Input
+
+![](images/cf52a377cddc9c76686caac5f96eeeedbf5cd58d4b320a19ffa471a16f68e799.jpg)
+
+![](images/a135bf462b7ed8908da210fa27b76fc13e66506d7423fa79ae973b52d003ac22.jpg)
+
+![](images/275cc4fa92dcba15f2ac7b645d781648b3c6385fa008281ea1d9c5eb58f4be01.jpg)
+
+![](images/c1b1a460acf65765b364b69a1323443f48eef8bb4ae1e85ed588b0ff2043fce5.jpg)  
+Multi-degradation Input  
+Figure 8. Comparisons on progressive and composite restorations.
+
+![](images/49ebea9b3c201ab2c2be3efe4ca88f3728b32415b1bec015e11c6a6a3ffb3ca1.jpg)  
+Dehazing  $\rightharpoonup$  Derainaging  $\rightarrow$  LLIIE PSNR:24.25dB  
+Deraining  $\rightarrow$  Dehazing  $\rightarrow$  LLIIE PSNR:23.15dB
+
+![](images/73c19d490d17eb2a226d59253781d77344ac6dd2c2860d5c65d5614f65a9e679.jpg)  
+PSNR:24.61dB  
+$\rightharpoonup$  Dehazing  $\rightarrow$  Deraining PSNR:29.22dB
+
+![](images/023e4900d0c154077a908f050bac90015edff65bc43e7ff2b94622fc52658feb.jpg)  
+Composite (1:1:1) PSNR: 21.18dB  
+Composite (1:1:1) PSNR: 22.47dB
+
+Table 5. Ablation experiments of DiffRes. The metrics are reported on the average of the restoration tasks with snow, haze, rainstreak, and low-light degradations.  
+
+<table><tr><td>Method</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>Baseline (Stable Diffusion)</td><td>15.33</td><td>0.423</td><td>0.655</td></tr><tr><td>+ Visual Modulator (replace \(\hat{F}_S^i\) with \(F\))</td><td>15.90</td><td>0.435</td><td>0.651</td></tr><tr><td>+ Visual Branch w/o Channel-Attn</td><td>15.28</td><td>0.419</td><td>0.648</td></tr><tr><td>+ Noise Decoupling</td><td>21.49</td><td>0.617</td><td>0.351</td></tr><tr><td>+ Noise Decoupling w/o Channel-Attn (replace \(\hat{A}_S^i\) with \(A_S^i\))</td><td>19.32</td><td>0.538</td><td>0.577</td></tr><tr><td>+ Noise Decoupling w/o Cross-Attn (replace \(\hat{F}_S^i\) with \(F\))</td><td>20.95</td><td>0.608</td><td>0.374</td></tr><tr><td>+ Noise Decoupling + Visual Modulator (Full FDI Adapter)</td><td>24.14</td><td>0.699</td><td>0.280</td></tr></table>
+
+sented in Table 5. We begin with the initial stable diffusion by adding the proposed components of our FDI adapter. We observe that high-quality image restoration requires both degradation guidance from the FDI and feature regularization from the visual modulator. The output tends to retain some corrupted content without noise decoupling, and it generates more artifacts without the visual modulator.
+
+# 5. Conclusion
+
+Image restoration is challenging, even with the advances offered by Diffusion-based Text-to-Image (T2I) models. We explore the linear separability of features in the pretrained BLIP-2, and its potential across various image restoration tasks. Combining this with the multi-scale features subject to the input reference images, we propose a novel Feature Difference Instruction (FDI), to efficiently inject the degradation-aware guidance into the pretrained text-to-image models. Taking advantage of inversion-based diffusion and reference-based FDI adapter, we achieved a flexible tuning-based pipeline, namely DiffRes, to efficiently restore arbitrary hybrid degradations in a unified framework. To enable all-in-one and mixed-degradation learning, we further introduce an additional classifier providing adjustable weights for the composable FDI adapter. Extensive experiments on 10 restoration tasks and other translation applications demonstrate the effectiveness and superiority of our unified network over strong baselines. We hope that our method takes the research community one step closer to transferring the knowledge of vision-language models to more CV tasks in the future.
+
+# Acknowledgment
+
+This work was supported in part by the National Natural Science Foundation of China (U2336212), Fundamental Research Funds for the Zhejiang Provincial Universities (226-2024-00208), and the Earth System Big Data Platform of the School of Earth Sciences, Zhejiang University. Chao Wang is supported by the CSIRO Data61 top-up scholarship.
+
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+# Adapting to Observation Length of Trajectory Prediction via Contrastive Learning
+
+Ruiqi Qiu
+
+2200891@stu.neu.edu.cn
+
+Siqi Luo
+
+2300925@stu.neu.edu.cn
+
+Jun Gong *
+
+gongjun@ise.neu.edu.cn
+
+Bowen Zhang
+
+2470807@stu.neu.edu.cn
+
+Xinyu Zhang
+
+2200981@stu.neu.edu.cn
+
+Yi Cen
+
+2370875@stu.neu.edu.cn
+
+Northeastern University, China
+
+# Abstract
+
+The ability to adapt to varying observation lengths is crucial for human trajectory prediction tasks, particularly in scenarios with limited observation lengths or missing data. Existing approaches mainly focus on introducing novel architectures or additional structural components, which substantially increase model complexity and present challenges for integration into existing models. We argue that current network architectures are sufficiently sophisticated to handle the Observation Length Shift problem, with the key challenge lying in improving feature representation for trajectories with limited lengths. To tackle this issue, we introduce a general and effective contrastive learning approach, called Contrastive Learning for Length Shift (CLLS). By incorporating contrastive learning during the training phase, our method encourages the model to extract length-invariant features, thus mitigating the impact of observation length variations. Furthermore, to better accommodate length adaptation tasks, we introduce a lightweight RNN network that, combined with CLLS, achieves state-of-the-art performance in both general prediction and observation length shift tasks. Experimental results demonstrate that our approach outperforms existing methods across multiple widely-used trajectory prediction datasets.
+
+# 1. Introduction
+
+Human trajectory prediction tasks involve forecasting potential future trajectories of individuals while considering various influential factors, with significant applications in autonomous driving, human-computer interaction, and intelligent security. Early attempts at human trajectory prediction relied on manually designed features based on prior knowledge [10, 20, 24]. Subsequently, data-driven models
+
+began to be widely applied in this field. Although these works have achieved notable performance, they mainly focus on idealized experimental conditions. In real-world scenarios, obtaining complete observable trajectories is often impractical under extreme circumstances, considering upstream tracking failures or unexpected events. Many existing datasets lack annotations for instantaneous pedestrians [40], and discard trajectory data with short durations during preprocessing, resulting in poor performance with limited observation lengths, potentially leading to significant safety risks in practical applications.
+
+While training data plays a crucial role in the Observation Length Shift problem, many studies still focus on structural improvements to accommodate more diverse observation lengths [14, 15, 22, 31, 36]. These methods require additional model structures or specialized networks to handle abnormal observation lengths and do not truly enable existing models to adapt to varying lengths.
+
+Previous work [4] has indicated that the last two frames before prediction contribute  $80.3\%$  and  $8.3\%$  respectively to prediction results. In most cases, relying solely on the last two frames of information is sufficient to make accurate predictions of future trajectories, as demonstrated by models specifically trained on limited observation length [14, 36]. We think that existing networks suffer from overfitting to complete observation trajectories, leading to a performance decline when face with varying observation lengths. Therefore, within existing network architecture, it becomes critical to ensure that the model can effectively extract length invariant information with different observation lengths.
+
+To address the above limitations, we propose a contrastive learning method applicable to different networks: Contrastive Learning for Length Shift (CLLS). This method enables models to achieve better performance under any limited observation length without additional inference
+
+structures. The method comprises data augmentation based on random length masking, nonlinear mapper, and contrastive loss. Since many network structures involve a time dimension, we use random length masking methods to generate input trajectories of different observable lengths. The generated masked trajectories, along with random rotations and scaling, form positive pairs for contrastive learning. Additionally, we propose a lightweight RNN network for Length Shift(RNLS), that selectively extracts meaningful time dimension information through iteration. Experimental results demonstrate that our method outperforms existing length adaptation approaches across various model types. Our proposed RNN network, combined with the CLLS method, achieves state-of-the-art performance across multiple datasets.
+
+As mentioned above, our contributions can be summarized as follows:
+
+- We propose a Contrastive Learning for Length Shift (CLLS) approach applicable to various models, improving their prediction performance for trajectories of different observation lengths.  
+- We introduce a lightweight RNN model for Length Shift, called RNLS, to better extract key temporal information selectively.  
+- We investigated how contrastive learning can enhance the predictive capabilities of models across varying observation lengths.
+
+# 2. RELATED WORK
+
+# 2.1. Trajectory Prediction
+
+Early trajectory prediction relied on manual feature design [10, 20, 24], but these methods struggled with complex social behaviors. Subsequently, RNN-based models [1, 8, 11, 19, 28, 35] gain widespread adoption in this field. Social LSTM [1] introduced recurrent networks for trajectory prediction, while Social GAN [8] used GANs for multimodal trajectory generation. Ivanovic and Pavone [11] applied CVAE to model pedestrian uncertainty, and Mangalam et al. [19] improved performance by incorporating pedestrian intent. To model social relationships, many studies used topological graphs with CNN [21, 29] or Attention [34, 37, 38] mechanisms. Social-STGCNN [21] used CNNs for relationship graphs, while SGCN [29] introduced sparse directed graphs to reduce redundancy. Recent work leverages large language models for trajectory prediction, such as Kuo et al. [12] utilize language intermediate representations for trajectory prediction, while Bae et al. [3] employ prompt-based methods to achieve numerical predictions for trajectory forecasting.
+
+# 2.2. Contrastive Learning in Trajectory Prediction
+
+Contrastive learning has been widely used in trajectory prediction. To address long-tail problems, Makansi et al. [18] differentiate positive and negative samples based on difficulty levels to address long-tail problems, while Wang et al. [33] employed clustering and specialized prediction heads for long-tail samples. Similarly, contrastive learning has been employed to enhance the model's ability to capture features of different motion patterns. Cheng et al. [6] treated same-person trajectories as positive samples and different-person trajectories as negative samples to learn latent motion habits. Halawa et al. [9] distinguish positive and negative samples based on action membership, promoting the learning of distinct action features. Liu et al. [17] used collision danger points as negative samples to reduce collisions. However, these methods are only applicable to high-dimensional trajectory features of equal length and do not address the problem under varying observation lengths.
+
+# 2.3. Trajectory Prediction for Length Shift
+
+Variable-length trajectory prediction has gained increasing attention in recent years. Monti et al. [22] employ knowledge distillation to transfer knowledge from networks trained on complete trajectories to student networks handling limited observation lengths. Sun et al. [31] incorporate scene semantic information under limited observation lengths and proposed a Mixture-of-Experts (MOE) architecture to enhance prediction performance under extremely limited observations. Li et al. [14] propose bidirectional diffusion to estimate past and future trajectories when observation length is limited. Xu and Fu [36] identify that position encoding and layer normalization are the root causes of length bias in Transformer structures and proposed using different subnetworks for predictions at different lengths. Li et al. [15] design a length-agnostic knowledge distillation (LaKD) module to dynamically transfer knowledge across trajectories. While these methods have contributed significantly to improving model performance under limited observation lengths, a truly unified model capable of adapting to arbitrary observation lengths has yet to emerge.
+
+# 3. Approach
+
+We define the trajectory prediction task as follows: In a scene with  $N$  agents, the observation sequence of length  $t_{o}$  for the i-th pedestrian is denoted as  $x^{(i)} = \{x_1^{(i)},\dots ,x_{t_o}^{(i)}\}$ , where  $x_{t}\in \mathbb{R}^{t_{o}\times d}$ . Our objective is to make the model's predicted sequence  $\hat{y}^{(i)}\in \mathbb{R}^{t_p\times 2}$  as close as possible to the ground truth  $y^{(i)}$ . Besides, in length shift task, we additionally defined the unobservable length as  $t_{unobs}$ .
+
+In the following, we first introduce Contrastive Learning for Length Shift (CLLS) in Section 3.1. This approach constructs positive sample pairs for contrastive learning
+
+![](images/f1671c978452a7acaa800265af0f54540df531f538e75568b81de4a23fec84d1.jpg)  
+Figure 1. An illustration of our Approach. (a) The CLLS method consists of data augmentation, nonlinear projector, and contrastive loss, with the encoder comes from the base model. The method is only executed during the training phase, meaning it incurs no additional inference cost. (b) RNLS comprises a trajectory encoder, social attention, feature predictor, and trajectory decoder. The target trajectory features output by the target encoder follow two paths: one flows through a projector to participate in contrastive loss computation, while the other is fused with the features output by the social attention via Add & Norm. This fused representation is then processed by the feature predictor and trajectory decoder to generate the final trajectory.
+
+through data augmentation techniques such as random length masking, rotation, and scaling, thereby achieving the extraction of length-invariant features. Subsequently, in Section 3.2, we propose A RNN Network for Length Shift (RNLS), which integrates CLLS into a lightweight RNN network.
+
+# 3.1. Contrastive Learning for Length Shift(CLLS)
+
+To enable a single model to adapt to varying observation lengths, we propose that an appropriate training methodology and dataset design can be employed. An intuitive idea involves utilizing contrastive learning to extract length-invariant features. Drawing inspiration from SimCLR [7], which was proposed for unsupervised image learning, we present a novel contrastive learning method for trajectory prediction called Contrastive Learning for Length Shift (CLLS). This method enhances the encoder's ability to extract invariant features from trajectories of different lengths. The core idea is to minimize the feature space discrepancy between differently augmented trajectories from the same sample. The method consists of several key components: Data Augmentation, Nonlinear Projector, and Contrastive Loss. The primary goal is to enable the model to learn consistent representations regardless of trajectory length variations.
+
+Data Augmentation Based on Length Shift. The key to contrastive learning is the construction of positive and negative samples. During the training phase, we employ a random length masking approach to construct limited ob
+
+servation trajectories. Specifically, starting from an original trajectory of length  $t_{o}$ , we mask  $t_{unobs}$  unobservable frames using the first observable frame. The augmented data is denoted as  $\tilde{x}$ , which can be expressed by the following formula:
+
+$$
+\left\{ \begin{array}{l l} \tilde {x} _ {t} = x _ {t _ {u n o b s} + 1}, & t = 1, \dots , t _ {u n o b s} \\ \tilde {x} _ {t} = x _ {t}, & t = t _ {u n o b s} + 1, \dots , t _ {o} \end{array} \right. \tag {1}
+$$
+
+where  $t_{unobs}$  is randomly selected from  $[1, t_o - 2]$ , and  $t_{unobs}$  denotes the length of unobservable frames. For different samples within a batch, random masking of varying lengths is applied. Additionally, for the same sample, different lengths are masked in each epoch. To enhance model performance, we additionally incorporated random rotation and scaling as data augmentation methods. In practical applications, for trajectories shorter than  $t_o$ , the first observable frame can be used to pad the sequence to achieve the required length of  $t_o$ .
+
+Nonlinear Projector maps the encoded feature representations to a space where the contrastive loss applied. Chen et al. [7] mentioned that the additional nonlinear projector can learn to be invariant to data transformation, so as to avoid the loss of key information due to comparative learning. We employ an MLP as a hidden layer to obtain  $z = \sigma (Wh)$ , where  $z\in \mathbb{R}^{t_{o}d}$ ,  $\sigma$  represents the ReLU activation function, and  $h$  denotes the encoded hidden layer features.
+
+Contrastive Loss. For a given trajectory, three augmented versions are generated using random length mask-
+
+ing, scaling, and rotation, forming a set of positive samples. Meanwhile, augmented trajectories from other trajectories within the same batch constitute the negative samples. A batch contains  $B$  samples. The augmented samples from the same observation trajectory are denoted as a positive sample set  $\Phi$ , while the other  $3(B - 1)$  samples serve as negative samples with respect to the target trajectory. Cosine similarity is used to measure the similarity between sample features, denoted as  $sim(z_i,z_j) = \frac{z_i^\top z_j}{||z_i||||z_j||}$ . The conatrastive loss function is defined as:
+
+$$
+\mathcal {L} _ {c l, \Phi} = - \log \frac {\sum_ {i , j \in \Phi , i \neq j} \exp \left(\operatorname {s i m} \left(z _ {i} , z _ {j}\right) / \tau\right)}{\sum_ {k = 1 , k \neq i} ^ {3 B} \exp \left(\operatorname {s i m} \left(z _ {i} , z _ {k}\right)\right) / \tau)} \tag {2}
+$$
+
+Here,  $\tau$  represents the temperature parameter, which controls the emphasis on hard samples and helps achieve a more uniform distribution in the feature space [32].
+
+# 3.2. A RNN Network For Length Shift (RNLS)
+
+To address the discrepancy between observation and prediction trajectory lengths, the main approaches include using RNN [28, 35] or Transformer [38] for autoregressive generation, or employing one-shot methods [2, 21, 29] that generate complete trajectories in a single shot. With the success of GPT series large language models[5, 23], autoregressive methods have demonstrated powerful capabilities in generative tasks with variable lengths. We think that RNN-based recursive prediction paradigms can better accommodate the Observation Length Shift problem. Limited observable sequences can enhance the model's comprehension of temporal relationships and focus more attention on adjacent time frames, thereby minimizing the impact of unobservable information on prediction outcomes. Consequently, we introduce an RNN network for Length Shift (RNLS).
+
+The model comprises four key modules: (1) a target trajectory encoder for encoding the target's historical trajectory; (2) a social attention module for modeling interactions between the target and neighboring pedestrians; (3) a future prediction module using RNNs to iteratively predict future features; and (4) a trajectory decoder for generating the final predicted trajectory, as illustrated in Fig. 1.
+
+Trajectory Encoder. For each frame in the observation sequence, in addition to the target's current coordinate position  $(p_t^x,p_t^y)$ , we incorporate the cosine value of the motion angle  $\theta_{t}$  to represent spatial orientation changes and the temporal index  $t$  to express temporal characteristics:
+
+$$
+x _ {t} = \left[ p _ {t} ^ {x}, p _ {t} ^ {y}, \cos \theta_ {t}, t \right] \tag {3}
+$$
+
+All temporal data, after normalization, is fed into a MLP layer with ReLU activation functions and encoded to obtain the  $i$ -th target trajectory feature encoding  $T_{target}^{(i)} \in \mathbb{R}^{t_o \times d}$ :
+
+$$
+T _ {t a r g e t} ^ {(i)} = M L P \left(x ^ {(i)}\right) \tag {4}
+$$
+
+Social Attention is utilized to model the interactions between the prediction target and its neighbors. Moreover, incorporating social relations can mitigate potential performance degradation in contrastive learning caused by similar target trajectories within the same batch. To model the relationship at time  $t$ , we follow previous work [35] and compute the euclidean distance  $d_t$  between neighbors and the target at time  $t$ , the cosine of the motion angle  $\alpha_t$ , the cosine of the azimuth angle  $\beta_t$ , and the sequence index  $t$  to form the input vector, which is then encoded through MLP:
+
+$$
+R _ {t} = \left[ d _ {t}, \cos \alpha_ {t}, \cos \beta_ {t}, t \right] \tag {5}
+$$
+
+$$
+T _ {n e i g h b o r} ^ {(i)} = M L P \left(R ^ {(i)}\right) \tag {6}
+$$
+
+Here,  $T_{\text{neighbor}}^{(i)} \in \mathbb{R}^{t_o \times n \times d}$ , where  $n$  is the number of observable neighbors. We followed the approach in [34] by selecting the nearest  $n$  pedestrians to the target as neighbors. To model the influence of different neighbors at different timestamps on the target, following the concept from [38], we flatten the neighbor and time dimensions to obtain  $T_{\text{neighbor}}^{(i)} \in \mathbb{R}^{t_o n \times d}$ . Using neighbor features as Key and Value, and target features as Query, we employ cross-attention to enable the Query to retrieve key features from different pedestrians at different timestamps, thoroughly exploring the relationships between pedestrian movements at different times:
+
+$$
+N ^ {(i)} = \operatorname {C r o s s A t t n} \left(T _ {\text {t a r g e t}} ^ {(i)}, T _ {\text {n e i g h b o r}} ^ {' (i)}\right) \tag {7}
+$$
+
+$$
+E ^ {(i)} = \operatorname {L a y e r N o r m} \left(N ^ {(i)} + T _ {\text {t a r g e t}} ^ {(i)}\right) \tag {8}
+$$
+
+Feature Predictor. The observed trajectory sequence features  $E_{t}^{(i)}$  are passed through the RNN's hidden layer  $h_{t}^{(i)}$  to iteratively transmit sequence information, then the  $h_{t_o}^{(i)}$  is fed into another RNN to iteratively generate future predicted sequences. Here, GRU modules are consistently used for all RNN operations:
+
+$$
+E _ {t, n e w} ^ {(i)}, h _ {t} ^ {(i)} = G R U \left(E _ {t - 1} ^ {(i)}, h _ {t - 1} ^ {(i)}\right), t = 1, 2, \dots , t _ {o} \tag {9}
+$$
+
+$$
+E _ {t} ^ {(i)}, h _ {t} = G R U \left(E _ {t - 1} ^ {(i)}, h _ {t - 1} ^ {(i)}\right), t = t _ {o} + 1, \dots , t _ {o} + t _ {p} \tag {10}
+$$
+
+where  $h_0$  is initialized as a zero matrix. It should be noted that the  $E_{t, new}^{(i)}$  output from the first GRU does not participate in the next iteration. The GRU only transmits historical feature information through the state matrix  $h_t$  at this stage. During the prediction phase, we directly use the previous iteration's output  $E_t^{(i)}$  as the input for the next  $E_{t+1}^{(i)}$ .
+
+Trajectory Decoder. The feature dimensions from the previous stage's output are directly decoded by MLP:
+
+$$
+\hat {y} ^ {\prime (i)} = M L P \left(E ^ {(i)}\right) \tag {11}
+$$
+
+This output  $\hat{y}^{(i)}\in \mathbb{R}^{t_p\times 2k}$  is reshaped to obtain the final multi-modal trajectory  $\hat{y}^{(i)}\in \mathbb{R}^{t_p\times k\times 2}$ .
+
+Loss Functions. The loss function consists of two parts: contrastive loss and prediction loss. First, the trajectory encoder output is passed through an MLP with ReLU activation function to compute the contrastive loss  $\mathcal{L}_{cl}$ . Then, the prediction loss function is calculated as the average of the L2 norm of the difference between predicted and actual coordinates along the temporal dimension. The complete loss function is obtained by summing these two components:
+
+$$
+\mathcal {L} _ {p r e d} = \frac {1}{3 B t _ {p}} \sum_ {i = 1} ^ {3 B} \sum_ {t = 1} ^ {t _ {p}} \| y _ {t} ^ {(i)} - \hat {y} _ {t} ^ {(i)} \| _ {2} \tag {12}
+$$
+
+$$
+\mathcal {L} = \mathcal {L} _ {p r e d} + \omega \mathcal {L} _ {c l} \tag {13}
+$$
+
+$\omega$  controls the ratio between the two loss functions. It should be noted that the prediction loss employs a winnertakes-all process [27], where only the result closest to the groundtruth will be back-propagated.
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Protocols.
+
+We evaluated our method on three public datasets: ETHUCY, SDD, and NBA, which include pedestrian trajectories, social interactions, and scene information across diverse urban settings.
+
+ETH-UCY [13, 25] is a standard benchmark for pedestrian trajectory prediction, comprising five video clips from four city scenes: eth, hotel, univ, and zara. The dataset uses real-world coordinates and fixed annotation intervals. We adopted the "leave-one-out" strategy for training and testing, consistent with prior works.
+
+SDD [26] is widely used for tasks like object detection, tracking, and trajectory prediction. It includes 60 bird's-eye view videos from Stanford University, featuring over 11,000 labeled individuals (pedestrians, bicycles, vehicles), 185,000 individual interactions, and 40,000 individual-scene interactions. Compared to ETH-UCY, SDD offers richer interactions and more complex scene structures.
+
+NBA [16, 39] presents a challenging benchmark with complex human interactions. It contains player coordinates at 25 FPS from the 2012-2013 NBA season, along with sports events like passing and shooting.
+
+We used the widely tested Average Displacement Error (ADE) and Final Displacement Error (FDE) to measure the performance of our network. Note that we used the best-of-20 validation method, which means that the prediction with the lowest ADE and FDE among 20 sampled predictions will be used to measure the accuracy of the model. We have:
+
+$$
+E r r _ {t} ^ {(i)} = \left\| p _ {t} ^ {(i)} - \hat {p} _ {t} ^ {(i)} \right\| \tag {14}
+$$
+
+$$
+A D E ^ {(i)} = \frac {1}{t _ {p}} \sum_ {t = t _ {o} + 1} ^ {t _ {o} + t _ {p}} E r r _ {t} ^ {(i)} \tag {15}
+$$
+
+$$
+F D E ^ {(i)} = \operatorname {E r r} _ {t _ {o} + t _ {p}} ^ {(i)} \tag {16}
+$$
+
+# 4.2. Implementation Details.
+
+Model Training. All MLPs in the RNLS are implemented with 2-layer FC networks, each followed by a ReLU activation function. The nonlinear projector in CLLS uses a single FC layer with ReLU activation. Following Xu et al. [35], we process data with 12 future frames and 8 observation frames. All networks are trained using the Adam optimizer, with feature dimension set to 128, the number of neighbors  $n$  set to 20, batch size of 512,  $\omega = 0.1$ , and  $\tau = 0.07$ . Experiments are conducted on a single RTX 3090 GPU. Isolated Training (IT) setting indicates training the model directly using specified limited observation lengths to predict the next 12 frames.
+
+# 4.3. Comparisons with Other Length Shift Methods.
+
+Instantaneous trajectory prediction. To thoroughly validate our proposed CLLS method, we compare against four: IT, DTO [22], MOE [31], and BCDiff [14]. Following previous work [14], we evaluate on Trajectory++ [28], PCC-SNet [30], SGCN [29], and SocialVAE [35] models with observation length set to 2 frames in the validation set. In the CLLS setup, we added a projector after the encoder of four models and incorporated the output features of augmented trajectories into the contrastive loss computation. This contrastive loss is subsequently added with the pre-existing loss functions to partake in the training process.
+
+As shown in Tab. 1, our method outperforms existing models on Trajectory++, SGCN, and SocialVAE for instantaneous observation length tasks, and surpasses the IT method on most datasets. It is noteworthy that our model did not perform well on PCCSNet, which may be attributed to: 1) interference from augmented samples in PCCSNet's memory bank structure, and 2) PCCSNet lacks explicit modeling of interactions among neighbors. Since other negative samples in the same batch may follow paths similar to the positive samples, the absence of social relations could lead to performance degradation. Additionally, our model performed poorly on the ZARA1 dataset in Trajectory++, possibly due to the left-turn intersection in the ZARA scene and Trajectory++'s preprocessing step of subtracting mean coordinates, which may disrupt the motion distribution during rotation augmentation.
+
+Comparison across varying observation lengths. To evaluate our model's performance across various observation lengths, we conducted comparative experiments with BCDiff [14] using the Trajectory++ [28] model, as shown in
+
+<table><tr><td>Model</td><td>Methods</td><td>ETH</td><td>HOTEi</td><td>UNIV</td><td>ZARA1</td><td>ZARA2</td><td>AVG</td><td>SDD</td></tr><tr><td rowspan="5">Trajectory++</td><td>IT</td><td>0.76/1.43</td><td>0.30/0.56</td><td>0.36/0.74</td><td>0.22/0.42</td><td>0.18/0.34</td><td>0.36/0.70</td><td>13.07/22.88</td></tr><tr><td>MOE</td><td>0.64/1.12</td><td>0.20/0.33</td><td>0.33/0.62</td><td>0.22/0.42</td><td>0.17/0.32</td><td>0.31/0.56</td><td>11.71/19.54</td></tr><tr><td>DTO</td><td>0.70/1.23</td><td>0.22/0.45</td><td>0.32/0.62</td><td>0.22/0.42</td><td>0.17/0.33</td><td>0.33/0.61</td><td>12.32/20.79</td></tr><tr><td>BCDiff</td><td>0.61/1.09</td><td>0.22/0.45</td><td>0.28/0.53</td><td>0.22/0.41</td><td>0.18/0.33</td><td>0.29/0.53</td><td>11.56/19.32</td></tr><tr><td>CLLS</td><td>0.57/0.83</td><td>0.12/0.18</td><td>0.25/0.47</td><td>0.25/0.51</td><td>0.17/0.33</td><td>0.27/0.46</td><td>10.05/17.42</td></tr><tr><td rowspan="5">PCCSNet</td><td>IT</td><td>0.34/0.65</td><td>0.14/0.25</td><td>0.31/0.63</td><td>0.23/0.46</td><td>0.16/0.37</td><td>0.24/0.47</td><td>9.19/17.71</td></tr><tr><td>MOE</td><td>0.31/0.57</td><td>0.13/0.21</td><td>0.25/0.53</td><td>0.20/0.41</td><td>0.14/0.31</td><td>0.20/0.41</td><td>8.40/16.08</td></tr><tr><td>DTO</td><td>0.33/0.64</td><td>0.14/0.24</td><td>0.31/0.62</td><td>0.22/0.46</td><td>0.15/0.35</td><td>0.23/0.46</td><td>8.93/16.92</td></tr><tr><td>BCDiff</td><td>0.30/0.56</td><td>0.13/0.20</td><td>0.25/0.52</td><td>0.18/0.37</td><td>0.14/0.31</td><td>0.19/0.39</td><td>8.32/15.87</td></tr><tr><td>CLLS</td><td>0.28/0.54</td><td>0.12/0.20</td><td>0.32/0.67</td><td>0.20/0.42</td><td>0.15/0.32</td><td>0.21/0.43</td><td>8.80/17.11</td></tr><tr><td rowspan="5">SGCN</td><td>IT</td><td>0.88/1.66</td><td>0.55/1.16</td><td>0.38/0.71</td><td>0.30/0.54</td><td>0.25/0.46</td><td>0.47/0.91</td><td>15.40/25.69</td></tr><tr><td>MOE</td><td>0.74/1.41</td><td>0.45/0.85</td><td>0.38/0.71</td><td>0.29/0.54</td><td>0.25/0.45</td><td>0.42/0.79</td><td>14.45/24.88</td></tr><tr><td>DTO</td><td>0.80/1.56</td><td>0.49/1.02</td><td>0.38/0.71</td><td>0.30/0.54</td><td>0.25/0.46</td><td>0.44/0.86</td><td>14.99/25.07</td></tr><tr><td>BCDiff</td><td>0.66/1.18</td><td>0.34/0.62</td><td>0.38/0.70</td><td>0.30/0.54</td><td>0.25/0.44</td><td>0.39/0.72</td><td>13.67/23.92</td></tr><tr><td>CLLS</td><td>0.68/1.20</td><td>0.30/0.53</td><td>0.36/0.69</td><td>0.28/0.52</td><td>0.24/0.44</td><td>0.37/0.68</td><td>11.57/19.64</td></tr><tr><td rowspan="5">SocialVAE</td><td>IT</td><td>0.64/1.10</td><td>0.21/0.34</td><td>0.27/0.51</td><td>0.22/0.39</td><td>0.18/0.34</td><td>0.30/0.54</td><td>9.56/16.10</td></tr><tr><td>MOE</td><td>0.57/1.01</td><td>0.17/0.29</td><td>0.26/0.44</td><td>0.22/0.36</td><td>0.17/0.32</td><td>0.28/0.48</td><td>9.12/14.98</td></tr><tr><td>DTO</td><td>0.61/1.06</td><td>0.18/0.31</td><td>0.25/0.43</td><td>0.22/0.38</td><td>0.17/0.33</td><td>0.29/0.50</td><td>9.28/15.58</td></tr><tr><td>BCDiff</td><td>0.53/0.91</td><td>0.17/0.27</td><td>0.24/0.40</td><td>0.21/0.37</td><td>0.16/0.26</td><td>0.26/0.44</td><td>9.05/14.86</td></tr><tr><td>CLLS</td><td>0.47/0.71</td><td>0.15/0.22</td><td>0.22/0.38</td><td>0.20/0.34</td><td>0.14/0.24</td><td>0.24/0.38</td><td>9.02/13.26</td></tr></table>
+
+Table 1. ADE/FDE metrics of different length-adaptive methods on the ETH-UCY and SDD datasets with an observation length of 2 frames. Bold means the best. IT represents the baseline model trained directly on 2 frames observations to predict the subsequent 12 frames.
+
+Tab. 2. Results demonstrate that our model consistently outperforms BCDiff across all observation lengths. Compared to BCDiff, our CLLS method maintains superior performance across all observation lengths while introducing no additional inference computation to the baseline model, truly achieving adaptation to arbitrary observation lengths with a single model.
+
+# 4.4. Comparisons with Other Models
+
+As shown in Tabs. 3 and 4, our model achieves state-of-the-art performance on the ETH, ZARA1, and ZARA2 datasets within the ETH-UCY benchmark, surpassing existing methods in terms of average metrics. On the more diverse SDD dataset, we exceed the second-best performance by  $7.7\%$  in ADE. For the NBA dataset, our model surpasses the second-best performance by  $9.7\% / 12.4\%$  in Rebound-ing and  $4.7\% / 6.8\%$  in Scoring, demonstrating strong generalization capabilities across multiple datasets.
+
+# 4.5. Ablation Study
+
+Selection of projector. As shown in Tab. 5, we evaluated several projector: 1) no proj: using encoded features directly for contrastive loss; 2) linear: using linear projector
+
+via Fc layer; 3) MLP: single FC layer with ReLU activation; 4) CNN: aggregating features through convolution kernels; 5) Self-Attention: self-attention mechanism. While no projection shows optimal performance under complete observation length, MLP and Self-Attention outperform the no-projection setting as unobservable length increases.
+
+Impact of different data augmentation methods. We investigated the impact of different data augmentation methods, as illustrated in Tab. 6. Length masking proves crucial among the three augmentation methods, with its absence leading to significant performance degradation in both baseline performance and length adaptation. Combining either rotation or scaling with length masking significantly improves the model's predictive capability across different observation lengths. The combination of all three methods yields further improvements, surpassing the IT training setting.
+
+CLLS Hyperparameter Analysis. Tab. 7 presents experimental results for hyperparameters  $\omega$  and  $\tau$  in the contrastive loss. Variations in  $\alpha$  affect the model's emphasis on prediction accuracy versus length-invariant feature extraction tasks, with this distinction becoming more pronounced as the unobservable length increases. Additionally, accord-
+
+<table><tr><td>Dataset</td><td>Methods</td><td>Tunobs = 1</td><td>Tunobs = 2</td><td>Tunobs = 3</td><td>Tunobs = 4</td><td>Tunobs = 5</td><td>Tunobs = 6</td></tr><tr><td rowspan="3">ETH/UCY</td><td>Trajectory++ &amp; BCDiff</td><td>0.31/0.55</td><td>0.30/0.54</td><td>0.30/0.53</td><td>0.29/0.53</td><td>0.32/0.57</td><td>0.34/0.60</td></tr><tr><td>Trajectory++ &amp; CLLS</td><td>0.30/0.51</td><td>0.30/0.50</td><td>0.29/0.50</td><td>0.29/0.49</td><td>0.28/0.48</td><td>0.28/0.48</td></tr><tr><td>RNLS &amp; CLLS</td><td>0.20/0.33</td><td>0.20/0.33</td><td>0.21/0.33</td><td>0.21/0.34</td><td>0.21/0.35</td><td>0.22/0.36</td></tr><tr><td rowspan="3">SDD</td><td>Trajectory++ &amp; BCDiff</td><td>11.86/19.78</td><td>11.81/19.71</td><td>11.68/19.50</td><td>11.56/19.32</td><td>11.92/20.01</td><td>12.33/20.98</td></tr><tr><td>Trajectory++ &amp; CLLS</td><td>9.94/17.10</td><td>9.96/17.16</td><td>10.00/17.24</td><td>10.08/17.34</td><td>9.93/17.09</td><td>10.05/17.42</td></tr><tr><td>RNLS &amp; CLLS</td><td>7.44/11.42</td><td>7.41/11.39</td><td>7.41/11.46</td><td>7.48/11.55</td><td>7.62/11.92</td><td>8.02/12.70</td></tr></table>
+
+Table 2. ADE/FDE metrics on the ETH-UCY and SDD datasets with varying observation lengths. Bold means the best.  $T_{\text{unobs}}$  means unobservation lengths.  
+
+<table><tr><td>Models</td><td>ETH</td><td>HOTEL</td><td>UNIV</td><td>ZARA1</td><td>ZARA2</td><td>AVG</td><td>SDD</td></tr><tr><td>Social GAN</td><td>0.60/1.19</td><td>0.52/1.02</td><td>0.44/0.84</td><td>0.22/0.43</td><td>0.29/0.58</td><td>0.41/0.81</td><td>27.3/41.4</td></tr><tr><td>Social-STGCNN</td><td>0.64/1.11</td><td>0.49/0.85</td><td>0.44/0.79</td><td>0.34/0.53</td><td>0.30/0.48</td><td>0.44/0.75</td><td>20.8/33.2</td></tr><tr><td>PECNet</td><td>0.54/0.87</td><td>0.18/0.24</td><td>0.35/0.60</td><td>0.22/0.39</td><td>0.17/0.30</td><td>0.29/0.48</td><td>10.0/15.9</td></tr><tr><td>Trajectory++</td><td>0.55/0.98</td><td>0.21/0.34</td><td>0.35/0.64</td><td>0.22/0.42</td><td>0.16/0.31</td><td>0.30/0.54</td><td>11.4/20.1</td></tr><tr><td>AgentFormer</td><td>0.45/0.75</td><td>0.14/0.22</td><td>0.25/0.45</td><td>0.18/0.30</td><td>0.14/0.24</td><td>0.23/0.39</td><td>8.7/14.9</td></tr><tr><td>SocialVAE</td><td>0.41/0.58</td><td>0.13/0.19</td><td>0.21/0.36</td><td>0.17/0.29</td><td>0.13/0.22</td><td>0.21/0.33</td><td>8.1/11.7</td></tr><tr><td>EqMotion</td><td>0.40/0.61</td><td>0.12/0.18</td><td>0.23/0.43</td><td>0.18/0.32</td><td>0.13/0.23</td><td>0.21/0.35</td><td>7.9/11.9</td></tr><tr><td>LED</td><td>0.39/0.58</td><td>0.11/0.17</td><td>0.26/0.43</td><td>0.18/0.26</td><td>0.13/0.22</td><td>0.21/0.33</td><td>8.5/11.7</td></tr><tr><td>LMTraj-SUP</td><td>0.41/0.51</td><td>0.12/0.16</td><td>0.22/0.34</td><td>0.20/0.32</td><td>0.17/0.27</td><td>0.22/0.32</td><td>7.8/10.1</td></tr><tr><td>RNLS &amp; CLLS (Ours)</td><td>0.38/0.55</td><td>0.12/0.18</td><td>0.23/0.41</td><td>0.17/0.29</td><td>0.13/0.21</td><td>0.20/0.32</td><td>7.2/11.0</td></tr></table>
+
+Table 3. ADE/FDE metrics of existing methods on the ETH-UCY and SDD datasets under the full 8-frame observation length.  
+
+<table><tr><td></td><td>Rebounding</td><td>Scoring</td></tr><tr><td>Trajectory++</td><td>0.98/1.93</td><td>0.73/1.46</td></tr><tr><td>BiTraP</td><td>0.83/1.72</td><td>0.74/1.49</td></tr><tr><td>SGNet-ED</td><td>0.78/1.55</td><td>0.58/1.30</td></tr><tr><td>SocialVAE</td><td>0.72/1.37</td><td>0.64/1.17</td></tr><tr><td>RNLS &amp; CLLS (Ours)</td><td>0.65/1.20</td><td>0.61/1.09</td></tr></table>
+
+Table 4. ADE/FDE metrics of existing methods on the NBA dataset under the full 8-frame observation length.  
+
+<table><tr><td>Methods</td><td>Tunobs = 0</td><td>Tunobs = 2</td><td>Tunobs = 4</td><td>Tunobs = 6</td></tr><tr><td>no proj</td><td>7.17/10.99</td><td>7.20/11.09</td><td>7.38/11.40</td><td>8.23/12.94</td></tr><tr><td>linear</td><td>7.20/10.95</td><td>7.26/11.25</td><td>7.31/11.37</td><td>8.15/12.87</td></tr><tr><td>MLP</td><td>7.22/10.98</td><td>7.24/11.16</td><td>7.31/11.50</td><td>7.97/12.54</td></tr><tr><td>CNN</td><td>7.23/11.17</td><td>7.33/11.47</td><td>7.43/11.76</td><td>8.03/12.94</td></tr><tr><td>Attention</td><td>7.19/11.13</td><td>7.21/11.22</td><td>7.36/11.53</td><td>7.97/12.71</td></tr></table>
+
+ing to [32] changes in  $\tau$  influence the model's attention to difficult samples. Considering ADE/FDE across different lengths, we selected  $\omega = 0.1$  and  $\tau = 0.07$  as the final
+
+Table 5. Ablation studies of nonlinear projector on the SDD dataset.  $T_{unobs}$  means unobservation lengths. Lower is better.  
+
+<table><tr><td>Methods</td><td>Tunobs = 0</td><td>Tunobs = 2</td><td>Tunobs = 4</td><td>Tunobs = 6</td></tr><tr><td>IT</td><td>7.64/11.87</td><td>7.71/12.14</td><td>7.76/12.24</td><td>7.98/12.68</td></tr><tr><td>w/o mask</td><td>7.59/11.92</td><td>10.62/17.69</td><td>14.04/23.56</td><td>44.47/75.38</td></tr><tr><td>w/o resize</td><td>7.49/11.62</td><td>7.61/11.70</td><td>7.63/11.80</td><td>8.23/13.03</td></tr><tr><td>w/o rotate</td><td>7.57/11.84</td><td>7.47/11.79</td><td>7.61/11.96</td><td>8.16/12.90</td></tr><tr><td>Full</td><td>7.25/11.16</td><td>7.27/11.27</td><td>7.33/11.44</td><td>8.05/12.08</td></tr></table>
+
+Table 6. Ablation studies of data augmentation methods on the SDD dataset.  $T_{unobs}$  means unobservation lengths. IT means the baseline model trained directly on  $t_o - T_{unobs}$  frames observations to predict the subsequent 12 frames.
+
+model parameters.
+
+# 4.6. Qualitative Analysis
+
+T-SNE Visualization for Feature Distribution. We proposed CLLS to enable extraction of length-invariant features under varying observation lengths. To validate this, we applied T-SNE dimensionality reduction to trajectory encoding features for different observation lengths, denoted as  $z_{\text{unobs},t_{\text{unobs}}} \in \mathbb{R}^{B \times 2}$ , where  $B$  represents the dataset size. We visualized the differences between these features and those with unobservable length 6 ( $z_{\text{unobs},6}$ ), as shown in Fig. 2. Compared to the original Src model, our CLLS
+
+![](images/9b9470639ffc9f3a808564e2165063b3791ef285c886d75f6cfc8056592f4b90.jpg)  
+(a)  $z_{unobs,0} - z_{unobs,6}$
+
+![](images/8a27b4d42ddb7e5ec0dba6da3e31ce0222979b11e8dda694f6b81cae6499a513.jpg)  
+(b)  $z_{unobs,2} - z_{unobs,6}$  
+Figure 2. Scatter plots of T-SNE dimensionality reduction on encoding feature differences with various observation lengths on the SDD dataset.  $z_{\text{unobs},t_{\text{unobs}}}$  represents the encoded features after projector of trajectories with unobservable length  $t_{\text{unobs}}$ . CLLS and Src represent the original RNLS model and the model enhanced by contrastive learning.
+
+![](images/6fea96ba97ae7f7d2b02ed331c407be3138a41c17c555e46889c4f374535aa37.jpg)  
+(c)  $z_{unobs,4} - z_{unobs,6}$
+
+<table><tr><td>ω</td><td>τ</td><td>Tunobs=0</td><td>Tunobs=2</td><td>Tunobs=4</td><td>Tunobs=6</td></tr><tr><td>10</td><td>0.07</td><td>7.29/11.15</td><td>7.29/11.20</td><td>7.41/11.57</td><td>8.04/12.73</td></tr><tr><td>1</td><td>0.07</td><td>7.21/11.16</td><td>7.27/11.27</td><td>7.33/11.44</td><td>8.05/12.08</td></tr><tr><td>0.1</td><td>0.07</td><td>7.22/10.98</td><td>7.24/11.16</td><td>7.31/11.50</td><td>7.97/12.54</td></tr><tr><td>0.01</td><td>0.07</td><td>7.13/11.05</td><td>7.18/11.22</td><td>7.28/11.39</td><td>8.04/12.58</td></tr><tr><td>0.1</td><td>0.01</td><td>7.15/11.08</td><td>7.22/11.31</td><td>7.39/11.58</td><td>8.00/12.69</td></tr><tr><td>0.1</td><td>0.1</td><td>7.16/11.03</td><td>7.24/11.18</td><td>7.35/11.30</td><td>7.98/12.58</td></tr><tr><td>0.1</td><td>0.5</td><td>7.16/11.20</td><td>7.15/11.31</td><td>7.25/11.41</td><td>7.91/12.64</td></tr></table>
+
+Table 7. Ablation experiments on hyperparameters of the contrastive loss on the SDD dataset.  $T_{unobs}$  means unobservation lengths. Lower is better.
+
+![](images/ccb002636e92e8b5f72a561505a30ab33e1a618975ed9b2d1a8d2f6716681e12.jpg)  
+(a) Src Model.  
+Figure 3. Line plots of mean encoding features along the temporal dimension for trajectories with different unobservation lengths in the SDD dataset.  $CLLS$  and  $Src$  represents the original RNLS model and the model enhanced by contrastive learning.
+
+![](images/86e01b1cb2fb815d0d286f74cf9b3dd5f7a281eaab9a26049aa05a14f6618ce9.jpg)  
+(b) CLLS Model.
+
+model demonstrates features more closely aligned with the x-axis zero point, indicating that CLLS helps extract more consistent features across different observation lengths, facilitating adaptation to the Length Shift problem.
+
+What Improves the Model's Adaptability to Different Lengths? We analyzed the cause by examining differences in temporal feature encoding across various unobservable trajectory lengths. Specifically, we computed the average feature values at each frame for both the original Src model
+
+and our CLLS model. As illustrated in Fig. 3, in the Src model, feature values gradually decrease for unobservable frames, showing an inflection point at the first observable frame, followed by increasing feature values. The CLLS model exhibits two characteristics: 1) It assigns higher feature values to the first observable frame and the subsequent frame, as evidenced by sudden changes in frames 5 and 6 for unobs 4; 2) After the first two observable frames, features show a decline before rising again. This indicates that through contrastive learning, the model pays additional attention to truncation positions.
+
+# 4.7. Limitations.
+
+The contrastive learning approach introduces certain invariance in encoder feature extraction, potentially sacrificing some fine-grained features and affecting basic model performance. Besides, length-based, scaling, and rotation data augmentation methods are ineffective for map-based data, which is somewhat constrained by the model's processing approach.
+
+# 5. Conclusion
+
+This paper introduces CLLS, a contrastive learning method for the Length Shift problem. It constructs positive samples via random length masking, rotation, and scaling, using encoded features from a nonlinear projector for contrastive loss calculation. We also propose a lightweight RNN combining MLP and GRU with CLLS, achieving SOTA performance on ETH-UCY, SDD, and NBA datasets. Experiments demonstrate CLLS's superiority over existing length-adaptive methods in both instantaneous and multi-observation prediction tasks. Ablation studies validate the nonlinear projector design, data augmentation strategies, and hyperparameter selection. Feature visualization further demonstrates CLLS's effectiveness. We hope our research provides valuable insights for addressing length shift problems.
+
+# References
+
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+# Adapting to the Unknown: Training-Free Audio-Visual Event Perception with Dynamic Thresholds
+
+Eitan Shaar $^{1*}$   
+Ariel Shaulov $^{2*}$   
+Gal Chechik $^{1,3}$   
+Lior Wolf $^{2}$
+
+$^{1}$ Bar-Ilan University  $^{2}$ Tel-Aviv University  $^{3}$ NVIDIA
+
+# Abstract
+
+In the domain of audio-visual event perception, which focuses on the temporal localization and classification of events across distinct modalities (audio and visual), existing approaches are constrained by the vocabulary available in their training data. This limitation significantly impedes their capacity to generalize to novel, unseen event categories. Furthermore, the annotation process for this task is labor-intensive, requiring extensive manual labeling across modalities and temporal segments, limiting the scalability of current methods. Current state-of-the-art models ignore the shifts in event distributions over time, reducing their ability to adjust to changing video dynamics. Additionally, previous methods rely on late fusion to combine audio and visual information. While straightforward, this approach results in a significant loss of multimodal interactions. To address these challenges, we propose AudioVisual Adaptive Video Analysis  $(AV^2A)$ , a model-agnostic approach that requires no further training and integrates a score-level fusion technique to retain richer multimodal interactions.  $AV^2A$  also includes a within-video label shift algorithm, leveraging input video data and predictions from prior frames to dynamically adjust event distributions for subsequent frames. Moreover, we present the first training-free, open-vocabulary baseline for audio-visual event perception, demonstrating that  $AV^2A$  achieves substantial improvements over naive training-free baselines. We demonstrate the effectiveness of  $AV^2A$  on both zero-shot and weakly-supervised state-of-the-art methods, achieving notable improvements in performance metrics over existing approaches. Our code is available on Github.
+
+# 1. Introduction
+
+Video event recognition, which involves the temporal localization and classification of events using both audio and
+
+![](images/89c528b87b17d498a85ae9385ada4aa0a9c6e3369fcfbbcce4de42d4b272325c.jpg)  
+Figure 1. Overview of the AVVP task. Audio-visual event perception focuses on predicting the temporal boundaries of events within a video that are exclusively visible (shown in blue), exclusively audible (shown in red), or both audible and visible (shown in purple).
+
+visual cues (see Figure 1), is essential for a wide range of applications, including video content analysis, autonomous driving, multimedia indexing, and personalized content recommendation systems [5, 27, 30]. Despite the recognized importance of this task, current approaches face substantial limitations that hinder their effectiveness and adaptability in open-world scenarios.
+
+A primary limitation in previous state-of-the-art methods [2, 5, 10, 12, 18, 19, 21] is their inability to dynamically adjust to evolving events in the video, leading to an oversight of changes in event distribution over time. This issue stems from the reliance on fixed thresholds for event prediction, which restricts the model's capacity to adapt to evolving patterns and contextual shifts within the video sequence. Moreover, the current state-of-the-art methods often employ a late fusion strategy, where audio and visual information are processed independently and then merged by intersecting the predicted labels from both modalities to obtain audio-visual predictions. While this approach simplifies model design, it limits the potential to capture the rich multimodal interactions needed for complex event detection [5, 18].
+
+Another major limitation of existing methodologies [2, 5, 10, 12, 18, 19, 21] is their reliance on fixed-vocabulary datasets. This reliance significantly restricts these mod
+
+els' ability to generalize to novel or evolving event categories—a capability that is essential for open-world environments where the range of possible event types is inherently diverse and continuously evolving [2, 30]. Addressing this challenge requires developing models that can move beyond pre-defined vocabularies and adapt to new events without extensive re-training. Lastly, the annotation process is labor-intensive, time-consuming, and costly, making it difficult to scale existing approaches to larger datasets or to adapt them for open-world deployment [12].
+
+To address these challenges, we propose a model-agnostic approach requiring no additional training, termed Audio-Visual Adaptive Video Analysis  $(\mathrm{AV}^2\mathrm{A})$ . Our method integrates a score-level fusion mechanism that combines audio and visual cues at an initial processing stage, thereby preserving richer multimodal interactions essential for accurate and context-aware event recognition. This approach enhances the alignment of audio and visual information, improving the model's capacity to recognize complex event patterns. Additionally,  $\mathrm{AV}^2\mathrm{A}$  incorporates a novel within-video label-shift mechanism designed to operate within video contexts, leveraging both input video data and predictions from prior frames to dynamically adjust event distributions for subsequent frames, achieved via dynamic thresholds that adapt over time. By aligning model expectations with recurring or evolving events, this mechanism enables  $\mathrm{AV}^2\mathrm{A}$  to capture temporal dependencies. In scenarios where events frequently recur or evolve, the dynamic thresholds capability ensures that the model remains adaptable and responsive to changing contexts. Furthermore, by leveraging foundation models [4, 22, 37] we introduce the first training-free, open-vocabulary baseline through  $\mathrm{AV}^2\mathrm{A}$ . This approach circumvents the limitations of fixed vocabularies and reduces the need for additional data annotations. Our primary contributions are as follows:
+
+- We present  $\mathrm{AV}^2\mathrm{A}$ , a model-agnostic approach that incorporates a score-level fusion strategy to combine audio and visual cues, preserving critical multimodal interactions. Additionally, our approach applies a within video label-shift mechanism that dynamically adjusts the predicted event distribution based on prior context, enhancing temporal adaptability.  
+- We introduce the first training-free approach specifically tailored for open-world audio-visual event perception, capable of recognizing and adapting to unseen events without the constraints of a fixed vocabulary.  
+- Through comprehensive evaluations on the AVE [27] and LLP [28] datasets, we demonstrate that our approach achieves state-of-the-art results in both zero-shot and training-free settings, showcasing its robustness and versatility.  
+- We illustrate the efficacy of our label-shift mechanism through experimental applications on existing state-of
+
+the-art weakly supervised methods, demonstrating consistent improvements across all metrics without additional training. These findings underscore the potential of leveraging temporal patterns directly within existing models.
+
+# 2. Related Work
+
+Weakly-supervised Audio-Visual Event Perception. To fully exploit the potential of both audio and visual modalities for weakly-supervised video analysis, [27] introduce the audio-visual event (AVE) localization task to leverage both modalities for weakly-supervised video understanding. In AVE, the model detects when an event is both audible and visible, pinpointing its temporal boundaries. Approaches often use attention strategies [11, 31, 32, 34] or cross-modal interactions [14, 23-25], while others incorporate regularization like background suppression [33] and positive sample propagation [36]. Unlike AVE, the audio-visual video parsing (AVVP) task [28] accounts for misalignment between audio and visual signals. To address this, multimodal multiple instance learning (MMIL [28]) frameworks have been employed [2, 5, 10, 12, 18, 19, 21], enabling the model to identify relevant instances across modalities without the need for strict temporal synchronization. These methods typically include techniques such as audio-visual track swapping [30] and cross-modality enhancement [12]. Currently, most methods target either AVE or AVVP separately due to the different properties between the two tasks. Furthermore, all of the above methods are restricted to a closed vocabulary, requiring extensive training to recognize events, which limits their ability to generalize to new, unseen events.
+
+Audio & Visual Zero-Shot Methods. Audio-visual zero-shot learning was first introduced in [20] with the Coordinated Joint Multimodal Embedding (CJME) model, which aligns video, audio, and text in a shared feature space using triplet loss. Building on this, [15] developed the Audio-Visual Generalized Zero-shot Learning Network (AVGZSLNet), which employs a cross-modal decoder and composite triplet loss to enhance the alignment of audio and video embeddings with text. The Audio-Visual Cross-Attention (AVCA) framework [17] further facilitates information exchange between modalities, achieving state-of-the-art performance in audio-visual zero-shot classification and introducing three novel benchmarks for AV-ZSL. Additionally, the Temporal Cross-Attention Framework (TCAF) [16] extends AVCA by leveraging temporal information. While [3] shows promising signs for zero-shot audio-visual event perception, the field remains largely underexplored, with significant opportunities for deeper exploration and advancement.
+
+![](images/c785d5e1641193fd919a3855dfcadc27d746bc8d133c2927ac7ad068a7a4cfd4.jpg)  
+Figure 2. Overview of  $\mathrm{AV}^2\mathrm{A}$ . The process begins with category selection, where the input video clip passes through a video-level score-level fusion module (blue) to select relevant categories based on a threshold  $\tau_{f}$ . These categories guide segment-level score-level fusion, where a dynamic threshold module (orange) updates thresholds  $\pmb{\tau}_{t}$  via our label-shift technique, using the soft confusion matrix  $M$  from prior predictions  $\mathcal{Y}_1,\dots ,\mathcal{Y}_{t - 1}$  and segment scores  $P_{av}^{1},\ldots ,P_{av}^{t - 1}$ , cosine similarity between segments and  $P_{av}^{t}$ . Finally, predicted candidates are validated against a confidence threshold  $\tau_r$ , retaining only those above it. This figure illustrates the process for audio-visual events; audio and visual events are handled similarly.
+
+Label Shift Estimation. Label shift estimation refers to the task of inferring the label distribution in a target domain using labeled source data and unlabeled samples from the target domain [6]. Earlier methods [1, 26, 35] often rely on explicit modeling of the conditional probability  $P(X = x \mid Y = y)$ , a requirement that becomes impractical for high-dimensional data, such as images. More recently [13] proposed BBSE, a method that leverages a black box predictor  $\hat{f}$  to estimate label shift between source and target distributions. Using predictions from  $\hat{f}$ , BBSE constructs a confusion matrix  $M = p_{s}(\hat{y}, y) \in \mathbb{R}^{k \times k}$  on source data with  $k$  classes, where  $y$  is the true label and  $\hat{y}$  is the predicted label, which may be a hard label ( $\hat{y} = \arg \max \hat{f}(x)$ ) or a soft probability vector,  $\hat{f}(x) = [p(\hat{y} = 1|x), \dots, p(\hat{y} = k|x)]$ , which is the distribution over classes predicted by  $\hat{f}$  for a given input  $x$ . The label shift estimate  $\hat{w}$  is then calculated as  $\hat{w} = M^{-1}\hat{\mu}$ , where  $M$  is the estimated confusion matrix and  $\hat{\mu}$  represents the distribution of predicted labels in the target data, derived by applying  $\hat{f}$  to the target samples. This correction factor  $\hat{w}$  aligns the target label distribution with the source distribution. In contrast to prior approaches, we explore the integration of input data as a component within our label shift estimation method. To the best of our knowledge, this work is the first to adapt label shift estimation within video contexts.
+
+# 3. Method
+
+We present a framework for audio-visual event perception that is entirely training-free. Central to our approach is a dy
+
+namic thresholds mechanism, which adjusts threshold values over time-based on the input video data and previous segment predictions, see Figure 2. The method enables precise detection of audio, visual, and audio-visual events.
+
+Problem Setup And Notations. Given an input video divided into  $T$  non-overlapping segments, our objective is to temporally localize and identify audio, visual, and audio-visual events present for each segment  $1 \leq t \leq T$ . Each segment  $t$  can contain zero or more events, which makes this a multi-label problem. The events to be identified are drawn from a set of  $C$  possible categories, defined for each benchmark. The Given video consists of audio  $A$  and video frames  $V$ :
+
+$$
+\begin{array}{l} A = \left\{a _ {1}, a _ {2} \dots , a _ {T} \right\}, \quad V = \left\{v _ {1}, v _ {2}, \dots , v _ {T} \right\} \\ a _ {t} \in \mathbb {R} ^ {1 \times F}, v _ {t} \in \mathbb {R} ^ {3 \times H \times W} \\ \end{array}
+$$
+
+where  $a_{t}$  and  $v_{t}$  are the corresponding audio and video visual frame at segment  $t$ ,  $H$  and  $W$  are the height and width for each frame, and  $F$  is number of frequency bins for each audio snippet  $a_{t}$ .
+
+We define two types of vector scores: video-level vector scores and segment-level vector scores. Both types are calculated by a foundation model (FM), combined with a sigmoid function  $\sigma$  to address the multi-label classification problem. Our method operates in an open-vocabulary setting, where the label set  $C$  is defined per video at inference time, even ones not seen during hyper-parameter tuning, unlike the baselines which are restricted to labels from
+
+a predefined set. Instead,  $C$  consists of user-defined textual descriptions, such as "an image of a military helicopter" or "the sound of helicopter rotor blades".
+
+Video-level scores are represented by  $P_{a}$  and  $P_{v}$  for audio and visual data, from the entire video's audio  $A$  and visual  $V$ .
+
+$$
+P _ {a} = \sigma (F M (C, A)), \quad P _ {v} = \sigma (F M (C, V)) \tag {1}
+$$
+
+$$
+P _ {a}, P _ {v} \in [ 0, 1 ] ^ {| C |}
+$$
+
+Segment-level vector scores capture more localized information. These are denoted as  $P_{a}^{t}$  and  $P_{v}^{t}$  for audio and visual scores, respectively, in each segment  $t$  based on segment-specific audio  $a_{t}$  and video frame  $v_{t}$ .
+
+$$
+P _ {a} ^ {t} = \sigma (F M (C, a _ {t})), \quad P _ {v} ^ {t} = \sigma (F M (C, v _ {t})) \tag {2}
+$$
+
+$$
+P _ {a} ^ {t}, P _ {v} ^ {t} \in [ 0, 1 ] ^ {| C |}
+$$
+
+Each element in both types of score vectors represents the score that a specific category  $c$  occurs.
+
+Effective audio-visual event recognition is based on the ability to leverage complementary information from both audio and visual modalities. Our score-level fusion is straightforward, we integrate audio and video scores using a weighted sum to create an audio-visual representation.
+
+$$
+P _ {a v} = \alpha P _ {a} + (1 - \alpha) P _ {v} \tag {3}
+$$
+
+$$
+P _ {a v} ^ {t} = \alpha P _ {a} ^ {t} + (1 - \alpha) P _ {v} ^ {t} \tag {4}
+$$
+
+$$
+P _ {a v}, P _ {a v} ^ {t} \in [ 0, 1 ] ^ {| C |}
+$$
+
+where  $P_{av}, P_{av}^{t}$  are the audio-visual vector scores at the video-level and at segment-level  $t$  respectively, and  $\alpha \in [0,1]$  serves as a scalar weight that determines the contribution of the audio score  $P_{a}, P_{a}^{t}$  relative to the visual score  $P_{v}, P_{v}^{t}$ .
+
+For generality, we will focus on identifying and localizing audio-visual events from this point forward. It is important to note that the processes for localizing and identifying audio and visual events are conducted in the same manner, using  $\alpha = 1$  for audio events and  $\alpha = 0$  for visual events in Equations 3 and 4.
+
+In our framework, we first want to ensure that only the relevant event categories are retained. We apply a selection step for the video-level vector  $P_{av}$ , discarding categories that do not exceed a predefined threshold  $\tau_f$ . This ensures us that only the most relevant event categories  $\hat{C}_{av}$  are preserved for further analysis.
+
+$$
+\hat {\mathcal {C}} _ {a v} = \left\{c \mid P _ {a v} [ c ] > \tau_ {f}, \quad \forall c \in C \right\}, \tag {5}
+$$
+
+where  $P_{av}[c]$  represents the audio-visual classification score for category  $c$  is being presented in the video.
+
+<table><tr><td>Method</td><td>α</td><td>τ0</td><td>τr</td><td>τf</td><td>λ</td></tr><tr><td>AV2A (CLIP [22] + CLAP [4])</td><td>0.45</td><td>0.75</td><td>0.75</td><td>0.5</td><td>1.0</td></tr><tr><td>AV2A (LanguageBind [37])</td><td>0.5</td><td>0.75</td><td>0.75</td><td>0.55</td><td>2.5</td></tr><tr><td>AV2A (MGN-MA [18])</td><td>0.3</td><td>0.55</td><td>-</td><td>-</td><td>0.5</td></tr><tr><td>AV2A (JoMoLD [2])</td><td>0.4</td><td>0.5</td><td>-</td><td>-</td><td>0.5</td></tr><tr><td>AV2A (CMPAE [5])</td><td>0.45</td><td>0.5</td><td>-</td><td>-</td><td>0.5</td></tr></table>
+
+Table 1. Hyperparameters for each baseline using  ${\mathrm{{AV}}}^{2}\mathrm{\;A}$  .
+
+To adapt to the content of the video domain, we apply thresholds for each category  $c \in \hat{\mathcal{C}}_{av}$  that change over time. We initialize the threshold for each category with the same predefined value, denoted as  $\tau^0$ , which serves as the initial threshold at segment  $t = 1$ .
+
+$$
+\boldsymbol {\tau} _ {t = 1} = \left[ \begin{array}{c c} \tau^ {0} & \forall c \in \hat {\mathcal {C}} _ {a v} \end{array} \right]
+$$
+
+Then, we predict events for segment  $t$  in the following way:
+
+$$
+\mathcal {Y} _ {t} = \left[ y _ {c} ^ {t} \mid \forall c \in \hat {\mathcal {C}} _ {a v} \right] \tag {6}
+$$
+
+$$
+\text {W h e r e} \quad y _ {c} ^ {t} = \left\{ \begin{array}{l l} 1 & \text {i f} P _ {a v} ^ {t} [ c ] > \boldsymbol {\tau} _ {t} [ c ], \\ 0 & \text {o t h e r w i s e} \end{array} \right.
+$$
+
+where  $P_{av}^{t}[c]$  represents the audio-visual score of category  $c$  being presented at segment  $t$  and  $\pmb{\tau}_{t}[c]$  is the category threshold for category  $c$  at segment  $t$ .
+
+To modify our dynamic thresholds, we estimate for each segment  $t$  the ratio  $\hat{w}_t$  between the predictions generated from segments  $1, \ldots, t-1$  and those from segment  $t$  across each category  $c$ .
+
+To perform this estimation, we first define a soft confusion matrix  $M$ , where each entry represents the score that a given segment  $t$  has the true category  $c$  but it's predicted category is  $\hat{c}$ , averaged over all samples. Let  $M_p \in \mathbb{R}^{(t-1) \times |\hat{C}_{av}|}$  be the matrix of prediction scores where each row is given by  $P_{av}^t$  (Eq. 4), which is the prediction score vector for segment  $t$ . We also define  $M_y \in \mathbb{R}^{(t-1) \times |\hat{C}_{av}|}$  as the matrix of the predicted categories where each row  $\mathcal{V}_t$  is predictions for segment  $t$ . The soft confusion matrix  $M \in \mathbb{R}^{|\hat{C}_{av}| \times |\hat{C}_{av}|}$  is defined as:
+
+$$
+M = \frac {1}{t - 1} \left(M _ {p}\right) ^ {T} \cdot M _ {y},
+$$
+
+i.e., each entry  $M_{\hat{c},c}$  in  $M$  is given by:
+
+$$
+M _ {\hat {c}, c} = \frac {1}{t - 1} \sum_ {i = 1} ^ {t - 1} P _ {a v} ^ {i} [ \hat {c} ] \cdot y _ {c} ^ {i}.
+$$
+
+$M_{\hat{c},c}$  captures the average score up to segment  $t - 1$  for instances where the model's predicted score for the category  $\hat{c}$  aligns with segments where the predicted category is  $c$ . Additionally, we propose incorporating the input data as a
+
+<table><tr><td></td><td colspan="2">Audio</td><td colspan="2">Visual</td><td colspan="2">Audio Visual</td><td colspan="2">Type@AV</td><td colspan="2">Event@AV</td></tr><tr><td></td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td></tr><tr><td rowspan="2">CLIP [22] + CLAP [4] with AV2A</td><td>17.6</td><td>15.1</td><td>18.8</td><td>17.8</td><td>30.0</td><td>25.6</td><td>22.1</td><td>19.5</td><td>18.3</td><td>16.2</td></tr><tr><td>32.7 ± .01</td><td>28.5 ± .01</td><td>43.5 ± .01</td><td>41.5 ± .01</td><td>55.1 ± .06</td><td>48.2 ± .04</td><td>43.8 ± .04</td><td>39.4 ± .01</td><td>34.7 ± .01</td><td>31.2 ± .01</td></tr><tr><td rowspan="2">LanguageBind [37] with AV2A</td><td>20.3</td><td>17.5</td><td>21.3</td><td>20.0</td><td>24.3</td><td>21.0</td><td>22.0</td><td>19.5</td><td>20.8</td><td>18.4</td></tr><tr><td>40.9 ± .09</td><td>35.9 ± .12</td><td>57.4 ± .04</td><td>54.4 ± .09</td><td>59.1 ± .1</td><td>52.3 ± .13</td><td>52.4 ± .04</td><td>47.5 ± .04</td><td>43.4 ± .04</td><td>38.9 ± .06</td></tr></table>
+
+Table 2. Comparison of training-free methods on the LLP dataset, reporting AVVP metrics.
+
+scaling factor for  $\hat{w}_t$ . We use cosine similarity between the visual features of the current segment  $t$ , and the previous segment  $t - 1$  as our scaling factor. The estimated ratio  $\hat{w}_t$  is computed as follows:
+
+$$
+\hat {w} _ {t} = M ^ {- 1} P _ {a v} ^ {t} \cdot \frac {x _ {t} \cdot x _ {t - 1}}{\| x _ {t} \| \| x _ {t - 1} \|}, \tag {7}
+$$
+
+where  $M$  is the estimated soft confusion matrix,  $P_{av}^{t}$  is the score vector for segment  $t$  and  $x_{t}$  is denoted as the corresponding visual feature vector produced from the foundation model. The estimated ratio  $\hat{w}_{t}$ , computed independently for each test video at inference time, quantifies the change in the score for each category  $c$  between consecutive segments  $t - 1$  and  $t$ . Specifically, the ratio captures how the score vector  $P_{av}^{t}$  for the current segment  $t$  has shifted relative to the previous segments. The cosine similarity serves as a scaling factor, providing a measure of alignment between the feature vectors of adjacent segments. This ensures that if two segments are highly similar in content, any score changes are emphasized less, while more significant score changes in dissimilar segments are weighted more heavily. Thus, the ratio  $\hat{w}_{t}$  not only reflects changes in category scores but also incorporates segment continuity, offering a refined measure of temporal dynamics in the event patterns across segments.
+
+Following this, we update the category thresholds  $\pmb{\tau}_{t}$  for each segment  $t$ . This update employs an exponential decay function to gradually reduce the thresholds, ensuring that the adjustments become smaller over time and preventing excessive reductions as the process progresses. Here,  $\pmb{\tau}_{1}$  represents the initial threshold vector, while  $\mathbf{z}$  is a vector tracking the cumulative count of occurrences for each category  $c \in \hat{C}_{av}$  up to time  $t - 1$ . The exponential decay,  $e^{-\lambda \mathbf{z}}$  is applied element-wise, meaning that each component  $z_{i}$  in  $\mathbf{z}$  undergoes a separate transformation  $e^{-\lambda z_i}$ , allowing each category's threshold adjustment to be scaled individually according to its occurrence frequency. Here,  $\lambda$  is the decay constant in the exponential decay function, controlling the rate at which threshold adjustments decrease.
+
+$$
+\boldsymbol {\tau} _ {t} = \boldsymbol {\tau} _ {t - 1} - \boldsymbol {\tau} _ {1} e ^ {- \lambda \mathbf {z}} \cdot \hat {w} _ {t} \tag {8}
+$$
+
+$$
+\boldsymbol {\tau} _ {t}, \mathbf {z}, w _ {t} \in \mathbb {R} ^ {1 \times | \hat {\mathcal {C}} _ {a v} |},
+$$
+
+After obtaining all  $\mathcal{Y}_1, \ldots, \mathcal{Y}_T$ , we define a candidate  $S_k$ , which is the predicted audio-visual localization for event category  $c$ , where  $k$  represents the index of the multiple predicted candidates.  $S_k$  is constructed to capture the maximal-length interval during which the score  $P_{av}^t[c]$  remains above  $\pmb{\tau}_t[c]$  to each segment  $t$ , meaning that  $y_c^t = 1$  holds true continuously throughout the entire candidate duration, such as:
+
+$$
+S _ {k} = \left(i _ {c} ^ {n}, j _ {c} ^ {n}, c\right) \quad \text {s u c h t h a t} \quad \exists n \leq T, \exists c \in \hat {\mathcal {C}} _ {a v} ,
+$$
+
+Where:
+
+$$
+i _ {c} ^ {n} = \min \{t \mid y _ {c} ^ {t} = 1, t > j _ {c} ^ {n - 1} \}
+$$
+
+$$
+j _ {c} ^ {n} = \max  \left\{t \mid y _ {c} ^ {t} = 1, t \geq i _ {c} ^ {n} \right\}
+$$
+
+$$
+\text {s u c h} \quad y _ {c} ^ {t} = 1, \quad \forall t \in \left[ i _ {c} ^ {n}, j _ {c} ^ {n} \right] \quad .
+$$
+
+Here,  $i_c^n$  and  $j_c^n$  denote the start and end indices of the candidate  $S_k$ , respectively, and  $c$  represents the event category associated with the candidate  $S_i$  and  $n$  is the number of candidates for the same category  $c$ .
+
+To further refine the predicted candidates, each candidate  $S_{k}$  is validated based on its associated audio  $A'$  and video frames  $V'$ , where:
+
+$$
+A ^ {\prime} = \{a _ {i}, \dots , a _ {j} \}, \quad V ^ {\prime} = \{v _ {i}, \dots , v _ {j} \}.
+$$
+
+Here,  $i$  and  $j$  represent the start and end timestamps of the predicted candidate. The candidate scores are computed as:
+
+$$
+P _ {a} ^ {\prime} = \sigma \left(F M \left(\hat {\mathcal {C}} _ {a v}, A ^ {\prime}\right)\right), \quad P _ {v} ^ {\prime} = \sigma \left(F M \left(\hat {\mathcal {C}} _ {a v}, V ^ {\prime}\right)\right) \tag {9}
+$$
+
+where  $P_{a}^{\prime}$  and  $P_{v}^{\prime}$  denote the audio and visual scores for all categories  $\hat{C}_{av}$  between timestamps  $i$ ,  $j$ . We compute the audio-visual score  $P_{av}^{\prime}$ , which is computed as described in Equation 3 with  $P_{a}^{\prime}$  and  $P_{v}^{\prime}$ . We apply a confidence threshold,  $\tau_{r}$ , to the audio-visual score  $P_{av}^{\prime}[c]$  for the predicted category  $c$  associated with a candidate. If  $P_{av}^{\prime}[c]$  surpasses  $\tau_{r}$ , the candidate is deemed valid; otherwise, it is discarded. Our framework employs a total of  $T \cdot |\hat{C}_{av}| + 2$  thresholds, specifically  $\{\tau_1, \dots, \tau_T\}, \tau_f$ , and  $\tau_r$ . The output of our framework consists of these valid candidates.
+
+<table><tr><td></td><td colspan="2">Audio</td><td colspan="2">Visual</td><td colspan="2">Audio-Visual</td><td colspan="2">Type@AV</td><td colspan="2">Event@AV</td></tr><tr><td></td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td></tr><tr><td>MGN-MA [18]</td><td>60.7</td><td>51.0</td><td>55.5</td><td>52.4</td><td>50.6</td><td>44.4</td><td>55.6</td><td>49.3</td><td>57.2</td><td>49.2</td></tr><tr><td>with AV2A&#x27;s dynamic thresholds</td><td>60.8</td><td>51.0</td><td>55.6</td><td>52.7</td><td>51.9</td><td>45.5</td><td>56.1</td><td>49.7</td><td>57.3</td><td>49.3</td></tr><tr><td>JoMoLD [2]</td><td>61.3</td><td>53.9</td><td>63.8</td><td>59.9</td><td>57.2</td><td>49.6</td><td>60.8</td><td>54.5</td><td>59.9</td><td>52.5</td></tr><tr><td>with AV2A&#x27;s dynamic thresholds</td><td>61.4</td><td>53.9</td><td>64.1</td><td>61.0</td><td>57.7</td><td>50.9</td><td>61.1</td><td>55.2</td><td>60.0</td><td>52.7</td></tr><tr><td>CMPAE [5]</td><td>64.4</td><td>57.5</td><td>66.1</td><td>63.3</td><td>59.5</td><td>52.4</td><td>63.3</td><td>57.7</td><td>62.9</td><td>56.3</td></tr><tr><td>with AV2A&#x27;s dynamic thresholds</td><td>64.7</td><td>58.0</td><td>66.3</td><td>63.4</td><td>59.9</td><td>52.7</td><td>63.6</td><td>58.0</td><td>63.0</td><td>56.7</td></tr></table>
+
+Table 3. Performance of state-of-the-art weakly supervised methods and their improvements with  ${\mathrm{{AV}}}^{2}\mathrm{\;A}$  ’s dynamic thresholds mechanism on the LLP dataset.  
+
+<table><tr><td>Method</td><td>Accuracy(%)</td></tr><tr><td>DG-SCT [3]</td><td>64.7</td></tr><tr><td rowspan="2">CLIP [22] + CLAP [4] with AV²A</td><td>38.2 ± 2.87</td></tr><tr><td>68.5 ± 0.16</td></tr><tr><td rowspan="2">LanguageBind [37] with AV²A</td><td>32.9 ± 1.27</td></tr><tr><td>72.8 ± 0.14</td></tr></table>
+
+Table 4. Comparison with zero-shot methods on AVE datasets, reporting AVEL metrics.
+
+# 4. Experiments
+
+We assess the performance of  $\mathrm{AV^2A}$  on two widely adopted datasets, AVE [27] and LLP [28], through comprehensive experiments demonstrating its improvements in both training-free and zero-shot settings. Additionally, we apply our novel dynamic thresholds technique to state-of-the-art weakly supervised methods, achieving significant performance enhancements without additional training. An extensive ablation study further highlights the contribution of each component in our approach.
+
+# 4.1. Experimental setup
+
+Datasets. We evaluate our approach on two datasets, AVE [27] and LLP [28].
+
+The Audio-Visual Event (AVE) dataset [27] consists of 4,143 YouTube videos spanning 28 categories derived from AudioSet [7], with each video clip lasting 10 seconds. The AVE [27] dataset focuses on recognizing audiovisual events that are both visible and audible across multiple time segments within a video, that is to say, it provides synchronized audio and visual signals, along with precise frame-level annotations that indicate the temporal locations of these events.
+
+The Look, Listen, and Parse (LLP) dataset [28] is a comprehensive audio-visual benchmark designed for studying event perception in unconstrained, real-world videos.
+
+It comprises 11,849 YouTube video clips, each lasting 10 seconds and covering 25 diverse event categories that involve various audio-visual interactions. The dataset provides video-level event labels, including both single and multiple overlapping events. The LLP dataset suits weakly-supervised learning, providing video-level annotations without precise event boundaries.
+
+Evaluation Metrics. Consistent with previous work, we evaluate using F1-scores for audio, visual, and audio-visual events at both segment and event levels. Additionally, we report aggregate metrics, Type@AV and Event@AV, computed at segment and event levels as well. For a comprehensive explanation of these metrics, refer to [28]. For the AVE dataset, in line with [27], we use overall accuracy as the evaluation metric.
+
+For hyperparameter optimization, we performed a search over 200 samples from the LLP validation set for the training-free methods, while using the full validation set of LLP for the weakly-supervised methods. Since only  $\mathrm{AV}^2\mathrm{A}$  's dynamic threshold mechanism is applied, optimizing the  $\tau_{r}$  and  $\tau_{f}$  values is unnecessary for the MGN-MA [18], JoMoLD [2], and CMPAE [5] methods. All hyperparameters used for each baseline are listed in Table 1.
+
+# 4.2. Comparison with State-of-the-art Methods
+
+Baselines. In our approach to training-free compression, we employ three foundational models to create two training-free baseline methods, upon which we implement  $\mathrm{AV^2A}$ . The first baseline employs the LanguageBind model [37], which provides both text-visual and text-audio similarity measurements. The second baseline combines the CLIP [22] and CLAP [4] models, where CLIP captures text-visual similarities, and CLAP supplies text-audio similarities; we refer to this baseline as CLIP-CLAP. For the evaluation of the CLIP-CLAP and LanguageBind baselines, a single static threshold is applied to predict categories across segments, creating two naive baselines. For weakly-supervised compression, we adopt three methodologies: JoMoLD [2],
+
+![](images/d103a532068cd21fdfa29f5df213d3342e4836188f58d2fdde787961736473df.jpg)  
+(a)  
+Figure 3. Performance analysis of  $\mathrm{AV^2A}$ , based on the LanguageBind [37] model, showcasing predictions on audio-visual events, specifically those occurring simultaneously in both audio and video. Comparisons highlight (a) improvements and (b) failure-cases relative to state-of-the-art weakly supervised baselines.
+
+![](images/91cc9de8215cd3d5a41604792e85c6e9b139982a84ab8ea0dedeeb12f62a22ee.jpg)  
+(b)
+
+which performs joint modality learning for improved cross-modal representations; MGN-MA [18], which leverages multi-granularity networks to enhance modality alignment; and the state-of-the-art method CMPAE [5], that integrates adaptive encoding to capture complex, high-quality cross-modal associations.
+
+AVVP Evaluation. In this experiment, we employ two baselines, CLIP-CLAP and LanguageBind, which are constructed as described in Section 4.2. As shown in Table 2, applying  $\mathrm{AV}^2\mathrm{A}$  to the baselines CLIP-CLAP and LanguageBind results in metric improvements across the board. Specifically, when  $\mathrm{AV}^2\mathrm{A}$  is integrated with the naive CLIP-CLAP baseline, it achieves a  $21.7\%$  improvement in segment-level Type@AV, which measures average segment performance across audio, visual, and audio-visual settings. Additionally,  $\mathrm{AV}^2\mathrm{A}$  enhances performance by  $19.9\%$  in
+
+event-level Type@AV, which evaluates the average event performance across these setups. Furthermore, AV $^2$ A improves the naive LanguageBind baseline by  $30.4\%$  and  $28\%$  in segment-level and event-level Type@AV, respectively.
+
+We further validate  $\mathrm{AV}^2\mathrm{A}$  's dynamic thresholds mechanism on the AVVP benchmark by applying it on top of current state-of-the-art weakly supervised methods, specifically, CMPAE [5], JoMoLD [2], and MGN-MA [18]. In this experiment, we apply the dynamic thresholds mechanism (Eq. 8) to these methods, as they already employ a relevant class selection stage that closely aligns with our approach; however, these methods used static thresholds to predict events over time. The results, presented in Table 3, indicate that our dynamic thresholds outperform the static thresholds technique without additional training, establishing a new state-of-the-art in video parsing. To imple
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Audio</td><td colspan="2">Visual</td><td colspan="2">Audio Visual</td><td colspan="2">Type@AV</td><td colspan="2">Event@AV</td></tr><tr><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td><td>segment</td><td>event</td></tr><tr><td>\( AV^2A(LanguageBind [37]) \)</td><td>40.9</td><td>35.9</td><td>57.4</td><td>54.4</td><td>59.1</td><td>52.3</td><td>52.4</td><td>47.5</td><td>43.4</td><td>38.9</td></tr><tr><td>w/o cosine similarity</td><td>40.8</td><td>35.9</td><td>57.3</td><td>54.3</td><td>58.8</td><td>51.8</td><td>52.3</td><td>47.3</td><td>43.3</td><td>38.8</td></tr><tr><td>w/o dynamic thresholds</td><td>40.7</td><td>35.1</td><td>56.9</td><td>55.2</td><td>55.1</td><td>47.2</td><td>52.2</td><td>47.2</td><td>43.0</td><td>37.8</td></tr><tr><td>w/o refine segments</td><td>38.9</td><td>34.1</td><td>53.6</td><td>50.9</td><td>57.9</td><td>51.1</td><td>50.2</td><td>45.4</td><td>41.4</td><td>37.0</td></tr><tr><td>w/o relevant class selection</td><td>33.4</td><td>29.3</td><td>40.2</td><td>38.4</td><td>39.7</td><td>34.3</td><td>37.8</td><td>34.0</td><td>34.8</td><td>31.4</td></tr></table>
+
+Table 5. Ablation study results on the LLP dataset.
+
+ment our dynamic threshold mechanism in the audio-visual regime, it is essential to apply our score-level fusion stage (Eq.4), as the audio-visual scores required for the dynamic thresholds mechanism are unavailable in the methods standard form due to their late-fusion strategy.
+
+AVE Evaluation. As shown in Table 4, we compare  $\mathrm{AV}^2\mathrm{A}$  with three zero-shot baselines: the CLIP-CLAP baseline [4, 22], the LanguageBind baseline [37], and the state-of-the-art DG-SCT method [3]. Notably,  $\mathrm{AV}^2\mathrm{A}$  outperforms DG-SCT [3], achieving improvements of  $3.8\%$  and  $8.1\%$  when built upon the CLIP-CLAP and Language-Bind baselines, respectively. To ensure a fair zero-shot comparison, we used the same hyperparameters identified during tuning on the LLP validation set, as detailed in Section 4.2. Please note that we did not apply  $\mathrm{AV}^2\mathrm{A}$  on the DG-SCT baseline, as the trained checkpoints and features were not made available.
+
+Method Efficiency. In our experiments, inference times across all weakly-supervised methods were of the same order of magnitude, with our method achieving  $\sim 2.49$  seconds per video. However, our primary efficiency advantage lies in the fact that  $\mathrm{AV^2A}$  requires no additional training, unlike the weakly-supervised baselines. For comparison, the weakly-supervised methods trainable parameters are as follows: MGN-MA [18] has  $\sim 4.3M$ , JoMoLD [2] has  $\sim 4.5M$ , and CMPAE [5] has  $\sim 5.6M$ . In addition to the trainable parameters, the above methods employ three pretrained, fixed models to generate input features: ResNet152 [8], VGGish [9], and R(2+1)D [29]. This procedure adds  $\sim$  2.68 seconds to the inference time per video.
+
+# 4.3. Ablation study
+
+We conducted an ablation study using the LanguageBind baseline [37] to investigate the contributions of each component of our method. The results, detailed in Table 5, illustrate the impact of these components on performance. The first row presents our complete method, with the LanguageBind model [37]. The second row of the table represents the model configuration without cosine similarity in the label shift method, effectively demonstrating the method's per
+
+formance when excluding the cosine similarity between adjacent frames. The third row highlights the effect of omitting the dynamic threshold mechanism, employing fixed thresholds instead. Additionally, the fourth row reports the outcome when the refinement of segments is removed, resulting in candidate event segments being used as final predictions. Lastly, we examined the model without the relevant class selection process, using the entire class set from the outset. Note that in each row, only the specified stage is pruned, while the remainder of the pipeline remains unchanged. The findings indicate that each component of our method contributes positively to the overall performance, reinforcing the importance of their inclusion.
+
+# 5. Limitations
+
+Our reliance on foundation models for extracting audiovisual similarities may introduce biases and limit the accuracy of short-duration or rapid events (Figure 3). These models, trained on longer, distinct events, struggle with subtle changes. Since  $\mathrm{AV}^2\mathrm{A}$  requires no training or fine-tuning, improvements in foundation models should enhance audiovisual perception.
+
+# 6. Conclusion
+
+In this paper, we introduce the first training-free, open-vocabulary approach for audio-visual perception via  $\mathrm{AV}^2\mathrm{A}$ , a model-agnostic method for robust event perception.  $\mathrm{AV}^2\mathrm{A}$  improves weakly-supervised baselines by replacing static thresholds with a within-video label shift mechanism, enhancing adaptability to temporal variations in event distribution. Applied to zero-shot and weakly-supervised settings,  $\mathrm{AV}^2\mathrm{A}$  achieves new state-of-the-art results without additional training.
+
+# 7. Acknowledgments
+
+This work was supported by the Tel Aviv University Center for AI and Data Science (TAD), and by a Vatat data-science grant to GC and the Bar-Ilan University data-science institute.
+
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+# Adaptive Dropout: Unleashing Dropout across Layers for Generalizable Image Super-Resolution
+
+Hang Xu Jie Huang Wei Yu Jiangtong Tan Zhen Zou Feng Zhao*
+
+MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition  
+University of Science and Technology of China
+
+{xuhang0609, hj0117, patrick914y, jttan, zouzhen}@mail.ustc.edu.cn, fzhao956@ustc.edu.cn
+
+# Abstract
+
+Blind Super-Resolution (blind SR) aims to enhance the model's generalization ability with unknown degradation, yet it still encounters severe overfitting issues. Some previous methods inspired by dropout, which enhances generalization by regularizing features, have shown promising results in blind SR. Nevertheless, these methods focus solely on regularizing features before the final layer and overlook the need for generalization in features at intermediate layers. Without explicit regularization of features at intermediate layers, the blind SR network struggles to obtain well-generalized feature representations. However, the key challenge is that directly applying dropout to intermediate layers leads to a significant performance drop, which we attribute to the inconsistency in training-testing and across layers it introduced. Therefore, we propose Adaptive Dropout, a new regularization method for blind SR models, which mitigates the inconsistency and facilitates application across intermediate layers of networks. Specifically, for training-testing inconsistency, we re-design the form of dropout and integrate the features before and after dropout adaptively. For inconsistency in generalization requirements across different layers, we innovatively design an adaptive training strategy to strengthen feature propagation by layer-wise annealing. Experimental results show that our method outperforms all past regularization methods on both synthetic and real-world benchmark datasets, also highly effective in other image restoration tasks. Code is available at https://github.com/xuhang07/Adpative-Dropout.
+
+# 1. Introduction
+
+Blind SR [7, 13, 18, 37, 43] aims to recover high-quality images from low-quality images without knowing the degradation kernel. However, even with better real-world degradation simulation [52, 57, 68] and more expressive model
+
+![](images/ea92a1c0cc6e0ceab4f08dd15040214086aba36c8b7f25228895d70a2f4ecf25.jpg)  
+Figure 1. Placing dropout before the final convolutional layer can enhance the generalization performance of blind SR models, whereas placing it elsewhere has the opposite effect due to the inconsistency introduced. Our method effectively addresses the inconsistency allowing it to be easily applied to intermediate layers.
+
+architectures [2, 34, 35], blind SR models still encounter a severe over-fitting problem. Therefore, appropriate regularization terms [12, 53, 59] or training strategies [3, 49] are urgently needed to enhance the generalization of blind SR models. In the past, Kong et al. [29] first introduced regularization into blind SR, adding dropout before the last convolutional layer of the model, which effectively improved the model's generalization ability. Subsequently, Wang et al. [56] argued that dropout could harm the recovery of high-frequency image information and proposed Simple-Align, which feeds low-quality images obtained from different degradations of the same image into the network and aligns the features before the last convolutional layer, encouraging the model to be degradation-invariant.
+
+It is worth noting that the above regularization methods all target the features before the last convolutional layer, while the features at intermediate layers are only implicitly impacted [25, 45, 46]. However, we find this indirect impact hard to regularize the features at intermediate layers to be degradation-invariant [19, 24, 38], and instead exacerbates the imbalance between channels, indicating the necessity of explicit regularization for intermediate features. Therefore,
+
+we explore a new solution that regularizes the intermediate features on the shoulder of Dropout [29], which further elevates the generalization ability of blind SR models.
+
+We rethink the dropout technique for this task. In previous discussions [29, 48], it is not suitable for dropout to be directly applied in regression problems like SR. But Kong et al. [29] improved the model's generalization ability by adding dropout before the last convolutional layer, and indicated that adding it elsewhere led to performance drop. This raises the question of what causes this phenomenon. To analyze the reason, we conduct detailed experiments and attribute the performance decline to the inconsistency brought by directly applying dropout to intermediate layers. Specifically, as shown in Figure 2(b), directly applying dropout to intermediate layers introduces training-testing inconsistency, which harms the expressiveness of features considering the mean shift in the distribution fitted during training. Moreover, we observe that different layers of the network impact generalization differently, with shallow layers influencing general feature extraction and deep layers influencing degradation handling. Among them, general feature representation can consistently play a role in content reconstruction, while degradation representation needs regularization to perform well on unseen data. However, directly applying dropout to intermediate layers doesn't take into account the inconsistency in generalization requirements across different layers. These two types of inconsistency essentially require us to strike a balance between the fitting ability and generalization ability of the network.
+
+In this paper, we introduce Adaptive Dropout for blind SR models to enhance generalization, consisting of the adaptive dropout format and the adaptive training strategy as shown in Figure 3. The key design of our method lies in its consideration of the balance between feature expressiveness and degradation generalization. Concretely, we redesign the format of dropout to adaptively integrate the dropouted feature with the original feature, which effectively mitigates training-testing inconsistency. Furthermore, considering the differing generalization requirements across different layers, we introduce the adaptive training strategy which adaptively helps blind SR models achieve a balance between fitting ability and generalization ability while satisfying the generalization requirements across different layers by layer-wise annealing. It is worth noting that, since our method is easy to integrate with Dropout [29], we unify them and treat them as a whole to help blind SR models improve generalization. We show the superiority of our proposed method in Figure 1 and summarize our main contributions as follows:
+
+- We specifically analyze the inconsistency introduced by directly applying dropout to intermediate layers, including training-testing inconsistency and the inconsistency in the generalization requirements across different layers.
+
+- We introduce Adaptive Dropout that adaptively integrates the dropouted feature with the un-dropouted one. Moreover, we introduce an adaptive training strategy that achieves an elegant trade-off between fitting and generalizing across different layers by introducing different adaptive weight formats and layer-wise annealing.  
+- We validate the effectiveness of Adaptive Dropout on multiple synthetic datasets and real-world datasets. It is also highly effective in other image restoration tasks.
+
+# 2. Related Work
+
+# 2.1. Blind Super-Resolution
+
+To deal with complicated degradation kernels [11] in the real world, blind SR [51, 65] is introduced into the field of super-resolution, which aims to recover high-resolution images even though the degradations are unknown. Compared with implicit degradation modeling [28, 47, 70], which requires large datasets during training, explicit degradation modeling [32, 62] performs better, where the degradations are added into images as data augmentation during training. DASR [36] introduces a new degradation scheme containing four types of degradation (bicubic, blur, noise, JPEG). Then in Real-ESRGAN [57], applying the degradation scheme twice has proved helpful in generating low-resolution images closer to the real world, and has become a regular part of data augmentation when training blind SR models. However, just training blind SR models with a large degradation pool brings a severe problem: the SR network learns to overfit the distribution of specific degradations rather than the distribution of natural images [29, 65, 68]. The problem forces researchers to find a proper training strategy to help blind SR models generalize better.
+
+# 2.2. Regularization methods for blind SR
+
+For models of another field [20, 22, 23], regularization [12, 53, 59], normalization [5, 60, 61], and other modules [8, 14, 21] are widely used as training strategies to improve the network's generalization performance. However, for blind SR models, few researchers pay attention to the training strategies. Previously, researchers focused more on improving the network's generalization ability to unknown degradations through complex degradation paradigms [52, 57, 68] and network designs [2, 34, 35], while overlooking the fact that training strategies are also an important factor affecting the network's generalization performance. Recently, Kong et al. [29] demonstrated that dropout can also be applied to blind SR models and should be added before the last convolutional layer while adding dropout to other locations (such as within the residual blocks) leads to a decline in model performance. Simple-Align [56] shows the side-effect of dropout and provides a better choice as regularization, where two low-resolution images obtained from the same high-resolution image but with different degradations
+
+![](images/0f3ffc21edd85d21237c709889ced704a9228e29d0d1829844c5e9b4cc7da9f9.jpg)  
+(a) imbalance between feature channels at intermediate layers
+
+![](images/4bacc1ec879de55736b680b1379ca3917af07206c59fffe68ef2b93a6fa685c7.jpg)  
+(b) training-testing inconsistency accumulation  
+(c) differing responses of features at different layers to dropout  
+Figure 2. The source of our motivation. (a) shows the imbalance between shallow feature channels, which is not well constrained by past methods. Mask channel index refers to the position of the channel we mask when adopting channel ablation. (b) compares the results of adding dropout to more blocks, indicating the accumulation of training-testing inconsistency along layers. (c) demonstrates the different behaviors of shallow and deep features when faced with dropout, as summarized in the text. We attribute this to the differing generalization requirements of different layers. Specifically, deep features more prominently represent information related to training degradations. Regularizing degradation representations alleviates the network's overfitting to training degradations, but directly applying dropout in deep layers also impairs the expressiveness of feature representations, leading to the performance shown in the chart. Shallow features, which contain more general representations, exhibit more consistent performance across wider degradations after being regularized.
+
+![](images/69fc28fc1af3196a7ff28632d48785b9101b3176ee908fa2c17190066c279506.jpg)
+
+are fed into the network, and the statistics of the outputs before the last convolutional layer are aligned across different dimensions. However, we argue that dropout is still a great choice and can be added into all blocks in a different way.
+
+# 3. Motivation
+
+# 3.1. Intermediate layers need explicit regularization
+
+Both Dropout [29] and Simple-Align [56] regularize features before the final convolutional layer which directly impact the quality of restoration. So applying constraints to these features can effectively enhance the model's generalization ability. Meanwhile, regularizations targeting the final layer also serve as implicit constraints on intermediate layers. However, we argue this indirect constraint is insufficient to generalize the features at intermediate layers.
+
+We evaluate the balance between channels in the intermediate layers under different regularization with channel ablation [44] and show the results in Figure 2(a). Specifically, we sequentially occlude each channel to obtain a new feature map, which is then normalized to ensure the conservation of total energy, input into subsequent layers, and calculate the PSNR. Surprisingly, adding regularization only to the final layer doesn't improve the generalization of the features at intermediate layers, while stronger regularization exacerbates the imbalance between channels. In contrast, we explicitly regularize the features at intermediate layers resulting in a smaller performance decrease when conducting channel ablation [44]. This indicates the necessity of explicit regularization of the features at intermediate layers.
+
+As a widely used regularization method, we want to incorporate dropout into intermediate layers of Blind SR networks to explicitly regularize features there. Although Kong et al. [29] argue that dropout can only be applied before the last convolutional layer and not to intermediate lay
+
+ers, they lack an in-depth analysis of the reasons behind this. Therefore, we delve deeper by analyzing the issues brought about by dropout, seeking a reasonable approach to explicitly regularize features at intermediate layers.
+
+# 3.2. Inconsistency when directly applying dropout
+
+In Dropout [29], the impact of applying dropout to the network's intermediate layers was analyzed, leading to the following conclusions: (1) Applying dropout to the intermediate layers of the network rather than the final layer results in a performance decline. (2) Applying more dropout comes to more performance declines. (3) Applying dropout closer to the output layer results in better model performance.
+
+Overall, we attribute these three conclusions to the inconsistency brought by applying dropout to the intermediate layers, including that between the training and testing phases, and that among different layers of the network. Considering that the performance of Blind SR networks in unseen degradations and unseen scenarios is a joint effect of their fitting and generalization ability, improving generalization requires ensuring fitting ability. However, the inconsistency severely undermines the network's fitting ability. Below, we separately explain the causes of the inconsistency and provide corresponding solutions.
+
+Point 1: The training-testing inconsistency. For conclusion (1) and (2) brought by Dropout [29], We attribute them to the training-testing inconsistency [27, 33] caused by applying dropout directly at intermediate layers. Moreover, when applying more dropout to intermediate layers, this inconsistency accumulates along the direction of information propagation, leading to the representations obtained from training not being well utilized during inference. In other words, the feature representations learned are losing their expressiveness. We illustrate the accumulation of inconsistency in 2, where the inconsistency is manifested as the shift
+
+![](images/05fc19e39c76333b434ae7235b4917223d07c97cae855f92f02c2d3a4465092e.jpg)  
+Figure 3. Overall schema of our proposed adaptive dropout. Adaptive dropout consists of two components. (a) The adaptive dropout format adaptively couples the features before and after dropout, thereby achieving a balance between the network's fitting ability and generalization ability while alleviating the training-testing inconsistency. (b) Considering the different generalization requirements of features at different layers, we design an adaptive training strategy and its two variants. Regarding Implicit Adaptive Dropout, it adaptively adjusts the weight  $w$  through a module, with different designs for shallow and deep layers. Regarding Explicit Adaptive Dropout, it initializes  $w$  in all blocks and explicitly anneals it block-by-block during training, as shown in the algorithm beside.
+
+in features at intermediate layers after applying dropout.
+
+First, we introduce the training-testing inconsistency brought by dropout. We take channel dropout as an example. Consider a feature map  $x_{k} \in \mathbb{R}^{c \times h \times w}$ . When applying channel dropout to  $x_{k}$ , it is multiplied by a dropout mask  $a_{k} \in \mathbb{R}^{c}$  which comes from a Bernoulli distribution during training:  $\hat{x}_{k} = a_{k}x_{k}$ . During training and testing, the mean of  $\hat{x}_{k}$  remains the same, but there is a variance shift. Then after passing through the activation function, the variance shift leads to the mean shift which harms the expressiveness of the feature presentations. This issue does not exist when dropout is added before the last convolutional layer, with no activation function following it. Assume we have  $x_{k}$  with a mean  $\mu$  and variance  $\sigma^2$ :
+
+$$
+\mathbf {v a r} [ \hat {x _ {k}} ] = \left\{ \begin{array}{l l} \frac {1}{1 - p} (\mu^ {2} + \sigma^ {2}) - \mu^ {2}, & \text {d u r i n g t r a n i n g} \\ \sigma^ {2}, & \text {d u r i n g i n f e r e n c e} \end{array} \right.
+$$
+
+Then, the relative deviation of the variance of  $\hat{x_k}$  during
+
+training can be expressed as  $s_k$ :
+
+$$
+\begin{array}{l} s _ {k} = \frac {\operatorname {v a r} _ {\text {t r a i n i n g}} \left[ \hat {x} _ {k} \right]}{\operatorname {v a r} _ {\text {i n f e r e n c e}} \left[ \hat {x} _ {k} \right]} - 1 \\ = \frac {1}{1 - p} \left(\frac {\mu^ {2}}{\sigma^ {2}} + 1\right) - \frac {\mu^ {2}}{\sigma^ {2}} - 1 \\ = \frac {p}{1 - p} (\frac {\mu^ {2}}{\sigma^ {2}} + 1) \\ \end{array}
+$$
+
+So reducing  $s_k$  can decrease the training-testing inconsistency, while also reducing the inconsistency accumulation.
+
+Solution 1: Adaptive dropout format. Integrating the dropouted feature with the original feature is a natural thought, considering we need to enhance the generalization of features while ensuring their expressiveness. Therefore, we introduce an adaptive dropout format to Blind SR, as shown in Figure 3(a). the basic format can be expressed as:
+
+$$
+f (x) = w x + (1 - w) d r o p o u t (x, p) \tag {1}
+$$
+
+Where  $x$  represents the feature map, dropout refers to dropout operations,  $w$  represents the weighted coefficients, and  $p$  represents the dropout rate. We can calculate the relative deviation of the variance introduced by the adaptive
+
+![](images/6ead3c4c68cb992345bce3d30fda67540f089cd7bd0d5e393e3b067790c63412.jpg)  
+Figure 4. Our exploration for mitigating the inconsistency in generalization requirements across different layers. The left and right figures respectively show the model performance using different regularizations on Set5 and Set14. With consideration of how to better retain the fitting ability of SR models, a learnable weighted structure yields better results than the standard one.
+
+dropout format in the same way:
+
+$$
+\begin{array}{l} \operatorname {v a r} \left[ x _ {k} ^ {a d} \right] = \frac {(1 - w) ^ {2}}{1 - p} \left(\mu^ {2} + \sigma^ {2}\right) - \mu^ {2} \\ s _ {k} ^ {a d} = \frac {(1 - w) ^ {2} p}{1 - p} (\frac {\mu^ {2}}{\sigma^ {2}} + 1) \\ \end{array}
+$$
+
+Compared with standard dropout which can be viewed as a special case of adaptive dropout format when  $w = 0$ , adaptive dropout format reduces the variance shift by  $(1 - w)^2$  leading to less training-testing inconsistency and inconsistency accumulation when applying it into multiple blocks.
+
+Point 2: The inconsistency in generalization requirements across different layers. For conclusion (3) brought by Dropout [29], we attribute this to the differing generalization requirements of shallow and deep layers. Prior works [40, 64] have found that representations extracted from the shallow layers are more generalized, while the representations extracted from the deep layers show strong task relevance. For blind SR, the extraction of general features is crucial for image reconstruction, regardless of the degradation the low-quality image has undergone. However, task-specific representations may not perform well on test images, considering that these representations may overfit the degradations of the train set without regularization. Therefore, providing deeper features with greater perturbation without compromising fitting ability helps the model avoid overfitting to specific degradations in the training pool. To support this point, we verify the performance on Set5 with different degradations when dropout is directly applied at different layers, presenting the main results in Figure 2(c). It can be observed that after being regularized, deep features result in differing performance across various degradations, whereas shallow features exhibit the opposite behavior, indicating their differing generalization requirements.
+
+Solution 2: Adaptive training strategy. In the basic format of adaptive dropout,  $x$  represents the complete transmission of information,  $dropout(x)$  represents the regularizations on features and  $w$  represents the trade-off between fitting ability and generalization ability. Considering the differing generalization requirements of different layers, it is reasonable to set different  $w$  for each layer or block.
+
+![](images/7b36687589461f62ab5cdf1162f752af44215816cae81dfad4320b0438d6ac40.jpg)  
+Figure 5. Our exploration for the adaptive training strategy. The graph on the left shows the trend of changes in  $w$  across different layers when we use the learnable weight structure. The graph on the right illustrates the performance differences between vector  $w$  and value  $w$ , where vector  $w$  performs better on more complex datasets while value  $w$  performs better on others.
+
+![](images/df7396a0148d212d11b8fca11f973cbdbb0e2602d1864a03615eea57da777c01.jpg)
+
+However, there is no clear guidance on how to apply different perturbations to different layers. So we design an experiment where we couple  $x$  and dropout(x) with learnable weights  $w$  and  $1 - w$  for each block, to help uncover the patterns guiding the application of adaptive dropout format. Also, we simply use an adaptive dropout format with  $w = 0.5$  as a comparison.
+
+Understandably, this learnable weighted structure yields more significant effects than the simple application of the adaptive dropout format as illustrated in Figure 4, for the former one ensures the network's fitting ability since the network adjusts  $w$  towards fitting the train set. Then, we present the changes in  $w$  across different blocks in Figure 5(a) to identify the patterns of the network's adaptive adjustment of  $w$ : First,  $w$  in each block gradually approaches 1, indicating that the model itself slowly reduces the perturbation of features, which represents the requirements of SR network for fitting ability. Second, compared to deeper blocks, the  $w$  values in shallower blocks approach 1 more rapidly, representing the requirements for generalization ability across different layers. We can summarize that the network is performing an adaptive annealing process from shallow to deep layers. This layer-wise annealing training strategy, which we refer to as the adaptive training strategy shown in Figure 3(b), aligns with our requirement to address the inconsistency in generalization needs across different layers. We divide the training phase into generalization and fitting stages, referring to the periods when intermediate layer features are perturbed and not perturbed, respectively. The shallow layers of the network enter the fitting stage earlier, ensuring that the model's general feature representations have good expressiveness. The deep layers remain in the generalization stage for a longer time, ensuring that the model does not overfit the degradations of the train set, thereby performing well on unseen degradations. Additionally, the adaptive training strategy effectively addresses the inconsistency accumulation issue, enabling the network to eliminate perturbations from the source.
+
+# 4. Methods
+
+To further improve the generalization of blind SR networks, we propose adaptive dropout, where the adaptive dropout format and adaptive training strategy are the core designs of our method. Below, we separately introduce them in detail.
+
+# 4.1. Adaptive Dropout format
+
+In Equation 1, we presented the basic form of the adaptive dropout format, so here we specifically discuss the hyperparameters, Integration, and application in networks.
+
+Hyper-parameters. The adaptive dropout format has two hyper-parameters,  $w$  and  $p$ . However, we find that setting  $p$  to 0.5 and adjusting  $w$  alone is sufficient to achieve better generalization performance in blind SR networks. Therefore, we simply set  $p$  to 0.5 to simplify our method design.
+
+Integration. Since the proposed adaptive dropout targets the intermediate features of the network, it can effectively be integrated with Dropout [29] which targets features before the last convolutional layer. We still retain the original format of dropout before the last convolutional layer for it doesn't bring the training-testing inconsistency.
+
+Application. In CNN-based SR networks [30, 69], using multiple adaptive dropout within the same block does not improve performance on unseen degradation. We speculate that this might excessively constrain the network's fitting capability within the same training time. For SwinIR [34] where dropout is generally not used under normal settings, we reintroduce this regularization method and replace all dropout with adaptive dropout, which is also applicable to other transformer-based SR networks [9, 15].
+
+# 4.2. Adaptive Training Strategy
+
+Previously, we discovered that the network implicitly employs a layer-wise annealing strategy through our attempt to adaptively adjust the learnable  $w$ . Given this, we argue that explicitly applying this strategy can also yield good results and design two variants for adaptive dropout.
+
+Implicit Adaptive Dropout with different formats of  $w$ . We implicitly adopt the adaptive training strategy by treating  $w$  as an estimizable variable and letting the neural network learn the optimal  $w$  just as our attempt to adaptively adjust the learnable  $w$ . To better weigh the importance of each channel, we use a network similar to channel attention [16], where the weight  $w_{i}$  can be obtained by:
+
+$$
+\begin{array}{l} w _ {i} = \operatorname {s i g m o i d} \left(f _ {2} \left(\operatorname {R e L U} \left(f _ {1} \left(x _ {k}\right)\right)\right)\right) \\ \hat {x} _ {k} = w x _ {k} + (1 - w) \text {d r o p o u t} (x _ {k}) \\ \end{array}
+$$
+
+Where  $f_{1}$  and  $f_{2}$  represent linear projection,  $x_{k}$  means the original feature, and  $\hat{x_k}$  means the coupled feature. According to specific requirements,  $w_{i}$  can take the format of  $[B,C]$ , where  $B$  means the batch size and  $C$  means the number of channels, meaning that different weights are learned for each channel of the feature, referred to as
+
+vector w. It can also take the format of  $[B,1]$ , meaning that the same weight is shared across all channels, referred to as value w. The former introduces more randomness and variability compared to the latter. The impact of this randomness is shown in Figure 5(b): in more complex datasets, Manga109 and Urban100, vector w achieves better results than value w, whereas in simpler datasets, Set14 and BSD100, the opposite is true. Therefore, we use them in different blocks to strike a balance between the two. Considering that we should reduce disturbances in the shallow layers, we apply value w in the shallow layers and vector w in the deeper layers.
+
+Explicit Adaptive Dropout with layer-wise annealing. We explicitly adopt the adaptive training strategy by initializing  $w$  for all blocks and then annealing it block-by-block during training. Specifically, for every  $t$  training iteration, we set the  $w$  to 0 in one block, repeating the operation from shallow to deep layers, where  $t$  is related to the total number of training iterations. In this way, general feature representations can be sufficiently preserved, while degradation-related representations can be sufficiently constrained.
+
+# 5. Experiments
+
+Experimental settings. We follow the multi-degradation settings and experimental configurations outlined in Dropout [29]. For training, we utilize the HR images from the DIV2K dataset [1]. During training, we employ L1 loss and the Adam optimizer [10]. The batch size is set to 16, and the size of the LR images is  $32 \times 32$ . We adopt a cosine annealing strategy to dynamically adjust the learning rate, with an initial learning rate set to  $2 \times 10^{-4}$ . We train for a total of 500,000 iterations. For testing, we use the synthetic datasets Set5 [4], Set14 [63], BSD100 [41], Manga109 [42], and Urban100 [17], as well as the real-world datasets NTIRE 2018 SR challenge data [54], RealSR [6], and DrealSR [58]. We compare our approach with Dropout [29] and Simple-Align [56].
+
+Comparison with baseline models. We present the experimental results for the baseline with different regularization in Table 1. It can be observed that our proposed adaptive dropout significantly outperforms the baseline and comparison methods across all degradation settings in all datasets. Based on the experimental results, we can draw the following conclusions: (1) Both Implicit Adaptive Dropout and Explicit Adaptive Dropout can bring more performance increase compared with Dropout [29], for both of these variants explicitly regularize features at intermediate layers, encouraging models to learn more general features representations. (2) Explicit Adaptive Dropout generally outperforms Implicit Adaptive Dropout, considering that Implicit Adaptive Dropout focuses more on maintaining the model's fitting ability. We show the comparison results on RealSR-ResNet [30] and SwinIR [34] in Figure 6.
+
+![](images/ae0b3a2e555511bd5671585a1845b89f3fa314d50215948aa4073bd056007533.jpg)  
+Figure 6. Comparison with other regularization methods [29, 56].
+
+![](images/3259fa57874df1ba588872d0aa4db3522bfbd041a853bda13c728d9ec5ecfbdc.jpg)
+
+![](images/89459d860335babf3de17727cf2115dbf7265e377ae2f78eb0dfdffaa98ff281.jpg)
+
+![](images/93a23cba36da2499d7bd251bbaac3217906ad5d311398f0a0c11e11297fb5760.jpg)
+
+Table 1. The PSNR (dB) results of models with  $\times 4$ . We test them on eight types of degradations or multi-degradations (b is blur, n is noise, j is jpeg). Red and Blue indicate the best and the second-best performance, respectively.  
+
+<table><tr><td rowspan="2">Models</td><td rowspan="2">Regularization</td><td colspan="2">Set5 [4]</td><td colspan="2">Set14 [63]</td><td colspan="2">BSD100 [41]</td><td colspan="2">Manga109 [42]</td><td colspan="2">Urban100 [17]</td></tr><tr><td>clean</td><td>blur</td><td>clean</td><td>blur</td><td>clean</td><td>blur</td><td>clean</td><td>blur</td><td>clean</td><td>blur</td></tr><tr><td rowspan="4">SRResNet [30]</td><td>None</td><td>24.89</td><td>24.76</td><td>22.60</td><td>22.50</td><td>23.06</td><td>22.99</td><td>18.42</td><td>18.75</td><td>21.24</td><td>21.06</td></tr><tr><td>Dropout [29]</td><td>25.67</td><td>25.34</td><td>23.11</td><td>22.92</td><td>23.37</td><td>23.24</td><td>18.87</td><td>19.14</td><td>21.58</td><td>21.31</td></tr><tr><td>Explicit Adaptive Dropout</td><td>26.11</td><td>25.39</td><td>23.42</td><td>23.20</td><td>23.76</td><td>23.59</td><td>19.40</td><td>19.62</td><td>21.87</td><td>21.48</td></tr><tr><td>Implicit Adaptive Dropout</td><td>26.09</td><td>25.56</td><td>23.47</td><td>23.21</td><td>23.73</td><td>23.50</td><td>19.51</td><td>19.69</td><td>21.90</td><td>21.40</td></tr><tr><td rowspan="4">SwinIR [34]</td><td>None</td><td>26.25</td><td>26.03</td><td>23.76</td><td>23.47</td><td>23.91</td><td>23.83</td><td>19.10</td><td>19.19</td><td>22.18</td><td>21.90</td></tr><tr><td>Dropout [29]</td><td>26.32</td><td>26.08</td><td>23.80</td><td>23.36</td><td>23.90</td><td>23.87</td><td>19.15</td><td>19.30</td><td>22.27</td><td>21.99</td></tr><tr><td>Explicit Adaptive Dropout</td><td>26.54</td><td>26.21</td><td>23.92</td><td>23.56</td><td>24.09</td><td>23.59</td><td>19.22</td><td>19.39</td><td>22.41</td><td>22.19</td></tr><tr><td>Implicit Adaptive Dropout</td><td>26.46</td><td>26.12</td><td>23.95</td><td>23.41</td><td>24.01</td><td>23.50</td><td>19.31</td><td>19.44</td><td>22.32</td><td>22.16</td></tr><tr><td></td><td></td><td>noise</td><td>jpeg</td><td>noise</td><td>jpeg</td><td>noise</td><td>jpeg</td><td>noise</td><td>jpeg</td><td>noise</td><td>jpeg</td></tr><tr><td rowspan="4">SRResNet [30]</td><td>None</td><td>22.02</td><td>23.72</td><td>20.81</td><td>21.84</td><td>20.34</td><td>22.48</td><td>19.74</td><td>18.30</td><td>19.73</td><td>20.60</td></tr><tr><td>Dropout [29]</td><td>21.87</td><td>24.04</td><td>20.61</td><td>22.16</td><td>21.00</td><td>22.70</td><td>18.25</td><td>18.62</td><td>19.58</td><td>20.89</td></tr><tr><td>Explicit Adaptive Dropout</td><td>22.41</td><td>24.38</td><td>21.14</td><td>22.46</td><td>21.48</td><td>23.00</td><td>18.67</td><td>19.07</td><td>19.90</td><td>21.11</td></tr><tr><td>Implicit Adaptive Dropout</td><td>22.41</td><td>24.36</td><td>21.15</td><td>22.51</td><td>21.53</td><td>23.00</td><td>18.76</td><td>19.20</td><td>19.90</td><td>21.15</td></tr><tr><td rowspan="4">SwinIR [34]</td><td>None</td><td>22.96</td><td>24.37</td><td>21.56</td><td>23.04</td><td>22.12</td><td>23.04</td><td>18.71</td><td>18.95</td><td>20.56</td><td>21.32</td></tr><tr><td>Dropout [29]</td><td>23.12</td><td>24.41</td><td>21.59</td><td>23.09</td><td>22.10</td><td>23.08</td><td>18.73</td><td>19.03</td><td>20.67</td><td>21.38</td></tr><tr><td>Explicit Adaptive Dropout</td><td>23.63</td><td>24.68</td><td>21.67</td><td>23.29</td><td>22.24</td><td>23.29</td><td>18.92</td><td>19.27</td><td>20.85</td><td>21.52</td></tr><tr><td>Implicit Adaptive Dropout</td><td>23.49</td><td>24.49</td><td>21.69</td><td>23.19</td><td>22.19</td><td>23.28</td><td>19.02</td><td>19.31</td><td>20.74</td><td>21.40</td></tr><tr><td></td><td></td><td>b+n</td><td>b+j</td><td>b+n</td><td>b+j</td><td>b+n</td><td>b+j</td><td>b+n</td><td>b+j</td><td>b+n</td><td>b+j</td></tr><tr><td rowspan="4">SRResNet [30]</td><td>None</td><td>23.31</td><td>23.44</td><td>21.81</td><td>21.70</td><td>22.27</td><td>22.34</td><td>18.60</td><td>18.53</td><td>20.46</td><td>20.30</td></tr><tr><td>Dropout [29]</td><td>23.51</td><td>23.67</td><td>21.87</td><td>22.01</td><td>22.24</td><td>22.54</td><td>18.94</td><td>18.81</td><td>20.48</td><td>20.53</td></tr><tr><td>Explicit Adaptive Dropout</td><td>23.74</td><td>23.80</td><td>22.15</td><td>22.29</td><td>22.48</td><td>22.81</td><td>19.26</td><td>19.23</td><td>20.57</td><td>20.66</td></tr><tr><td>Implicit Adaptive Dropout</td><td>23.65</td><td>23.73</td><td>22.12</td><td>22.29</td><td>22.44</td><td>22.78</td><td>19.51</td><td>19.29</td><td>20.50</td><td>20.63</td></tr><tr><td rowspan="4">SwinIR [34]</td><td>None</td><td>23.80</td><td>23.84</td><td>22.20</td><td>22.26</td><td>22.61</td><td>22.82</td><td>19.07</td><td>19.02</td><td>20.89</td><td>20.79</td></tr><tr><td>Dropout [29]</td><td>24.00</td><td>23.93</td><td>22.40</td><td>22.24</td><td>22.68</td><td>22.80</td><td>19.12</td><td>18.98</td><td>20.92</td><td>20.91</td></tr><tr><td>Explicit Adaptive Dropout</td><td>24.24</td><td>24.27</td><td>22.91</td><td>22.41</td><td>22.81</td><td>23.05</td><td>19.25</td><td>19.29</td><td>21.00</td><td>20.96</td></tr><tr><td>Implicit Adaptive Dropout</td><td>24.18</td><td>24.30</td><td>22.78</td><td>22.36</td><td>22.80</td><td>23.05</td><td>19.31</td><td>19.37</td><td>20.92</td><td>20.94</td></tr><tr><td></td><td></td><td>n+j</td><td>b+n+j</td><td>n+j</td><td>b+n+j</td><td>n+j</td><td>b+n+j</td><td>n+j</td><td>b+n+j</td><td>n+j</td><td>b+n+j</td></tr><tr><td rowspan="4">SRResNet [30]</td><td>None</td><td>23.21</td><td>22.70</td><td>21.59</td><td>21.44</td><td>22.24</td><td>22.05</td><td>18.25</td><td>18.43</td><td>20.42</td><td>20.10</td></tr><tr><td>Dropout [29]</td><td>23.55</td><td>22.99</td><td>21.86</td><td>21.64</td><td>22.39</td><td>22.17</td><td>18.57</td><td>18.71</td><td>20.64</td><td>20.23</td></tr><tr><td>Explicit Adaptive Dropout</td><td>23.71</td><td>23.10</td><td>22.09</td><td>21.84</td><td>22.59</td><td>22.31</td><td>18.95</td><td>19.04</td><td>20.79</td><td>20.29</td></tr><tr><td>Implicit Adaptive Dropout</td><td>23.74</td><td>23.10</td><td>22.13</td><td>21.84</td><td>22.60</td><td>22.32</td><td>19.07</td><td>19.10</td><td>20.81</td><td>20.27</td></tr><tr><td rowspan="4">SwinIR [34]</td><td>None</td><td>23.67</td><td>22.99</td><td>22.11</td><td>21.82</td><td>22.61</td><td>22.34</td><td>18.79</td><td>18.80</td><td>20.98</td><td>20.45</td></tr><tr><td>Dropout [29]</td><td>23.65</td><td>23.09</td><td>22.17</td><td>21.84</td><td>22.64</td><td>22.33</td><td>18.75</td><td>18.84</td><td>21.12</td><td>20.55</td></tr><tr><td>Explicit Adaptive Dropout</td><td>23.82</td><td>23.18</td><td>22.30</td><td>22.19</td><td>22.78</td><td>22.50</td><td>18.82</td><td>18.91</td><td>21.15</td><td>20.57</td></tr><tr><td>Implicit Adaptive Dropout</td><td>23.76</td><td>23.13</td><td>22.23</td><td>22.19</td><td>22.57</td><td>22.39</td><td>18.87</td><td>19.10</td><td>21.02</td><td>20.56</td></tr></table>
+
+Comparison with Simple-Align. The comparison results between our method and Simple-Align [56] are also shown in Figure 6. Our proposed method outperforms SimpleAlign [56] on all synthetic datasets, with notable improvements on the more complex datasets Manga109 and Urban100, showing better generalization ability on complex scenarios. The detailed data is in supplementary material.
+
+To further demonstrate the effectiveness of our method, we compare it with previous methods on real-world datasets, for low-resolution images collected from the real
+
+world are far more challenging to reconstruct than synthetic low-resolution images. RealSR [6] and DRealSR [58] are the latest two paired datasets for real-world superresolution, and we show the comparison results of these two datasets in Figure 7 and Table 2. We also conduct tests on the realistic NTIRE 2018 SR challenge data [54], and the results are presented in Table 2. Our method outperforms Simple-Align [56] on all five real-world datasets.
+
+Applications in single-degradation task. Adaptive Dropout also works well for generalization tasks of single
+
+Table 2. Comparison with Simple-Align [56] on synthetic datasets and real-world datasets.  
+
+<table><tr><td rowspan="2">Models+Regularization</td><td colspan="5">Synthetic dataset</td><td colspan="5">Real-world dataset</td></tr><tr><td>Set5</td><td>Set14</td><td>BSD100</td><td>Manga109</td><td>Urban100</td><td>RealSR</td><td>DRealSR</td><td>mild</td><td>difficult</td><td>wild</td></tr><tr><td>SRResNet+Simple-Align [56]</td><td>24.05</td><td>22.31</td><td>22.70</td><td>19.11</td><td>20.80</td><td>24.63</td><td>27.14</td><td>17.19</td><td>18.05</td><td>17.81</td></tr><tr><td>SRResNet+Explicit Adaptive Dropout</td><td>24.10</td><td>22.34</td><td>22.73</td><td>19.15</td><td>20.81</td><td>25.07</td><td>27.51</td><td>17.29</td><td>18.18</td><td>17.91</td></tr><tr><td>SRResNet+Implicit Adaptive Dropout</td><td>24.05</td><td>22.32</td><td>22.75</td><td>19.24</td><td>20.84</td><td>25.16</td><td>27.51</td><td>17.32</td><td>18.18</td><td>17.92</td></tr><tr><td>RRDB+Simple-Align [56]</td><td>24.33</td><td>22.51</td><td>22.90</td><td>19.14</td><td>21.05</td><td>24.76</td><td>27.00</td><td>17.14</td><td>18.08</td><td>17.81</td></tr><tr><td>RRDB+Explicit Adaptive Dropout</td><td>24.40</td><td>22.56</td><td>22.97</td><td>19.27</td><td>21.00</td><td>25.39</td><td>27.46</td><td>17.62</td><td>18.33</td><td>18.04</td></tr><tr><td>RRDB+Implicit Adaptive Dropout</td><td>24.38</td><td>22.61</td><td>22.91</td><td>19.30</td><td>20.96</td><td>25.35</td><td>27.53</td><td>17.27</td><td>18.20</td><td>17.90</td></tr></table>
+
+![](images/98699aecd315a7fbf258c628a5241393d8c1dcb04f862d5003e76e75a9de6792.jpg)  
+Figure 7. Comparison with Simple-Align [56] on real-world datasets.
+
+degradation scenarios. We adopt our proposed methods on image denoising, image draining, and image dehazing. For image deraining, we train RCDNet [55] and Restormer [67] on Rain100L [26] and test them on Rain100H [26]. For image denoising, we follow Chen et al. [8], and train SwinIR on Gaussian noise. For image dehazing, we train FFANet [50] on ITS Dataset [31] and test it on OTS Dataset [31]. Results in Figure 3 illustrate that our methods help models generalize better on unseen degradation.
+
+Applications in generative models. We show the results on generative IR in Tab. 4, where our methods work well on both GAN-based and diffusion-based blind SR models.
+
+Table 3. The performance of the model in single degradation tasks when augmented with explicit adaptive dropout.  
+
+<table><tr><td>task</td><td colspan="2">models</td><td>PSNR</td><td>SSIM</td></tr><tr><td rowspan="4">derain</td><td rowspan="2">RCDNet</td><td>None</td><td>17.36</td><td>0.554</td></tr><tr><td>w/ ours</td><td>17.59</td><td>0.565</td></tr><tr><td rowspan="2">Restormer</td><td>None</td><td>29.46</td><td>0.887</td></tr><tr><td>w/ ours</td><td>29.79</td><td>0.898</td></tr><tr><td rowspan="2">dehaze</td><td rowspan="2">FFANet</td><td>None</td><td>20.26</td><td>0.881</td></tr><tr><td>w/ ours</td><td>21.09</td><td>0.883</td></tr><tr><td rowspan="2">denoise</td><td rowspan="2">SwinIR</td><td>None</td><td>26.14</td><td>0.665</td></tr><tr><td>w/ ours</td><td>26.40</td><td>0.681</td></tr></table>
+
+Ablation study. We conduct ablation study on different components of Adaptive Dropout as shown in Table 5. It can be observed that both the adaptive dropout format and the adaptive training strategy contribute to improving the
+
+Table 4. Generative IR with our methods  
+
+<table><tr><td>model</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>MANIQA↑</td></tr><tr><td>ResShift [66]</td><td>22.55</td><td>0.6732</td><td>0.40</td><td>0.2906</td></tr><tr><td>ResShift+ours</td><td>22.69</td><td>0.6754</td><td>0.38</td><td>0.3211</td></tr><tr><td>RealEsgan [57]</td><td>23.19</td><td>0.6812</td><td>0.31</td><td>0.2549</td></tr><tr><td>RealEsgan+ours</td><td>23.64</td><td>0.6881</td><td>0.24</td><td>0.2560</td></tr></table>
+
+Table 5. Ablation Study. The left table demonstrates the effectiveness of our method's components. The right table indicates the optimal hyperparameters for Implicit Adaptive Dropout.  
+
+<table><tr><td>dropout</td><td>strategy</td><td>PSNR</td><td>w</td><td>SRResNet</td><td>RRDB</td></tr><tr><td>None</td><td>X</td><td>25.66</td><td>0.5</td><td>25.83</td><td>26.09</td></tr><tr><td>standard</td><td>X</td><td>24.33</td><td>0.6</td><td>25.94</td><td>26.22</td></tr><tr><td>standard</td><td>✓</td><td>24.89</td><td>0.7</td><td>26.07</td><td>26.43</td></tr><tr><td>adaptive</td><td>X</td><td>25.89</td><td>0.8</td><td>26.00</td><td>26.59</td></tr><tr><td>adaptive</td><td>✓</td><td>26.07</td><td>0.9</td><td>25.86</td><td>26.50</td></tr></table>
+
+![](images/b5b5f9c91804bf35df8886452fe146cbf0c5b01e5459131eb146bfce2601594b.jpg)  
+Figure 8. Quantitative generalization performance compared with other regularization methods.
+
+![](images/71a8f1626a4512a727fdece4541d01d4ad423c78025b6953841762ddf1eacb60.jpg)
+
+model's generalization capability. Moreover, we select the optimal  $w$  for Implicit Adaptive Dropout. More results of ablation study will be presented in supplementary materials. Quantitative analysis of generalization performance. To further compare generalization performance, we use SRGA [39], the first generalization performance metric in the low-level domain, to demonstrate the effectiveness of our proposed method. We show the SRGA under different levels of degradation in Figure 8, where a lower SRGA indicates better generalization performance. Our proposed method achieves lower SRGA on most degradations.
+
+# 6. Conclusion
+
+In this work, we first focus on the need for explicit regularization of intermediate layers in BSR networks to enhance generalization performance, and specifically analyze why dropout cannot be directly applied to intermediate layers. Subsequently, we propose Adaptive Dropout, a regularization method that can be applied anywhere in the network, further improving the network's generalization performance. We hope that this research will draw more attention to the training strategies for SR tasks.
+
+# 7. Acknowledgement
+
+This work was supported by the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC.
+
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+# Adaptive Keyframe Sampling for Long Video Understanding
+
+Xi Tang $^{1*}$ , Jihao Qiu $^{1*}$ , Lingxi Xie, Yunjie Tian $^{2}$ , Jianbin Jiao $^{1}$ , Qixiang Ye $^{1}$ $^{1}$ University of Chinese Academy of Sciences  
+ $^{2}$ University at Buffalo, SUNY
+
+{tangxi19,qiujihao19}@mails.ucas.ac.cn {jiaojb,qxye}@ucas.ac.cn
+
+# Abstract
+
+Multimodal large language models (MLLMs) have enabled open-world visual understanding by injecting visual input as extra tokens into large language models (LLMs) as contexts. However, when the visual input changes from a single image to a long video, the above paradigm encounters difficulty because the vast amount of video tokens has significantly exceeded the maximal capacity of MLLMs. Therefore, existing video-based MLLMs are mostly established upon sampling a small portion of tokens from input data, which can cause key information to be lost and thus produce incorrect answers. This paper presents a simple yet effective algorithm named Adaptive Keyframe Sampling (AKS). It inserts a plug-and-play module known as keyframe selection, which aims to maximize the useful information with a fixed number of video tokens. We formulate keyframe selection as an optimization involving (1) the relevance between the keyframes and the prompt, and (2) the coverage of the keyframes over the video, and present an adaptive algorithm to approximate the best solution. Experiments on two long video understanding benchmarks validate that AKS improves video QA accuracy (beyond strong baselines) upon selecting informative keyframes. Our study reveals the importance of information pre-filtering in video-based MLLMs. Our codes are available at https://github.com/ncTimTang/AKS
+
+# 1. Introduction
+
+"You can't manage what you can't measure."
+
+Peter Drucker
+
+Recent years have witnessed a rapid development of multimodal large language models (MLLMs) [14, 22, 41, 60] for open-world visual understanding. Among the large corpus of research in MLLMs, a straightforward and important direction is to generalize them to video data. Compared to still images, videos contain richer and more complex visual
+
+![](images/7b0128813733e98617432ed8d189c6c8bb349bb92222f3d35a23366c8e297fce.jpg)  
+Figure 1. The accuracy of video-based MLLMs heavily relies on the quality of keyframes. The above example shows a long video from VideoMME [9] where keyframes are marked with green stars. The same MLLM (i.e., LLaVA-Video [62]) is used for answering the question. Uniform sampling (the default setting in [62]) finds irrelevant frames (the MLLM mostly performs a random guess), while our algorithm (AKS) finds keyframes and produces the correct answer.
+
+content, thus raising serious challenges to MLLMs including key information retrieval, summarization, logical inference, etc. Many benchmarks [9, 48] have been established to evaluate MLLMs for video understanding.
+
+A typical framework of image-based MLLMs involves encoding the input image into a set of visual tokens and feeding them as the context of LLMs. When this framework was transplanted to videos, especially long videos, a difficulty arose from the limited capacity of MLLMs, i.e., the maximal number of visual tokens that MLLMs can process is much fewer than that of an entire video; in other words, not all video tokens can be perceived by MLLMs. To bridge the gap, recent approaches [20, 49] often sam
+
+pled a small portion of frames from the input video; consequently, the performance of these MLLMs heavily relies on the quality of selected frames (i.e., keyframes). Despite its importance, the keyframe selection algorithm has not been carefully designed, e.g., LLaVA-Video [62] simply applied a uniform sampling strategy which, as shown in Figure 1, is prone to losing important information and thus leads to incorrect outputs of video understanding.
+
+This paper presents a systematic study on keyframe selection and reveals its importance to video understanding and beyond. We formulate keyframe selection as a plug-and-play module before the MLLM's visual encoder; its goal is to maximize the usefulness of the keyframes in video understanding. Intuitively, we propose two key aspects to be considered, namely, (1) relevance (i.e., how the keyframes are related to the question) and (2) coverage (i.e., how the keyframe set covers the useful information in the entire video). Specifically, we quantify the target by (1) computing relevance between each candidate frame and the prompt using a vision-language (VL) model, and (2) estimating coverage by recursively partitioning the video into bins and counting the number of keyframes within each bin. We show that maximizing relevance and coverage alone produces simple baselines for keyframe selection, while a proper tradeoff between them, obtained by the proposed Adaptive Keyframe Sampling (AKS) algorithm, leads to the best practice of video understanding.
+
+We evaluate our approach on LongVideoBench [48] and VideoMME [9], two benchmarks for long video understanding. We investigate three frame-based MLLMs (Qwen2VL [43], LLaVA-OV [15], and LLaVA-Video [62]) as the baseline and insert AKS as an off-the-shelf module to improve the quality of keyframes. Our approach achieves consistent accuracy gain throughout all tests. Specifically, when AKS is integrated with LLaVA-Video-7B, we set new records on these two benchmarks with 7B models. We further validate that the improvement owes to higher-quality keyframes found by AKS, demonstrating that MLLMs become stronger with more informative visual contexts. Our study reveals that pre-filtering visual data is crucial and will be a long-lasting research topic for MLLMs in perceiving high-dimensional data, e.g., long videos, and even 4D data.
+
+# 2. Related Work
+
+Large language models (LLMs) and multimodal LLMs (MLLMs). LLMs [2-5, 7, 38, 42, 54, 59] have marked a new era in AI, showcasing significant potential in unifying various tasks covering language understanding and generation. To extend LLMs for visual understanding, the community has focused on aligning visual and language data within a unified feature space [32]. There are generally two types of approaches, (1) internal adaptation, such as [1], that integrates cross-attention mechanisms within LLMs to
+
+achieve vision-language alignment, and (2) external adaptation, such as [6, 17, 22], that trains additional modules for the same purpose. Consequently, vision foundation models [8, 13, 24, 32, 39, 40, 61] have evolved into multimodal LLMs (MLLMs) [14, 22, 41, 60], enabling them to perform language-guided visual understanding tasks.
+
+Video-based MLLMs. Researchers have extended MLLMs to video understanding. Early efforts in this area include VideoChat [18], Video-ChatGPT [26], VideoLLaMA [56], Video-LLaVA [20], LanguageBind [63], and Valley [25], etc. Different from still images, videos contain rich content that, when encoded as visual tokens, exceed the maximal context capacity of MLLMs. Most of the above methods have sampled video frames to fit MLLMs; some of them, such as Video-ChatGPT [26], introduced more efficient video features. There are also studies on instance-level video understanding have been proposed, such as LEGO [19] for moment retrieval, PG-Video-LLaVA [27] for video grounding, and Artemis [31] for video referring, enriching the corpus of video understanding.
+
+MLLMs for Long Video Understanding. Going one step further, long video understanding faces greater challenges due to the increased difficulty of keyframe selection, leading to significant loss of critical information. While some MLLMs (e.g., Kangaroo [23], LLaVA-Video [62], LongVILA [50] and LongVA [58]) extend the context length of language model to allow more frames to be encoded and processed, many others have designed specific strategies to mitigate this issue.
+
+For example, MovieChat [36] employed both short-term and long-term memory banks to compress and preserve video content. Similarly, MA-LMM [11] and VideoStreaming [30] used a Q-former and a small language model (phi2 [12]), to condense video data, while LongVLM [47] and CrossGET [35] adopted token merging, VCWE [46] adopted token pooling and LongVU [34] adopted token compression to decrease the number of video tokens. These approaches aim to reduce the number of video tokens, but there is often no guarantee that key information in the video can be preserved. To identify the key information, Seeling [10] picked the most dominant frames, while ignoring the relevance to the prompt. VideoAgent [44] and VideoTree [45] opted to select keyframes solely using language (from the LLMs), which can miss important visual cues. This work presents a simple yet effective algorithm that maximally preserves important information for long video understanding.
+
+# 3. Method
+
+# 3.1. Preliminaries
+
+Within a broad range of video understanding tasks, the model receives a video clip and a text instruction as input
+
+![](images/8d5529a56867ed5f020a73dc05b5cf9ff46053041f432e0b07f46ba87b2e6434.jpg)  
+Figure 2. The overall framework of our approach. We insert a plug-and-play module, Adaptive Keyframe Sampling (AKS, marked in green frames) into the MLLM to improve the quality of sampled keyframes. Each red dot indicates a prompt-frame matching score (i.e.,  $r(\mathbf{Q}, \mathbf{F}_t)$ , see Section 3.2). AKS follows a recursive, judge-and-split optimization for keyframe selection (see Section 3.3).
+
+and is required to output a text answer. Without loss of generality, we denote the video as  $\mathbf{V} \in \mathbb{R}^{T \times W \times H \times C}$ , where  $T$  is the number of frames and  $W, H, \text{and } C$  denote the width, height, and number of channels, respectively. We consider each frame an image  $\mathbf{V}_t$  ( $t \in \{1, 2, \dots, T\}$ ) and apply a pre-trained encoder (e.g., the CLIP ViT-L model [32]) to extract a set of visual tokens  $\mathbf{F}_t$  from it. The text instruction (a.k.a., prompt) is denoted as  $\mathbf{Q}$ .
+
+The overall pipeline of our algorithm is illustrated in Figure 2. We use a regular MLLM that addresses video understanding with the template [User: <video-tokens> <text-instruction> Assistant: ], where the video tokens and text instruction are projected into the same feature space using an MLP. For simplicity, we denote the MLLM as a function of  $G(\{\mathbf{F}_t\})$  where we omit the LLM part and only focus on the visual tokens as contexts. With a limited capacity of visual contexts (i.e., the number of video tokens cannot exceed a specific value), the above pipeline encounters difficulty in dealing with long videos where not all video content can be perceived by the MLLM.
+
+A straightforward solution is to select keyframes from the input video for token extraction. In other words, the goal is to design a selection function  $\mathrm{KS}_M(\mathbf{Q},\mathbf{F})$  that outputs an index set,  $\mathcal{I}\subseteq \{1,2,\dots,T\}$  and  $|\mathcal{I}| = M$  , indicating the  $M$  best keyframes (  $M$  is pre-defined according to the context capacity of the MLLM). Video tokens extracted from the keyframes (i.e.,  $\{\mathbf{F}_t\mid t\in \mathrm{KS}_M(\mathbf{Q},\mathbf{F})\}$  compose of the context of the MLLM. As shown in Figure 1, the qual
+
+ity of keyframe selection is crucial for video understanding, but the function  $\mathrm{KS}_M(\mathbf{Q},\mathbf{F})$  has not been well studied in the community. As an example, a recent MLLM for video understanding [62] simply performed uniform sampling for keyframe selection; with the function  $\mathrm{KS}_M(\cdot)$  not using  $\mathbf{Q}$  and  $\mathbf{F}$  at all, it cannot guarantee to find useful information for question answering.
+
+In what follows, we establish two principles of keyframe selection (Section 3.2), after which we will present AKS, our optimization algorithm (Section 3.3).
+
+# 3.2. Principles of Keyframe Selection
+
+The keyframe selection function  $\mathrm{KS}_M(\mathbf{Q},\mathbf{F})$  is to maximize the amount of useful information, i.e.,
+
+$$
+\operatorname {K S} _ {M} (\mathbf {Q}, \mathbf {F}) = \arg \max  _ {| \mathcal {I} | = M} G ^ {\prime} \left(\left\{\mathbf {F} _ {t} \mid t \in \mathcal {I} \right\}\right). \tag {1}
+$$
+
+Here, we assume  $G'(\cdot)$  to be a complementary function of  $G(\cdot)$ , indicating the MLLM's confidence about its output. Eqn (1) is mathematically intractable due to two reasons. First, the optimization involves exponentially many candidates of  $\mathcal{I}$ . Second and more importantly, the function  $G'(\cdot)$  is difficult to estimate because there is no supervision for keyframe selection - even when a training set is available and one can compare the output of  $G(\cdot)$  with the ground-truth answer, it is not guaranteed that a correct answer corresponds to a perfect set of keyframes, and vice versa.
+
+We propose a heuristic method to approximate Eqn (1).
+
+# Q: How many outfits did the male protagonist change in total in the video?
+
+![](images/2c2d3576da6b71771e8c28345863fb3606bb6be4656f9c239dc3d81b6d01fbd5.jpg)  
+A: The male protagonist changed 5 outfitsits in total in the video.  
+Figure 3. An example of adaptive sampling (ADA). 8 keyframes are to be selected from the input video. Each red dot indicates a prompt-frame matching score,  $r(\mathbf{Q}, \mathbf{F}_t)$ . At Level-0 and Level-1, all bins are split into two sub-bins; at Level-2, only the rightmost bin is further partitioned while the top-2 scores are sampled from the other three bins. Level-3 has reached the maximal depth.
+
+Intuitively, a set of keyframes is informative when the following conditions are satisfied. (1) The relevance between each frame and the prompt is high, i.e., the visual data is useful for question answering. (2) The coverage of the selected frames is sufficient to comprehensively answer the question. Note that the coverage is difficult to quantify, and the second principle is closely related to preventing redundant frames (e.g., neighboring frames with almost the same visual content) from being selected, because (when the size of  $|\mathcal{I}|$  is fixed) they can potentially reduce the amount of other useful information and thus harm the coverage of the entire keyframe set.
+
+Following the analysis above, we reformulate the right-hand side of Eqn (1), yielding:
+
+$$
+\mathrm {K S} _ {M} (\mathbf {Q}, \mathbf {F}) = \arg \max  _ {| \mathcal {I} | = M} \sum_ {t \in \mathcal {I}} r (\mathbf {Q}, \mathbf {F} _ {t}) + \lambda \cdot c (\mathcal {I}). \tag {2}
+$$
+
+Here we introduce two quantities,  $r(\mathbf{Q},\mathbf{F}_t)$  as the relationship between the prompt  $\mathbf{Q}$  and the  $t$  -th frame  $\mathbf{F}_t$  ,and  $c(\mathcal{I})$  as the coverage of the entire keyframe set over the time axis.  $\lambda$  is the balancing hyper-parameter.
+
+Computing  $r(\mathbf{Q},\mathbf{F}_t)$ . This involves a vision-language (VL) module to measure whether  $\mathbf{F}_t$  contains information for answering  $\mathbf{Q}$ . Although the target MLLM itself  $G(\cdot)$  can play the role, its high computational cost can bring a major burden. In practice, we choose a cheaper VL model (e.g., CLIP [32] or BLIP ITM [16]) for replacement.
+
+Estimating  $c(\mathcal{I})$ . Measuring coverage is an open problem which is related to the homogeneity of data distribution. In
+
+mathematics, Ripley's  $K$ -function [33] is a popular way to measure homogeneity. Given the timestamp set  $\mathcal{I}$  and any search radius  $r < T$ , the  $K$ -function of  $r$ , denoted as  $\hat{K}(r)$ , is proportional to the number of  $(t_i, t_j)$  pairs satisfying  $|t_i - t_j| < r$ . The distribution of  $\mathcal{I}$  is considered homogeneous (i.e., covering the entire time axis) if  $\hat{K}(r)$  is approximately proportional to  $r^2$ .
+
+To adapt  $K$ -function to computing coverage (closely related but a bit different from homogeneity) as well as reducing computational overhead, we introduce bins with width  $r$  and approximate  $\mathbb{I}(|t_i - t_j| < r)$  as whether  $t_i$  and  $t_j$  fall into the same bin. We perform a recursive partition. At the first level, we set 2 bins with the bin width being  $T/2$ , i.e., the time axis  $[0, T)$  is partitioned into 2 non-overlapping bins,  $[0, T/2)$  and  $[T/2, T)$ . With the numbers of keyframes falling within these bins being  $m_1$  and  $m_2$ ,  $c(\mathcal{I})$  adds a penalty term  $|m_1 - m_2|$  since an uneven distribution implies weak coverage in the bin with fewer keyframes. At the second level, each of  $[0, T/2)$  and  $[T/2, T)$  is further partitioned into two bins, and the same calculation continues. The recursion stops at the  $L$ -th level, where  $L \leqslant \lceil \log_2 M \rceil$  is a hyper-parameter.
+
+# 3.3. Adaptive Keyframe Sampling
+
+With the complex definition of  $c(\mathcal{I})$ , it is difficult to find a closed-form or accurate optimization for Eqn (2). This part discusses an approximation. Compared to the baseline that only relies on  $r(\mathbf{Q}, \mathbf{F}_t)$  scores, we name such methods timestamp-aware optimization for its ability to consider
+
+timesteps for better keyframe selection results.
+
+We first discuss two special cases. (1) When  $\lambda = 0$  (i.e., coverage is neglected), Eqn (2) is solved by simply selecting the top-  $M$  frames of the largest scores. We name this strategy TOP, short for 'top sampling'; as shown in Figure 5, in some cases, it results in all keyframes being located within a small range of time and the MLLM missing important information in other moments. (2) When  $\lambda \rightarrow +\infty$  (i.e., coverage is strictly guaranteed), Eqn (2) is solved by selecting the frame within the highest score in each bin as the keyframe (when the number of bins exceeds  $M$ , the champion frames with the highest scores are preserved). We name this strategy BIN, short for 'binned sampling'. This situation further degenerates to the uniform sampling baseline [62] if a dummy VL model is used for scoring (i.e.,  $r(\mathbf{Q},\mathbf{F}_t)$  is a constant over  $t$ ). We name this strategy UNI, short for 'uniform sampling'.
+
+In other cases  $(0 < \lambda \ll +\infty)$ , we adopt a hierarchical optimization method that follows the definition of  $c(\mathcal{I})$ . At the first level, we determine how to allocate  $M$  keyframes into two bins,  $[0,T / 2)$  and  $[T / 2,T)$ . We recall the relevance scores of all frames,  $r(\mathbf{Q},\mathbf{F}_t)$ , and compute the average scores over all frames (denoted as  $s_{\mathrm{all}}$ ) and over  $M$  frames with the highest scores (denoted as  $s_{\mathrm{top}}$ ). If there is only one keyframe to be selected, or  $s_{\mathrm{top}} - s_{\mathrm{all}}$  surpasses a threshold,  $s_{\mathrm{thr}}$ , we believe that it is important to guarantee the top-scored frames to be sampled (i.e., maximizing the first term of Eqn (2)), so the algorithm directly returns the top- $M$  frames as keyframes. Otherwise, we split the current bin into two sub-bins with the number of keyframes evenly allocated (i.e., maximizing the second term of Eqn (2)), and then recursively call the above programs in the sub-bins. We name this strategy ADA, short for 'adaptive sampling'. Note that the hyper-parameter  $\lambda$  is not explicitly tuned; its role is replaced by  $s_{\mathrm{thr}}$ .
+
+Figure 3 uses an example to show how adaptive sampling (ADA) works. ADA is a compromise between the special cases, TOP and BIN. As we shall see in experiments (see Section 4.4), ADA absorbs the advantages of TOP and BIN and achieves the best practice of video understanding.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup and Details
+
+Dataset and evaluation. We utilize the popular LMMsEval [57] to evaluate the performance of AKS. We use two popular benchmarks LongVideoBench [48], and VideoMME [9], for long video understanding. The length of videos in this dataset can exceed one hour, so the quality of keyframe selection plays a crucial role in visual understanding. We establish AKS beyond three recent video-based MLLMs (see the next paragraph). We do not tune the parameters of these MLLMs, but only change the input
+
+Table 1. Video-based question answering accuracy  $(\%)$  of different approaches on LongVideoBench (LVB) val and VideoMME (V-MME). AKS is applied upon three baseline approaches. Frames and LLM indicate the number of video frames fed into the MLLM and the number of parameters in the LLM part, respectively.  
+
+<table><tr><td>Method</td><td>Frames</td><td>LLM</td><td>LVB val</td><td>V-MME</td></tr><tr><td>GPT-4V [28]</td><td>256</td><td>-</td><td>61.3</td><td>59.9</td></tr><tr><td>GPT-4o [29]</td><td>256</td><td>-</td><td>66.7</td><td>71.9</td></tr><tr><td>Gemini-1.5-Flash [37]</td><td>256</td><td>-</td><td>61.6</td><td>70.3</td></tr><tr><td>Gemini-1.5-Pro [37]</td><td>256</td><td>-</td><td>64.0</td><td>75.0</td></tr><tr><td>VideoLLaVA [20]</td><td>8</td><td>7B</td><td>39.1</td><td>39.9</td></tr><tr><td>MiniCPM-V 2.6 [52]</td><td>64</td><td>8B</td><td>54.9</td><td>60.9</td></tr><tr><td>PLLaVA [49]</td><td>32</td><td>34B</td><td>53.2</td><td>-</td></tr><tr><td>VILA [21]</td><td>-</td><td>40B</td><td>-</td><td>60.1</td></tr><tr><td>Qwen2-VL [43]</td><td>32</td><td>7B</td><td>55.5</td><td>57.6</td></tr><tr><td>Qwen2-VL w/ AKS</td><td>32</td><td>7B</td><td>60.5</td><td>59.9</td></tr><tr><td>LLaVA-OV [15]</td><td>32</td><td>7B</td><td>54.8</td><td>56.5</td></tr><tr><td>LLaVA-OV w/ AKS</td><td>32</td><td>7B</td><td>59.3</td><td>58.4</td></tr><tr><td>LLaVA-Video [62]</td><td>64</td><td>7B</td><td>58.9</td><td>64.4</td></tr><tr><td>LLaVA-Video w/ AKS</td><td>64</td><td>7B</td><td>62.7</td><td>65.3</td></tr></table>
+
+frames into those selected by AKS. To highlight the importance of keyframe selection, we do not use video subtitles to assist question answering. This setting also allows us to weaken the impact of the LLM's strength and maximally focus on visual understanding.
+
+Implementation details. We investigate three video-based MLLMs as our baseline, namely, Qwen2VL [43], LLaVA-OV [15], and LLaVA-Video [62]. LongVideoBench and VideoMME contain multi-choice questions; to answer these questions, these MLLMs followed a similar prompt involving the question (in text), video frames (as tokens), and options (in text). Specifically, as the strongest baseline, LLaVA-Video used SigLIP [55] as its vision encoder and Qwen2-7B [51] as its large language model. With capacities to process up to 32 or 64 video frames, these MLLMs offer basic abilities of video understanding, but they were built upon uniformly sampled keyframes and can miss important information.
+
+To reduce computational costs, we sample the candidate frames from the raw video at 1 frame per second. The prompt (in text) and each  $t$ -th frame (as image) are fed into the text and visual encoders of BLIP [16] to obtain  $\mathbf{Q}$  and  $\mathbf{F}_t$ , after which  $r(\mathbf{Q},\mathbf{F}_t)$  is computed via image-text matching (ITM), i.e., the similarity between  $\mathbf{Q}$  and  $\mathbf{F}_t$ . One can also replace BLIP with other vision-language models (e.g., CLIP [32]); see the ablation in Section 4.4. We use ADA sampling unless otherwise specified.
+
+# 4.2. Comparison to the State-of-the-Art
+
+Quantitative results. We first compare the accuracy of video question answering between our approach and
+
+![](images/87e4ef58bbfc2be99d17857885577043862133052b3de7299c251acbc264695a.jpg)  
+Q: After entering the museum, where did the short-haired woman in a black coat, black long skirt, and black mask visit first?  
+Qwen2-VL-7B  
+Qwen2-VL-7B w/AKS  
+A: Bronze statues.  
+A: Sculptures.
+
+![](images/da0cc0fabf0a0f32973553314f4dee641f3879c98f2c8e82b0dc9db65aa42c7b.jpg)  
+Qwen2-VL-7B w/ AKS
+
+![](images/b0233adb69d5bf98d7c72448d0323f782ab0bbd0f8219dbd2597797d62c12294.jpg)  
+Q: How long does it take to drive from the Earth to the Moon according to the video?  
+Qwen2-VL-7B  
+A:19 days.  
+A:160 days.
+
+![](images/973ac8bd228aa8ea1ec8bb920eec799dc3db3075897605f76009591dad87c5db.jpg)
+
+![](images/344de7c6d13ddf4701370f3b6d93141070f0e01f8907f506eb3c4e63720d09f9.jpg)  
+Q: A white-lettered title says 'How much data do we need?' The word 'dog' appears on the far right. When the image of a shaking dog appears, what changes occur in the black scene?  
+LLaVA-OV-7B  
+LLaVA-OV-7B w/ AKS
+
+![](images/a009ce9c874a76eef82aa2e584cdbc0cc97a44d5f67f30adb729ffa829710fde.jpg)  
+A: The image of the shaking dog gradually enlarges.  
+A: The arrow on the right  
+side is labeled 'not dog'  
+LLaVA-OV-7B w/ AKS
+
+![](images/86a1f88c69c31d508a8d6c71384e6869360029c7ea3cf9153cdc0450b530ce92.jpg)  
+Q: What are the moves in the last scene of this dance?  
+LLaVA-OV-7B  
+A: Passe and then chasse.
+
+![](images/56dc67ee4558b93aae2237af1e89287b962167ca2553ee9f024a0687533fb2dd.jpg)  
+Q: Two men wearing straw hats and grey clothes stand in a grass field holding long knives. What does the house behind them look like?  
+LLaVA-Video-7B  
+LLaVA-Video-7B w/ AKS  
+A:Wooden house.  
+A: Straw hut.
+
+![](images/e595a01ac6da574940c206cf887326c21613639b2f05187be397c741de79407b.jpg)  
+LLaVA-Video-7B w/AKS  
+Figure 4. AKS improves the baseline MLLMs for video understanding. The left three examples come from LongVideoBench while the right three come from VideoMME. Green stars indicate keyframes selected by AKS (note that 64 keyframes are selected for each video).
+
+![](images/0539bd3a383ee61448e5abeee37e13910c46abb3763f696baa7a7113633c0133.jpg)  
+Q: What does the monkey do to the woman?  
+LLaVA-Video-7B  
+A: Climbing on her.  
+A:Pulling her hair.
+
+![](images/92acfbe02502d2e8434992e74d9b4a535a01b54519b03e0230469e32a8c52d69.jpg)  
+A:Kneel down on one  
+knee and lean back.
+
+some recent MLLMs. Results are summarized in Table 1. AKS brings consistent accuracy gain over three baselines, e.g., upon Qwen2VL, the improvement is  $5.0\%$  on LongVideoBench and  $2.3\%$  on VideoMME; even upon LLaVA-Video, the strongest baseline, these numbers are  $3.8\%$  and  $0.9\%$ , respectively. These improvements not only make our method surpass other competitors with a similar computational complexity (i.e., input no more than 64 frames, LLM no larger than 7B), but also allow it to achieve higher levels set by larger models (e.g., with AKS, LLaVA-Video-7B reports  $62.7\%$  on LongVideoBench, which is  $0.8\%$  higher than the LLaVA-Video-72B model without AKS, and  $1.4\%$  and  $1.1\%$  higher than GPT-4V and Gemini1.5-Flash, two proprietary models using 256 input frames). We also compare AKS with other long video understanding methods. Please see the supplementary material for more details.
+
+Qualitative results. In Figure 4, we display representative video understanding results of AKS (based on LLaVA-Video-7B) and others. One can see that the selected keyframes are closely related to the question; this allows the MLLM, with a limited capacity of context, to get a comprehensive view of question-related content and thus obtain the correct answer. As a side comment, we find that VideoMME contains many questions that require a high-level comprehension of the video content in which uniform sampling is a safe choice; nevertheless, AKS still finds more
+
+Table 2. Video-based question answering accuracy (\%) of different sampling strategies. LLaVA-Video-7B with AKS is tested. Please refer to Section 3.3 for the explanations of these abbreviations and Section 4.3 for the analysis of results.
+
+<table><tr><td>Sampling</td><td>LongVideoBench val</td><td>VideoMME</td></tr><tr><td>UNI</td><td>58.9</td><td>64.4</td></tr><tr><td>TOP</td><td>62.4</td><td>63.7</td></tr><tr><td>BIN</td><td>60.2</td><td>65.2</td></tr><tr><td>ADA</td><td>62.7</td><td>65.3</td></tr></table>
+
+informative frames and improves the accuracy, although the gain is smaller than that on LongVideoBench. Please also see the supplementary material for more examples.
+
+# 4.3. Diagnostic on Keyframe Selection
+
+This part aims to diagnose how AKS works and ablates design choices of AKS. We build our test upon the strongest baseline, LLaVA-Video.
+
+MLLMs benefit from better keyframes. To show how keyframe selection impacts video understanding, we test different strategies described in Section 3.3. Table 2 lists the results. Beyond the baseline (i.e., UNI sampling), ADA sampling (our default choice in Section 4.2) achieves the best practice, while each of TOP and BIN samplings is better than the other in one benchmark. Note that the MLLM (i.e., LLaVA-Video-7B) remains unchanged throughout all these tests. In other words, all the improvements owe to
+
+![](images/78e40caa9915e93c0c1b5478203c5f4a3ec5d30d90a6540dcfa2f81fa5dd2a82.jpg)  
+Figure 5. Two examples of how different sampling strategies impact video understanding. The left case comes from LongVideoBench (focusing on one moment) and the right one comes from VideoMME (relying on multiple moments). Each curve shows the  $r(\mathbf{Q}, \mathbf{F}_t)$  score over time, and the yellow circles indicate the position of sampled keyframes. We also annotate the number of true keyframes and the reason for each failure case below the answer.
+
+AKS in selecting higher-quality keyframes.
+
+Visualizing keyframe selection. Figure 5 shows two representative examples and explains how the style of questions varies across LongVideoBench and VideoMME and how it impacts the preference between TOP and BIN. Many questions of LongVideoBench are focused on a simple moment (e.g., 'What is a person doing at a specific time point?'), so TOP sampling (i.e., without constraints in temporal distribution) often works well in locating these keyframes, while BIN sampling limits the number of keyframes within each bin and results in information loss. On the contrary, the questions of VideoMME often require the model to collect information from multiple moments (e.g., 'How many times does something happen?'), so BIN sampling is a safe choice to locate keyframes in different bins, while TOP sampling can lose information in weak peaks. ADA sampling absorbs the advantages of TOP and BIN strategies and adaptively allocates keyframes to the desired position (see the example in Figure 3) – this is why it achieves the best results in both benchmarks.
+
+Figure 6 shows an interesting example that, on the same input video, AKS selects different sets of keyframes based on the prompt. This increases the flexibility that a frozen MLLM can adapt to different scenarios.
+
+# 4.4. Ablative Studies
+
+The frequency of sampling keyframe candidates. To decrease the extra computational cost brought by AKS, we sample fewer keyframe candidates (i.e., one frame per 2/4/8/10 seconds, and compare the results with the standard 1-fps method. Results are summarized in Table 3. On LongVideoBench, even at 0.1 fps, all results are higher
+
+![](images/cbe540af45097accb022ba94b2fae5615df6726177c30327e1fdb2ae83b1ee5c.jpg)  
+Q: How many cubs is the mother bear with when the filmer encounters her downstream of the river?
+
+![](images/691e801bdcb8c520444e6d063ddf7524414b41f98f9c312ebf1457fa32f46d8a.jpg)  
+A: 2 cubs are with the mother bear.
+
+Q: What is the main food of the brown bear in the video?
+
+![](images/105dea74b28bf1cbc53e0cb575a1ba65deeb92fe2b9824763cddcef3cb4bf3a3.jpg)  
+A:Salmon.
+
+Q: Why does the mother brown bear in make her cubs run to higher ground?
+
+![](images/729a92480eacc5d13b8bb7d78c284b0186c620f69ac644db333f40aa43872ec1.jpg)  
+A: Because she spotted two adult male brown bears that might kill the cubs.  
+Figure 6. AKS selects different keyframe sets to answer different questions. All answers are correct.
+
+than the baseline (i.e.,  $57.4\%$ ,  $57.9\%$ ,  $58.9\%$  at 16, 32, 64 frames). VideoMME shows a similar trend, and 0.25 fps seems a safe option to surpass the baseline. It is worth exploring more efficient pre-filtering algorithms towards a better tradeoff between accuracy and efficiency.
+
+The VL model for computing  $r(\mathbf{Q},\mathbf{F}_t)$  scores. We analyze the impact of using different VL models for computing prompt-frame relevance. We study three options, i.e., BLIP [16] (the default choice in this paper), Sevilla (used in [53]), and CLIP [32]. Results are summarized in Table 4. We find that BLIP works better on LongVideoBench while CLIP works better on VideoMME. This is because
+
+Table 3. Question answering accuracy  $(\%)$  w.r.t. different sampling frequencies. LLaVA-Video-7B is used as the MLLM.  
+
+<table><tr><td rowspan="2">Frames of MLLM</td><td rowspan="2">1</td><td colspan="4">Sampling Frequency (fps)</td></tr><tr><td>0.5</td><td>0.25</td><td>0.125</td><td>0.1</td></tr><tr><td colspan="6">LongVideoBench val</td></tr><tr><td>16</td><td>61.6</td><td>60.7</td><td>60.6</td><td>61.1</td><td>59.4</td></tr><tr><td>32</td><td>61.9</td><td>62.1</td><td>59.8</td><td>60.2</td><td>58.5</td></tr><tr><td>64</td><td>62.7</td><td>62.2</td><td>61.8</td><td>60.1</td><td>60.1</td></tr><tr><td colspan="6">VideoMME</td></tr><tr><td>16</td><td>62.2</td><td>63.0</td><td>62.2</td><td>61.0</td><td>61.6</td></tr><tr><td>32</td><td>64.6</td><td>64.7</td><td>65.1</td><td>64.4</td><td>64.4</td></tr><tr><td>64</td><td>65.3</td><td>65.1</td><td>64.9</td><td>64.0</td><td>64.2</td></tr></table>
+
+Table 4. Question answering accuracy  $(\%)$  w.r.t. different VL scorers. LLaVA-Video-7B is used as the MLLM.  
+
+<table><tr><td>Frames</td><td>Uniform</td><td>BLIP</td><td>Sevila</td><td>CLIP</td></tr><tr><td colspan="5">LongVideoBench val</td></tr><tr><td>16</td><td>57.4</td><td>61.6</td><td>59.2</td><td>60.2</td></tr><tr><td>32</td><td>57.9</td><td>61.9</td><td>60.9</td><td>61.9</td></tr><tr><td>64</td><td>58.9</td><td>62.7</td><td>61.5</td><td>62.2</td></tr><tr><td colspan="5">VideoMME</td></tr><tr><td>16</td><td>60.6</td><td>62.2</td><td>63.0</td><td>63.1</td></tr><tr><td>32</td><td>63.9</td><td>64.6</td><td>63.7</td><td>65.0</td></tr><tr><td>64</td><td>64.4</td><td>65.3</td><td>65.1</td><td>65.6</td></tr></table>
+
+Table 5. Ablating  $L$  and  ${s}_{\text{thr }}$  together. Left: LVB,Right: V-MME.  
+
+<table><tr><td>L</td><td>sthr</td><td>0.0</td><td>0.2</td><td>0.4</td><td>0.6</td><td>0.8</td><td>1.0</td></tr><tr><td>1</td><td>62.4/63.8</td><td>62.4/64.0</td><td>62.5/64.2</td><td>62.0/64.1</td><td>61.8/63.8</td><td>61.9/64.0</td><td></td></tr><tr><td>2</td><td>62.4/63.8</td><td>62.0/64.0</td><td>62.4/64.0</td><td>61.8/63.5</td><td>61.7/63.4</td><td>62.0/63.6</td><td></td></tr><tr><td>3</td><td>62.4/63.8</td><td>62.7/64.0</td><td>62.6/54.5</td><td>62.1/64.4</td><td>62.2/64.4</td><td>62.1/64.4</td><td></td></tr><tr><td>4</td><td>62.4/63.8</td><td>62.6/64.1</td><td>62.7/64.3</td><td>62.2/64.9</td><td>62.1/65.0</td><td>62.2/65.0</td><td></td></tr><tr><td>5</td><td>62.4/63.8</td><td>62.6/64.1</td><td>62.2/64.7</td><td>61.7/65.0</td><td>61.3/65.3</td><td>61.7/65.2</td><td></td></tr><tr><td>6</td><td>62.4/63.8</td><td>62.6/64.0</td><td>62.3/64.5</td><td>61.8/65.0</td><td>61.3/65.1</td><td>61.4/65.1</td><td></td></tr></table>
+
+CLIP was trained on generic image-text pairs while BLIP learned from object-level data - correspondingly, questions in LongVideoBench and VideoMME are more focused on objects and global perception, respectively.
+
+ADA hyper-parameters,  $L$  and  $s_{\mathrm{thr}}$ . Lastly, we study the impact of  $L$  and  $s_{\mathrm{thr}}$ . Results are summarized in Table 5. One can see that LongVideoBench prefers smaller  $L$  and  $s_{\mathrm{thr}}$  values than VideoMME. This is because the key information on LongVideoBench is more concentrated (i.e., many questions are related to single moments) while that on VideoMME is more diverse (multi-moment data are required for question answering). AKS offers a flexible ability to switch between different 'modes' and achieves better results in both datasets.
+
+# 4.5. Generalization to Other Tasks
+
+Being an off-the-shelf algorithm, AKS is easily applied to other video understanding tasks. Here we showcase two examples known as video referring and captioning. For this
+
+Q: What is the woman in sunglasses doing in the video?
+
+Referring
+
+![](images/ae56309c0fe82fc62d9188786789c6163b1291268d2104d984c81cfc7f0026f0.jpg)  
+Figure 7. Extending AKS for video referring and captioning. The baseline results are produced upon uniform keyframe sampling. Red and green texts indicate incorrect and correct descriptions.
+
+Baseline: The woman in sunglasses is walking through a lush garden with greenery and flowers.  
+w/AKS: The woman in sunglasses is sitting at a table with a drink, possibly enjoying the view.
+
+Q: What is the shirtless man doing in the video?
+
+Referring
+
+![](images/89c7cee228b0aed1eae054f155ff7fccc05a87d082751324b6356195c038c484.jpg)
+
+Baseline: The shirtless man shirt is leading the donkeys.
+
+w/AKS: The shirtless man is standing in a small, rectangular pool with turquoise water.
+
+Q: Please describe this video about a temple.
+
+Captioning
+
+![](images/7f96803ba199c5a59ea274b7a068e02bf1e6eb2dcb22f0df6bfec667eacdf202.jpg)
+
+Baseline: The video opens with a view of a lush tropical landscape, featuring tall palm trees and a mountain range in the background. The sky is overcast, and there's a sense of tranquility. As the video progresses, the camera pans to reveal more of the forested area, with dense foliage and a few buildings visible in the distance. The colors are vibrant, with greens of various shades dominating the scene. There are no visible texts or subtitles in the video.
+
+w/AKS: The video opens with a blurry shot of a temple structure, followed by a clearer view of the temple's intricate carvings and statues. The temple appears to be made of stone and is adorned with detailed sculptures of mythical creatures and deities. The sky is visible in the background, suggesting that the temple is outdoors. The video then transitions to a close-up of a statue, highlighting its craftsmanship and the texture of the stone. The final frames show a wider shot of the temple, emphasizing its grandeur and the surrounding natural environment.
+
+purpose, we use the LLaVA-Video-7B model, switch the text prompt into 'What is [target] doing in the video?' or 'Please describe this video.', and remove the options. Qualitative results are shown in Figure 7. As seen, to obtain a comprehensive description of long videos, it is crucial to locate keyframes and feed them into the MLLM as visual contexts. AKS benefits from its keyframe selection ability and helps the MLLM to generate much better answers.
+
+# 5. Conclusions
+
+This paper focuses on improving the ability of MLLMs for long video understanding. The main difficulty arises from the limited capacity of MLLMs which urges us to feed informative visual tokens into the model. For this purpose, we present the Adaptive Keyframe Sampling (AKS) algorithm which (1) uses a vision-language model to estimate the relevance and (2) applies an adaptive optimization algorithm to facilitate the coverage of selected keyframes. Quantitative and qualitative studies validate the effectiveness of AKS over different baselines and benchmarks. Our work reveals that a pre-filtering stage brings considerable benefit to video understanding and advocates for further studies in this direction.
+
+# Acknowledgements
+
+This work was supported by National Natural Science Foundation of China (NSFC) under Grant 62225208 and 62450046 and CAS Project for CAS Project for Young Scientists in Basic Research under Grant No.YSBR-117.
+
+# References
+
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\ No newline at end of file
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+# Adaptive Markup Language Generation for Contextually-Grounded Visual Document Understanding
+
+Han Xiao $^{1,2\dagger}$ , Yina Xie $^{2}$ , Guanxin Tan $^{2}$ , Yinghao Chen $^{2}$ , Rui Hu $^{2}$ , Ke Wang $^{1}$ , Aojun Zhou $^{1}$ , Hao Li $^{1}$ , Hao Shao $^{1}$ , Xudong Lu $^{1,2\dagger}$ , Peng Gao $^{4}$ , Yafei Wen $^{2}$ , Xiaoxin Chen $^{2}$ , Shuai Ren $^{2\dagger \boxtimes}$ , Hongsheng Li $^{1,3 \boxtimes}$ $^{1}$ CUHK MMLab  $^{2}$ vivo AI Lab  $^{3}$ CPII under InnoHK  
+ $^{4}$ Shanghai AI Lab & Shenzhen Institute of Advanced Technology, CAS {1155229123@link,hsli@ee}.cuhk.edu.hk shuai. ren@vivo.com
+
+# Abstract
+
+Visual Document Understanding has become essential with the increase of text-rich visual content. This field poses significant challenges due to the need for effective integration of visual perception and textual comprehension, particularly across diverse document types with complex layouts. Moreover, existing fine-tuning datasets for this domain often fall short in providing the detailed contextual information for robust understanding, leading to hallucinations and limited comprehension of spatial relationships among visual elements. To address these challenges, we propose an innovative pipeline that utilizes adaptive generation of markup languages, such as Markdown, JSON, HTML, and TiKZ, to build highly structured document representations and deliver contextually-grounded responses. We introduce two fine-grained structured datasets: DocMark-Pile, comprising approximately 3.8M pretraining data pairs for document parsing, and DocMark-Instruct, featuring 624k fine-tuning data annotations for grounded instruction following. Extensive experiments demonstrate that our proposed model significantly outperforms existing state-of-the-art MLLMs across a range of visual document understanding benchmarks, facilitating advanced reasoning and comprehension capabilities in complex visual scenarios. Our code and models are released at https://github.com/Euphoria16/DocMark.
+
+# 1. Introduction
+
+Text-rich visual content, including multi-page documents and various multimedia formats, is ubiquitous in our daily
+
+lives. Consequently, Visual Document Understanding has emerged as a fundamental task that encompasses document classification, information extraction, and document-related visual question answering. This area presents significant challenges, as it requires seamless integration of visual perception with textual comprehension, along with the ability to navigate the complex interactions between these modalities. Such capabilities not only represent a fundamental cognitive skill in humans, but are also essential for the advancement of artificial intelligence systems.
+
+In recent years, Multimodal Large Language Models (MLLMs) have demonstrated remarkable progress in handling multi-modal tasks. Notably, there has been a growing focus on enhancing the capabilities of MLLMs in visual document comprehension. Existing efforts mainly aim to improve the representation of vision encoders originally designed for natural images, which are usually trained on relatively low-resolution datasets. Such efforts include scaling up the input resolution [6, 13, 26, 29], retraining vision encoders on text-rich images [7, 32, 54], and leveraging compositions of different encoders [25, 27].
+
+The core challenge in performing visual document understanding tasks lies in the efficient representation and effective perception of the visual content and its layout information present in the images. However, unlike Large Language Models (LLMs), whose training data generally include comprehensive descriptions and detailed reasoning, common fine-tuning datasets in the MLLM domain usually contain only questions and brief answers. As shown in Fig. 1, answers derived from PDF documents often consist of only a short phrase or a single number, even though understanding various parts of the document is required to answer the question. Similarly, datasets related to charts often lack a structural interpretation of the image content, resulting in challenges for effective analysis. Fine-tuning on
+
+![](images/34bfee56795dfd40e1b7d3d37f09d26380cc6397cb452e7b13088e405c6adde4.jpg)
+
+![](images/4ae6a0ec47d169112228128003912dc4fb9468b38cae7469df33873d00c47407.jpg)  
+Figure 1. Comparison of existing Data annotations and model Predictions: InternVL2-2B vs. our DocMark-2B. Existing datasets consist primarily of questions and brief answers, often resulting in model hallucinations. In contrast, our model effectively converts documents into structured markup languages, offering critical contextual information that enhances the accurate interpretation of the content.
+
+such data frequently leads to hallucinations and insufficient understanding of the contextual and spatial relationships among various visual elements in the documents. Moreover, visual documents come in a wide range of types, exhibiting different semantic content, multiple levels of granularity, and complex layouts. This variety requires adaptive encoding and perception of document images to fully capture their inherent complexity. These observations raise a critical question: How can we build contextually grounded training data and devise effective training pipelines to generalize across a wide range of document images?
+
+In this paper, we propose the adaptive generation of markup languages by the MLLM to facilitate a comprehensive understanding and provision of explicit context for various visual documents. Document images are often linked to their source codes, termed markup languages, which are both well-structured and easy to read. Examples include Markdown or LaTeX for PDF documents, HTML for webpages, and TikZ for scientific diagrams—all preserving rich semantic and layout information crucial for describing diverse document types. Furthermore, their structured nature and clarity make them readily interpretable by pretrained language models, providing valuable contextual information for enhanced document comprehension. To achieve this goal, we introduce DocMark-Pile, a compre
+
+hensive pretraining dataset of 3.8M paired data, designed to parse documents into their corresponding markup languages. This dataset covers a diverse range of visual document types, including natural scene images, dense documents, receipts, LaTeX formulas, web pages, tables, charts, and mathematical diagrams. The markup languages extend beyond basic text recognition and grounding, enabling code generation in formats such as Markdown, LaTeX, HTML, JSON, and TikZ. Building on the pretrained MLLM, we develop an adaptive generation pipeline by fine-tuning on DocMark-Instruct, a chain-of-thought-like reasoning dataset consisting of 624k annotations. Rather than manually specify which markup language to generate by the pretrained model, we let the model itself identify the most suitable type for each document, extracting useful context as intermediate rationales for answering questions. This approach mimics human-like reasoning, as a person first scans a visual document, then localizes and retrieves contextually relevant information to address specific queries. Similarly, when presented with a question, our model generates the most suitable markup languages, such as HTML for webpages, to extract relevant information and formulate answers. This fine-tuning pipeline enables our model to automatically adapt the appropriate markup language to the document type. Furthermore, it simulates human-like reasoning by disentangling perception from reasoning, encouraging the model to provide essential rationales for accurate answers. Extensive experiments demonstrate that our models substantially outperform existing state-of-the-art MLLMs on several challenging visual document understanding tasks.
+
+Our contributions can be summarized as follows:
+
+1. We propose a novel pipeline that adaptively uses various markup languages to bridge the gap between visual inputs and linguistic understanding and significantly enhance document comprehension capabilities.  
+2. We introduce two fine-grained structured datasets, DocMark-Pile and DocMark-Instruct, tailored for pretraining in specialized document parsing and fine-tuning on contextually-grounded instruction following. These datasets enable our model to effectively process complex document formats, including Plain Text, Markdown, LaTeX, HTML, JSON, and TikZ.  
+3. Extensive experiments demonstrate that our model consistently outperforms state-of-the-art multimodal LLMs across various model sizes, excelling in both markup parsing and downstream reasoning tasks.
+
+# 2. Related Work
+
+# 2.1. Multi-modal large language models (MLLMs).
+
+The field of Natural Language Processing (NLP) has seen remarkable advancements, particularly with the rise of
+
+Large Language Models (LLMs) [39, 40, 43]. The GPT series by OpenAI [39] has harnessed the power of massive model scaling, featuring architectures with billions and even trillions of parameters. To enhance instruction-following abilities, models like InstructGPT [41] and ChatGPT [39] have been developed, exhibiting exceptional fluency and versatility across various open-domain conversation tasks. Moreover, the instruction tuning based on open-source LLMs [51] has gained great popularity. Motivated by the advancements achieved by LLMs, recent research [12, 27, 44] has explored the application of LLMs for multi-modal tasks. Prevalent methods involve adapting the Linear Projector [28] or QFormer [24] to align vision encoder outputs with the textual feature space of LLMs. Nevertheless, existing methods struggle with comprehensive scene understanding due to limitations in visual representations. To mitigate this, several strategies have been proposed: utilizing composition of multiple vision encoders [25, 27], employing visual encoders designed for high-resolution inputs [13], and implementing dynamic resolution strategies to partition high-resolution images into multiple low-resolution segments [6, 26, 29]. While these strategies have shown advancements, they still struggle with complex understanding and reasoning tasks. This shortcoming arises from the fact that the pretraining and finetuning datasets used for MLLM training typically contain limited contextual information and lack a thorough reasoning process. In this paper, we address this gap by designing an adaptive markup generation pipeline aimed at producing explicit contextual information, which is crucial for effectively performing comprehensive reasoning tasks.
+
+# 2.2. Visual Document Understanding
+
+Recent advancements in multimodal large language models (MLLMs) have significantly enhanced visual document understanding tasks by employing autoregressive training on document images. UReader [59] introduces a Shape-adaptive Cropping Module to divide high-resolution images into low-resolution sub-images, effectively capturing rich text information. Similarly, Monkey utilizes a sliding window approach to minimize redundancy across different views of the same document. Models such as DocOwl 1.5 [14], LLaVA-Next [29], and InternVL [6] have explored the utility of OCR pretraining and dynamic partition techniques to address various aspect ratios. LLaVA-Read [63] integrates bi-resolution images and additional OCR encoders to improve textual information encoding. Other approaches, including DocPedia [9] and CogAgent [13], employ diverse encoding strategies to enhance visual representations. Despite these progress, challenges persist in processing complex document formats, particularly in interpreting their layout information. Additionally, existing document instruction datasets are often limited to questions and
+
+short answers, which can lead to hallucinations and restrict deeper contextual understanding. Since visual documents are typically high-structured data tied to their source codes, we develop contextually-grounded training data through markup language parsing and reasoning tasks. By training on structured document representations, our method aims to leverage the code interpretation capabilities of LLMs to further enhance visual document understanding.
+
+# 3. Method
+
+# 3.1. DocMark-Pile: Multi-Task Pretraining for Markup Language Conversion
+
+Visual document understanding encompasses various tasks, such as comprehending paragraphs from PDF documents, interpreting numerical data in charts and tables, and retrieving information from receipts, among others. Most documents are generated from source code or can be converted into structured representations. These structured formats act as markup languages, which define the structure of various elements, helping to convey meaning and organize the content effectively. To enhance the model's ability to understand and interpret a wide range of visual document types, we propose a multi-task pretraining dataset, DocMark-Pile, which focuses on translating documents into their corresponding markup languages. To ensure comprehensive coverage of document understanding scenarios, we utilize six distinct markup languages: plain text, Markdown, LaTeX, HTML, JSON, and TiKZ, as demonstrated in Fig. 2. Each format serves a unique purpose, which we will elaborate on below. For data acquisition, we utilize publicly available datasets as well as synthetic methods while maintaining the consistency between images and markup languages.
+
+# 3.1.1 Specialized Task Design
+
+Document to TXT Plain Text is the simplest format for basic content extraction from documents, as it retains all the textual information contained in the image. We primarily adopt this format for natural photos and regional text images, as these types of images typically contain straightforward textual information that can be extracted without formatting complexities. For natural photos, we utilize public datasets including TextOCR [47], COCO-Text [52], HierText [33], LSVT [49], RCTW-17 [45], and CTW1500 [62]. These datasets cover a wide range of scenarios, including advertising posters, signage, product labels, and image subtitles. Additionally, they often include bounding box annotations for the target text. We leverage these annotations to formulate text grounding tasks that require the model to recognize both the text and its coordinates within the image. For regional text images, we further incorporate datasets such as IC13 [17], IC15 [18], Union14ML [15], and Wor
+
+![](images/5cd7bd3ae78c5396973ee0a7cf92235501664721a3af23003bca29a8a4665bd5.jpg)  
+Figure 2. Overview of our DocMark-Pile dataset for pretraining on various markup language generation tasks. Due to the length of the answer, we have omitted a part of the content for better display.
+
+![](images/25b51b649d847daa48eee4f3836711f85cb154fe644ed1fd3a48b841bf45cd93.jpg)  
+Figure 3. Domain distribution of our DocMark-Pile dataset. (a) Distributions of different markup language parsing tasks. (b) Distributions of different image types.
+
+![](images/58007835f31a6626bc5e7c22f3d3b545a412fb777b7f6c9a1ff66544c9180aa5.jpg)
+
+dArt [55]. These images consist exclusively of regions containing text, which are usually in the form of single lines or curved text. We standardize the training data format by reading the text in the order from left to right and top to bottom, including additional bounding box coordinates for the text grounding task.
+
+Document to Markdown Markup is a lightweight syntax which enables basic formatting options such as bold, italics, headings, and lists. Markdown can be easily converted to and from other formats like HTML and LaTeX. We employ the Markdown format for dense text documents and tables because it effectively represents their structured content. For dense text documents, we primarily source our data from arXiv, where we obtain articles along with their corresponding source code and compiled PDFs. Following the process established in [13], we convert the PDFs into images while simultaneously translating the LaTeX code into Markdown format. Since many articles include complex formulas that cannot be successfully compiled in Markdown, we filter these instances during the conversion process. For tables, we draw from publicly available datasets, including PubTabNet [64], SynthTabNet [38], TabRecSet [58], TableGraph [57], and SciTSR [8]. We select these datasets because their annotations contain the original table content. Since many of these annotations are
+
+provided in HTML format, we convert them into Markdown format to meet the requirements of our task.
+
+Document to LaTeX LaTeX allows for the precise modeling of academic papers, particularly due to its capability to typeset complex mathematical formulas and scientific notation. We gather images converted from mathematics and science textbooks and exam papers, since these images typically contain numerous formulas and equations that must be accurately represented in LaTeX format. Subsequently, we utilize Mathpix to generate annotations for these documents. In addition, we incorporate handwritten mathematical expression recognition datasets, including HME100K [61] and MathWriting [11], which convert handwritten mathematical formulas into LaTeX format. We further enrich these data sources with additional rendered images. We first extract original mathematical expressions from our collected corpora, then use the Python library Matplotlib to render them as formula images. Subsequently, we apply data augmentation techniques, such as affine transformations and the addition of Gaussian noise, to enhance the robustness of the model in recognizing images under various backgrounds and display conditions.
+
+Document to HTML For webpage understanding, we introduce the task of parsing webpages into HTML formats. We utilize WebSight [22], a synthetic dataset consisting of HTML codes and their corresponding screenshots. Additionally, we augment our dataset by scraping real website images and HTML codes. Since many real website screenshots contain sparse content, directly learning from their HTML code often fails to extract useful information due to the noise. To address this, we introduce a webpage summarization task, which focuses on identifying and interpreting the key points and core content within a webpage. Specifically, we extract only the main elements of the page, such as the title, content, and other essential information. By focusing on the summary of key elements, this approach reduces the complexity and noise inherent in real website data, enhancing the quality of the pretraining data.
+
+Document to JSON To facilitate structured information extraction, we utilize JSON (JavaScript Object Notation) format, which represents information as key-value pairs, enhancing both readability and conciseness. This extraction is particularly valuable in scenarios involving cards, receipts, and forms, where summarizing and retrieving important data such as names, dates, and addresses from images is critical. To achieve this, we leverage several public datasets, including CORD [42], POIE [21], SVRD [60], WildReceipt [48], and XFUND [56], whose annotations can be easily converted into JSON format. In addition to textual information, we incorporate structured data from charts. We represent this information in a Python dictionary that encompasses fields such as "title", "source", "x-axis", "y-axis", and "value". For chart-related data, we utilize the PlotQA [37] dataset, which contains meta-information about chart content. Moreover, we augment our dataset by rendering various types of chart images. This involves randomly creating textual labels and numerical values. Then we employ Matplotlib to produce diverse chart images, including bar plots, scatter plots, line plots, and dot plots, using randomly sampled fonts and colors.
+
+Document to TikZ TikZ is a markup language commonly used for creating scientific figures. To construct our dataset, we leverage the open-source training sets of DaTikZv1 [1] and DaTikZv2 [2], which contain TikZ graphics collected from arXiv papers and artificial examples, along with their corresponding TikZ programs. Additionally, we extract scientific drawings from a curated corpus of mathematical and scientific textbooks and employ a trained model from [2] to convert these illustrations into TikZ code. Recognizing that conversion may not always be accurate, we take the necessary step of recompiling the TikZ code and use the re-generated images in our training. We also exclude any instances that fail to compile, ensuring that the TikZ code remains consistent with the figures.
+
+# 3.1.2 Dataset Statistics
+
+DocMark-Pile, a comprehensive dataset for document understanding, comprises 3.8 million examples of diverse markup language parsing tasks and image types.
+
+**Markup Language Categories:** We visualize the distribution of different language parsing tasks in Fig. 2, showcasing the percentage of each task type. This highlights the diversity of our dataset. In our data annotation, we prepend the special tokens such as  $\langle \mathrm{md} \rangle$  and  $\langle \mathrm{md} \rangle$  or  $\langle \mathrm{json} \rangle$  and  $\langle \mathrm{json} \rangle$  to the beginning and end of answers to indicate the corresponding markup language category.
+
+Image Types: Our dataset covers a wide range of image types, encompassing a comprehensive representation of visual documents. For clarity, we categorize text-dense materials like academic papers, textbooks, exam papers, and
+
+receipts under "documents", which constitutes the largest portion of the dataset.
+
+# 3.2. Adaptive Markup Language Generation During Fine-tuning
+
+# 3.2.1 Adaptive Generation Pipeline
+
+Through multi-task pretraining for versatile markup language generation, our model gains enhanced abilities to understand both visual content and layout information in diverse documents. We further fine-tune the model using instruction-tuning datasets, equipping it with the skills to handle downstream tasks such as open-ended question-answering related to document contexts. Previous methods primarily utilize questions and brief answers from public benchmark training sets, limiting their ability for deeper comprehension. In contrast, our model's ability to generate structured markup languages offers a significant advantage. These generated markup languages can serve as auxiliary context cues that facilitate more complex reasoning tasks. Being highly concise and structured, markup languages encode textual information efficiently and can be processed effectively by language models pre-trained on extensive text and code corpora.
+
+Motivated by chain-of-thought reasoning widely employed in the domain of LLMs, we design an adaptive markup language generation pipeline to enhance reasoning abilities. Rather than manually determining the markup language type to generate by the pretrained model as a prefix, we let our model automatically generate the appropriate markup language as an intermediate step to derive answers. This mirrors the human-like chain-of-thought reasoning; when reading documents such as PDFs or textbook pages, humans first scan the content, then localize and retrieve relevant information to answer specific questions.
+
+In our adaptive pipeline, the model automatically determines the appropriate markup language type and identifies contextually relevant information to answer the question. We implement this as a two-round conversational process as follows:
+
+$$
+Q _ {1}: \text {T o a n s w e r t h e q u e s t i o n :} <   Q u e s t i o n >, \quad \text {e x t r a c t t h e r e l e v a n t c o m p e x t f r o m t h e i m a g e}.
+$$
+
+$$
+A _ {1}: <   t y p e > <   C o n t e x t > <   / t y p e >
+$$
+
+$$
+\begin{array}{l} Q _ {2}: \text {B a s e d o n t h e i m a g e a n d e x t r a c t e d c o n t e x t ,} \\ \text {a n s w e r t h e q u e s t i o n : <   Q u e s t i o n >} \end{array} \tag {1}
+$$
+
+$$
+A _ {2}: <   A n s w e r >
+$$
+
+In this pipeline, the model is first asked to provide the essential contextual information to address the specific question  $<  \text{Question}>$ . It then outputs this context as  $<  \text{Context}>$ , serving as an intermediate rationale in the process. Special tokens  $<  \text{type}>$  and  $<  / \text{type}>$  indicate
+
+![](images/43aeef0bbed0874c420c9f991d786b6720b488991bca92a77dd3d7c94430c959.jpg)  
+Figure 4. Overview of our adaptive markup language generation framework. (a) During pretraining, the model learns to parse documents into corresponding markup language representations, enhancing its structural understanding capabilities. (b) In the finetuning phase, the model is optimized to identify and extract relevant information as intermediate rationales to formulate precise answers.
+
+the markup language type. In the second round, the model derives the final answer by utilizing both the image and the context provided in the first round. This structured approach ensures that the model systematically processes and retains critical contextual information, thereby enhancing its ability to generate accurate and contextually grounded answer akin to human thought processes.
+
+# 3.2.2 DocMark-Instruct: CoT Reasoning Data Construction
+
+To enable our model with adaptive generation capabilities, it is essential to curate a dataset formatted as described in template (1). However, existing fine-tuning datasets only contain question-answer pairs and lack the detailed CoT reasoning process. To address this gap, we propose an efficient method for constructing the required data, DocMark-Instruct. Most questions in common training datasets within the document domain are closely related to the textual information present in the images. We observe that these questions can often be answered directly by providing the corresponding markup language to a powerful language model, thus eliminating the need for visual input. Therefore, we first utilize our pretrained model to convert images into their corresponding markup languages. Next, we employ ChatGPT-3.5, a freely accessible large language model known for its robust language understanding and generation capabilities, to create additional annotations. We input the question-answer pairs and the entire markup language text into it, asking it to retrieve the necessary information to answer the questions, finally producing 624k annotations. Our data construction pipeline circumvents the high annotation
+
+costs typically associated with proprietary MLLMs such as GPT4-V, making it a practical and accurate solution for developing comprehensive CoT reasoning datasets.
+
+# 3.2.3 Training and Inference
+
+During the fine-tuning phase, we concatenate the two-round dialogue data for the forward process and apply Cross-Entropy loss on both answers,  $A_{1}$  and  $A_{2}$ . In the inference phase, we first input  $Q_{1}$  to prompt the model to generate the adaptive markup language context. Following this, we formulate  $Q_{2}$  to obtain the final response. Importantly, our training pipeline is also compatible with common training data that lacks the CoT reasoning process. Users can directly ask the model to answer a question by omitting the CoT prompt described in template (1).
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Model Architecture We adopt the InternVL [7] architecture for our model due to its enhanced visual representation capabilities. We use the pretrained InternViT [7] as the visual encoder and utilize InternLM-2B [50] and InternLM-8B [50], known for their robust linguistic understanding abilities. We adopt MLP layers to project the image into visual tokens, which are further concatenated with text tokens. As our work focuses on incorporating adaptive markup language generation to improve visual document understanding, we do not explore additional resolution scaling strategies in this paper. Instead, we employ the dynamic resolution method proposed in InternVL2 [6], which demonstrates efficacy in modeling high-resolution
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2" colspan="2">Text Recognition</td><td rowspan="2">HME100K</td><td colspan="3">ChartQA-SE</td><td colspan="2">KIE</td><td rowspan="2">DaTikZ-test</td></tr><tr><td>AP@strict</td><td>AP@slight</td><td>AP@high</td><td>FUNSD</td><td>SROIE</td></tr><tr><td>Paddle OCR</td><td>140</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CAN-ABM [23]</td><td></td><td></td><td>64.3</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>OneChart [4]</td><td></td><td></td><td></td><td>72.0</td><td>82.9</td><td>85.9</td><td></td><td></td><td></td></tr><tr><td>Nougat [3]</td><td></td><td></td><td></td><td></td><td></td><td></td><td>55.4</td><td>33.6</td><td></td></tr><tr><td>DT-DS1.3B [2]</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.22</td></tr><tr><td>DT-CL7B [2]</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.68</td></tr><tr><td>DocMark-2B</td><td>247</td><td>67.2</td><td>73.8</td><td>85.2</td><td>86.5</td><td>64.1</td><td>54.2</td><td>0.39</td><td></td></tr><tr><td>DocMark-8B</td><td>252</td><td>73.4</td><td>75.4</td><td>85.5</td><td>87.1</td><td>68.5</td><td>59.6</td><td>0.64</td><td></td></tr></table>
+
+Table 1. Performance comparison with expert models on specialized tasks. The best results are marked in bold.
+
+document images. Specifically, the input image is split into several sub-images of resolution  $448 \times 448$ , with a maximum of 12 sub-images used in our training settings.
+
+Training Settings Our model is trained through a two-stage process. In the first stage, we utilize DocMark-Pile to empower the model with markup language parsing abilities. Additionally, we incorporate the image captioning dataset LLaVA-558K [28] to ensure alignment between the visual input and text tokens. We pre-train the model for one epoch with a learning rate of 2e-5 and a total batch size of 128. In the second stage, we fine-tune our model on the proposed CoT Reasoning dataset DocMark-Instruct. As described in Sec. 3.2.2, we create additional CoT annotations for the training sets of TextVQA [46], DocVQA [36], InfographicsVQA [35], ChartQA [34], DVQA [16], XFUND [56], and Geo170K [10]. Apart from DocMark-Instruct, we also integrate general instruction tuning data from ShareGPT4V [5] and text-only multi-turn conversation datasets [20, 65]. This integration preserves the model's capacity for general understanding and conversational interaction. We fine-tune our model on these datasets for one epoch with a learning rate of 1e-5 and a total batch size of 128.
+
+# 4.2. Evaluation on Markup Language Generation Abilities
+
+Evaluation Settings The ability to generate accurate markup languages is crucial for our model to understand complex document formats and provide adaptive context for facilitating downstream task reasoning. We comprehensively evaluate our model on specialized tasks and compare it with domain-expert models. We utilize the text recognition benchmark in [31], which covers a broad range of scene texts. We also assess our model's accuracy in expressing formulas present in images using the LaTeX format, utilizing the test set of HME100K [61]. Moreover, we adopt the ChartQA-SE benchmark proposed in [4] and report AP@strict, AP@slight, and AP@high metrics. We also evaluate on FUNSD and SROIE for key information extraction task. These metrics measure the accuracy of the
+
+structural extraction results compared to the ground-truth values. For TiKZ code generation, we use the DaTikZ test set proposed in [2]. We report the average of image similarity and code similarity to assess the code consistency. By thoroughly evaluating our model across these diverse tasks, we aim to demonstrate its capability to accurately generate markup languages, thereby facilitating effective visual document understanding and reasoning.
+
+Results. We present the comparison results of our model against various expert models in Tab. 1. As can be seen, our DocMark models outperform the expert models by a significant margin on the text recognition and HME100K [61] benchmarks. Moreover, our model demonstrates impressive capabilities in structural information extraction, particularly on the ChartQA-SE [4] and KIE tasks. On DaTiKZ-test [2], DocMark-8B achieves performance nearly on par with DTCL $_{7B}$ , without additional search costs for TiKZ code generation. These results showcase the model's effectiveness in markup language conversion, enhancing visual perception and supporting contextually grounded reasoning.
+
+# 4.3. Evaluation on Downstream Understanding tasks
+
+Evaluation Settings To validate the effectiveness of adaptive markup language generation, we evaluate the model's performance on a range of downstream tasks for document understanding. We adopt diverse evaluation benchmarks that encompass a wide variety of multi-modal scenarios. We report accuracy on TextVQA [46] to assess the model's ability to answer questions related to natural scene text. Additionally, we evaluate performance on DocVQA [36], InfoVQA [35], AI2D [19], and ChartQA [34] for comprehension of text-dense documents and charts. To assess the model's general OCR abilities, we utilize OCRBench [31], a comprehensive benchmark containing various text-related images. For webpage understanding, we report the WebQA accuracy as proposed in VisualWebBench [30]. Furthermore, we evaluate the model's math reasoning performance using MathVision [53] dataset to validate its ability to interpret complex mathematical diagrams.
+
+<table><tr><td>Method</td><td>LLM</td><td>TextVQVal</td><td>DocVQVal</td><td>InfoVQVal</td><td>ChartQA</td><td>AI2D</td><td>OCRBench</td><td>WebQA</td><td>MathVision</td></tr><tr><td colspan="10">Lightweight Specialist Models</td></tr><tr><td>Donut</td><td>-</td><td>43.5</td><td>67.5</td><td>11.6</td><td>41.8</td><td>30.8</td><td>-</td><td>-</td><td></td></tr><tr><td>Pix2Struct-Base</td><td>-</td><td>-</td><td>72.1</td><td>38.2</td><td>56.0</td><td>40.9</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Pix2Struct-Large</td><td>-</td><td>-</td><td>76.6</td><td>40.0</td><td>58.6</td><td>42.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td colspan="10">Multimodal LMMs</td></tr><tr><td>Vary-toy</td><td>1.8B</td><td>-</td><td>65.6</td><td>-</td><td>59.1</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MiniCPM-V-2</td><td>2.8B</td><td>74.1</td><td>69.7</td><td>37.9</td><td>59.8</td><td>62.6</td><td>594</td><td>-</td><td>15.1</td></tr><tr><td>InternVL2</td><td>2B</td><td>73.2</td><td>86.0</td><td>57.6</td><td>76.4</td><td>74.2</td><td>783</td><td>66.5</td><td>15.7</td></tr><tr><td>DocMark (Ours)</td><td>2B</td><td>74.8</td><td>87.8</td><td>61.2</td><td>79.8</td><td>82.5</td><td>813</td><td>70.1</td><td>18.8</td></tr><tr><td>Ureader</td><td>7B</td><td>57.6</td><td>80.7</td><td>46.4</td><td>70.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DocPedia</td><td>7B</td><td>60.2</td><td>47.1</td><td>15.2</td><td>46.9</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Vary</td><td>7B</td><td>-</td><td>76.3</td><td>-</td><td>66.1</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Monkey</td><td>9B</td><td>67.6</td><td>66.5</td><td>36.1</td><td>65.1</td><td>62.6</td><td>514</td><td>-</td><td>-</td></tr><tr><td>TextMonkey</td><td>9B</td><td>64.3</td><td>66.7</td><td>28.6</td><td>59.9</td><td>-</td><td>558</td><td>-</td><td>-</td></tr><tr><td>CogAgent</td><td>17B</td><td>76.1</td><td>81.6</td><td>44.5</td><td>68.4</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DocOwl2</td><td>8B</td><td>66.7</td><td>80.7</td><td>46.4</td><td>70.0</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>InternVL2</td><td>8B</td><td>77.4</td><td>90.8</td><td>72.8</td><td>82.2</td><td>83.7</td><td>794</td><td>77.5</td><td>20.2</td></tr><tr><td>DocMark (Ours)</td><td>8B</td><td>78.0</td><td>89.8</td><td>68.3</td><td>84.2</td><td>86.2</td><td>823</td><td>78.9</td><td>21.1</td></tr></table>
+
+Table 2. Performance comparisons on downstream document understanding tasks. The best results are marked in bold.
+
+![](images/159ed93e65e209d0d27be2d91a8495032c8b46ee27698a73dc7513c38c384c62.jpg)  
+Figure 5. Ablation study on employing different training dataset strategies.
+
+Results We present the comparison results on downstream understanding tasks in Tab. 2. Our DocMark models consistently outperform state-of-the-art multimodal large language models across nearly all benchmarks, both for the 2B and 7B parameter sizes. Notably, DocMark significantly enhances performance on common document understanding tasks, while also achieving remarkable results on MathVision, demonstrating its effectiveness in addressing complex multimodal math problems. Furthermore, our models show significant improvements in general OCR and webpage understanding, as highlighted by the results on OCRBench and WebQA. When compared to state-of-the-art models like the InternVL2 series, DocMark achieves superior accuracy with substantially less training data. These results illustrate that the proposed framework greatly enhances document understanding and reasoning capabilities.
+
+# 4.4. Ablation Study
+
+To investigate the impact of proposed datasets, we examine various training dataset strategies using DocMark-2B. We train the model without incorporating DocMark-Pile and DocMark-Instruct, relying solely on image-caption datasets and general question-answering datasets for fine-tuning. We report the accuracy of the model on four document-related QA datasets for analysis. Subsequently, we integrate DocMark-Pile for model pretraining and employ DocMark-Instruct for fine-tuning. As illustrated in Fig. 5, the absence of DocMark-Pile significantly degrades model performance, particularly for text-dense documents and structured data. Furthermore, incorporating DocMark-Instruct substantially enhances performance when built upon DocMark-Pile pretraining, demonstrating its effectiveness in improving reasoning capabilities. We provide more performance analysis in our supplementary.
+
+# 5. Conclusion
+
+In this paper, we have introduced an innovative framework that utilizes adaptive markup language generation to enhance visual document understanding. Our approach addresses the core challenge of efficiently representing and perceiving visual content and layout information in images by incorporating specialized pretraining tasks and an adaptive generation pipeline. The proposed method not only improves the versatility of MLLMs in handling complex document formats, but also enables them to perform chain-of-thought reasoning to produce contextually grounded answers. Extensive experiments demonstrated that our models outperform existing state-of-the-art approaches on several challenging visual document understanding tasks.
+
+# Acknowledgments
+
+This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by NSFC-RGC Joint Fund Project N_CUHK498/24, by the National Natural Science Foundation of China (No.62206272). Hongsheng Li is a PI of CPII under the InnoHK.
+
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+# Adaptive Non-uniform Timestep Sampling for Accelerating Diffusion Model Training
+
+Myunsoo Kim $^{1*}$  Donghyeon Ki $^{1*}$  Seong-Woong Shim $^{1}$  Byung-Jun Lee $^{1,2}$ $^{1}$ Korea University  $^{2}$ Gauss Labs Inc.
+
+{m970326, peopleln, ssw030830, byungjunlee}@korea.ac.kr
+
+# Abstract
+
+As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions grow more complex, training these models to convergence becomes increasingly computationally intensive. While diffusion models are typically trained using uniform timestep sampling, our research shows that the variance in stochastic gradients varies significantly across timesteps, with high-variance timesteps becoming bottlenecks that hinder faster convergence. To address this issue, we introduce a non-uniform timestep sampling method that prioritizes these more critical timesteps. Our method tracks the impact of gradient updates on the objective for each timestep, adaptively selecting those most likely to minimize the objective effectively. Experimental results demonstrate that this approach not only accelerates the training process, but also leads to improved performance at convergence. Furthermore, our method shows robust performance across various datasets, scheduling strategies, and diffusion architectures, outperforming previously proposed timestep sampling and weighting heuristics that lack this degree of robustness.
+
+# 1. Introduction
+
+In recent years, diffusion models have demonstrated their high expressive power and achieved significant success across a wide range of domains, including image [9, 23, 24], video [18, 35], text [4, 12, 22], audio generation [26], combinatorial optimization [25, 30], reinforcement learning [1, 15, 32], and more. However, with the increasing complexity of target data distributions, achieving convergence in diffusion model training has become increasingly computationally demanding. For example, training images with Stable-Diffusion-2.0 [24] requires 24,000 A100 GPU hours, while Open-Sora [35] requires 48,000 H800 GPU hours.
+
+![](images/6c2a13a96a5c9fe4ad8b858487429a32a7bf816f8a718676e1974069a759a755.jpg)  
+Figure 1. Comparison of FID scores of our approach and other acceleration methods against relative wall clock time, where 1D represents the time it takes for the baseline to converge. Although our learning method is initially slower than the heuristics due to its learning-based nature, it converges to a point with better optimality within 1D, and achieves a significantly lower FID score by 1.2D.
+
+hours for video training. These high computational costs not only pose significant barriers to advancing generative AI applications but also have negative environmental consequences.
+
+While numerous studies have explored ways to accelerate diffusion model training, our research specifically targets modifications to the uniform training process of diffusion models across diffusion timesteps. It is well recognized that non-uniform training schemes over timesteps can enhance training speed. For example, several heuristics have been proposed [7, 11, 17, 31].
+
+However, the underlying reasons for the success of these methods remain largely unexplored, and they are often regarded as heuristics that may have potential limitations in robustness across diverse experimental conditions.
+
+Through a series of experiments, we observed significant variation in the stochastic gradient variance across different diffusion training timesteps.
+
+We hypothesize that this variability plays a key role in the imbalanced training observed with uniform sampling
+
+and may explain the effectiveness of previously proposed heuristics in improving diffusion model training. However, due to the strong interdependence of gradients across different timesteps, we found that this insight alone does not directly lead to optimal acceleration in diffusion training.
+
+To this end, we propose a more direct approach by developing an efficient algorithm designed to sample timesteps that are estimated to yield the greatest reduction in the objective. This algorithm approximates the impact of gradient updates for each timestep on the variational lower bound and increases the sampling frequency of specific timesteps that require further optimization.
+
+This enables the diffusion training process to converge significantly faster than previous heuristics across various settings. To summarize, our three main contributions are as follows:
+
+1. Through an analysis of gradient variance in diffusion model training, we offer an explanation for why a nonuniform training process across timesteps can lead to faster convergence.  
+2. Unlike previous heuristic-based diffusion acceleration methods, we propose a learning-based approach that adaptively samples timesteps by approximately minimizing the variational bound on the negative log-likelihood.  
+3. We conduct experiments across various image datasets, noise scheduling strategies and diffusion architectures to demonstrate the robustness of our method.
+
+# 2. Related Works
+
+Non-uniform training of diffusion models Several studies have explored timestep-wise non-uniform training of diffusion models to accelerate training. These approaches can be categorized into two main groups:
+
+- 1) Weighting methods: These methods apply hand-designed weightings to the loss at each timestep. For example, P2 [7] assigns greater weights to timesteps containing perceptually rich content and lesser weights to those involving imperceptible details. Similarly, MinSNR [11] adjusts loss weights based on clamped signal-to-noise ratios.  
+- 2) Sampling methods: These approaches use hand-designed samplers to select timesteps in a non-uniform manner. For instance, Log-Normal [17] samples timesteps from a log-normal distribution. SpeeD [31] modifies sampling probabilities to downweight timesteps with lower losses and prioritize those with rapidly changing process increments.
+
+While these heuristics have proven effective in accelerating diffusion model training, their direct relationship to the underlying objective remains unclear, raising concerns about their applicability in new, potentially more effective settings that may emerge in the future.
+
+Learning to optimize (L2O) L2O is a field in machine learning focused on learning optimization algorithm. It typically involves a meta-training set composed of multiple training and validation datasets. Using this meta-training set, L2O learns to update parameters based on gradients to minimize validation set errors, either through supervised learning [3, 33] or reinforcement learning [6, 20]. Although our objective similarly focuses on learning to optimize, we address a more challenging task by not assuming metatraining set for transfer learning. Instead, we focus on learning to optimize in an online manner, without the benefit of prior training data.
+
+# 3. Background: Diffusion Models
+
+Diffusion model [14, 27] consists of two key processes: a predefined forward noising process and a reverse denoising process, which is learned through variational inference to match the forward process.
+
+Forward process Starting with data  $x_0 \sim q(x_0)$ , the forward process operates as a Markov-Gaussian process that incrementally introduces noise, generating a sequence of noisy latent variables  $\{x_1, x_2, \ldots, x_T\}$ :
+
+$$
+q \left(x _ {t} \mid x _ {t - 1}\right) := \mathcal {N} \left(x _ {t}; \sqrt {1 - \beta_ {t}} x _ {t - 1}, \beta_ {t} I\right), \tag {1}
+$$
+
+where  $\beta_{t}$  is a noise schedule. Latent variables can be equivalently sampled by  $x_{t} \coloneqq \sqrt{\bar{\alpha}_{t}} x_{0} + \sqrt{1 - \bar{\alpha}_{t}} \epsilon$ ,  $\epsilon \sim \mathcal{N}(0, I)$ , where  $\bar{\alpha}_{t} \coloneqq \prod_{s=1}^{t} (1 - \alpha_{s})$  and  $\alpha_{t} \coloneqq 1 - \beta_{t}$ .
+
+Reverse process Diffusion models generate data  $x_0$  from  $x_{T}$  through the learned reverse process  $p_{\theta}(x_{t - 1}|x_t)$ , gradually denoising the latent variables from a Gaussian noise:
+
+$$
+p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) := \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, t\right), \sigma_ {t} ^ {2} I\right), \tag {2}
+$$
+
+$$
+\mu_ {\theta} \left(x _ {t}, t\right) := \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} \left(x _ {t}, t\right)\right) \tag {3}
+$$
+
+where  $\sigma_t^2$  is a variance of the denoising process, and  $\mu_{\theta}$  is parameterized as proposed by Ho et al. [14] for further simplification.  $\epsilon_{\theta}$  is a deep neural network with parameter  $\theta$  that predicts the noise vector  $\epsilon$  based on  $x_{t}$  and  $t$ .
+
+Training The training of a diffusion model is achieved by optimizing the variational lower bound on the log-likelihood, which is expressed as a sum of KL-divergence terms comparing Gaussian distributions and can be reformulated in terms of the normalized noise:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {V L B}} (\theta) := \mathbb {E} _ {x _ {0}} \left[ \sum_ {t} D _ {\mathrm {K L}} \left(q \left(x _ {t - 1} \mid x _ {t}, x _ {0}\right) \| p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right)\right) \right] \\ = \mathbb {E} _ {x _ {0}, \epsilon , t} \left[ \frac {\beta_ {t} ^ {2}}{2 \sigma_ {t} ^ {2} \alpha_ {t} (1 - \bar {\alpha} _ {t})} \| \epsilon - \epsilon_ {\theta} (x _ {t}, t) \| ^ {2} \right], \tag {4} \\ \end{array}
+$$
+
+![](images/1e5ab18fe8599423585678385759bfefa30ad1d345da7caa10590fccb331d67f.jpg)
+
+![](images/10972fd68b16344fb1ec67d22ce41493a59457368b2b1740688594f15fa04e61.jpg)
+
+![](images/78334cd5ba00bc2bbaa2134e3086dd94f14fc77820d63606095032e128e7754d.jpg)
+
+![](images/bbdf93126d79f24d916b627f6c9011562423a1bd9b0d2e49c55461c0d64e7c88.jpg)  
+Figure 2. Comparison of gradient variance (top) and diffusion loss (bottom) over timesteps for three different noise schedules: linear, cosine, and quadratic. The color bar on the right indicates the progression of epochs, with red representing the early epochs and blue representing the later epochs. The results are based on training DDPM [14] with  $\mathcal{L}_{\mathrm{DDPM}}$  for 20 epochs.
+
+![](images/7e9cb76a40b26b1c20ed9bfb1e74f1150dd5dde874605bce0d26c276b69c89a7.jpg)
+
+![](images/6ad845b55cdef6e4f25acf3d9ed28e0b605848cb2cede07136409e7ba5db7787.jpg)
+
+where  $t \sim \mathcal{U}\{1, T\}$ . A standard way to train a diffusion model is to ignore the constant terms [14], resulting in an objective of:
+
+$$
+\mathcal {L} _ {\mathrm {D D P M}} (\theta) := \mathbb {E} _ {x _ {0}, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) \| ^ {2} \right]. \tag {5}
+$$
+
+# 4. Demystifying Non-Uniform Diffusion Model Training Across Timesteps
+
+In this section, we offer a hypothesis explaining why nonuniform training strategies may offer advantages over the uniform training approach used by Ho et al. [14]. For simplicity, we begin by assuming an independent parameterization across timesteps, expressed as:
+
+$$
+\epsilon_ {\theta} \left(x _ {t}, t\right) = \epsilon_ {\theta_ {t}} \left(x _ {t}\right), \quad \forall t, \tag {6}
+$$
+
+with a independent set of parameters  $\theta = \{\theta_t\}_{t=1}^T$  for each timestep. This parameterization allows us to have independent optimization objective per timestep, i.e.,  $\mathcal{L}_{\mathrm{VLB}}(\theta) = \sum_{t=1}^{T} \mathbb{E}_{x_0, \epsilon}[\mathcal{L}_t(\theta)]$  with
+
+$$
+\mathcal {L} _ {t} (\theta) := c _ {t} \| \epsilon - \epsilon_ {\theta_ {t}} (x _ {t}) \| ^ {2}, \quad c _ {t} := \frac {\beta_ {t} ^ {2}}{2 \sigma_ {t} ^ {2} \alpha_ {t} (1 - \bar {\alpha} _ {t})}. \tag {7}
+$$
+
+We now have divided the problem into  $T$  independent subproblems, where the training with uniform timestep sampling corresponds to uniformly selecting one of these subproblems  $\mathcal{L}_t$  and performing a stochastic gradient step on its corresponding parameter  $\theta_t$ . Informally, if certain subproblems are particularly more challenging and require more iterations to optimize, there is a potential for improvement through non-uniform training strategies.
+
+In this sense, we assess the difficulty of these subproblems by measuring a variance of stochastic gradients,  $\operatorname{Var}_{x_0,\epsilon}[\nabla_{\theta_t}\mathcal{L}_t(\theta)]$ . It is well known that the convergence of stochastic gradient descent is only guaranteed with the learning rates that scale with the variance of the gradient:
+
+Theorem 1. [Garrigos and Gower [10], informal] Given a few reasonable assumptions, for every  $\varepsilon > 0$ , we can guarantee that  $\mathbb{E}\left[\mathcal{L}_t(\theta_K) - \inf \mathcal{L}_t\right] \leq \varepsilon$  provided that
+
+$$
+\gamma = \mathcal {O} \left(\frac {1}{\sqrt {K}} \left(\operatorname {V a r} _ {x _ {0}, \epsilon} \left[ \nabla_ {\theta_ {t}} \mathcal {L} _ {t} \left(\theta_ {*}\right) \right]\right) ^ {- \frac {1}{2}}\right), \tag {8}
+$$
+
+$$
+K \geq \mathcal {O} \left(\frac {1}{\varepsilon^ {2}} \operatorname {V a r} _ {x _ {0}, \epsilon} \left[ \nabla_ {\theta_ {t}} \mathcal {L} _ {t} \left(\theta_ {*}\right) \right]\right). \tag {9}
+$$
+
+Here,  $\gamma$  is the learning rate of Stochastic Gradient Descent (SGD),  $\theta_{K}$  is the parameter after  $K$  steps of gradient updates, and  $\theta_{*}$  is the optimal parameter.  $K$  is the total number of iterations required to achieve the accuracy  $\varepsilon$ .
+
+In short, Theorem 1 suggests that the learning rate should be scaled inversely proportional to the standard deviation of stochastic gradient. With an appropriately adjusted learning rate, the number of iterations needed for SGD to converge increases in proportion to the gradient's variance. Since modern optimizers like Adam [19] are designed to ensure convergence by inversely scaling the learning rate with the exponential moving standard deviation, we can infer that the iterations required for a subproblem  $\mathcal{L}_t$  to converge will approximately grow in proportion to the variance of the stochastic gradient at the optimal parameter.
+
+![](images/e12850ae528d0330879b9983d90285e58859a1d3cd3cbfe8f09dc8e21adc4bb9.jpg)  
+Figure 3. Adaptive Non-Uniform Timestep Sampling. Visualization of the overall architecture of our algorithm. Following an update from  $\theta_{k}$  to  $\theta_{k + 1}$ , we compute the set  $\{\delta_{k,\tau}^{t}\}_{\tau = 1}^{T}$  based on  $\theta_{k}$  and  $\theta_{k + 1}$ , and add it to a queue. A feature selection method is then applied to identify  $|S|$  timesteps that best explains  $\Delta_k^t$  from this queue. Then a timestep sampler  $\pi_{\phi}$  is trained to maximize  $\tilde{\Delta}_k^t$ , which samples timestep  $s$ $t$  that is expected to achieve the largest reduction in the diffusion loss. This process continues iteratively to minimize the diffusion loss at the chosen timesteps.
+
+Gradient variance of diffusion model Considering that the gradient variance at each timestep reflects the difficulty of the optimization problem at that specific timestep, we present the measured gradient variance during diffusion model training in the top row of Fig. 2. The results clearly indicate an imbalance in gradient variance across timesteps. Notably, for all three schedules, the gradient variances at early timesteps are significantly higher than those at later timesteps, and this trend persists without fading quickly. Since the variance at optimal parameters serves as a lower bound on the number of gradient iterations required for convergence (Theorem 1), we can anticipate that the early timesteps might pose a bottleneck to training efficiency when timesteps are sampled uniformly.
+
+The bottom row of Fig. 2 shows the actual timestepwise diffusion loss, and as expected, it shows that the loss near later timesteps decreases substantially faster than the loss near early timesteps. These results suggest that oversampling early timesteps and undersampling later timesteps could enhance overall training efficiency by effectively addressing the bottleneck presented by the subproblems at early timesteps.
+
+Interdependence of  $\mathcal{L}_t$  We have motivated the nonuniform sampling of timesteps by showing that we have varying gradient variance across timesteps, and this leads to a conclusion of non-uniform sampler that samples proportional to the gradient variance. However, without the assumption of independence across subproblems  $\mathcal{L}_t$  based on a specific parameterization, the optimality of such a sampler is not guaranteed.
+
+Fig. 4 illustrates the extent of interdependence among subproblems during diffusion model training. The figure reveals that the loss increase in untrained timesteps is
+
+significantly greater than the loss reduction in the trained timesteps, highlighting the strong interdependence between subproblems. Given that gradient variance can differ by up to a hundredfold (Fig. 2), it is evident that sampling in proportion to the gradient variance alone would likely be insufficient to effectively reduce the loss at later timesteps. Later through experiments, we confirmed that sampling timesteps in proportion to gradient variance yields poor performance (Tab. 4).
+
+# 5. Adaptive Non-Uniform Timestep Sampling for Diffusion Model Training
+
+Building on the need for non-uniform timestep sampling scheme discussed in the previous section, this section introduces an adaptive timestep sampler  $\pi$ , designed to enhance the training efficiency of diffusion models. We present a method for jointly training this sampler with the diffusion model in an online manner. This approach accelerates the diffusion training process with  $\pi$ , without requiring prior training data for its optimization.
+
+# 5.1. Non-uniform Timestep Sampler
+
+We propose a non-uniform timestep sampling strategy for diffusion model training, utilizing a timestep sampler  $\pi$  to improve training efficiency:
+
+$$
+\theta \leftarrow \theta - \gamma \nabla_ {\theta} \mathcal {L} _ {t}, t \sim \pi (\cdot | x _ {0}), \mathcal {L} _ {t} = c _ {t} \| \epsilon - \epsilon_ {\theta} (x _ {t}, t) \| ^ {2}, \tag {10}
+$$
+
+where  $c_{t}$  is a schedule-dependent constant as defined in Eq. (7). Note that we no longer use independent parameterization across timesteps.
+
+To leverage the fact that diffusion train loss is similar across closely related timesteps, we parameterize a neural
+
+![](images/eaea7cd9bbb7f6bbc0da176dedbd61cab75b8c52bbf719a9b8e002716953d9a0.jpg)  
+Figure 4. Difference in diffusion loss observed (after and before model update) after training a diffusion model by sampling only timesteps within the range [0, 200). A significant increase in loss is notably observed for the unsampled timesteps.
+
+network that generates two positive real scalars, which are then used to sample  $t$  from a Beta distribution:
+
+$$
+a, b \sim \pi_ {\phi} (\cdot | x _ {0}), \quad a > 0, b > 0, \quad t \sim \operatorname {B e t a} (a, b). \tag {11}
+$$
+
+This ensures our timestep sampler accounts for the high correlation between similar timesteps. For simplicity, we will continue to denote this process as  $t \sim \pi_{\phi}(\cdot | x_0)$ .
+
+Our goal is to train the timestep sampler  $\pi_{\phi}$  to minimize the original objective, the variational lower bound  $\mathcal{L}_{\mathrm{VLB}}$  as effectively as possible within a finite number of training steps. To achieve this, we seek to optimize the sampler  $\pi_{\phi_k}$  to sample timesteps  $t$  that yield the greatest reduction of  $\mathcal{L}_{\mathrm{VLB}}$  at each iteration  $k$ . In other words, the sampler  $\pi_{\phi_k}$  is trained to maximize the difference in  $\mathcal{L}_{\mathrm{VLB}}$  before and after updating the diffusion model at gradient step  $k$  using the sampled timestep  $t$ :
+
+$$
+\phi_ {k} = \arg \max  _ {\phi_ {k}} \mathbb {E} _ {x _ {0}, \epsilon , t \sim \pi_ {\phi_ {k}} (\cdot | x _ {0})} \left[ \Delta_ {k} ^ {t} \right], \quad \text {w h e r e} \tag {12}
+$$
+
+$$
+\Delta_ {k} ^ {t} = \frac {1}{T} \sum_ {\tau = 1} ^ {T} \delta_ {k, \tau} ^ {t} = \frac {1}{T} \sum_ {\tau = 1} ^ {T} \mathcal {L} _ {\tau} (\theta_ {k}) - \mathcal {L} _ {\tau} (\theta_ {k} - \gamma \nabla_ {\theta_ {k}} \mathcal {L} _ {t}).
+$$
+
+With such an optimized  $\phi_{k}$ , the diffusion model utilizing the sampler  $\pi_{\phi_k}$  would be able to adaptively select the best timesteps throughout the training process, minimizing  $\mathcal{L}_{\mathrm{VLB}}$  after the update  $\theta_{k}$ . In practice, we also include entropy regularization for the sampler  $\pi_{\phi}$  in  $\Delta_k^t$  to avoid premature convergence.
+
+Look-ahead challenge Evaluating  $\mathcal{L}_{\tau}(\theta_k - \gamma \nabla_{\theta_k}\mathcal{L}_t)$  requires computing how  $\theta$  changes after the update, which inherently involves a look-ahead process across different  $ts$ , making it computationally infeasible. To develop a practical algorithm, we opt for a single gradient update of  $\phi_k$ , using the last update of  $\theta$  as a reference. By applying the likelihood ratio gradient, we use the following update for  $\phi_k$ :
+
+$$
+\phi_ {k + 1} = \phi_ {k} + \gamma \cdot \Delta_ {k} ^ {t} \cdot \nabla_ {\phi_ {k}} \log \pi_ {\phi_ {k}} (\cdot | x _ {0}), \tag {13}
+$$
+
+Algorithm 1 Training DM with Timestep Sampler  
+Parameter:  $\epsilon_{\theta},\pi_{\phi}$    
+1: for gradient step  $k$  do   
+2:  $x_0\sim q(x_0),\epsilon \sim \mathcal{N}(0,I)$    
+3:  $a,b\sim \pi_{\phi_k}(\cdot |x_0),t\sim \mathrm{Beta}(a,b)$    
+4:  $x_{t} = \sqrt{\bar{\alpha}_{t}} x_{0} + \sqrt{1 - \bar{\alpha}_{t}}\epsilon$    
+5:  $\theta_{k + 1} = \theta_k - \gamma \cdot \nabla_{\theta_k}\| \epsilon -\epsilon_{\theta_k}(x_t,t)\| ^2$    
+6: if  $k$  mod  $f_{S} = 0$  then   
+7:  $\tilde{\Delta}_k^t =$  approximate  $\Delta_k^t$  with Algorithm 2   
+8:  $\phi_{k + 1} = \phi_k + \gamma \cdot \tilde{\Delta}_k^t\nabla_{\phi_k}\log \pi_{\phi_k}(a,b|x_0)$    
+9: end if   
+10: end for
+
+Algorithm 2 Approximation of  $\Delta_k^t$  
+Input:  $\theta_{k},\theta_{k + 1}$    
+Initialize: fixed-size queue  $Q$    
+1: Sample one  $x_0$  randomly from dataset   
+2: Calculate  $\{\delta_{k,\tau}^{t}\}_{\tau = 1}^{T}$  for the sampled  $x_0$    
+3: Push  $\{\delta_{k,\tau}^{t}\}_{\tau = 1}^{T}$  into queue  $Q$    
+4: if  $|Q| > 1$  then   
+5: Determine the set of timesteps  $S$  using a feature selec tion method with queue  $Q$    
+6: end if   
+7: return  $\tilde{\Delta}_k^t = \frac{1}{|S|}\sum_{\tau \in S}\delta_{k,\tau}^t$  for  $x_0s$  in current mini-batch
+
+where we use the identity  $\nabla_{\phi}\pi_{\phi} = \pi_{\phi}\cdot \nabla_{\phi}\log \pi_{\phi}$ . This is a stochastic approximation using sampled  $\epsilon$  and the Beta distribution parameters  $a$  and  $b$ . Algorithm 1 outlines the training procedure based on this gradient update for  $\phi_{k}$ . Note that  $c_{t}$  is not explicitly included in the algorithm, as it can be effectively subsumed into the sampler  $\pi_{\phi}$  if needed.
+
+# 5.2. Approximation of  $\Delta_k^t$
+
+Even with the reduced computation offered by the surrogate algorithm described above, evaluating  $\Delta_k^t$  still requires calculating the exact objective  $\mathcal{L}_{\mathrm{VLB}}$  before and after updating  $\theta_{k}$ , i.e.,  $\Delta_k^t = \mathcal{L}_{\mathrm{VLB}}(\theta_k) - \mathcal{L}_{\mathrm{VLB}}(\theta_{k + 1})$ . Fortunately, by leveraging the correlation between the losses of nearby timesteps, we can accurately approximate  $\Delta_k^t$  using a small set of timesteps  $S\subset \{t\}_{t = 1}^{T}$ , i.e.,
+
+$$
+\Delta_ {k} ^ {t} \approx \tilde {\Delta} _ {k} ^ {t} = \frac {1}{| S |} \sum_ {\tau \in S} \delta_ {k, \tau} ^ {t} = \frac {1}{| S |} \sum_ {\tau \in S} \mathcal {L} _ {\tau} \left(\theta_ {k}\right) - \mathcal {L} _ {\tau} \left(\theta_ {k + 1}\right). \tag {14}
+$$
+
+To determine  $S$ , for each  $k$ , we calculate  $\{\delta_{k,\tau}^t\}_{\tau = 1}^T$  for a single  $x_0$  and store these values in a queue. Using any off-the-shelf feature selection algorithm, we then identify the top  $|S|$  timesteps that best explain  $\Delta_k^t$  based on the data from the queue, with  $|S|$  being a hyperparameter. We mainly used a very small subset  $|S| = 3$  to approximate  $\Delta_k^t$ . Later through experiments, we demonstrate that this
+
+<table><tr><td></td><td colspan="5">Linear</td><td colspan="3">Cosine</td><td colspan="4">Quadratic</td></tr><tr><td></td><td>0.2M</td><td>0.4M</td><td>0.6M</td><td>0.8M</td><td>1.0M</td><td>0.2M</td><td>0.4M</td><td>0.6M</td><td>0.2M</td><td>0.4M</td><td>0.6M</td><td>0.8M</td></tr><tr><td>DDPM [14]</td><td>8.16</td><td>6.03</td><td>5.37</td><td>4.28</td><td>3.19</td><td>3.74</td><td>3.14</td><td>3.14</td><td>4.04</td><td>4.32</td><td>3.01</td><td>3.01</td></tr><tr><td>P2 [7]</td><td>6.45</td><td>5.21</td><td>4.83</td><td>4.70</td><td>4.70</td><td>5.64</td><td>5.21</td><td>5.04</td><td>4.93</td><td>4.06</td><td>3.74</td><td>3.66</td></tr><tr><td>Min-SNR [11]</td><td>4.40</td><td>3.51</td><td>3.28</td><td>3.16</td><td>3.16</td><td>3.51</td><td>3.07</td><td>3.07</td><td>4.76</td><td>4.17</td><td>4.17</td><td>4.17</td></tr><tr><td>Log-normal [17]</td><td>5.38</td><td>4.36</td><td>3.92</td><td>3.60</td><td>3.60</td><td>4.55</td><td>3.89</td><td>3.78</td><td>4.78</td><td>3.81</td><td>3.61</td><td>3.51</td></tr><tr><td>SpeeD [31]</td><td>4.08</td><td>3.66</td><td>3.57</td><td>3.57</td><td>3.57</td><td>4.12</td><td>3.57</td><td>3.57</td><td>3.99</td><td>3.54</td><td>3.52</td><td>3.52</td></tr><tr><td>Ours</td><td>3.99</td><td>3.21</td><td>3.10</td><td>2.94</td><td>2.94</td><td>3.87</td><td>3.06</td><td>3.00</td><td>3.96</td><td>3.07</td><td>2.95</td><td>2.95</td></tr></table>
+
+Table 1. Performance (FID) comparison on the CIFAR-10 dataset across different acceleration methods utilizing Linear, Cosine, and Quadratic schedules. We reported the lowest FID score achieved for each training duration. The algorithm achieving the lowest FID score is highlighted in bold.  
+
+<table><tr><td></td><td>100 epochs</td><td>300 epochs</td></tr><tr><td>LDM</td><td>12.87</td><td>8.72</td></tr><tr><td>P2</td><td>10.69</td><td>6.88</td></tr><tr><td>Min-SNR</td><td>10.87</td><td>6.83</td></tr><tr><td>Log-normal</td><td>12.81</td><td>7.28</td></tr><tr><td>SpeeD</td><td>14.40</td><td>7.98</td></tr><tr><td>Ours</td><td>10.94</td><td>6.62</td></tr></table>
+
+Table 2. Performance (FID) comparison on the CelebA-HQ  $256 \times$  256 dataset across different acceleration methods. The algorithm achieving the lowest FID score is highlighted in bold.
+
+small subset is sufficient for achieving strong performance with respect to wall-clock time (Fig. 7).
+
+The process of approximating  $\Delta_k^t$  using this feature selection approach is described in Algorithm 2. Note in practice, we further reduce the computational burden by updating  $\phi$  only once per  $f_{S}$  gradient iterations of the diffusion model. The overall structure of our algorithms is in Fig. 3. The computational overhead introduced by the proposed timestep sampling mechanism is in Appendix Sec. 9.
+
+# 6. Experiments
+
+In all experiments, we trained each diffusion architecture with its official implementation. Simultaneously, the timestep sampler  $\pi_{\phi}$  was trained using  $\Delta_k^t$ , which approximates the change in  $\mathcal{L}_{\mathrm{VLB}}$  before and after updating the diffusion model. We begin by evaluating the effectiveness of our learning method in comparison to heuristic approaches in Sec. 6.1. Then we assess the compatibility of our model with heuristic approaches in Sec. 6.2. Finally, we present additional analyses to further support our method in Sec. 6.3.
+
+Experimental Setup Frechet Inception Distance (FID) [13] is used to evaluate both the fidelity and coverage of
+
+generated images. We mainly used a machine equipped with NVIDIA RTX 4090 GPUs to train the models. Detailed hyperparameter values and implementation details can be found in Appendix Sec. 10 and Sec. 11.
+
+# 6.1. Comparison to Heuristic Acceleration Methods
+
+Comparison across various noise schedules To compare our model and other acceleration techniques across various noise schedules, we used the CIFAR-10  $32 \times 32$  dataset [2], utilizing DDPM [14] as the backbone architecture.
+
+Tab. 1 demonstrates that our method, despite its learning-based nature, generally achieves faster convergence and better performance at each iteration compared to heuristic approaches [7, 11, 17, 31]. Moreover, our method demonstrates consistent robustness across different noise schedules. In contrast, while Min-SNR performs the best among heuristic approaches with linear and cosine noise schedules, its performance declines significantly with a quadratic noise schedule. As illustrated in Fig. 5, our method achieves robust performance by adaptively sampling timesteps throughout the training process, whereas heuristic approaches rely on fixed sampling strategies. Furthermore, Fig. 1 shows that our method also achieves faster convergence in terms of wall-clock time compared to heuristic approaches.
+
+Comparison on high resolution images To evaluate the acceleration methods on high-resolution images, we used the CelebA-HQ  $256\times 256$  dataset [16], utilizing LDM [24] as the backbone architecture. Tab. 2 demonstrates that although heuristic methods initially achieve better performance, our learning-based approach surpasses them over time. We also found that P2 performs comparably well in this setting relative to the results in Tab. 1, suggesting that the performance of heuristics can vary across different settings. Visualizations of the generated CelebA-HQ images from our method and baselines are in Appendix Sec. 12.
+
+![](images/cc6ef70acc6871a7dad6abc3028d2647b2ad6a7c3bacaa4baf8b14a300150a98.jpg)  
+Figure 5. Visualization of timestep sampling schemes of our method, Min-SNR, P2, Log-Normal, and SpeeD. For weighting methods (Min-SNR, P2), weights at each timestep are converted to probabilities. The color bar on the right represents the progression of epochs, providing a view of how each scheduling method samples timesteps across the training process.
+
+# 6.2. Compatibility with Heuristic Approaches
+
+In Sec. 6.1, we demonstrated that while our learning-based method initially accelerates more slowly than the heuristic approaches due to its learning-based nature, it ultimately converges to a point with better optimality in later iterations. However, we found that heuristic weighting schemes can be incorporated into our model to achieve faster convergence from the beginning as well. Indeed, heuristic weightings can be regarded as part of the schedule-dependent constant  $c_{t}$ , and can be effectively subsumed into our sampler  $\pi_{\phi}$  (Sec. 5.1). Thus, our sampler can effectively account for the additional weight incorporated into the diffusion loss through heuristic approaches.
+
+To assess the compatibility of our model with heuristic approaches, we trained our model along with Min-SNR weighting on the ImageNet  $256 \times 256$  benchmark [8]. We used the encoder from LDM [24] to convert images of dimensions  $256 \times 256 \times 3$  into latent representations of size  $32 \times 32 \times 4$ . We used U-ViT [5] as our diffusion backbone. Tab. 3 shows that our method with heuristic weighting can achieve faster convergence from the beginning as well, ultimately converging to a lower FID score compared to the baseline.
+
+# 6.3. Analysis
+
+Analysis of non-uniform timestep sampling Fig. 6 (right column) illustrates the timestep distribution sampled by our method when applied to DDPM. Fig. 6 (left, center column) illustrates the variations in gradient variance and diffusion loss observed when training DDPM using  $\mathcal{L}_{\mathrm{VLB}}$  rather than  $\mathcal{L}_{\mathrm{DDPM}}$ , without incorporating our proposed method. Training with  $\mathcal{L}_{\mathrm{VLB}}$  differs from the conventional diffusion training with  $\mathcal{L}_{\mathrm{DDPM}}$  (Fig. 2) in that  $\mathcal{L}_{\mathrm{VLB}}$  weights the losses across timesteps differently using
+
+<table><tr><td></td><td>0.2M</td><td>0.4M</td><td>0.6M</td><td>0.8M</td><td>1.0M</td></tr><tr><td>Min-SNR</td><td>11.5</td><td>6.73</td><td>5.28</td><td>4.80</td><td>4.54</td></tr><tr><td>Min-SNR +Ours</td><td>11.3</td><td>6.59</td><td>5.19</td><td>4.66</td><td>4.33</td></tr></table>
+
+Table 3. Performance (FID) comparison on the ImageNet  $256 \times$  256 dataset between Min-SNR and our method with Min-SNR. The algorithm achieving the lowest FID score is highlighted in bold.  
+
+<table><tr><td></td><td>0.2M</td><td>0.4M</td><td>0.6M</td><td>0.8M</td><td>1.0M</td></tr><tr><td>Variance</td><td>21.3</td><td>16.0</td><td>13.5</td><td>12.1</td><td>11.3</td></tr><tr><td>Ours</td><td>3.99</td><td>3.21</td><td>3.10</td><td>2.94</td><td>2.94</td></tr></table>
+
+Table 4. Performance (FID) comparison on the CIFAR-10 dataset between our method and the approach that samples timesteps proportional to gradient variance. We reported the lowest FID score achieved for each training duration. The algorithm achieving the lowest FID score is highlighted in bold.
+
+$c_{t}$ . Since  $c_{t}$  has larger values at later timesteps, it leads to increased loss and gradient variance at these timesteps, especially with the cosine schedule as shown in Fig. 6.
+
+In Sec. 4, we argued that the number of iterations required for convergence would be proportional to the gradient variance at convergence, assuming independence across timesteps. The timestep sampling distributions shown in the plots support this intuition, with the linear schedule heavily sampling low timesteps and the cosine schedule sampling predominantly from both low and high timesteps. This suggests that the direction that most effectively reduces the original objective,  $\mathcal{L}_{\mathrm{VLB}}$ , somewhat aligns with sampling timesteps that exhibit higher gradient variance. On the other
+
+![](images/d87f1f67d475a349a8be8debe711032c2d19b863e4afb0f328ec2c58c8f95a58.jpg)
+
+![](images/92d89d1bbcd4333ff72411fd5aa7879cec8fd8f71e82eb0d8d44368efbf744bb.jpg)
+
+![](images/14dbc871b3c3469cc75438787daf11ad20de222e40e7514cf89fb4ae766ec2b2.jpg)
+
+![](images/99733aab40dc4d47eb354e4a6ea984f984de37fb839d8150b45ea58438a2f2f1.jpg)  
+Figure 6. (Left, Center) Comparison of gradient variance (top) and diffusion loss (bottom) over timesteps for linear and cosine schedules. The color bar on the right indicates the progression of epochs. Unlike the results presented in Fig. 2, these results are based on training DDPM [14] with  $\mathcal{L}_{\mathrm{VLB}}$  for 20 epochs. (Right) Visualization of our model's timestep distributions over training, with a linear schedule (top) and a cosine schedule (bottom).
+
+![](images/692c07629cfd794e0524019f7e63effa18e59c77749d64d821ba63499a3e7c0e.jpg)
+
+![](images/644b24e135693d85e075de8711f6ba5a2b15775d1ae07593b877cf1fe715eb70.jpg)
+
+![](images/f3fa4342f0fd2dcbe02a8505e2d55152aac6179928b4a362574e589b92777894.jpg)  
+Figure 7. Comparison of FID scores of baseline and our method against relative wall clock time, where 1D represents the time it takes for the baseline to converge.  $|S|$  denotes the number of timesteps used in our model to approximate  $\Delta_k^t$ .
+
+hand, Tab. 4 demonstrates that sampling timesteps in proportion to gradient variance results in poor performance, likely due to the interdependencies among the subproblems  $\mathcal{L}_t$ .
+
+Ablation study on  $|S|$  Fig. 7 illustrates the effect of varying the number of selected timesteps  $|S|$  on the performance of our proposed model. All choices of  $|S|$  show acceleration over the baseline, suggesting that we can approximate  $\Delta_k^t$  using only a small subset of timesteps. We observed that  $|S| = 3$  achieves the best performance in terms of wall clock time. Thus, we primarily used  $|S| = 3$  to approximate  $\Delta_k^t$  throughout our experiments.
+
+# 7. Conclusion
+
+In this paper, we discovered the variations in stochastic gradient variance across different diffusion training timesteps and argued that such variation can potentially lead to slow convergence. However, the strong interdependence of gradients across different timesteps suggests that this insight, on its own, does not directly result in optimal acceleration of diffusion training. To this end, we propose a more direct approach that estimates the impact of gradient updates on the variational lower bound for each timestep and adjusts the sampling frequency to prioritize timesteps that require further optimization. Experimental results demonstrate that our method significantly accelerates the convergence of the diffusion training process compared to previous heuristics, while also exhibiting robust performance across various datasets, scheduling strategies, and diffusion architectures.
+
+Limitations and future work Our learning-based method incurs higher computational costs compared to heuristic approaches, with resource demands increasing significantly in larger problem domains. Furthermore, we have not yet explored the application of our method within the score-based diffusion framework, which combines score-based generative modeling with diffusion probabilistic modeling and shows notable results in image generation tasks [17, 29, 34]. Addressing these limitations in terms of computational efficiency and extending the method's applicability within score-based diffusion models remains a promising direction for future research.
+
+# 8. Acknowledgements
+
+This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2022-II220311, Development of Goal-Oriented Reinforcement Learning Techniques for Contact-Rich Robotic Manipulation of Everyday Objects, No. RS-2024-00457882, AI Research Hub Project, and No. RS-2019-II190079, Artificial Intelligence Graduate School Program (Korea University)), the IITP(Institute of Information & Coucommunications Technology Planning & Evaluation)-ITRC(Information Technology Research Center)(IITP-2024-RS-2024-00436857) grant funded by the Korea government (Ministry of Science and ICT), the NRF (RS-2024-00451162) funded by the Ministry of Science and ICT, Korea, BK21 Four project of the National Research Foundation of Korea, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(RS-2025-00560367).
+
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+and editing with text-guided diffusion models. arXiv preprint arXiv:2112.10741, 2021. 1  
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+![](images/c5805fb244e757f2af892bb1e2a5b92fe3380343986226bc6a3e68637f852e77.jpg)
+
+# Adaptive Parameter Selection for Tuning Vision-Language Models
+
+Yi Zhang $^{1*}$  Yi-Xuan Deng $^{3}$  Meng-Hao Guo $^{2}$  Shi-Min Hu $^{2\dagger}$
+
+$^{1}$ State Key Laboratory of Virtual Reality Technology and Systems, SCSE, Beihang University  $^{2}$ BNRist, Department of Computer Science and Technology, Tsinghua University  $^{3}$ Zhili College, Tsinghua University
+
+# Abstract
+
+Vision-language models (VLMs) like CLIP have been widely used in various specific tasks. Parameter-efficient fine-tuning (PEFT) methods, such as prompt and adapter tuning, have become key techniques for adapting these models to specific domains. However, existing approaches rely on prior knowledge to manually identify the locations requiring fine-tuning. Adaptively selecting which parameters in VLMs should be tuned remains unexplored. In this paper, we propose CLIP with Adaptive Selective Tuning (CLIP-AST), which can be used to automatically select critical parameters in VLMs for fine-tuning for specific tasks. It opportunely leverages the adaptive learning rate in the optimizer and improves model performance without extra parameter overhead. We conduct extensive experiments on 13 benchmarks, such as ImageNet, Food101, Flowers102, etc, with different settings, including few-shot learning, base-to-novel class generalization, and out-of-distribution. The results show that CLIP-AST consistently outperforms the original CLIP model as well as its variants and achieves state-of-the-art (SOTA) performance in all cases. For example, with the 16-shot learning, CLIP-AST surpasses GraphAdapter and PromptSRC by  $3.56\%$  and  $2.20\%$  in average accuracy on 11 datasets, respectively. Code will be publicly available.
+
+# 1. Introduction
+
+With the rise of large-scale image-text pretraining, vision-language models (VLMs) [8, 29, 38, 44, 45, 54] have shown strong capabilities in multimodal representation. These models learn the distribution between visual and textual features by jointly training on large-scale image and text paired data, which enables them to perform well across specific tasks. For example, CLIP [38], trained with hundreds of
+
+![](images/358210848e0670062756819ff42dfeb77ba6f70cbd45efa2cef7617f3b23c181.jpg)  
+Figure 1. Comparison of fine-tuning methods across key dimensions. Prompt tuning and adapter tuning rely on prior knowledge to define positions for fine-tuning. In contrast, our method performs adaptive selective tuning. It automatically identifies the most critical positions for tuning. Additionally, no extra parameters are introduced, improving efficiency and performance.
+
+millions of image-text pairs using the contrastive learning framework, aligns image and text representations in a high-dimensional feature space, which gives CLIP strong generalization capabilities and makes it widely used in various applications [7, 10, 24, 43, 47, 51, 56, 58, 61].
+
+While CLIP has shown strong general capabilities, its performance often remains suboptimal on specific tasks without task-oriented fine-tuning. However, performing full fine-tuning on large pre-trained models often introduces challenges, including increased computational cost, potential overfitting, and reduced transferability across diverse tasks and domains. Parameter-efficient fine-tuning (PEFT) [2, 4, 15, 27] has been widely adopted to mitigate the computational cost and overfitting risks associated with the full fine-tuning of large pre-trained models.
+
+Although PEFT reduces computational costs and improves results, most existing methods rely on prior knowledge to decide which model components to fine-tune. These methods typically introduce specialized learnable modules at predefined positions in the model. For example, prompt
+
+tuning [41, 59, 60] incorporates learnable prompt vectors at the input layer or specific transformer layers of CLIP, guiding the model's representation learning. In contrast, adapter tuning [15, 32, 37, 46] inserts additional lightweight modules within the transformer layers or at the final layer of CLIP to adapt to new tasks. However, these methods rely on the manual selection of model locations for finetuning, which can be suboptimal and often results in extra parameter overhead. Automatically selecting and finetuning the most critical parameters remains underexplored. Accurately selecting critical parameters can effectively address these limitations, thereby enhancing model performance without extra parameter costs.
+
+To tackle this challenge, as illustrated in Fig. 1, we propose CLIP with Adaptive Selective Tuning (CLIP-AST), which aims to automatically select and fine-tune the most important parameters in CLIP without inserting extra learnable modules. CLIP-AST leverages the adaptive learning rate feature of the AdamW optimizer [28], where the effective learning rate of a parameter is inversely proportional to the second-moment estimate of its gradients. Parameters with lower second-moment estimates receive higher effective learning rates, allowing them to adapt quickly to new tasks. Conversely, parameters with higher second-moment estimates receive smaller updates, preventing large adjustments due to noisy gradients. By utilizing this property, we use second-moment estimates as importance scores to select and fine-tune the most critical parameters for the task.
+
+Building on the dynamic learning rate property in the optimizer, CLIP-AST introduces adaptive selective fine-tuning. For each transformer layer, we rank the parameters based on importance scores and fine-tune the top  $K$  most important ones while freezing the others. This adaptive selective fine-tuning preserves the knowledge of the pretrained model. It enhances task-specific adaptation without extra parameters during training and inference.
+
+The main contributions are as follows:
+
+- We propose CLIP-AST, a novel method that automatically selects and fine-tunes the most critical parameters in CLIP without extra parameters, thus maintaining the same inference efficiency as the original CLIP model.  
+- We introduce an automatic parameter identification strategy based on AdamW's adaptive learning rates to select important parameters with lower second-moment estimates of the gradient.  
+- Extensive experiments on 13 benchmark datasets demonstrate that CLIP-AST consistently outperforms the original CLIP and its variants, achieving state-of-the-art performance.
+
+# 2. Related Work
+
+Vision-Language Models. Vision-Language Models (VLMs) [18, 29, 38, 44, 54] aim to efficiently handle
+
+cross-modal tasks by jointly learning visual and linguistic information. Some methods, such as CLIP [38] and ALIGN [18], utilize hundreds of millions or even billions of image-text pairs for training to bridge the gap between visual and textual data. The vast amount of training data enables VLMs to exhibit exceptional capabilities. Among these models, the most representative is the CLIP model, which employs contrastive learning to map images and texts into the same feature space, thereby achieving efficient zero-shot learning. Due to its powerful cross-modal and zero-shot capabilities, CLIP has been widely used in various downstream tasks [10, 25, 30, 36, 43, 48, 51, 56, 58]. However, a gap exists between most downstream tasks and the original CLIP model, necessitating fine-tuning for effective transfer. Therefore, this work investigates the fine-tuning of CLIP, allowing CLIP to be effectively adapted to specific domains while maintaining its strong performance.
+
+Parameter-Efficient Fine-Tuning for VLMs. Recently, with the rapid development of parameter-efficient fine-tuning (PEFT) [15, 16, 27] in the field of NLP, it has become a common paradigm for fine-tuning VLMs. Common PEFT methods include adapters [4, 11, 15, 22, 32, 37, 46], which introduce additional lightweight trainable module, as well as prompt tuning [19, 59, 60], which optimizes input prompts. In the context of applying PEFT to VLMs, CoOp [60] modifies the static text encoder prompts in the original CLIP model into adaptable, trainable vectors. TipAdapter [55] develops a key-value caching mechanism to facilitate efficient knowledge retrieval. PromptSRC [21] implements a self-regulation technique to mitigate overfitting. MMA [52] introduces a multimodal adapter to enhance the alignment between text and visual representations. Unlike previous methods, which choose the fine-tuning locations based on prior knowledge, we automatically find the important parameters in the original model that need to be trained and complete the fine-tuning of the model.
+
+Selective Fine-tuning. Unlike approaches that retrain all model weights or add new trainable modules, selective fine-tuning [12, 40, 53, 57] focuses on training specific parameters within the model to achieve fine-tuning. A notable example is linear probing [3, 13, 38], where only the model's last layer is trained. However, restricting training to the last layer often yields suboptimal results. BitFit [53] introduces bias-only fine-tuning, which adjusts only the bias parameters (or a subset of them), keeping the rest of the model parameters fixed. These methods, however, rely on empirical insights or observations to select parameters for training, like the previous PEFT methods for VLMs. In contrast, BSR [40] introduces a systematic selective fine-tuning approach that identifies critical layers by comparing outputs from pre-trained and fine-tuned models. Layers showing significant output changes are prioritized for
+
+![](images/26bfb40258aa1182bab0a7de42800e1785e477746da1d2eb0155158fa53bf9ce.jpg)  
+Figure 2. Overview of the proposed CLIP-AST pipeline, consisting of (a) transformer fine-tuning and (b) (c) adaptive selective fine-tuning stages. In (a), we fine-tune the transformer layers of both visual and text encoders to extract parameter importance scores. (b) illustrates the process of ranking sub-layer parameters using importance scores, followed by the adaptive selection of the top  $K$  sub-layers. (c) shows the selective fine-tuning process where only the most important sub-layers are updated while other components remain frozen, enhancing efficiency without compromising model performance.
+
+fine-tuning based on task adaptability. SPT [12] takes a data-driven approach by computing parameter sensitivity on downstream tasks. It identifies the most impactful parameters and employs structured fine-tuning methods (e.g., LoRA or Adapter) rather than direct adjustments. Despite these advances, adaptive selective fine-tuning for CLIP remains relatively unexplored. This work addresses this gap by introducing an automated method for identifying the modules in CLIP that benefit most from fine-tuning, advancing the efficiency and effectiveness of fine-tuning for vision-language models.
+
+# 3. Method
+
+As illustrated in Fig. 2, CLIP-AST includes two stages: transformer fine-tuning and adaptive selective fine-tuning. Initially, we fine-tune the pre-trained layers of the transformer to extract importance scores from the optimizer. The optimizer measures the importance of parameters by estimating the second-order moments of the gradients in each transformer layer, as described in Sec. 3.1. After a few iterations, these scores are ranked to select the parameters requiring training, as specified in Sec. 3.2. Then, the important parameters in each layer of the transformer are fine
+
+tuned to complete the fine-tuning of CLIP.
+
+# 3.1. Transformer Fine-Tuning
+
+To assess the importance of all the parameters of the transformer layer in the pre-trained CLIP model, as shown in Fig. 2 (a), we first fine-tune the CLIP transformer block. The CLIP model includes a visual encoder  $\mathrm{E_v}$  and a textual encoder  $\mathrm{E_t}$ , both responsible for mapping images and text into a unified feature space. This design facilitates the interaction of features across different modalities. During the fine-tuning of CLIP's transformer, we first sampled a batch of training data from the dataset, which included N images  $\mathbf{X} \in \mathbb{R}^{N \times 3 \times H \times W}$ , corresponding labels  $\mathbf{Y} \in \mathbb{R}^N$ , and the names of  $C$  classes  $\mathbf{T} = \{\mathbf{T}_k\}, k \in \{1, \dots, C\}$  in the dataset. Subsequently, the visual encoder  $\mathrm{E_v}$  extracts visual embeddings  $\mathbf{G} \in \mathbb{R}^{N \times D}$  from the  $\mathbf{X}$ :
+
+$$
+\begin{array}{l} [ \mathbf {G} _ {\mathbf {0}}, \mathbf {I} _ {\mathbf {0}} ] = \operatorname {P a t c h E m b e d d i n g} (\mathbf {X}), \\ [ \mathbf {G} _ {\mathbf {L}}, \mathbf {I} _ {\mathbf {L}} ] = \operatorname {T r a n s f o r m e r} ([ \mathbf {G} _ {\mathbf {0}}, \mathbf {I} _ {\mathbf {0}} ]), \tag {1} \\ [ \mathbf {G}, \mathbf {I} ] = \operatorname {V i s u a l P r o j} ([ \mathbf {G} _ {\mathbf {L}}, \mathbf {I} _ {\mathbf {L}} ]), \\ \end{array}
+$$
+
+where  $\mathbf{G}_0$  and  $\mathbf{I}_0$  represent the initial global and visual embeddings generated by the PatchEmbedding block from the input visual  $\mathbf{X}$ . The Transformer block processes these
+
+embeddings through multiple layers to refine the features, resulting in  $\mathbf{G}_{\mathbf{L}}$  and  $\mathbf{I}_{\mathbf{L}}$ , which are the final global and visual embeddings at the last layer. Finally, the VisualProj block projects these embeddings onto a feature space, producing  $\mathbf{G}$  and  $\mathbf{I}$  as the final visual embeddings.
+
+For the text encoder  $\mathrm{E_t}$ , the class names  $T$  are combined with a predefined template (e.g., "a photo of [CLASS]") to generate class descriptions  $\mathbf{T}_{\mathbf{p}}$ . Then, each class description is sent to the text encoder to obtain the corresponding class embeddings  $\mathbf{W} \in \mathbb{R}^{C \times D}$ :
+
+$$
+\mathbf {W _ {0}} = \operatorname {T e x t E m b e d d i n g} (\mathbf {T _ {p}}),
+$$
+
+$$
+\mathbf {W} _ {\mathbf {L}} = \operatorname {T r a n s f o r m e r} \left(\mathbf {W} _ {\mathbf {0}}\right), \tag {2}
+$$
+
+$$
+\mathbf {W} = \operatorname {T e x t P r o j} \left(\mathbf {W} _ {\mathbf {L}}\right).
+$$
+
+Here,  $\mathbf{W}_0$  represents the initial text embeddings generated by the TextEmbedding layer. In contrast,  $\mathbf{W}_{\mathbf{L}}$  is the feature produced by passing  $\mathbf{W}_0$  through multiple layers of the transformer, extracting semantic information further at each layer. Finally, TextProj projects the text features into a unified feature space, producing  $\mathbf{W}$  as the final text embedding that aligns with the visual features.
+
+After obtaining the  $\mathbf{G}$  and  $\mathbf{W}$ , we first calculate the probability  $\hat{y}_{i,j}$  of each image being predicted for each class and then calculate the loss function with the label:
+
+$$
+\hat {y} _ {i, j} = \frac {\exp (\sin (\mathbf {G} _ {i} , \mathbf {W} _ {j}) / \tau)}{\sum_ {k = 1} ^ {c} \exp (\sin (\mathbf {G} _ {i} , \mathbf {W} _ {k}) / \tau)},
+$$
+
+$$
+\mathcal {L} _ {\mathrm {C E}} = - \frac {1}{N} \sum_ {j = 1} ^ {N} \sum_ {i = 1} ^ {C} y _ {i, j} \log \left(\hat {y} _ {i, j}\right), \tag {3}
+$$
+
+where  $\sin (\cdot ,\cdot)$  represents the cosine similarity function,  $\tau$  is a temperature parameter.
+
+Fine-tuning the transformer requires only a few training iterations. As its name implies, only the transformer part of the two encoders is trainable during the training process. After training, we can obtain parameter importance scores  $v$ , which are embedded within the AdamW optimizer.
+
+# 3.2. Adaptive Selective Fine-tuning
+
+After transformer fine-tuning, we introduce the adaptive selective fine-tuning strategy, which uses the square root of the second-moment estimate of the gradient in the AdamW optimizer [28] as importance scores. The parameter update process in the  $i$ -th iteration of AdamW optimization can be described as follows. First, we compute the gradient  $g_{i}$  with respect to the model parameters  $\theta$ :
+
+$$
+g _ {i} = \nabla_ {\theta} f \left(\theta_ {i - 1}\right). \tag {4}
+$$
+
+Next, we update the first-moment estimate  $m_{i}$  and the second-moment estimate  $v_{i}$ :
+
+$$
+\begin{array}{l} m _ {i} = \beta_ {1} \cdot m _ {i - 1} + (1 - \beta_ {1}) \cdot g _ {i}, \tag {5} \\ v _ {i} = \beta_ {2} \cdot v _ {i - 1} + (1 - \beta_ {2}) \cdot g _ {i} ^ {2}, \\ \end{array}
+$$
+
+where  $\beta_{1}$  and  $\beta_{2}$  are the hyperparameters controlling the exponential decay rates for the moment estimates. To correct the bias introduced in the early stages of optimization, we compute the bias-corrected estimates:
+
+$$
+\hat {m} _ {i} = \frac {m _ {i}}{1 - \beta_ {1} ^ {i}}, \quad \hat {v} _ {i} = \frac {v _ {i}}{1 - \beta_ {2} ^ {i}}. \tag {6}
+$$
+
+The final parameter update rule is then expressed as:
+
+$$
+\theta_ {i} = \left(\theta_ {i - 1} - \alpha \cdot \lambda \cdot \theta_ {i - 1}\right) - \frac {\alpha}{\sqrt {\hat {v} _ {i}} + \epsilon} \cdot \hat {m} _ {i}, \tag {7}
+$$
+
+where  $\alpha$  denotes the learning rate,  $\lambda$  represents the weight decay coefficient that controls the strength of regularization applied to the model parameters, and  $\epsilon$  is a small constant added for numerical stability to prevent division by zero.
+
+In our adaptive selective fine-tuning, the importance of each parameter is assessed using the square root of the second-moment estimate of gradient  $\hat{v}_i$ , which has the same dimensionality as the parameter itself. Specifically, we compute the scalar average importance score  $v^{\prime}$  of the transformer layer sub-layer parameter  $i$  as follows:
+
+$$
+v _ {i} ^ {\prime} = \operatorname {A v g} \left(\frac {1}{\sqrt {\hat {v} _ {i}}}\right). \tag {8}
+$$
+
+This score measures the magnitude of parameter updates during training. A higher  $v_{i}^{\prime}$  means the parameter receives larger updates, suggesting it is more actively involved in learning and adapting to the task-specific data. Such parameters will likely capture essential features and contribute significantly to model predictions. Conversely, a lower  $v_{i}^{\prime}$  implies that the parameter receives smaller updates, possibly because it requires less adjustment or is less sensitive to the current data.
+
+By focusing on parameters with higher importance scores, we can adaptively and selectively fine-tune the model, prioritizing the most influential for the specific task. This selective fine-tuning strategy maintains model performance while reducing computational costs, as it concentrates updates on the most critical components without compromising the overall model integrity.
+
+During the adaptive selective fine-tuning, shown in Fig. 2 (b) and (c), we select the most important components at the sub-layer level (e.g., weights or biases of the linear $_q$  layer). For each layer in the transformer module, we select the top  $K$  important parameters of the sub-layer for training while freezing all others. This adaptive selective fine-tuning strategy enhances the efficiency and effectiveness of the model, allowing for focused updates that improve task-specific adaptation without compromising overall model integrity.
+
+# 3.3. Loss Function
+
+We utilize the self-consistency loss (SCL) [21] to mitigate overfitting during selective fine-tuning. SCL employs an additional frozen CLIP model to extract original visual embeddings  $\tilde{\mathbf{G}}$  and textual embeddings  $\tilde{\mathbf{W}}$  from the training data. By using an L1 loss, SCL enforces consistency between the features produced by the frozen model and the features produced by the fine-tuned model:
+
+$$
+\mathcal {L} _ {\mathrm {S C L - i m a g e}} = \sum_ {i = 1} ^ {d} | \tilde {\mathbf {G}} - \mathbf {G} |, \tag {9}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {S C L - t e x t}} = \sum_ {i = 1} ^ {d} | \tilde {\mathbf {W}} - \mathbf {W} |.
+$$
+
+In addition, SCL introduces logit-level consistency regularization, further strengthening the constraints and maximizing the alignment of features before and after training. This is achieved by minimizing the Kullback-Leibler divergence to align the trained logit distribution with the logits generated by the frozen CLIP model, as expressed in the following formula:
+
+$$
+\mathcal {L} _ {\mathrm {S C L - l o g i t s}} = \mathcal {D} _ {\mathcal {K L}} (\operatorname {s i m} (\tilde {\mathbf {G}}, \tilde {\mathbf {W}}), \operatorname {s i m} (\mathbf {G}, \mathbf {W})). \tag {10}
+$$
+
+Finally, we incorporate the cross-entropy loss discussed in Sec. 3.1. The total loss our model aims to minimize is a combination of these types of losses, represented by the equation:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {c e}} + \lambda_ {1} \cdot \mathcal {L} _ {\mathrm {S C L - i m a g e}} + \lambda_ {2} \cdot \mathcal {L} _ {\mathrm {S C L - t e x t}} + \lambda_ {3} \cdot \mathcal {L} _ {\mathrm {S C L - l o g i t s}}, \tag {11}
+$$
+
+where  $\lambda_{1},\lambda_{2}$  and  $\lambda_{3}$  are weights that balance the contributions of  $\mathcal{L}_{\mathrm{SCL - image}}$ $\mathcal{L}_{\mathrm{SCL - text}}$  and  $\mathcal{L}_{\mathrm{SCL - logits}}$  , respectively.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Few-shot learning. We aim to evaluate the model's ability to generalize with limited labeled examples in the few-shot learning setting. We simulate a low-shot scenario by providing only a few labeled samples per class, typically 1, 2, 4, 8, 16. In this setting, we use the 11 commonly used classification datasets introduced in Sec. 4.2 to reflect the few-shot tasks in the real world. The performance under this setting is measured by top-1 accuracy.
+
+Base-to-novel class generalization. The base-to-novel class generalization setting evaluates the model's adaptability to novel classes it has not seen during fine-tuning. In this setting, the model is trained on a base set of classes with 16-shot per class and is then tested on novel classes, assessing its capability to transfer knowledge from the base classes to novel, unseen classes. Following the previous work [21, 60], we partition the dataset into base and novel
+
+classes, ensuring no overlap between the two. The metrics include the top-1 accuracy of the base class (Base) and the novel class (Novel), as well as the harmonic mean (HM) of the two.
+
+Out-of-distribution setting. In the out-of-distribution setting, we test the model's robustness against data that differs from the training distribution. This setting aims to assess the model's ability to handle unexpected inputs. We train on ImageNet as an in-distribution dataset and test on out-of-distribution datasets. The performance is evaluated for average accuracy on both in-distribution and out-of-distribution samples.
+
+# 4.2. Datasets
+
+For few-shot learning and base-to-novel class generalization, we conduct experiments on 11 commonly used classification benchmarks, including Caltech101 [9], DTD [5], EuroSAT [14], FGVC Aircraft [31], Flowers102 [33], Food101 [1], ImageNet [6], OxfordPets [34], StanfordCars [23], SUN397 [50], UCF101 [42]. For the out-of-distribution setting, We use ImageNet-Sketch [49] and ImageNetV2 [39] as out-of-distribution datasets.
+
+# 4.3. Implementation details
+
+For the adaptive selective fine-tuning stage, the preprocessing steps during training include randomly cropping the input images, with the crop size ranging from 0.5 to 1.0 times the original image size. The cropped images are then resized to a fixed size of  $224 \times 224$  pixels. Next, each image undergoes horizontal flipping with a probability of 0.5. Finally, each channel of the images is normalized. We use the AdamW optimizer for training. For the few-shot learning and out-of-distribution settings, we train for 30 epochs, and for the base-to-novel class generalization setting, we train for 20 epochs. To ensure a fair comparison, we follow previous methods [21, 52] and use the ViT-B/16 CLIP model. For the transformer fine-tuning stage, we train for 1 epoch, with other settings being the same as adaptive selective fine-tuning. All experiments are implemented using the Jittor [17] and PyTorch [35] frameworks.
+
+# 4.4. Comparison with State-of-the-art
+
+Few-shot learning. In this setting, we benchmark CLIP-AST against state-of-the-art (SOTA) few-shot learning methods, including CoOp [60], Tip-Adapter [55], PromptSRC [21], and GraphAdapter [26]. As shown in Tab. 1, CLIP-AST consistently achieves the highest average accuracy across the ImageNet dataset as the shot count increases, demonstrating that our proposed method is on par with, or even surpasses, previously introduced methods such as prompt tuning and adapters. To further clarify the comparison, we present the overall and detailed results for 11 datasets at varying shot levels in Fig. 3. Notably, CLIP-
+
+![](images/481df7a03aa1fc1694dfcc4b6bf7f071358851d1489b041ae7a95ec389e52951.jpg)
+
+![](images/a7c56c7d3ea38bd8b76f142fc62a805ba6b83f56854d10ed06a568bc2a7b6599.jpg)
+
+![](images/3bcf8dcc5989bfab30f6df6096498b68177fa50a2d2642559224abcfb472f018.jpg)
+
+![](images/7a49bfc259f747554d52e56a335e65ab7ecdc59ea483c89cbc85a25977302d4d.jpg)
+
+![](images/bb254d56a71e21ed36e5b2806042d9a1eb064a106507548196750ba4d5c230f8.jpg)
+
+![](images/9709a07453b2ce56b30489f186fd4091857b7657c308a01abf2175df05fdb7a3.jpg)
+
+![](images/6d25450eadfa80fe1571777fc7ec856de772bb5cd644dd8380348196b9b47b88.jpg)
+
+![](images/403fbddf990e2824b24ef30b11ba409058102275911c6df61dc3dd8962324db9.jpg)
+
+![](images/cb20e67dc552fcbad98c2038171c2da09a78ff856b90afea4f8c95d5f92852ce.jpg)  
+Figure 3. Comparison with previous SOTA across 11 datasets under 1, 2, 4, 8, and 16-shot settings demonstrates that our approach consistently outperforms existing methods, setting a new SOTA.
+
+![](images/762149bd283e0e3bb660dd5afcd7837dc12c5bf614890836ad168d3b4363f848.jpg)
+
+![](images/c210fd05523c9cca76a527ca3ebf4e4aa4ceca49f656a3622baceb504ec79bd5.jpg)
+
+![](images/ccbf6db553a6d07f679e29e46a0247699536fbda4a1002dcbf6f3caa1b9e3551.jpg)
+
+AST achieves an average accuracy improvement of  $2.21\%$  over the SOTA across 11 datasets. Across all datasets, our method outperforms previous SOTA approaches, with particularly substantial improvements on certain datasets. For instance, on FGVC Aircraft, CLIP-AST achieves approximately  $10\%$  higher accuracy with 16-shot, surpassing other methods such as PromptSRC and CoOp, which are specifically designed for prompt optimization. Moreover, as the sample count increases, the performance advantage of our model over prior methods also becomes more obvious. The consistent progress achieved by CLIP-AST on different levels under different samples demonstrates that our proposed fine-tuning method is a simple yet highly effective strategy in the few-shot learning setting.
+
+Base-to-novel class generalization. In this setting, we evaluate the ability of CLIP-AST to generalize from base to novel classes by comparing it with state-of-the-art methods in Tab. 2, where CLIP-AST consistently performs favorably in both base and novel class recognition tasks. CLIP-AST achieves the highest harmonic mean (HM) across multiple datasets, indicating robust performance in both base and novel classes. For example, on the EuroSAT dataset, our method achieves an HM improvement of approximately  $4.37\%$  compared to MMA. This demonstrates the capability of CLIP-AST to generalize from base to novel classes.
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">Number of Shot</td></tr><tr><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td></tr><tr><td>CLIP [38]</td><td colspan="5">Zero-shot 66.92</td></tr><tr><td>CoOp [60]</td><td>66.33</td><td>67.07</td><td>68.73</td><td>70.63</td><td>71.87</td></tr><tr><td>CoCoOp [59]</td><td>69.43</td><td>69.78</td><td>70.39</td><td>70.63</td><td>70.83</td></tr><tr><td>Tip-Adapter [55]</td><td>67.55</td><td>68.58</td><td>69.82</td><td>71.42</td><td>73.28</td></tr><tr><td>PromptSRC [21]</td><td>68.13</td><td>69.77</td><td>71.07</td><td>72.33</td><td>73.17</td></tr><tr><td>GraphAdapter [26]</td><td>69.80</td><td>70.50</td><td>71.40</td><td>71.40</td><td>73.40</td></tr><tr><td>CLIP-AST (Ours)</td><td>70.29</td><td>71.13</td><td>71.81</td><td>72.90</td><td>73.91</td></tr></table>
+
+Table 1. Compared with the previous SOTA methods in the ImageNet dataset with the few-shot learning setting.
+
+ity of CLIP-AST to maintain high accuracy across varying class distributions without overfitting to base classes. Our results illustrate that selective fine-tuning in a base-to-new setting allows CLIP-AST to balance learning across class distributions effectively. By avoiding overfitting to base classes, our approach maintains strong generalization to novel classes. The gains across both base and novel categories prove that CLIP-AST can manage the trade-off between base and novel class performance.
+
+Out-of-distribution setting. In this setting, we assess the out-of-distribution robustness of CLIP-AST by comparing it with leading methods in Tab. 3. CLIP-AST achieves su
+
+<table><tr><td>Dataset</td><td></td><td>CLIP [38]</td><td>CoCoOp [59]</td><td>MaPLe [20]</td><td>PromptSRC [21]</td><td>MMA [52]</td><td>CLIP-AST (Ours)</td></tr><tr><td rowspan="3">Average</td><td>Base</td><td>69.34</td><td>80.47</td><td>82.28</td><td>84.26</td><td>83.20</td><td>85.94</td></tr><tr><td>Novel</td><td>74.22</td><td>71.69</td><td>75.14</td><td>76.10</td><td>76.80</td><td>76.99</td></tr><tr><td>HM</td><td>71.70</td><td>75.83</td><td>78.55</td><td>79.97</td><td>79.87</td><td>81.06</td></tr><tr><td rowspan="3">Caltech101</td><td>Base</td><td>96.84</td><td>97.96</td><td>97.74</td><td>98.10</td><td>98.40</td><td>98.71</td></tr><tr><td>Novel</td><td>94.00</td><td>93.81</td><td>94.36</td><td>94.03</td><td>94.00</td><td>94.00</td></tr><tr><td>HM</td><td>95.40</td><td>95.84</td><td>96.02</td><td>96.02</td><td>96.15</td><td>96.30</td></tr><tr><td rowspan="3">DTD</td><td>Base</td><td>53.24</td><td>77.01</td><td>80.36</td><td>83.37</td><td>83.20</td><td>84.03</td></tr><tr><td>Novel</td><td>59.90</td><td>56.00</td><td>59.18</td><td>62.97</td><td>65.63</td><td>65.34</td></tr><tr><td>HM</td><td>56.37</td><td>64.85</td><td>68.16</td><td>71.75</td><td>73.38</td><td>73.52</td></tr><tr><td rowspan="3">EuroSAT</td><td>Base</td><td>56.48</td><td>87.49</td><td>94.07</td><td>92.90</td><td>85.46</td><td>95.90</td></tr><tr><td>Novel</td><td>64.05</td><td>60.04</td><td>73.23</td><td>73.90</td><td>82.34</td><td>81.72</td></tr><tr><td>HM</td><td>60.03</td><td>71.21</td><td>82.35</td><td>82.32</td><td>83.87</td><td>88.24</td></tr><tr><td rowspan="3">FGVC Aircraft</td><td>Base</td><td>27.19</td><td>33.41</td><td>37.44</td><td>42.73</td><td>40.57</td><td>48.98</td></tr><tr><td>Novel</td><td>36.29</td><td>23.71</td><td>35.61</td><td>37.87</td><td>36.33</td><td>38.21</td></tr><tr><td>HM</td><td>31.09</td><td>27.74</td><td>36.50</td><td>40.15</td><td>38.33</td><td>42.93</td></tr><tr><td rowspan="3">Flowers102</td><td>Base</td><td>72.08</td><td>94.87</td><td>95.92</td><td>98.07</td><td>97.77</td><td>97.91</td></tr><tr><td>Novel</td><td>77.80</td><td>71.75</td><td>72.46</td><td>76.50</td><td>75.93</td><td>77.73</td></tr><tr><td>HM</td><td>74.83</td><td>81.71</td><td>82.56</td><td>85.95</td><td>85.48</td><td>86.66</td></tr><tr><td rowspan="3">Food101</td><td>Base</td><td>90.10</td><td>90.70</td><td>90.71</td><td>90.67</td><td>90.13</td><td>90.57</td></tr><tr><td>Novel</td><td>91.22</td><td>91.29</td><td>92.05</td><td>91.53</td><td>91.30</td><td>91.11</td></tr><tr><td>HM</td><td>90.66</td><td>90.99</td><td>91.38</td><td>91.10</td><td>90.71</td><td>90.84</td></tr><tr><td rowspan="3">ImageNet</td><td>Base</td><td>72.43</td><td>75.98</td><td>76.66</td><td>77.60</td><td>77.31</td><td>78.44</td></tr><tr><td>Novel</td><td>68.14</td><td>70.43</td><td>70.54</td><td>70.73</td><td>71.00</td><td>70.22</td></tr><tr><td>HM</td><td>70.22</td><td>73.10</td><td>73.47</td><td>74.01</td><td>74.02</td><td>74.10</td></tr><tr><td rowspan="3">OxfordPets</td><td>Base</td><td>91.17</td><td>95.20</td><td>95.43</td><td>95.33</td><td>95.40</td><td>96.23</td></tr><tr><td>Novel</td><td>97.26</td><td>97.69</td><td>97.76</td><td>97.30</td><td>98.07</td><td>97.37</td></tr><tr><td>HM</td><td>94.12</td><td>96.43</td><td>96.58</td><td>96.30</td><td>96.72</td><td>96.80</td></tr><tr><td rowspan="3">Stanford Cars</td><td>Base</td><td>63.37</td><td>70.49</td><td>72.94</td><td>78.27</td><td>78.50</td><td>84.21</td></tr><tr><td>Novel</td><td>74.89</td><td>73.59</td><td>74.00</td><td>74.97</td><td>73.10</td><td>74.05</td></tr><tr><td>HM</td><td>68.65</td><td>72.01</td><td>73.47</td><td>76.58</td><td>75.70</td><td>78.80</td></tr><tr><td rowspan="3">SUN397</td><td>Base</td><td>69.36</td><td>79.74</td><td>80.82</td><td>82.67</td><td>82.27</td><td>83.05</td></tr><tr><td>Novel</td><td>75.35</td><td>76.86</td><td>78.70</td><td>78.47</td><td>78.57</td><td>78.12</td></tr><tr><td>HM</td><td>72.23</td><td>78.27</td><td>79.75</td><td>80.52</td><td>80.38</td><td>80.51</td></tr><tr><td rowspan="3">UCF101</td><td>Base</td><td>70.53</td><td>82.33</td><td>83.00</td><td>87.10</td><td>86.23</td><td>87.38</td></tr><tr><td>Novel</td><td>77.50</td><td>73.45</td><td>78.66</td><td>78.80</td><td>80.03</td><td>79.12</td></tr><tr><td>HM</td><td>73.85</td><td>77.64</td><td>80.77</td><td>82.74</td><td>82.20</td><td>83.05</td></tr></table>
+
+perior performance on both in-distribution (ImageNet) and out-of-distribution target datasets (ImageNet-Sketch and ImageNet-V2). CLIP-AST achieves the highest average accuracy across these datasets, notably achieving a  $2.04\%$  improvement over the next-best method on ImageNet-V2. This robust performance on challenging out-of-distribution tasks highlights the strength of our method for maintaining model generalization beyond the source distribution. These results demonstrate that CLIP-AST can effectively mitigate the domain shift, balancing in-distribution and out-of-distribution accuracy.
+
+# 4.5. Ablation Study
+
+In our ablation study using the few-shot learning setting, we first analyzed our selected approach's training and inference efficiency compared to previous fine-tuning paradigms. Then, we conducted an ablation study across 11 datasets. We extensively evaluated different approaches to selective fine-tuning and then performed a detailed ablation test on the hyperparameters of the CLIP-AST.
+
+Training and inference efficiency analysis. We compare the training and inference efficiency of various methods in Tab. 4. Our method achieves the highest accuracy of  $85.64\%$  while maintaining competitive training and infer
+
+Table 2. Compared with the previous SOTA methods in the baseto-novel class generalization setting, where the model is trained on the base class with 16-shot and evaluated on the base class and novel class.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Source ImageNet</td><td colspan="2">Target</td><td rowspan="2">Avg Acc(%)</td></tr><tr><td>-Sketch</td><td>-V2</td></tr><tr><td>CLIP [38]</td><td>66.73</td><td>46.15</td><td>60.83</td><td>57.90</td></tr><tr><td>CoOp [60]</td><td>71.51</td><td>47.99</td><td>64.20</td><td>61.23</td></tr><tr><td>CoCoOp [59]</td><td>71.02</td><td>48.75</td><td>64.07</td><td>61.28</td></tr><tr><td>Tip-Adapter [55]</td><td>73.23</td><td>46.82</td><td>65.01</td><td>61.68</td></tr><tr><td>MaPLe [20]</td><td>70.72</td><td>49.15</td><td>64.07</td><td>61.31</td></tr><tr><td>PromptSRC [21]</td><td>71.27</td><td>49.55</td><td>64.35</td><td>61.72</td></tr><tr><td>MMA [52]</td><td>71.00</td><td>49.13</td><td>64.33</td><td>61.48</td></tr><tr><td>CLIP-AST (Ours)</td><td>73.87</td><td>48.37</td><td>66.37</td><td>62.87</td></tr></table>
+
+Table 3. Compared with the previous SOTA methods in the out-of-distribution setting, where the model is trained on the ImageNet dataset with 16-shot and evaluated on the ImageNet-V2 and ImageNet-Sketch benchmarks.  
+
+<table><tr><td>Method</td><td>Tuning Type</td><td>Train time(s)</td><td>Inference FPS</td><td>Acc(%)</td></tr><tr><td>CLIP [38]</td><td>-</td><td>0</td><td>1323</td><td>66.12</td></tr><tr><td>CoCoOp [59]</td><td>Prompt</td><td>2280</td><td>54</td><td>72.00</td></tr><tr><td>Tip-Adapter [55]</td><td>Adapter</td><td>30</td><td>1280</td><td>83.09</td></tr><tr><td>PromptSRC [21]</td><td>Prompt</td><td>630</td><td>1236</td><td>74.70</td></tr><tr><td>MMA [52]</td><td>Adapter</td><td>135</td><td>1113</td><td>83.60</td></tr><tr><td>CLIP-AST (Ours)</td><td>Adaptive Selection</td><td>100</td><td>1323</td><td>85.64</td></tr></table>
+
+Table 4. Comparison of training time, inference efficiency, and accuracy across different methods. All methods are compared using a single NVIDIA 4090 GPU, trained for 10 epochs on the StanfordCars dataset.
+
+ence efficiency. All methods were trained for 10 epochs on the StanfordCars dataset. Our method requires only 100 seconds of training time, less than needed for prompt tuning methods. The inference speed is also the same as the original CLIP model and faster than both prompt and adapter tuning methods. This indicates that our selective fine-tuning method improves performance and maintains high efficiency during the training and inference stages.
+
+Adaptive selective fine-tuning schemes. Our ablation study, summarized in Tab. 5, evaluates the impact of different selective fine-tuning schemes on model performance. We start with a baseline where neither the image encoder nor the text encoder is fine-tuned, resulting in an average accuracy of  $65.21\%$ . Fine-tuning only the image encoder or only the text encoder using the adaptive selection strategy yields average accuracies of  $84.04\%$  and  $81.95\%$ , respectively, indicating significant contributions from both encoders. Next, We compared BitFit [53], which utilizes a priori fixed selection of bias as a training parameter, and found that the method performs poorly. We also compared the global granularity for adaptive selection, where the top  $K$  important types of sub-layers are trained across the entire transformer, with the layer granularity selection, where the top  $K$  important layers are trained within each layer. These results highlight the effectiveness of finer-grained layer granularity selection.
+
+Hyperparameters in adaptive selection. In Fig. 4, we per
+
+<table><tr><td>Trainable
+Image Encoder</td><td>Trainable
+Text Encoder</td><td>Scheme for
+Selecting Trainable Layers</td><td>Avg Acc(%)</td></tr><tr><td>X</td><td>X</td><td>-</td><td>65.21</td></tr><tr><td>✓</td><td>X</td><td>layer granularity</td><td>84.04</td></tr><tr><td>X</td><td>✓</td><td>layer granularity</td><td>81.95</td></tr><tr><td>✓</td><td>✓</td><td>fixed bias</td><td>79.96</td></tr><tr><td>✓</td><td>✓</td><td>global granularity</td><td>84.25</td></tr><tr><td>✓</td><td>✓</td><td>layer granularity</td><td>85.05</td></tr></table>
+
+Table 5. Ablation of selective fine-tuning schemes. Fixed bias trains the bias parameters, global granularity chooses the most important top  $K$  sub-layers across the model, and layer granularity picks the most important top  $K$  sub-layers within each transformer layer. Avg Acc is the average accuracy across 11 datasets in the few-shot learning setting with 16-shot.
+
+formed an ablation on the hyperparameters of adaptive selection. First, we ablated the number of epochs for transformer fine-tuning used to obtain the importance scores and found that the number of epochs had little impact on the results. Next, we ablated the number of training layers  $K$ . We found that smaller or larger values of  $K$  did not lead to optimal results, possibly due to underfitting and overfitting. Ultimately, we chose 6 sub-layers as the hyperparameter for the few-shot learning setting.
+
+![](images/3723e73ba8bade9667eba3c470cc1833b058e5112bf82bddf7376ba4f0aa6174.jpg)  
+Figure 4. Ablation of epoch for transformer fine-tuning and the number of training layers in adaptive selective fine-tuning.
+
+![](images/ae51a7d5223995606768ffb4986ee0f353fe337257b667c09463f5f0013b10a0.jpg)  
+Figure 6. T-SNE visualization of image features before (left) and after (right) training. After training, features form clearer clusters, showing improved class separation.
+
+# 4.6. Visualization
+
+Statistics of training parameter selection. In Fig. 5, we visualize the parameter selection results in the few-shot setting for 16-shot across 11 datasets. Firstly, we observe that the sub-layers chosen for both the image and text encoders are similar but not identical. Notably, some sub-layers are consistently selected across different layers, indicating that these sub-layers might be responsible for extracting general features. Additionally, the sub-layers selected by the transformer layer are also different, indicating that the functions responsible for shallow and deep layers are not the same.
+
+Image feature analysis before and after training. In Fig. 6, we visualize the distribution of image features extracted by the model before and after training using T-SNE [38]. On the left, the features are scattered with significant overlap between different classes, indicating that the model has not yet effectively distinguished visual features. After training (right side), the features form compact and distinct clusters, demonstrating that the model has successfully learned to extract discriminative features.
+
+![](images/3d36bd10b1f926c8c5a013cfd7e15a59c43bbab630883afbee537112649dbae3.jpg)  
+Figure 5. Heatmaps of adaptive parameter selection for image (left) and text (right) encoders across 11 datasets in the 16-shot setting.
+
+![](images/0f629c6dc9b020631d420131c154a056be84b369070c1384a7938240fc580b71.jpg)
+
+# 5. Conclusion
+
+We introduce CLIP-AST, an adaptive selective fine-tuning method for VLMs that addresses the limitations of existing PEFT approaches for CLIP. Unlike traditional methods that rely on the manual selection of adaptation positions, CLIP-AST uses the adaptive learning rate mechanism of the AdamW optimizer to automatically select critical parameters with lower second-moment estimates of their gradients. This enables selective fine-tuning of key sublayers, preserving pre-trained knowledge, reducing overfitting, and minimizing computational costs. Extensive experiments show that CLIP-AST outperforms the original CLIP model and achieves exceptional performance across numerous benchmarks. Overall, it provides a robust framework for efficient fine-tuning of VLMs, with potential for application in other multimodal architectures and further enhancements in parameter selection strategies. Future work could explore extending this approach to other multimodal architectures and further refine the parameter selection criteria for even greater performance gains.
+
+Acknowledgement. This work was supported by the National Natural Science Foundation of China (project Nos. 62220106003, 623B2057), the Research Grant of Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology.
+
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\ No newline at end of file
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+# Adaptive Part Learning for Fine-Grained Generalized Category Discovery: A Plug-and-Play Enhancement
+
+Qiyuan Dai $^{1}$  Hanzhuo Huang $^{1}$  Yu Wu $^{2}$  Sibei Yang $^{3\dagger}$ $^{1}$ School of Information Science and Technology, ShanghaiTech University  
+ $^{2}$ Wuhan University  $^{3}$ Sun Yat-sen University
+
+# Abstract
+
+Generalized Category Discovery (GCD) aims to recognize unlabeled images from known and novel classes by distinguishing novel classes from known ones, while also transferring knowledge from another set of labeled images with known classes. Existing GCD methods rely on self-supervised vision transformers such as DINO for representation learning. However, focusing solely on the global representation of the DINO CLS token introduces an inherent trade-off between discriminability and generalization. In this paper, we introduce an adaptive part discovery and learning method, called APL, which generates consistent object parts and their correspondences across different similar images using a set of shared learnable part queries and DINO part priors, without requiring any additional annotations. More importantly, we propose a novel all-min contrastive loss to learn discriminative yet generalizable part representation, which adaptively highlights discriminative object parts to distinguish similar categories for enhanced discriminability while simultaneously sharing other parts to facilitate knowledge transfer for improved generalization. Our APL can easily be incorporated into different GCD frameworks by replacing their CLS token feature with our part representations, showing significant enhancements on fine-grained datasets.
+
+# 1. Introduction
+
+Trained on large-scale annotated data [9, 25] and simplified by the "closed-world" assumption, where the test data to be classified adheres to predefined training classes, deep learning models [10, 17, 34] have made remarkable progress in image recognition, even surpassing human abilities. However, in practical real-world scenarios, this assumption often fails to hold true. This is not only due to the high expense of fully annotating data but, more importantly, due to the impossibility of predefining all categories because of the
+
+inherent variability and openness of the real world, where novel classes emerge alongside the known ones. Therefore, Generalized Category Discovery (GCD) [40] seeks to challenge the "closed-world" assumption and adapt to an "open-world" scenario. In GCD, only a subset of data is labeled with known categories, aiming to assign a category label to each remaining data point, potentially encompassing both known and novel categories.
+
+Two primary challenges arise in GCD: 1) Discriminability: accurately discerning between known and novel classes, and correctly categorizing each; 2) Generalization: transferring shared knowledge from known to novel classes to recognizing novel classes without annotations. State-of-the-art GCD methods [40, 42, 43] primarily exploit the benefits of generalization representation via self-supervised vision transformers (ViT) like DINO [4] to uphold fundamental generalization capabilities. On one hand, to improve semantic discriminability, some approaches utilize an explicit parametric classifier on known data [43] or learn prompt-adapted backbones [42, 45]. On the other hand, to safeguard generalization capabilities, they introduce entropy regularization to mitigate bias towards tending to predict known categories [43] or incorporate shared dynamic concepts [30], hierarchies [31], or memory bank [45] to enhance shared semantics between known and novel classes.
+
+However, an inherent trade-off arises between discriminability and generalization when utilizing the image semantics at the global level, namely, the feature representation of ViT's [cls] token, in current GCD methods, particularly in open-world fine-grained recognition. The strong discriminability at the global level impedes the potential for generalization. The global semantics are rooted in fine-grained local semantics, with the [cls] token's representation obtained through self-attention over local patches [4, 10]. Introducing significant differences in the global semantics of similar categories, such as crested auklet and parakeet auklet as shown in Figure 1, can improve discriminability but also lead to similarly notable distinctions in their local semantics (refer to Figure 1b). Consequently, this impedes the sharing and knowledge transfer of local
+
+![](images/7dfe19f402f22d03f0894ba409b5b40eae8cdda1450a9c7ffb1a7b07ecdb5c44.jpg)  
+Figure 1. Comparison of discriminability and generalization between our and existing GCD methods that use global CLS token representation. We (a) allow similar parts in similar classes to be shared to achieve knowledge transfer and generalization, while (d) exploiting discriminative parts to distinguish novel classes from similar known classes. In contrast, the existing GCD methods (b) cannot distinguish different parts within the image, or (c) are easy to classify novel images into similar known classes when using superclass-based generalization. (e) demonstrates the integration of our APL into existing GCD frameworks, and (f) presents the improvements over diverse baselines.
+
+![](images/304e5475080fb0619cf5d3c2092cf5cf33fdf23b2de12c7ed5f2a7e0b1bf8517.jpg)
+
+semantics, such as the legs, which should inherently be similar across the two classes. As a contrast, Figure 1a showcases our discriminable yet shareable local semantics. On the contrary, strong generalization on similar categories could impact discriminability on novel categories. Hierarchical or superclass-based generalization may result in similar features among different categories within the same superclass, posing challenges in distinguishing novel categories from their similar known counterparts, as shown in Figure 1c. This occurs because supervised learning on labeled data only emphasizes differences between similar known classes, leaving the discriminative fine-grained cues of novel categories easily overlooked due to the lack of explicit supervision. However, our model can distinguish between similar novel and known classes, such as rhinoceros akulet and crested aklet, thanks to our discriminative local semantics (such as the head), as shown in Figure 1d.
+
+In this study, we aim to improve discriminability while preserving generalization through a unified perspective, namely, adaptive part representation learning (APL): highlighting discriminative fine-grained local semantics to distinguish similar but distinct categories (e.g., created auklet and parakeet auklet distinguishable by their heads), while also allowing for the sharing of their other local semantics (e.g., legs), thereby facilitating knowledge transfer and generalization. Specifically, our APL comprises two main components: 1) Consistent part discovery and correspondence, which learns to decompose images into meaningful semantic parts that can be shared and corresponded one-to-one between similar categories, as illustrated in Figure 3c. However, unsupervised object part discovery and correspondence, without part or even object mask annotations, presents challenges. Unfortunately, even though DINO's patch features are capable of perceiving object parts [29], naive image partition yields fragmented regions, lacking
+
+meaningful parts. Similarly, clustering image patches into a fixed number of groups overlooks the complexity of different scenes, including scenes with missing parts due to occlusion and augmentations, resulting in the noisy part discovery and subsequent incorrect correspondences, as shown in Figure 3a. Therefore, unlike prior methods, we identify object parts using a set of learnable part queries, guided by DINO's part prior. Each image's patches are then hardassigned to these queries, forming object parts associated with the same query, as shown in Figure 2. Queries with empty tokens handles potential missing parts. Additionally, inducing shared part queries from all images enhances robustness compared to single-image clustering and naturally establishes correspondences between parts of different images by using queries as bridges. 2) Diverse and adaptive part representation learning acquires more discriminative semantic parts of fine-grained objects while preserving shared parts for improved generalizability across various classes. To achieve this, we propose two learning objectives: adaptive part contrastive learning and query diversity. Firstly, we propose all-min contrastive learning on semantic parts, ensuring that all corresponding parts of positive samples are similar while only constraining the least similar parts of negative samples to be dissimilar. This enables the adaptive discovery of discriminative parts, while leaving the generalizable parts of negative samples unconstrained, thereby making object part features shareable and generalizable to similar classes. Next, we constrain the diversity between queries, ensuring that each query can focus on and highlight specific semantic parts and details, thus avoiding collapsing into a global semantic representation.
+
+Our APL which improves GCD through discriminative yet generalizable part discovery without relying on a specific GCD network architecture(refer to Figure 1e), is integrated into the widely used SimGCD [43] as well as the lat
+
+est SPTNet [42] and CMS [7] to demonstrate its effectiveness. In summary, our contributions are multi-faceted: (1) To the best of our knowledge, we are the first to introduce and differentiate between different object parts for GCD by emphasizing discriminative parts to enhance discriminability, while simultaneously sharing other parts to facilitate knowledge transfer for improved generalization. (2) We propose a simple yet effective unsupervised object part discovery method that seamlessly integrates with GCD frameworks to achieve consistent and corresponding part discovery and segmentation across similar images with the same or different categories. (3) We propose a novel all-min contrastive learning objective to adaptively select and constrain only the most discriminative parts of negative pairs, fostering discriminative yet generalizable representation learning. (4) Our APL is incorporated into the classic SimGCD, recent SPTNet and CMS GCD frameworks, achieving consistent performance improvements across all fine-grained datasets(refer to Figure 1f) and enhancing the average accuracy by  $3.7\%$ $2.9\%$  and  $3.7\%$  respectively.
+
+# 2. Related Works
+
+Generalized Category Discovery (GCD) [40] extends the novel category discovery (NCD) to a more realistic setting, where unlabeled data contains samples of both known and novel classes. The pioneering work [40] utilizes the self-supervised pre-trained DINO [4] as the initialization of the feature extractor, in conjunction with semi-supervised k-means clustering. It integrates supervised contrastive learning [14, 19, 37] on labeled data for distinguishing known classes, along with unsupervised contrastive learning on different views of both labeled and unlabeled data. Later, DCCL [30] introduces dynamic conception generation to consider inter-class relationships, using infomap to dynamically generate pseudo-labels. SimGCD [43], unlike prior clustering-based approaches, directly employs a parameterized classification head. This circumvents the constraint of clustering methods, which cannot classify individual samples directly, resulting in notable efficiency enhancements. Building upon SimGCD, SPTNet [42] introduces spatial prompt tuning to enable the model to leverage information from local regions, while CMS [7] modifies the classification head for hierarchical clustering and enhances feature generalization through the mean shift technique. Some other methods [44, 46] leverage local-level information, but [44] exploits the structural characteristics of 3D point clouds to facilitate part discovery, whereas [46] fails to obtain semantically meaningful part information.
+
+Unsupervised Object Part Discovery. To enhance fine-grained image understanding, certain studies advance from the image-level to the object-level and subsequently to an even finer part-level comprehension. Early works [5, 49] such as ProtoPNet [5] explore the utilization of part-level
+
+information to enhance classification. It introduces prototypes into convolutional networks to represent object parts. However, the lack of ground truth or priors for accurate object parts limits the robustness of the part information obtained by these methods [1, 20, 21, 33, 38]. Other methods [24, 28, 48] rely on fully annotated object parts to learn part segmentation, aiming to segment images into distinct regions corresponding to different parts of objects. Recently, with the emergence of DINO [4], some methods use DINO for part discovery. For instance, [8] employ frozen DINO to extract part features for help learning part segmentation. Similarly, VLPart [35] utilizes DINO to establish correspondence between novel parts and base parts, but it still relies on annotations of object parts in base categories. In this paper, by leveraging DINO's coarse part conception, our proposed shared part queries, and novel all-min contrastive loss, we automatically, unsupervised, discover consistent object parts and establish correspondences between them across different images.
+
+# 3. Method
+
+# 3.1. Preliminary
+
+Problem Statement. The Generalized Category Discovery (GCD) entails categorizing images during inference, with these images potentially belonging to either labeled known classes or unlabeled novel classes during training. Formally, learning from a labeled set  $\mathcal{D}_l = \{(I_i,c_i)\}_{i = 1}^{N_l}\subset \mathcal{I}_l\times \mathcal{C}_l$  and an unlabeled set  $\mathcal{D}_u = \{I_i\}_{i = 1}^{N_u}\subset \mathcal{I}_u$ , each image  $I_{i}\in \mathbb{R}^{H\times W\times 3}$  in both sets is with height  $H$  and width  $W$ , the GCD aims to accurately categorizes each image  $I_{i}\in \mathcal{I}_{u}$  within the label space of unlabeled set  $\mathcal{C}_u$ , where  $\mathcal{C}_l\subset \mathcal{C}_u$ . Given that the labeled label space  $\mathcal{C}_l$  is a subset of the unlabeled label space  $\mathcal{C}_u$ , GCD not only requires discriminability to distinguish between labeled known classes in  $\mathcal{C}_l$  and remaining novel classes in  $\mathcal{C}_u - \mathcal{C}_l$ , but also transfer shared knowledge from known to novel classes.
+
+DINO Architecture. DINO [4, 29] adopts the standard Vision Transformer (ViT) [11] architecture. Given an image  $I$ , DINO initially divides it into a sequence of non-overlapping patch tokens. Each token is then projected into a hidden representation vector via a linear or convolutional layer, resulting in token vectors denoted as  $X_{\mathrm{patch}} \in \mathbb{R}^{N \times C}$ , where  $N$  is the number of patch tokens, and  $C$  specifies vector dimension. To represent the global image feature, an additional learnable CLS token is concatenated to  $X_{\mathrm{patch}}$ . Subsequently, all tokens, patch tokens  $X_{\mathrm{patch}}$  and CLS token, integrated with positional embeddings [11], are fed into the Transformer layers that contain several multi-head self-attention [39] (MSA) and feed-forward networks (FFN). Within the multiple transformer layers, the CLS token interacts with image patch tokens  $X_{\mathrm{patch}}$  through MSA, aggregating global features. Finally, DINO develops robust
+
+![](images/4f7bb0383d9b678ffc51014b702a73814c492fdfb4900bfebc88f15e1fb5b07f.jpg)  
+Figure 2. Overall framework of APL. APL achieves consistent and corresponding part discovery, serving as a plug-and-play enhancement.
+
+visual representations, denoted by  $F = [F_{\mathrm{patch}}, F_{\mathrm{CLS}}]$  with token features  $F_{\mathrm{patch}} \in \mathbb{R}^{N \times C}$  and CLS feature  $F_{\mathrm{CLS}} \in \mathbb{R}^{1 \times C}$ , achieved through view-invariant self-supervised pretraining [4, 29]. The DINO architecture is formulated as:
+
+$$
+F _ {0} = \phi (\mathrm {P E}, [ X _ {\mathrm {C L S}}, X _ {\mathrm {p a t c h}} ]),
+$$
+
+$$
+\left[ F _ {\text {p a t c h}}, F _ {\mathrm {C L S}} \right] \leftarrow F _ {l = L}, F _ {l} = \operatorname {F F N} \left(\operatorname {M S A} \left(F _ {l - 1}\right)\right), \tag {1}
+$$
+
+where  $[\cdot ,\cdot ]$  denotes concatenation, PE represents position encoding,  $\phi$  is the fusion function of position encoding and tokens [4], and  $l$  and  $L$  represent the index of the  $l$ -th transformer layer and the total number of transformer layers, respectively.
+
+Part Perception in DINO. With self-supervised pretraining and ViT architecture, DINO exhibits many functionalities that are absent in fully supervised training [11] or ConvNet [18] networks, one of which is the perception of object parts. Previous works [4, 8] find that in the MSA interactions between the CLS token and image patch tokens, the overall attention scores from all  $M$  attention heads can roughly reveal the foreground object, while attention scores of each individual head can highlight semantically meaningful parts of the object. Specifically, we use the attention scores from the final-layer MSA of DINO to obtain part attention. In the  $m$ -th attention head, with the features of the CLS token denoted as  $F_{\mathrm{CLS}}^{m} \in \mathbb{R}^{1 \times \frac{C}{M}}$  and the features of the patch tokens as  $F_{\mathrm{patch}}^{m} \in \mathbb{R}^{N \times \frac{C}{M}}$ , the calculation of  $m$ -th part attention  $A_{m}$  is as follows:
+
+$$
+W _ {m} = \operatorname {S o f t m a x} (\frac {\operatorname {P r o j} _ {\mathrm {Q}} ^ {m} \left(F _ {\mathrm {C L S}} ^ {m}\right) * \operatorname {P r o j} _ {\mathrm {K}} ^ {m} \left(\left[ F _ {\mathrm {C L S}} ^ {m} , F _ {\text {p a t c h}} ^ {m} \right]\right) ^ {\top}}{\sqrt {C}}),
+$$
+
+$$
+A _ {m} \leftarrow W _ {m} [ 1, 2: N + 1 ], \tag {2}
+$$
+
+where  $\mathrm{Proj}_Q^m$  and  $\mathrm{Proj}_K^m$  denote projection matrix of  $m$ -th head,  $\top$  represents matrix transpose. The  $W_{m} \in \mathbb{R}^{1 \times (N + 1)}$  denotes the attention scores between the CLS token and all tokens, encompassing both the CLS token and patch tokens. Specifically, the attention scores  $A_{m} \in \mathbb{R}^{1 \times N}$  for patch tokens highlight potential patch regions where parts could be located, essentially constituting the part attention in the  $m$ -th head.
+
+# 3.2. Consistent Part Discovery and Correspondence
+
+The Motivation for Introducing Object Parts is to highlight discriminative object parts for enhanced discriminability, while simultaneously sharing other parts to facilitate knowledge transfer for improved generalization. Since GCD requires learning from unlabeled data, DINO—a self-supervised, pre-trained model that learns from unlabeled images and their augmentations—is a natural choice for existing GCD methods [42, 43] seeking to obtain generalizable visual representations. Existing GCD methods predominantly use the global semantics of images, particularly the features of DINO's CLS token, for classification or clustering to categorize images. However, these global features may lead to a trade-off between discriminating similar categories and generalizing from similar known to novel ones, as detailed in Sec 1. Therefore, we advocate for integrating local semantics, such as object parts, into GCD. Notably, object parts are not merely naive supplements of fine-grained local semantics to global features. More crucially, by delineating the roles of different object parts, discriminative parts can effectively differentiate similar categories, while also allowing for the sharing of other parts across these categories, thereby improving both discriminability and generalization.
+
+Three Principles of Our Part Discovery. (1) Consistency: object parts in images of the same category should be consistent, especially when some images may have missing parts. For instance, in cars, parts like windows, tires, and hoods are common, but due to image augmentation or occlusion, some images may only feature partial parts. Simple single-image-based grouping or clustering on DINO's patch features is highly unreliable, potentially leading to meaningless or inconsistent discoveries of object parts across images, as shown in Figure 3a. (2) Correspondence: some object parts of similar categories should correspond to each other, facilitating the identification of both discriminative and shareable parts. For instance, dogs and cats share common parts like the head, tail, and body. However, only by matching their corresponding parts can we identify the head as potentially more discriminative, while body features may be better suited for sharing and generalizing to other canid species. (3) Efficiency: part discovery should be seamlessly integrated into existing GCD frame
+
+![](images/92db7bb599f6467ea0e37907db04e9baf2b27fdcfff0e8d926cd242db0da4eef.jpg)  
+(a) Visualization of K-means
+
+![](images/bf070389aee70507cab71985c59cf251641759e61c543a575086bb5725ac664d.jpg)
+
+![](images/a8ff66cbd1acf82409e62230b50e7d26f35f559b48ba4c56e6eaecc46839bda8.jpg)  
+(c) Visualization of Ours  
+(d) Correspondence & Consistency  
+Figure 3. Part discovery by (a) K-means, (b) DINO priors, and (c) ours. Only ours demonstrates consistency in handling partial parts and correspondences between similar images.
+
+![](images/d1d09c65f8b8bbbebd184fc9dd1f5215e40becf1e53633745159f06f1fb14831.jpg)
+
+works without the need for additional annotations, external models, or significant computational complexity.
+
+Consistent Part Discovery and Correspondence. To adhere to our third principle of efficiency, we propose directly leveraging DINO, drawing inspiration from its perceptual abilities for object parts (see Sec 3.1), and integrating part discovery into the online learning process of GCD. However, DINO's part perception is too sensitive to variations among different images, thus failing to meet our principles of consistency and correspondence, as shown in Figure 3b. Therefore, instead of solely depending on DINO's part perception, we leverage it as a prior to facilitate learning a set of shared learnable part queries across all images for object discovery, as shown in Figure 2. These cross-image, unified part queries not only ensure more robust object discovery compared to single-image-based methods but also naturally serve as bridges for building correspondence between different images. Specifically, let us denote the set of learnable part queries as  $Q \in \mathbb{R}^{T \times C}$ , where  $T$  is the number of queries and  $C$  is the dimension number. First, for an input image  $I$ , we extract its DINO part priors  $F_{\text{prior}} \in \mathbb{R}^{M \times C}$  based on DINO's  $M$  part attentions  $[A_1, A_2, \dots, A_M]$  and DINO patch features  $F_{\text{patch}}$ , defined in Sec 3.1. Then, we transform the shared learnable queries  $Q$  into image-specific ones  $Q_I \in \mathbb{R}^{T \times C}$  via cross-attention between  $Q$  and the prior  $F_{\text{prior}}$ , as formulated below:
+
+$$
+F _ {\text {p r i o r}} = \left[ \epsilon \left(A _ {1}\right) * F _ {\text {p a t c h}}, \dots , \epsilon \left(A _ {M}\right) * F _ {\text {p a t c h}} \right], \tag {3}
+$$
+
+$$
+Q _ {I} = \operatorname {P r o j} _ {\mathrm {Q}} (Q) * \operatorname {P r o j} _ {\mathrm {K}} \left(F _ {\text {p a r t}}\right) ^ {\top} / \sqrt {C},
+$$
+
+where  $\epsilon$  represents a threshold filter function to transform  $A_{m}$  into a binary matrix to highlight the part regions,  $\mathrm{Proj}_{\mathrm{Q}}$  and  $\mathrm{Proj}_{\mathrm{K}}$  are the learnable projection matrices. The  $\epsilon (A_m)*F_{\mathrm{patch}}$  represents the feature of the  $m$ -th part in DINO, and the features from all heads form DINO's part priors  $F_{\mathrm{prior}}$ . Part queries  $Q_{\mathrm{I}}$  encode the features of potential object parts in image  $I$ . Next, object parts are identified
+
+by hard-assigning image patches to the queries based on the similarity of their features  $F_{\mathrm{patch}}$  and  $Q_{\mathrm{I}}$ , where patches within the same query constitute a potential object part. As the hard assignment, which is the arg max over similarities, is not differentiable, we approximate the hard assignment and preserve differentiability by Gumbel-Softmax distribution [13, 26], as formulated as follows:
+
+$$
+H _ {\mathfrak {g}} = \operatorname {s o f t m a x} \left(\left(\frac {\operatorname {P r o j} _ {\mathrm {Q}} \left(Q _ {I}\right) * \operatorname {P r o j} _ {\mathrm {K}} \left(F _ {\text {p a t c h}}\right) ^ {\top}}{\sqrt {C}} + G\right) / \tau\right),
+$$
+
+$$
+H _ {\text {p a r t}} = \left(\operatorname {o n e} _ {-} \operatorname {h o t} \left(\arg \max  _ {N} \left(H _ {\mathfrak {g}}\right)\right)\right) ^ {\top} - \operatorname {s g} \left(H _ {\mathfrak {g}}\right) + H _ {\mathfrak {g}},
+$$
+
+$$
+P _ {\text {p a r t}} = H _ {\text {p a r t}} * F _ {\text {p a t c h}}, \tag {4}
+$$
+
+where each Gumbel noise  $g_{n} \in G$  with  $g_{n} = -\log (-\log (u_{n}))$  and  $u_{n}$  are i.i.d. samples drawn from Uniform(0,1),  $\tau$  is the temperature.  $\mathrm{Proj}_{\mathrm{Q}}$  and  $\mathrm{Proj}_{\mathrm{K}}$  denote the learnable projection matrices of  $Q_{I}$  and  $F_{\mathrm{patch}}$ . The  $H_{\mathfrak{g}}$  approximates sampling the one-hot  $(\arg \max_{N}(\mathrm{Proj}_{\mathrm{Q}}(Q_I)*\mathrm{Proj}_{\mathrm{K}}(F_{\mathrm{patch}})^{\top} / \sqrt{C} +G))$  where  $\arg \max_{N}$  selects the corresponding patch token with the highest attention score for each part query, and one-hot transforms the patch token index into a one-hot vector.  $sg$  represents the stop gradient operator. The resulting binary  $H_{\mathrm{part}} \in \mathbb{R}^{T\times N}$  indicates the hard assignment from  $N$  patches to  $T$  part queries. Each  $H_{t} \in \mathbb{R}^{1\times N}$  within  $H_{\mathrm{part}}$  represents a potential part, with indices containing a value of 1 indicating which patches belong to that specific part. The  $P_{t} \in \mathbb{R}^{1\times C}$  within  $P_{\mathrm{part}}$  represents the feature of each part  $H_{t}$ .
+
+Our query hard assignment for part discovery can adaptively handle consistency and situations where some parts are absent. In such cases, when an object part is too small and its constituent patches are scattered, the corresponding query becomes a meaningless placeholder for the potential missing part. Additionally, it ensures part correspondence across images. For images  $I_{a}$  and  $I_{b}$ , their respective parts  $H_{\mathrm{part}}^{a}$  and  $H_{\mathrm{part}}^{b}$  are obtained through shared part queries  $Q$ . Consequently, parts corresponding to same query, such as  $H_{t}^{a}$  and  $H_{t}^{b}$  of the  $t$ -th query, align with each other.
+
+# 3.3. Diverse and Adaptive Part Learning
+
+While object parts are meant to represent distinct components, without constraints on the learning of randomly initialized learnable parts, they easily correspond to arbitrary image regions rather than meaningful parts or collapse into identical global patches. Additionally, automatically distinguishing discriminative and transferable object parts enables learning their respective representations, crucial for enhancing GCD from both discriminative and generalizable perspectives. Therefore, we propose a novel all-min contrastive learning objective combined with a diverse loss to facilitate part learning.
+
+All-min Contrastive Learning. Its core idea involves (1) constraining all corresponding object parts in a positive pair
+
+to be more similar than non-corresponding pairs, where positive pairs originate from images of the same class in the labeled set or from images and their augmentations in both the labeled and unlabeled sets. This fosters the learning of distinct parts within a class and consistency among parts across images of the same class. (2) In negative pairs of images from different classes, we only enforce dissimilarity on the most dissimilar corresponding part, leaving the similarity of their other corresponding parts unconstrained. This approach capitalizes on the least similar corresponding part's discriminative power in distinguishing between the two images, while permitting other parts to be similar to facilitate the sharing of similar components for generalization. Specifically, for a batch of images denoted as  $B$ , our all-min contrastive loss is formulated as follows:
+
+$$
+\mathcal {L} _ {\text {a l l - m i n}} = - \frac {1}{| B |} \sum_ {I _ {a} \in B} \log \frac {\sum_ {I _ {b +} \in S ^ {+} (I _ {a})} \sum_ {t = 1} ^ {T} \exp \left(\sin \left(P _ {t} ^ {a} , P _ {t} ^ {b +}\right) / \tau\right)}{\sum_ {I _ {b -} \in S ^ {-} (I _ {a})} \exp \left(\min  _ {t \in [ 1 , T ]} \sin \left(P _ {t} ^ {a} , P _ {t} ^ {b -}\right) / \tau\right)}, \tag {5}
+$$
+
+where  $I_{a}$  represents an image in the batch  $B$ , the sim means the cosine similarity between corresponding parts from two different images or two different augmentation, the sets  $S^{+}(I_{a})$  and  $S^{-}(I_{a})$  represent the set of positive and negative image samples of  $I_{a}$ , respectively. If  $I_{a}$  is labeled, i.e.,  $I_{a} \in \mathcal{D}_{l}$ , the positive set  $S^{+}(I_{a})$  consists of labeled images  $I_{i} \in \mathcal{D}_{l}$  whose class  $c_{i}$  is the same as the class  $c_{a}$  of image  $I_{a}$ , i.e.,  $S^{+}(I_{a}) = \{I_{i} \in \mathcal{D}_{l} : c_{i} = c_{a}\} \cap B$ . Otherwise, the set only contains augmentation images, i.e.,  $S^{+}(I_{a}) = \{I_{i} \in B : \mathrm{ID}(I_{i}) = \mathrm{ID}(I_{a})\}$ , where ID returns the id of the image. Contrary to the positive sets, if  $I_{a}$  is labeled, the negative set consists of labeled images with different classes from  $I_{a}$ , i.e.,  $S^{-}(I_{a}) = \{I_{i} \in \mathcal{D}_{l} : c_{i} \neq c_{a}\} \cap B$ . For unlabeled  $I_{a}$ , we randomly sample some images from  $B$  as negative samples, ensuring that not all parts of these images are similar to each corresponding part of  $I_{a}$ , and use the similarity of all positive pairs in the batch as the threshold for sampling negative images.
+
+Diverse Object Parts. To prevent different part queries from collapsing onto the same semantic parts, we apply diversity loss to the part queries, encouraging them to focus on distinct object parts. Specifically, we constrain that different parts within an image are orthogonal:
+
+$$
+\mathcal {L} _ {\mathrm {d i v}} = \sum_ {P _ {t} \in P _ {p a r t}} \sum_ {\hat {P} _ {t} \in P _ {p a r t} \backslash P _ {t}} \max  (0, \operatorname {s i m} \left(P _ {t}, \hat {P} _ {t}\right)), \tag {6}
+$$
+
+where  $P_{t}$  and  $\hat{P}_t$  are the part features of two different parts within an image, and sim denotes the cosine similarity.
+
+# 3.4. A Plug-and-Play Integration
+
+Since our part discovery and learning do not rely on any specific GCD framework but only require a DINO backbone adopted by all existing GCD methods, we can integrate it into various GCD frameworks, such as the parameterized
+
+classification head in SimGCD [43] and SPTNet [42]. The parametrized framework freezes most layers of DINO and only tunes the final layer, treating the features of the [CLS] token,  $F_{\mathrm{token}}$ , as the sample's feature representation for class prediction. Its learning objective includes both representation learning with InfoNCE loss and parametric classification on  $F_{\mathrm{token}}$  [42, 43], formulated as follows:
+
+$$
+\mathcal {L} _ {\mathrm {G C D}} = (1 - \lambda) \left(\mathcal {L} _ {\mathrm {c l s}} ^ {u} + \mathcal {L} _ {\mathrm {r e p}} ^ {u}\right) + \lambda \left(\mathcal {L} _ {\mathrm {c l s}} ^ {s} + \mathcal {L} _ {\mathrm {r e p}} ^ {s}\right) \tag {7}
+$$
+
+where  $\lambda$  is the balance factor,  $\mathcal{L}_{\mathrm{cls}}^u +\mathcal{L}_{\mathrm{rep}}^u$  and  $\mathcal{L}_{\mathrm{cls}}^{s} + \mathcal{L}_{\mathrm{rep}}^{s}$  represent the sum of representation learning loss and parametric classification loss on labeled and unlabeled sets, respectively.
+
+To solely showcase the discriminative yet generalizable effectiveness of our object parts, we simply pool the features from different parts to obtain an overall part feature, which replaces the feature  $F_{\mathrm{CLS}}$  of CLS token for both classification prediction and feature representation learning, as illustrated in Figure 2b. The overall learning objective of the model is as follows:
+
+$$
+\mathcal {L} _ {\text {o v e r a l l}} = (1 - \lambda) \left(\mathcal {L} _ {\mathrm {c l s}} ^ {u} + \mathcal {L} _ {\mathrm {r e p}} ^ {u}\right) + \lambda \left(\mathcal {L} _ {\mathrm {c l s}} ^ {s} + \mathcal {L} _ {\mathrm {r e p}} ^ {s}\right) + \mathcal {L} _ {\mathrm {d i v}} + \mathcal {L} _ {\text {a l l - m i n}} \tag {8}
+$$
+
+# 4. Experiment
+
+# 4.1. Experiment Setup
+
+Datasets. We follow previous approaches [40, 43] to evaluate our method on four fine-grained and three generic image classification datasets. Following them, we adopt the same partitioning strategy across these datasets: for all fine-grained datasets [22, 27, 36, 41], CIFAR-10 [23], and ImageNet-100 [9],  $50\%$  of the classes are considered as known classes, with the remaining classes treated as novel classes. For CIFAR-100 [23], 80 classes are designated as known classes. Within these known classes,  $50\%$  samples from each class are chosen to construct the labeled set  $\mathcal{D}_l$ , while the remaining samples constitute the unlabeled set  $\mathcal{D}_u$ , along with the images of novel classes. For detailed information, please refer to the Appendix.
+
+Evaluation Metric. We evaluate the effectiveness of our method on unlabeled dataset  $\mathcal{D}_u$  using clustering accuracy, following [7, 42, 43]. The accuracy is defined as ACC  $= \frac{1}{|\mathcal{D}_u|}\sum_{i = 1}^{|\mathcal{D}_u|}1(y_i = f^* (\hat{y}^i))$ , where  $f^{*} = \arg \max_{f\in \mathcal{F}}\sum_{i = 1}^{M}1(y_{i} = f(\hat{y}^{i}))$ , and  $\mathcal{F}$  is all possible matching between the predicted labels with the ground truth.
+
+# 4.2. Comparison with the State-of-the-Art Methods
+
+Table 1 compares our method with state-of-the-art models (SOTAs) on fine-grained datasets, including the SSB benchmark and the Herbarium19 dataset. Our method achieves state-of-the-art performance across multiple datasets and
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">CUB</td><td colspan="3">Stanford Cars</td><td colspan="3">FGVC-Aircraft</td><td colspan="3">Herbarium-19</td></tr><tr><td>All</td><td>Known</td><td>Novel</td><td>All</td><td>Known</td><td>Novel</td><td>All</td><td>Known</td><td>Novel</td><td>All</td><td>Known</td><td>Novel</td></tr><tr><td>k-means [2]</td><td>34.3</td><td>38.9</td><td>32.1</td><td>12.8</td><td>10.6</td><td>13.8</td><td>16.0</td><td>14.4</td><td>16.8</td><td>13.0</td><td>12.2</td><td>13.4</td></tr><tr><td>RS+ [15]</td><td>33.3</td><td>51.6</td><td>24.2</td><td>28.3</td><td>61.8</td><td>12.1</td><td>26.9</td><td>36.4</td><td>22.2</td><td>27.9</td><td>55.8</td><td>12.8</td></tr><tr><td>UNO+ [12]</td><td>35.1</td><td>49.0</td><td>28.1</td><td>35.5</td><td>70.5</td><td>18.6</td><td>40.3</td><td>56.4</td><td>32.2</td><td>28.3</td><td>53.7</td><td>14.7</td></tr><tr><td>ORCA [3]</td><td>35.3</td><td>45.6</td><td>30.2</td><td>23.5</td><td>50.1</td><td>10.7</td><td>22.0</td><td>31.8</td><td>17.1</td><td>20.9</td><td>30.9</td><td>15.5</td></tr><tr><td>GCD [40]</td><td>51.3</td><td>56.6</td><td>48.7</td><td>39.0</td><td>57.6</td><td>29.9</td><td>45.0</td><td>41.1</td><td>46.9</td><td>35.4</td><td>51.0</td><td>27.0</td></tr><tr><td>CiPR [16]</td><td>57.1</td><td>58.7</td><td>55.6</td><td>47.0</td><td>61.5</td><td>40.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GPC [47]</td><td>52.0</td><td>55.5</td><td>47.5</td><td>38.2</td><td>58.9</td><td>27.4</td><td>43.3</td><td>40.7</td><td>44.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DCCL [30]</td><td>63.5</td><td>60.8</td><td>64.9</td><td>43.1</td><td>55.7</td><td>36.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>PromptCAL [45]</td><td>62.9</td><td>64.4</td><td>62.1</td><td>50.2</td><td>70.1</td><td>40.6</td><td>52.2</td><td>52.2</td><td>52.3</td><td>37.0</td><td>52.0</td><td>28.9</td></tr><tr><td>PMI [6]</td><td>62.7</td><td>75.7</td><td>56.2</td><td>43.1</td><td>66.9</td><td>31.6</td><td>-</td><td>-</td><td>-</td><td>42.3</td><td>56.1</td><td>34.8</td></tr><tr><td>SimGCD [43]</td><td>60.3</td><td>65.6</td><td>57.7</td><td>53.8</td><td>71.9</td><td>45.0</td><td>54.2</td><td>59.1</td><td>51.8</td><td>43.0</td><td>58.0</td><td>35.1</td></tr><tr><td>Ours (SimGCD)</td><td>64.5</td><td>68.1</td><td>62.1</td><td>60.1</td><td>77.6</td><td>51.2</td><td>56.6</td><td>60.2</td><td>54.8</td><td>44.9</td><td>58.1</td><td>37.9</td></tr><tr><td>Δ</td><td>+4.2</td><td>+2.5</td><td>+4.4</td><td>+6.3</td><td>+5.7</td><td>+6.2</td><td>+2.4</td><td>+1.1</td><td>+3.0</td><td>+1.9</td><td>+0.1</td><td>+2.8</td></tr><tr><td>SPTNet [42]</td><td>65.8</td><td>68.8</td><td>65.1</td><td>59.0</td><td>79.2</td><td>49.3</td><td>59.3</td><td>61.8</td><td>58.1</td><td>43.4</td><td>58.7</td><td>35.2</td></tr><tr><td>Ours (SPTNet)</td><td>68.5</td><td>73.1</td><td>66.2</td><td>62.3</td><td>80.7</td><td>53.4</td><td>60.9</td><td>63.5</td><td>59.6</td><td>47.3</td><td>66.6</td><td>37.0</td></tr><tr><td>Δ</td><td>+2.7</td><td>+4.3</td><td>+1.1</td><td>+3.3</td><td>+1.5</td><td>+4.1</td><td>+1.6</td><td>+1.7</td><td>+1.5</td><td>+3.9</td><td>+7.9</td><td>+1.8</td></tr><tr><td>CMS [7]</td><td>68.2</td><td>76.5</td><td>64.0</td><td>56.9</td><td>76.1</td><td>47.6</td><td>56.0</td><td>63.4</td><td>52.3</td><td>36.4</td><td>54.9</td><td>26.4</td></tr><tr><td>CMS†</td><td>66.6</td><td>74.8</td><td>62.6</td><td>56.1</td><td>76.4</td><td>47.1</td><td>54.1</td><td>61.7</td><td>50.3</td><td>35.9</td><td>55.1</td><td>25.6</td></tr><tr><td>Ours (CMS†)</td><td>69.2</td><td>75.3</td><td>66.1</td><td>62.1</td><td>81.8</td><td>52.6</td><td>57.9</td><td>66.0</td><td>53.8</td><td>38.4</td><td>57.2</td><td>28.2</td></tr><tr><td>Δ</td><td>+2.6</td><td>+0.5</td><td>+3.5</td><td>+6.0</td><td>+5.4</td><td>+5.5</td><td>+3.8</td><td>+4.3</td><td>+3.5</td><td>+2.5</td><td>+2.1</td><td>+2.6</td></tr></table>
+
+consistently outperforms our three baselines, SimGCD [43] SPTNet [42] and CMS [7]. Specifically, compared to SO-TAs, we achieve average improvements of  $2.2\%$  on the SSB dataset across novel categories and notable enhancements on the more challenging Herbarium dataset, with improvements of  $3.9\%$ ,  $7.9\%$ , and  $1.8\%$  across all, known, and novel categories, respectively.
+
+Compared to the pioneering parameterized-head SimGCD, we achieve direct performance improvements on the four fine-grained datasets, with gains of  $4.2\%$ ,  $6.3\%$ ,  $2.4\%$ , and  $1.9\%$ , respectively. This indicates the effectiveness of our part discovery, as we simply replace the CLS token used by SimGCD in representation learning and class prediction with the average of our different part features. Particularly, we note that our improvements on novel classes are even more significant, with gains of  $4.4\%$ ,  $6.2\%$ ,  $3.0\%$ ,  $2.8\%$ , respectively. This indicates that our method, by distinguishing between discriminative and transferable parts within similar categories and facilitating feature sharing among transferable parts, aids in the generalization from known to novel classes. Moreover, compared to SPTNet, which also utilizes local information, our method still obtains performance gains of  $2.7\%$ ,  $3.3\%$ ,  $1.6\%$ , and  $3.9\%$ , respectively, demonstrating the positive impact of our explicit object part discovery and utilization.
+
+Table 1. Evaluation on the Semantic Shift Benchmark (SSB) and Herbarium-19 benchmarks.  ${}^{ \dagger  }$  represents our reproduced result.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">CIFAR-10</td><td colspan="2">CIFAR-100</td><td colspan="2">ImageNet-100</td></tr><tr><td>All</td><td>Novel</td><td>All</td><td>Novel</td><td>All</td><td>Novel</td></tr><tr><td>InfoSieve [31]</td><td>94.8</td><td>93.4</td><td>78.3</td><td>70.5</td><td>80.5</td><td>73.8</td></tr><tr><td>SelEx [32]</td><td>95.9</td><td>94.8</td><td>82.3</td><td>76.3</td><td>83.1</td><td>77.8</td></tr><tr><td>Ours(SimGCD)</td><td>97.1</td><td>98.2</td><td>80.9</td><td>79.5</td><td>83.2</td><td>78.5</td></tr></table>
+
+Table 2. Evaluation on generic image recognition datasets.
+
+Unlike SPTNet, which implicitly enhances attention to local information through spatial visual prompts, our method directly extracts semantically meaningful object parts from images adaptively, which is more intuitive and interpretable. Additionally, by introducing our part learning loss on part tokens, we emphasize the diversity of parts and their adaptive discrimination between paired images, enhancing feature discriminability and generalization compared to globally unified visual prompts. In contrast to DCCL and InfoSieve, which top-down establish category relationships hierarchically or superclass-based, our approach establishes relationships from bottom to top through parts, resulting in enhanced generalization and boosting the accuracy of novel categories by  $7.0\%$  and  $7.1\%$  on the Stanford Cars and FGVC-Aircraft datasets, respectively.
+
+Additionally, We compare our APL's effectiveness on a range of generic image recognition datasets with other methods which focus on fine-grained generalized category discovery. Table 2 presents results on CIFAR-10, CIFAR-100 and ImageNet-100. Unlike fine-grained datasets, they require fewer fine-grained parts to distinguish between similar but different categories and share less knowledge across vastly different categories. Despite this, we consistently outperform all our baselines, with improvements of  $3.4\%$ ,  $3.2\%$  and  $0.7\%$  on novel categories of CIFAR-10, CIFAR-100 and ImageNet-100, respectively. We present the t-SNE visualization of our method in Figure 4 and the comparison of similarity distribution of parts in Figure 5.
+
+# 4.3. Ablation Study
+
+We employ SimGCD as the baseline and conduct ablation studies to validate the effectiveness of different components
+
+in our APL. More ablations are shown in the Appendix.
+
+Part Discovery. Table 3 showcases the results of different approaches and various variants of our method for part discovery. (1) Compared to the baseline SimGCD, the decreased performance observed (row 2) when clustering patches from individual images to discover parts indicates that naively incorporating local information can introduce noise. Moreover, single-image clustering struggles with consistency and lacks robustness. (2) Directly treating our extracted part priors  $F_{\text{prior}}$ , defined in Equ 3, as parts and using them to complement the CLS feature in SimGCD slightly improves its performance, demonstrating the positive impact of meaningful part information in GCD (row 3). (3) Moreover, we further introduce our learnable part queries to iteratively and dynamically query the DINO priors  $F_{\text{prior}}$  and image patches  $F_{\text{patch}}$  to address the consistency and correspondence challenges in GCD's part discovery (row 4). The significant performance improvements, i.e.,  $4.1\%$  on novel categories, demonstrate the robustness of using learnable queries to capture cross-image shared part semantics. (4) We enhance the soft assignment of learnable queries with image patch features  $F_{\text{patch}}$  from the previous model to a hard assignment based on the Gumbel-Softmax, defined in Equ 4, which led to further improvements of  $1.6\%$ .
+
+<table><tr><td colspan="2">Method</td><td>All</td><td>Known</td><td>Novel</td></tr><tr><td>1</td><td>SimGCD</td><td>53.8</td><td>71.9</td><td>45.0</td></tr><tr><td>2</td><td>1+k-Means</td><td>51.0</td><td>70.3</td><td>41.7</td></tr><tr><td>3</td><td>1+DINO part prior</td><td>55.1</td><td>73.9</td><td>46.0</td></tr><tr><td>4</td><td>3+Learnable queries</td><td>58.5</td><td>74.7</td><td>50.1</td></tr><tr><td>5</td><td>4+Hard assignment</td><td>60.1</td><td>77.6</td><td>51.2</td></tr></table>
+
+Table 3. Ablation study of part discovery.  
+
+<table><tr><td colspan="2">Method</td><td>All</td><td>Known</td><td>Novel</td></tr><tr><td>1</td><td>SimGCD + part discovery</td><td>55.1</td><td>72.5</td><td>46.7</td></tr><tr><td>2</td><td>1+ part contrastive loss</td><td>55.2</td><td>73.2</td><td>46.5</td></tr><tr><td>3</td><td>1+ min-max contrastive loss</td><td>57.8</td><td>75.7</td><td>49.1</td></tr><tr><td>4</td><td>1+ diversity loss</td><td>56.7</td><td>72.0</td><td>49.6</td></tr><tr><td>5</td><td>3+ diversity loss</td><td>60.1</td><td>77.6</td><td>51.2</td></tr></table>
+
+Table 4. Ablation study of learning objectives.
+
+Part Learning Objective. Table 4 presents the performance of our method under various part learning objectives. (1) The baseline, developed on the SimGCD framework, integrates our part discovery, specifically  $P_{\text{part}}$ , as defined in Equ 4. However, it only incorporates the SimGCD loss  $\mathcal{L}_{GCD}$  from Equ 7 and does not employ any of our part learning losses. (2) Row 2 extends the baseline by implementing a common contrastive loss among parts, ensuring that all parts of positive samples are similar, whereas all parts of negative samples are dissimilar. The results indicate
+
+![](images/1b64418c19f8cabf13d890a74409e529a6c74c091f10ae5cb70b8888cfbb0091.jpg)
+
+![](images/a9bd52c8e288bc944f8fdf488a445c673e9409ca1d0ba04b106529d50a86c41e.jpg)
+
+![](images/5ba6779117d21db02f004d14b96873b8287baa32aed53f612ec623af34331b71.jpg)  
+(a) SimGCD Part t-SNE  
+(c) SimGCD Representation t-SNE
+
+![](images/c42f9e870c6897449e7ffa08488a4d6495d4e9bec425ee2c85560e493bbafe0b.jpg)  
+(b) Ours(SimGCD) Part t-SNE  
+(d) Ours(SimGCD) Representation t-SNE
+
+![](images/0ccb918a04e8d92b8b09d4360ee6d8c77ee4363ab0532e2565788a8d358483a2.jpg)  
+Figure 4. t-SNE visualization of part features on CUB-200 and image features on randomly sampled 10 classes on CIFAR-100. Each color represents a specific part (category).  
+Figure 5. The similarity distribution of discriminative parts between similar but distinct categories.
+
+no improvement for novel categories but a slight enhancement in known categories, attributed to enhanced discriminability among fine-grained object parts across images. (3) When we substitute our all-min contrastive loss, we observe significant improvements of  $2.7\%$ ,  $2.8\%$ ,  $2.4\%$  in the all, known, and novel categories, respectively. It adaptively identifies the most discriminative part in negative samples to boost discriminability, while permitting similarity in other parts to enhance the transferability of shared parts across different categories. (4) We also evaluate the independent effect of diversity loss on our baseline, showing that emphasizing the distinctiveness of various parts within an image effectively enhances the discriminability of part-level features. (5) Finally, we validate the combined effects of the two part learning losses.
+
+# 5. Conclusion
+
+This paper underscores the trade-off between discriminability and generalization in existing methods and introduces APL, which enhances both aspects simultaneously and seamlessly integrates into GCD frameworks. APL utilizes DINO prior and introduces novel all-min contrastive and diversity loss functions to enhance knowledge transfer, resulting in superior performance across benchmarks. Acknowledgment: This work was supported by the National Natural Science Foundation of China (No.62206174).
+
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+# Adaptive Rectangular Convolution for Remote Sensing Pansharpening
+
+Xueyang Wang, Zhixin Zheng, Jiandong Shao, Yule Duan, Liang-Jian Deng*  
+University of Electronic Science and Technology of China, Chengdu, China
+
+xywang.uestc@std.uestc.edu.cn; zhengzx@std.uestc.edu.cn; shamy@std.uestc.edu.cn  
+yule.duan@outlook.com; liangjian.deng@uestc.edu.cn
+
+# Abstract
+
+Recent advancements in convolutional neural network (CNN)-based techniques for remote sensing pansharpening have markedly enhanced image quality. However, conventional convolutional modules in these methods have two critical drawbacks. First, the sampling positions in convolution operations are confined to a fixed square window. Second, the number of sampling points is preset and remains unchanged. Given the diverse object sizes in remote sensing images, these rigid parameters lead to suboptimal feature extraction. To overcome these limitations, we introduce an innovative convolutional module, Adaptive Rectangular Convolution (ARConv). ARConv adaptively learns both the height and width of the convolutional kernel and dynamically adjusts the number of sampling points based on the learned scale. This approach enables ARConv to effectively capture scale-specific features of various objects within an image, optimizing kernel sizes and sampling locations. Additionally, we propose ARNet, a network architecture in which ARConv is the primary convolutional module. Extensive evaluations across multiple datasets reveal the superiority of our method in enhancing pansharpening performance over previous techniques. Ablation studies and visualization further confirm the efficacy of ARConv. The source code can be available at https://github.com/WangXueyang-uestc/ARConv.
+
+# 1. Introduction
+
+High-quality remote sensing imagery plays a pivotal role in various domains, including military and agriculture. However, existing technologies are only capable of capturing low-resolution multispectral images (LRMS) and high-resolution panchromatic images (PAN). While LRMS imagery preserves rich spectral signatures, it is compromised by limited spatial resolution. Conversely, PAN imagery exhibits superior spatial granularity but lacks multispectral discriminability due to its grayscale representa
+
+![](images/2535d77fb82a4a1150465fa44c0c517bc93ba6e480e01e1b6ffab74aee1ed405.jpg)
+
+![](images/d8f072a72e73f5c453e80c01572205cde7b1aa7fcd485feeed874a0a395d9126.jpg)  
+Figure 1. Top row: The flowchart of remote sensing pansharpening via a DL-based approach. Bottom row: An example of our Adaptive Rectangular Convolution (ARConv), boasting two distinct advantages: 1) its convolution kernels can adaptively modify sampling positions in accordance with object sizes; 2) the quantity of sampling points is dynamically determined across various feature maps, for instance, achieving a  $5 \times 3$  adaptive rectangular convolution, which, to our knowledge, is the first attempt.
+
+tion. As illustrated in Fig. 1, pansharpening addresses this dichotomy through synergistic fusion to synthesize high-resolution multispectral (HRMS) imagery. Many pansharpening methods have been proposed [20], among which traditional methods are divided into Component Substitution (CS) [4, 28], Multi-Resolution Analysis (MRA) [30, 32], and variational optimization (VO) [11, 26]. Recent paradigm shifts toward deep learning have catalyzed extensive deployment of convolutional neural networks (CNNs) in this domain. Different from traditional methods, the input feature of PAN and LRMS images is extracted mainly through convolutional kernels. However, standard convo
+
+lution has two major drawbacks. First, its sampling positions are fixed within a square window of a determined size, which restricts its ability to deform, thereby preventing it from adaptively finding the sampling locations. Second, the number of sampling points of the convolutional kernel is predetermined, making it challenging to adaptively capture features at different scales. In remote sensing images, the scale differences between different objects can be significant, such as small cars and large buildings, which standard convolutions are not adept at capturing, leading to inefficient feature extraction.
+
+In recent years, many innovative convolutional methods have been proposed. Spatial adaptive convolution methods, such as PAC [25], DDF [40], LAGConv [16], and CANConv [9], can adaptively generate different convolution kernel parameters based on various spatial locations, enabling them to accommodate different spatial regions. However, these methods have yet to fully consider the rich scale information present in remote sensing images. Shape-adaptive convolutions, such as Deformable Convolution [5, 41], can adaptively adjust the position of each sampling point by learning offsets to extract features of objects with different shapes. Although this provides significant flexibility, the number of learnable parameters increases quadratically with the kernel size, making it difficult to achieve convergence on small datasets. Furthermore, it cannot adjust the number of sampling points based on the shape of the convolution kernel, which further limits its performance. Multiscale convolutions, such as pyramid convolution [10], can extract information at different scales within the same feature map. However, the size of their convolution kernels is predetermined, while the features in the image may exhibit different patterns and structures across scales. This can lead to imprecise feature fusion between scales, potentially affecting the model's overall performance.
+
+Based on the above analysis, we propose the Adaptive Rectangular Convolution (ARConv), which can not only adaptively adjust the sampling positions but also the number of sampling points, as shown in Fig. 1. The former is achieved by learning only two parameters: the height and width of the convolution kernel, without incurring additional computational burden as the kernel size increases. The latter selects an appropriate number of sampling points based on the average level of the learned height and width. Moreover, we introduce affine transformation to ARConv, which brings spatial adaptability. All of this enables our module to effectively extract features from objects of varying sizes in the feature map. The main contributions of this paper are summarized as follows:
+
+1. ARConv is proposed as a module that can adaptively adjust the sampling positions and change the number of sampling points, enabling it to effectively capture scale-specific features of various objects in remote
+
+sensing images. Based on ARConv and the U-net architecture [23, 35], ARNet is introduced.
+
+2. The relationship between the learned height and width of the convolution kernel and the actual object sizes is explored through heatmap visualizations. A certain level of correlation is observed, which validates the effectiveness of the proposed method.  
+3. The effectiveness of ARConv is validated by comparing it with various pansharpening methods across multiple datasets. The results demonstrate that ARConv achieves outstanding performance.
+
+# 2. Related Works
+
+![](images/d1e8b2c4e6b28cfb1c42797ca64bf8d31dc9113435084c55af3ce1e12bfdabd7.jpg)
+
+![](images/485afb8e59a1cba51eec7eaaa2c4ac12f62653bad312d521925868f84a785b7e.jpg)
+
+![](images/e62733f0aa6d6edb532b62022b36680d3146c437b66c1684810d8c97ef0ec7e7.jpg)  
+Figure 2. Diagrams illustrating the working principles of four types of convolutional kernels. (a) Standard Convolution. (b) Deformable Convolution [5, 41]. (c) Multi-scale Convolution [10, 18]. (d) Our proposed Convolution (ARConv).
+
+![](images/ecb097f6610b34b38fb5d969924743f41d02a931e41af39c566c5d1386937a96.jpg)
+
+# 2.1. Adaptive Convolution
+
+Standard convolution, with its fixed shape and size, exhibits limited flexibility in handling geometric transformations, posing challenges in adapting to the varying scales and shapes of objects commonly encountered in visual tasks. Deformable Convolution [5, 41] was the pioneering approach to address this limitation by learning an offset matrix that adjusts the sampling positions at each pixel, as visualized in Fig. 2. This advancement enabled the convolutional kernel to deform in an unsupervised manner for the first time. Building on the concept of deformable convolution, Dynamic Snake Convolution [22] specifically optimizes feature extraction for tubular structures by employing carefully designed loss constraints to guide the deformation of convolutional kernels. Scale-adaptive Convolution [39] extends this flexibility by allowing the convolutional kernel to learn scaling ratios, dynamically modifying the receptive field to better capture features at different scales.
+
+The aforementioned convolutional paradigms face a flexibility-efficiency trade-off: excessive deformability in-
+
+creases computational load with dense sampling points, while rigid structures fail to adapt to irregular objects. Moreover, fixed sampling point counts restrict dynamic adjustments to learned kernel geometries.
+
+# 2.2. Multi-scale Convolution
+
+Multi-scale convolution enhances the analysis of input data by utilizing convolutional kernels of different sizes, which facilitates the extraction of feature information across different scales. In comparison, standard convolution is restricted to capturing features at a single scale. Pyramidal Convolution (PyConv) [10] addresses this limitation by employing a hierarchical structure within each layer, utilizing a pyramid of convolutional kernels of diverse scales to process the input feature map comprehensively, as described in Fig. 2. To enhance computational efficiency and reduce the overall parameter count, the depth of each kernel—defined by the number of channels participating in the convolution operations is adaptively adjusted based on the pyramid level. Selective Kernel Networks [18] further refine this approach by incorporating a soft attention mechanism that dynamically selects the most relevant feature maps generated from multi-scale convolutions, thereby increasing the network's adaptability to variations in spatial resolution. However, these convolutional modules still cannot adaptively adjust the sampling positions and the number of sampling points of the convolution kernel based on the sizes of various objects in the feature map.
+
+# 2.3. Motivation
+
+Remote sensing images exhibit considerable variety in context, with objects differing significantly in size. Using convolutional kernels of varying sizes is more effective for extracting features from different regions compared to using fixed-size kernels. Traditional shape-adaptive convolutions can modify sampling positions to align with object shapes but cannot adjust the number of sampling points based on the shape of the kernel. Additionally, some deformable strategies require learning many parameters, leading to higher computational costs. While multi-scale convolutions can capture features at various scales within the same feature map, their kernel sizes remain fixed thus cannot adaptively adjust sampling positions based on the feature map's content. To overcome these limitations, we introduce Adaptive Rectangular Convolution (ARConv), a novel module that treats the height and width of the convolutional kernel as learnable parameters. This allows the shape of the kernel to adjust dynamically based on the size of different objects. With sampling points evenly distributed within a rectangular deformable region, ARConv can flexibly modify sampling positions and adjust the number of points according to the average size of the learned kernels in each feature map. Unlike conventional deformable convolutions
+
+[5], our approach requires learning only two parameters, minimizing computational overhead as the number of sampling points increases. To further enhance adaptability, we apply an affine transformation to the kernel's output, improving spatial flexibility.
+
+# 3. Methods
+
+This section details the design of ARConv and ARNet. The implementation of ARConv follows four steps: (1) Learning the height and width feature maps of the convolutional kernel. (2) Selecting the number of convolutional kernel sampling points. (3) Generating the sampling map. (4) The implementation of the convolution. In ARNet, the standard convolution layers of U-Net [23, 35] are replaced with ARConv modules to more effectively capture rich scale information for the pansharpening task. The overall architecture of ARConv is presented in Fig. 3.
+
+# 3.1. Adaptive Rectangular Convolution
+
+# 3.1.1. Learning the Height and Width of Convolution
+
+The learning process can be mathematically formulated as:
+
+$$
+\mathbf {y} _ {i} = f _ {\theta_ {i}} (\mathbf {X}), \quad i \in \{1, 2 \}, \tag {1}
+$$
+
+where  $\mathbf{X} \in \mathbb{R}^{H \times W \times C_{in}}$  represents the input feature map.  $H$  and  $W$  denote the height and width of the feature map, respectively, and  $C_{in}$  denotes the number of input channels. Besides,  $f_{\theta_i}(\cdot)$  corresponds to two subnets responsible for predicting the height and width of the convolutional kernel, each consists of two components: a shared feature extractor and distinct height-width learners with  $\theta_i$  representing the associated parameters. The output feature maps are denoted as  $\mathbf{y}_i \in \mathbb{R}^{H \times W \times 1}$ , where  $\mathbf{y}_1$  is the height feature map and  $\mathbf{y}_2$  is the width feature map, which are referred to as  $\mathbf{h}$  and  $\mathbf{w}$  in the Fig. 3, respectively. The final layer of the height-width learner is a Sigmoid function, where  $\operatorname{Sigmoid}(x) = \frac{1}{1 + e^{-x}}$ . So,  $\mathbf{y}_i \in (0,1)$ , which only represent relative magnitudes thus cannot directly correspond to the height and width of the convolutional kernel, we adopt the following method to constrain their range of values.
+
+$$
+\mathbf {y} _ {i} = a _ {i} \cdot \mathbf {y} _ {i} + b _ {i}, \quad i \in \{1, 2 \}, \tag {2}
+$$
+
+where  $a_{i}$  and  $b_{i}$  are modulation factors that constrain the range of height and width. Thus, the height of the convolutional kernel is constrained within the range  $(b_{1}, a_{1} + b_{1})$ , the width within  $(b_{2}, a_{2} + b_{2})$ .
+
+The height and width feature maps are fed into the second part, which will be detailed later, where the number of sampling points for the convolution kernel,  $k_{h} \cdot k_{w}$ , is selected. Each feature map of height and width is then duplicated  $k_{h} \cdot k_{w}$  times. Subsequently, a meshgrid operation is applied that aims to evenly distribute the sampling points in the kernel to generate the scaling matrix  $Z_{ij} \in \mathbb{R}^{k_h \times k_w}$  at each location of the pixels  $(i,j)$ .
+
+![](images/7239bdd78b07f6a98c3aeeda43a6c61d59574435dacc8f4c009fdd41bb1a5538.jpg)  
+Figure 3. Overview of the ARConv architecture. (1)Learning the kernel's height and width: The model dynamically predicts convolutional kernel height and width through feature-driven parameter estimation. (2)Selecting the number of sampling points: Optimal kernel size is derived by aggregating spatial statistics from the predicted height and width dimensions. (3)Generating the sampling map: The sampling positions are determined using learnable offset parameters, with  $p_0$  serving as the spatial anchor point. At last, the adaptive convolution is applied on the generated sampling map, enhanced by affine transformation.
+
+# 3.1.2. Selecting the Number of Sampling Points
+
+First, we calculate the mean of all the values in  $\mathbf{y}_1$  and  $\mathbf{y}_2$  to obtain the average level of the learned height and width. Then, the number of sampling points in the convolutional kernel in vertical and horizontal directions are derived from  $k_h = \phi (\lfloor \overline{\mathbf{y}}_1\rfloor),k_w = \phi (\lfloor \overline{\mathbf{y}}_2\rfloor)$  where  $\lfloor x\rfloor$  represents the floor of  $x,m$  and  $n$  denote the modulation coefficients that map the height and width of the convolutional kernel to the number of sampling points. The function  $\phi (\cdot)$  can be expressed as follows:
+
+$$
+\phi (x) = x - [ x \text {i s e v e n} ], \tag {3}
+$$
+
+Here,  $[\cdot ]$  denotes the Iverson bracket. Given a fixed height and width of the convolutional kernel, the larger the values of  $m$  and  $n$ , the fewer the sampling points and the sparser their distribution. From Eq. (3), we only select convolutional kernels with an odd number of sampling points. When  $\lfloor \frac{\bar{y}_1}{n}\rfloor$  or  $\lfloor \frac{\bar{y}_2}{m}\rfloor$  is even, we choose the nearest odd number that is smaller than the even number. Finally, the number of sampling points is:
+
+$$
+N = k _ {h} \cdot k _ {w}. \tag {4}
+$$
+
+# 3.1.3. Generating the Sampling Map
+
+In standard convolution, the process involves sampling from the input feature map  $\mathbf{X}$  using a regular grid  $\mathbf{G}$ , followed
+
+by a weighted summation of these sampled values with weights w. For example,
+
+$$
+\mathbf {G} = \left\{(- 1, - 1), (- 1, 0), \dots , (1, 0), (1, 1) \right\}, \tag {5}
+$$
+
+corresponds to a kernel covering a  $3 \times 3$  region on the input map with no gaps between sampled points.
+
+Formally, the standard convolution operation for one position  $\mathbf{p}_0$  can be expressed as,
+
+$$
+\mathbf {y} \left(\mathbf {p} _ {0}\right) = \sum_ {\mathbf {g} _ {n} \in \mathbf {G}} \mathbf {w} \left(\mathbf {g} _ {n}\right) \cdot \mathbf {x} \left(\mathbf {p} _ {0} + \mathbf {g} _ {n}\right), \tag {6}
+$$
+
+where  $\mathbf{y}$  is the output feature map,  $\mathbf{w}$  denotes the parameters of covolutional kernel and  $\mathbf{g}_n$  represents the offsets of grid  $\mathbf{G}$  relative to position  $\mathbf{p}_0$ .
+
+For ARConv, we use  $\mathbf{G} \in \mathbb{R}^{k_h \times k_w}$  to denote the offset matrix of the standard convolution with kernel size  $k_h \times k_w$ , which is shared across all pixels. The element at the  $i$ -th row and  $j$ -th column of  $\mathbf{G}$ , denoted by  $g_{ij}$ , is defined as:
+
+$$
+g _ {i j} = \left(\frac {2 i - k _ {h} - 1}{2}, \frac {2 j - k _ {w} - 1}{2}\right). \tag {7}
+$$
+
+Next, we define  $\mathbf{Z}_0\in \mathbb{R}^{k_h\times k_w}$  as the scale matrix at position  $\mathbf{p}_0$  , which is computed in the first part. The element at the  $i$  -th row and  $j$  -th column of  $\mathbf{Z}_0$  , denoted by  $z_{ij}$  , is
+
+![](images/6dfc212b8557f708722b08d9d7b87b0f814808c749f8d313bcfe98d3edb92d2f.jpg)  
+Figure 4. Overall architecture of ARNet. ARNet replaces the standard convolution in U-Net's Resblock with ARConv to create AR-Resblock. The model has down-sampling blocks to extract high-level features and up-sampling blocks to restore spatial resolution with transposed convolutions. Skip connections help transfer detailed spatial information.
+
+given by:
+
+$$
+z _ {i j} = \left(\frac {h _ {0}}{k _ {h}}, \frac {w _ {0}}{k _ {w}}\right), \tag {8}
+$$
+
+where  $h_0$  and  $w_0$  represent the height and width of the learned convolutional kernel at position  $\mathbf{p}_0$ , respectively. The offset matrix of ARConv at position  $\mathbf{p}_0$ , denoted by  $\mathbf{R}$ , is then computed as:
+
+$$
+\mathbf {R} = \mathbf {Z} _ {0} \odot \mathbf {G}, \tag {9}
+$$
+
+where  $\odot$  denotes element-wise multiplication. The element at the  $i$ -th row and  $j$ -th column of  $\mathbf{R}$ , denoted by  $r_{ij}$ , is given by:
+
+$$
+r _ {i j} = \left(\frac {\left(2 i - k _ {h} - 1\right) h _ {0}}{2 k _ {h}}, \frac {\left(2 j - k _ {w} - 1\right) w _ {0}}{2 k _ {w}}\right). \tag {10}
+$$
+
+It is evident that, in most cases, the sampling points do not coincide with the center of the grid points. Therefore, interpolation is required to estimate their pixel values. In this context, we employ bilinear interpolation, and its mathematical formulation is as follows:
+
+$$
+\mathbf {t} (x, y) = \mathbf {w} _ {x} ^ {\mathrm {T}} \mathbf {T} \mathbf {w} _ {y}, \tag {11}
+$$
+
+where  $\mathbf{t}(x,y)$  represents the pixel value at the coordinates  $(x,y)$ .
+
+$$
+\mathbf {T} = \left( \begin{array}{l l} \mathbf {t} \left(x _ {0}, y _ {0}\right) & \mathbf {t} \left(x _ {0}, y _ {1}\right) \\ \mathbf {t} \left(x _ {1}, y _ {0}\right) & \mathbf {t} \left(x _ {1}, y _ {1}\right) \end{array} \right), \tag {12}
+$$
+
+where  $(x_0,y_0),(x_0,y_1),(x_1,y_0),(x_1,y_1)$  are the coordinates of the four grid points closest to  $(x,y)$ .
+
+$$
+\mathbf {w} _ {x} = \left( \begin{array}{c} 1 - w _ {x} \\ w _ {x} \end{array} \right), \mathbf {w} _ {y} = \left( \begin{array}{c} 1 - w _ {y} \\ w _ {y} \end{array} \right), \tag {13}
+$$
+
+where  $w_{x} = \frac{x - x_{0}}{x_{1} - x_{0}}, w_{y} = \frac{y - y_{0}}{y_{1} - y_{0}}$ . They represent the normalized interpolation weights in the  $x$ -direction and  $y$ -direction, respectively.
+
+In summary, the convolution operation we proposed can be mathematically expressed as:
+
+$$
+\mathbf {y} \left(\mathbf {p} _ {0}\right) = \sum_ {\mathbf {r} _ {n} \in \mathbf {R}} \mathbf {w} \left(\mathbf {r} _ {n}\right) \cdot \mathbf {t} \left(\mathbf {p} _ {0} + \mathbf {r} _ {n}\right), \tag {14}
+$$
+
+where  $\mathbf{y}(\mathbf{p}_0)$  refers to the pixel value at position  $\mathbf{p}_0$  in the output feature map  $\mathbf{y}$ ,  $\mathbf{w}$  denotes the parameters of covolutional kernel,  $\mathbf{r}_n$  enumerates the elements in  $\mathbf{R}$ ,  $\mathbf{t}(\mathbf{p}_0 + \mathbf{r}_n)$  calculates the pixel value at position  $\mathbf{p}_0 + \mathbf{r}_n$ .
+
+Whether using standard convolution or our method, each pixel in an image corresponds to a sampling window during the convolution operation. In standard convolution, the sampling points are all located at the grid centers, and the sampling window simply slides across the image with a fixed stride. However, in ARConv, the size of the sampling window varies for each pixel, making the traditional approach unsuitable. In practice, rather than generating a unique convolutional kernel for every pixel, we use an equivalent approach. We adopt an expansion technique, extracting the values at the locations of the sampling points corresponding to the sampling window at each pixel and assembling them into a new grid  $\mathbf{P}_0$ , which replaces the original pixel  $\mathbf{p}_0$ , where  $\mathbf{P}_0 \in \mathbb{R}^{k_h \times k_w \times C_{in}}$ ,  $\mathbf{p}_0 \in \mathbb{R}^{1 \times 1 \times C_{in}}$ . After completing the expansion for each pixel, we obtain the final sampling map  $\mathbf{S}$ , which belongs to  $\mathbb{R}^{(k_hH) \times (k_wW) \times C_{in}}$ .
+
+# 3.1.4. The Implementation of the Convolution
+
+In this part, we apply a convolution to  $\mathbf{S}$  for feature extraction, using a kernel size and stride both set to  $(k_h,k_w)$ . To introduce spatial adaptability, we apply an affine transformation to the output feature map. We use two sub-networks,
+
+Table 1. Performance benchmarking on the WV3 dataset was conducted using 20 reduced-resolution and 20 full-resolution samples. The top-performing results are highlighted in bold, while the second-best are indicated with an underline.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Reduced-Resolution Metrics</td><td colspan="3">Full-Resolution Metrics</td></tr><tr><td>SAM↓</td><td>ERGAS↓</td><td>Q8↑</td><td>Dλ↓</td><td>Ds↓</td><td>HQNR↑</td></tr><tr><td>EXP [1]</td><td>5.800 ± 1.881</td><td>7.155 ± 1.878</td><td>0.627 ± 0.092</td><td>0.0232 ± 0.0066</td><td>0.0813 ± 0.0318</td><td>0.897 ± 0.036</td></tr><tr><td>MTF-GLP-FS [31]</td><td>5.316 ± 1.766</td><td>4.700 ± 1.597</td><td>0.833 ± 0.092</td><td>0.0197 ± 0.0078</td><td>0.0630 ± 0.0289</td><td>0.919 ± 0.035</td></tr><tr><td>TV [21]</td><td>5.692 ± 1.808</td><td>4.856 ± 1.434</td><td>0.795 ± 0.120</td><td>0.0234 ± 0.0061</td><td>0.0393 ± 0.0227</td><td>0.938 ± 0.027</td></tr><tr><td>BSDS-PC [29]</td><td>5.429 ± 1.823</td><td>4.698 ± 1.617</td><td>0.829 ± 0.097</td><td>0.0625 ± 0.0235</td><td>0.0730 ± 0.0356</td><td>0.870 ± 0.053</td></tr><tr><td>CVPR2019 [12]</td><td>5.207 ± 1.574</td><td>5.484 ± 1.505</td><td>0.764 ± 0.088</td><td>0.0297 ± 0.0059</td><td>0.0410 ± 0.0136</td><td>0.931 ± 0.0183</td></tr><tr><td>LRTCFPan [37]</td><td>4.737 ± 1.412</td><td>4.315 ± 1.442</td><td>0.846 ± 0.091</td><td>0.0176 ± 0.0066</td><td>0.0528 ± 0.0258</td><td>0.931 ± 0.031</td></tr><tr><td>PNN [19]</td><td>3.680 ± 0.763</td><td>2.682 ± 0.648</td><td>0.893 ± 0.092</td><td>0.0213 ± 0.0080</td><td>0.0428 ± 0.0147</td><td>0.937 ± 0.021</td></tr><tr><td>PanNet [38]</td><td>3.616 ± 0.766</td><td>2.666 ± 0.689</td><td>0.891 ± 0.093</td><td>0.0165 ± 0.0074</td><td>0.0470 ± 0.0213</td><td>0.937 ± 0.027</td></tr><tr><td>DiCNN [15]</td><td>3.593 ± 0.762</td><td>2.673 ± 0.663</td><td>0.900 ± 0.087</td><td>0.0362 ± 0.0111</td><td>0.0462 ± 0.0175</td><td>0.920 ± 0.026</td></tr><tr><td>FusionNet [6]</td><td>3.325 ± 0.698</td><td>2.467 ± 0.645</td><td>0.904 ± 0.090</td><td>0.0239 ± 0.0090</td><td>0.0364 ± 0.0137</td><td>0.941 ± 0.020</td></tr><tr><td>DCFNet [36]</td><td>3.038 ± 0.585</td><td>2.165 ± 0.499</td><td>0.913 ± 0.087</td><td>0.0187 ± 0.0072</td><td>0.0337 ± 0.0054</td><td>0.948 ± 0.012</td></tr><tr><td>LAGConv [16]</td><td>3.104 ± 0.559</td><td>2.300 ± 0.613</td><td>0.910 ± 0.091</td><td>0.0368 ± 0.0148</td><td>0.0418 ± 0.0152</td><td>0.923 ± 0.025</td></tr><tr><td>HMPNet [27]</td><td>3.063 ± 0.577</td><td>2.229 ± 0.545</td><td>0.916 ± 0.087</td><td>0.0184 ± 0.0073</td><td>0.0530 ± 0.0555</td><td>0.930 ± 0.011</td></tr><tr><td>CMT [24]</td><td>2.994 ± 0.607</td><td>2.214 ± 0.516</td><td>0.917 ± 0.085</td><td>0.0207 ± 0.0082</td><td>0.0370 ± 0.0078</td><td>0.943 ± 0.014</td></tr><tr><td>CANNet [9]</td><td>2.930 ± 0.593</td><td>2.158 ± 0.515</td><td>0.920 ± 0.084</td><td>0.0196 ± 0.0083</td><td>0.0301 ± 0.0074</td><td>0.951 ± 0.013</td></tr><tr><td>Proposed</td><td>2.885 ± 0.590</td><td>2.139 ± 0.528</td><td>0.921 ± 0.083</td><td>0.0146 ± 0.0059</td><td>0.0279 ± 0.0068</td><td>0.958 ± 0.010</td></tr></table>
+
+$\mathbf{M}_{\alpha}$  and  $\mathbf{B}_{\beta}$ , to predict the matrices  $\mathbf{M}$  and  $\mathbf{B}$  for the affine transformation, with  $\alpha$  and  $\beta$  as the parameters of these networks. The final output feature map is given by:
+
+$$
+\mathbf {y} = \mathbf {S K} \otimes \mathbf {S} \odot \mathbf {M} \oplus \mathbf {B}, \tag {15}
+$$
+
+where  $\mathbf{y} \in \mathbb{R}^{H \times W \times C_{out}}$  is the output feature map.  $\mathbf{SK} \in \mathbb{R}^{C_{in} \times k_h \times k_w \times C_{out}}$  is the parameter of the selected convolutional kernel,  $\otimes$  represents the convolution operation,  $\odot$  represents element-wise multiplication and  $\oplus$  represents elements-wise plus.
+
+# 3.2. ARNet Architecture
+
+This section details the construction of ARNet which is shown at Fig. 4. Our network draws inspiration from the U-net architecture [23, 35], a well-known model in image segmentation that uses an encoder-decoder structure with skip connections to retain spatial information. In ARNet, we replace the standard convolutional layers in ResBlock [14] with our ARConv. The data flow proceeds as follows: First, the MS image is upsampled to match the resolution of the PAN image, generating the LRMS image. Next, the PAN and LRMS images are concatenated along the channel dimension and input into the network. ARNet involves a series of downsampling and upsampling steps, with ARConv layers at different depths adapting to find the optimal parameters for feature extraction at various scales. Finally, the learned details are injected back into the LRMS image [6, 15], refining it and producing the final output image with enhanced resolution and detail.
+
+# 4. Experiments
+
+# 4.1. Datasets, Metrics and Training Details
+
+We evaluate the effectiveness of our method on several datasets, including 8-band data captured by the WorldView3 (WV3) sensor, as well as 4-band data captured by
+
+the QuickBird (QB) and the GaoFen-2 (GF2) sensors. Although we use a supervised learning approach, ground truth data is not directly available, so we apply Wald's protocol [7, 34] to construct our dataset. All three datasets are accessible from a public repository [8]. For test sets with different resolutions, we use different evaluation metrics. Specifically, we employ SAM [3], ERGAS [33], and Q8 [13] to assess the performance of ARNet on the reduced-resolution dataset, and  $D_{s}$ ,  $D_{\lambda}$ , and HQNR [2] to evaluate its performance on the full-resolution dataset. During training, we employ the  $l_{1}$  loss function along with the Adam optimizer [17], using a batch size of 16. Given that our method involves selecting convolutional kernels based on the learned height and width—an approach that can complicate convergence—we designate the initial 100 epochs as an exploratory phase. During this phase, we allow the model to explore different configurations. After these 100 epochs, we randomly select a combination of convolutional kernels from the 16 batches based on the results obtained and then fix this selection for the remainder of the training. Further details on the dataset and training procedure are provided in the supplementary material Sec. 7.1 and 7.2.
+
+# 4.2. Results
+
+The outstanding performance of ARNet has been thoroughly demonstrated through a comprehensive evaluation on the WV3, QB, and GF2 benchmark datasets. Tab. 1 to 3 provide a detailed comparison of ARNet against various state-of-the-art techniques, including traditional methods, general deep learning methods, and specialized convolution-based deep learning approaches similar to proposed work, such as LAGConv [16] and CANConv [9], more details can be found in supplementary material Sec. 7.3. The results clearly indicate that ARNet consistently delivers high-quality performance across different
+
+Table 2. Performance benchmarking on the QB dataset using 20 reduced-resolution samples. Best in bold; second best underlined.  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q4↑</td></tr><tr><td>EXP [1]</td><td>8.435±1.925</td><td>11.819±1.905</td><td>0.584±0.075</td></tr><tr><td>TV [21]</td><td>7.565±1.535</td><td>7.781±0.699</td><td>0.820±0.090</td></tr><tr><td>MTF-GLP-FS [31]</td><td>7.793±1.816</td><td>7.374±0.724</td><td>0.835±0.088</td></tr><tr><td>BDSD-PC [29]</td><td>8.089±1.980</td><td>7.515±0.800</td><td>0.831±0.090</td></tr><tr><td>CVPR19 [12]</td><td>7.998±1.820</td><td>9.359±1.268</td><td>0.737±0.087</td></tr><tr><td>LRTCFPan [37]</td><td>7.187±1.711</td><td>6.928±0.812</td><td>0.855±0.087</td></tr><tr><td>PNN [19]</td><td>5.205±0.963</td><td>4.472±0.373</td><td>0.918±0.094</td></tr><tr><td>PanNet [38]</td><td>5.791±1.184</td><td>5.863±0.888</td><td>0.885±0.092</td></tr><tr><td>DiCNN [15]</td><td>5.380±1.027</td><td>5.135±0.488</td><td>0.904±0.094</td></tr><tr><td>FusionNet [6]</td><td>4.923±0.908</td><td>4.159±0.321</td><td>0.925±0.090</td></tr><tr><td>DCFNet [36]</td><td>4.512±0.773</td><td>3.809±0.336</td><td>0.934±0.087</td></tr><tr><td>LAGConv [16]</td><td>4.547±0.830</td><td>3.826±0.420</td><td>0.934±0.088</td></tr><tr><td>HMPNet [27]</td><td>4.617±0.404</td><td>3.404±0.478</td><td>0.936±0.102</td></tr><tr><td>CMT [24]</td><td>4.535±0.822</td><td>3.744±0.321</td><td>0.935±0.086</td></tr><tr><td>CANNet [9]</td><td>4.507±0.835</td><td>3.652±0.327</td><td>0.937±0.083</td></tr><tr><td>Proposed</td><td>4.430±0.811</td><td>3.633±0.327</td><td>0.939±0.081</td></tr></table>
+
+Table 3. Performance benchmarking on the GF2 dataset using 20 reduced-resolution samples. Best in bold; second best underlined.  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q4↑</td></tr><tr><td>EXP [1]</td><td>1.820±0.403</td><td>2.366±0.554</td><td>0.812±0.051</td></tr><tr><td>TV [21]</td><td>1.918±0.398</td><td>1.745±0.405</td><td>0.905±0.027</td></tr><tr><td>MTF-GLP-FS [31]</td><td>1.655±0.385</td><td>1.589±0.395</td><td>0.897±0.035</td></tr><tr><td>BDSD-PC [29]</td><td>1.681±0.360</td><td>1.667±0.445</td><td>0.892±0.035</td></tr><tr><td>CVPR19 [12]</td><td>1.598±0.353</td><td>1.877±0.448</td><td>0.886±0.028</td></tr><tr><td>LRTCFPan [37]</td><td>1.315±0.283</td><td>1.301±0.313</td><td>0.932±0.033</td></tr><tr><td>PNN [19]</td><td>1.048±0.226</td><td>1.057±0.236</td><td>0.960±0.010</td></tr><tr><td>PanNet [38]</td><td>0.997±0.212</td><td>0.919±0.191</td><td>0.967±0.010</td></tr><tr><td>DiCNN [15]</td><td>1.053±0.231</td><td>1.081±0.254</td><td>0.959±0.010</td></tr><tr><td>FusionNet [6]</td><td>0.974±0.212</td><td>0.988±0.222</td><td>0.964±0.009</td></tr><tr><td>DCFNet [36]</td><td>0.872±0.169</td><td>0.784±0.146</td><td>0.974±0.009</td></tr><tr><td>LAGConv [16]</td><td>0.786±0.148</td><td>0.687±0.113</td><td>0.981±0.008</td></tr><tr><td>HMPNet [27]</td><td>0.803±0.141</td><td>0.564±0.099</td><td>0.981±0.020</td></tr><tr><td>CMT [24]</td><td>0.753±0.138</td><td>0.648±0.109</td><td>0.982±0.007</td></tr><tr><td>CANNet [9]</td><td>0.707±0.148</td><td>0.630±0.128</td><td>0.983±0.006</td></tr><tr><td>Proposed</td><td>0.698±0.149</td><td>0.626±0.127</td><td>0.983±0.007</td></tr></table>
+
+![](images/542ec6ef40287cef2089ebd6813b02e78d06fdbf619d5d88329aadc66f4234a1.jpg)  
+Figure 5. Qualitative comparison of benchmark methods on WV3 reduced-resolution dataset. Top: RGB outputs; Bottom: residuals vs. ground truth. See Suppl. Sec. 7.5 for details.
+
+datasets, showcasing remarkable robustness. Moreover, visual assessments reveal that the images generated by ARNet are the closest to the ground truth, illustrating the ability of our convolutional approach to effectively adapt to varying object sizes and extract features at appropriate scales. For further details on the benchmark tests and visual examples, please refer to the supplementary material Sec. 7.5.
+
+Table 4. Ablation study on WV3 reduced-res dataset: HWA (height and width adaptation), NSPA (sampling points adaptation), AT (affine transformation).  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q8↑</td></tr><tr><td>(a) w/o HWA</td><td>2.925±0.593</td><td>2.171±0.557</td><td>0.920±0.085</td></tr><tr><td>(b) w/o NSPA</td><td>2.911±0.603</td><td>2.152±0.565</td><td>0.921±0.083</td></tr><tr><td>(c) w/o AT</td><td>3.020±0.614</td><td>2.269±0.562</td><td>0.916±0.085</td></tr><tr><td>Proposed</td><td>2.885±0.590</td><td>2.139±0.528</td><td>0.921±0.083</td></tr></table>
+
+# 4.3. Ablation Study
+
+To assess the impact of different components in ARConv, we conducted ablation experiments by selectively removing certain modules: (a) without height and width adaptation, (b) without the number of sampling points adaptation, and (c) without affine transformation. The results are shown in Tab. 4. The performance drop in (a) and (b) highlights the effectiveness of ARConv in adapting to different object sizes. In (c), the sharp decline indicates limited flexibility in
+
+our deformation strategy, which is effectively mitigated by introducing spatial adaptability through affine transformation. Notably, the computational cost of this transformation does not increase with kernel size.
+
+Table 5. Performance of different convolution kernel height and width learning ranges on WV3 reduced-resolution dataset.  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q8↑</td></tr><tr><td>(a) 1-3</td><td>2.923±0.600</td><td>2.164±0.546</td><td>0.919±0.085</td></tr><tr><td>(b) 1-9</td><td>2.896±0.588</td><td>2.145±0.544</td><td>0.921±0.084</td></tr><tr><td>(c) 1-18</td><td>2.885±0.590</td><td>2.139±0.528</td><td>0.921±0.083</td></tr><tr><td>(d) 1-36</td><td>3.044±0.646</td><td>2.216±0.578</td><td>0.916±0.087</td></tr><tr><td>(e) 1-63</td><td>3.066±0.593</td><td>2.249±0.554</td><td>0.912±0.095</td></tr></table>
+
+# 4.4. Discussion
+
+Different Height and Width Learning Ranges: To assess the impact of different convolutional kernel heights and widths on ARNet's performance, we designed five sets of experiments with varying height and width ranges: (a) 1-3, (b) 1-9, (c) 1-18, (d) 1-36, and (e) 1-63. In (a), the kernel size is fixed at  $3 \times 3$ , while in (b) to (e), the maximum kernel size is  $7 \times 7$ . As shown in Tab. 5, ARNet's performance initially improves with an increasing height and width range but declines beyond an optimal setting in case (c). This pattern arises because a smaller range results in densely packed sampling points that capture excessive noise, while a larger
+
+![](images/cb2bc89b5eb872725eff935d9bf0468b29f586763eea1ba38c8e21cb164bde7b.jpg)  
+Input
+
+![](images/2cc8b5b8e143cdfbfa22798715d0bcef82731ff777e1fff42097fc98254b8496.jpg)  
+Figure 6. Heatmaps of the heights and widths learned at each pixel by convolutional kernels at different layers. The input image is a sample from the WV3 dataset. In the heatmaps, various colors represent different heights and widths captured by the convolutional kernels.
+
+range spreads sampling points too sparsely, reducing the kernel's ability to capture fine details.
+
+Table 6. Performance on the WV3 reduced-resolution dataset when replacing convolution kernels in other pansharpening methods with ARConv.  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q8↑</td></tr><tr><td>FusionNet [6]</td><td>3.325±0.698</td><td>2.467±0.645</td><td>0.904±0.090</td></tr><tr><td>AR-FusionNet</td><td>3.171±0.650</td><td>2.395±0.630</td><td>0.911±0.087</td></tr><tr><td>LAGNet [16]</td><td>3.104±0.559</td><td>2.300±0.613</td><td>0.910±0.091</td></tr><tr><td>AR-LAGNet</td><td>3.083±0.643</td><td>2.277±0.547</td><td>0.916±0.085</td></tr><tr><td>CANNet [9]</td><td>2.930±0.593</td><td>2.158±0.515</td><td>0.920±0.084</td></tr><tr><td>AR-CANNet</td><td>2.885±0.590</td><td>2.139±0.528</td><td>0.921±0.083</td></tr></table>
+
+Replacing the Convolutional Modules in other Networks: We integrate ARConv as a plug-and-play module, replacing the original convolution layers in pansharpening networks such as FusionNet [6], LAGNet [16], and CANNet [9] to demonstrate ARConv's effectiveness. The results in Tab. 6 indicate that ARConv significantly enhances the performance of these networks. Additional details on this experiment are provided in the supplementary materials Sec. 7.4.
+
+Convolutional Kernel Visualization: Fig. 6 shows the height and width feature maps learned by the convolutional kernels at different layers of ARNet. The overall heatmaps reveal the contours of various objects in the RGB image, especially in the outermost layers of the network. Although the intermediate layers appear disordered, they capture deeper semantic information, such as object sizes in the RGB image. For example, in the height heatmap of the fourth layer, the outline of a tilted building is faintly visible, with a thin blue line along the edges. This indicates that the learned heights of the convolutional kernels are smaller at the edges, reflecting the adaptation of the kernels to the
+
+building's dimensions. Please refer to supplementary material in Sec. 7.6 for more visualizations.
+
+Table 7. Performance comparison between ARConv and DCNv2 on WV3 reduced-resolution.  
+
+<table><tr><td>Methods</td><td>SAM↓</td><td>ERGAS↓</td><td>Q8↑</td></tr><tr><td>Ours</td><td>2.881±0.590</td><td>2.149±0.531</td><td>0.921±0.084</td></tr><tr><td>DCNv2 [41]</td><td>3.151±0.679</td><td>2.425±0.656</td><td>0.915±0.083</td></tr></table>
+
+Comparison with DCNv2: We removed the affine transformation from ARConv and adopted the same modulation method as DCNv2 [41]. Both models were trained for 600 epochs on the WV3 dataset. The results are shown in Tab. 7, where it is evident that our performance surpasses DCNv2. This may be because the deformation strategy in DCNv2 requires learning a larger number of parameters, which can hinder convergence in sharpening tasks.
+
+# 5. Conclusion
+
+In conclusion, we introduce an adaptive rectangular convolution module, ARConv, which dynamically learns height- and width-adaptive convolution kernels for each pixel based on the varying sizes of objects in the input image. By adjusting the number of sampling points according to the learned scale, ARConv overcomes the traditional limitations of fixed sampling shapes and point counts in convolution kernels. Integrated seamlessly into U-net as a plug-and-play module, ARConv forms ARNet, which has demonstrated outstanding performance across multiple datasets. Additionally, the visualization studies confirm that our convolutional kernels can effectively adjust their height and width based on the size and shape of objects, offering a novel solution for the pansharpening task.
+
+# 6. Acknowledgement
+
+This work was supported in part by the NSFC (12271083, 62273077), Sichuan Province's Science and Technology Empowerment for Disaster Prevention, Mitigation, and Relief Project (2025YFNH0001), and the Natural Science Foundation of Sichuan Province (2024NSFJQ0013).
+
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+# Adaptive Unimodal Regulation for Balanced Multimodal Information Acquisition
+
+Chengxiang Huang $^{1,\dagger}$  Yake Wei $^{2,\dagger}$  Zequn Yang $^{2}$  Di Hu $^{2,*}$
+
+$^{1}$ Beijing University of Posts and Telecommunications  $^{2}$ Renmin University of China
+
+huangchengxiang2021@bupt.edu.cn, {yakewei,zqyang,dihu}@ruc.edu.cn
+
+# Abstract
+
+Sensory training during the early ages is vital for human development. Inspired by this cognitive phenomenon, we observe that the early training stage is also important for the multimodal learning process, where dataset information is rapidly acquired. We refer to this stage as the prime learning window. However, based on our observation, this prime learning window in multimodal learning is often dominated by information-sufficient modalities, which in turn suppresses the information acquisition of information-insufficient modalities. To address this issue, we propose Information Acquisition Regulation (InfoReg), a method designed to balance information acquisition among modalities. Specifically, InfoReg slows down the information acquisition process of information-sufficient modalities during the prime learning window, which could promote information acquisition of information-insufficient modalities. This regulation enables a more balanced learning process and improves the overall performance of the multimodal network. Experiments show that InfoReg outperforms related multimodal imbalanced methods across various datasets, achieving superior model performance. The code is available at https://github.com/GeWu-Lab/InfoReg_CVPR2025.
+
+# 1. Introduction
+
+Learning during early developmental ages in humans and animals is important for skill impairments [15, 21, 42]. Similarly, in deep learning, recent studies have found that models learn in stages, with early learning being especially important for effective information acquisition [2, 18].
+
+The above circumstance motivates us to investigate the process of information acquisition in the multimodal scenario. Due to the presence of multiple modalities, multimodal learning networks are expected to capture sufficient information from each modality [12, 38]. To observe the
+
+![](images/7cf323c97c21a2b3804989957739d2906a13ec7719c82c114aabe86d30ea6459.jpg)  
+(a) Multimodal scenario.
+
+![](images/a6f26098d83e22e2db345aef829c3d1c8442a6b712fb5dfc91971c903094ae55.jpg)  
+(b) Unimodal scenario.  
+Figure 1. (a). Information amount variation of the audio encoder, video encoder, and multimodal model during the training process on CREMA-D [7]. (b). Information amount variation of the audio and video modalities when trained independently on CREMA-D.
+
+information acquisition of different modalities, we use the trace of the Fisher Information Matrix [2, 10] to investigate the information amount of each modality in multimodal models. However, based on our observation, the amount of information in multimodal models is not well consistent with intuitive expectations. Firstly, as shown in Figure 1a, the green curve, representing the overall multimodal network, demonstrates a rapid increase in information amount during the early periods. Information acquisition is most rapid in this early stage, which we refer to as the prime learning window, reaching a peak at the end of this period, followed by a subsequent decline. Secondly, for audio modality, its overall trend closely aligns with the overall multimodal model, and shows a high information acquisition amount during the prime learning window. These findings align with our expectation that modality information could be acquired effectively within the prime learning window. However, the video modality, represented by the blue curve, shows a much lower information acquisition amount during the prime learning window. Although the video modality is capable of effective information acquisition in the unimodal scenario in Figure 1b, it fails to do so in the multimodal scenario when trained jointly with the audio modality. These observations suggest that information-insufficient modalities, like video, experience suppressed information acquisition during the prime learn
+
+<table><tr><td>Method</td><td>Accuracy</td></tr><tr><td>Video in Joint training (50 epochs)</td><td>35.14</td></tr><tr><td>Video in Joint training (100 epochs)</td><td>35.36</td></tr><tr><td>Video in InfoReg (50 epochs)</td><td>49.65</td></tr></table>
+
+Table 1. Comparison of performance for the video modality between Joint training and InfoReg on the CREMA-D dataset. Simply extending the training time (100 epochs) cannot compensate for the suppressed video modality.
+
+ing window due to the stronger information acquisition capacity of information-sufficient modalities, such as audio. Moreover, as the multimodal model's capacity for information acquisition diminishes in later stages, the imbalance observed during the prime learning window cannot be compensated for by simply extending the training time, as demonstrated in Table 1.
+
+Recent studies have investigated the problem of imbalanced learning across modalities in multimodal learning [17, 30, 39]. Although several studies have made progress in addressing this issue [8, 26, 33, 40], their methods typically apply adjustments across the entire training process without recognizing the importance of the prime learning window. Consequently, the effectiveness of these methods is significantly constrained. Our research reveals that the prime learning window plays a vital role in multimodal learning. In this window, there is a significant imbalance in information acquisition across modalities. Therefore, effective adjustment within this window is essential for achieving balanced information acquisition across modalities.
+
+Based on the above analysis, information-insufficient modalities experience a significantly reduced information acquisition amount during the prime learning window due to suppression from information-sufficient modalities. To address this imbalance, we slow the information acquisition rate of information-sufficient modalities within this window, thereby allowing information-insufficient modalities to improve their acquisition. Hence, we propose our method, Information Acquisition Regulation (InfoReg). In InfoReg, the process begins by determining whether information-sufficient modalities are within the prime learning window. If so, a unimodal regulation term is applied to regulate the Fisher Information [2, 10], thereby restricting these modalities acquire information. As a result, InfoReg promotes a more balanced information acquisition across modalities, enhancing the overall performance of the model. Our extensive experiments across multiple datasets show that InfoReg achieves superior performance and improves modality balance by helping information-insufficient modalities acquire more information during the prime learning window. Additionally, InfoReg enhances feature quality, supporting prior research on the link between early-stage information acquisition and robust feature representation [1, 2]. These results collectively validate
+
+the effectiveness of our approach.
+
+Our main contributions are summarized as follows:
+
+- Firstly, we identify the prime learning window in multimodal learning, a critical period where imbalances in information acquisition significantly impact modality balance and overall performance.  
+- Secondly, We analyze the imbalance of Fisher Information among modalities and propose InfoReg, a method that regulates the information acquisition of information-sufficient modalities during the prime learning window.  
+- Finally, we validate InfoReg on multiple datasets and settings, demonstrating its considerable improvement while maintaining balanced performance across modalities.
+
+# 2. Related Work
+
+# 2.1. Multimodal imbalance learning
+
+Jointly training multiple modalities is intuitively expected to enhance performance [28]. However, imbalanced learning across modalities poses substantial challenges, hindering the effective training of multimodal networks [3, 16, 34, 35, 45]. Previous studies have investigated the imbalanced learning problem across modalities in multimodal learning networks [30, 39], where certain modalities tend to dominate, limiting the learning of other modalities. This imbalance can degrade overall performance and lead to significant disparities between modalities, sometimes even causing multimodal learning to underperform compared to single-modality scenarios [30]. To address this problem, many methods [26, 30, 39-41] have been proposed, primarily focusing on balancing the optimization of each modality throughout the training process. Specifically, OGM [30] balances modalities by adjusting the gradients of welllearned modalities. MMPareto [40] leverages an optimized Pareto front to balance the performance across modalities, aiming to improve the generalization of multimodal models. Despite the successes of previous work, they have largely overlooked the impact of different training periods on information acquisition across various modalities. We have recognized this issue and designed a method accordingly. By slowing down the information acquisition rate of information-sufficient modalities, our approach alleviates the suppression of information-insufficient modalities, allowing them to acquire more information in the early stages, effectively balancing the performance of different modalities. This leads to considerable improvements in both overall performance and modality balance.
+
+# 2.2. Early stages in deep learning
+
+The learning process of deep learning models consists of two main phases: an initial phase of information acquisition from the dataset, followed by a phase of gradual information compression or forgetting [1, 18, 20, 46]. Recent stud
+
+ies highlight the crucial role of early-stage learning in shaping feature representation and overall model performance [11, 13, 19, 25, 47], similar to findings in neuroscience [6, 15, 21, 43]. Further, the information missed during the early stages cannot be recovered by extending the training duration later on [2]. We define this early important learning period as the prime learning window. However, previous research has overlooked the importance of the prime learning window in multimodal learning. Our findings reveal that balancing information acquisition among modalities during this window leads to considerable performance improvements in multimodal models.
+
+# 3. Method
+
+# 3.1. Multimodal learning framework
+
+For convenience, let the dataset be denoted by  $D = \{(x_{n},y_{n})\}_{n = 0,1,\ldots ,N - 1}$ , where each  $x_{n}$  contains inputs from  $M$  modalities:  $x_{n} = (x_{n}^{1},x_{n}^{2},\dots,x_{n}^{M})$ . The target label  $y_{n}\in \{1,2,\ldots \}$  represents the class of sample  $x_{n}$ . For each modality  $m$ , where  $m\in \{1,2,\dots,M\}$ , the input is processed through the corresponding encoder  $\varphi^m (w_m,\cdot)$ . Here,  $w_{m}$  are the weights of encoder  $m$ . After feature extraction, the outputs are concatenated and passed to a single-layer linear classifier. Finally, one joint multimodal cross-entropy loss  $\mathcal{L}_{joint}(w)$  is utilized to optimize the model.
+
+# 3.2. Fisher Information in multimodal learning
+
+Following previous work [1, 32] that uses the Kullback-Leibler (KL) divergence to measure the information contained in the weights of a unimodal network, the information acquisition process for a single modality  $m$  can be evaluated by this metric. Given the posterior distribution  $p_{w_m}(y|x;D)$ , encoded by the unimodal encoder with weights  $w_{m}$  and its prior distribution  $q_{w_m}(y|x)$ , the mutual information is defined as follows:
+
+$$
+D _ {K L} \left(p _ {w _ {m}} \| q _ {w _ {m}}\right) = \int p _ {w _ {m}} (y | x; D) \log \frac {p _ {w _ {m}} (y | x ; D)}{q _ {w _ {m}} (y | x)} d y. \tag {1}
+$$
+
+However, quantifying the information a unimodal encoder acquires from the dataset is challenging because the ground truth prior distribution  $q_{w_m}(y|x)$  is not accessible. As an alternative, inspired by [2], the rate of information acquisition from the dataset can be estimated by calculating the KL divergence between distributions encoded by weights at successive moments in training. Specifically, given a perturbation  $w_m' = w_m + \delta w_m$ . The discrepancy between the distributions  $p_{w_m}(y|x;D)$  and  $p_{w_m'}(y|x;D)$  reflects the rate of information acquisition and can be defined as:
+
+$$
+D _ {K L} \left(p _ {w _ {m}} \| p _ {w _ {m} ^ {\prime}}\right) = \int p _ {w _ {m}} (y | x; D) \log \frac {p _ {w _ {m}} (y | x ; D)}{p _ {w _ {m} ^ {\prime}} (y | x ; D)} d y. \tag {2}
+$$
+
+Further, the KL divergence can be approximated to second order by applying the Taylor expansion:
+
+$$
+D _ {K L} \left(p _ {w _ {m}} \| p _ {w _ {m}} ^ {\prime}\right) \approx \frac {1}{2} \delta w _ {m} ^ {T} F _ {m} \delta w _ {m}, \tag {3}
+$$
+
+where  $F_{m}$  is the Fisher Information Matrix (FIM) [10], and is defined as:
+
+$$
+F _ {m} = \mathbb {E} _ {y \sim p _ {w}} \left[ \nabla_ {w _ {m}} \operatorname {l o g p} _ {w _ {m}} (y | x) \nabla_ {w _ {m}} \operatorname {l o g p} _ {w _ {m}} (y | x) ^ {T} \right]. \tag {4}
+$$
+
+The FIM plays a crucial role in quantifying the amount of information captured by the deep neural network [2, 24] and acts as a local measure, assessing how small perturbations in the model's parameters influence its output [4]. Additionally, the FIM is a semi-definite approximation of the Hessian matrix, providing insights into the curvature of the loss landscape at a given point during training [29, 36].
+
+In multimodal learning, for a unimodal encoder  $\varphi^m$ , the gradient of the encoder can be expressed as:
+
+$$
+g _ {\varphi^ {m}} \left(w _ {m}, x _ {n} ^ {m}\right) = \nabla_ {w _ {m}} \operatorname {l o g p} _ {w _ {m}} \left(y _ {n} \mid x _ {n} ^ {m}\right) = \nabla_ {w _ {m}} \mathcal {L} _ {\text {j o i n t}} \left(w _ {m}\right). \tag {5}
+$$
+
+Based on this, the Fisher Information Matrix  $F_{m}$  can be reformulated as:
+
+$$
+F _ {m} = \mathbb {E} _ {x _ {n} ^ {m} \sim X ^ {m}} \left[ g _ {\varphi^ {m}} \left(w _ {m}, x _ {n} ^ {m}\right) g _ {\varphi^ {m}} \left(w _ {m}, x _ {n} ^ {m}\right) ^ {T} \right]. \tag {6}
+$$
+
+However, computing  $F_{m}$  directly is computationally expensive. To address this, we use the trace of the Fisher Information Matrix, denoted as  $Tr(F_{m})$ , to measure the amount of information captured by the deep neural network. This trace can be computed more efficiently and is defined as:
+
+$$
+T r \left(F _ {m}\right) = \mathbb {E} _ {x _ {n} ^ {m} \sim X ^ {m}} \left[ \| g _ {\varphi^ {m}} \left(w _ {m}, x _ {n} ^ {m}\right) \| ^ {2} \right]. \tag {7}
+$$
+
+As shown in Figure 1,  $Tr(F_m)$  could effectively measure the amount of information acquired and identify the prime learning window.
+
+As illustrated in Figure 3a, information-sufficient modalities will exhibit significantly larger values of  $g_{\varphi^m}$  during the prime learning window. Due to the squared term in Equation 7, these substantial differences in  $g_{\varphi^m}$  between modalities are further amplified, thereby making the imbalance in Fisher Information even more pronounced. This indicates that information-sufficient modalities have a clear advantage in the information acquisition during the prime learning window and dominate the overall information acquisition of the multimodal model.
+
+# 3.3. Information acquisition regulation
+
+To address the Fisher Information imbalance observed during the prime learning window, our method regulates the Fisher Information of information-sufficient modalities in this important period to slow down their information acquisition, thereby promoting information acquisition in other
+
+![](images/434dbdb3b33e2583b1ef4a8f7ea57cc19fa4bcf3c07c514a8eaab2f71c27bb6e.jpg)  
+Figure 2. Overview of InfoReg. This figure shows the main components and workflow of InfoReg. The left side presents our overall framework, while the right side highlights the adaptive unimodal regulation. During the training, InfoReg first identifies the information-sufficient modalities, then evaluates whether they are in the prime learning window, and finally applies adaptive unimodal regulation.
+
+![](images/c3eff40809783071366345f4d3d292d65b3f8d8c8fee907efd3d0102f36e5c29.jpg)
+
+![](images/9b48934115dc3ab80f7c1d9f02e49c3699db72e4a431a3077421a99242390340.jpg)  
+(a) Gap between  $g_{\varphi^m}$ .  
+Figure 3. (a). The gradient gap between the audio modality and video modality on CREMA-D. (b). The  $Tr(F_m)$  gap between the audio modality and video modality on CREMA-D.
+
+![](images/cbf681cd658d23f2f8133591d7010d89cdbed1b6e694ab8b14814f57eb076092.jpg)  
+(b) Gap between  $Tr(F_m)$ .
+
+modalities. Our method consists of the following main components:
+
+- Evaluate the prime learning window for information-sufficient modalities: We first identify the information-sufficient modalities and then evaluate whether they fall within the prime learning window.  
+- Adaptive unimodal regulation: For information-sufficient modalities, we apply adaptive unimodal regulation to approximately regulate the Fisher Information.
+
+# 3.3.1 Evaluating the prime learning window.
+
+Inspired by OGM [30], performance scores are used to identify information-sufficient modalities. Afterward, an assessment is made to determine whether these information-sufficient modalities are in the prime learning window. For each iteration, assume that training has reached epoch  $t$  and is currently processing batch  $b$ , where  $b \in \{0,1,\dots,B - 1\}$  and  $B$  represent the total number of batches. The perfor
+
+mance score for each modality is given by:
+
+$$
+s _ {m; b} ^ {t} = \mathbb {E} _ {x _ {n} ^ {m} \sim X ^ {m}} \left[ - l o g \left(s o f t m a x (\varphi^ {m} (x _ {n} ^ {m})) _ {y _ {n}}\right) \right]. \quad (8)
+$$
+
+Then, we define its performance gap  $\Delta_{m}$  relative to other modalities to determine information-sufficient modalities during the prime learning window. Let  $C_m$  represent the number of modalities with performance scores less than  $s_{m;b}^{t}$ :
+
+$$
+C _ {m} = \left| \left\{m ^ {\prime} \in [ M ] \backslash \{m \}; s _ {m ^ {\prime}; b} ^ {t} <   s _ {m; b} ^ {t} \right\} \right|. \tag {9}
+$$
+
+The performance gap  $\Delta_{m}$  can then be expressed as:
+
+$$
+\Delta_ {m} = \frac {1}{C _ {m}} \sum_ {\substack {m ^ {\prime} \in [ M ] \backslash \{m \}; s _ {m ^ {\prime}; b} ^ {t} <   s _ {m; b} ^ {t}}} \left(s _ {m; b} ^ {t} - s _ {m ^ {\prime}; b} ^ {t}\right), \tag{10}
+$$
+
+where  $\Delta_{m}$  measures the average performance difference between  $m$  and all lower or equally performing modalities. This ensures that for the lowest-performing modality, where  $s_{m:b}^{t}$  is minimal,  $\Delta_{m}$  will be 0.
+
+After identifying information-sufficient modalities based on  $s_{m;b}^{t}$ , the following criterion is used to determine whether these modalities are in the prime learning window:
+
+$$
+\frac {T r \left(F _ {m} ^ {t - 1}\right) - T r \left(F _ {m} ^ {t - 2}\right)}{T r \left(F _ {m} ^ {t - 1}\right)} > K, \tag {11}
+$$
+
+where  $K$  is a positive hyperparameter that controls the threshold for inclusion. Equation 11 reflects the relative changing rate of  $Tr(F_m)$ . A large value of this rate indicates that the information amount in the unimodal encoder is rapidly increasing. Conversely, a small or negative value suggests that information acquisition has slowed down or is even decreasing.
+
+![](images/ec10b4d104311611bc6e86808586762da53efc8aecdebd3f28d2a81486497f40.jpg)  
+Figure 4. The cosine similarities of gradients across different batches within the prime learning window.
+
+Algorithm 1 Pipeline of InfoReg  
+Input: Training dataset  $D$  , number of epochs  $T$  , number of batches  $B$  of each batch, hyperparameter  $\beta ,K$    
+1: for  $t = 0,1,\dots ,T - 1$  do   
+2: if  $t <   2$  then   
+3: Update model parameters;   
+4: Calculate  $Tr(F_m^t)$  by Equation 7;   
+5: Continue;   
+6: end if   
+7: Calculate  $\frac{Tr(F_m^{t - 1}) - Tr(F_m^{t - 2})}{Tr(F_m^{t - 1})}$  .   
+8: for  $b = 0,1,\dots ,B - 1$  do   
+9: Randomly selects a batch of data from  $D$  .   
+10: Calculate the performance scores  $s_{m;b}^{t}$  for different modalities by Equation 8;   
+11: Calculate  $\Delta_{m}$  by Equation 10;   
+12: Decide information-sufficient modalities by  $s_{m;b}^{t}$  .   
+13: Calculate  $\alpha$  by Equation 16;   
+14: if  $\frac{Tr(F_m^{t - 1}) - Tr(F_m^{t - 2})}{Tr(F_m^{t - 1})} >K$  and  $\Delta_{m} > 0$  then   
+15: Calculate the regulation term by Equation 12;   
+16: Add adaptive unimodal regulation term;   
+17: end if   
+18: Update model parameters;   
+19: end for   
+20: Calculate  $Tr(F_m^t)$  by Equation 7.   
+21: end for
+
+# 3.3.2 Adaptive unimodal regulation.
+
+During the prime learning window, information-sufficient modalities dominate the model's information acquisition, limiting the ability of information-insufficient modalities to acquire information. Therefore, it becomes essential to regulate information acquisition of information-sufficient modalities in this window. However, directly calculating  $Tr(F_m^t)$  requires complete gradient information across the entire dataset, making it impractical to regulate effectively. Additionally, calculating  $Tr(F_m^t)$  over a full epoch is ineffective for adjusting the model at each iteration. To address this, we introduce a regulation term  $P_{m;b}^{t}$  to approximately
+
+regulate the Fisher Information:
+
+$$
+P _ {m; b} ^ {t} = \frac {\alpha}{2} \| w _ {m; b} ^ {t} - w _ {m} ^ {t - 1} \| ^ {2}, \tag {12}
+$$
+
+where  $\alpha$  is a parameter that controls the degree of regulation. This regulation term is proportional to  $Tr(F_{m;b}^{t})$  for each batch. Let the gradient  $g_{\varphi^m}$  be denoted as  $g, Tr(F_{m;b}^{t})$  in each batch can be defined as:
+
+$$
+T r \left(F _ {m; b} ^ {t}\right) = \frac {1}{b} \sum_ {k = 0} ^ {b} \| g _ {k} ^ {t} \| ^ {2}. \tag {13}
+$$
+
+The regulation term  $P_{m;b}^{t}$  can be written as:
+
+$$
+\begin{array}{l} P _ {m; b} ^ {t} = \frac {\alpha}{2} \parallel w _ {m; b} ^ {t} - w _ {m} ^ {t - 1} \parallel^ {2} \\ = \frac {\alpha}{2} \| - \eta \sum_ {k = 0} ^ {b} g _ {k} ^ {t} \| ^ {2} \\ = \frac {\alpha \eta^ {2}}{2} \left(\sum_ {k = 0} ^ {b} \| g _ {k} ^ {t} \| ^ {2} + 2 \sum_ {0 \leq z <   k \leq b} g _ {z} ^ {t} \left(g _ {k} ^ {t}\right) ^ {T}\right), \tag {14} \\ \end{array}
+$$
+
+where  $\eta$  represents the learning rate. The high dimensionality of  $g_{b}^{t}$  results in the gradients  $g_{z}^{t}(g_{k}^{t})^{T}$  becoming approximately orthogonal for any two batches  $z$  and  $k$ . The detailed proof is provided in the Appendix. As illustrated in Figure 4, we compare the cosine similarities between gradients of different batches, and the results confirm that they are approximately orthogonal. Then,  $P_{m;b}^{t}$  can be approximated as:
+
+$$
+P _ {m; b} ^ {t} = \frac {\alpha \eta^ {2}}{2} \sum_ {k = 0} ^ {b} \| g _ {k} ^ {t} \| ^ {2}. \tag {15}
+$$
+
+According to the Equation 13 and Equation 15, the unimodal regulation term  $P_{m;b}^{t}$  regulates  $Tr(F_{m;b}^{t})$ , thereby limiting the amount of information acquired by the information-sufficient modalities. To modulate the impact of  $P_{m;b}^{t}$ , we define  $\alpha$  as a dynamic parameter:
+
+$$
+\alpha = \exp (\beta * \tanh  \left(\Delta_ {m}\right)), \tag {16}
+$$
+
+where  $\beta$  is a hyperparameter controlling the sensitivity of  $\alpha$  to the performance gap  $\Delta_{m}$ . A higher value of  $\alpha$  results in stronger regulation, thereby tightly constraining the information acquisition for information-sufficient modalities. This adaptive regulation ensures balance and prevents any single modality from dominating during the prime learning window. Overall, our method is shown in Algorithm 1 and illustrated in Figure 2.
+
+# 4. Experiments
+
+# 4.1. Dataset and experimental settings
+
+CREMA-D [7] is an emotion recognition dataset with recordings of actors expressing six emotions, providing
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">CREMA-D</td><td colspan="3">Kinetics Sounds</td></tr><tr><td>Accuracy</td><td>Acc audio</td><td>Acc video</td><td>Accuracy</td><td>Acc audio</td><td>Acc video</td></tr><tr><td>Joint training</td><td>66.61</td><td>58.99</td><td>35.14</td><td>65.67</td><td>53.13</td><td>36.01</td></tr><tr><td>OGM [30]</td><td>68.70</td><td>56.84</td><td>39.52</td><td>66.63</td><td>53.39</td><td>40.16</td></tr><tr><td>Greedy [44]</td><td>67.82</td><td>59.17</td><td>40.17</td><td>66.54</td><td>53.15</td><td>37.82</td></tr><tr><td>PMR [9]</td><td>66.92</td><td>57.83</td><td>38.91</td><td>66.33</td><td>53.42</td><td>36.17</td></tr><tr><td>AGM [26]</td><td>69.71</td><td>59.32</td><td>43.72</td><td>66.54</td><td>53.12</td><td>37.24</td></tr><tr><td>InfoReg</td><td>71.90</td><td>60.03</td><td>49.65</td><td>69.31</td><td>54.16</td><td>44.73</td></tr></table>
+
+Table 2. Comparison with imbalanced multimodal learning methods. All the methods only use one multimodal loss. Bold and underline represent the best and second best respectively.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">CREMA-D</td><td colspan="3">Kinetics Sounds</td></tr><tr><td>Accuracy</td><td>Acc audio</td><td>Acc video</td><td>Accuracy</td><td>Acc audio</td><td>Acc video</td></tr><tr><td>Joint training</td><td>66.61</td><td>58.99</td><td>35.14</td><td>65.67</td><td>54.13</td><td>36.01</td></tr><tr><td>Joint training*</td><td>70.81</td><td>60.52</td><td>55.23</td><td>68.71</td><td>55.23</td><td>44.18</td></tr><tr><td>G-Blending [39]</td><td>69.11</td><td>60.14</td><td>51.29</td><td>68.33</td><td>54.22</td><td>42.31</td></tr><tr><td>MMPareto [40]</td><td>73.08</td><td>60.83</td><td>58.92</td><td>71.11</td><td>56.47</td><td>53.39</td></tr><tr><td>InfoReg*</td><td>75.71</td><td>61.63</td><td>61.22</td><td>72.03</td><td>57.21</td><td>53.57</td></tr></table>
+
+Table 3. Comparison with imbalanced multimodal learning methods with unimodal loss. Joint training* and InfoReg* denote Joint training with unimodal loss and InfoReg with unimodal loss, respectively. Bold and underline represent the best and second best.
+
+audio-visual samples to examine how auditory and visual cues convey emotion. Kinetics Sounds [5, 22] is designed for human action recognition, featuring 31 action classes from varied video sources, allowing analysis of audio-visual integration in dynamic activity recognition. CMU-MOSI [48] is a sentiment analysis dataset with short video clips including audio, visual, and text modalities, suitable for exploring multimodal sentiment expression.
+
+For our model architecture, we employ ResNet-18 [14] as the backbone for the CREMA-D and Kinetics Sounds, while for the CMU-MOSI, we use a transformer-based model [27]. All models are trained from scratch to ensure that the feature extraction processes are fully optimized for our specific tasks and datasets. Additionally, we implement a late fusion method to integrate uni-modal features from different modalities.
+
+# 4.2. Comparison with related imbalanced methods
+
+To evaluate the effectiveness of InfoReg in addressing information acquisition imbalance across modalities, we compare InfoReg with several imbalanced multimodal learning approaches, including G-Blending [39], OGM [30], Greedy [44], PMR [9], AGM [26], and MMPareto [40]. Of these methods, G-Blending [39] and MMPareto [40] utilize both unimodal and multimodal losses, while OGM [30], Greedy [44], PMR [9], and AGM [26] rely only on unimodal loss. In our evaluation framework, Joint training denotes the widely used baseline for imbalanced multimodal learning, utilizing concatenation fusion with a single multimodal cross-entropy loss function [26, 30]. Mean
+
+while, Joint training* represents the scenario where both unimodal and multimodal joint losses are applied simultaneously.
+
+As shown in Table 2 and Figure 5a, we conduct experiments on CREMA-D and Kinetics Sounds using InfoReg and several related methods that employ only multimodal loss. Based on the results, we first observe that all imbalanced methods achieve improved performance, indicating the significance of the modality imbalance issue and the need for balancing unimodal learning. Furthermore, InfoReg consistently outperforms other methods, especially with a notable improvement in the video modality. This suggests that regulating information acquisition during the prime learning window effectively balances information gain across modalities, enabling information-sufficient modalities to acquire more information and enhancing overall model performance.
+
+Additionally, we provide experiments with methods incorporating both multimodal loss and unimodal loss. Here, Joint training* and InfoReg* indicate both multimodal loss and unimodal loss are applied. As shown in Table 3, all methods with unimodal loss achieve notable improvements over Joint training. This improvement is attributed to the inclusion of unimodal loss, which facilitates more efficient information retrieval from individual modalities, thereby enhancing overall performance. Moreover, InfoReg* continues to outperform other approaches and achieve better modality balance. This indicates that, with unimodal assistance, InfoReg can still effectively balance information acquisition across modalities, thereby achieving good modal-
+
+![](images/e868cad48dbc5109b456602d0a1e4bba9bb1e2ce7022bec3d2758a95ee2673c6.jpg)  
+(a) Comparison of accuracy.
+
+![](images/1c9f7e8d132d18cfac0619057b7afb7cf588fbc88ae6c4573bdd25b969a380ca.jpg)  
+(b)  $Tr(F)$  for both modalities.
+
+![](images/aea9597f91fcab45a9bfe5f7f715ba47568990b010a060666eea77a353c25646.jpg)  
+(c) Comparison of  $Tr(F)$ .
+
+![](images/bac74c4fb44a2ac06c56420f70c0b91914f4c2d11f840a73c06ede300e585ff0.jpg)  
+Figure 5. (a). The overall accuracy, audio accuracy, and video accuracy of InfoReg are compared with Joint training. (b). The value of  $Tr(F)$  in InfoReg for both modalities. (c). The value of  $Tr(F)$  of the video modality in InfoReg compared with that of Joint training. All experiments are conducted on CREMA-D.  
+(a) InfoReg.  
+Figure 6. The representations of the video modality on CREMA-D by t-SNE [37] in InfoReg and Joint training are shown. "Extended Joint training" refers to Joint training that is extended to 100 epochs.
+
+![](images/3a51648b2b8178e8422be35eecdd45927f8cad612f77931df4109a88099c9f13.jpg)  
+(b) Joint training.
+
+![](images/25fb1f86eecc8cafc729c10181c2aa159d2b3532ec84d2de1808b63fade6595b.jpg)  
+(c) Extended Joint training.
+
+ity balance and model performance.
+
+# 4.3. Evaluating information acquisition
+
+We conduct experiments on CREMA-D to evaluate the effectiveness of InfoReg in enhancing information acquisition for information-insufficient modalities during the prime learning window. Firstly, As shown in Figure 5b, we observe that both modalities exhibit gradually growing values of  $Tr(F)$  within the prime learning window, indicating that each modality acquires sufficient information early on. On one hand, the information-sufficient modality, audio, continues to acquire adequate information despite the regulation during the prime learning window, allowing it to maintain good performance throughout training. On the other hand, the information-insufficient modality also acquires sufficient information, as InfoReg alleviates the suppression of its information acquisition by the information-sufficient modality. Secondly, we compare the  $Tr(F)$  values for the video modality in InfoReg during the prime learning window with those in Joint training. As shown in Figure 5c, the  $Tr(F)$  values for the video modality in InfoReg are consistently higher than those in Joint training, indicating a considerable improvement in information acquisition for the video modality during the prime learning window. This enhancement enables the multimodal model to learn more comprehensive information during the prime learning window, thereby improving the model's overall performance.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">CREMA-D</td></tr><tr><td>WTP</td><td>PLW</td><td>Other periods</td></tr><tr><td>Joint training</td><td>66.61</td><td>-</td><td>-</td></tr><tr><td>OGM [30]</td><td>68.70</td><td>68.76</td><td>67.13</td></tr><tr><td>AGM [26]</td><td>69.71</td><td>69.54</td><td>67.41</td></tr><tr><td>PMR [9]</td><td>66.92</td><td>66.99</td><td>66.57</td></tr><tr><td>InfoReg</td><td>69.03</td><td>71.90</td><td>67.22</td></tr></table>
+
+Table 4. Comparison of performance during the whole training process, prime learning window, and other periods. "WTP" denotes the whole training process, and "PLW" refers to the prime learning window. "Other periods" indicates adjustments made outside the prime learning window. Bold and underline represent the best and second best respectively.
+
+# 4.4. Importance of the prime learning window
+
+Unlike other methods, InfoReg introduces adjustments exclusively during the prime learning window. To evaluate the importance of the prime learning window in addressing the imbalanced multimodal learning problem, we compare the performance of several related methods with adjustments made exclusively during the prime learning window and during other periods. Firstly, all methods show considerable improvements when adjustments are made exclusively during the prime learning window. Specifically, the performance achieved by these methods during the prime learning window is comparable to that achieved by adjusting throughout the whole training process. This highlights the necessity of making adjustments within the prime learning
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Fusion strategies</td></tr><tr><td>Gated</td><td>SUM</td><td>FiLM</td><td>Concat</td></tr><tr><td>Joint training</td><td>65.32</td><td>64.38</td><td>66.67</td><td>66.61</td></tr><tr><td>InfoReg</td><td>69.18</td><td>70.12</td><td>70.23</td><td>71.90</td></tr></table>
+
+Table 5. Comparison of different fusion strategies.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">CMU-MOSI</td></tr><tr><td>Accuracy</td><td>Macro F1</td></tr><tr><td>Joint training</td><td>61.09</td><td>60.74</td></tr><tr><td>OGM [30]</td><td>61.88</td><td>61.32</td></tr><tr><td>PMR [9]</td><td>61.47</td><td>60.98</td></tr><tr><td>AGM [26]</td><td>61.39</td><td>60.43</td></tr><tr><td>InfoReg</td><td>62.31</td><td>62.03</td></tr></table>
+
+Table 6. Comparison with imbalanced multimodal learning methods on the CMU-MOSI dataset. Bold and underline represent the best and second best respectively.
+
+window. Secondly, adjustments made during other periods show significantly lower performance compared to those made during the prime learning window and the whole training process, indicating that late-stage adjustments are unnecessary due to the lack of additional information at this stage. Overall, our method focuses on balancing information acquisition exclusively within the prime learning window, effectively enhancing underrepresented modalities during this period and resulting in strong performance.
+
+To further evaluate the importance of the prime learning window, we use t-SNE [37] to compare the features learned by the video modality using InfoReg on CREMA-D against those learned through Joint training and extended Joint training. As illustrated in Figure 6, InfoReg yields higher-quality features due to sufficient information acquisition in the prime learning window. This aligns with previous studies, which have concluded that the quality of feature learning is highly correlated with the amount of information acquired early in training [1]. Notably, as shown in Figure 6b and Figure 6c, extending the training period does not compensate for the information loss experienced by the video modality during the prime learning window. Our experiments highlight the critical role of the prime learning window in information acquisition.
+
+# 4.5. The influence of fusion strategies
+
+We evaluate the performance of InfoReg with four different fusion strategies, including Gated [23], SUM, FiLM [31], and Concat. For the Gated, SUM, and FiLM strategies, we measured the performance of each modality individually by zeroing out the features of other modalities. As shown in Table 5, InfoReg demonstrates consistently robust performance across various fusion strategies. This highlights the adaptability and scalability of InfoReg across different fusion approaches.
+
+![](images/86efaad7f52035cd8b34b68a78c7b3bf8dcd8805ca0d92a7393aced667d9c7a5.jpg)  
+(a) Accuracy with different  $\beta$
+
+![](images/2e9afecd84163d6821c7c6fb69ecc1c109b9e94795a0bb3604b194e776736200.jpg)  
+(b) Accuracy with different  $\beta$
+
+![](images/8bbf987d71a92cf5d999f449d3df71e4009a41914e347e82b10479fa4f9272d5.jpg)  
+Figure 7. (a). The overall accuracy of different  $\beta$  on CREMA-D. (b). The overall accuracy of different  $\beta$  on Kinetics Sounds.  
+(a) Accuracy with different  $K$  
+Figure 8. (a). The overall accuracy of different  $K$  on CREMA-D. (b). The overall accuracy of different  $K$  on Kinetics Sounds.
+
+![](images/f672555dcab5ab7923629b27ae962e520f4bcf384cb38e82b078450336372aed.jpg)  
+(b) Accuracy with different  $K$
+
+# 4.6. Extension to more complex settings
+
+To validate that our method continues to perform well in more complex settings, we conducted experiments on CMU-MOSI using a Transformer architecture following [27]. As shown in Table 6, InfoReg continues to perform effectively in these more challenging scenarios, outperforming other related methods. This demonstrates the good scalability of InfoReg, highlighting its ability to extend to more complex transformer-based architectures and scenarios involving more than two modalities.
+
+# 4.7. Hyperparameter sensitivity analysis
+
+The hyperparameter  $\beta$ , controlling the regulation term's strength, is selected from  $\{0.1, 0.3, 0.5, 0.7, 0.9, 1.0\}$ . A larger  $\beta$  increases the regulation degree of the information-sufficient modalities. Our results (Figure 7) show that  $\beta = 0.9$  provided the best accuracy. Similarly, the hyperparameter  $K$ , which serves as the threshold for determining whether the model is within the prime learning window, is chosen from  $\{0.01, 0.02, 0.04, 0.06, 0.08, 0.1\}$ . Figure 8 indicates that  $K = 0.04$  yields the best performance.
+
+# 5. Conclusion
+
+In this paper, we identify that there is a prime learning window in multimodal learning, and one modality's information acquisition can be suppressed by others during this stage. Then, we propose the Information Acquisition Regulation algorithm. It aims to address the imbalance in information acquisition across modalities by regulating the acquisition rates of information-sufficient modalities during the prime learning window. Our method promotes a more balanced learning process, accordingly enhancing model performance. Experiments across multiple datasets show that our method alleviates imbalanced multimodal learning and then achieves superior performance.
+
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+# Adv-CPG: A Customized Portrait Generation Framework with Facial Adversarial Attacks
+
+Junying Wang $^{1}$  Hongyuan Zhang $^{2,3}$  Yuan Yuan $^{1,*}$
+
+$^{1}$ School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, Xi'an, China  
+ $^{2}$ The University of Hong Kong, Hong Kong SAR, China  $^{3}$ Institute of Artificial Intelligence (TeleAI), China Telecom, Shanghai, China  
+junyingwang959@163.com, hyzhang98@gmail.com, y.yuan.ieee@gmail.com
+
+![](images/edb8b59e5db5e053bc145b719686c716cd19bc52930a333a13bb2cbbf1b57766.jpg)  
+Figure 1. The proposed Adv-CPG generates safe portraits that can deceive malicious face recognition systems. First row: original image. Second row: customized portrait based on the text prompt, without protection via Adv-CPG. Third row: customized portrait based on the scene text prompt, with protection via Adv-CPG. Fourth row: comparison with existing methods. The yellow number over each image: confidence score returned by Face++ when using the adversarial example for identity matching with the target (higher is better).
+
+# Abstract
+
+Recent Customized Portrait Generation (CPG) methods, taking a facial image and a textual prompt as inputs, have attracted substantial attention. Although these methods generate high-fidelity portraits, they fail to prevent the generated portraits from being tracked and misused by malicious face recognition systems. To address this, this paper proposes a Customized Portrait Generation framework with facial Adversarial attacks (Adv-CPG). Specifically, to achieve facial privacy protection, we devise a lightweight local ID encryptor and an encryption enhancer. They implement progressive double-layer encryption protection by directly injecting the target identity and adding additional identity guidance, respectively. Furthermore, to accomplish
+
+fine-grained and personalized portrait generation, we develop a multi-modal image customizer capable of generating controlled fine-grained facial features. To the best of our knowledge, Adv-CPG is the first study that introduces facial adversarial attacks into CPG. Extensive experiments demonstrate the superiority of Adv-CPG, e.g., the average attack success rate of the proposed Adv-CPG is  $28.1\%$  and  $2.86\%$  higher compared to the SOTA noise-based attack methods and unconstrained attack methods, respectively.
+
+# 1. Introduction
+
+Diffusion models [35, 38] have exhibited impressive superiority in the field of text-to-image (T2I) synthesis, especially for image customization tasks [10, 26]. Among these, Customized Portrait Generation (CPG) creates a portrait image that is visually consistent with the reference facial image,
+
+Table 1. Comparison of different facial privacy protection methods (noised-based vs. unrestricted) between unrestricted (stealthy), natural outputs, flexible text-guided adversaries, customized portraits, and fine-grained faces.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="2">Noise-Based</td><td colspan="7">Unrestricted</td></tr><tr><td rowspan="2">PGD [33]</td><td rowspan="2">TIP-IM [54]</td><td colspan="3">Makeup-Based</td><td colspan="3">Facial Semantic Invariant</td><td>Customized Portrait</td></tr><tr><td>Aav-Makeup [56]</td><td>Clip2Protect [43]</td><td>GIFT [27]</td><td>DiffAM [47]</td><td>SD4Privacy [1]</td><td>Adv-Diffusion [29]</td><td>Adv-CPG (Ours)</td></tr><tr><td>Stealthiness</td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Natural Outputs</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Text Guided Customized Portrait</td><td></td><td></td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td>✓</td></tr><tr><td>Fine-Grained Face</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td></tr></table>
+
+while simultaneously adhering to additional prompts. Early CPG approaches [8, 15, 39] achieve admirable high-fidelity results but require fine-tuning at test time, which limits their practicability. Recent test-time tuning-free methods [28, 50, 51, 55] typically inject visual features of the reference face and textual features from language prompts, leading to consistent and high-fidelity portrait generation with the promise of large-scale deployment. However, to the best of our knowledge, current CPG methods lack facial security mechanisms to protect the generated high-fidelity portraits from being tracked and abused by malicious face recognition (FR) systems.
+
+Meanwhile, although existing noise-based [6, 54] and unrestricted [21, 45] adversarial attack methods have achieved satisfactory facial privacy protection, they merely operate on the original face, which meets the protection needs of users but falls short of their portrait customization requirements. In the current social media-enriched era, a safe and attractive personalized portrait is highly coveted by many people.
+
+To address these two issues, this paper proposes a Customized Portrait Generation framework with facial Adversarial attacks (Adv-CPG). It generates portraits that can not only be abused by malicious FR systems, but also have fine-grained and customized features. Specifically, Adv-CPG aims to generate customized portraits with attack semantics (adversarial examples) that can deceive FR systems, leading to misidentifications and thus enabling facial privacy protection. As shown in Fig. 2, the Multi-Modal Image Customizer (MMIC) is essential for fine-grained portrait generation, while the ID Encryptor (En1) and Encryption Enhancer (En2) offers progressive two-layer protection. The following are the key contributions:
+
+- First Customized Portrait Generation Framework with Facial Adversarial Attacks: Adv-CPG is the first work introducing facial adversarial attacks into SD-based CPG. As illustrated in Fig. 1, the adversarial examples of Adv-CPG exhibit physical attack capabilities and stealthiness (for facial privacy protection), together with high fidelity and fine-grained features (for portrait generation).  
+- Progressive Facial Privacy Protection: We accomplish progressive two-layer protection superior to any single-layer protection. Specifically, En1 elegantly realizes global protection by injecting target identities directly
+
+into the identity-dependent layer, and En2 achieves local protection by cost-effectively adding identity guidance.
+
+- Fine-Grained Customized Portrait Generation: AdvCPG achieves fine-grained and high-fidelity portrait generation, which is not available for other protection methods. This is attributed to the designed SD-based MMIC capable of generating controlled fine-grained facial features. Additionally, it allows for scenario and action customization with text prompts.
+
+Comparative experiments with state-of-the-art attack methods highlight the superior performance of Adv-CPG. Moreover, Adv-CPG facilitates tuning-free operation during testing, ensuring high performance at minimal training costs.
+
+# 2. Related Work
+
+Text-to-Image Diffusion Models. Advancement in diffusion models [35, 38, 46] has significantly propelled recent progress in text-conditional image and video generation [8, 10, 26, 34]. Current research is dedicated to improving the performance of these models in multiple ways, such as exploring high-quality large-scale text image datasets [41, 42, 58], upgrading the base model [38], and improving the controllability of the model [20, 39, 49, 57]. Lately, the Stable Diffusion XL (SDXL) [35] has been widely pursued due to its relatively low computational cost and impressive capability of portrait generation. Thus, Adv-CPG builds on SDXL but can be extended to other T2I diffusion models.
+
+Customized Portrait Generation. CPG [28, 50] aims to generate a portrait image that is visually consistent with the reference facial image while adhering to additional prompts. Depending on whether or not fine-tuning is performed during testing, mainstream CPG methods can be divided into two categories. Early approaches [8, 15, 39] require resource-intensive backpropagation, with each fine-tuning taking tens of minutes or hours to complete. Recent test-time tuning-free methods [11, 19, 28, 48, 50, 51, 55] utilize extra modules to insert image semantics, giving pretrained models visual inference comprehension, and are promising for large-scale deployment. Inspired by these, Adv-CPG follows the test-time tuning-free paradigm.
+
+Adversarial Attacks on Face Recognition. The adversarial attack methods are generally categorized into noise-based methods and unrestricted methods. Conventional noise-based approaches [6, 9, 33, 54] exploit adding  $\ell_p$
+
+![](images/a03255895ceae8fc5750e701c42353271ae81e5fd6b3f3e57c7f37c8744de41f.jpg)  
+Figure 2. The overall framework of the proposed Adv-CPG. The framework comprises three key modules: [A] a multi-modal image customizer (MMIC), [B] an ID encryptor (En1), and [C] an encryption enhancer (En2). En1 and En2 enable incremental facial privacy protection, and MMIC achieves fine-grained and personalized portrait generation.
+
+boundary perturbations directly in the pixel space, which struggles with black-box transferability [52] and stealthiness [36]. Recent unrestricted methods concentrate on learning perturbations in the semantic space, further improving transferability and stealthiness [21, 45]. Based on adding extra makeup or not, mainstream unconstrained methods are further divided into two categories. Among them, makeup-based approaches [17, 25, 27, 43, 44, 47, 56] organize perturbations as makeup (or hat) for the adversarial examples, while facial semantic invariant methods [1, 3, 31, 60] generate adversarial examples visually consistent with the original face. For clarity, Table 1 shows the features of various methods (noised-based vs. unrestricted).
+
+# 3. Methodology
+
+Problem Definition. A high-quality adversarial example should ensure that a human regards it as the same person as the original face (stealthiness), and meanwhile lead the malicious FR systems to misclassify it as another identity in black-box attack scenarios (physical attack capability and transferability). It involves a two-fold implication. Firstly, the original face  $\mathbf{I}_o$  and the generated adversarial example  $\mathbf{I}_{adv}$  should be visually consistent to human observers  $(\mathbf{I}_{adv} = G(\mathbf{I}_o), H(\mathbf{I}_{adv}) \approx H(\mathbf{I}_o))$ . Among it,  $H(\cdot)$  denotes visual results by human observers, and  $G(\cdot)$  indicates the strong generative model to be implemented by the proposed method, which generates the adversarial example  $\mathbf{I}_{adv}$  conditional on the original face  $\mathbf{I}_o$ . Secondly, the target image  $\mathbf{I}_t$  and the adversarial example  $\mathbf{I}_{adv}$  should maintain
+
+identity consistent, which is formulated as follows
+
+$$
+\underset {\mathbf {I} _ {a d v}} {\arg \max } F \left(\mathbf {I} _ {t}, \mathbf {I} _ {a d v}\right), \tag {1}
+$$
+
+where  $F(\cdot)$  denotes the identity similarity between this pair of faces measured by the face verification system. Generally, a FR system predicts that two faces belong to the same identity if  $F(\cdot) \geq \tau$ , where  $\tau$  is the system threshold. In this paper, beyond the physical attack capability, transferability, and stealthiness, the proposed Adv-CPG also satisfies the personalized needs of users, which makes an effort to explore high-fidelity, refined facial generation, and natural background introduction for adversarial examples.
+
+# 3.1. Preliminaries
+
+Stable Diffusion. Stable Diffusion (SD) [38, 59] has recently emerged as an increasingly popular T2I model. SD consists of four key components: an encoder  $\mathcal{E}$  and a decoder  $\mathcal{D}$  for mapping between the original pixel space and the low-dimensional latent space, a U-Net denoiser  $\epsilon_{\theta}$  for generating denoised diffusion images, and a CLIP-based [37] pre-trained text encoder  $\mathcal{T}$ . Following the mainstream denoising diffusion probabilistic model (DDPM) [14], SD is formulated as a forward diffusion process and a  $T$ -steps backward denoising process. In the diffusion phase, random Gaussian noise  $\epsilon$  is gradually added to the initial latent  $\mathbf{z}_0$  to yield the noisy latent  $\mathbf{z}_t$  at different timesteps  $t \in [1, T]$ . Then denoising U-Net is trained by the loss
+
+$$
+\mathcal {L} _ {\mathrm {S D}} = \mathbb {E} _ {\mathbf {z} _ {0}, \mathbf {C}, \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), t} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, t, \mathbf {C}) \| \right], \tag {2}
+$$
+
+where  $\mathbf{C}$  is the optional additional condition embedding.
+
+Image Prompt Adapter (IP-Adapter). Recent test-time tuning-free CPG methods [10, 50] utilize the IP-Adapter [55] to accomplish visual information injection, drawing widespread attention. Specifically, IP-Adapter extracts features of the reference image and feeds them into an additional cross-attention layer, which can be formulated as
+
+$$
+\left\{ \begin{array}{l} \mathbf {z} ^ {\prime} = \operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) + \lambda \cdot \operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K} ^ {i}, \mathbf {V} ^ {i}), \\ \mathbf {K} = \mathbf {C} _ {t} \mathbf {W} _ {K}, \mathbf {V} = \mathbf {C} _ {t} \mathbf {W} _ {V}, \mathbf {K} ^ {i} = \mathbf {C} _ {i} \mathbf {W} _ {K} ^ {i}, \mathbf {V} ^ {i} = \mathbf {C} _ {i} \mathbf {W} _ {V} ^ {i}, \end{array} \right. \tag {3}
+$$
+
+where Attention  $(\mathbf{Q},\mathbf{K},\mathbf{V})$  is the original textual cross-attention layer, Attention  $(\mathbf{Q},\mathbf{K}^i,\mathbf{V}^i)$  is the added visual cross-attention layer,  $\mathbf{Q}$  is the spatial feature,  $\mathbf{C}_t$  and  $\mathbf{C}_i$  are textual feature and image feature, and  $\mathbf{W}_K,\mathbf{W}_V,\mathbf{W}_K^i$  ,and  $\mathbf{W}_V^i$  are the trainable weights of the linear layers.
+
+# 3.2. Model Overview
+
+Pipeline Overview. To enable facial privacy protection and CPG, Adv-CPG is designed with three key modules: an ID encryptor (En1), an encryption enhancer (En2), and a multimodal image customizer (MMIC), as shown in Fig. 2. Furthermore, based on the working state of MMIC, the generation process of Adv-CPG can be divided into two stages: 1) Progressive Facial Privacy Protection Stage: The original text prompt without enhancement is utilized for initial background introductions. In particular, En1 and En2 play important roles in achieving incremental facial privacy protection in this stage, which is stated in Section 3.3. 2) Fine-Grained Customized Portrait Generation Stage: In this stage, the detailed facial feature generated by the MMIC is utilized to accomplish fine-grained portrait generation, while the other modules are integrated to maintain a balance between identity features and visual semantics. MMIC is explained in detail in Section 3.4.
+
+Training Phase. Adv-CPG is built on the pre-trained SDXL [35], which is a SOTA T2I diffusion model. During training, only MMIC and En1 participate. Only the parameters of the ID projector in En1 will be optimized, while other parameters including the parameters of the SD model will be frozen. The loss during training is formulated as
+
+$$
+\mathcal {L} _ {\mathrm {C P G}} = \mathbb {E} _ {\mathbf {z} _ {0}, \mathbf {C} _ {i d}, \mathbf {C} _ {i}, \mathbf {C} _ {t}, \boldsymbol {\epsilon}, t} \left[ \| \boldsymbol {\epsilon} - \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, \mathbf {C} _ {i d}, \mathbf {C} _ {i}, \mathbf {C} _ {t}\right) \| \right], \tag {4}
+$$
+
+where  $\mathbf{C}_{id}$  is the encrypted ID feature generated from En1, and  $\mathbf{C}_i$  and  $\mathbf{C}_t$  are the image feature and the improved text feature generated from MMIC, respectively. The augmented text feature  $\mathbf{C}_t$  is formed by concatenating the original text prompt with the fine-grained facial description, which is described in Section 3.4.
+
+Inference Phase. During the inference phase, MMIC, En1, and En2 are involved. Meanwhile, the straightforward delayed primacy condition similar to Fastcomposer [51] and ConsistentID [19] is employed. By replacing the initial
+
+text feature with the augmented text feature after a specific step, Adv-CPG effectively balances fine-grained facial preservation and personalized scene introduction. Notably, the generation process is divided into two stages depending on whether or not the augmented text is used, which corresponds to the dual-stage pipeline (1) Progressive Facial Privacy Protection Stage and 2) Fine-Grained Customized Portrait Generation Stage).
+
+# 3.3. Progressive Facial Privacy Protection
+
+In this stage, MMIC extracts the textual feature from the initial prompt and the visual feature from the original face. This stage does not use fine-grained facial descriptions, intending to enable the En1 and En2 to achieve facial privacy protection by learning the target identity. Specifically, the structures of these two modules are presented as follows.
+
+ID Encryptor (En1). The designed En1 is based on the IP-Adapter, which injects the target ID features directly into the SD model. Previous CPG researches [28] merely require ensuring that the generated portraits are highly similar in visual semantics to the original face image. In contrast, Adv-CPG guarantees not only a high visual semantic similarity with the original face but also a high similarity of identity features between the generated adversarial example and the target image. In this study, we leverage both the fuzzy semantic information extracted by the CLIP image encoder and ID embeddings in the target images extracted by the white-box FR model. This approach enables the learning of a robust powerful ID feature to guide the learning process effectively. Specifically, the powerful target ID feature generated by the Adv-CPG can be represented as
+
+$$
+\mathbf {C} _ {i d} = \alpha \cdot \mathcal {I} (\mathbf {I} _ {t}) + \beta \cdot \sum_ {i} \left(\operatorname {F R} _ {i} (\mathbf {I} _ {t})\right), \tag {5}
+$$
+
+where  $\mathcal{I}$  is the pre-trained CLIP image encoder and  $\mathrm{FR}_i(\cdot)$  denotes the  $i$ -th pre-trained white-box FR model. Then, the target ID feature is directly injected into the identity-related cross-attention layer like PuLID [10] and InstantID [50].
+
+Encryption Enhancer (En2). Inspired by Adv-Diffusion [29] and FreeTuner [53], additional ID guidance is introduced as an encryption enhancement. Specifically, in each denoising step, the current noise reconstructed image  $\mathcal{D}(\widetilde{\mathbf{z}}_0)$  and the target image  $\mathbf{I}_t$  are used to generate an ID gradient as
+
+$$
+\left\{ \begin{array}{l} \mathbf {g} _ {t} = \lambda_ {s} \nabla_ {\widetilde {\mathbf {z}} _ {0}} F (\mathcal {D} (\widetilde {\mathbf {z}} _ {0}), \mathbf {I} _ {t}), \\ \hat {\mathbf {z}} _ {t - 1} := \mathbf {z} _ {t - 1} + \boldsymbol {\sigma} _ {t} \mathbf {g} _ {t} \end{array} \right. \tag {6}
+$$
+
+where  $F(\cdot)$  is the ID similarity of the image pairs,  $\lambda_{s}$  is the guidance strength, and the generated ID gradient  $\mathbf{g}_t$  is used to update the prediction noise for identity enhancement.
+
+# 3.4. Fine-Grained Customized Portrait Generation
+
+After certain steps in the protection phase, fine-grained portrait generation will be implemented. In this stage, the de
+
+![](images/b3e5cfcfcc8801a491cce6bbace33e59fb91dbccd8d6abcdb56205c4d88f8568.jpg)  
+Figure 3. Visual quality comparison of adversarial examples generated by 4 types of adversarial methods on the CelebA-HQ dataset. The images generated by Adv-CPG implement both portrait customization and effective facial privacy protection. Red/blue (1/2) numbers below each image: confidence scores returned by Face++ and Aliyun (higher is better). Reference column: makeup reference for DiffAM.
+
+tailed facial description in MMIC is utilized to generate the detailed features. En1 and En2 continued to be integrated for a balance between CPG and facial privacy protection. Specifically, the structure of MMIC is stated as follows.
+
+Multi-Modal Image Customizer (MMIC). Observing that the initial IP-Adapter is susceptible to inconsistent facial details, the text feature is refined into fine-grained face text features. Initially, a multi-modal large model, LLaVA1.5 [30], is introduced as the facial description model to obtain detailed textual facial description by the prompt "Describe this person's facial features, including face, ears, eyes, nose, and mouth". Then the detailed facial description and the original text prompt are concatenated and fed into the CLIP text encoder for generating the augmented text feature  $\mathbf{C}_t$ . Meanwhile, for a high visual semantic similarity with the original face, the CLIP image encoder is employed on the original face to extract the visual semantic features  $\mathbf{C}_i$ . Then the features  $\mathbf{C}_t$  and  $\mathbf{C}_i$  obtained by MMIC are injected in parallel into the decoupled cross-attention layer for fine-grained portrait generation.
+
+# 4. Experiments
+
+# 4.1. Experimental Setting
+
+Implementation Details. Adam [24] is set as the optimizer, the learning rate is set to  $10^{-4}$ , and the training is performed on 4 NVIDIA 3090 GPUs with a batch size of 8. In addition, a 50-step DDIM [46] sampler is employed and the scale of the classifier guidance setting is set to 5. In the training pro
+
+cess, we remove  $50\%$  of the background information from the characters with a  $25\%$  probability to minimize interference. At the same time, we replace the original text embedding with zero text embedding with  $10\%$  probability. In the inference process, delayed topic conditioning [23, 51] is employed to resolve conflicts between text embeddings, semantic information embeddings, and identity embeddings.
+
+Datasets. During the training phase, we employ the fine-grained face dataset FGID [19], from which 30,000 CelebA [32] and 42,500 SFHQ [2] annotations are selected. During the testing phase, three publicly available face datasets are used following a similar protocol [21, 29], including FFHQ [23], CelebA-HQ [22], and LFW [18]. Among them, FFHQ and CelebA-HQ are used for face verification and LFW are used for face identification. For face verification, 1000 images with different identities are randomly selected as source images and randomly divided into 5 groups for FFHQ and CelebA-HQ datasets. Meanwhile, we select 5 images for each group. Consequently, each dataset forms 5 groups with 200 source-target image pairs in each group. For face identification, 500 identities are randomly selected from the LFW and one image of each identity is put into the gallery set and another image is put into the probe set. The attack setting is similar to GIFT [27].
+
+Benchmark. Multiple adversarial attack benchmarking schemes are implemented for more fair performance comparisons, including 5 noise-based methods and 12 unconstrained methods. For noise-based one, the chosen methods consist of FGSM [9], MI-FGSM [6], PGD [33], TI-
+
+Table 2. Attack success rate (ASR %) of black-box attack under the face verification task. For each column, the other three models are used as surrogates to generate the adversarial examples. -: non-existent. MF: acronym for MobileFace. Bolded and labeled in light blue (1): the best. Underlined (2): the second. ↑/↓: performance comparison of Adv-CPG vs. the prior SOTA.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Dataset
+ASR% on FR Model ↑</td><td colspan="4">FFHQ</td><td colspan="4">CelebA-HQ</td><td rowspan="2">Average</td></tr><tr><td>IR152</td><td>IRSE50</td><td>FaceNet</td><td>MF</td><td>IR152</td><td>IRSE50</td><td>FaceNet</td><td>MF</td></tr><tr><td>Clean</td><td>—</td><td>3.14</td><td>4.73</td><td>1.49</td><td>8.96</td><td>4.64</td><td>5.74</td><td>1.06</td><td>13.27</td><td>5.38</td></tr><tr><td rowspan="5">Noise-Based</td><td>FGSM (ICLR&#x27;15) [9]</td><td>9.86</td><td>48.53</td><td>4.23</td><td>51.48</td><td>12.07</td><td>45.81</td><td>1.35</td><td>53.02</td><td>28.29</td></tr><tr><td>MI-FGSM (CVPR&#x27;18) [6]</td><td>46.31</td><td>69.24</td><td>20.62</td><td>69.26</td><td>46.53</td><td>70.57</td><td>27.09</td><td>58.94</td><td>51.07</td></tr><tr><td>PGD (ICLR&#x27;18) [33]</td><td>31.64</td><td>75.38</td><td>18.59</td><td>63.12</td><td>41.87</td><td>63.23</td><td>19.62</td><td>57.34</td><td>46.35</td></tr><tr><td>TI-DIM (CVPR&#x27;19) [7]</td><td>43.57</td><td>65.89</td><td>14.72</td><td>53.31</td><td>35.13</td><td>62.38</td><td>13.68</td><td>52.84</td><td>42.69</td></tr><tr><td>TIP-IM (ICCV&#x27;21) [54]</td><td>46.25</td><td>67.38</td><td>59.82</td><td>52.03</td><td>41.26</td><td>57.29</td><td>39.07</td><td>49.56</td><td>51.58</td></tr><tr><td rowspan="7">Makeup-Based</td><td>Adv-Hat (ICPR&#x27;21) [25]</td><td>13.77</td><td>15.36</td><td>5.26</td><td>9.83</td><td>5.04</td><td>16.88</td><td>4.91</td><td>12.64</td><td>10.46</td></tr><tr><td>Adv-Makeup (JICAI&#x27;21) [56]</td><td>10.03</td><td>25.57</td><td>1.08</td><td>20.38</td><td>12.68</td><td>19.95</td><td>1.37</td><td>22.11</td><td>14.15</td></tr><tr><td>AMT-GAN (CVPR&#x27;22) [17]</td><td>11.52</td><td>56.02</td><td>9.74</td><td>41.32</td><td>12.09</td><td>53.26</td><td>4.87</td><td>47.95</td><td>29.60</td></tr><tr><td>Clip2Protect (CVPR&#x27;23) [43]</td><td>52.12</td><td>86.53</td><td>45.01</td><td>76.29</td><td>47.63</td><td>80.96</td><td>42.57</td><td>73.64</td><td>63.09</td></tr><tr><td>GIFT (ACMMM&#x27;24) [27]</td><td>69.72</td><td>87.64</td><td>54.49</td><td>82.93</td><td>73.84</td><td>83.72</td><td>56.48</td><td>86.37</td><td>74.40</td></tr><tr><td>DFPP (arXiv&#x27;24) [44]</td><td>54.25</td><td>90.63</td><td>52.13</td><td>80.09</td><td>46.38</td><td>80.59</td><td>45.37</td><td>72.13</td><td>69.20</td></tr><tr><td>DiffAM (CVPR&#x27;24) [47]</td><td>67.24</td><td>90.30</td><td>64.96</td><td>89.56</td><td>65.09</td><td>89.66</td><td>62.99</td><td>84.51</td><td>76.79</td></tr><tr><td rowspan="5">FacialSemanticInvariant</td><td>DiffProtect (arXiv&#x27;23) [31]</td><td>57.62</td><td>60.14</td><td>49.38</td><td>67.52</td><td>58.64</td><td>79.34</td><td>24.69</td><td>75.91</td><td>59.16</td></tr><tr><td>DPG (arXiv&#x27;24) [60]</td><td>34.87</td><td>76.82</td><td>36.57</td><td>69.03</td><td>42.89</td><td>62.47</td><td>35.83</td><td>66.42</td><td>53.11</td></tr><tr><td>SD4Privacy (ICME&#x27;24) [1]</td><td>51.31</td><td>79.94</td><td>43.57</td><td>71.55</td><td>66.89</td><td>79.96</td><td>53.49</td><td>74.58</td><td>65.16</td></tr><tr><td>Adv-Diffusion(AAAI&#x27;24) [29]</td><td>50.93</td><td>81.76</td><td>30.84</td><td>67.52</td><td>52.84</td><td>81.67</td><td>34.95</td><td>70.78</td><td>58.91</td></tr><tr><td>P3-Mask (ECCV&#x27;25) [3]</td><td>73.18</td><td>85.35</td><td>57.92</td><td>70.69</td><td>73.47</td><td>83.40</td><td>60.24</td><td>69.64</td><td>71.74</td></tr><tr><td>Portraits</td><td>Adv-CPG (Ours)</td><td>75.26↑2.1</td><td>91.03↑0.4</td><td>63.84↓1.1</td><td>89.94↑0.4</td><td>76.96↑3.1</td><td>88.72↓0.9</td><td>63.50↑0.5</td><td>87.95↑1.6</td><td>79.65↑2.9</td></tr></table>
+
+Table 3. Attack success rate (ASR %) of black-box attack under the face identification task. For each column, the other three models are used as surrogates to generate the adversarial examples. R1-T: Rank-1-Targeted. R5-T: Rank-5-Targeted. Bolded and labeled in light blue (1): the best. Underlined (2): the second. ↑/↓: performance comparison of Adv-CPG vs. the prior SOTA.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">FR Model
+ASR% ↑</td><td colspan="2">IR152</td><td colspan="2">IRSE50</td><td colspan="2">FaceNet</td><td colspan="2">MobileFace</td><td colspan="2">Average</td></tr><tr><td>R1-T</td><td>R5-T</td><td>R1-T</td><td>R5-T</td><td>R1-T</td><td>R5-T</td><td>R1-T</td><td>R5-T</td><td>R1-T</td><td>R5-T</td></tr><tr><td rowspan="3">Noise-based</td><td>MI-FGSM (CVPR&#x27;18)</td><td>3.0</td><td>13.2</td><td>3.8</td><td>12.6</td><td>8.4</td><td>22.0</td><td>7.8</td><td>20.6</td><td>5.75</td><td>17.10</td></tr><tr><td>TI-DIM (CVPR&#x27;19)</td><td>8.2</td><td>14.2</td><td>4.2</td><td>13.8</td><td>17.8</td><td>32.2</td><td>21.4</td><td>43.8</td><td>12.90</td><td>26.00</td></tr><tr><td>TIP-IM (ICCV&#x27;21)</td><td>9.8</td><td>29.8</td><td>7.4</td><td>27.8</td><td>25.8</td><td>55.8</td><td>31.8</td><td>52.6</td><td>18.70</td><td>41.50</td></tr><tr><td rowspan="4">Unrestricted</td><td>Clip2Protect (CVPR&#x27;23)</td><td>17.8</td><td>51.8</td><td>10.6</td><td>35.2</td><td>27.2</td><td>54.4</td><td>39.0</td><td>67.8</td><td>23.65</td><td>52.30</td></tr><tr><td>GIFT (ACMMM&#x27;24)</td><td>21.2</td><td>57.2</td><td>34.6</td><td>49.4</td><td>33.2</td><td>65.6</td><td>41.2</td><td>67.6</td><td>32.55</td><td>59.95</td></tr><tr><td>DFPP (arXiv&#x27;24)</td><td>14.8</td><td>41.4</td><td>13.6</td><td>37.2</td><td>25.2</td><td>53.8</td><td>36.6</td><td>60.4</td><td>22.55</td><td>48.20</td></tr><tr><td>SD4Privacy (ICME&#x27;24)</td><td>15.6</td><td>26.8</td><td>23.4</td><td>41.2</td><td>33.6</td><td>53.8</td><td>31.8</td><td>49.8</td><td>26.10</td><td>42.90</td></tr><tr><td></td><td>Adv-CPG (Ours)</td><td>24.4↑3.2</td><td>56.4↓0.8</td><td>33.8↓0.8</td><td>51.2↑1.8</td><td>36.6↑3.0</td><td>67.4↑1.8</td><td>43.4↑2.2</td><td>70.4↑2.6</td><td>34.55↑2.0</td><td>61.35↑1.4</td></tr></table>
+
+DIM [7], and TIP-IM [54]. The 12 unconstrained methods can be further categorized into 7 makeup-based methods: Adv-Hat [25], Adv-Makeup [56], AMT-GAN [17], Clip2Protect [43], GIFT [27], DFPP [44], and DiffAM [47], and 5 facial semantic invariant methods: DiffProtect [31], DPG [60], SD4Privacy [1], Adv-Diffusion [29], and P3Mask [3]. Among them, the single-objective variant of TIP-IM [7] is utilized in this experiment for a fair comparison.
+
+Target FR Models. Following Clip2Protect, 4 widely used deep FR models are selected to evaluate the attack performance of Adv-CPG and SOTA attack methods in black-box settings. In particular, these models are IR152 [12], IRSE50 [16], FaceNet [40], and MobileFace [5]. At the same time, two commercial FR APIs (Face++<sup>1</sup> and Aliyun<sup>2</sup>) are selected in the experiment to evaluate the per
+
+formance of different adversarial attack methods.
+
+Evaluation Metrics. This work is evaluated from the privacy protection perspective (face verification and face identification) and image quality perspective. For face verification, the attack success rate (ASR) [4] (the ratio of successfully attacked adversarial examples to all adversarial examples) is reported as the evaluation metric. For face identification, the Rank-N target ASR is used as the metric, i.e., at least one of the top N images belongs to the target identity after ranking the similarity of all the images in the gallery set with the probe image. As for commercial FR APIs, the confidence scores returned by FR servers are directly used as the metric. To evaluate the quality of adversarial examples, the FID, PSNR, and SSIM scores are utilized as the quality metrics [13]. A lower FID, a larger PSNR, and a larger SSIM demonstrate a higher degree of
+
+![](images/61b4fa116006d45cb5da1b4211a1cf7e76e7d2fc18474d357bfb287ea313ea02.jpg)  
+Figure 4. The confidence scores  $(\uparrow)$  returned from commercial APIs, Face++ and Aliyun. Adv-CPG has higher and more stable confidence scores than state-of-the-art noise-based and makeup-based facial privacy protection methods.
+
+Table 4. Quantitative evaluations of image quality for different adversarial examples. The FID, PSNR, and SSIM scores of black-box attacks on the CelebA-HQ dataset for 4 types of methods (noise-based, makeup-based, facial semantic invariant, and portrait-based).  
+
+<table><tr><td>Method (Metric)</td><td>PGD</td><td>TIP-IM</td><td>Adv-Makeup</td><td>AMT-GAN</td><td>CLIP2Protect</td><td>DiffAM</td><td>SD4Privacy</td><td>Adv-Diffusion</td><td>Adv-CPG</td></tr><tr><td>FID ↓</td><td>78.92</td><td>38.7325</td><td>4.2282</td><td>34.5703</td><td>26.1272</td><td>26.1015</td><td>26.4078</td><td>22.5751</td><td>26.0758</td></tr><tr><td>PSNR ↑</td><td>27.96</td><td>33.2106</td><td>34.5152</td><td>19.5048</td><td>19.3542</td><td>20.5260</td><td>26.8864</td><td>28.8501</td><td>29.9996</td></tr><tr><td>SSIM ↑</td><td>0.8573</td><td>0.9236</td><td>0.9850</td><td>0.7924</td><td>0.6025</td><td>0.8861</td><td>0.8092</td><td>0.8046</td><td>0.8978</td></tr></table>
+
+similarity between the two compared images.
+
+# 4.2. Comparison Results
+
+Comparison on Black-Box Attacks. For face verification experiments, the threshold  $\tau$  is set as FAR@0.01 (false acceptance rate) for each selected FR model, i.e., IR152 (0.167), IRSE50 (0.241), FaceNet (0.409), and MobileFace (0.302). Table 2 reports the quantitative results of the proposed Adv-CPG and the 17 benchmark methods on the FFHQ and CelebA-HQ datasets against the dominant FR models under the black-box attack setting. In terms of ASR, the proposed method can achieve an average absolute gain of about  $28.1\%$  and  $2.86\%$  compared to the SOTA noise-based method (TIP-IM) and unconstrained method (DiffAM), respectively. In addition, most of the methods are weakly transferable on FaceNet due to the obvious differences in the FaceNet architecture. In contrast, Adv-CPG still generates robust adversarial examples with strong transferability, which demonstrates the effectiveness of facial privacy protection from the perspective of fine-grained face generation and customized background generation. For face identification experiments, Table 3 reports the ASR results of the proposed Adv-CPG and 7 well-performing methods on the LFW dataset. Notably, since some works are initially trained to impersonate target identity in the face verification tasks, and others employ untargeted identity strategies, they are not included in Table 3. In most cases, the results of the proposed Adv-CPG are superior to recent approaches under Rank-1 and Rank-5 settings.
+
+Comparison on Image Quality. Fig. 3 illustrates the visual quality comparison of adversarial examples generated by different methods. We select 2-4 methods with superior performance from noised-based, unrestricted makeup
+
+based, and unrestricted facial semantic invariant methods as the benchmark for comparison. In experiments, we prepare makeup text prompts (e.g., "red lipstick with blue eyeshadow") to the CLIP2Protect method for generating the specified makeup, reference makeup images for the DiffAM method, and scene text prompts (e.g., "in the park") to Adv-CPG for generating the specific scene. In contrast to the noise-based method TIP-IM, the adversarial examples of Adv-CPG are more natural, with no obvious noise patterns. In terms of unrestricted makeup-based approaches, CLIP2Protect generates reasonable and high-quality makeup, and DiffAM achieves outstanding performance in terms of precision and refinement. For the unconstrained facial semantic invariant approach, both SD4Privacy and Adv-Diffusion achieve very minimal changes to the facial part by operating at the semantic level. However, these methods only operate on the original face, which can only satisfy users' protection requirements but not more personalized demands. In contrast, Adv-CPG generates head-and-shoulders/half-body portraits with high fidelity of facial parts, high attack success rate, and natural overall appearance by a simple textual scene prompt. As a result, this greatly satisfies the social and customization needs of users while successfully protecting facial privacy.
+
+Meanwhile, Table 4 quantitatively demonstrates the image quality evaluation results by reporting the FID, PSNR, and SSIM scores of different methods on the CelebA-HQ dataset. Among all quantitative evaluations, Adv-Makeup performs the best. The reason is that Adv-makeup only generates eye shadow, not full-face makeup, which makes minimal modifications to the image. However, as shown in Table 2, the low ASR of Adv-Makeup in the experiment prevents it from standing out among diverse attack meth
+
+![](images/bf9892f99c2b38d08d7138804d6b3286dc39deb8768d88cb8939537e0f7bc0e6.jpg)  
+Origin w/o Protection Protection w.r.t. Target1, Target2, Target3, and Targe4  
+Figure 5. Visual comparison of adversarial examples for different target identities. First column: original face. Second column: personalized portrait without protection. Third/Fourth/Fifth/Sixth column: personalized portrait with protection to target-1/2/3/4.
+
+ods. In summary, Adv-CPG obtains comparatively low FID scores and high PSNR and SSIM scores, indicating that the images generated by Adv-CPG are relatively natural.
+
+# 4.3. Attack Performance on Commercial APIs
+
+The quantitative attack results of different attack methods in face verification settings on commercial APIs (Face++ and Aliyun) are presented in Fig. 4. For benchmarking, recent methods are chosen, including 4 unrestricted makeup-based methods and 5 unrestricted facial semantical invariant methods. In experiments, we perform facial privacy protection on 100 randomly selected images from each of the CelebA-HQ and FFHQ datasets and report the confidence scores from the two APIs. The confidence score ranges from 0 to 100, with a higher score indicating a higher similarity between the adversarial example and the target image. The results demonstrate that the average confidence scores of Adv-CPG on each API are about 77.5 and 63.0, respectively, which is superior to current SOTA methods, and the attack effectiveness is comparatively stable. In addition, since these two APIs can effectively simulate facial privacy protection scenarios in the real world, it further evidences the high black-box attack capability of Adv-CPG.
+
+# 4.4. Ablation Study
+
+Robustness on Different Target Identities. Generating adversarial examples with any given target face holds higher practical value. Therefore, four target images are randomly selected from the FFHQ and CelebA-HQ datasets to evaluate the impact of target identity on the quality of the adversarial examples. As shown in Fig. 5, Adv-CPG generates
+
+![](images/4d9e3ebeeea7441206b822e7040a7e529e75e5b9e1e9ee39d0dfe882eff1d8a3.jpg)  
+Figure 6. Qualitative impact of the encryption degree on the generated adversarial examples is demonstrated. As the encryption increases, the face features change towards the target identity.
+
+Table 5. The impact of ID encryptor and encryptor enhancer on the ASR ( $\% \uparrow$ ) of the generated adversarial examples compared to the CelebA-HQ dataset. MF: acronym for MobileFace.  
+
+<table><tr><td>Method (ASR)</td><td>IR152</td><td>IRSE50</td><td>FaceNet</td><td>MF</td><td>Average</td></tr><tr><td>w/o Encryptor</td><td>54.67</td><td>62.83</td><td>39.62</td><td>67.04</td><td>56.04</td></tr><tr><td>w/o Enhancer</td><td>69.35</td><td>80.74</td><td>54.38</td><td>79.59</td><td>71.02</td></tr><tr><td>Adv-CPG</td><td>76.96</td><td>88.72</td><td>63.50</td><td>87.95</td><td>79.28</td></tr></table>
+
+high-fidelity attack examples for different targets, which indicates that Adv-CPG is robust to changes in target identity.
+
+Different levels of Identity Encryption. Fig. 6 illustrates the qualitative impact of the adversarial examples generated during a set of incremental identity encryptions (including ID Encryptor and encryption enhancer). As the level of encryption increases, the more similar the facial features in the target identity and the adversarial examples.
+
+Effectiveness of ID Encryptor and Enhancer. To verify the effectiveness of the ID encryptor and encryption enhancer on the generated adversarial examples, three settings (no ID encryptor, no encryption enhancer, and the original setting) on the CelebA-HQ dataset are employed to evaluate the changes of the ASR. As shown in Table 5, both the ID encryptor and encryption enhancer achieve facial privacy protection, especially the ID encryptor effectively achieves target learning by directly injecting the target identity.
+
+# 5. Conclusion
+
+This paper presents Adv-CPG, a novel customized portrait generation framework with facial adversarial attacks. By injecting the target identity and adding additional identity guidance, Adv-CPG achieves progressive facial privacy protection. Further, by generating the detailed facial feature in the second stage, Adv-CPG achieves fine-grained portrait generation. Experimental results demonstrate that Adv-CPG surpasses current methods, enabling robust black-box attacks against diverse FR models and commercial APIs while achieving high-quality and customized portrait generation. Future work could explore the application of this facial privacy protection paradigm to other facial manipulation tasks, such as face editing and face swapping, to fully protect facial privacy in the age of artificial intelligence.
+
+# Acknowledgments
+
+This work was supported by National Key R&D Program of China under Grant No. 2024YFC3015500.
+
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+# Advancing Adversarial Robustness in GNeRFs: The IL2-NeRF Attack
+
+Nicole Meng $^{1,2}$
+
+Caleb Manicke
+
+Ronak Sahu2
+
+Caiwen Ding<sup>3</sup>
+
+Yingjie Lao
+
+# Abstract
+
+Generalizable Neural Radiance Fields (GNeRF) are recognized as one of the most promising techniques for novel view synthesis and 3D model generation in real-world applications. However, like other generative models in computer vision, ensuring their adversarial robustness against various threat models is essential for practical use. The pioneering work in this area, NeRFool, introduced a state-of-the-art attack that targets GNeRFs by manipulating source views before feature extraction, successfully disrupting the color and density results of the constructed views. Building on this foundation, we propose IL2-NeRF (Iterative  $L_{2}$  NeRF Attack), a novel adversarial attack method that explores a new threat model (in the  $L_{2}$  domain) for attacking GNeRFs. We evaluated IL2-NeRF against two standard GNeRF models across three benchmark datasets, demonstrating similar performance compared to NeRFool, based on the same evaluation metrics proposed by NeRFool. Our results establish IL2-NeRF as the first adversarial method for GNeRFs under the  $L_{2}$  norm. We establish a foundational  $L_{2}$  threat model for future research, enabling direct performance comparisons while introducing a smoother, image-wide perturbation approach in Adversarial 3D Reconstruction. Our code is available at: https://github.com/The-NRC-SCAR-Group/IL2-NeRF
+
+# 1. Introduction
+
+In recent years, machine learning has significantly advanced the field of computer vision, with numerous state-of-the-art (SOTA) models pushing the boundaries of 2D and 3D representation. Among these models, Neural Radiance Fields (NeRF) has emerged as a powerful method for reconstructing highly detailed 3D scenes from 2D images [9, 21, 33]. NeRF utilizes a deep learning model to represent a 3D scene as a continuous volumetric field, generating realistic views from any camera angle based on its learned representation of light and color radiance.
+
+As machine learning vision models see greater in-field deployment, security concerns around these models increase. Specifically, adversarial attacks can perturb images, in turn producing adversarial examples that machine learning models misclassify. The first proposed successful attack for GNeRF models was the NeRFOol attack under the  $L_{\infty}$  norm [8].
+
+Being the first adversarial attack proposed on GNeRF models, NeRFOol was the advent for analyzing robustness for a novel type of vision model. With this in mind, we are keen to present new attacks across new threat norms. Our main contributions can be summarized as follows:
+
+1. We introduce IL2-NeRF, the first adversarial attack on GNeRF models in the  $L_{2}$  domain, providing a novel threat model that applies uniform perturbations across the entire image and setting a foundation for future  $L_{2}$ -based attacks.  
+2. Technical Contribution: We utilize several unique factors, such as an independent perturbation variable and a weighted loss term, that presents a unique perspective on iterative attack algorithms. The traits we present here provide a framework for future algorithms to exploit GNeRF robustness.  
+3. Comprehensive Experimental Validation: We demonstrated the effectiveness of IL2-NeRF through rigorous experiments across multiple datasets (LLFF, DeepVoxels, Synthetic) and GNeRF models (IBRNet, GNT). The results showcase IL2-NeRF's comparable performance with existing methods like NeRFool in degrading 3D model outputs under varied conditions.
+
+# 2. Preliminaries
+
+In this section, we will formalize the loss objective of the NeRF and GNeRF pipelines. This allows us to define the NeRFool attack. Lastly, we propose the threat model we operate under. All of this serves as a preliminary to establish our new attack algorithm.
+
+# 2.1. NeRF Pipeline
+
+In computer vision, the 3D coordinate of the camera is stored in the form of the location  $(x,y,z)$  and direction  $(\theta, \phi)$ . The rays are formed and broken into  $r_o \in \mathbb{R}^3$  (ray ori
+
+gin/camera center) and  $r_d \in \mathbb{R}^3$  (ray direction) based on the image size.
+
+Each chunk's color and density can later be synthesized into the color along the ray. ie, the ray segment becomes  $r_t = r_o + t_ir_d$ , where  $t_i \sim \mathcal{U}[t_n + \frac{i}{N}(t_f - t_n), t_n + \frac{i+1}{N}(t_f - t_n)]$  [21].
+
+A rendering model is trained using a loss function comprised of multiple functions aggregated together to generate our final scene. The predicted color is a function of the camera's ray  $r(t)$  that is input into volume density function  $\sigma$ . The function  $T(t)$  denotes the likelihood that the ray will be transmitted from  $t_n$  to  $t$  without colliding with another rendered particle. Like the ray, the transmittance  $T$  is broken down into  $N$  evenly spaced bins partitioned from  $[t_n, t_f]$ . The function then aggregates these partitioned bins back into the full transmittance. The function then uses the sum to estimate the continuous integral  $C(r)$ .
+
+$$
+C (r) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (r (t)) c (r (t), d) d t, \tag {1}
+$$
+
+where  $T(t) = \exp \left(-\int_{t_n}^t\sigma (r(s))ds\right)$ .
+
+The estimated color takes in the continuous integral while using  $\delta_{i}$ , the distance between consecutive samples along the ray, in the exponential term  $\exp (-\sigma_i\delta_i)$  to model then calculate the attenuation of the ray as it travels, which can be given by
+
+$$
+\hat {C} (r) = \sum_ {i = 1} ^ {N} T _ {i} \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) c _ {i} \tag {2}
+$$
+
+where  $T_{i} = \exp \left(-\sum_{j = 1}^{i - 1}\sigma_{j}\delta_{j}\right)$
+
+After the volumetric rendering, we receive the learned image from that particular coordinate. We then use the generated 2D image against the ground truth image to calculate the Mean Squared Error (MSE) Loss from which the model learns and updates its weights. formally, the loss function is as follows
+
+$$
+\mathcal {L} = \sum_ {r \in \mathcal {R}} \left[ \| \hat {C} _ {c} (r) - C (r) \| _ {2} ^ {2} + \| \hat {C} _ {f} (r) - C (r) \| _ {2} ^ {2} \right] \tag {3}
+$$
+
+for all the accumulation of rays as  $\mathcal{R}$  where  $C_c(r)$  is the output from the coarsely ray-sampled NeRF model and  $C_f(r)$  is for the finely ray-sampled NeRF model.
+
+# 2.2. GNeRF Adaptations
+
+To enable cross-scene generalizations, subsequent work adopt CNN encoders to extract features  $\{E(\mathbf{I_i})\}$  from the source views  $\{\mathbf{I_i}\}$  [3, 17, 27, 31, 32]. Each sampled point  $x$  is transformed by some function  $\pi_{i}$ , producing feature vectors  $e = \{E(\mathbf{I_i})[\pi_i(x)]\}$  that the GNeRF model  $f$  can use to produce the density and color  $f(x,r_d,e) = (\sigma ,c)$ .
+
+# 2.3. NeRFool
+
+The original NeRF paper presents two attacks - one that samples a subset of rays, and one that perturbs all rays. We will explore the first NeRFool attack known as the "View Specific" attack [8].
+
+The view-specific attack adds perturbations  $\Delta = \{\delta_i\}$  to the RGB pixels of selected source view images  $(\mathbf{I}_i)$ . To minimize perturbations while maximizing loss,  $\Delta$  is optimized with a perturbation budget of  $\epsilon$  over a  $L_{\infty}$  norm constraint  $(\| \delta_i\|_{\infty}\leq \epsilon)$ . This gives us the attack objective
+
+$$
+\max  _ {\forall \delta_ {i} \in \Delta : \| \delta_ {i} \| _ {\infty} \leq \epsilon} \hat {\mathcal {L}} _ {r g b} \left(\mathcal {R} _ {t a r g e t}, f, \Delta\right) \tag {4}
+$$
+
+where  $f$  is the GNeRF model and  $R_{target}$  are the randomly sampled rays for the source view image.  $\hat{\mathcal{L}}_{rgb}$  is a modified loss function that uses a pseud-ground truth since the ground truth image might not be available. Formally, it is expressed as follows,
+
+$$
+\hat {\mathcal {L}} _ {r g b} (\mathcal {R}, f, \Delta) = \sum_ {r \in \mathcal {R}} \| \hat {C} (r, f _ {\Delta} ^ {a d v}) - \hat {C} (r, f ^ {c l e a n}) \| _ {2} ^ {2} \tag {5}
+$$
+
+where  $f_{\Delta}^{adv}$  is the output from the model with adversarial image and  $f^{clean}$  is the output from the model with clean image. Lastly,  $\delta_{i}$  is iteratively optimizing by updating at each step via gradient descent. An Adam Optimizer is used as follows:
+
+$$
+\delta_ {i} ^ {(t + 1)} = \operatorname {c l i p} \left(\delta_ {i} ^ {t} + \eta \cdot \operatorname {A d a m} \left(\nabla_ {\delta_ {i} ^ {t}} \hat {\mathcal {L}} _ {r g b}\right), - \epsilon , \epsilon\right) \tag {6}
+$$
+
+while keeping the sum between our source image and perturbation  $\mathbf{I}_i + \delta_i\in [0,1]$  within an expected pixel bound.
+
+# 2.4. Threat Model
+
+All adversarial attacks can be categorized as black-box or white-box attacks [19]. White-box attacks assume the attackers have full access to the target victim model, such as model parameters or the training data set. In contrast, black-box attacks are implemented without prior knowledge of the target victim model, except for the model output [15].
+
+While most existing GNeRF attacks operate under the  $L_{\infty}$  norm, focusing on individual pixel perturbations, the  $L_{2}$  norm offers a more uniform and holistic approach to perturbations across the entire image, which can be more realistic and challenging for generative models to counter [1, 4, 5, 18, 23]. By introducing the  $L_{2}$  norm in this setting, we provide a new threat model that broadens the scope for evaluating adversarial robustness in GNeRF. Both types of attacks work by applying perturbations under a specified norm. Most popular attacks work under the  $L_{\infty}$  norm, where updates are performed coordinate-wise and bounded by a specified  $\epsilon$  term [6, 7, 10, 11, 14, 16]. However, attacks that work exclusively in the  $L_{2}$  norm, or Euclidean
+
+distance, have gained notoriety, especially in the black-box domain [22, 24, 26, 29, 35].
+
+The NeRFool attack requires the model loss and the rotation and translation matrix, making it a white-box attack. We work under the same assumption that we have access to rotation and translation matrices and can compute model loss. Unlike NerFool, which works under the  $L_{\infty}$  norm, we introduce an iterative algorithm that works under the  $L_{2}$  norm. The following sections explain our threat model's formalism and efficiency.
+
+# 3. IL2-NeRF: NeRFOol in L2 Domain
+
+In this section, we present IL2-NeRF, an iterative attack that perturbs NeRF source images in Euclidean distance. We draw insight from both the NeRFOol and PGD attacks.
+
+# 3.1. Motivation
+
+Current adversarial approaches to GNeRF only focus on the  $L_{\infty}$  norm, which targets maximal per-pixel perturbations [12, 13]. While effective, this approach tends to introduce highly localized perturbations, emphasizing individual pixel changes without a unified impact across the image [1, 4]. In contrast, the  $L_{2}$  norm threat model offers a different perspective, allowing for smoother, more evenly distributed perturbations across all pixels [4, 23]. This uniformity in perturbation can be particularly advantageous for generative models, where coherent transformations across the image may be more perceptually relevant than isolated pixel deviations [5, 18, 23].
+
+From this, we derive that  $L_{2}$  perturbations can provide a realistic setting for GNeRF adversarial attacks, as they resemble noise patterns that affect the entire image uniformly, mimicking real-world imaging artifacts. Exploring the  $L_{2}$  norm thus enables us to assess GNeRF models' robustness in an alternative threat model that may reflect practical adversarial scenarios more accurately than  $L_{\infty}$ . This work introduces the first attack under the  $L_{2}$  norm for GNeRF models, establishing a baseline for future explorations in this domain and enabling direct comparisons in the  $L_{2}$  threat space.
+
+# 3.2.Objective
+
+We work under a similar objective as the original NeRFool attack, but we rework the formalism to include minimizing adversarial perturbation as an objective. For an image-set  $\{x_{i}\}_{i = 1}^{N}$ , we want to find  $\{\delta_i\}_{i = 1}^N$  such that  $\forall \delta_{i}\in \Delta$
+
+$$
+\min  _ {\| \delta_ {i} \| _ {2}} \left(\max  \hat {\mathcal {L}} _ {r g b} \left(\mathcal {R} _ {t a r g e t}, f, \Delta\right)\right) \text {s . t .} \| \delta_ {i} \| _ {2} \leq \epsilon \tag {7}
+$$
+
+where  $f$  is the GNeRF model,  $R_{target}$  are the randomly sampled rays for the source view image, and  $\hat{\mathcal{L}}_{rgb}$  is a modified loss function defined in Eq. (5).
+
+# 3.3. Algorithm & Explanation
+
+# Algorithm 1 IL2-NeRF
+
+Input: Set of sampled rays  $\mathcal{R}_{tar}$ , GNeRF model  $f$ , Input images  $\{x\}_{i=1}^{N}$ , Number of Steps  $T$ , Step Size  $\alpha$ , Perturbation Limit  $\epsilon$
+
+Output:  $\delta_i^T$  for each  $x_{i}$
+
+1: for  $i \gets 1$  to  $N$  do  
+2:  $\delta_0^t\in \mathcal{U}[-\epsilon ,\epsilon ]$  
+3: for  $t\gets 1$  to  $T$  do  
+4:  $\delta_i^{\prime t} = \nabla_{\delta_i^{t - 1}}\tilde{\mathcal{L}}_{rgb}(\mathcal{R}_{rgb},f,\delta_{i - 1}^t)$  
+5:  $\tilde{\delta}_i^t = \delta_{i - 1}^t +\alpha \cdot \mathrm{sign}\left(\frac{\delta_i'^t}{||\delta_i'^t||_2}\right)$  
+6:  $\delta_i^t = \delta_{i - 1}^t +||\tilde{\delta}_i^t -\delta_{i - 1}^t ||_2$  
+7:  $\delta_i^t = \mathrm{clip}(\delta_i^t, -\epsilon, \epsilon)$  
+8: end for  
+9: end for  
+10: Return  $\{\delta_i^T\}_{i=1}^N$ ;
+
+The IL2-NeRF algorithm is an iterative adversarial attack method specifically designed for GNeRF models. Unlike traditional 2D adversarial attack methods, our method targets the volumetric representation of scenes within GNeRF, aiming to produce perturbations along rays that impact the rendered output views. Our algorithm uses gradient-based optimization, customizing the loss function to target the RGB and density of the final output. Specifically, in our implementation, we are taking the gradient over 8 different loss functions, each crafted upon GNeRF's unique 3D perspective.
+
+The pseudo-code of our algorithm is provided in Algorithm (1). We iterate through each source image and sample the initial perturbation from a Uniform distribution with upper and lower bounds set at our perturbation limit.
+
+At the  $i$ -th step, we take the gradient of our GNeRF model  $f$  when we add the last  $\delta_{i-1}$  perturbation to our source images and subset of rays, denoting this change in loss as  $\delta_{i-1}^{\prime}$ . From here, we add the product of the sign of  $L_2$  normalized  $\delta_{i-1}$  grad with a specified step size  $\alpha$  to  $\delta_{i-1}$ . We denote this as  $\tilde{\delta}_i$ . Note that Eq. (6) uses  $\eta$  to denote its learning rate.  $\alpha$  is a normalized learning rate determined by  $\alpha = \frac{\eta}{255}$ .
+
+To ensure that our final perturbation is added with respect to the  $L_{2}$  norm, we take the difference between  $\tilde{\delta}_i$  and  $\delta_{i - 1}$ , normalize this in  $L_{2}$ , and add this back  $\delta_{i - 1}$  to receive our current  $\delta_{i}$  term. To ensure our final perturbation stays within our perturbation limit  $\epsilon$ , we clip in the  $\epsilon$  ball.
+
+# 3.4. Key Technical Differences from PGD
+
+1. Ray-Based Perturbation vs. Pixel-Level Perturbation: Traditional PGD focuses on perturbing individual pixels in 2D images only [19]. In contrast, IL2-NeRF
+
+applies perturbations along both the sampled rays in 3D space  $(\mathcal{R}_{tar})$  and at a pixel-level, leveraging the GNeRF model's structure and targeting the volumetric rendering process. This combination of perturbing pixels and rays fundamentally changes how adversarial effects are achieved, as the perturbations influence the entire 3D scene rather than a single 2D representation.
+
+2. Customized Gradient-Based Optimization for RGB and Density Losses: Our algorithm uses gradient-based optimization, customizing the loss function to target both the RGB values and the density of the final output. Specifically, in our implementation, we compute the gradient over a weighted loss of 8 different loss functions, each designed to exploit GNeRF's unique 3D perspective. In contrast, traditional PGD typically uses only a single basic loss function, such as Cross Entropy, to guide perturbations in 2D adversarial attacks [2, 19]. These tailored loss functions in IL2-NeRF enable precise control over how the adversarial perturbations affect the rendered output in terms of both color and depth.  
+3. Direct Perturbation Optimization: Most adversarial attacks operate by creating an initial adversarial image and then directly optimizing the loss and perturbation of the adversarial image with respect to its clean counterpart [6, 7, 10, 11, 14, 16]. Our algorithm is unique in that we maintain our perturbation as a separate variable and update this using the gradient loss that our perturbed rays and images create.
+
+# 4. Experiments & Results
+
+To properly compare the performance of NeRFool with IL2-NeRF, we maintain a controlled environment where only one parameter is variable and the rest are fixed. We compare attack performance and pixel-wide perturbations between ground truth source images and the predicted outputs from feeding the perturbed source images.
+
+# 4.1. Experiment Setup
+
+Models We run both NeRFool and IL2-NeRF on two SOTA GNeRF methods: IBRNet [28] and GNT [27]. We use the pre-trained weights provided by their corresponding implementations.
+
+Datasets On IBRNet and GNT, we run experiments across three different datasets: LLFF [21], DeepVoxels [25], and Synthetic [20]. We present results for GNT on LLFF and DeepVoxels here. We run attacks on evaluation images from eight objects and scenes from LLFF, four objects in DeepVoxels, and eight objects from Synthetic.
+
+Attack Parameters To ensure a controlled experiment environment, we fix all hyperparameters besides our maximum perturbation factor  $\epsilon$ . For both NeRFool and IL2-NeRF, we fix the number of steps  $T$  to 1000. Both attacks use a learning rate of 1 (so  $\eta = 1$ ,  $\alpha = 1/255$ ) and four
+
+source views. The initial adversarial perturbation  $\delta_0$  is sampled uniformly from  $\mathcal{U}[-\epsilon, \epsilon]$ . Both attacks are set to perturb both color and density.
+
+Evaluating Attack Performance There are three metrics we use to evaluate attack performance. PSNR, or Peak Signal-to-Noise Ratio, represents the reconstruction accuracy and is our main metric [34]. A lower PSNR indicates a poor scene generation and thus a more successful attack.
+
+SSIM, or structural similarity, compares the local patterns of pixel intensities by normalizing using the mean intensity and taking luminance as a contrast comparison [30]. A lower SSIM score indicates a more successful attack.
+
+LPIPS, or Learned Perceptual Image Patch Similarity, takes the  $L_{2}$  distance between averaged unit-normalized channels for an image [34]. Unlike PSNR and SSIM, a higher LPIPS score means a more successful attack.
+
+Comparing Epsilon We vary  $\epsilon$  starting at 8 for IL2-NeRF and consider powers of two until we perform similarly to NeRFool. As a benchmark, we fix the perturbation factor  $\epsilon$  to 8 for NeRFool. It is important to note that the  $\epsilon$  values imply different interpretations of perturbation magnitudes when working under different norms (such as  $L_{\infty}$  and  $L_{2}$ ).
+
+For an  $L_{\infty}$  attack like NeRFool with  $\epsilon = 8$ , the perturbation constraint allows each pixel in the input to be independently perturbed by up to 8 units, which can lead to a large and consistent maximum distortion across all pixels.
+
+In contrast, for an  $L_{2}$  attack like ours,  $\epsilon = 8$  signifies that the total perturbation energy (i.e., the sum of squared perturbations across all pixels) must remain within 8. This constraint in the  $L_{2}$  norm distributes the perturbation across multiple dimensions, resulting in smaller individual pixel changes than the maximum possible under the  $L_{\infty}$  constraint.
+
+Thus, even though a large perturbation factor like  $\epsilon = 64$  in  $L_{2}$  may appear large, it actually enforces a more dispersed, lower-magnitude perturbation at the pixel level when compared to  $\epsilon = 8$  in  $L_{\infty}$ . This explains why the  $L_{2}$  norm attack with a higher  $\epsilon$  results in a smaller perceptible perturbation than the  $L_{\infty}$  attack with a smaller  $\epsilon$ .
+
+# 4.2. Experiment Evaluation
+
+LLFF Attack Results Tables 1, 2, 3 and 4 showcase results from varying  $\epsilon$  on IL2-NeRF when compared to NeR-Fool on  $\epsilon = 8$  across all scenes for the LLFF dataset on IBRNet. We interpret the IBRNet as our baseline GNeRF model and likewise LLFF as our most standard dataset for GNeRFs.
+
+Table 1 reports the PSNR value of NeRFool against IL2-NeRF on all eight scenes from the LLFF dataset. We compare NeRFool on  $\epsilon = 8$  to IL2-NeRF on five values of  $\epsilon$  from 8 to 256. For each scene, as our perturbation factor  $\epsilon$  increases, we notice the PSNR that IL2-NeRF achieves de
+
+LLFF PSNR  
+
+<table><tr><td></td><td>Model</td><td>ε =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>IBRNet</td><td>8</td><td>13.145</td><td>14.428</td><td>12.944</td><td>11.682</td><td>14.045</td><td>11.042</td><td>12.091</td><td>11.526</td><td>12.613</td></tr><tr><td>GNT</td><td>8</td><td>14.921</td><td>15.428</td><td>14.165</td><td>14.134</td><td>13.946</td><td>12.348</td><td>13.253</td><td>12.773</td><td>13.871</td></tr><tr><td rowspan="6">IL2-NeRF</td><td rowspan="4">IBRNet</td><td>8</td><td>21.581</td><td>25.214</td><td>24.605</td><td>22.967</td><td>18.696</td><td>17.960</td><td>24.172</td><td>20.188</td><td>21.923</td></tr><tr><td>16</td><td>20.590</td><td>24.296</td><td>21.652</td><td>21.458</td><td>18.450</td><td>17.438</td><td>21.071</td><td>18.355</td><td>20.414</td></tr><tr><td>64</td><td>16.825</td><td>17.852</td><td>15.862</td><td>15.742</td><td>16.740</td><td>14.030</td><td>16.120</td><td>14.240</td><td>15.926</td></tr><tr><td>128</td><td>14.900</td><td>15.220</td><td>14.299</td><td>13.945</td><td>14.708</td><td>11.950</td><td>13.837</td><td>12.731</td><td>13.949</td></tr><tr><td rowspan="2">GNT</td><td>256</td><td>13.02</td><td>13.193</td><td>13.462</td><td>12.028</td><td>12.212</td><td>9.920</td><td>12.518</td><td>11.485</td><td>12.230</td></tr><tr><td>256</td><td>13.381</td><td>13.367</td><td>14.449</td><td>12.394</td><td>11.912</td><td>10.151</td><td>12.649</td><td>11.453</td><td>12.470</td></tr></table>
+
+Table 1. PSNR of NeRFool vs. IL2-NeRF on IBRNet model, LLFF dataset. Note that a lower PSNR indicates a more successful attack.  
+LLFF SSIM  
+
+<table><tr><td></td><td>Model</td><td>ε =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>IBRNet</td><td>8</td><td>0.473</td><td>0.594</td><td>0.539</td><td>0.513</td><td>0.442</td><td>0.311</td><td>0.658</td><td>0.549</td><td>0.510</td></tr><tr><td>GNT</td><td>8</td><td>0.470</td><td>0.515</td><td>0.462</td><td>0.541</td><td>0.391</td><td>0.327</td><td>0.626</td><td>0.520</td><td>0.482</td></tr><tr><td rowspan="6">IL2-NeRF</td><td rowspan="4">IBRNet</td><td>8</td><td>0.694</td><td>0.836</td><td>0.790</td><td>0.809</td><td>0.641</td><td>0.565</td><td>0.908</td><td>0.792</td><td>0.754</td></tr><tr><td>16</td><td>0.670</td><td>0.825</td><td>0.740</td><td>0.784</td><td>0.631</td><td>0.548</td><td>0.881</td><td>0.767</td><td>0.731</td></tr><tr><td>64</td><td>0.564</td><td>0.705</td><td>0.570</td><td>0.635</td><td>0.551</td><td>0.426</td><td>0.764</td><td>0.656</td><td>0.609</td></tr><tr><td>128</td><td>0.485</td><td>0.579</td><td>0.487</td><td>0.516</td><td>0.442</td><td>0.320</td><td>0.686</td><td>0.567</td><td>0.510</td></tr><tr><td rowspan="2">GNT</td><td>256</td><td>0.405</td><td>0.435</td><td>0.451</td><td>0.390</td><td>0.271</td><td>0.184</td><td>0.616</td><td>0.437</td><td>0.399</td></tr><tr><td>256</td><td>0.353</td><td>0.307</td><td>0.388</td><td>0.356</td><td>0.180</td><td>0.144</td><td>0.545</td><td>0.365</td><td>0.330</td></tr></table>
+
+Table 2. SSIM of NeRFool vs. IL2-NeRF on IBRNet model, LLFF dataset. Note that a lower SSIM indicates a more successful attack.  
+LLFF LPIPS  
+
+<table><tr><td></td><td>Model</td><td>ε =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>IBRNet</td><td>8</td><td>0.477</td><td>0.407</td><td>0.471</td><td>0.479</td><td>0.409</td><td>0.566</td><td>0.447</td><td>0.484</td><td>0.468</td></tr><tr><td>GNT</td><td>8</td><td>0.375</td><td>0.338</td><td>0.391</td><td>0.358</td><td>0.369</td><td>0.421</td><td>0.351</td><td>0.388</td><td>0.374</td></tr><tr><td rowspan="6">IL2-NeRF</td><td rowspan="4">IBRNet</td><td>8</td><td>0.299</td><td>0.180</td><td>0.232</td><td>0.236</td><td>0.272</td><td>0.347</td><td>0.199</td><td>0.305</td><td>0.259</td></tr><tr><td>16</td><td>0.326</td><td>0.193</td><td>0.281</td><td>0.263</td><td>0.280</td><td>0.360</td><td>0.233</td><td>0.330</td><td>0.283</td></tr><tr><td>64</td><td>0.430</td><td>0.322</td><td>0.444</td><td>0.404</td><td>0.346</td><td>0.476</td><td>0.374</td><td>0.425</td><td>0.403</td></tr><tr><td>128</td><td>0.510</td><td>0.440</td><td>0.510</td><td>0.505</td><td>0.432</td><td>0.576</td><td>0.466</td><td>0.499</td><td>0.492</td></tr><tr><td rowspan="2">GNT</td><td>256</td><td>0.578</td><td>0.550</td><td>0.538</td><td>0.596</td><td>0.556</td><td>0.690</td><td>0.534</td><td>0.587</td><td>0.579</td></tr><tr><td>256</td><td>0.483</td><td>0.484</td><td>0.469</td><td>0.500</td><td>0.499</td><td>0.560</td><td>0.447</td><td>0.506</td><td>0.494</td></tr></table>
+
+Table 3. LPIPS of NeRFool vs. IL2-NeRF on IBRNet model, LLFF dataset. Note that a higher LPIPS indicates a more successful attack.  
+IBRNet LLFF Average L2 Distance  
+
+<table><tr><td></td><td>ε =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td>NeRFool</td><td>8</td><td>343.268</td><td>288.048</td><td>354.545</td><td>393.361</td><td>299.904</td><td>426.528</td><td>377.955</td><td>407.624</td><td>361.404</td></tr><tr><td rowspan="5">IL2-NeRF</td><td>8</td><td>126.494</td><td>85.853</td><td>94.222</td><td>114.872</td><td>176.605</td><td>192.003</td><td>100.132</td><td>148.946</td><td>129.891</td></tr><tr><td>16</td><td>142.021</td><td>95.403</td><td>128.997</td><td>137.913</td><td>181.555</td><td>203.898</td><td>138.884</td><td>184.992</td><td>151.708</td></tr><tr><td>64</td><td>218.791</td><td>195.606</td><td>249.270</td><td>252.401</td><td>220.501</td><td>304.433</td><td>240.540</td><td>298.844</td><td>247.548</td></tr><tr><td>128</td><td>274.809</td><td>264.418</td><td>293.947</td><td>308.864</td><td>278.835</td><td>384.506</td><td>310.953</td><td>352.868</td><td>308.650</td></tr><tr><td>256</td><td>339.786</td><td>333.319</td><td>323.590</td><td>382.289</td><td>372.280</td><td>483.862</td><td>360.341</td><td>405.359</td><td>375.103</td></tr></table>
+
+Table 4. Average L2 Difference between ground truth source images and predicted outputs when IBRNet is provided perturbed source images as input on LLFF dataset. Note that a lower L2 distance is desired.  
+IBRNet LLFF PSNR  
+
+<table><tr><td></td><td>η =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="3">IL2-NeRF</td><td>0.001</td><td>9.848</td><td>11.571</td><td>11.231</td><td>9.547</td><td>10.332</td><td>8.179</td><td>25.500</td><td>9.406</td><td>11.952</td></tr><tr><td>0.05</td><td>9.849</td><td>11.561</td><td>10.899</td><td>9.587</td><td>10.282</td><td>8.143</td><td>13.932</td><td>9.525</td><td>10.473</td></tr><tr><td>0.1</td><td>9.906</td><td>11.558</td><td>10.886</td><td>9.531</td><td>10.326</td><td>8.135</td><td>13.795</td><td>9.612</td><td>10.469</td></tr></table>
+
+Table 5. PSNR of IL2-NeRF on IBRNet and GNT models with variable learning rate, LLFF dataset. Note that a lower PSNR indicates a more successful attack.
+
+![](images/5ffef1ce845b569c4f309708d243a96c81dcc23e5064f8df2778c74ca60a8b21.jpg)  
+Figure 1. Visual comparing predicted images on four LLFF scenes from IBRNet on NeRFool and IL2-NeRF perturbed images on varying perturbation factors  $\epsilon$ .
+
+![](images/e82b5d5d85797fa6e9cb2c69d143c7bb2a9e5fa67d0d350fb9c70a01ec1eb940.jpg)  
+Figure 2. Visual comparing depth masks of Orchids predicted image from IBRNet on NeRFool and IL2-NeRF perturbed images on varying perturbation factors  $\epsilon$ .
+
+IBRNet LLFF SSIM  
+
+<table><tr><td></td><td>η =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="3">IL2-NeRF</td><td>0.001</td><td>0.296</td><td>0.327</td><td>0.388</td><td>0.291</td><td>0.150</td><td>0.089</td><td>0.876</td><td>0.319</td><td>0.342</td></tr><tr><td>0.05</td><td>0.295</td><td>0.330</td><td>0.387</td><td>0.292</td><td>0.150</td><td>0.089</td><td>0.686</td><td>0.323</td><td>0.319</td></tr><tr><td>0.1</td><td>0.292</td><td>0.328</td><td>0.385</td><td>0.292</td><td>0.150</td><td>0.090</td><td>0.686</td><td>0.323</td><td>0.318</td></tr></table>
+
+Table 6. SSIM of IL2-NeRF on IBRNet and GNT models with variable learning rate, LLFF dataset. Note that a lower SSIM indicates a more successful attack.  
+IBRNet LLFF LPIPS  
+
+<table><tr><td></td><td>η =</td><td>Fern</td><td>Flower</td><td>Fortress</td><td>Horns</td><td>Leaves</td><td>Orchids</td><td>Room</td><td>T-Rex</td><td>Avg.</td></tr><tr><td rowspan="3">IL2-NeRF</td><td>0.001</td><td>0.604</td><td>0.583</td><td>0.571</td><td>0.628</td><td>0.586</td><td>0.711</td><td>0.295</td><td>0.626</td><td>0.576</td></tr><tr><td>0.05</td><td>0.603</td><td>0.583</td><td>0.571</td><td>0.626</td><td>0.585</td><td>0.713</td><td>0.468</td><td>0.623</td><td>0.597</td></tr><tr><td>0.1</td><td>0.605</td><td>0.586</td><td>0.573</td><td>0.626</td><td>0.584</td><td>0.713</td><td>0.467</td><td>0.623</td><td>0.597</td></tr></table>
+
+Table 7. LPIPS of IL2-NeRF on IBRNet and GNT models with variable learning rate, LLFF dataset. Note that a higher LPIPS indicates a more successful attack.
+
+IBRNet Synthetic PSNR  
+
+<table><tr><td></td><td>Chair</td><td>Drums</td><td>Ficus</td><td>Hotdog</td><td>Lego</td><td>Materials</td><td>Mic</td><td>Ship</td><td>Avg.</td></tr><tr><td>NeRFool</td><td>13.330</td><td>14.490</td><td>12.300</td><td>10.095</td><td>13.510</td><td>10.874</td><td>10.720</td><td>9.824</td><td>11.893</td></tr><tr><td>IL2-NeRF</td><td>13.727</td><td>11.758</td><td>13.327</td><td>12.286</td><td>11.104</td><td>9.024</td><td>10.450</td><td>9.780</td><td>11.432</td></tr></table>
+
+Table 8. PSNR of NeRFool vs. IL2-NeRF on IBRNet, Synthetic dataset. Note that a lower PSNR indicates a more successful attack.  
+IBRNet Synthetic SSIM  
+
+<table><tr><td></td><td>Chair</td><td>Drums</td><td>Ficus</td><td>Hotdog</td><td>Lego</td><td>Materials</td><td>Mic</td><td>Ship</td><td>Avg.</td></tr><tr><td>NeRFool</td><td>0.855</td><td>0.861</td><td>0.818</td><td>0.797</td><td>0.829</td><td>0.802</td><td>0.803</td><td>0.663</td><td>0.804</td></tr><tr><td>IL2-NeRF</td><td>0.791</td><td>0.700</td><td>0.763</td><td>0.754</td><td>0.635</td><td>0.640</td><td>0.735</td><td>0.581</td><td>0.700</td></tr></table>
+
+Table 9. SSIM of NeRFool vs. IL2-NeRF on IBRNet, Synthetic dataset. Note that a lower SSIM indicates a more successful attack.  
+IBRNet Synthetic LPIPS  
+
+<table><tr><td></td><td>Chair</td><td>Drums</td><td>Ficus</td><td>Hotdog</td><td>Lego</td><td>Materials</td><td>Mic</td><td>Ship</td><td>Avg.</td></tr><tr><td>NeRFool</td><td>0.231</td><td>0.221</td><td>0.236</td><td>0.263</td><td>0.232</td><td>0.252</td><td>0.244</td><td>0.386</td><td>0.258</td></tr><tr><td>IL2-NeRF</td><td>0.338</td><td>0.378</td><td>0.337</td><td>0.383</td><td>0.418</td><td>0.397</td><td>0.352</td><td>0.456</td><td>0.820</td></tr></table>
+
+Table 10. LPIPS of NeRFool vs. IL2-NeRF on IBRNet, Synthetic dataset. Note that a higher LPIPS indicates a more successful attack.  
+Deep Voxels PSNR  
+
+<table><tr><td></td><td>Model</td><td>Armchair</td><td>Cube</td><td>Greek</td><td>Vase</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>IBRNet</td><td>9.500</td><td>13.982</td><td>11.688</td><td>11.437</td><td>11.652</td></tr><tr><td>GNT</td><td>13.070</td><td>17.991</td><td>15.532</td><td>19.540</td><td>16.533</td></tr><tr><td rowspan="2">IL2-NeRF</td><td>IBRNet</td><td>8.660</td><td>11.829</td><td>12.067</td><td>10.235</td><td>10.700</td></tr><tr><td>GNT</td><td>11.959</td><td>13.874</td><td>13.414</td><td>13.312</td><td>13.140</td></tr></table>
+
+Table 11. PSNR of NeRFool vs. IL2-NeRF on IBRNet and GNT models, DeepVoxels dataset. Note that a lower PSNR indicates a more successful attack.  
+DeepVoxels SSIM  
+
+<table><tr><td></td><td>Model</td><td>Armchair</td><td>Cube</td><td>Greek</td><td>Vase</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>IBRNet</td><td>0.760</td><td>0.668</td><td>0.772</td><td>0.761</td><td>0.745</td></tr><tr><td>GNT</td><td>0.833</td><td>0.826</td><td>0.789</td><td>0.921</td><td>0.842</td></tr><tr><td rowspan="2">IL2-NeRF</td><td>IBRNet</td><td>0.728</td><td>0.591</td><td>0.760</td><td>0.684</td><td>0.691</td></tr><tr><td>GNT</td><td>0.796</td><td>0.253</td><td>0.684</td><td>0.781</td><td>0.629</td></tr></table>
+
+Table 12. SSIM of NeRFool vs. IL2-NeRF on IBRNet and GNT models, DeepVoxels dataset. Note that a lower PSNR indicates a more successful attack.  
+Deep Voxels LPIPS  
+
+<table><tr><td></td><td>Model</td><td>Armchair</td><td>Cube</td><td>Greek</td><td>Vase</td><td>Avg.</td></tr><tr><td rowspan="2">NeRFool</td><td>NeRFool</td><td>0.303</td><td>0.285</td><td>0.291</td><td>0.231</td><td>0.278</td></tr><tr><td>GNT</td><td>0.188</td><td>0.139</td><td>0.191</td><td>0.076</td><td>0.149</td></tr><tr><td rowspan="2">IL2-NeRF</td><td>IL2-NeRF</td><td>0.360</td><td>0.373</td><td>0.314</td><td>0.291</td><td>0.335</td></tr><tr><td>GNT</td><td>0.231</td><td>0.676</td><td>0.266</td><td>0.190</td><td>0.331</td></tr></table>
+
+Table 13. LPIPS of NeRFool vs. IL2-NeRF on IBRNet and GNT models, DeepVoxels dataset. Note that a higher LPIPS indicates a more successful attack.
+
+creases monotonically, closer to NeRFool. Once we reach  $\epsilon = 256$ , the PSNR of IL2-NeRF is lower than NeRFool for five out of eight scenes, achieving a PSNR that is on-average 0.383 lower.
+
+Table 2 shows the SSIM value of NeRFool against IL2-NeRF on all eight scenes from the LLFF dataset. At  $\epsilon = 128$ , IL2-NeRF achieves a lower SSIM across two scenes than NeRFool  $\epsilon = 8$ : Flower and Fortress. Furthermore, the average SSIM that IL2-NeRF achieves is exactly the same as the average SSIM that NeRFool achieves at  $\epsilon = 8$  of 0.510.
+
+We also see that at  $\epsilon = 256$ , IL2-NeRF achieves a lower SSIM than NeRFool across all scenes. IL2-NeRF at  $\epsilon = 256$  achieves an average SSIM of 0.399, which is a difference of 0.111 lower than the average SSIM of NeRFool  $\epsilon = 8$  on LLFF.
+
+Table 3 holds the LPIPS value of NeRFool against IL2-NeRF on all eight scenes from the LLFF dataset. Starting at  $\epsilon = 128$ , IL2-NeRF achieves a higher LPIPS across all scenes when compared to NeRFool  $\epsilon = 8$ . NeRFool  $\epsilon = 8$  achieves an average LPIPS of 0.468 whereas IL2-NeRF  $\epsilon = 128$  achieves an average LPIPS of 0.492, a difference of 0.24. At  $\epsilon = 256$ , IL2-NeRF achieves an average LPIPS of 0.579, resulting in a difference of 0.111.
+
+To test this trend that IL2-NeRF receives better attack metrics for  $\epsilon = 256$  when compared to NeRFOol  $\epsilon = 8$ , we run our attacks on the GNT model as well for LLFF. Table 1 shows us that IL2-NeRF achieves a lower PSNR on seven out of eight scenes for  $\epsilon = 256$ . Likewise, Tables 2 and 3 tells us IL2-NeRF earns a higher SSIM and lower LPIPS across all scenes.
+
+Overall, for IBRNet, IL2-NeRF  $\epsilon = 128$  performs comparably to NeRFool  $\epsilon = 8$ , with worse average PSNR and better LPIPS. On both IBRNet and GNT, IL2-NeRF  $\epsilon = 256$  outperforms NeRFool  $\epsilon = 8$  across most scenes in LLFF for PSNR and all scenes on LLFF for SSIM and LPIPS. This proves that  $L_{2}$  attacks can surpass  $L_{\infty}$  attacks on GNeRFs.
+
+LLFF Perturbation Results PSNR, SSIM and LPIPS were all the metrics used to study adversarial perturbations in NeRFool [8]. To complete our analysis, we need to consider the immediate affects that our perturbed images have on GNeRF scene generation. We report these findings in Table 4 and visuals in Figure 1 and 2.
+
+Table 4 shows the average  $L_{2}$  distance across all our ground-truth source images and the predicted images.
+
+These predicted images are produced by the GNeRF model after feeding in the perturbed source images for each scene in LLFF. Up to  $\epsilon = 128$  for IL2-NeRF, all  $L_{2}$  distances for each scene are smaller than the  $L_{2}$  distances for each scene for NeRFool  $\epsilon = 8$ .
+
+Five out of our eight scenes achieve a lower average  $L_{2}$  distance for IL2-NeRF at  $\epsilon = 256$  than NeRFool on  $\epsilon = 8$ : Fern, Fortress, Horns, Room, and T-Rex. The average  $L_{2}$  distance across all scenes for IL2-NeRF is 375.103, which is larger than the averaged L2 distance across all scenes for NeRFool  $\epsilon = 8$  of 361.404 by 13.699. Despite this, if we remove the two scenes with the largest difference between NeRFool  $\epsilon = 8$  and IL2-NeRF  $\epsilon = 256$ , Leaves and Orchids, the average for IL2-NeRF becomes 357.447.
+
+We provide a visual for these predicted images in Figure 1. We show the GNeRF outputs for images in four scenes of LLFF from top to bottom: Fern, Flower, T-Rex and Room. At  $\epsilon = 8$ , 16, IBRNet's output have very minimal degradations. It is not until  $\epsilon = 64$  that IBRNet produces noticeable perturbations, but these are not as intense as NeRFool  $\epsilon = 8$ . At  $\epsilon = 128$ , 256, the IBRNet outputs appear similarly distorted as from providing NeRFool  $\epsilon = 8$  as input.
+
+To better visualize these differences in degradations, we provide another visual in Figure 2. This figure shows the depth mask of our predicted scenes for the Orchid scene in LLFF. These depth masks provide a clear visual for where artifacts are added as we can compare the intensity and addition of said artifacts as we vary  $\epsilon$ .
+
+Again, we notice that at  $\epsilon = 8,16$ , any perturbations added by IL2-NeRF are minimally visible. Artifacts that create clear contrast with the remaining depth mask are noticeable at  $\epsilon = 64$ . At  $\epsilon = 128,256$ , these artifacts intensify and start to consume most of the depth mask, similar to NeRFool  $\epsilon = 8$ .
+
+From Tables 1, 2 and 3 we have found that IL2-NeRF  $\epsilon = 256$  outperforms NeRFOol  $\epsilon = 8$  by our attack metrics. We wish to study if this trend holds across different datasets. For subsequent experiments on new datasets, we fix  $\epsilon = 256$  for IL2-NeRF.
+
+Learning Rate LLFF Results Tables 5, 6 and 7 report our attack metrics that result from varying the learning rate  $\eta$ , where  $\alpha = \frac{\eta}{255}$ , when we run IL2-NeRF on IBRNet on the LLFF dataset with fixed perturbation factor  $\epsilon = 128$ . We use three learning rates 0.001, to 0.05, to 0.1 to study the effects of perturbations on a log scale smaller than  $\eta = 1$ .
+
+Table 5 compares the PSNR of running IL2-NeRF on all scenes of LLFF on IBRNet when  $\eta$  is variable. Interestingly, as  $\eta$  increases, PSNR does not always follow a monotonic behavior for all scenes. Here, the PSNR for Flower, Fortress, Orchids and Room decreases as  $\eta$  increases.
+
+Tables 6 and 7 show SSIM and LPIPS, respectively, when we vary  $\eta$ . We see that across all scenes, as we varied  $\eta$  from 0.001 to 0.1 the change in SSIM and LPIPS is neg-
+
+ligible. This validates using a learning rate  $\eta \geq 1$  for our attack setting.
+
+DeepVoxels Attack Results Tables 11, 12 and 13 report results from running NeRFool  $\epsilon = 8$  and IL2-NeRF  $\epsilon = 256$  on all four scenes of the DeepVoxels dataset on both IBRNet and GNT.
+
+Table 11 compares the PSNR that both attacks achieve on DeepVoxels. Here, IL2-NeRF achieves a lower PSNR on three out of four scenes for IBRNet and all scenes for GNT. Likewise, Table 12 and Table 13 shows that IL2-NeRF gives us a lower SSIM and higher LPIPS respective on both IBRNet and GNT.
+
+Synthetic Attack Results Tables 8, 9 and 10 showcase results from running NeRFool  $\epsilon = 8$  and IL2-NeRF  $\epsilon = 256$  on all eight scenes of the Synthetic dataset.
+
+As shown in Table 11, IL2-NeRF achieves a lower PSNR on five out of eight scenes for IBRNet. Furthermore, Table 12 and Table 13 shows that IL2-NeRF gives us a lower SSIM and higher LPIPS respective on both IBRNet.
+
+Experiment Conclusion We have shown that for our base model IBRNet, on our most standard dataset LLFF that IL2-NeRF at  $\epsilon = 128$  produces comparable metrics to NeRFool  $\epsilon = 8$ . We have further shown that across all three datasets and two models that IL2-NeRF at  $\epsilon = 256$  outperforms NeRFool at  $\epsilon = 8$ .
+
+We acknowledge that there is future work in exploring adversarial methods that produce better metrics under smaller  $L_{2}$ -norm bounds. However, our adversarial algorithm proves that it is possible for  $L_{2}$  adversarial attacks to achieve success in compromising GNeRF robustness.
+
+# 5. Conclusion
+
+By introducing IL2-NeRF, we have laid the groundwork for future studies in  $L_{2}$ -based adversarial robustness for GNeRFs. Our baseline threat model and metrics provide a foundation for advancing adversarial 3D reconstruction, offering a new perspective on how  $L_{2}$  domain attacks can improve robustness testing for neural radiance fields.
+
+As machine learning models see further deployment across social and ethical fields, this research aims to highlight vulnerabilities to drive safer model deployment by examining potential risks. Our work paves the way for future adversarial attacks on GNeRF models that work under the  $L_{2}$  threat model. The advent of  $L_{2}$  attacks on GNeRFs will open the door for geometric-based methods and black-box attacks for evaluating GNeRF robustness.
+
+# Acknowledgments
+
+This research was supported in part by NSF SaTC-2426299, SaTC-2413046, and CNS-2505747.
+
+# References
+
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+# Advancing Generalizable Tumor Segmentation with Anomaly-Aware Open-Vocabulary Attention Maps and Frozen Foundation Diffusion Models
+
+Yankai Jiang $^{1}$ , Peng Zhang $^{2}$ , Donglin Yang $^{3}$ , Yuan Tian $^{1}$ , Hai Lin $^{2}$ , Xiaosong Wang $^{1}$
+
+$^{1}$ Shanghai AI Laboratory  $^{2}$ Zhejiang University  $^{3}$ The University of British Columbia
+
+jiangyankai@pjlab.org.cn, lin@cad.zju.edu.cn, wangxiaosong@pjlab.org.cn
+
+# Abstract
+
+We explore Generalizable Tumor Segmentation, aiming to train a single model for zero-shot tumor segmentation across diverse anatomical regions. Existing methods face limitations related to segmentation quality, scalability, and the range of applicable imaging modalities. In this paper, we uncover the potential of the internal representations within frozen medical foundation diffusion models as highly efficient zero-shot learners for tumor segmentation by introducing a novel framework named DiffuGTS. DiffuGTS creates anomaly-aware open-vocabulary attention maps based on text prompts to enable generalizable anomaly segmentation without being restricted by a predefined training category list. To further improve and refine anomaly segmentation masks, DiffuGTS leverages the diffusion model, transforming pathological regions into high-quality pseudo-healthy counterparts through latent space inpainting, and applies a novel pixel-level and feature-level residual learning approach, resulting in segmentation masks with significantly enhanced quality and generalization. Comprehensive experiments on four datasets and seven tumor categories demonstrate the superior performance of our method, surpassing current state-of-the-art models across multiple zero-shot settings. Codes are available at https://github.com/Yankai96/DiffuGTS.
+
+# 1. Introduction
+
+Generalizable tumor segmentation (GTS) represents a fundamental challenge within medical image analysis [3, 7, 22, 28, 45], stemming from both the diversity of tumor types and the variability across imaging modalities. Current AI models for multi-tumor segmentation [6, 14, 28, 49, 51] rely heavily on comprehensively annotated training data, limiting their ability to generalize beyond a restricted set of categories. This makes it challenging to address unseen diseases in clinical scenarios where the available training data may
+
+not adequately represent the diversity of real-world cases.
+
+With development of vision-language models (e.g., CLIP [34]), some methods [20, 22, 23] have paved the way for unseen tumor segmentation through the zero-shot generalization ability of vision-language alignment between segmentation regions and text prompts. However, in medical imaging, the visual cues of tumors are often subtle and ambiguous. Without a large amount of high-quality image-text pairs for training, segmenting unseen tumor categories using text prompts alone is highly challenging. Furthermore, the vision-language alignment process based on contrastive learning is not necessarily optimal for pixel-level segmentation, as the training objective is not directly optimized for spatial and relational understanding. As a result, these methods are often limited in segmentation quality.
+
+Another promising direction towards GTS is tumor synthesis [7, 19, 45], which enables label-free tumor segmentation by creating artificial yet realistic medical images. However, current tumor synthesis methods are unable to encompass all tumor types, as simulating tumors with irregular shapes or those not encountered during diffusion model training poses significant challenges [16, 45]. Consequently, achieving GTS relying solely on synthetic medical data remains an intricate problem.
+
+Motivated by the above challenges, we take an innovative approach towards GTS. Our key insight is that, despite the challenges in simulating tumors, a medical foundation diffusion model (MFDM) trained on large-scale data is capable of learning and understanding rich, diverse anatomical structures and organ-specific knowledge [16]. Moreover, this valuable knowledge is already embedded within its internal representations. Therefore, instead of synthesizing data for model training, we uncover the potential of pretrained MFDMs as highly efficient semantic feature extractors and demonstrate that their internal image representations can be repurposed, through carefully designed strategies, as effective zero-shot learners for the GTS task.
+
+To this end, we propose DiffuGTS, a novel framework with strong zero-shot capabilities that leverages frozen
+
+![](images/e2defc41642f78bbdb187269b21148e2d90a86a1491da69d68254e387f3cddd3.jpg)  
+Text Prompt  
+(a) Text Prompts and Input Images  
+Figure 1. We propose DiffuGTS, a novel framework that utilizes and extends the capabilities of a frozen medical foundational diffusion model for advanced zero-shot tumor segmentation across various anatomical regions and imaging modalities. (a) DiffuGTS employs descriptions of both normal and abnormal categories to generate open-vocabulary text-attribute attention maps (b) for anomaly segmentation through cross-modal feature interactions. Furthermore, DiffuGTS leverages the frozen diffusion model to refine anomaly segmentation masks (c) by synthesizing pseudo-healthy equivalents and applying pixel-level and feature-level residual learning, significantly surpassing the performance of existing zero-shot lesion segmentation methods [20, 22, 23].
+
+![](images/0f022900a867c040c1e5f1f9e3d39796a5d5f1f61997e2cb3d9b14a51b5c7fe9.jpg)  
+Input Image
+
+![](images/34534944dea62d4ac440fc56b8f6f438a842baaaff4afcb29617f50c63b72db9.jpg)  
+Organ Attention Map  
+(b) Anomaly-Aware Open-Vocabulary Attention Maps
+
+![](images/8a8ed6b373cb60653f8eaf0b1c58cb44d1d38889ac18a0e899b14fe57cff8036.jpg)  
+Tumor Attention Map
+
+![](images/c1fc347e8426563c67a600fe5c24f71884a43fdd67282469c46e4aa4b9033d8a.jpg)  
+Synthetic Pseudo-Healthy  
+sk Refinement with Frozen Diffusion Model
+
+![](images/c2eec87020a068e0c45cf834d14901239c659e05eb3d970dec31fe8405fd0cad.jpg)  
+Segmentation Result
+
+![](images/1f655b24647bfb3815af869a7c0cb4a8789bd09b957c4b6b8ece59ee9606213c.jpg)  
+Ground Truth
+
+MFDMs for generalizable tumor segmentation. We utilize the cross-modal interactions between the internal visual representations of frozen MFDMs and text prompts for anomaly detection to construct a set of novel anomaly-aware open-vocabulary attention (AOVA) maps to achieve zero-shot tumor detection. The AOVA maps repurpose and recalibrate the diverse anatomical knowledge from MFDMs for unseen anomaly segmentation, improving efficiency and enabling generalization to unseen image modalities.
+
+Furthermore, we leverage the generative capabilities of frozen MFDMs to refine the anomaly segmentation masks derived from AOVA maps. We first adopt a training-free latent space inpainting strategy that transforms pathological regions into pseudo-healthy equivalents, conditioned on the anomaly segmentation masks. Then, a novel pixel-level and feature-level residual learning approach generates refined segmentation masks by identifying discrepancies between the original pathological regions and their corresponding pseudo-healthy equivalents, enabling substantial advancements in zero-shot tumor segmentation performance.
+
+Extensive experiments across multiple datasets validate the superiority of DiffuGTS (Fig. 1), significantly surpassing previous SOTA methods under various challenging
+
+zero-shot settings. In a nutshell, our work offers: (1) an effective and efficient framework with novel designs capable of segmenting unseen tumors across diverse anatomical regions and imaging modalities in a zero-shot manner; (2) superior performance: comparisons with various methods across four datasets demonstrate that our method establishes a new state-of-the-art for generalizable tumor segmentation; (3) in-depth analysis: multiple visualizations imply the strong zero-shot capabilities of AOVA maps for anomaly detection and the efficacy of mask refinement with frozen MFDMs, while key ablation experiments demonstrate the effectiveness of our strategies.
+
+# 2. Related Work
+
+Zero-Shot 3D Medical Image Segmentation. Existing zero-shot 3D medical image segmentation methods fall primarily into two categories: SAM [25]-based methods [2, 37, 39, 47] and methods based on vision-language alignment [22, 23]. SAM-based 3D medical image segmentation methods [2, 37, 39, 47] demonstrate promising zero-shot performance in segmenting certain organs, particularly larger organs with clear boundaries. However, they
+
+primarily focus on organ segmentation and have not been evaluated or proven effective when confronted with unseen lesions that have less defined structures. Recently, some methods [22, 23], achieve competitive language-driven zero-shot tumor segmentation performance by matching mask proposals with text descriptions through contrastive learning. However, relying only on weak supervision from text descriptions, these methods are limited to compromised zero-shot performance. DiffuGTS takes a huge step further by leveraging frozen MFDMs to achieve significantly superior zero-shot tumor segmentation performance across different image modalities and various anatomical regions.
+
+Diffusion Models for Medical Image Segmentation. Diffusion models have recently demonstrated significant potential in various medical image segmentation tasks [17, 24, 35, 42-44]. The majority of diffusion-based segmentation methods [8, 11, 17, 35, 42-44] focus on enhancing the segmentation quality of specific organs or tissues under fully supervised settings. Some methods [7, 16, 45], on the other hand, focus on generating additional medical data along with corresponding annotations to supple training data. However, tumor synthesis remains a challenging issue, primarily due to concerns about the quality of synthetic data and the limited diversity of synthesizable categories. In contrast, DiffuGTS focuses on leveraging the frozen diffusion models for zero-shot tumor segmentation.
+
+Diffusion Models for Medical Anomaly Detection. Diffusion models have shown substantial promise in enhancing the precision of medical anomaly detection by transforming pathological inputs into pseudo-healthy outputs and then computing the difference between the original and synthetic images [5, 41]. Current methods [4, 5, 41, 46] mainly focus on enhancing the quality of generated pseudo-healthy outputs. However, these methods are tailored for specific anatomical regions (e.g., brain or chest) and are restricted to handling particular tumor categories, failing to generalize across diverse diseases and image modalities—a critical aspect that our paper seeks to address.
+
+# 3. Method
+
+DiffuGTS first explores internal representations from a frozen foundational diffusion model, MAISI [16], to efficiently leverage anatomical features and create anomaly-aware open-vocabulary attention (AOVA) maps for tumor detection (Sec.3.1). Subsequently, it employs the frozen foundational diffusion model to synthesize pseudo-healthy images conditioned on the AOVA maps, allowing for the extraction of tumor segmentation masks by analyzing the pixel-level and feature-level discrepancies between the original diseased images and their pseudo-healthy counterparts (Sec.3.2). Fig. 2 illustrates the pipeline of DiffuGTS. We elaborate on the details of our design in the following.
+
+# 3.1. Formulation of AOVA Maps
+
+To facilitate generalizable tumor localization across diverse anatomical regions, we introduce anomaly-aware open-vocabulary attention maps, which allow us to control attention heatmaps for constructing anomaly segmentation masks using text prompts (see Fig. 1). This approach establishes a direct correlation between the spatial anatomical layout and the semantic content of diagnostic text descriptions, eliminating the constraints imposed by a predefined category list during training. As a result, it enables zero-shot generalization to previously unseen tumor categories.
+
+Visual Feature Extraction. In contrast to existing zero-shot tumor segmentation methods [22, 23], which typically require the training of versatile vision encoders, we directly and efficiently utilize feature representations from a frozen foundational diffusion model. Specifically, we exploit the internal image features from MAISI's VAE encoder [16]. For an input 3D volume  $\mathcal{I}$ , the MAISI VAE encoder transforms  $\mathcal{I}$  into multi-scale image features  $F_{l} \in \mathbb{R}^{H_{l} \times W_{l} \times D_{l} \times C_{l}}$ ,  $l \in \{1, 2, 3\}$ . Here,  $l$  denotes the three internal stages, while  $H_{l}, W_{l}, D_{l}$ , and  $C_{l}$  represent the height, width, depth, and channel dimensions of  $F_{l}$ , respectively.
+
+Since we fix the parameters of the VAE encoder  $V_{E}$  which is not originally optimized for segmentation tasks, there is a potential gap between the generative and discriminative representation space. Therefore, we perform visual feature adaptation to tailor representations for segmentation tasks, while maintaining the VAE encoder's rich anatomical knowledge. At each level  $l$ , a learnable feature adapter, encompassing two layers of linear transformations and a residual connection, projects the image features  $F_{l}$  for adaptation, represented as:  $\mathcal{F}_l = \alpha T_l(F_l) + (1 - \alpha)F_l$ . Here,  $T_{l}(\cdot)$  denotes the learnable parameters of the linear transformations. A constant value  $\alpha$  serves as the residual ratio to adjust the degree of preserving the original knowledge for improved zero-shot performance. By default, we set  $\alpha = 0.1$ .
+
+Textual Prompt Composition. To explicitly provide hints and prompt the model for effective anomaly detection, we adopt text prompts for the construction of cross-modal correlations between vision and language features. Specifically, we leverage descriptions of both normal and abnormal categories. For normal organs, the predefined template is: "A nomal CT scan/MRI of {organ name}" For tumors, the template is: "An abnormal CT scan/MRI of {disease name}." We extract text embeddings  $e \in \mathbb{R}^{N \times d}$  from normal and abnormal prompts using a pre-trained frozen text encoder [48], where  $N$  and  $d$  denotes the number of training categories and feature dimension.
+
+Text-Driven Region-Level Anomaly Detection. For the construction of AOVA maps, we use the features of text prompts to control the attention heatmaps derived from the cross-attention matrices. At each image feature level  $l \in \{1,2,3\}$ , the text features first undergo dimension reduction
+
+![](images/bc370d85d0625bc4956a26421aec26bbe69cb688aff713cd181f99a6aea26d33.jpg)  
+Figure 2. The architecture of DiffuGTS for generalizable tumor segmentation.
+
+through a Multi-Layer Perception (MLP), adapting them to be compatible with the image features in terms of dimension size and thus enhances computational efficiency. Then, the text embeddings  $e$  are projected using the key projections  $\mathcal{W}_K^l$  to generate attribution keys  $K_{l} = \mathcal{W}_{K}^{l}(e)\in \mathbb{R}^{N\times C_{l}}$ . Similarly, we project the image features  $\mathcal{F}_l$  using the query projections  $\mathcal{W}_Q^l$  to generate pixel queries  $Q_{l} = \mathcal{W}_{Q}^{l}(\mathcal{F}_{l})\in$ $\mathbb{R}^{H_l\times W_l\times D_l\times C_l}$ . The attribution keys  $K_{l}$  are combined with the pixel queries  $Q_{l}$ , creating the cross-attention matrices  $A(Q_{l},K_{l}) = \mathrm{Softmax}\left(\frac{Q_{l}K_{l}^{T}}{\sqrt{C_{l}}}\right)\in \mathbb{R}^{H_{l}\times W_{l}\times D_{l}\times N}$ . These cross-attention matrices weigh the influence of text features for both normal and abnormal objects on the image's pixels, establishing a direct correlation between the anatomical spatial layout and the semantic content of the descriptions for normal and abnormal categories.
+
+We aggregate cross-attention matrices across  $l$  feature levels to generate the AOVA maps as:
+
+$$
+M _ {\mathcal {I}, e} = \sum_ {l = 1} ^ {3} \mathbf {R I} \left(A \left(Q _ {l}, K _ {l}\right)\right) \in \mathbb {R} ^ {H \times W \times D \times N}. \tag {1}
+$$
+
+Here,  $\mathbf{RI}(\cdot)$  denotes the reshape operation using bilinear interpolation for resizing  $A(Q_{l},K_{l})$  of varying resolutions to the original input image resolution.
+
+We optimize the AOVA maps  $M_{\mathcal{I},e}$  for anomaly detection through three training objectives. First, we feed each AOVA map into a MLP layer to obtain the class embedding  $g_i \in \mathbb{R}^d$ ,  $i \in [1,N]$ . We use the  $g_i$  to predict an anomaly score ascore = Sigmoid(MaxPool(g)):  $\mathbb{R}^d \to [0,1]$  so that a binary classification can be performed using binary cross-entropy loss:  $\mathcal{L}_{ano} = \mathrm{BCE}(th(ascore),\mathcal{C})$ . Here,  $th(\cdot)$  denotes a threshold set to 0.5, and  $\mathcal{C} \in \{-, +\}$  represents the image-level anomaly annotation, where '+' indicates an anomalous sample and '-' denotes a normal one.
+
+Then, for AOVA maps classified as abnormal, we align their corresponding class embeddings  $g_{i}$  with the text embeddings of abnormal categories. Conversely, for maps classified as normal, we align their class embeddings  $g_{i}$  with the text embeddings of normal categories. The alignment is achieved by a CLIP-style contrastive learning [34]
+
+approach. The similarity score between each class embedding and text embedding is computed by a dot product normalized by a temperature parameter  $\tau$ :  $s(g_i, e_j) = \frac{g_i \cdot e_j}{\tau}$ . Then the similarity score is refined through a contrastive loss function defined as:
+
+$$
+\mathcal {L} _ {s i m} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log \frac {\exp (s (g _ {i} , e _ {j}))}{\sum_ {j = 1} ^ {N} \exp (s (g _ {i} , e _ {j}))}. \tag {2}
+$$
+
+This contrastive learning aligns the AOVA maps with text embeddings, enabling open-set anomaly detection that generalizes to unseen categories.
+
+Moreover, we convert  $N$  AOVA maps into  $N$  binary segmentation masks for normal and abnormal categories through a Sigmoid operation, and supervise these masks with partially labeled segmentation annotations  $\mathcal{S}$  using a Dice loss [31]:  $\mathcal{L}_{\text{dice}} = \text{Dice}(\text{Sigmoid}(M_{\mathcal{I},e}), \mathcal{S})$ .
+
+During training, text descriptions for all categories are provided, and healthy cases for every organ are utilized, enabling the network to differentiate normal organs from tumors and thereby achieve zero-shot generalization for lesions. The overall loss function for AOVA map optimization is:  $\mathcal{L}_{AOVA} = \lambda_1\mathcal{L}_{ano} + \lambda_2\mathcal{L}_{sim} + \lambda_3\mathcal{L}_{dice}$ . We set  $\lambda_{1} = \lambda_{2} = \lambda_{3} = 1.0$  as default.
+
+# 3.2. Mask Refinement with Frozen Diffusion Model
+
+The AOVA maps can accurately localize tumors using open-vocabulary text prompts, as shown in Fig. 1. However, during zero-shot inference, the masks generated by such text-driven anomaly detection are inherently limited in quality due to the absence of fine-grained, pixel-level supervision for unseen tumor categories. To further enhance zero-shot segmentation performance, we propose utilizing a frozen latent diffusion model from MAISI [16] to refine the lesion masks. This is achieved by synthesizing a pseudo-healthy equivalent of the target diseased organ through an inpainting task. The tumor region can then be obtained by computing the discrepancies between the input image and the synthetic image. The tumor mask refined through this process is significantly more precise than the anomaly segmentation map.
+
+Training-Free Latent Space Inpainting. MAISI [16] integrates a ControlNet [50] to synthesize a healthy organ conditioning on the given organ mask. However, as shown in Fig. 3, it does not ensure that the organ regions unaffected by the disease are preserved, which significantly hinders the performance of tumor segmentation based on differences between images. A key aspect of anomaly segmentation is to ensure fidelity to the original scan in areas unaffected by pathology [5, 41]. To achieve this, we reformulate the original conditional generation process of MAISI as latent space inpainting, leveraging the anomaly segmentation mask as conditions to guide the organ synthesis.
+
+Let the latent representation of the input 3D volume  $\mathcal{I}$ , generated by the VAE encoder  $V_{E}$ , be denoted as  $z = V_{E}(\mathcal{I}) \in \mathbb{R}^{h \times w \times d \times c}$ . To compensate for the issue that anomaly segmentation maps of unseen tumors cannot always precisely capture tumor boundaries, we first enlarge the tumor region in the anomaly segmentation mask using a coefficient  $\beta$  to ensure that the entire tumor region can be covered by the mask. Then, we extend the training-free strategy proposed in [30], which enables conditioning the inpainting task on the known region, thereby eliminating the need for fine-tuning the MAISI [16] model. Specifically, we obtain an intermediate latent code by regenerating the potential tumor region from the model's output while sampling other normal regions from the input. The reverse step at timestep  $t$  is formulated as follows:
+
+$$
+z _ {t - 1} ^ {\text {o t h e r}} \sim \mathcal {N} \left(\sqrt {\bar {\alpha} _ {t}} z, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {3}
+$$
+
+$$
+z _ {t - 1} ^ {\text {t u m o r}} \sim \mathcal {N} \left(\mu_ {\theta} \left(z _ {t}, t\right), \Sigma_ {\theta} \left(z _ {t}, t\right)\right), \tag {4}
+$$
+
+$$
+z _ {t - 1} = \left(1 - D \left(M _ {L}\right)\right) \otimes z _ {t - 1} ^ {\text {o t h e r}} + D \left(M _ {L}\right) \otimes z _ {t - 1} ^ {\text {t u m o r}}. \tag {5}
+$$
+
+Here,  $\odot$  represents element-wise multiplication,  $D(\cdot)$  is the downsampling operation,  $\overline{\alpha} = \Pi_{s=1}^{t}(1 - \beta_{s})$  and  $\beta_{s}$  denotes the variance of Gaussian noise at timestep  $s$  according to a variance schedule predefined in MAISI[16]. Unlike the standard RePaint [30] method, which operates in pixel space, we adapt the enlarged mask  $M_{\mathrm{L}}$  to match the latent space dimensions by downsampling it using nearest-neighbor interpolation, as in LatentPaint [12]. After obtaining the final step output latent embeddings  $z_{0} \in \mathbb{R}^{h \times w \times d \times c}$ , we then use the frozen VAE decoder  $V_{D}$  in MAISI to generate the pseudo-healthy image  $\mathcal{H} = V_{D}(z_{0}) \in \mathbb{R}^{H \times W \times D}$ . In Fig. 3, we show that the pseudo-healthy images generated using our extended, training-free latent space inpainting strategy preserve the healthy regions of the organ to a much greater extent, significantly outperforming the results obtained by directly applying the MAISI model for organ synthesis. We provide the illustration of our one-step reverse process in the supplementary material.
+
+Pixel-Level and Feature-Level Residual Learning. We first obtain the pixel-level residual map  $P_r$  by performing element-wise subtraction between the normalized input volume  $\mathcal{I}$  and its pseudo-healthy variant  $\mathcal{H}: P_r =$
+
+![](images/8e3877a7bcc85b7f4c8aa12f80b78e8efce14de2f254fc0659150dd1c8dcadd0.jpg)  
+Figure 3. Synthesizing pseudo-healthy images directly using MAISI or utilizing the training-free latent space inpainting.
+
+$\mathcal{I} \ominus \mathcal{H} \in \mathbb{R}^{H \times W \times D}$ . This pixel-level residual map, commonly used in previous medical anomaly detection methods [5, 26, 38, 41], offers computational efficiency and intuitively highlights pixel-level discrepancies between images. However, its accuracy is highly contingent upon the quality of the synthesized images; any inconsistencies in generation can lead to pixel variations that compromise segmentation performance. Thus, we propose a novel pixel-level and feature-level residual learning to obtain the final tumor segmentation masks. This method combines  $P_r$  with a feature-level residual map that highlights the differences between  $\mathcal{I}$  and  $\mathcal{H}$  in latent space to effectively discriminate tumors.
+
+Specifically, we obtain the feature-level residual map by performing element-wise subtraction as follows:  $f_r = z \ominus z_0$ . Compare with the pixel-level residual map,  $f_r$  incorporates a deeper semantic understanding, capturing complex structural and pattern changes rather than merely pixel-level brightness or density variations. Then we align  $f_r$  with its corresponding text embeddings of prompts  $e_j$  to obtain feature-level anomaly segmentation maps  $F_r = \Psi(f_r \cdot \psi(e_j)) \in \mathbb{R}^{H \times W \times D}$ . Here,  $\Psi$  and  $\psi$  represent the upsampling and linear projection operations, respectively. Finally, a Dice loss [31] is adopted to supervise  $F_r$  with segmentation annotations  $S$ :  $\mathcal{L}_{Seg} = \mathrm{Dice}(\mathrm{Sigmoid}(F_r), S)$ . During inference, we combine the pixel-level and feature-level residual maps to get the overall anomaly segmentation maps  $R_{\mathrm{pf}} = \beta_1 P_r + \beta_2 F_r$ , where  $\beta_1$  and  $\beta_2$  are weighting factors set to 0.5 by default. We convert  $R_{\mathrm{pf}}$  into a binary segmentation mask by applying Otsu thresholding [32].
+
+# 4. Experiments
+
+Dataset Construction. We consider both public and private datasets encompassing 6 organs and 7 tumor categories, sourced from multiple centers. These datasets include MSD [3], KiTS23 [18], BraTS23 [1], and an in-house MRI liver tumor segmentation dataset. We also utilized data from 404 patients who showed no signs of pathology from the TotalSegmentator [40] dataset as normal samples for anomaly detection training. The total number of CT and MRI scans used for training and testing in our study is 3,933. We adopted various zero-shot testing settings for evaluation. Detailed descriptions of these datasets and the pre-processing are provided in the supplementary material.
+
+Evaluation Metrics. The Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD) are utilized
+
+<table><tr><td rowspan="3">Method Type</td><td rowspan="3">Method</td><td colspan="10">MSD Dataset</td><td colspan="2">KiTS23 Dataset</td></tr><tr><td colspan="2">Pancreas Tumor</td><td colspan="2">Lung Tumor</td><td colspan="2">Liver Tumor</td><td colspan="2">Colon Tumor</td><td colspan="2">Hepatic Vessel Tumor</td><td colspan="2">Kidney Tumor</td></tr><tr><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td></tr><tr><td rowspan="3">SAM-based Methods</td><td>SAM 2 [47]</td><td>26.65</td><td>38.77</td><td>15.39</td><td>15.96</td><td>42.75</td><td>50.22</td><td>13.08</td><td>21.40</td><td>38.92</td><td>49.08</td><td>36.48</td><td>42.59</td></tr><tr><td>SaLIP [2]</td><td>31.28</td><td>44.33</td><td>20.05</td><td>20.77</td><td>48.39</td><td>56.90</td><td>19.33</td><td>27.02</td><td>44.18</td><td>55.84</td><td>39.11</td><td>45.24</td></tr><tr><td>H-SAM [10]</td><td>35.19</td><td>50.02</td><td>25.36</td><td>26.11</td><td>53.03</td><td>60.44</td><td>23.02</td><td>30.67</td><td>51.85</td><td>61.24</td><td>45.57</td><td>52.16</td></tr><tr><td>3D Zero-Shot Lesion</td><td>ZePT [22]</td><td>39.40</td><td>54.76</td><td>30.02</td><td>31.23</td><td>59.16</td><td>68.72</td><td>33.85</td><td>42.31</td><td>55.83</td><td>65.72</td><td>48.75</td><td>54.91</td></tr><tr><td>Segmentation Methods</td><td>Malenia [23]</td><td>40.26</td><td>55.82</td><td>32.75</td><td>33.92</td><td>59.83</td><td>70.08</td><td>34.72</td><td>42.59</td><td>59.71</td><td>69.98</td><td>55.37</td><td>61.16</td></tr><tr><td rowspan="4">Medical Anomaly Detection Methods</td><td>DDPM-MAD [41]</td><td>28.52</td><td>40.18</td><td>25.70</td><td>26.81</td><td>43.54</td><td>51.03</td><td>13.97</td><td>21.84</td><td>39.57</td><td>49.62</td><td>36.55</td><td>42.72</td></tr><tr><td>MVFA [20]</td><td>32.77</td><td>45.63</td><td>24.49</td><td>25.07</td><td>49.25</td><td>57.72</td><td>20.44</td><td>27.87</td><td>45.28</td><td>56.14</td><td>40.81</td><td>46.29</td></tr><tr><td>THOR [5]</td><td>29.45</td><td>41.06</td><td>27.73</td><td>28.98</td><td>47.68</td><td>56.40</td><td>18.36</td><td>26.51</td><td>41.33</td><td>52.05</td><td>38.39</td><td>44.64</td></tr><tr><td>DiffuGTS</td><td>43.61</td><td>58.48</td><td>42.94</td><td>44.01</td><td>63.23</td><td>73.58</td><td>38.72</td><td>45.60</td><td>62.76</td><td>72.35</td><td>59.80</td><td>65.99</td></tr></table>
+
+Table 1. Zero-shot tumor segmentation performance (%) on MSD [3] and KiTS23 [18] with the leave-one-out setting. All the competing methods are implemented using the official code. The best result is in light blue.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="2">In-house</td><td colspan="2">MSD-Brain</td><td colspan="2">BraTS23</td></tr><tr><td colspan="2">Liver Tumor</td><td colspan="2">Brain Tumor</td><td colspan="2">Brain Tumor</td></tr><tr><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td></tr><tr><td>SAM 2 [47]</td><td>15.43</td><td>19.50</td><td>10.04</td><td>12.52</td><td>8.65</td><td>11.39</td></tr><tr><td>SaLIP [2]</td><td>21.65</td><td>25.19</td><td>17.33</td><td>19.65</td><td>15.24</td><td>18.48</td></tr><tr><td>H-SAM [10]</td><td>26.24</td><td>29.37</td><td>19.50</td><td>21.97</td><td>17.69</td><td>21.45</td></tr><tr><td>ZePT [22]</td><td>28.03</td><td>33.15</td><td>19.54</td><td>22.02</td><td>17.87</td><td>21.69</td></tr><tr><td>Malenia [23]</td><td>29.03</td><td>33.87</td><td>19.83</td><td>22.58</td><td>17.94</td><td>21.95</td></tr><tr><td>DDPM-MAD [41]</td><td>15.78</td><td>19.59</td><td>16.11</td><td>18.74</td><td>15.08</td><td>17.51</td></tr><tr><td>MVFA [20]</td><td>22.56</td><td>26.74</td><td>19.42</td><td>21.89</td><td>17.47</td><td>21.19</td></tr><tr><td>THOR [5]</td><td>16.47</td><td>20.11</td><td>18.35</td><td>20.06</td><td>17.04</td><td>20.25</td></tr><tr><td>DiffuGTS</td><td>50.31</td><td>54.28</td><td>47.51</td><td>49.75</td><td>44.70</td><td>46.21</td></tr></table>
+
+Table 2. Zero-shot tumor segmentation performance  $(\%)$  of unseen modalities on the in-house MRI liver tumor dataset, MSD-Brain [3], and BraTS23 [1]. The best result is in light blue.
+
+to evaluate tumor segmentation performance. For all evaluation metrics,  $95\%$  CIs were calculated, and a  $p$ -value cutoff of less than 0.05 was used to define statistical significance.
+
+Implementation Details. We utilize MAISI [16] as the frozen foundational diffusion model, which is capable of conditional generation from segmentation masks of 127 anatomical structures. We leverage the frozen 3D VAE encoder in MAISI as the feature extraction backbone. The overall loss for training DiffuGTS is  $\mathcal{L} = \mathcal{L}_{AOVA} + \mathcal{L}_{Seg}$ . We employ AdamW optimizer [29] with a warm-up cosine scheduler of 50 epochs. The batch size is set to 2 per GPU with a patch size of  $128 \times 128 \times 128$ . The training process uses an initial learning rate of  $1e^{-4}$ , a momentum of 0.9, and a weight decay of  $1e^{-5}$ , running on 4 NVIDIA A100 GPUs with DDP for 1000 epochs.
+
+Competing Methods and Baselines. In this study, we consider various state-of-the-art methods which could segment unseen tumors in zero-shot settings as competing methods, including: (i) SAM [25, 36]-based methods (Adapted SAM 2 [47], SaLIP [2], and H-SAM [10]), which need manual or automatic-generated prompts during testing. (ii) 3D Zeroshot tumor segmentation methods (ZePT [22] and Malenia [23]), which rely on vision-language alignment. (iii) Medical anomaly detection methods (DDPM-MAD [41], MVFA [20], and THOR [5]).
+
+# 4.1. Main Results
+
+We compare DiffuGTS with a series of representative SOTA methods under various zero-shot settings to assess their generalizability to unseen tumors across various anatomical regions and imaging modalities.
+
+Generalization to Unseen Tumors. We conducted experiments for zero-shot generalization to unseen tumors across different anatomical regions under a leave-one-out setting. In this configuration, we considered the KiTS23 [18] along with five tumor segmentation datasets from MSD [3], including liver, colon, pancreas, lung, and hepatic vessel tumors. Each dataset was designated in turn as the unseen category (left out), while the remaining datasets were used for training. This approach allowed us to gauge the model's performance when confronted with various unseen tumor categories, thereby assessing its capacity for generalization.
+
+The results are shown in Tab. 1. Compared with the competing SAM-based methods, DiffuGTS demonstrates a notable performance enhancement, achieving at least a  $12.84\%$  improvement in DSC and a  $13.22\%$  increase in NSD. Due to the lack of specific knowledge about unseen tumors and the fragility of prompts, most SAM-based methods fall short in zero-shot tumor segmentation. Additionally, in real-world scenarios, obtaining precise prompts—such as points or bounding boxes derived from ground truth—is extremely challenging, further limiting the applicability of SAM-based methods. DiffuGTS also outperforms zero-shot lesion segmentation methods ZePT [22] and Malenia [23] by a large margin of at least  $4.74\%$  in DSC. Although ZePT and Malenia align mask regions with textual descriptions and knowledge, relying solely on weak supervision from vision-language alignment signals is insufficient to accurately capture the boundaries of unseen tumors. In contrast, DiffuGTS builds upon similar vision-language alignment, while further leveraging the capabilities of the diffusion model to refine language-driven segmentation results, significantly improving performance.
+
+Moreover, DiffuGTS maintains a substantial lead, with a  $15.80\%$  improvement in DSC compared to medical anomaly detection methods DDPM-MAD [41],
+
+![](images/a0a2ea31703aacad7f1270b30b10c61696076e2e15f0a8daf87793ab944c8eec.jpg)  
+Figure 4. Qualitative visualizations of zero-shot segmentation results on MSD [3]. The results presented from rows one to three correspond, in order, to liver tumors, colon tumors, and pancreatic tumors. We present the visualizations on other datasets in the supplemental material.
+
+MVFA [20], and THOR[5]. These results indicate that the proposed AOVA maps, combined with the utilization of the foundational diffusion model, effectively and significantly improve the model's accuracy and generalizability in segmenting unseen tumors across diverse anatomical regions.
+
+Generalization to Unseen Image Modalities. In this setup, we used KiTS23 [18] and four CT tumor segmentation datasets from the MSD [3], including colon, pancreas, lung, and hepatic vessel tumors, to train the models and then tested them on three MRI datasets, including an in-house MRI liver tumor dataset, MSD-Brain [3], and BraTS23 [1]. This experimental setup defines a much more challenging scenario, where models must handle both unseen tumor types and imaging modalities. The results are shown in Tab. 2. DiffuGTS surpass the competing methods by at least  $21.28\%$  in DSC. Due to the significant differences between modalities, most competing methods suffer a considerable drop in performance. This is because even the visual features of the same anatomical structures can vary greatly across different modalities. As shown in row four of Fig. 1, our method generates high-quality pseudo-healthy brain images, where the tumor regions significantly differ from the original, leading to a substantial improvement in tumor segmentation performance. At the same time, the text-driven AOVA map accurately captures the potential tumor locations, benefiting from the internal representations of the frozen VAE encoder. These results further support our motivation, showing that effectively leveraging diverse anatomical knowledge from medical foundational diffusion models, and adapting them for zero-shot tumor segmentation through innovative designs, leads to significantly improved cross-modality generalizability and robustness.
+
+Computation Efficiency. As shown in Tab. 3, the number of trainable parameters in DiffuGTS is significantly smaller compared to traditional encoder-decoder-based methods, as it utilizes internal features from MAISI, eliminating the
+
+<table><tr><td>Method Efficiency</td><td>DiffuGTS</td><td>ZePT [22]</td><td>DDPM-MAD [41]</td><td>THOR [5]</td></tr><tr><td>Trainable Params</td><td>284.96M</td><td>745.94M</td><td>733.27M</td><td>783.42M</td></tr><tr><td>FLOPs</td><td>12876.48G</td><td>3886.95G</td><td>6895.53G</td><td>7143.30G</td></tr></table>
+
+Table 3. Computational cost comparison between DiffuGTS and some competing methods. The FLOPs is computed based on input with spatial size  $128 \times 128 \times 128$  on the same A100 GPU.
+
+need to train a large image encoder and decoder. However, using MAISI for feature extraction and generation results in higher computational costs in terms of FLOPs compared to other methods. This substantial computational overhead is a current limitation of foundational models. Efficient knowledge distillation algorithms present a promising solution, enabling the distillation and reuse of knowledge from foundational models while reducing computational costs. Nonetheless, this approach lies beyond the scope of this study and is reserved for future work.
+
+Qualitative Analysis. Fig. 4 shows the qualitative results (leave-one-out setting) and demonstrates the merits of DiffuGTS. Most competing methods suffer from segmentation incompleteness-related failures and misclassification of background regions as tumors (false positives). DiffuGTS generates results that are more consistent with the ground truth in comparison with all other competing models.
+
+# 4.2. Ablation Study and Discussions
+
+Ablation studies were conducted by training on the KiTS23 and four CT tumor datasets of MSD, including colon, pancreas, lung, and hepatic vessel tumors, followed by testing on the MSD liver and brain tumor datasets to evaluate generalization to unseen tumors and modalities.
+
+Significance of Leveraging Frozen Internal Representations of MAISI with Adapters. We examine the contribution of adapting the internal representations from MAISI's VAE encoder  $V_{E}$  for GTS. We experiment with three al
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">MSD Liver Tumor</td><td colspan="2">MSD Brain Tumor</td></tr><tr><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td></tr><tr><td>DiffuGTSScratch (nnUNet Encoder)</td><td>60.40</td><td>70.37</td><td>32.18</td><td>34.49</td></tr><tr><td>DiffuGTSw/oAdapter (MAISIVE)</td><td>60.89</td><td>70.75</td><td>33.92</td><td>35.90</td></tr><tr><td>DiffuGTSFine-tuning (MAISIVE)</td><td>61.18</td><td>71.59</td><td>34.76</td><td>36.65</td></tr><tr><td>DiffuGTSAdapter (MAISIVE)</td><td>63.23</td><td>73.58</td><td>47.51</td><td>49.75</td></tr></table>
+
+ternatives: (1) training with an nnUNet [21] image encoder from scratch, (2) directly using internal features from frozen  $V_{E}$  without adapters, and (3) fine-tuning  $V_{E}$  instead of adopting adapters. The results are reported in Tab. 4. All these alternatives lead to significant performance degradation. Training with nnUNet's image encoder from scratch misses out on the rich anatomical knowledge embedded in  $V_{E}$ . Directly using internal features from  $V_{E}$  without an adapter is also suboptimal, as these features are optimized for a generative task, creating a gap with the requirements of semantic segmentation. Fine-tuning  $V_{E}$  without adapters results in the network overfitting to seen categories, leading to the loss of the original knowledge gained from diffusion training. In contrast, our strategy employs an adapter that repurposes  $V_{E}$  for the GTS task while preserving its learned knowledge by keeping the parameters frozen.
+
+Why Does DiffuGTS Generalize Well? In Tab. 5, we examine the contribution of two key components of DiffuGTS. (1) Importance of AOVA maps. We replace the AOVA maps with a query-based Mask2Former [9] backbone, which is widely used in open-vocabulary [15, 27, 33] or zero-shot [13, 22, 23] segmentation methods. This leads to a significant performance drop of  $2.02\%$  in DSC and  $1.95\%$  in NSD for unseen liver tumor segmentation, as well as a drop of  $10.94\%$  in DSC and  $11.26\%$  in NSD for unseen brain tumor segmentation in MRI. Mask2Former updates its object queries based on the features of the training images. This additional parameter optimization leads to overfitting of the object queries to the seen categories, thereby degrading performance on unseen tumors. In contrast, our AOVA directly uses text embeddings to establish cross-modal correlations, thereby better leveraging the frozen VAE encoder's generalization capabilities. (2) Effectiveness of mask refinement (MR) with frozen MAISI. We demonstrate that utilizing the MAISI model for mask refinement  $(\mathrm{AOVA} + \mathrm{MR})$  significantly improves segmentation performance compared to relying solely on text-driven anomaly maps for mask predictions (AOVA only). This supports our motivation that employing frozen foundation diffusion models for mask refinement improves the quality of text-driven segmentation masks. Furthermore, removing the mask refinement process with diffusion models leads to a more pronounced performance decline than substituting AOVA with Mask2Former. This underscores the importance of using mask refinement to enhance the model's
+
+Table 4. Ablation study of leveraging frozen internal representations of MAISI with adapters. "w/o" denotes "without".  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">MSD Liver Tumor</td><td colspan="2">MSD Brain Tumor</td></tr><tr><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td></tr><tr><td>DiffuGTS (Mask2Former [9] + MR)</td><td>61.21</td><td>71.63</td><td>36.57</td><td>38.49</td></tr><tr><td>DiffuGTS (AOVA only)</td><td>59.94</td><td>70.11</td><td>20.14</td><td>22.90</td></tr><tr><td>DiffuGTS (AOVA + MR)</td><td>63.23</td><td>73.58</td><td>47.51</td><td>49.75</td></tr></table>
+
+Table 5. Ablation study of the proposed AOVA maps and mask refinement process with diffusion models.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">MSD Liver Tumor</td><td colspan="2">MSD Brain Tumor</td></tr><tr><td>DSC↑</td><td>NSD↑</td><td>DSC↑</td><td>NSD↑</td></tr><tr><td>DiffuGTS (Pr)</td><td>61.85</td><td>71.82</td><td>38.79</td><td>40.66</td></tr><tr><td>DiffuGTS (Fr)</td><td>61.94</td><td>72.05</td><td>41.14</td><td>43.27</td></tr><tr><td>DiffuGTS (Pr + Fr)</td><td>63.23</td><td>73.58</td><td>47.51</td><td>49.75</td></tr></table>
+
+Table 6. Ablation study of the proposed pixel-level and feature-level residual learning.
+
+![](images/941c3bd9b59d3afe604bf2f5b6997337428b300507d99eca3a2f63e556e04cf9.jpg)  
+Figure 5. Visualization illustrating how utilizing pixel-level and feature-level residual learning improves performance.
+
+zero-shot generalization ability.
+
+Effectiveness of pixel-level and feature-level Residual Learning. In Tab. 6, we compare the effect of using pixel-level residual maps  $P_r$ , feature-level residual maps  $F_r$ , or a combination of both in calculating the final segmentation results. It can be observed that combining pixel-level and feature-level residual maps leads to a better segmentation performance. Fig. 5 provides a visual comparison, illustrating the enhancement achieved by incorporating feature-level residual learning over relying solely on pixel-level residuals like previous methods [5, 41].
+
+# 5. Conclusions
+
+In this work, we unlock advanced generalizable tumor segmentation from frozen medical foundation diffusion models by introducing a novel framework named DiffuGTS. DiffuGTS employs a series of carefully designed strategies to initially construct anomaly-aware open-vocabulary attention maps for tumor detection. It then utilizes a frozen medical foundational diffusion model for further anomaly mask refinement, demonstrating superior zero-shot tumor segmentation capabilities across various anatomical regions and imaging modalities. We hope our method provides insights into efficiently leveraging foundation diffusion models for zero-shot tumor segmentation tasks.
+
+# Acknowledgments
+
+This work is funded by the National Key R&D Program of China under grants No.2022ZD0160700 and is supported by Shanghai Artificial Intelligence Laboratory.
+
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+# Advancing Manga Analysis: Comprehensive Segmentation Annotations for the Manga109 Dataset
+
+Minshan Xie $^{1}$ , Jian Lin $^{2}$ , Hanyuan Liu, Chengze Li $^{2}$ , Tien-Tsin Wong $^{3}$
+
+<sup>1</sup>Centre for Perceptual and Interactive Intelligence (CPII), Hong Kong SAR
+
+$^{2}$ Saint Francis University, Hong Kong SAR  $^{3}$ Monash University, Australia
+
+msxie92@gmail.com, {jlin,czli}@sfu.edu.hk, drhanyuanliu@gmail.com, TT.Wong@monash.edu
+
+# Abstract
+
+Manga, a popular form of multimodal artwork, has traditionally been overlooked in deep learning advancements due to the absence of a robust dataset and comprehensive annotation. Manga segmentation is the key to the digital migration of manga. There exists a significant domain gap between the manga and the natural images, that fails most existing learning-based methods. To address this gap, we introduce an augmented segmentation annotation for the Manga109 dataset, a collection of 109 manga volumes, that offers intricate artworks in a rich variety of styles. We introduce a detailed annotation that extends beyond the original simple bounding boxes to the segmentation masks with pixel-level precision. It provides object category, location, and instance information that can be used for semantic segmentation and instance segmentation. We also provide a comprehensive analysis of our annotation dataset from various aspects. We further measure the improvement of the state-of-the-art segmentation model after training it with our augmented dataset. The benefits of this augmented dataset are profound, with the potential to significantly enhance manga analysis algorithms and catalyze the novel development in digital art processing and cultural analytics. This annotation, named MangaSeg, is publicly available at https://huggingface.co/datasets/MS92/MangaSegmentation.
+
+# 1. Introduction
+
+Comic is a popular form of visual storytelling that delights readers with its unique blend of art and narrative. There are roughly two typical types of comics: Japanese-style manga, mainly produced in black-and-white (B/W), and color comics, produced in color. Current AI research in image analysis and synthesis usually regards comics as one kind of image. However, there exists a significant domain gap between comic and natural photographs, especially for B/W manga. Due to the lack of color, manga artists utilize
+
+screentone (pattern) to distinguish and/or represent regions/ textures/emotions. Such screentones do not exist in natural photographs and introduce the domain gap.
+
+To cope with comic-specific tasks, there exist color illustration/comic datasets, such as DanbooRegion [56], COMICS [18] and BCBld [9], to allow fine-tuning of models originally trained on natural images [43], for successful color comic adaptation. However, they are less successful in B/W manga due to the large domain gap. The most well-known and popular large-scale B/W manga dataset available is Manga109 [11]. Unfortunately, the original annotation of Manga109 is limited to bounding boxes (Figure 1(a)). They are not detail enough for effective fine-tuning the natural-photo-trained models on fine-grained recognition, because the screentone often confuses the models.
+
+To better understand the region semantics and high-level elements of B/W manga, a more accurate segmentation is crucial to enable a deeper understanding of the visual and textual elements in a manga. This requires the segmentation of a manga page into meaningful regions, including individual manga panels, characters, faces, speech balloons, texts, and links between characters and balloons. In this paper, we introduce our annotation-augmented Manga109 dataset, named MangaSeg. Our major contribution includes meticulously creating over 700,000 segmentation annotations for 10,130 double-sided manga pages, and their meticulous categorization into frames (or panels), balloons, texts, character faces, and character bodies. Such annotations enable the full potential of machine learning in analyzing B/W manga for various applications. Figures 1(b)-(d) provide a glimpse of the pages from the Manga109 dataset and our augmented annotations.
+
+It seems that the bounding boxes from the original Manga109 dataset can be used as the starting point for obtaining accurate segmentation. But they are too rough to be useful. For instance, the body bounding box, may not enclose the whole body, but enclose the irrelevant background. Instead, to obtain the precise segmentation, we start with the original manga pages without any annotation, and then
+
+![](images/192a331d160cb83734e532b89d0a6e4c7a4ca5808237f444d5d84c9b99794297.jpg)  
+(a) Bounding box annotations  
+Figure 1. Sample page from Manga109. Frames (panels), balloons, texts, character faces, and bodies are annotated with their segmentation masks. Note that the masks are annotated at the instance-level. YumeiroCooking ©Kurita Riku, from the Manga109 dataset. [1, 11]
+
+![](images/0dc8d96094a0dec1b17e4119ae1a4b50e5523313e7d6ae885e1b45af36ddb9a3.jpg)
+
+![](images/97a106e040338de619891d37d9be5684ccc4c8ac5191a1cefba1c4ac5d5f11dc.jpg)  
+(b) Segmentation frames (panels)
+
+![](images/9255bd557447453fa1e46fca4f28a95c544a46471faeef538c0dc8ff8c58ca4e.jpg)  
+annotation with  
+with(c) Segmentation loons and texts
+
+![](images/35b02d07c51cdcf83bb3c1414ed1cf4f17ea51cb05a12fe9409739ce3489710d.jpg)
+
+![](images/9e0fceeb470fcd0c95f0561442e81dae9f27de8f9c38f5bed684d3719b36d685.jpg)  
+notation with bal+
+
+![](images/1fcab4863937c03770065038f5b388ae791fd16ac906959bd60f2a091354dd8c.jpg)  
+(d) Segmentation atacter faces and body
+
+![](images/777a437acb44b1e3c63cd04b5e5303aa41628781b00a5130fa47f4af093c2661.jpg)
+
+we perform multiple state-of-the-art identification methods tailored for panels [33], text [8], balloon [29], character bodies [25], and character faces [21, 43, 58], to obtain the initial annotations. These annotations are then manually corrected, before being used to fine-tune the Segment Anything Model (SAM) [21] with low-rank adaptation (LoRA) [16]. The finetuned LoRA-SAM can generate the first-round annotation, which may still contain errors and require manual correction for the next round of fine-tuning of LoRA-SAM. This correction-finetuning process is repeated several times to obtain our final augmented annotation with accurate boundaries.
+
+With the proposed annotation, we design a new benchmark that includes existing popular segmentation methods. The results demonstrate that with our detailed segmentation annotation, current state-of-the-art models can achieve much better performance. The genre-rich Manga109 imagery coupled with our fine-grained annotation forms an invaluable asset for machine learning endeavors and empirical evaluations of various manga applications, including manga translation [22, 53], manga content indexing [24, 32], adaptation to devices with various display resolutions or aspect ratios (smartphones, tablet, laptops, etc.) [55], and even automatic manga generation [37, 52, 60]. Our contribution can be summarized as follows:
+
+- We meticulously create augmented segmentation annotation for the Manga109 dataset, a large-scale and diverse manga dataset, containing 109 volumes of manga. To the best of our knowledge, it is the first large-scale segmentation annotation dataset with such accuracy.  
+- We benchmark current baseline methods on this newly constructed dataset, revealing the limitation of existing state-of-the-art segmentation models when applied to black-and-white (B/W) manga images.
+
+# 2. Related Work
+
+# 2.1. Manga/Comic Datasets
+
+Due to copyright issues and the costs associated with manual labeling, the availability of manga/comic datasets suitable for
+
+academic research is quite limited. Table 1 summarises the characteristics of our dataset compared to previous efforts. Among various datasets proposed over years, many no longer exist [17, 31, 51], and many others are not available [7, 15, 20, 35].
+
+The eBDtheque [12] and DCM772 [32] datasets provide detection annotations for panels, characters, text lines, and some occurrences of characters' faces. The COMICS [18] dataset was constructed using a collection of 3,948 comic books, with images scraped from the Digital Comic Museum<sup>1</sup>. The BCBId [9] dataset comprises 3,327 images from 64 Bangla comics. Another recent dataset, PopManga [44], includes 57,318 images from 100 of the most popular manga of all time. However, the full dataset is not publicly available; only a small test set of 1,925 images, collected from Manga Plus by Shueisha<sup>2</sup>, has been released. Lastly, the well-known Manga109 dataset [11] is a publicly available comprehensive collection of manga images, consisting of 109 manga volumes drawn by professional manga artists in Japan.
+
+These datasets include bounding box annotations for frames/panels, text regions, character faces, character bodies, and balloons. These annotations are crucial for tasks like character recognition, text detection, and panel segmentation, thus enabling detailed analysis and understanding of manga images. Some datasets also explore links between text and characters for dialogue transcription [24, 44, 45], enriching the annotation scope from object detection and character re-identification to onomatopoeia detection and speaker identification. These annotations are essential for tasks like dialogue understanding and character identification, thus facilitating the comprehensive comic analysis.
+
+CoMix [50] is a benchmark for evaluating various tasks in comic analysis. It contains 3.8k images gathered from 100 books, annotated with 130K objects across 4 classes (i.e., panels, characters, face, texts), 30K text-character links, and 33K character clusters with 16K identified names. The dataset is compiled from several sources, including
+
+Table 1. Public available Manga/Comic dataset annotations  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Style</td><td rowspan="2">#volume</td><td rowspan="2">#page</td><td colspan="7">Annotations</td></tr><tr><td>Type</td><td>Source</td><td>#frame</td><td>#text</td><td>#face</td><td>#body</td><td>#balloon</td></tr><tr><td>eBDthefeque [12]</td><td>Mix</td><td>25</td><td>100</td><td>Bounding Box</td><td>Human</td><td>850</td><td>—</td><td>—</td><td>1,620</td><td>\( 1,081^{a)} \)</td></tr><tr><td>COMICS [18, 47]</td><td>Comics</td><td>3,948</td><td>198,657</td><td>Bounding Box</td><td>Pesudo\( ^b) \)</td><td>1,229,664</td><td>2,498,657</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Comic3w [14]</td><td>Mix</td><td>103</td><td>29,485</td><td>Segmentation</td><td>Human</td><td>169,421</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>DCM772 [32]</td><td>Comics</td><td>27</td><td>772</td><td>Bounding Box</td><td>Human</td><td>4,500</td><td>\( 7,972^{d)} \)</td><td>5,469</td><td>10,902</td><td>6,415</td></tr><tr><td>BCBId [9]</td><td>Bangla</td><td>64</td><td>3,327</td><td>Bounding Box</td><td>Human</td><td>21,000</td><td>35,000</td><td>—</td><td>29,000</td><td>19,000</td></tr><tr><td>PopManga(Dev) [44]</td><td>Manga</td><td>100</td><td>55,393</td><td>Bounding Box</td><td>Mix</td><td>\( 264,067^{b)} \)</td><td>459,615</td><td>—</td><td>487,367</td><td>—</td></tr><tr><td>PopManga(Test) [44]</td><td>Manga</td><td>25</td><td>1,925</td><td>Bounding Box</td><td>Human</td><td>—</td><td>20,843</td><td>—</td><td>18,778</td><td>—</td></tr><tr><td>Manga109 [1, 3]</td><td>Manga</td><td>109</td><td>\( 10,130^{c)} \)</td><td>Bounding Box</td><td>Human</td><td>103,900</td><td>\( 209,383^{e)} \)</td><td>118,715</td><td>157,152</td><td>—</td></tr><tr><td>MangaSeg (Ours)</td><td>Manga</td><td>109</td><td>\( 10,130^{c)} \)</td><td>Segmentation</td><td>Human</td><td>103,900</td><td>209,383</td><td>118,715</td><td>157,152</td><td>130,180</td></tr></table>
+
+${}^{a)}$  Segmentation annotation.  ${}^{b)}$  Pseudo-annotation (automatically annotated).  ${}^{c)}$  Double-sided pages.  
+$d$  ) The annotations for text have two types, narrative boxes and balloons. (narrative boxes: 1,557, balloons: 6,415)  
+e) The annotations for text have two types, text/dialog labeled in bounding boxes and onomatopoeia in polygon shapes. (Text/Dialog: 147,918, onomatopoeia: 61,465)
+
+DCM Comics[32], eBDthquee [12], PopManga [44], and Manga109 [11]. It supports multi-task evaluation, including object detection, speaker identification, character re-identification, reading order, and multi-modal reasoning tasks such as character naming and dialogue generation.
+
+Among the datasets mentioned, Manga109 stands out as the only one offering a substantial number of publicly available black-and-white manga images. In contrast, other datasets primarily feature color comics or have limited quantities. Furthermore, the bounding box annotations in Manga109 adhere to the metadata framework for manga [30], which classifies manga objects into three categories: visual objects (characters, items, scene texts), dialog (speech, thought, narration, monologue), and symbols (lines, onomatopoeia, marks). Consequently, we chose Manga109 as the ideal dataset for developing augmented segmentation annotations and advancing manga analysis.
+
+# 2.2. Segmentation for Manga Understanding
+
+With the advancement of deep learning techniques, neural networks are increasingly used to process black-and-white manga images [23, 26, 53, 54, 57]. Among these tasks, segmenting individual manga components often serves as a crucial input for subsequent manga-related tasks. Identifying and isolating different panels and characters within a manga page facilitates manga generation [52]. Segmenting text and speech balloons simplifies manga translation and editing [27, 29]. For manga colorization, segmentation allows the precise application of colors to specific regions, such as characters, backgrounds, and objects [36, 52]. Additionally, segmentation enables automated editing tasks like resizing, repositioning, and enhancing specific elements within a manga page [49, 55]. However, these segmentation inputs are usually manually annotated, posing challenges for automated manga production and processing large volumes
+
+of manga images.
+
+Recently, Segment Anything Model (SAM) [21, 39] has demonstrated superior performance on various segmentation tasks. However, it is tailored for extracting texture features in natural images and often fails when applied to screened manga. Additionally, there are limited datasets with segmentation annotations, except for frame annotations from [14] and balloon annotations from [12]. To enhance manga analysis through segmentation, we propose developing a segmentation dataset specifically for manga images, providing valuable training data for machine learning models.
+
+# 3. Dataset Construction and Segmentation Annotation
+
+# 3.1. Metadata Framework
+
+The original Manga109 dataset [1] defines four categories of annotations (Text, Frames, Character faces, and Character bodies). Onomatopoeia annotation is recently added [3]. Figure 3 explains the meaning of each category. Note that all these original annotations are in the form of bounding boxes. Similarly, our augmented segmentation annotations for Manga109 follow the existing metadata framework, but our annotations are presented in the form of segmentation mask with pixel-level precision (Figures 1(b)-(d) & 3). In addition to the original five original categories, we introduce one more essential category: balloon, which plays a crucial role in various modern manga applications, including manga inpainting and motion manga [53].
+
+Frame: A frame/panel serves as a visual container (or a window) within a comic page, encapsulating a specific scene or moment. Typically, a comic page comprises multiple panels, each containing visual elements such as characters, backgrounds, and text. The reader follows the implicit ordering of panels to understand the narration. While rectangular panels
+
+![](images/a39931dbc62d5eeea5f99342c85ddf7000ea69e421665dc6fa8bc9b30bdf1ae4.jpg)  
+Figure 2. Overview diagram of our annotation pipeline. We first collected coarse segmentation annotations through existing methods and then refined them through iterative annotations with manual correction and automatic refinement. YukiNoFuruMachi ©Yamada Uduki, YamatoNoHane ©Saki Kaori, UltraEleven ©Yabuno Tenya, Watanabe Tatsuya [11]
+
+![](images/24037a745e8d049184eef3a3ac0bac8e3aa4592b362808a6f177849621fec006.jpg)  
+Figure 3. In our annotation, we define six object categories: frame, text/dialog, onomatopoeia, character body, character face, and balloon. For better visualization, we highlight their boundaries in the figure. AppareKappore ©Kanno Hirosh. The manga image is from the Manga109 dataset [1, 11].
+
+are common, they can also be in irregular shapes. Although various panel detection methods exist [33, 40, 41, 44, 45], most of them did not perform well on extracting panels with irregular shapes [14].
+
+Text: Text plays a pivotal role in comics, conveying character dialogue, monologues, and narrative information. Most text appears within bounded white regions called speech balloons, overlaid on characters or backgrounds. Additionally, some text is directly embedded into the picture without being enclosed by the balloon to indicate the sound and/or importance. This text is referred to as onomatopoeia [3]. Therefore, text can be further categorized into dialog and onomatopoeia. Previous research has explored methods for detecting and segmenting text regions in comics [2, 38, 40, 44, 45].
+
+Face and body: The faces and bodies of characters consti
+
+tute the essential visual components in comics. A face region includes the eyebrows, cheeks, and chin, while a body region encompasses body parts such as the head, hair, main body, and limbs. Some comics use animals, such as dogs and cats, as main characters, and we treat them similarly to human characters in terms of annotation. Previous researchers have explored face or body detection [44, 45, 48]. Some attempts have been made for character instance segmentation for color illustration [35, 46], but they did not perform well on B/W manga due to the domain gap of the training data.
+
+Balloon: Speech balloons, also known as dialogue bubbles, play a crucial role in conveying the thinking, conversation, and emotion of the characters. These bounded white regions may overlay characters or backgrounds within panels. Detecting and positioning these speech balloons accurately is essential for creating engaging manga panels. Moreover, their existence also impacts the digital reproduction of manga applications, such as motion manga. Balloon detection and extraction have been explored in previous works [4, 24, 29, 42].
+
+# 3.2. Building Segmentation Annotation
+
+Considering the high cost of manual labeling, we propose a semi-automatic workflow for constructing our MangaSeg annotation, as illustrated in Figure 2. This workflow consists of two stages: coarse annotation collection and iterative annotation refinement.
+
+# 3.2.1 Coarse Annotation Collection Stage
+
+Initially, images are automatically annotated using multiple existing methods tailored for each category of content to obtain the coarse labels. Note that our segmentation annotation is instance-level, i.e., labeling each object individually. We utilize state-of-the-art segmentation methods tailored for
+
+![](images/b436d7ce1ea5321e7aeb9d2576e57f106cf6ab0e5efa7bf8b8d39c59fe1af969.jpg)  
+(a) Input manga
+
+![](images/105b49b7b43156d928c14c01c2172ff3e360d3a349f1a9e1f56ffeb4cbf6a491.jpg)
+
+![](images/d26505bef64774788ed13104aef51fbef4d1ae52effb2e43ff497360272002b6.jpg)
+
+![](images/22d57f9fc0c7766bd8db7413e75e467b8fb1608549cc1170991fb374562b3c66.jpg)  
+(b) Structural line [23]  
+(d) GroundedSAM [39] on (a)
+
+![](images/78e4b19cb9b756ae567b602aa32f2c7fd7dc0a8f4574abae67eaddc2f6d5e716.jpg)  
+(e) Colorized [58] using (b) and (c)  
+(f) GroundedSAM [39] on (e)  
+Figure 4. We facilitate the segmentation of facial regions by first coloring body regions using ControlNet [58] with structural line as guidance [23]. YamatoNoHane ©Saki Kaori. The manga image is from the Manga109 dataset. [1, 11]
+
+![](images/099f40f7325701eb00abdd4607c5994e912228eda8e0269200b99d2925c227dd.jpg)  
+(c) Our instance mask
+
+panels [33], balloons [29], character bodies [25], to obtain the initial annotations. Specifically, the text annotation is achieved by assigning the text mask extracted by [8] to the corresponding instance labels in the bounding box annotations [1] of dialog and polygonal shape annotations [3] of onomatopoeia (as shown in Figure 3).
+
+Face Segmentation via Colorization. For character faces, existing methods perform poorly on black-and-white (B/W) manga images. These methods are primarily designed to understand patterns from color images, whereas manga character faces are presented in B/W with an exaggerated style that significantly differs from natural photographs. To address this challenge, we propose an innovative approach. We leverage recent stable diffusion models [43, 58] to initially colorize the B/W manga images. The accuracy of the colorization is not crucial in this context. Subsequently, we input these colorized manga images into GroundedSAM [39] with a text prompt "human face" to effectively extract the faces (Figure 4). To prevent the generation of unintended content in non-facial areas of the B/W images, we colorize only the previously extracted character body regions.
+
+# 3.2.2 Iterative Annotation Refinement Stage
+
+After obtaining the coarse annotations, we further perform a refinement stage, which involves iterative process involving manual correction and SAM fine-tuning. Human-in-the-loop annotation was performed to refine the coarse annotations and create the refined annotations, which are used to fine-tune the SAM model. Additional human-in-the-loop annotation was conducted to verify the coarse annotations. In total, 10 annotators were involved, and the entire dataset collection and annotation process took 6 months.
+
+Phase 1: Manual Annotation Correction. In this phase, the collected segmentation masks are used to assist the human annotation. Annotators are asked to annotate the mask of each target object in every manga image using precise
+
+pixel-level editing tools, such as "brush" and "eraser." Due to the low quality of most collected segmentation masks (as shown in Table 2), the process is slow, with most images requiring mask annotation from scratch. Therefore, we first used the original bounding box annotations from the Manga109 dataset to evaluate the coarse segmentation results and then annotated from the manga volume with higher accuracy. Additionally, to mitigate the potential bias of individual annotators, we employed multiple human annotators.
+
+Phase 2: Finetuned SAM Annotation. Initially, human annotators manually corrected coarse annotations to create the initial set of annotations across several volumes. These initial annotations were then used to fine-tune a representative segmentation model (such as LoRA-SAM [25, 59]). The fine-tuned SAM model automatically pre-labeled the remaining unlabeled images, albeit coarsely. These pre-labeled annotations in Phase 2 are further corrected by human annotators in Phase 1. The entire correction-finetuning process iterates in a human-in-the-loop manner until it converges on well-labeled annotations.
+
+Quality Control. To maintain a high standard of annotation quality, we introduce a verification step. We use the bounding box annotation of Manga109 to verify the quality of our annotated masks as "satisfactory" (IoU  $> = 0.9$ ) or "unsatisfactory" (IoU  $< 0.9$ ). Unsatisfactory masks are sent back to the iterative annotation pipeline for refinement.
+
+# 4. Experiments
+
+In this section, we evaluate the performance improvements of various existing methods when trained with our augmented annotation. First, we introduce the experimental settings, including the selected baseline methods and implementation details. Then, experiments are carefully designed to report the performance from multiple perspectives, with various baseline methods and datasets.
+
+# 4.1. Experimental Settings
+
+Representative Baselines. We use state-of-the-art segmentors for each type of manga component as baseline methods.  
+- Frame: For frame/panel segmentation, we compare with [33], which identifies panel/frame blocks by recursively splitting the panel block into sub-blocks and fitting the boundaries with splitting lines.  
+- Balloon: We compare with Liu et al. [29] which extracts text balloons by identifying closed white areas containing text.  
+- Text: We compare with [19] which employs YOLOv5 to detect and segment each text region in manga using Manga109 bounding-box annotations and a manga dataset with pixel-level text annotations created by [8].  
+- Character body: We compare with an instance-aware image segmentation model [25] that generates segmenta
+
+tion masks for characters in cartoon images and manga. They achieve this by introducing a dataset of paired images along with their instance labeling masks.
+
+- Character faces: There is no tailored method for extracting the character faces in manga images.
+
+The above frame and balloon baseline methods are not learning-based. Currently, there are no deep-learning-based models specifically designed to segment manga frames, balloons, and character faces, primarily because of the scarcity of available datasets and annotations.
+
+Grounded SAM. To be comprehensive, we additionally compare our method with the state-of-the-art image segmentation technique known as Grounded Segment Anything (GroundedSAM) [39]. Given a text prompt (e.g., "panel," "balloon," and "text"), the model returns bounding boxes and segmentation masks corresponding to that prompt.
+
+SOTA Detector with SAM. Considering that GroundingDINO [28] applied in GroundedSAM may not effectively detect the desired objects in manga images when using text prompts, we also compare our approach with baselines that integrate state-of-the-art manga detectors with the Segment Anything Model (SAM) [21]. Specifically, we compare our method with two approaches: DASSDet [48], which detects character faces and character bodies, and Magi [44], which detects frames/panels, text lines, and character bodies.
+
+Finetuned SAM. To demonstrate the effectiveness of our augmented segmentation annotations, we achieve precise component segmentation by fine-tuning a representative model. We extend the original Segment Anything Model (SAM) [21] to detect manga components at the instance level. This extension involves fine-tuning the SAM mask decoder model with additional instance tokens, which includes finetuning the image encoder as well [25]. This dataset is split into three subsets: 80-10-10 for training, validation, and test sets, respectively. We split the dataset based on volumes to avoid similar images in three sets. In this work, we use the Pytorch toolkit [34] to conduct all experiments on four nVidia GeForce RTX 3090 GPUs with a batch size of 8.
+
+# 4.2. Evaluation Metrics
+
+In our study, we leverage three classical segmentation metrics for evaluation: Box AP [10], Mask AP [13], and Boundary AP [6].
+
+- Bounding Box Average Precision (BAP) computes the precision of the predicted bounding boxes against their corresponding ground truths. It assesses how accurately the model localizes objects.  
+- Instance Mask Average Precision (MAP) measures the precision of the instance masks. It evaluates how well the model captures the shape and boundaries of individual instances.  
+- Boundary Average Precision (BdAP) focuses on the
+
+precision over the boundary area of the instance. This metric focuses on the quality of segmentation near object contours.
+
+For text and onomatopoeia segmentation, which often feature thin and irregular shapes, achieving high mask AP and Boundary AP scores can be challenging due to the difficulties in accurately segmenting these thin regions. In contrast, segmentation of other components with regular shapes generally yields higher AP scores across all metrics, as these shapes are easier to fit accurately around the objects.
+
+# 4.3. Benchmark results
+
+We conducted multiple evaluations with all analyses conducted on a separately prepared test dataset. This dataset comprises 927 manga samples with diversity in visual content and style. All of them have been manually labeled for ground-truth segmentation. The models were not exposed to any samples from this test set during training. The mean Average Precision (mAP@0.5) scores for each segmentor are reported in Table 2. Figure 5 shows segmentation results generated by different methods.
+
+In terms of frame/panel and balloon extraction, our model performs better than two handcrafted methods, [33] and [29], and shows a  $50\%$  and  $25\%$  AP improvement, respectively (Table 2). Additionally, our trained model generates results more effectively and achieves real-time performance. In terms of text extraction [19], which was trained on datasets with paired manga images and their corresponding labeling masks, performs better than GroundedSAM [39] (Table 2). This demonstrates the importance of segmentation annotation in the dataset. Note that [19] extracts manga text using UNet architecture while SAM decodes the mask using a decoder with an upsampling factor of 8. Thus, [19] shows higher performance on precise localization, resulting in higher mask AP and boundary AP. However, the skip connection of UNet may also introduce more noise, leading to lower box AP than finetuned SAM. For character body, [25] trained a segmentor using synthetic paired segmentation of color illustrations, and adapted it to manga by employing a bounding box loss for Manga109 [11]. As they trained on the entire Manga109 dataset, they achieved higher scores on the test set. For onomatopoeia, our model shows a low AP score, even though it is still the best among all competitors. This may be due to the scarcity of onomatopoeia in manga images, resulting in many false positives in our results. Further improvement in onomatopoeia segmentation could be achieved by collaborating with additional heuristic designs.
+
+The result also demonstrates that the model fine-tuned with our augmented dataset significantly enhances the performance of the original model [21]. It achieves over  $60\%$  average precision (AP) for all manga components compared to GroundedSAM [39]. By employing dedicated object detectors [44, 48], more precise segmentation results for
+
+Table 2. Segmentation using existing methods and our finetuned SAM on the test set. For SOTA detectors + SAM (DASSDet+SAM and Magi+SAM), we list two BAP scores, one for detected bounding box by the SOTA detector, and the other for segmentation results by SOTA detector + SAM.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Frame/Panel</td><td colspan="3">Balloon</td><td colspan="3">Text/Dialog</td><td colspan="3">Onomatopoeia</td><td colspan="3">Body</td><td colspan="3">Face</td></tr><tr><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td><td>BAP↑</td><td>MAP↑</td><td>BdAP↑</td></tr><tr><td>[33]</td><td>0.424</td><td>0.413</td><td>0.324</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>[29]</td><td>—</td><td>—</td><td>—</td><td>0.683</td><td>0.688</td><td>0.686</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>[19]</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.574</td><td>0.754</td><td>0.754</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>[25]</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.948</td><td>0.923</td><td>0.910</td><td>—</td><td>—</td><td>—</td></tr><tr><td>DASSDet[48]+SAM[21]</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.865/0.804</td><td>0.792</td><td>0.752</td><td>0.887/0.820</td><td>0.824</td><td>0.798</td></tr><tr><td>Magi[44]+SAM[21]</td><td>0.709/0.664</td><td>0.634</td><td>0.382</td><td>—</td><td>—</td><td>—</td><td>0.333/0.247</td><td>0.025</td><td>0.025</td><td>—</td><td>—</td><td>—</td><td>0.835/0.729</td><td>0.719</td><td>0.681</td><td>—</td><td>—</td><td>—</td></tr><tr><td>GroundedSAM [39]</td><td>0.354</td><td>0.326</td><td>0.235</td><td>0.158</td><td>0.171</td><td>0.161</td><td>0.077</td><td>0.008</td><td>0.008</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.283</td><td>0.269</td><td>0.237</td><td>0.326</td><td>0.324</td><td>0.304</td></tr><tr><td>Ours</td><td>0.954</td><td>0.977</td><td>0.955</td><td>0.914</td><td>0.956</td><td>0.954</td><td>0.645</td><td>0.688</td><td>0.688</td><td>0.373</td><td>0.272</td><td>0.272</td><td>0.860</td><td>0.884</td><td>0.869</td><td>0.781</td><td>0.852</td><td>0.839</td></tr></table>
+
+![](images/7d61ac54ab8607e3907c836eaa09b432462e036a64a30a7aee2545f1b7a808f1.jpg)  
+Figure 5. Segmentation using existing methods. From the top to bottom rows, our targets to segment are frame, balloon, text, body, and face. (a) shows baselines for different categories [8, 25, 29, 33]. YukiNoFuruMachi ©Yamada Uduki, YamatoNoHane ©Saki Kaori, UltraEleven ©Yabuno Tenya, Watanabe Tatsuya [11]
+
+some components (e.g. frame, body, face) can be generated. However, segmentation may be disturbed by screentones or irrelevant components, as shown in Figures 5(b) and (c). The distinctive features of manga in our augmented dataset improve the ability of the model to handle the exaggerated drawing styles and the B/W screentone-filled characteristics of manga more effectively. More qualitative results are included in supplementary materials.
+
+# 4.4. Potential Usages
+
+The augmented annotations might improve downstream tasks beyond segmentation. With the precise segmentation mask
+
+(or the silhouette) for each character, it is now possible to automatically identify the pose of each character, as shown in Figure 6. This is not feasible with the original bounding box annotation. We will include annotations for poses in the future following our proposed annotation pipeline. The pose estimation can help to improve the semantic understanding of the current action of each character in each panel. Besides, the segmentation of the character head and orientation also helps the estimation of facial expression (thanks to the precise boundary silhouette, it is possible now to identify the head orientation). Moreover, the content of manga images can be understood by providing additional hints about each
+
+![](images/9c7209a2853557067673b37aff21c3f4d11dfbf0a9bec7ecfbae98e4acb813ed.jpg)  
+Figure 6. Our pipeline can also facilitate other applications, such as manga pose extraction. ShimatteIkouze ©Yoshimori Mikio. The manga image is from the Manga109 dataset. [1, 11]
+
+structural component and the spatial relationship. Manga colorization can also be achieved with the color prior from corresponding components of the color comic (Figure 6(d)).
+
+Beyond its immediate benefits, our annotation opens up other groundbreaking possibilities for the research community. By collaborating with the detailed content annotations in Manga109 [1], e.g. character identification, we can explore additional use cases, like instance-level manga colorization. The impact of manga instance segmentation extends beyond creators and editors. It enriches the overall manga reading experience by enabling dynamic adaptations and interactive features. We enthusiastically invite contributions from the community to further explore the potential applications of our segmentation annotation.
+
+# 5. Limitations and Discussions
+
+There are still limitations in our current work regarding segmentation annotations in manga. Although we provide pixel-level annotation for various manga elements, some ambiguity remains in these annotations. Manga artists sometimes overlap multiple contents together (the three frames on the top-left corner in Figure 7(b)), leading to confusion even among human annotators. Speech balloons, in some cases, may exceed and occlude the boundary of panel boundaries. Currently, we ignore this occlusion and label the panel with a polygonal shape. In other cases, no explicit boundary exists for the panel. For other elements, we provide accurate pixel-level annotation as much as possible. Balancing the need for precise segmentation with the presence of occlusion remains an open problem. Moreover, we found difficulties in labeling the detail boundaries for character faces, especially on the region around hair (Figure 4 (d)). Hair strands, intricate hairstyles, and variations in shading make accurate pixel-level annotation challenging. Nevertheless, we believe our publicly available annotation can motivate further refinement in these areas. Besides, artists usually use different types of balloons to enclose various types of dialogue (such
+
+![](images/8a1dbb0b9c9325ddf4611c5beb6da3d20bdbcc14c2206323590e370c4d524226.jpg)  
+(a) Input manga
+
+![](images/1843f50313ffb8a4cf8abe6c058b85ef9df8296ae56321a639a74ca1442a7f65.jpg)  
+(b) Frame
+
+![](images/8181606a9d756b0c2fbd212ca57e4859082039f61768380021963719db1baa69.jpg)  
+(c) Balloon  
+Figure 7. Ambiguities in segmentation. (b) Manga artists may use frames without explicit boundaries or sometimes the frame boundaries are behind the exaggerated balloon. (c) Speech balloons typically have a closed shape, while some balloons may have open or irregular boundaries. YukiNoFuruMachi ©Yamada. The manga image is from the Manga109 dataset. [1, 11]
+
+as speech and thought). Speech balloons typically have a closed shape, while thought balloons may have irregular boundaries (as shown by the red balloon in Figure 7(c)). In our work, we annotate these balloons along their inner boundaries, which can benefit applications like automatic manga translation [22]. However, there are cases where we may need segmentation masks along the outer boundaries, such as in manga inpainting [53]. This aspect could be further improved with additional annotations.
+
+# 6. Conclusions
+
+Well-crafted image datasets have played critical roles in advancing image processing technologies. In this paper, we built an Augmented Segmentation Annotation on the Manga109 dataset, a dataset of a variety of 109 Japanese manga books. We also explain the annotation framework and annotation process to build our segmentation annotation with pixel-level precision. Furthermore, our preliminary experiments highlight the critical role played by our augmented segmentation annotations in instance segmentation of manga components. These annotations effectively bridge the gap for manga-related applications that necessitate the identification and precise segmentation of individual manga elements. We hope that our augmented segmentation annotation can contribute to and inspire the further development of manga research.
+
+# Acknowledgement
+
+We express our sincere gratitude to Aizawa Yamakata Matsui Lab and the authors involved in the development of the Manga109 dataset. The Manga109 dataset has been an invaluable resource for our work, enabling us to explore novel approaches and validate our findings.
+
+This research was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. UGC/FDS11/E02/23), and by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Fund (InnoHK).
+
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+# Advancing Multiple Instance Learning with Continual Learning for Whole Slide Imaging
+
+Xianrui Li
+
+Dept. of Computer Science City University of Hong Kong xianrui.li@my.cityu.edu.hk
+
+Yufei Cui
+
+Noah's Ark Lab, Huawei Canada Montreal, Quebec, Canada yufei.cui@huawei.com
+
+Jun Li
+
+Guangzhou Bingli Technology Co., Ltd. Guangzhou, Guangdong
+
+Antoni B. Chan
+
+Dept. of Computer Science City University of Hong Kong abchan@cityu.edu.hk
+
+# Abstract
+
+Advances in medical imaging and deep learning have propelled progress in whole slide image (WSI) analysis, with multiple instance learning (MIL) showing promise for efficient and accurate diagnostics. However, conventional MIL models often lack adaptability to evolving datasets, as they rely on static training that cannot incorporate new information without extensive retraining. Applying continual learning (CL) to MIL models is a possible solution, but often sees limited improvements. In this paper, we analyze CL in the context of attention MIL models and find that the model forgetting is mainly concentrated in the attention layers of the MIL model. Using the results of this analysis we propose two components for improving CL on MIL: Attention Knowledge Distillation (AKD) and the Pseudo-Bag Memory Pool (PMP). AKD mitigates catastrophic forgetting by focusing on retaining attention layer knowledge between learning sessions, while PMP reduces the memory footprint by selectively storing only the most informative patches, or "pseudo-bags" from WSIs. Experimental evaluations demonstrate that our method significantly improves both accuracy and memory efficiency on diverse WSI datasets, outperforming current state-of-the-art CL methods. This work provides a foundation for CL in large-scale, weakly annotated clinical datasets, paving the way for more adaptable and resilient diagnostic models.
+
+# 1. Introduction
+
+The advancement of AI technology has significantly transformed medical imaging, with notable progress in whole slide image (WSI) analysis [28]. In particular, develop
+
+ments in multiple instance learning (MIL) have enhanced the diagnostic accuracy and efficiency of deep learning models applied to WSIs [15, 29], substantially reducing diagnostic time and minimizing misdiagnosis rates. Despite these advancements, most MIL methodologies currently rely on a static framework [5, 8], wherein models are optimized using a fixed dataset. This static approach creates a critical limitation in terms of knowledge updating. As medical technology evolves rapidly, new data is continually generated [3, 4, 13], often with variations in imaging equipment, acquisition methods, and standardized settings. These factors alter the labels and distribution patterns of new datasets, making it essential for models to adapt to these changes [21]. Full retraining of models using both new and historical data, however, is resource-intensive and time-consuming. Consequently, continual learning (CL) [7, 24] emerges as an efficient solution to this challenge, enabling models to incrementally integrate new information and thereby maintain their diagnostic relevance without the prohibitive costs of full retraining. However, CL faces catastrophic forgetting [11], where models lose previously acquired knowledge when learning new information, addressed by regularization-based, architectural-based, and replay-based methods [22].
+
+Our research focuses on class-incremental learning (CIL), a specialized area within CL that holds particular promise for applications in medical imaging. As medical knowledge advances, disease annotations are becoming increasingly detailed, leading to a proliferation of diagnostic categories. This development creates a pressing need for models capable of continually incorporating new classes of medical information [5] while retaining previously acquired knowledge, i.e., class-incremental learning. Moreover, re
+
+search suggests that models trained across multiple medical domains often achieve superior performance compared to those restricted to single domains [6], underscoring the potential of multi-domain learning to enhance diagnostic accuracy and generalizability.
+
+Applying CL to WSI presents unique challenges due to the substantial data complexity and annotation demands associated with WSIs. Each WSI contains gigabytes of pixel data, making detailed annotations costly and time-consuming due to required expert input. Most WSIs only have slide-level labels without detailed annotations. To address this limitation, MIL has become a widely adopted strategy in WSI analysis. In the MIL paradigm, each WSI is conceptualized as a "bag" of smaller "patches" allowing models to be trained using high-level, whole-slide labels rather than exhaustive pixel- or patch-level annotations. In particular, attention MIL [9, 15, 20, 30] first uses an attention network to obtain an attention weight on each patch, with which a slide-level feature vector is calculated via the weight and the patch-level features. Finally, the slide-level feature serves as the input to a slide-level classifier.
+
+Recent advancements have begun to explore the integration CIL within the MIL framework, with encouraging results [5, 8]. Some studies have proposed new frameworks specifically designed for CIL in WSI, yet these often require substantially more parameters and show only moderate performance improvements in conventional settings. Other approaches attempt to adapt existing CIL techniques for use with MIL models, also yielding only limited enhancements. Through our investigation of MIL under CIL, we have identified a critical insight: the patterns of forgetting in attention MIL classification models under CIL differ significantly from those observed in traditional image classification models. Specifically, our theoretical analysis and model visualizations indicate that model forgetting in MIL is concentrated primarily in the attention network, rather than in other layers like the classifier (logit) layer.
+
+Based on our findings, we propose two effective and adaptable methods that improve the performance of traditional MIL models in CIL scenarios. The first method, attention knowledge distillation (AKD), addresses forgetting by imposing constraints on the attention layers during CL training. By using distillation techniques to transfer knowledge from previous models to the current one, AKD balances the retention of prior knowledge with the assimilation of new information. The second method, the pseudo-bag memory pool (PMP), mitigates the high memory demands of replaying WSI data by using a patch importance scoring technique to selectively sample critical patches, thereby substantially reducing memory requirements. Together, AKD and PMP provide a robust framework for enhancing MIL in CL settings, addressing both knowledge retention and memory efficiency while accommodating the specific
+
+challenges posed by WSIs.
+
+In summary, our work presents three major contributions to MIL and continual learning research:
+
+- To the best of our knowledge, this is the first attempt to theoretically and experimentally explore the fundamental reasons for the catastrophic forgetting of attention MIL in CIL. Compared to classical classification models where forgetting occurs mainly in the classification layer, we show that attention MIL experiences forgetting primarily in the attention layer.  
+- We have developed a specialized knowledge distillation strategy tailored for attention networks in MIL, which significantly enhances model performance during CL, empirically approaching the upper limit achievable through joint training.  
+- We introduce a novel pseudo-bag memory pool method, which effectively facilitates the implementation of replay-based approaches in MIL, offering a new direction for memory management in this context.
+
+# 2. Related Work
+
+# 2.1. Multiple Instance Learning (MIL)
+
+Many MIL models leverage bag representations to predict the slide label. For instance, ABMIL [9] generates a bag representation by calculating weighted patch features, enabling it to focus on the most informative patches within a slide. Building on this approach, CLAM [15] refines this with instance clustering for multi-category tasks. TransMIL [20] proposes a correlated MIL framework that integrates multi-head self-attention and spatial information to capture global correlations across the an image. Similarly, DTFD [29] employs a two-tier framework with ABMIL as the foundational module in each tier, aiming to capture hierarchical features across different levels of granularity.
+
+While these models demonstrate strong performance on static datasets, they generally do not account for scenarios involving non-stationary data. In dynamic environments where data distributions may shift over time, traditional MIL approaches such as CLAM [15] and TransMIL [20] are vulnerable to issues like catastrophic forgetting.
+
+# 2.2. Continual Learning (CL)
+
+CL methodologies in computer vision are generally categorized into three main approaches. The first, regularization-based methods, seek to address catastrophic forgetting by constraining the gradients of model parameters like EWC [11] and MAS [1]. However, these methods often produce suboptimal results in complex environments like realistic pathology data. The second category, model architecture-based methods, involves modifying network structures through strategies like compression and expansion to incorporate new knowledge without overwriting ex
+
+isting information. Approaches such as PNN [19] and Pack-Net [16] exemplify this technique, which, while theoretically robust for retaining prior knowledge, tends to suffer from scalability issues as an extension of the MIL model is not as simple as the classical classification model. Finally, replay-based methods utilize selective reintroduction of past data samples to reinforce memory, helping models to maintain prior knowledge during the training of new tasks, like DER [2] and GEM [14]. Nevertheless, these methods face challenges related to memory pool configuration and sample selection, which are critical since WSI datasets only contain hundreds of samples, and a WSI may be too large to store in the memory.
+
+# 2.3. Class-incremental learning in MIL
+
+Recent studies have increasingly explored the application of class-incremental learning (CIL) within MIL. ConSlide [8] combines fast and slow learning, substituting the WSI buffer with a region buffer. This adaptation effectively reduces memory pool requirements and enables efficient data replay. Alternatively, MICIL [5] adopts a regularization-based strategy that builds on the LwF [12] paradigm.
+
+In contrast to these approaches, through theoretical analysis and model visualizations, we identify that model forgetting is primarily concentrated in the attention layers. Based on our findings, we then propose two new methods that focus on preserving knowledge learned by the attention network, which provide a significant boost to MIL performance in CIL scenarios.
+
+# 3. Motivation
+
+# 3.1. Problem Statement
+
+MIL. In the WSI MIL classification problem, the WSI  $\mathcal{X}$  comprises a bag of patches,  $\mathbf{P} = \{\mathbf{p}_n\}_{n=1}^N$ , and is associated with the bag-label  $y$ , where  $N$  is the number of patches, which varies with different bags. The objective of MIL is to predict the bag-level  $y$  label with the patches in the bag.
+
+We follow the standard formulation of ABMIL [9]. ABMIL classifies a WSI in three steps following the MIL paradigm. First, a WSI is divided into  $N$  patches, and a bag of patch features is obtained via a fixed feature extractor  $g(\cdot)$ ,  $\mathbf{H} = \{\mathbf{h}_n\}_{n=1}^N$ , where the  $n$ -th patch feature is  $\mathbf{h}_n = g(\mathbf{p}_n) \in \mathbb{R}^d$ , and  $d$  is the dimension of the feature vector. Second, the patch features are aggregated to compute a bag-level (slide-level) feature  $z$ :
+
+$$
+\mathbf {z} = \mathbf {H} \mathbf {a} = \sum_ {n = 1} ^ {N} a _ {n} \mathbf {h} _ {n}, \tag {1}
+$$
+
+where  $a_{n}$  is the normalized attention score of the nth patch,
+
+$$
+a _ {n} = \frac {\exp \left\{\mathbf {w} ^ {\top} (\tanh  (\mathbf {V} _ {1} \mathbf {h} _ {n}) \circ \sigma (\mathbf {V} _ {2} \mathbf {h} _ {n})) \right\}}{\sum_ {m = 1} ^ {N} \exp \left\{\mathbf {w} ^ {\top} (\tanh  (\mathbf {V} _ {1} \mathbf {h} _ {m}) \circ \sigma (\mathbf {V} _ {2} \mathbf {h} _ {m})) \right\}}, (2)
+$$
+
+Table 1. Test Accuracy of CLAM and TransMIL on Task 1 using different combinations of its attention/classifier from CL task sessions  $(t)$ . The diagonal cells (blue) correspond to the accuracy of fine-tuned model  $(\theta_t, \phi_t)$  after each task session.
+
+<table><tr><td rowspan="2" colspan="2">CLAM</td><td colspan="3">Attention θt</td></tr><tr><td>t=1</td><td>t=2</td><td>t=3</td></tr><tr><td rowspan="3">Classifier φt</td><td>t=1</td><td>0.8621</td><td>0.1552</td><td>0.0517</td></tr><tr><td>t=2</td><td>0.8793</td><td>0.0000</td><td>0.0000</td></tr><tr><td>t=3</td><td>0.8448</td><td>0.0000</td><td>0.0000</td></tr><tr><td rowspan="2" colspan="2">TransMIL</td><td colspan="3">Attention θt</td></tr><tr><td>t=1</td><td>t=2</td><td>t=3</td></tr><tr><td rowspan="3">Classifier φt</td><td>t=1</td><td>0.8966</td><td>0.0345</td><td>0.0345</td></tr><tr><td>t=2</td><td>0.8966</td><td>0.0345</td><td>0.0000</td></tr><tr><td>t=3</td><td>0.8276</td><td>0.0345</td><td>0.0000</td></tr></table>
+
+and  $\theta = (\mathbf{w},\mathbf{V}_1,\mathbf{V}_2)$  are learnable weight matrices, tanh and  $\sigma$  refer to the hyperbolic tangent and sigmoid activation functions, and  $\circ$  denotes the element-wise product. We denote  $\mathbf{a} = [a_n]_n = f_\theta (\mathbf{H})$  as the attention vector, where  $f_{\theta}$  is the attention network. Third, the bag label is predicted by a classifier  $\hat{y} = f_{\phi}(\mathbf{z})$ , where  $f_{\phi}$  is an MLP.
+
+CIL. CIL is a CL scenario consisting of training a model on tasks with disjoint label spaces. We define a sequence of datasets  $\mathcal{D} = \{\mathcal{D}_1, \mathcal{D}_2, \dots, \mathcal{D}_T\}$ , where the  $t$ -th dataset  $\mathcal{D}_t = \{\mathcal{X}, y, t\}_k$  contains tuples of the WSI sample  $\mathcal{X}$ , its corresponding label  $y \in \mathcal{Y}_t$  (where  $\mathcal{Y}_i \cap \mathcal{Y}_j = \emptyset$  for  $i \neq j$ ), and the task identifier  $t$  (available only during training). The subscript  $k$  means there are  $k$  samples for dataset  $\mathcal{D}_t$ . In CIL, the model needs to predict the classification label  $y$  with WSI  $\mathcal{X}$  as the input.
+
+# 3.2. Decoupling Experiments
+
+In this section, we investigate the cause of the performance degradation of CIL for MIL. Here we consider CLAM [15] and TransMIL [20] as a representative attention MIL. We define the attention network  $\theta$  as the sub-network that computes the attention scores from the patch features Eq. (2) for CLAM and Xiong et al. [26] for TransMIL), and we define the classifier  $\phi$  as the sub-network that takes the bag-level features  $\mathbf{z}$  and predicts the class label  $y$ .
+
+In our CL experiment after the  $T$ -th task session, we obtain a set of  $T$  fine-tuned model  $\{(\theta_t,\phi_t)\}_{t = 1}^T$ , which represents the evolution of the model when sequentially fine-tuning with new task data. To investigate the effect of CL, we then recombined the trained attention network  $\theta_{t}$  and classifier  $\phi_{t'}$  from different CL task sessions, and tested these "hybrid" models on Task 1 test data.
+
+We use Camelyon-TCGA for the benchmark, as described in the Sec. 5.1. The results for all pairs of attention/classifier are presented in Tab. 1. The significant decline of Task 1 accuracy after training on subsequent tasks is evident in the diagonal cells of the tables. However, exam
+
+![](images/caf2893fbf1dadcab888fe387aea2212e2a186602f317d635e3ed2cea53d23d3.jpg)  
+Figure 1. Example of the attention shift during CL for a Task 1 test image. (1) Input image with tumor area outlined in green. (2) The attention heat map for  $t = 1$  session. (3) and (4): the attention drift, relative to (2), after CL sessions  $t \in \{2,3\}$  for fine-tuning CL. The tumor areas are outlined in black. (5) and (6): the attention drift for our proposed method. Our method better preserves the attention much better than fine-tuning.
+
+Ining the 1st columns of the tables, we find that the performance does not decline much if the original attention layer  $\theta_{1}$  is used to replace the attention layers learned after subsequent tasks (i.e., used with classifier  $\phi_t$ ). Furthermore, if the classifier after each task is replaced with the original  $\phi_{1}$ , there is still a significant decline in Task 1 accuracy (in the 1st row of the tables). These two observations suggest that the drift of the fine-tuned attention network is the main cause of the performance decline of attention MIL in CL. Fig. 1 (2-4) illustrate the drift of CLAM's attention during subsequent CL sessions, where the attention on the tumor region (outlined region) is reduced after each CL session.
+
+# 3.3. Analysis of Parameter Update in MIL
+
+To explore the underlying mathematical mechanisms of catastrophic forgetting, we examine the gradient shifts in the attention network and classifier in the MIL model during training updates. As a foundational example, we employed the ABMIL [9] model, where the forward propagation is:
+
+$$
+f _ {\phi} = \boldsymbol {\phi} ^ {\top} \mathbf {H} \mathbf {a}, \tag {3}
+$$
+
+where  $\phi = [\phi_1,\dots ,\phi_d]^\top$  represents the logit layer of the binary classifier,  $\mathbf{a} = [a_{1},\dots ,a_{n}]^{\top}$  are the attention scores from Eq. (2), and  $\mathbf{H} = [\mathbf{h_1},\dots ,\mathbf{h_n}]$  are the feature vectors corresponding to patches in the WSI. In the binary classification setting, the model's loss function is
+
+$$
+L = \log (1 + e ^ {- y f _ {\phi}}). \tag {4}
+$$
+
+From this, the gradients w.r.t. each parameter in the model can be derived (see supplemental). The squared norm of the gradient w.r.t. each classifier weight  $\phi_{j}$  is:
+
+$$
+\left(\frac {\partial L}{\partial \phi_ {j}}\right) ^ {2} = y ^ {2} \sigma^ {2} (- y f _ {\phi}) z _ {j} ^ {2} \tag {5}
+$$
+
+![](images/93b687a47d11c1ab0666e46713631b118c6c44982a8a200d067e4acb6332973f.jpg)  
+Figure 2. Evolution of the distribution of gradient values of CLAM during CL for: (top) the attention network, (bottom) the classifier network. The data points are aggregated where each dot represents the mean of 50 consecutive training steps. The five colored dots at each aggregated step represent the minimum, maximum, and three quartiles (first, second, and third) of the gradient values. The vertical black dotted lines mark the transitions between tasks.
+
+where  $z_{j} = \sum_{i = 1}^{n}a_{i}H_{ij}$  represents the  $j$ -th element of the aggregated feature vector  $\mathbf{z}$  and  $H_{ij}$  is the  $ij$ -th element of  $\mathbf{H}$ . Similarly, the squared norm of the gradient w.r.t. each attention score  $a_{i}$  is:
+
+$$
+\left(\frac {\partial L}{\partial a _ {i}}\right) ^ {2} = y ^ {2} \sigma^ {2} (- y f _ {\phi}) \left(\boldsymbol {\phi} ^ {\top} \mathbf {h} _ {i}\right) ^ {2}. \tag {6}
+$$
+
+Through Eq. (5) and (6), we analyze the magnitude of the gradients with respect to different parameters in the attention network and the classifier. The main difference between the two equations are the terms  $z_{j}^{2}$  and  $\phi^{\top}\mathbf{h}_{i}$ . For the gradient of the classifier in Eq. (5), since the normalized attention a sums to 1 and  $\mathbf{H}$  is fixed for an image, then  $z_{j}$  is upper-bounded,  $\max z_{j} = \max_{i} H_{ij}$ . Thus each update step of  $\phi_{j}$  is always constrained within a specific range, which leads to the classifier's parameters only gradually updating during training. In the context of CL, when there is a significant shift in the data stream, like tasks switch, the classifier only undergoes slow updates, thereby retaining more of the previous knowledge.
+
+In contrast, the attention gradient in (Eq. (6)) directly reflects the importance the patch  $\mathbf{h}_i$  to the classifier  $\phi$ , and this gradient is unbounded - as the classifier becomes more confident  $(\|\phi\|^2$  increases), then the attention gradients increase. Therefore, when there is a significant change in the data stream during CL, i.e.,  $\mathbf{h}_i$  undergoes drastic changes, the gradient of the attention layer will also fluctuate significantly, especially on newly-seen patches with high logit scores  $(\phi^\top \mathbf{h}_i)$ , leading to catastrophic forgetting due to rapid model updates. Furthermore, if the newly seen patch with a high logit score is not informative or noisy, then the resulting large attention gradient makes the attention network overfit to this patch, causing generalization problems.
+
+In summary, the gradients of the classifier are bounded,
+
+while those in the attention layer (and the preceding attention network) are not. Thus, the attention network will be updated faster than the classifier, i.e., the loss decreases more when updating the attention network. Fig. 2 shows the distribution of gradient values of the attention network and the classifier of CLAM as it evolves over successive training steps in CL. During training on the second and third tasks, the maximum and minimum values of the gradient of the classifier gradually shrink and stabilize, but the gradient of the attention network keeps oscillating in a higher range. In the traditional image classification, Kessler et al. [10] found that the performance of CL largely depends on different classification heads across tasks. However, for MIL, we find that switching classification heads will no longer be effective, and our decoupling experiments in Sec. 3.2 further validate this theoretical finding.
+
+# 4. Methodology
+
+In this section, using our analysis in the previous section, we propose two methods for CL of attention-based MIL.
+
+# 4.1. Attention Knowledge Distillation
+
+Inspired by Sec. 3.3, we propose a plug-and-play method called attention knowledge distillation (AKD). Compared to the commonly used logits distillation in current CL approaches [2, 12], we focus on distillation of the attention layers since they drift faster in the MIL setting. Moreover, AKD can be combined with logits distillation to further enhance model performance. Previous CL works used the output logit of the classifier  $f_{\phi}(P)$  from previous tasks to mimic the original response for old samples. Therefore, their objective function for distillation is:
+
+$$
+\mathcal {L} _ {\text {l o g i t s}} = \mathbb {E} _ {\mathbf {z} \sim \mathcal {D} _ {t - 1}} \left[ D _ {K L} \left(f _ {\phi_ {t - 1}} (\mathbf {z}) \| f _ {\phi_ {t}} (\mathbf {z})\right) \right], \tag {7}
+$$
+
+where  $\phi_{t - 1}$  are the optimal parameters at the end of task  $t - 1$ ,  $\phi_t$  are the current parameters being optimized, and  $D_{KL}$  is the KL divergence.
+
+AKD directly optimizes the attention network using attention scores instead of the output logits of the model, reducing the interference caused to the classification layer. Specifically, consider bag feature  $\mathbf{z} = \sum_{n}a_{n}\mathbf{h}_{n}$ , AKD aims to ensure that after the model learns a new task, it retains the relative order of patch attention scores when inferring on previous tasks. In other words, after completing training on a new task, patches from previous tasks with previously high attention scores should continue to have high attention scores, and those with low scores should maintain relatively low scores. Therefore, we use KL divergence to enforce this relationship of the attention scores:
+
+$$
+\mathcal {L} _ {\text {a t t n}} = \mathbb {E} _ {\mathbf {H} \sim \mathcal {M}} \left[ D _ {K L} \left(f _ {\theta_ {t - 1}} (\mathbf {H}) \| f _ {\theta_ {t}} (\mathbf {H})\right) \right], \tag {8}
+$$
+
+where  $\theta_{t - 1}$  is the optimal attention network at the CL session  $t - 1$ , and  $\mathbf{H}$  are patch features sampled from the mem
+
+ory pool  $\mathcal{M}$ . Note that  $\mathcal{A} = f_{\theta_t}(\mathbf{H})$  represents the output produced by the attention network, which may encompass more than just the raw attention scores. Depending on the specific architecture of the network, the output can include various feature vectors derived from the attention process. For instance,  $\mathcal{A} = \{QK, QKV\}$  in the case of self-attention in TransMIL.
+
+# 4.2. Pseudo-Bag Memory Pool
+
+Traditional replay-based methods typically store thousands of samples in the memory pool – each sample occupies very little space, usually sized at 224x224 pixels, and having a large number of samples ensures that during replay training the model does not overfit. However, in WSI tasks, the entire dataset contains only a few hundred images due to the high costs of data collection and patient privacy concerns. Moreover, each WSI encompasses tens of billions of pixels, making it impractical to store too many raw WSIs directly in the memory pool.
+
+Recent research indicates that attention MIL models primarily utilize a small subset of patches from a WSI when calculating the bag feature  $\mathbf{z}$  [27, 30]. This suggests that the original slide can be distilled by removing low-contribution patches:  $\mathbf{P} = \{\mathbf{p}_n\}_{n=1}^N \to \hat{\mathbf{P}} = \{\mathbf{p}_n\}_{n=1}^K$ , where  $K \ll N$ . Yan et al. [27] demonstrated that the top few dozen patches with the highest attention scores account for over  $90\%$  of the model's attention. Therefore, one possible approach is to use patches with high attention scores (top- $K$ ) to approximate the original bag feature:
+
+$$
+\hat {\mathbf {z}} = \sum_ {n = 1} ^ {K} a _ {n} \mathbf {h} _ {n} \approx \mathbf {z} = \sum_ {n = 1} ^ {N} a _ {n} \mathbf {h} _ {n}. \tag {9}
+$$
+
+Thus, instead of storing the entire slide, we store the distilled slide (pseudo-bag) in the memory pool  $\mathcal{M} = \{(\hat{\mathbf{P}}_i,y_i)\}$  to approximate the data distribution of the WSI memory pool  $\mathcal{M} = \{(\mathbf{P}_i,y_i)\}$ . While using only the top-K patches is a tempting approach, it has been shown that other patches can also contribute valuable information [29].
+
+Therefore, we propose the MaxMinRand strategy to distill the essential information from the WSI:
+
+- MaxMinRand: selects  $K/2$  patches randomly and selects  $K/4$  patches with the highest and the lowest attention scores, respectively.
+
+We also consider other methods and will present them in Sec. 5.4. We adopt the reservoir sampling method [23] to update the slide-level memory pool. The reservoir sampling method can guarantee each slide-level sample shares the same probability of being stored and removed in the memory pool for the current task.
+
+# 4.3. Framework Overview
+
+The model's overall architecture, as depicted in Figure 3, follows a structured, task-oriented data flow. Input data is
+
+![](images/0ed88339450e9e1fd9d1853a328de2239a57f064a96c2d34b805f8c38623642c.jpg)  
+Figure 3. Overview of our framework architecture. The black arrows denote the forward pass for current data, including patch-wise slide processing, feature encoding, and memory pool updates. Orange rectangles represent patch-level features, while deep orange rectangles indicate bag-level feature representations. The green paths indicate the knowledge distillation process between teacher and student networks, incorporating both attention-based and logit-based distillation losses alongside cross-entropy supervision.
+
+sequentially fed into the model in alignment with the progression of tasks. At the conclusion of each task, a subset of distilled samples is retained in a buffer through the PMP (Pseudo-Bag Memory Pool) method. When training transitions to the next task, the model is provided with data from both the current task and the buffered samples. For data from the current task, the model engages in regular parameter updates, as our experiments suggest that interference from prior tasks can impede effective adaptation to new data. During the replay of buffered samples from previous tasks, the model applies AKD to mitigate forgetting of prior knowledge. The final loss function, integrating these components, is formulated as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {C E} + \alpha \mathcal {L} _ {a t t n} + \beta \mathcal {L} _ {\text {l o g i t s}}, \tag {10}
+$$
+
+where  $(\alpha, \beta)$  are hyperparameters that apply only to the data in the buffer. The complete process is outlined in Alg. 1.
+
+# 5. Experiments
+
+In this section we present experiments demonstrating the efficacy of our MIL methods on CL for WSIs.
+
+# 5.1. Setup
+
+Datasets. For class incremental learning (CIL), we utilized a skin cancer dataset [5], as well as three publicly available datasets for WSI analysis: Camelyon16 [4, 13], TCGALUNG [17], and TCGA-RCC [25]. These datasets represent diverse challenges in histopathology and support the evaluation of our method's ability to generalize across different cancer types and data distributions. Details about the datasets and preprocessing steps are in the Supplemental.
+
+We utilized two primary groups of datasets for class incremental learning tasks. First, we followed [5], which divides the skin cancer dataset into three class incremental
+
+Algorithm 1 Overview  
+1: Input: Attention network  $f_{\theta}$ , classifier  $f_{\phi}$ , number of tasks  $T$ , training set  $\mathcal{D} = \{\{(\mathbf{H}_i^t,y_i^t)\}_{i = 1}^{n_t}\}_{t = 1}^T$ $y_{i}^{t}\in \mathcal{V}$  , memory pool  $\mathcal{M}$    
+2: Initialize:  $f_{\theta},f_{\phi},\mathcal{M} = \emptyset$    
+3: for  $t = 1$  to  $T$  do   
+4: Obtain current task data  $\mathcal{D}_t = \{(H_i^t,y_i^t)\}_{i = 1}^{n_t}$    
+5: Combine current task and memory pool  $\bar{\mathcal{D}} = \mathcal{D}_t\cup \mathcal{M}$    
+6: for sample in  $\bar{\mathcal{D}}$  do   
+7: Obtain  $(\mathbf{H},y)$  from sample   
+8: Calculate attention outputs:  $\mathcal{A},z = f_{\theta}(\mathbf{H})$    
+9:  $\mathcal{L}_{CE} = \mathcal{L}_{CE}(f_{\phi}(\pmb {z}),Y)$    
+10: if  $(\mathbf{H},y)\in \mathcal{M}$  then   
+11: Obtain previous output  $(\tilde{\mathcal{A}},\tilde{f}_{\phi}(\pmb {z}))$  from sample.   
+12:  $\mathcal{L}_{attn} = \mathcal{L}_{KL}(\mathcal{A},\tilde{\mathcal{A}})$  (Eq. 8).   
+13:  $\mathcal{L}_{logits} = \mathcal{L}_{KL}(f_{\phi}(\pmb {z}),\tilde{f}_{\phi}(\pmb {z}))$    
+14: else   
+15:  $\mathcal{L}_{attn} = 0,\mathcal{L}_{logits} = 0$    
+16: end if   
+17:  $\mathcal{L} = \mathcal{L}_{CE} + \alpha \mathcal{L}_{attn} + \beta \mathcal{L}_{logits}$    
+18:  $(\theta ,\phi) = (\theta ,\phi) + \eta \nabla_{\theta ,\phi}(\mathcal{L})$    
+19:  $(\tilde{\mathbf{H}},y,\tilde{\mathcal{A}},\tilde{f}_{\phi}(\pmb {z})) = Distill(\mathbf{H},y,\mathcal{A},f_{\phi}(\pmb {z}))$    
+20:  $\mathcal{M}\gets$  reservoir(M,  $(\tilde{\mathbf{H}},y,\tilde{\mathcal{A}},\tilde{f}_{\phi}(\pmb {z})))$    
+21: end for   
+22: end for
+
+tasks. Each task within this group comprises two distinct class labels. The second group (denoted as Camelyon-TCGA) consists of the Camelyon16, TCGA-LUNG, and TCGA-RCC datasets, organized sequentially into three tasks based on dataset source: Camelyon16  $\rightarrow$  TCGALUNG  $\rightarrow$  TCGA-RCC. We employed cross-validation for Camelyon-TCGA. This structured progression enables the model to incrementally learn from different domains, demonstrating its ability to generalize across varied types of cancer and histopathological data.
+
+Models and CL methods. We employed CLAM [15] and TransMIL [20] as baseline MIL models. CLAM builds upon ABMIL by incorporating a multiclass categorization framework, making it particularly suitable for our experimental setup involving multiple cancer types. In contrast, TransMIL uses self-attention mechanisms instead of the
+
+gated-attention modules that our theoretical framework assumes. Despite this architectural difference, we apply our AKD to TransMIL to study the generality of our AKD.
+
+We compare performance with state-of-the-art CL methods for image classification, including experience replay (ER) [18], DER++ [2] and LwF [12], and a MIL-specific method, MICIL [5]. We also conduct joint training (JT) of the model using a single dataset of merged tasks, which is considered as the upper-bound performance of CL, and fine-tuning (FT) on each task dataset sequentially, which is the baseline performance.
+
+In the Skin Cancer dataset, each slide contains only a few hundred to a few thousand patches. Thus during CL on this dataset, we do not use our PMP to distill slides, and thus only apply our AKD or other CL methods. For replay-based methods, we set the memory pool size to 42 and use the parameters recommended in their papers for other methods.
+
+On the Camelyon-TCGA, to ensure training stability, we use a balanced memory pool, which maintains an equal number of samples for each class in the memory pool, applying reservoir sampling within each class. Each WSI comprises over 10k patches, presenting a significant memory challenge for CL methods. To manage this, we evaluate replay-based methods with different memory settings of 5, 10, and 30 WSIs for comprehensive comparison.
+
+Evaluation. To evaluate the performance of models across CL tasks, we primarily used balanced average accuracy (AACC) to measure the overall performance across all tasks. We also report backward transfer (BWT) and the intransigence measure (IM) to quantify the ability to retain and adapt. See the Supplemental for more details.
+
+# 5.2. Comparison with CL methods
+
+First, we conduct experiments on the Skin Cancer dataset, and the results are presented in Tab. 2. MICIL w/ ER is MICIL with experience replay. All CL methods significantly outperform the fine-tuning approaches. Among these methods, our approach achieves AACC performance that most closely reaches the theoretical upper bound of joint training. Furthermore, the results for BWT and IM indicate that our method keeps the effectiveness in mitigating catastrophic forgetting while facilitating continual adaptation to new information.
+
+The results on Camelyon-TCGA are presented in Tab. 3. Traditional CL methods face considerable challenges on this dataset, which includes over 2,000 large-scale WSIs. These methods struggle to perform effectively, particularly when applied to the TransMIL model, with some CL approaches even underperforming compared to the baseline fine-tuning method. This discrepancy arises because, despite their improved memory retention, traditional CL methods often fall short in adapting to new tasks, as reflected in their BWT and IM scores. In contrast, our method
+
+successfully addresses these limitations by integrating our AKD and PMP. This approach mitigates forgetting while also enhancing the model's ability to learn new tasks, resulting in performance gains of up to  $37\%$  over other methods when applied to the CLAM model.
+
+Finally, we note that despite the architectural differences in attention between CLAM and TransMIL, our experimental results indicate that TransMIL also works effectively with our proposed AKD, achieving strong outcomes across all evaluated metrics. This demonstrates the robustness and adaptability of the AKD method, even when applied to models with varying attention mechanisms.
+
+# 5.3. Visualizations
+
+Fig. 1 visualizes the heatmap of CLAM attention during different CL sessions. The model's attention shifts when an MIL model is trained sequentially from different tasks. We visualized a sample in the Task 1 test set. The model should ideally focus on the tumor region. However, during finetuning, the model tends to reduce its attention to the tumor region and pay much more attention to the normal region. In contrast, for our method, the tumor region is nearly white in the difference heatmap, maintaining the original attention on the important tumor areas. Moreover, the attention changes brought by our method are much lower than those of the fine-tuning method.
+
+# 5.4. Ablation Study
+
+As introduced in Sec. 4.2, we explored several strategies for constructing the pseudo-bag representation. Here, we compare the performance of MaxMinRand with the following alternatives:
+
+- Random: randomly selects  $K$  patches.  
+- Max: selects  $K$  patches with the highest attention scores.  
+- MaxMin: selects  $K/2$  patches with the highest atttnetion scores, and  $K/2$  with the lowest attention scores.  
+- MaxRand: selects  $K/2$  patches each from the Random strategy and Max strategy.
+
+Tab. 4 summarizes the results of these different strategies. Surprisingly, both Random-based and MaxMin-based strategies achieve comparable performance, suggesting that AKD does not heavily rely on patches with the highest attention scores. Instead, AKD appears to emphasize the global attention distribution.
+
+We also investigated the contribution of each component in our method to the overall results. As shown in Tab. 5, our proposed PMP method achieves a  $37\%$  and  $5\%$  improvement over the basic ER approach using entire WSI, without requiring additional storage. While the AKD method contributes a  $40\%$  and  $8\%$  improvement. The study clearly underscores the effectiveness of our method, as it enhances performance efficiently without imposing further storage
+
+Table 2. CL performance of CLAM and TransMIL on Skin Cancer dataset. The best performances are highlighted as bold.  
+
+<table><tr><td></td><td colspan="3">CLAM</td><td colspan="3">TransMIL</td></tr><tr><td>Methods</td><td>AACC↑</td><td>BWT↑</td><td>IM↓</td><td>AACC↑</td><td>BWT↑</td><td>IM↓</td></tr><tr><td>Joint training</td><td>0.7311</td><td>-</td><td>-</td><td>0.7647</td><td>-</td><td>-</td></tr><tr><td>Fine-tuning</td><td>0.3167</td><td>-0.8701</td><td>-0.1942</td><td>0.3000</td><td>-0.9239</td><td>-0.1771</td></tr><tr><td>LwF</td><td>0.3333</td><td>-0.8823</td><td>-0.2339</td><td>0.3000</td><td>-0.9239</td><td>-0.1923</td></tr><tr><td>MICIL</td><td>0.3000</td><td>-0.9239</td><td>-0.1923</td><td>0.3000</td><td>-0.8944</td><td>-0.2087</td></tr><tr><td>ER</td><td>0.5388</td><td>-0.3869</td><td>-0.0942</td><td>0.6050</td><td>-0.4041</td><td>-0.1356</td></tr><tr><td>DER++</td><td>0.5343</td><td>-0.4931</td><td>-0.1604</td><td>0.5329</td><td>-0.5124</td><td>-0.1356</td></tr><tr><td>MICIL w/ ER</td><td>0.5285</td><td>-0.4523</td><td>-0.1275</td><td>0.6275</td><td>-0.3705</td><td>-0.1356</td></tr><tr><td>Ours</td><td>0.5926</td><td>-0.4056</td><td>-0.1604</td><td>0.6418</td><td>-0.3741</td><td>-0.1523</td></tr></table>
+
+Table 3. CL performance of CLAM and TransMIL on Camelyon-TCGA dataset. The best performances are highlighted as bold. The standard deviations of BWT and IM metrics can be found in the supplementary material.  
+
+<table><tr><td colspan="3"></td><td colspan="3">CLAM</td><td colspan="3">TransMIL</td></tr><tr><td>CL Type</td><td>Method</td><td>Memory Size</td><td>AACC↑</td><td>BWT↑</td><td>IM↓</td><td>AACC↑</td><td>BWT↑</td><td>IM↓</td></tr><tr><td rowspan="2">Baselines</td><td>Joint training</td><td rowspan="2">-</td><td>0.858±0.016</td><td>-</td><td>-</td><td>0.818±0.027</td><td>-</td><td>-</td></tr><tr><td>Fine-tuning</td><td>0.296±0.014</td><td>-0.865</td><td>-0.014</td><td>0.290±0.002</td><td>-0.751</td><td>0.024</td></tr><tr><td rowspan="2">Regularization</td><td>LwF</td><td rowspan="2">-</td><td>0.295±0.013</td><td>-0.865</td><td>-0.013</td><td>0.296±0.010</td><td>-0.747</td><td>0.021</td></tr><tr><td>MICIL</td><td>0.295±0.008</td><td>-0.866</td><td>-0.013</td><td>0.294±0.011</td><td>-0.760</td><td>0.014</td></tr><tr><td rowspan="12">Rehearsal</td><td>ER</td><td rowspan="4">5 WSIs</td><td>0.294±0.010</td><td>-0.864</td><td>-0.012</td><td>0.296±0.008</td><td>-0.748</td><td>0.020</td></tr><tr><td>DER++</td><td>0.301±0.010</td><td>-0.857</td><td>-0.013</td><td>0.288±0.021</td><td>-0.752</td><td>0.025</td></tr><tr><td>MICIL w/ ER</td><td>0.289±0.013</td><td>-0.869</td><td>-0.010</td><td>0.290±0.009</td><td>-0.759</td><td>0.018</td></tr><tr><td>Ours</td><td>0.657±0.032</td><td>-0.329</td><td>-0.017</td><td>0.374±0.060</td><td>-0.635</td><td>0.018</td></tr><tr><td>ER</td><td rowspan="4">10 WSIs</td><td>0.352±0.063</td><td>-0.785</td><td>-0.017</td><td>0.297±0.012</td><td>-0.746</td><td>0.021</td></tr><tr><td>DER++</td><td>0.372±0.070</td><td>-0.760</td><td>-0.020</td><td>0.299±0.015</td><td>-0.738</td><td>0.024</td></tr><tr><td>MICIL w/ ER</td><td>0.298±0.006</td><td>-0.863</td><td>-0.015</td><td>0.302±0.016</td><td>-0.746</td><td>0.016</td></tr><tr><td>Ours</td><td>0.729±0.041</td><td>-0.217</td><td>-0.059</td><td>0.394±0.085</td><td>-0.595</td><td>0.024</td></tr><tr><td>ER</td><td rowspan="4">30 WSIs</td><td>0.494±0.058</td><td>-0.565</td><td>-0.011</td><td>0.308±0.011</td><td>-0.728</td><td>0.021</td></tr><tr><td>DER++</td><td>0.449±0.048</td><td>-0.645</td><td>-0.020</td><td>0.315±0.028</td><td>-0.739</td><td>0.006</td></tr><tr><td>MICIL w/ ER</td><td>0.308±0.021</td><td>-0.835</td><td>-0.006</td><td>0.298±0.019</td><td>-0.739</td><td>0.024</td></tr><tr><td>Ours</td><td>0.754±0.029</td><td>-0.177</td><td>-0.058</td><td>0.489±0.059</td><td>-0.460</td><td>0.018</td></tr></table>
+
+Table 4. Ablation study of different distillation methods for AKD on CLAM and TransMIL in Camelyon-TCGA dataset.  
+
+<table><tr><td>Method</td><td>CLAM AACC</td><td>TransMIL AACC</td></tr><tr><td>Random</td><td>0.695±0.010</td><td>0.391±0.065</td></tr><tr><td>MaxMin</td><td>0.679±0.025</td><td>0.391±0.054</td></tr><tr><td>Max</td><td>0.595±0.121</td><td>0.340±0.008</td></tr><tr><td>MaxRand</td><td>0.705±0.021</td><td>0.395±0.036</td></tr><tr><td>MaxMinRand</td><td>0.729±0.041</td><td>0.394±0.085</td></tr></table>
+
+Table 5. Ablation study on our components using CLAM on Camelyon-TCGA dataset.  
+
+<table><tr><td>Method</td><td>CLAM AACC</td><td>TransMIL AACC</td></tr><tr><td>ER</td><td>0.296±0.014</td><td>0.290±0.002</td></tr><tr><td>AKD</td><td>0.692±0.037</td><td>0.373±0.045</td></tr><tr><td>PMP</td><td>0.672±0.025</td><td>0.348±0.052</td></tr><tr><td>PMP+AKD</td><td>0.729±0.041</td><td>0.394±0.085</td></tr></table>
+
+demands, demonstrating a significant advancement in optimizing resource-constrained learning environments.
+
+# 6. Conclusion
+
+In this paper, our analysis reveals that the main cause of catastrophic forgetting in attention MIL models is the degradation of bag-level feature representations due to changes in the attention module. To address this, we propose a pseudobag memory pool (PMP) method to enable replay-based CL for MIL and an attention knowledge distillation (AKD) technique to preserve the attention relationships and maintain representation quality. Experiments on WSI datasets demonstrate the effectiveness of PMP and AKD in significantly improving CL performance for traditional MIL architectures. This work establishes an important foundation for further research on CL for gigapixel images and weakly-supervised learning in real-world clinical applications.
+
+Limitations. The current limitation is that our methods still need to store past patch features. While storing features largely reduces privacy risks compared to raw images, it may still pose privacy concerns. In the future, we will explore more privacy-friendly data replay methods.
+
+# References
+
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+# Advancing Myopia To Holism: Fully Contrastive Language-Image Pre-training
+
+Haicheng Wang $^{1,2\dagger}$ , Chen Ju $^{1\dagger\boxtimes}$ , Weixiong Lin $^{1,3}$ , Shuai Xiao $^{1\boxtimes}$ , Mengting Chen $^{1}$ , Yixuan Huang $^{1}$ , Chang Liu $^{1,3}$ , Mingshuai Yao $^{1}$ , Jinsong Lan $^{1}$ , Ying Chen $^{1}$ , Qingwen Liu $^{1}$ , Yanfeng Wang $^{3}$ $^{1}$  Taobao & Tmall Group of Alibaba  $^{2}$  Paris Elite Institute of Technology, Shanghai Jiao Tong University  
+ $^{3}$  School of Artificial Intelligence, Shanghai Jiao Tong University
+
+anakinSkywalker@sjtu.edu.cn, cju void@gmail.com, {shuai.xsh,yingchen}@alibaba-inc.com
+
+![](images/504e32e071780a6b721795db934902f9a84a1ab0e166cebd2f7fbb785e5ea778.jpg)  
+Figure 1. Myopia. OpenAI's CLIP [63] uses crude (image, text) web data for one-to-one contrastive alignment, causing serious myopia, i.e., bias to monotonous short texts and shallow visual expressivity. Holism. We advance one holistic CLIP paradigm, by updating colorful (image, multi-texts) data from diverse views, levels; and designing multi-to-multi constrastive learning for image-text part-to-part matching.
+
+# Abstract
+
+In rapidly evolving field of vision-language models (VLMs), contrastive language-image pre-training (CLIP) has made significant strides, becoming foundation for various downstream tasks. However, relying on one-to-one (image, text) contrastive paradigm to learn alignment from large-scale messy web data, CLIP faces a serious myopic dilemma, resulting in biases towards monotonous short texts and shallow visual expressivity. To overcome these issues, this paper advances CLIP into one novel holistic paradigm, by updating both diverse data and alignment optimization. To obtain colorful data with low cost, we use image-to-text captioning to generate multi-texts for each image, from multiple perspectives, granularities, and hierarchies. Two gadgets are
+
+proposed to encourage textual diversity. To match such (image, multi-texts) pairs, we modify the CLIP image encoder into multi-branch, and propose multi-to-multi contrastive optimization for image-text part-to-part matching. As a result, diverse visual embeddings are learned for each image, bringing good interpretability and generalization. Extensive experiments and ablations across over ten benchmarks indicate that our holistic CLIP significantly outperforms existing myopic CLIP, including image-text retrieval, open-vocabulary classification, and dense visual tasks. Project page is available to further promote the prosperity of VLMs: https://voidel220.github.io/Holism/.
+
+# 1. Introduction
+
+With the rapid recent advancement of large language models in NLP, Vision-Language Models (VLMs) have also thrived, driving progress in tasks like closed-set understanding, open-vocabulary learning, and AIGC generation [21,
+
+65, 72]. As the foundation of VLMs, Contrastive Language-Image Pre-training (CLIP) [63] plays a crucial role.
+
+OpenAI leads CLIP's prevailing solution and most later variants follow the precedent set, i.e., to bridge cross-modal embeddings effectively, CLIP first crawls 400M image-text pairs supplemented by simple cleaning, then optimizes via noisy contrastive learning for one-to-one alignment (Fig. 1). The paradigm rapidly expands data by extremely low manpower, and trains large-scale models to achieve strong performance. However, it also inevitably leads to bias in overfitting the web data: (1) One Sidedness. Crude text format is uniform, mostly presenting brief overviews without complex relationships, and some even carry the noise. (2) Visual Damage. A colorful image only matches one compact text, diverse vision is largely discarded, with only a glance being used. (3) Chaotic Semantics. Web texts are rather complicated with multi-level semantics, thus brutally aggregating them to the same image embedding fundamentally affects the pre-training quality. As a result, overfitting these biases doomed trained CLIP to be myopic, i.e., performing poorly in long-context understanding [85], fine-grained visual perception [3, 61], and complexity modeling [70].
+
+To jump out the myopic dilemma, we are motivated by one blind men and an elephant fable: combining cognition of multiple myopic men should give the holism. Concretely, image carries explosive information than text, e.g., people tell colors, objects, styles, events from multi-levels, multiviews for an image using various texts of varying lengths. Grouping all texts form full ideas of colorful vision.
+
+We accordingly propose an advanced pipeline for holistic contrastive language-image pre-training, updating data governance, model architecture and optimization paradigm. Firstly, data construction is primarily crucial, i.e., evolving from uni-view/level (image, text) pairs to multi-view/level (image, multi-texts) pairs. And naturally, we leverage powerful VLMs for image-to-text captioning to form multiple texts with a little manpower. To encourage diversity in captioned texts, specific implementations are divided into two groups: one is to use multiple VLMs from various training data or architectures, implicitly expecting text complementarity; another is to carefully design prompts with distinct spirits, e.g., focus guide, physical or sensory, gaze or glance, explicitly scattering text attention. Secondly, architecture needs to move forward to match (image, multi-texts) pairs. A vanilla idea is to reuse myopic CLIP's image encoder and text encoder, simply by encoding each text separately. Although feasible, it owns issues because an image covers colorful elements that cannot be sufficiently wrapped up by one embedding vector, which can cause serious visual damage. To tackle these issues, we modify the CLIP's image encoder into multi-branch visual outputs, covering two parameter-efficient schemes, i.e., one is to initialize some CLS tokens to output corresponding embeddings; another is to extend
+
+the MLP of last layers to some parallel parts. By this way, multiple visual embeddings are gained in one forward. Finally, optimization paradigm for such holistic CLIP also requires evolution. Different from one-to-multi-positive constrastive learning used by recent studies [19, 88], we here design novel multi-to-multi constrastive learning by comprehensive image-text part-to-part matching. As the result, cross-modal alignment is achieved at multiple perspectives, granularities, and hierarchies. An additional benefit is that, diverse visual embeddings learned for each image, actually form the good semantic decomposition, allowing us to customize (select and combine several embeddings) for different downstream tasks, i.e., generalizable and robust.
+
+On over ten datasets, we extensively experiment to prove the generic superiority of holistic CLIP, across image-align-text understanding, image-to-text generation. Mostly, holistic CLIP greatly outperforms myopic CLIP, sometimes by  $20\%$ . Thorough ablations are done to reveal each component's effectiveness, both quantitatively and qualitatively.
+
+Our main contributions are summarized as follows:
+
+- We pioneer to advancing contrastive language-image pre-training, from popular myopia to novel holism, by upgrading diverse data, model, and alignment paradigm.  
+- We develop one holistic CLIP pipeline, covering fully aligned data, multi-to-multi contrastive optimization. Colorful prompt spirits are designed to steer VLMs for multiview/level image-text pairs. Exact matching of part-to-part vision-language are cogitated for training alignment.  
+- We carry out numerous experiments to show superior gains of holism paradigm over prevalent myopic paradigm. Extensive ablations are studied for key components.
+
+# 2. Related Work
+
+Vision-Language Pre-training (VLP) [28, 84] uses large-scale web data for cross-modal alignment: CLIP [63], Florence [83], FILIP [79], as well as VideoCLIP [76]. In architectures, VLPs are mainly divided into: single tower [8, 38], twin towers [28, 44, 62], and bridge tower [41, 42, 91]. For optimization, image-text one-to-one contrastive learning [10, 24, 26, 41] is the mainstream, covering self supervision [46, 49], weak supervision [12, 14, 42] and partial supervision [35, 48]. As the foundation of VLMs, VLPs benefit many downstream tasks [6, 25, 37, 47, 54, 64, 65, 68].
+
+But, excessive bias in web data leads to severe myopia in VLPs, showing shallow visual expressivity and diminished capacity for complex long-contexts. Recent work [19, 39, 85, 88] make minor improvements, by simply adding hard-sample data to continue training. To tackle these issues, we fully advance CLIP from myopia to holism, by upgrading diverse data, model encoder, and alignment paradigm.
+
+Closed-set Alignment Understanding has benefited many potentials from VLPs. In the image domains, object classifi
+
+![](images/1c2ddc579b783a7aed24dd6a033018da58f0c1e72acb060de637298800f7b636.jpg)
+
+![](images/1361ea65de848ec8466b86557ff8bafbece161c0a6e67c22f1bc8272e3dfcfd6.jpg)  
+Figure 2. Pipeline Overview of Holistic CLIP. To evolve data from monotonous (image, text) pairs to colorful (image, multi-texts) pairs, we use powerful VLMs for captioning from multiple views, levels, and granularities. Diverse prompts are defined to encourage diversity. We then modify the CLIP image encoder into multi-branch, and optimize by multi-to-multi constractive learning for part-to-part matching. During inference, flexible embedding customizations are available for different tasks, showing good interpretability and generalization.
+
+cation [34, 90], image-text retrieval [7, 13, 14, 69, 74], segmentation [58, 80], caption [53, 60] all employ CLIP for improvements. When it comes to video domains [29, 32, 87], action recognition [31, 75], grounding [35, 46, 73], and temporal localization [30, 36] also gain solid progress.
+
+Open-Vocabulary Learning considers more realistic scenarios: generalize towards semantics that are unseen (zero-shot [72, 75, 89]) or using several support samples (few-shot [31, 33, 57, 78]). It describes concepts by free texts, then employ powerful VLPs to match text descriptions and visual samples. For image domains, object classification, detection, and segmentation are well explored [17, 55, 56, 77, 90]; while for video domains, recognition and localization of actions are mainly studied [2, 11, 27, 86].
+
+# 3. Method
+
+We advance contrastive language-image pre-trainings, from myopia to holism. Sec 3.1 reviews our motivation for holistic CLIP; Sec 3.2 reports image-text holistic alignment data, covering various views, levels and granularities; Sec 3.2 details multi-to-multi contrast for pipeline optimization.
+
+# 3.1. Motivation & Overview
+
+Due to overfitting bias from web data, prevailing contrastive language-image pre-training is revealed to be myopic, i.e., proficient in aligning short-text and main vision, but unable
+
+to understand complex, long or fine cases [3, 61, 85].
+
+To advance myopia to holism, we follow the plain fable of blind men and an elephant. In terms of information, one image is worth a thousand words. Regarding one image as an elephant, its paired text refers to the perception of the blind. When there are many blind men, these perceptions are multi-level, multi-granular, and multi-angle. One full-scale alignment can be formed by grouping all perceptions. As shown in Figure 2, we propose novel holistic CLIP, an advanced pipeline updating data governance, model architecture and optimization paradigm.
+
+# 3.2. All-Round Vision-Language Data
+
+To optimize contrastive language-image pre-training holistically, the data construction of multi-view/level alignment is primarily crucial. Hence, given the uni-view/level dataset  $\mathcal{D}_{\mathrm{myopia}} = (\mathcal{I},\mathcal{T})_{j = 1}^{N}$  collected from web, our propose is to describe diverse texts  $\{\mathcal{T}_i\}_{i = 1}^M$  for each image, which could somewhat complement each other and work together to obtain comprehensive information. The resultant (image,  $M$  -texts) pairs form dataset  $\mathcal{D}_{\mathrm{holism}} = (\mathcal{I},\{\mathcal{T}_i\}_{i = 1}^M)_j = 1$
+
+Due to the enormous size of descriptive texts, the labors are usually unaffordable. Motivated by the impressive performance, we naturally seek vision-language large models (VLMs)  $\Psi^{\mathrm{VLM}}$  for help, i.e., synthesize descriptive texts for images, from various perspectives/granularities.
+
+For specific implementations, one common idea [39, 50, 88] is to utilize  $M$ -VLMs for re-captioning, expecting that VLMs from various data or architectures should implicitly complement each other's information. Formally,
+
+$$
+\left\{\mathcal {T} _ {i} \right\} _ {i = 1} ^ {M} = \left\{\Psi_ {i} ^ {\mathrm {V L M}} (\mathcal {I}, \mathcal {P}) \right\} _ {i = 1} ^ {M}, \tag {1}
+$$
+
+where  $\mathcal{P}$  refers to prompts. This idea implicitly constrains prompt diversity by leveraging differences within  $M$ -VLMs themselves. Yet, it might face issues in practice: deploying multi-VLMs is highly complex. We thus take another pragmatic path to ensure feasibility, i.e., carefully designing diverse prompts to explicitly drive a single VLM. Specifically, prompts are responsible for captioning images in terms of breadth and depth, under four distinct spirits:
+
+Focus Guide indicates whether attention should be laid on foreground objects or general background substances. Physical or Sensory refers to describe solid nouns or feeling styles. Gaze or Glance define captions are dense long-details or compact short-overview. Complex Reasoning distinguishes relationship or sequence for entities.
+
+With above spirits, we could write  $M$  prompts  $\{\mathcal{P}_i\}_{i = 1}^M$  use a representative VLM [9] to output  $M$  colorful texts.
+
+$$
+\left\{\mathcal {T} _ {i} \right\} _ {i = 1} ^ {M} = \Psi^ {\mathrm {V L M}} \left(\mathcal {I}, \left\{\mathcal {P} _ {i} \right\} _ {i = 1} ^ {M}\right). \tag {2}
+$$
+
+These captioned texts, along with the raw texts of  $\mathcal{D}_{\mathrm{myopia}}$  constitute the ultimate data  $\mathcal{D}_{\mathrm{holism}}$ .
+
+Remark. In supplementary materials, we offer many qualitative cases of the defined prompts and captioned texts. For each image, we quantitatively calculate the similarity [71] between multi-texts obtained by Eq. (1) vs Eq. (2). Statistically, their mean/variance are  $0.58 / 0.043$  vs  $0.48 / 0.052$ , showing text diversity is pursued and colorful prompts are more effective. Table 9 also ablates for the text number. Besides, as web data is intricate,  $\mathcal{D}_{\mathrm{myopia}}$  carries noisy texts, building  $\mathcal{D}_{\mathrm{holism}}$  also finishes denoising by the way.
+
+# 3.3. Holistic Alignment Optimization
+
+We here take steps towards fully contrastive pre-training.
+
+# 3.3.1. Vanilla CLIP (O2O)
+
+Vanilla CLIP [63] deals with plain (one-image to one-text) pairs  $\mathcal{D}_{\mathrm{myopia}} = (\mathcal{I},\mathcal{T})_{j = 1}^{N}$ , hence it employs two separate encoders  $\Phi^{\mathrm{img}} / \Phi^{\mathrm{txt}}$  for modality embeddings, which can be referred to:  $\mathbf{v} = \Phi^{\mathrm{img}}(\mathcal{I})$ ,  $\mathbf{t} = \Phi^{\mathrm{txt}}(\mathcal{T})$ .
+
+The optimization loss is defined as the average of two symmetric InfoNCE losses  $(\mathcal{L}^{\mathrm{T2I}} + \mathcal{L}^{\mathrm{I2T}}) / 2$ , which is actually one-to-one contrastive learning between text-image:
+
+$$
+\mathcal {L} _ {\mathrm {O 2 O}} ^ {\mathrm {T 2 I}} = - \sum_ {j = 1} ^ {K} \log \frac {\exp \left(\left\langle \mathbf {v} _ {j} , \mathbf {t} _ {j} \right\rangle / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\left\langle \mathbf {v} _ {k} , \mathbf {t} _ {j} \right\rangle / \tau\right)}, \tag {3}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {O 2 O}} ^ {\mathrm {I 2 T}} = - \sum_ {j = 1} ^ {K} \log \frac {\exp (\langle \mathbf {t} _ {j} , \mathbf {v} _ {j} \rangle / \tau)}{\sum_ {k = 1} ^ {K} \exp (\langle \mathbf {t} _ {k} , \mathbf {v} _ {j} \rangle / \tau)},
+$$
+
+where  $\langle \cdot ,\cdot \rangle$  denotes the cosine similarity,  $\tau$  is one learnable temperature, and  $K$  refers to the batch size.
+
+Yet here, we are facing one holistic cross-modal dataset  $\mathcal{D}_{\mathrm{holism}} = (\mathcal{I},\{\mathcal{T}_i\}_{i = 1}^M)_{j = 1}^N$ , whose elements are the (one-image to  $M$ -texts) pairs. Thus, the CLIP pipeline urgently needs improvements. One intuitive idea is to transform InfoNCE into multi-positive contrastive learning [19, 50, 88].
+
+# 3.3.2. One-to-Multi Contrastive Learning (O2M)
+
+For modal embeddings, we also formalize image and text encoders as  $\Phi^{\mathrm{img}}$  and  $\Phi^{\mathrm{txt}}$ . Then naturally, the dual-modal embeddings can be calculated as follows:
+
+$$
+\mathbf {v} = \Phi^ {\mathrm {i m g}} (\mathcal {I}), \quad \{\mathbf {t} _ {i} \} _ {i = 1} ^ {M} = \Phi^ {\mathrm {t x t}} (\{\mathcal {T} _ {i} \} _ {i = 1} ^ {M}).
+$$
+
+For encoder optimization, a  $(\mathbf{v},\{\mathbf{t}_i\}_{i = 1}^M)$  pair is used to bring  $M$  texts and single image closer together in the embedding space. Let's take text-to-image loss as an example, one-to-multi-positive constrastive learning is:
+
+$$
+\mathcal {L} _ {\mathrm {O 2 M}} ^ {\mathrm {T 2 I}} = - \sum_ {j = 1} ^ {K} \sum_ {i = 1} ^ {M} \log \frac {\exp \left(\left\langle \mathbf {v} _ {j} , \mathbf {t} _ {i , j} \right\rangle / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\left\langle \mathbf {v} _ {k} , \mathbf {t} _ {i , j} \right\rangle / \tau\right)}, \tag {4}
+$$
+
+Although it sounds feasible, one-to-multi-positive contrastive learning still suffers from many issues: (1) Chaotic Semantics.  $M$  texts are from multi-view and multi-level, resulting in significant semantic differences. Brutally aggregating them at the same embedding position fundamentally affects the training procedure. (2) Visual Damage. An image covers colorful elements, which cannot be sufficiently wrapped up by one embedding vector. During the damage of vision diversity, the resultant image embeddings become inexplicable, losing the capacity to decompose effective information for different downstream tasks.
+
+# 3.3.3. Multi-to-Multi Contrastive Learning (M2M)
+
+To solve the above issues, we are inspired by one MoE intuition [16] from LLM sparsity: if there is corresponding text for induction, the image encoder could output differentiated expert branches to decompose diversity, achieving accurate part-to-part alignment without losing information.
+
+In terms of network architecture, we modify the classic image encoder  $\Phi^{\mathrm{img}}$  to enable the output of multi-branch visual embeddings. Concretely, two schemes are leveraged based on the  $\Phi^{\mathrm{img}}$  structure. (1)  $\Psi_{\mathrm{CLS}}$ . We initialize the  $H$  CLS tokens to output  $H$  different embeddings. (2)  $\Psi_{\mathrm{MLP}}$ . We extend the MLP of last three layers to parallel  $H$  parts.
+
+Table 1. Elementary Short-Text Retrieval. There are two solutions to get diverse texts of multi-level and multi-view: uni-VLM and multiprompt, or multi-VLMs and uni-prompt. For multi-VLMs, we employ InternVL2 [9], Minigpt4 [91], LLaVA1.5 [45], QwenVL2 [1], and set one unified prompt refer to [50]. For multi-prompt, we adopt InternVL2 and put prompt details in supplementary materials. For full comparisons under the same data, we also reproduce recent O2M methods [19, 50, 88] optimized by one-to-multi contrastive learning.  
+
+<table><tr><td rowspan="3" colspan="2">Method</td><td rowspan="3">Training Text</td><td rowspan="2" colspan="3">Caption</td><td colspan="6">MSCOCO</td><td colspan="6">Flickr30</td></tr><tr><td colspan="3">I2T</td><td colspan="3">T2I</td><td colspan="3">I2T</td><td colspan="3">T2I</td></tr><tr><td>VLM</td><td>Prompt</td><td>Num</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td colspan="2">CLIP [63]</td><td>CC3M</td><td>-</td><td>-</td><td>1</td><td>13.6</td><td>32.9</td><td>43.9</td><td>13.4</td><td>32.6</td><td>44.1</td><td>30.8</td><td>56.2</td><td>68.1</td><td>31.9</td><td>58.0</td><td>68.3</td></tr><tr><td rowspan="3" colspan="2">O2M [19, 50, 88]</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>20.0</td><td>42.9</td><td>54.3</td><td>20.1</td><td>42.9</td><td>53.8</td><td>50.5</td><td>74.4</td><td>83.2</td><td>49.1</td><td>74.7</td><td>82.6</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>24.5</td><td>48.6</td><td>59.9</td><td>26.3</td><td>49.4</td><td>60.9</td><td>60.7</td><td>81.3</td><td>88.1</td><td>61.7</td><td>83.2</td><td>88.8</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>27.1</td><td>51.8</td><td>64.3</td><td>27.9</td><td>53.8</td><td>64.5</td><td>63.9</td><td>85.3</td><td>88.9</td><td>63.8</td><td>84.4</td><td>89.7</td></tr><tr><td rowspan="6">Ours</td><td rowspan="3">ΨCLS</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>21.6</td><td>44.9</td><td>55.6</td><td>20.9</td><td>44.8</td><td>55.4</td><td>51.0</td><td>74.6</td><td>82.0</td><td>51.0</td><td>74.9</td><td>83.9</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>28.0</td><td>52.4</td><td>63.4</td><td>27.8</td><td>53.1</td><td>64.1</td><td>62.9</td><td>85.1</td><td>89.9</td><td>64.2</td><td>85.7</td><td>91.1</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>30.0</td><td>54.5</td><td>65.8</td><td>30.2</td><td>54.7</td><td>66.2</td><td>66.0</td><td>86.1</td><td>91.3</td><td>65.9</td><td>87.3</td><td>91.9</td></tr><tr><td rowspan="3">ΨMLP</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>20.1</td><td>43.7</td><td>55.0</td><td>20.6</td><td>43.4</td><td>55.1</td><td>50.9</td><td>74.8</td><td>82.8</td><td>51.2</td><td>75.7</td><td>83.8</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>28.2</td><td>53.0</td><td>64.4</td><td>27.4</td><td>52.4</td><td>64.0</td><td>63.7</td><td>85.3</td><td>90.6</td><td>63.9</td><td>85.8</td><td>90.5</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>31.2</td><td>55.7</td><td>66.5</td><td>30.7</td><td>55.9</td><td>66.9</td><td>66.5</td><td>86.4</td><td>91.2</td><td>66.4</td><td>86.9</td><td>92.2</td></tr><tr><td colspan="2">CLIP [63]</td><td>CC12M</td><td>-</td><td>-</td><td>1</td><td>25.2</td><td>49.4</td><td>61.9</td><td>25.3</td><td>50.0</td><td>61.7</td><td>56.9</td><td>81.6</td><td>87.4</td><td>55.2</td><td>81.9</td><td>87.6</td></tr><tr><td rowspan="3" colspan="2">O2M [19, 50, 88]</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>31.8</td><td>56.6</td><td>67.6</td><td>30.5</td><td>55.8</td><td>67.4</td><td>67.9</td><td>88.3</td><td>92.9</td><td>67.2</td><td>88.8</td><td>92.7</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>33.9</td><td>60.3</td><td>71.6</td><td>34.3</td><td>59.6</td><td>70.5</td><td>70.6</td><td>90.2</td><td>94.3</td><td>69.5</td><td>90.8</td><td>94.6</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>36.6</td><td>63.3</td><td>73.2</td><td>38.5</td><td>64.8</td><td>74.7</td><td>75.3</td><td>93.5</td><td>95.8</td><td>76.3</td><td>93.8</td><td>96.5</td></tr><tr><td rowspan="6">Ours</td><td rowspan="3">ΨCLS</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>32.7</td><td>58.6</td><td>69.3</td><td>32.6</td><td>58.4</td><td>68.6</td><td>69.0</td><td>90.4</td><td>94.1</td><td>68.3</td><td>89.8</td><td>94.9</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>36.3</td><td>63.1</td><td>73.4</td><td>37.6</td><td>63.1</td><td>73.7</td><td>76.5</td><td>93.1</td><td>96.0</td><td>76.2</td><td>92.6</td><td>96.3</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>39.4</td><td>64.9</td><td>74.6</td><td>40.8</td><td>66.0</td><td>75.9</td><td>77.3</td><td>93.7</td><td>96.8</td><td>79.0</td><td>94.0</td><td>96.7</td></tr><tr><td rowspan="3">ΨMLP</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>32.0</td><td>57.2</td><td>68.2</td><td>31.9</td><td>57.3</td><td>68.0</td><td>69.5</td><td>88.7</td><td>93.3</td><td>70.4</td><td>89.2</td><td>92.8</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>38.2</td><td>64.4</td><td>74.1</td><td>38.2</td><td>63.5</td><td>73.8</td><td>76.6</td><td>93.0</td><td>95.6</td><td>76.5</td><td>93.4</td><td>95.6</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>39.2</td><td>65.0</td><td>74.3</td><td>40.2</td><td>65.8</td><td>75.7</td><td>77.7</td><td>93.6</td><td>96.6</td><td>79.2</td><td>94.2</td><td>96.8</td></tr></table>
+
+To reduce appended parameters, we only apply this modification to the second FFN in MLP blocks. Finally, in one forward,  $H$  visual embeddings are obtained. Formally,
+
+$$
+\left\{\mathbf {v} _ {i} \right\} _ {i = 1} ^ {H} = \Psi_ {\mathrm {C L S}} (\mathcal {I}), \quad \left\{\mathbf {v} _ {i} \right\} _ {i = 1} ^ {H} = \Psi_ {\mathrm {M L P}} (\mathcal {I})
+$$
+
+Noting, both schemes only adds a small number of parameters (negligible for  $\Psi_{\mathrm{CLS}}$ ,  $3\% \times H$  for  $\Psi_{\mathrm{MLP}}$ ), so cost and speed for training and inference remain almost the same.
+
+After obtaining  $\{\mathbf{v}_i\}_{n = 1}^H$  we match it with the text embedding sequence  $\{\mathbf{t}_i\}_{i = 1}^M$ . Normally, we set  $M = H$  to achieve part-by-part matching, while for larger  $M$ , we set  $H < M$  and do grouped matching or free matching. We explain more details on asymmetric matching in supplementary materials. To optimize such one pipeline, we update to introduce multi-to-multi contrastive learning accordingly:
+
+$$
+\mathcal {L} _ {\mathrm {M} 2 \mathrm {M}} ^ {\mathrm {T} 2 \mathrm {I}} = - \sum_ {i = 1} ^ {K} \sum_ {j = 1} ^ {M} \log \frac {\exp \left(\left\langle \mathbf {v} _ {i , j} , \mathbf {t} _ {i , j} \right\rangle / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\left\langle \mathbf {v} _ {k , j} , \mathbf {t} _ {i , j} \right\rangle / \tau\right)}. \tag {5}
+$$
+
+The final optimization loss is  $\mathcal{L}_{\mathrm{M2M}} = (\mathcal{L}_{\mathrm{M2M}}^{\mathrm{T2I}} + \mathcal{L}_{\mathrm{M2M}}^{\mathrm{T2T}}) / 2$
+
+Inference. Unlike one-to-one CLIP, by one forward pass, we obtain  $H$  normalized image embeddings  $\{\mathbf{v}_i\}_{n=1}^H$ . To aggregate them for downstream tasks, there are many strategies, e.g., matching text embeddings with each image embeddings first, then taking max, norm max, or average (see Table 7 for details). Normally, we simply use the average to strike the balance between efficiency and performance.
+
+Besides, an additional benefit is our M2M learning well disentangles image embeddings, comparing to O2M learn
+
+ing, which allows for flexible embedding customizations when reasoning for specific tasks (see Table 8).
+
+# 4. Experiment
+
+# 4.1. Benchmark & Evaluation
+
+Training Datasets. CC3M [67] and CC12M [4] are popular for vision-language pre-training for their scale and diversity. They gather web images with alt-texts, followed by filtering and cleaning. However, most images are paired with brief, coarse-grained captions, often noisy due to captionor's bias.
+
+Re-Caption. We use powerful VLMs: InternVL2-8B [9], Minigpt4-7B [91], LLaVA1.5-13B [45], Qwen2VL-7B [1] to generate diverse (image, multi-texts) pairs. When utilizing multi-VLMs, we set the unified prompt refer to [50], ensuring the high quality of captioned texts. When adopting one VLM, we choose the classical InternVL2, and offer more details about the defined prompts and the statistics of captioned texts in supplementary materials.
+
+Testing Datasets & Metrics. For image classification, we employ ImageNet [15](-A/-R) validation set. For shot-text retrieval, MSCOCO [43] and Flickr30 [81] are two typical benchmarks. For long-context retrieval, we randomly select 5K data from Fashion200K [23] and Sharegpt4v [5] to form Fashion200-5K and Sharegpt4v-5K. For LongCLIP [85] comparison, we add Urban1K. To test the overall quality of embedding sequence, we train ClipCap [60] for image captioning and LLaVA1.5-13B [45] for all-round evaluations, by replacing vision backbone with our image encoder. All
+
+Table 2. Complex Long-Text Retrieval. On all datasets, our holistic CLIP, i.e.,  $\Psi_{\mathrm{CLS}}$  and  $\Psi_{\mathrm{MLP}}$ , shows the gratifying superiority. Using the same data, our M2M paradigm surpasses recent O2M learning [19, 50, 88] across all metrics, showing the superiority.  
+
+<table><tr><td rowspan="3" colspan="2">Method</td><td rowspan="3">Training Text</td><td rowspan="2" colspan="3">Caption</td><td colspan="6">Fashion200-5K</td><td colspan="6">Sharegpt4-5K</td></tr><tr><td colspan="3">I2T</td><td colspan="3">T2I</td><td colspan="3">I2T</td><td colspan="3">T2I</td></tr><tr><td>VLM</td><td>Prompt</td><td>Num</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td colspan="2">CLIP [63]</td><td>CC3M</td><td>-</td><td>-</td><td>1</td><td>2.2</td><td>6.2</td><td>9.5</td><td>2.6</td><td>7.4</td><td>11.8</td><td>11.0</td><td>25.9</td><td>37.1</td><td>10.2</td><td>26.0</td><td>36.4</td></tr><tr><td rowspan="3" colspan="2">O2M [19, 50, 88]</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>5.5</td><td>14.1</td><td>21.3</td><td>5.5</td><td>15.8</td><td>23.3</td><td>39.6</td><td>65.8</td><td>76.2</td><td>38.3</td><td>65.0</td><td>75.1</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>8.8</td><td>21.8</td><td>30.6</td><td>9.5</td><td>22.4</td><td>30.8</td><td>48.4</td><td>75.6</td><td>84.2</td><td>49.2</td><td>75.7</td><td>84.3</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>8.4</td><td>21.4</td><td>30.0</td><td>7.7</td><td>21.3</td><td>29.3</td><td>48.6</td><td>73.8</td><td>82.7</td><td>49.2</td><td>75.4</td><td>83.6</td></tr><tr><td rowspan="6">Ours</td><td rowspan="3">ΨCLS</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>5.5</td><td>15.2</td><td>21.7</td><td>6.1</td><td>16.5</td><td>23.8</td><td>41.3</td><td>66.7</td><td>77.0</td><td>39.9</td><td>66.3</td><td>76.2</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>9.0</td><td>23.0</td><td>32.0</td><td>9.5</td><td>24.4</td><td>32.8</td><td>51.2</td><td>76.8</td><td>85.4</td><td>52.4</td><td>77.5</td><td>85.5</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>9.2</td><td>22.2</td><td>30.4</td><td>9.0</td><td>22.2</td><td>31.0</td><td>49.4</td><td>75.1</td><td>83.3</td><td>50.6</td><td>76.9</td><td>84.4</td></tr><tr><td rowspan="3">ΨMLP</td><td rowspan="3">CC3M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>5.6</td><td>16.3</td><td>23.6</td><td>6.2</td><td>17.3</td><td>24.6</td><td>41.4</td><td>67.6</td><td>77.3</td><td>39.6</td><td>66.6</td><td>76.5</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>9.3</td><td>23.6</td><td>31.4</td><td>9.6</td><td>22.6</td><td>31.4</td><td>53.0</td><td>77.7</td><td>85.9</td><td>53.0</td><td>78.5</td><td>86.2</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>9.2</td><td>22.4</td><td>31.2</td><td>8.9</td><td>22.1</td><td>31.1</td><td>50.5</td><td>75.8</td><td>83.6</td><td>51.4</td><td>77.2</td><td>85.6</td></tr><tr><td colspan="2">CLIP [63]</td><td>CC12M</td><td>-</td><td>-</td><td>1</td><td>8.6</td><td>22.4</td><td>31.6</td><td>8.5</td><td>21.9</td><td>31.4</td><td>33.9</td><td>61.3</td><td>71.3</td><td>32.9</td><td>60.1</td><td>71.4</td></tr><tr><td rowspan="3" colspan="2">O2M [19, 50, 88]</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>12.2</td><td>28.7</td><td>38.8</td><td>11.5</td><td>28.0</td><td>38.3</td><td>54.5</td><td>78.2</td><td>86.0</td><td>53.9</td><td>79.0</td><td>87.0</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>13.2</td><td>29.5</td><td>39.6</td><td>13.8</td><td>31.2</td><td>41.3</td><td>54.8</td><td>80.2</td><td>87.8</td><td>56.0</td><td>81.2</td><td>88.7</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>15.9</td><td>35.0</td><td>45.2</td><td>16.0</td><td>35.1</td><td>46.2</td><td>61.0</td><td>83.5</td><td>90.2</td><td>62.4</td><td>84.6</td><td>90.6</td></tr><tr><td rowspan="6">Ours</td><td rowspan="3">ΨCLS</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>11.8</td><td>28.8</td><td>39.1</td><td>12.5</td><td>29.7</td><td>39.6</td><td>54.9</td><td>79.0</td><td>86.9</td><td>53.7</td><td>79.6</td><td>87.5</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>14.9</td><td>33.6</td><td>43.3</td><td>16.1</td><td>35.4</td><td>45.5</td><td>62.2</td><td>84.6</td><td>91.0</td><td>62.8</td><td>85.9</td><td>91.5</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>17.3</td><td>36.7</td><td>46.9</td><td>17.8</td><td>38.7</td><td>49.3</td><td>61.5</td><td>83.9</td><td>90.6</td><td>63.0</td><td>85.7</td><td>91.8</td></tr><tr><td rowspan="3">ΨMLP</td><td rowspan="3">CC12M+Caption</td><td>Uni</td><td>Uni</td><td>2</td><td>12.2</td><td>29.2</td><td>39.6</td><td>11.9</td><td>28.7</td><td>39.0</td><td>55.1</td><td>78.7</td><td>86.5</td><td>54.5</td><td>79.5</td><td>87.0</td></tr><tr><td>Uni</td><td>Multi</td><td>5</td><td>16.7</td><td>35.7</td><td>45.8</td><td>16.4</td><td>35.3</td><td>46.1</td><td>63.1</td><td>85.6</td><td>91.0</td><td>64.4</td><td>86.2</td><td>91.7</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>17.2</td><td>36.6</td><td>46.6</td><td>17.7</td><td>37.8</td><td>49.0</td><td>62.8</td><td>83.4</td><td>90.5</td><td>62.8</td><td>85.7</td><td>91.4</td></tr></table>
+
+above testing sets are standardized for the sake of fairness.
+
+We follow conventions for evaluation: using the Top-1/5 accuracy for classification; B@4 and CIDEr for captioning; R@1/5/10 for image-text retrieval; and follow [18] to evaluate LLaVA on [20, 22, 40, 51, 52, 59, 66, 82].
+
+# 4.2. Comparison with State-Of-The-Art
+
+Across many downstream tasks, we compare fully to vanilla CLIP [63] and its variants [19, 50, 85, 88] that use one-to-multi (O2M) contrastive learning to show our superiority.
+
+Elementary Short-Text Retrieval is evaluated in Table 1 on MSCOCO and Flickr30. We ablate both the multi-to-multi (M2M) learning paradigm and (image, multi-text) dataset, comparing it with the one-to-multi (O2M) approach. M2M consistently outperforms O2M, with gains of  $1.5 - 3\%$  on multi-VLMs data and  $0.3 - 1.5\%$  on multiprompts data. Notably, multi-prompts data see larger improvements  $(3 - 6\%)$  using either  $\Psi_{\mathrm{CLS}}$  or  $\Psi_{\mathrm{MLP}}$ . This highlights M2M's effectiveness in refining the embedding space, aligning diverse visuals with texts. By enabling holistic alignments, M2M fundamentally mitigates mis-clustering and demonstrates robust resistance to potential text noise, providing the cohesive embedding space.
+
+To enforce text diversity from VLMs, we use a variety of prompts reflecting multi-view and multi-level perspectives. Compared to using uni-view captions from InternVL2-8B, our approach yields significant improvements— $8 - 10\%$  on Flickr30 and  $5 - 7\%$  on MSCOCO. Notably, our multiprompt results match those from multi-VLMs datasets, which use more auxiliary knowledge and simplified (gen
+
+eral) texts. These findings suggest that our (image, multi-text) datasets combined with M2M contrastive learning create a more robust embedding space.
+
+Complex Long-Text Retrieval is implemented in Table 2 on the Fashion200-5K and Sharegpt4v-5K datasets, to evaluate the VLPs' efficacy in practical scenarios. In terms of pre-training optimization paradigm, the results illustrated that, M2M consistently outperforms O2M on (image, multi-texts) datasets, with gains of  $4 - 7\%$  on Sharegpt4v-5K and  $1 - 4\%$  on Fashion200-5K. And noting that, Fashion200-5K is particularly complex, with  $R@1$  scores only in the range of  $9 - 15\%$ , making these improvements quite substantial.
+
+When comparing models trained with (image, uni-text) versus (image, multi-texts) datasets, we observe marked advancements, with an  $8\%$  gain on Sharegpt4v-5K and a  $4\%$  gain on Fashion200-5K. Besides that, to obtain high-quality (image, multi-texts) pairs, explicit prompt differences surpass implicit VLMs groups, underscoring the value of holistic data construction for enhanced performance.
+
+In Table 4, we also compare with LongCLIP [85] and original OpenAI-CLIP. Although our method is only trained on CC12M (without Sharegpt4v data), it significantly outperforms OpenAI CLIP-B/16 trained with Laion400M and O2M trained on CC12M. Even though LongCLIP is finetuned using Sharegpt4v-1M data on OpenAI CLIP or O2M, its performance is still far below ours, proving our superiority of data curation and M2M learning.
+
+Zero-Shot Image Classification. For Table 3, we present evaluations on several widely-recognized benchmarks for classification. While M2M contrastive learning consistently
+
+Table 3. Zero-shot Image Classification on CC12m. Both diverse (image, multi-texts) data and M2M learning bring clear gains.  
+
+<table><tr><td rowspan="2" colspan="2">Method</td><td rowspan="2">Training Text</td><td colspan="3">Caption</td><td colspan="2">ImageNet</td><td colspan="2">ImageNet-A</td><td colspan="2">ImageNet-R</td></tr><tr><td>VLM</td><td>Prompt</td><td>Num</td><td>Top1</td><td>Top5</td><td>Top1</td><td>Top5</td><td>Top1</td><td>Top5</td></tr><tr><td colspan="2">CLIP [63]</td><td>CC12M</td><td>-</td><td>-</td><td>1</td><td>39.0</td><td>66.9</td><td>10.1</td><td>33.2</td><td>49.2</td><td>74.1</td></tr><tr><td rowspan="3" colspan="2">O2M [19, 50, 88]</td><td>CC12M</td><td>Uni</td><td>Uni</td><td>2</td><td>43.1</td><td>71.4</td><td>12.1</td><td>36.8</td><td>54.7</td><td>78.8</td></tr><tr><td rowspan="2">+Caption</td><td>Uni</td><td>Multi</td><td>5</td><td>45.8</td><td>74.3</td><td>17.6</td><td>46.4</td><td>59.6</td><td>81.4</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>46.5</td><td>75.0</td><td>16.0</td><td>44.9</td><td>60.7</td><td>83.5</td></tr><tr><td rowspan="6">Ours</td><td rowspan="3">ΨCLS</td><td>CC12M</td><td>Uni</td><td>Uni</td><td>2</td><td>43.5</td><td>71.6</td><td>12.0</td><td>36.5</td><td>54.9</td><td>79.2</td></tr><tr><td rowspan="2">+Caption</td><td>Uni</td><td>Multi</td><td>5</td><td>48.6</td><td>76.6</td><td>18.4</td><td>47.5</td><td>62.1</td><td>84.6</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>46.8</td><td>75.2</td><td>16.8</td><td>44.8</td><td>65.0</td><td>86.0</td></tr><tr><td rowspan="3">ΨMLP</td><td>CC12M</td><td>Uni</td><td>Uni</td><td>2</td><td>43.0</td><td>71.0</td><td>11.2</td><td>35.2</td><td>54.7</td><td>79.0</td></tr><tr><td rowspan="2">+Caption</td><td>Uni</td><td>Multi</td><td>5</td><td>48.1</td><td>76.6</td><td>19.0</td><td>48.1</td><td>61.6</td><td>84.0</td></tr><tr><td>Multi</td><td>Uni</td><td>5</td><td>46.6</td><td>75.3</td><td>16.3</td><td>44.7</td><td>63.9</td><td>85.5</td></tr></table>
+
+Table 4. Comparison with LongCLIP [85] & OpenAI CLIP.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Urban1k</td><td colspan="2">Fashion200-5k</td><td colspan="2">Sharegpt4v-5k</td></tr><tr><td>I2T</td><td>T2I</td><td>I2T</td><td>T2I</td><td>I2T</td><td>T2I</td></tr><tr><td>OpenAI-CLIP</td><td>68.1</td><td>56.1</td><td>13.1</td><td>12.0</td><td>49.4</td><td>45.8</td></tr><tr><td>+LongCLIP</td><td>78.9</td><td>79.5</td><td>13.0</td><td>12.3</td><td>53.1</td><td>57.0</td></tr><tr><td>O2M CC12M</td><td>72.0</td><td>71.2</td><td>13.2</td><td>13.8</td><td>54.8</td><td>56.0</td></tr><tr><td>+LongCLIP</td><td>77.2</td><td>77.1</td><td>13.2</td><td>13.6</td><td>62.4</td><td>63.7</td></tr><tr><td>M2M CC12M</td><td>79.6</td><td>81.9</td><td>16.7</td><td>16.4</td><td>63.1</td><td>64.4</td></tr></table>
+
+Table 5. Image-to-Text Captioning. We train ClipCap [60] using our holistic CLIP to show the power of M2M contrastive learning.  
+
+<table><tr><td rowspan="2" colspan="2">Method</td><td rowspan="2">Training Text</td><td colspan="2">COCO Caption</td></tr><tr><td>B@4</td><td>CIDEr</td></tr><tr><td colspan="2">O2M [19, 50, 88]</td><td>CC3M</td><td>26.5</td><td>74.7</td></tr><tr><td rowspan="2">Ours</td><td>ΨCLS</td><td>27.2</td><td>76.5</td><td></td></tr><tr><td>ΨMLP</td><td>27.6</td><td>76.7</td><td></td></tr><tr><td colspan="2">O2M [19, 50, 88]</td><td rowspan="3">CC12M</td><td>27.0</td><td>76.8</td></tr><tr><td rowspan="2">Ours</td><td>ΨCLS</td><td>28.6</td><td>81.6</td></tr><tr><td>ΨMLP</td><td>28.8</td><td>82.1</td></tr></table>
+
+yields substantial improvements, it is particularly noteworthy that models trained on the multi-prompts and uni-VLM setting outperform the multi-VLMs and uni-prompt setting. This further substantiates the critical role of comprehensive textual alignment in advancing model performance.
+
+Image-to-Text Captioning. Table 5 assesses the effectiveness of our holistic CLIP, for dense tasks such as captioning. We adapt ClipCap [60] by substituting its vision prefix through our pre-trained visual encoder. On both CC3M and CC12M datasets, consistent performance improvements are revealed by training with (image, multi-texts) pairs, again demonstrating that M2M paradigm's outstanding capability in effectively capturing and integrating semantics.
+
+All-Round Abilities. To further demonstrate our superiority for the whole visual sequence, we leverage LLaVA1.5-13B as the VLM and replace its visual backbone with pretrained visual encoder of holistic CLIP  $\Psi_{\mathrm{CLS}}$ . Table 6 evaluates on a diverse set of benchmarks [18]. Both M2M learning and (image, multi-texts) data produce significant advantages. Across nearly all the benchmarks, M2M consistently outperforms O2M, indicating that M2M not only captures powerful embedding summaries, but also enhances quality
+
+for the whole visual token sequence. Moreover, multi-view, multi-level texts markedly strengthen model's abilities, further validating the efficacy of our idea.
+
+# 4.3. Ablation Study
+
+To form our holistic CLIP pipeline, M2M contrastive learning and (image, multi-texts) paired data are the keys. Next, we dissect their effectiveness.
+
+Efficacy of Holistic Image-Text Data. We present models trained with (image, uni-text) pairs and (image, multi-texts) pairs in Table 1, 2, 3, and 6. In terms of performance, using prompts of diversified definitions to steer one VLM (InternVL2) reaches comparable results with using one prompt to drive substantially larger VLM pools, and both show significant gains. On object-oriented image classification and long-context retrieval, the former performs even better.
+
+Efficacy of Multi-to-Multi Contrastive Learning. Across various benchmarks using the same dataset, M2M consistently outperforms O2M, with especially notable gains under (image, multi-texts) settings. With the increase in text diversity (caption number from 2 to 5), the advantages of M2M are gradually becoming apparent, which is expected, given that M2M is designed for multi-to-multi matching. Table 6 further illustrates that M2M also strengthens embedding learning across the whole visual sequence.
+
+Moreover,  $\Psi_{\mathrm{CLS}}$  and  $\Psi_{\mathrm{MLP}}$  bring similar performance across all benchmarks, suggesting M2M contrastive learning itself is the principal driver behind these improvements.
+
+Fusion During Inference. When reasoning, we integrate the embedding set learned by the holistic CLIP to perform image-text matching tasks. In Table 7, three common fusion strategies are assessed, and the AVG-based fusion outperforms the others, in terms of performance. For the actual efficiency, the AVG-based one also wins: when calculating cosine similarity, we can first average on image embeddings, then take dot product with text embeddings, thus avoiding additional computational cost.
+
+Flexible Embedding Disentanglement. In the tables above, we average all image embeddings across tasks. However, since embeddings can be disentangled, we can
+
+Table 6. All-Round Embedding Quality on Whole Visual Token Sequence. We train LLaVA1.5-13B by replacing its vision backbone by our image encoder of pre-trained holistic CLIP  ${\Psi }_{\mathrm{{CLS}}}$  ,and the good results show better embeddings along the whole visual sequence.  
+
+<table><tr><td>Method</td><td>Training Text</td><td>Caption Prompt</td><td>MMBench EN [51]</td><td>CC Bench</td><td>MME</td><td>A- OKVQA</td><td>Hallusion Bench</td><td>MMVeT</td><td>OCR VQA</td><td>SEED BenchIMG</td><td>Science QA</td></tr><tr><td>O2M</td><td>CC3M</td><td rowspan="2">Multi</td><td>41.2</td><td>2.7</td><td>842.8</td><td>60.2</td><td>29.2</td><td>15.7</td><td>26.4</td><td>44.4</td><td>63.9</td></tr><tr><td>Ours</td><td>+Caption</td><td>41.7</td><td>2.9</td><td>944.6</td><td>63.2</td><td>32.2</td><td>16.4</td><td>26.3</td><td>47.9</td><td>64.1</td></tr><tr><td>O2M</td><td rowspan="2">CC12M</td><td rowspan="2">Uni</td><td>42.1</td><td>3.3</td><td>909.5</td><td>62.6</td><td>34.5</td><td>17.4</td><td>27.6</td><td>48.0</td><td>63.9</td></tr><tr><td>Ours</td><td>42.3</td><td>3.0</td><td>930.2</td><td>61.1</td><td>34.3</td><td>18.5</td><td>27.5</td><td>45.4</td><td>63.9</td></tr><tr><td>O2M</td><td rowspan="2">+Caption</td><td rowspan="2">Multi</td><td>42.6</td><td>3.3</td><td>966.7</td><td>61.2</td><td>34.3</td><td>17.9</td><td>27.1</td><td>45.5</td><td>64.6</td></tr><tr><td>Ours</td><td>50.3</td><td>5.9</td><td>997.5</td><td>64.5</td><td>38.9</td><td>19.7</td><td>27.8</td><td>51.2</td><td>65.4</td></tr></table>
+
+Table 7. Ablation Study for the Embedding Fusion. The AVG-based one surpasses others in both performance and efficiency.  
+
+<table><tr><td rowspan="2">Fusion Strategy</td><td colspan="2">COCO</td><td colspan="2">Flickr30</td><td rowspan="2">ImageNet-R Top-1</td></tr><tr><td>I2T</td><td>T2I</td><td>I2T</td><td>T2I</td></tr><tr><td>Max</td><td>36.3</td><td>35.8</td><td>74.0</td><td>73.8</td><td>60.5</td></tr><tr><td>Norm-Max</td><td>36.1</td><td>35.2</td><td>74.5</td><td>74.7</td><td>60.9</td></tr><tr><td>Average</td><td>38.2</td><td>38.2</td><td>76.6</td><td>76.5</td><td>61.6</td></tr></table>
+
+Table 8. Embedding Customization. On CC12M, we decompose embeddings and select parts to combine for specific tasks. 'Main-Obj' focuses on main objects, 'Long-Text' matches rich details.  
+
+<table><tr><td rowspan="2">Embedding Focus</td><td colspan="2">COCO</td><td colspan="2">Sharegpt4-5k</td><td rowspan="2">ImgNet Top-1</td><td rowspan="2">ImgNet-R Top-1</td></tr><tr><td>I2T</td><td>T2I</td><td>I2T</td><td>T2I</td></tr><tr><td>All</td><td>38.2</td><td>38.2</td><td>63.1</td><td>64.4</td><td>48.1</td><td>61.6</td></tr><tr><td>Main Obj</td><td>37.7</td><td>36.5</td><td>63.1</td><td>63.4</td><td>49.4</td><td>63.0</td></tr><tr><td>Long Text</td><td>38.5</td><td>38.0</td><td>63.5</td><td>64.7</td><td>48.9</td><td>62.8</td></tr></table>
+
+Table 9. Ablation Study for the Text Number on CC3M. Since visual embeddings are decomposable, we can tear down to fit for specific tasks. The more captions used, the better the performance.  
+
+<table><tr><td rowspan="2">Text Number</td><td rowspan="2">Text Similarity</td><td colspan="2">COCO</td><td colspan="2">Flickr30</td><td rowspan="2">ImageNet Top-1</td></tr><tr><td>I2T</td><td>T2I</td><td>I2T</td><td>T2I</td></tr><tr><td>2</td><td>0.56</td><td>20.1</td><td>20.6</td><td>50.9</td><td>51.2</td><td>29.1</td></tr><tr><td>3</td><td>0.52</td><td>25.3</td><td>25.4</td><td>58.8</td><td>58.3</td><td>33.7</td></tr><tr><td>4</td><td>0.50</td><td>28.9</td><td>29.0</td><td>61.7</td><td>63.2</td><td>38.9</td></tr><tr><td>5</td><td>0.48</td><td>28.2</td><td>27.4</td><td>63.7</td><td>63.9</td><td>38.8</td></tr><tr><td>use 4 of 5</td><td>0.48</td><td>28.9</td><td>29.2</td><td>64.3</td><td>63.9</td><td>40.0</td></tr></table>
+
+customize them during inference-for example, selecting partial embeddings suited to a specific task before averaging. Table 9 tests three simple customizations: focusing on main objects, rich details, or all information. Results show that different feature combinations enhance performance and improve interpretability.
+
+This disentanglement also enhances robustness by identifying and disabling noisy textual branches during inference, minimizing adverse effects. Notably, "noise" is task-dependent, but our method enables flexible denoising without retraining or fine-tuning, further improving stability.
+
+Efficacy of Text Number. Table 9 examines the impact of text quantity. As the model encounters more diverse descriptive texts, performance improves. Note that, adding a fifth text with background details enhances semantic representation but may affect some downstream tasks. To mitigate this, we exclude the background branch during infer
+
+![](images/92c139d2a57bc47980d7c4940460638aeecc87192b56b080d759e9ef867a16e8.jpg)  
+Background
+
+![](images/fbdbf23327194f562db8aaf9b8f3b81a58f62969dca0880b50e4dcc99f6a60d7.jpg)  
+Main Object
+
+![](images/e096ff2f2c9bc2f47630cf10287727455a8e02d458bc0529847622daf40919fe.jpg)  
+Details
+
+![](images/277f125a10dbd1eebc09ed9a26c2aca6d2f77198abb0426518f1565370187399.jpg)  
+Figure 3. Attention Visualization of Holistic CLIP's Vision. Vision is naturally decomposed by aligning with various texts.
+
+![](images/5e8305d46650eec1a44e11b0ee7472db5323a15ec9987eb6adcbc4c21181d201.jpg)
+
+![](images/43a93a2a0b1321521ad5c30454a5e0e7900d68d36009f567fa6cf1043c4f1e5e.jpg)
+
+ence, yielding optimal performance across tasks. Additionally, as text count increases from 2 to 5, the average similarity between texts decreases, indicating greater diversity.
+
+# 4.4. Visualization of Holistic Alignment
+
+To assess visual embedding quality, we highlight the top  $20\%$  of visual patches with the highest attention scores in red, with darker shades indicating higher scores (Fig. 3). Different text types guide distinct attention patterns, capturing multi-view and multi-level visual diversity. This alignment validates our M2M contrastive learning while also highlighting the impact of data diversity, emphasizing the need for holistic (image, multi-text) pairs.
+
+# 5. Conclusion
+
+This paper presents holistic CLIP to advance beyond myopic paradigms. By (image, multi-texts) data and multi-to-multi contrastive learning, we effectively improve the versatility and comprehensiveness of cross-modal embeddings. With extensive experiments and massive ablations, our idea shows superior performance in image-text retrieval, classification, many dense visual tasks, achieving notable gains over OpenAI's CLIP. This paper highlights the critical role of all-round aligned data and optimization for CLIP, inspiring the further prosperity of vision-language models.
+
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+# Advancing Semantic Future Prediction through Multimodal Visual Sequence Transformers
+
+Efstathios Karypidis $^{1,3}$  Ioannis Kakogeorgiou $^{1}$  Spyros Gidaris $^{2}$  Nikos Komodakis $^{1,4,5}$
+
+$^{1}$ Archimedes, Athena Research Center, Greece  $^{2}$ valeo.ai
+
+$^{3}$ National Technical University of Athens  $^{4}$ University of Crete  $^{5}$ IACM-Forth
+
+![](images/567807830d3b0c2ad126d6217455416461659b420d97e6d3aed85380f2fa776d.jpg)  
+Figure 1. Our framework predicts future semantic segmentation and depth maps using a multimodal transformer architecture. Leveraging masked visual modeling and cross-modal fusion, it excels in future semantic prediction, achieving state-of-the-art results in both tasks.
+
+# Abstract
+
+Semantic future prediction is important for autonomous systems navigating dynamic environments. This paper introduces FUTURIST, a method for multimodal future semantic prediction that uses a unified and efficient visual sequence transformer architecture. Our approach incorporates a multimodal masked visual modeling objective and a novel masking mechanism designed for multimodal training. This allows the model to effectively integrate visible information from various modalities, improving prediction accuracy. Additionally, we propose a VAE-free hierarchical tokenization process, which reduces computational complexity, streamlines the training pipeline, and enables end-to-end training with high-resolution, multimodal inputs. We validate FUTURIST on the Cityscapes dataset, demonstrating state-of-the-art performance in future semantic segmentation for both short- and mid-term forecasting. We provide the implementation code and model weights at https://github.com/Sta8is/FUTURIST.
+
+# 1. Introduction
+
+Future prediction is crucial for autonomous agents, enabling them to navigate complex, dynamic environments and make informed real-time decisions. By anticipating potential sce
+
+narios and future outcomes, these systems can effectively plan their actions, adapt to changing conditions, and ensure safe and efficient operation [15].
+
+Recent research has increasingly focused on predicting raw RGB values for future video frames [18, 24, 25, 28, 30, 45, 64, 80, 83, 84]. Although these methods can create realistic and diverse scenarios for simulation and testing, forecasting RGB frames remains highly challenging due to the data's inherent complexity and high-dimensional nature. An alternative approach is to predict semantic modalities, which offers several advantages [11, 41, 43, 47, 61]. First, forecasting semantic information simplifies the prediction process by avoiding the need to replicate low-level details that are often less critical for decision-making. Second, semantic modalities provide information that is directly relevant to an agent's tasks. For instance, when navigating around or avoiding a moving obstacle, predicting depth information is far more useful than modeling the scene's precise visual appearance.
+
+Motivated by these observations, we propose a novel framework for future semantic prediction. Our approach is built on a multimodal visual sequence transformer architecture that is optimized for the joint prediction of multiple modalities and trained using a masked visual modeling objective. It accepts inputs from various modalities across
+
+past frames and predicts the same set of modalities for future frames. This multimodal capability is crucial for practical applications, as different modalities often offer complementary insights that, when combined, enhance the agent's overall understanding of its environment. Moreover, using multiple semantic modalities has a synergistic effect: they can mutually improve the accuracy of future predictions due to the natural correlations between them, which transformers are well-suited to capture. Our experiments confirm the efficacy of this synergistic approach, which is also one of the contributions of this work.
+
+An important consideration in developing a multimodal video transformer is to make high-resolution images efficient for transformer processing while ensuring the easy integration of multiple modalities [3-5, 20, 31, 32, 42, 46, 67, 76]. A seemingly obvious approach, inspired by recent transformer-based video generative methods, might involve using Variational Autoencoder (VAE)-based embedding techniques [36, 55, 69, 79, 83, 84]. However, this approach comes with significant drawbacks, including the need to train separate VAEs for each modality, making it impractical for multimodal setups. Moreover, VAE-based methods face inherent challenges, such as difficulties in stabilizing training [17, 58], which further complicates the integration of diverse modalities. These limitations underscore the need for a more efficient solution to handle multimodal integration effectively. Thus, we adopt a VAE-free embedding strategy, employing a hierarchical embedding technique that progresses from pixel-level to patch-level embeddings for each modality. This end-to-end approach simplifies the training pipeline and eliminates the dependency on pre-trained VAEs. To further improve the efficiency and effectiveness of our transformer training, we introduce a cross-modality fusion mechanism within our embedding process. This technique reduces the token sequence length by merging tokens from different modalities that share the same spatial-temporal location, producing a more compact and computationally efficient representation.
+
+A key aspect of our approach is that our multimodal transformer can be trained without ground truth label maps for any modality. Instead, we demonstrate that using pseudo-labels generated by off-the-shelf foundation models [65, 82] is sufficient. Remarkably, even under this relaxed supervision, we demonstrate that our multimodal visual sequence transformer generalizes well and achieves state-of-the-art performance.
+
+In summary, our contributions are the following:
+
+- We introduce FUTURIST, a method for future multimodal semantic prediction using a simple, efficient, unified transformer architecture that leverages a masked visual modeling task and offers easy adaptation to various modalities. To our knowledge, this is the first work to employ a transformer architecture for multimodal seman
+
+tic future prediction, addressing a gap in prior research.
+
+- We propose a simple hierarchical tokenization process integrated directly into our multimodal transformer, eliminating the need for costly VAE-based tokenization methods and enabling end-to-end training.  
+- We develop a specifically adapted masking mechanism for multimodal training, enabling the model to efficiently leverage visible information across modalities.  
+- Finally, we demonstrate the effectiveness of our unified approach by applying it to future semantic segmentation and depth prediction (see Figure 1), achieving state-of-the-art results in both domains, highlighting the synergistic benefits of leveraging multimodal information for future prediction.
+
+# 2. Related Work
+
+Future Video Forecasting. Future video forecasting and generation have garnered significant attention [49] in the computer vision and machine learning communities due to their potential applications in various domains, including autonomous driving and robotics. Early approaches to this task often relied on recurrent neural networks (RNNs) such as Convolutional Long Short Term Memory (Conv-LSTM) architectures [7, 19, 38, 47, 73, 75, 78] to capture temporal dependencies in video sequences. However, these methods frequently struggled with long-term predictions and maintaining visual consistency and realism. Other works have leveraged generative adversarial networks (GANs) and variational autoencoders (VAEs) [2, 7, 37, 72, 79] to produce more realistic and diverse future frames. More recently, techniques leveraging diffusion models [18, 27, 28], demonstrate impressive visual results capturing both spatial and temporal relationships. Finally, inspired from their success in natural language models, some works extend the ideas of auto-regressive and masked modeling objectives to images [8, 9] and videos [24, 74, 83, 84] and employ pure transformer models in conjunction with a tokenization module [17, 58, 70]. In our work, we propose a method that directly predicts semantic modalities for future frames without the need for complex tokenization modules, offering a simpler and more efficient approach to future forecasting.
+
+Semantic Future Prediction. Future segmentation and depth prediction aim to use past frames to predict the segmentation masks and depth maps of future frames. In semantic segmentation, Luc et al. [43] introduced the first method for predicting future semantics by exploring different input configurations. They experimented with using previous RGB frames, past segmentation maps, or a combination of both. Their results showed that a two-phase approach—predicting future frame pixel values and then using these predictions to generate segmentation masks—was less effective. We further validate this finding by applying recent diffusion-based, state-of-the-art driving world mod
+
+![](images/4a71c333974aaa77dbdea68369e136c5ca4bd17b17d2fa484a6a51f1d61e5561.jpg)  
+Figure 2. End-to-End Trainable Multimodal Visual Sequence Transformer. Our framework employs modality-specific embedders to map inputs into tokens. Then, these token embeddings are fused through token-wise concatenation to form the combined input embedding  $\mathbf{Z}$ . Next, a masked transformer processes  $\mathbf{Z}$ , capturing spatiotemporal dependencies between modalities, and outputs  $\tilde{\mathbf{Z}}$ . Finally, modality-specific decoders produce future frame predictions for each modality based on  $\tilde{\mathbf{Z}}$ , enabling efficient and accurate multimodal semantic future prediction within a unified architecture. Tokens are shown in 2D (not flattened) for visualization purposes.
+
+els for future RGB frame generation.
+
+To better capture the temporal nature of videos, several approaches have been proposed. Focusing on the architecture, [47, 66] integrated ConvLSTM modules, while [10] introduced an attention mechanism. [11] adopted a teacher-student framework, where the student performs the forecasting task, and the teacher provides semantic guidance through knowledge distillation. Another promising direction involves flow-based forecasting [12, 33, 62, 63, 68], where the prediction model uses optical flow information. Jin et al. [33] developed a method that predicts both optical flow and future semantic segmentations by allowing the segmentation model to leverage motion features from a flow-predicting network. Terwilliger et al. [68] further improved this by using a convolutional LSTM to predict optical flow and then warp the last segmentation mask. In a similar approach, Ciamarra et al. [12] applied optical flow warping to instance segmentation forecasting.
+
+In recent work, [62, 63] proposed the F2MF model, which extends the F2F (Feature-to-Feature) approach [44], where features are regressed from observed frames, by warping deep features to generate future semantic segmentation. For instance and panoptic segmentation forecasting, several methods [22, 23, 54] have been proposed that extend beyond semantic boundaries to predict individual object instances. For future depth prediction, Liu et al. [41, 48] tackled the problem of predicting depth maps for unobserved frames. Depth prediction was also explored in [13, 29, 53] as part of multimodal prediction, where depth was combined with other modalities like optical flow, semantic segmentation, and scene understanding to enhance the accuracy and robustness of future scene interpretations.
+
+In our work, we also focus on multimodal semantic future prediction. However, unlike prior approaches, we use a multimodal visual sequence transformer rather than convolutional or recurrent neural networks. We treat the next-frame prediction task as a masked visual modeling problem [8, 24]. By using transformer architectures [71], we can better model long-range dependencies in the data. For an extended related work regarding multimodal learning with Transformers, refer to Suppl. Sec. 6.
+
+# 3. Multimodal Visual Sequence Transformer
+
+We propose FUTURIST, a flexible framework for semantic future prediction that processes video sequences in a spatially dense, multimodal way. Our framework uses a video sequence of  $N_{c}$  frames from timesteps  $\{t - N_{c} + 1,\dots ,t\}$  as context for making predictions. These input frames may represent any semantic modality, such as semantic segmentation or depth maps, or multiple modalities simultaneously. The objective is to predict future frames for the input modalities in a frame-wise autoregressive manner, with a focus on the short-term  $(t + 1)$  and mid-term  $(t + 3)$  future, consistent with previous studies [11, 40, 43, 44].
+
+To accomplish this, we use a multimodal visual sequence transformer and approach the next-frame prediction task as a masked visual modeling problem [8, 24]. The transformer processes a sequence of  $N = N_{c} + N_{p}$  frames, comprising both context frames  $(N_{c})$  and target future frames  $(N_{p})$ . Future frames are either fully or partially masked at the input, with the transformer's task being to predict the missing values. Typically, we set  $N_{p} = 1$ , predicting one future frame at a time. An overview of this method is shown in Figure 2.
+
+While our framework can model individual modalities
+
+![](images/30a3b8da5884d053b6f53b399d9833feb6a55f835fbec1ae256c2e37f9df8cd2.jpg)  
+Figure 3. Modality Embedder. Our method embeds per-pixel values and aggregates them into patch tokens.
+
+like semantic segmentation or depth maps, it is particularly effective in jointly modeling these visual modalities. Moreover, it is adaptable and can incorporate other modalities such as instance or panoptic segmentation and optical flow.
+
+Pseudo-Labeled Multimodal Training Dataset. Manual annotation of video sequences for semantic segmentation or depth maps is labor-intensive. To address this, we generate these maps using off-the-shelf pretrained models. Specifically, we use Segmenter [65], a well-established transformer model for semantic segmentation, along with DepthAnythingV2 [82], a foundation model that offers improved depth maps compared to its predecessor [81].
+
+# 3.1. VAE-free Multimodal Embedder
+
+Integrated Per-Modality Tokenization Process. For each modality  $\mathcal{I}$ , let  $\mathbf{X}_{\mathcal{I}} \in \mathcal{L}_{\mathcal{I}}^{N \times H \times W}$  represent a video sequence of  $N$  frames, where  $\mathcal{L}_{\mathcal{I}}$  is the set of possible discrete pixel values for modality  $\mathcal{I}$ . For instance,  $\mathcal{L}_{\mathcal{I}}$  could be semantic labels for segmentation or discrete depth values for depth prediction. To make high-resolution images manageable for transformer processing, most generative transformer methods pre-train VAE-based tokenizers that convert high-resolution images to a reduced set of token embeddings,  $L$ , where  $L \ll H \cdot W$ .
+
+Instead of using pre-trained VAE-based tokenizers, we propose a simple two-stage hierarchical tokenization process, illustrated in Figure 3, that is integrated directly into the video transformer model. First, our tokenizer performs per-pixel embedding, converting  $\mathbf{X}_{\mathcal{I}}$  into continuous per-pixel embeddings  $\mathbf{X}_{\mathcal{I}}^{E} \in \mathbb{R}^{N \times H \times W \times C_{\mathcal{I}}}$  using a trainable embedding matrix  $W_{\mathcal{I}} \in \mathbb{R}^{|C_{\mathcal{I}}| \times C_{\mathcal{I}}}$ . To reduce memory usage and the number of parameters, we use low-dimensional embeddings (e.g.,  $C_{\mathcal{I}} = 10$ ). Next, we convert  $\mathbf{X}_{\mathcal{I}}^{E}$  into patch token embeddings by dividing it into  $P \times P$  patches, flattening them, and applying a linear projection with parameters  $W_{\mathcal{I}}' \in \mathbb{R}^{(P^2 \cdot C_{\mathcal{I}}) \times d_{\mathcal{I}}}$ . This results in the final token embeddings  $\mathbf{Z}_{\mathcal{I}} \in \mathbb{R}^{(N \cdot L) \times d_{\mathcal{I}}}$ , where  $L = \frac{H \cdot W}{P^2}$  and  $d_{\mathcal{I}}$  is the embedding dimension for modality  $\mathcal{I}$ . By default, we use  $P = 16$  as patch size. By using low-dimensional embeddings in the first stage, we ensure that the number of parameters  $(P^2 \cdot C_{\mathcal{I}}) \times d_{\mathcal{I}}$  in  $W_{\mathcal{I}}'$  remains manageable.
+
+Our approach simplifies tokenization compared to other video generative transformers that often rely on complex VAE-based tokenizers, with either continuous [39, 69] or discrete tokenization strategies [83, 84], such as VQ-VAE
+
+[17, 58, 70]. In contrast, our VAE-free method integrates tokenization directly into the video transformer model. This integration streamlines the training process by enabling end-to-end training of the entire video generation pipeline and eliminates the need for training separate tokenization models for each modality. This reduces computational overhead and results in a more efficient and scalable framework for future semantic prediction.
+
+Efficient Multimodality Fusion. We aim to leverage the transformer's ability to capture dependencies across modalities while keeping computation manageable when processing all  $K$  available modalities. Concatenating the  $K$  per-modality video sequences into a single long sequence of length  $K \cdot N \cdot L$  would slow down processing due to the quadratic complexity of self-attention. Instead, we adopt an early fusion approach to create a combined embedding  $\mathbf{Z} \in \mathbb{R}^{(N \cdot L) \times d}$ , where  $d$  is the transformer's hidden dimension, by merging the per-modality embeddings  $\{\mathbf{Z}_{\mathcal{T}_i}\}_{i=1}^K$  along the embedding dimension.
+
+Specifically, we explored two simple early-fusion strategies: (i) CONCAT, which concatenates embeddings across the embedding dimension, i.e.,  $\mathbf{Z} = \mathrm{concat}(\mathbf{Z}_{\mathcal{I}_1},\mathbf{Z}_{\mathcal{I}_2},\ldots ,\mathbf{Z}_{\mathcal{I}_K})\in \mathbb{R}^{(N\cdot L)\times d}$ . Here, embedding dimensions are chosen such that  $\sum_{i = 1}^{K}d_{\mathcal{I}_i} = d$  (e.g., for segmentation  $\mathcal{S}$  and depth  $\mathcal{D}$ , we set  $d_{\mathcal{S}} = d_{\mathcal{D}} = \frac{d}{2}$ ). (ii) ADD, where embeddings are summed, i.e.,  $\mathbf{Z} = \sum_{i = 1}^{K}\mathbf{Z}_{\mathcal{I}_i}$ . Here, the per-modality embedding dimensions are set to  $d$ . Our experiments show that CONCAT gives better results, and we use it by default.
+
+# 3.2. Multimodal Masking Strategies
+
+During training, we keep all tokens from the  $N_{c}$  context (past) frames intact and randomly mask a subset of tokens from the  $N_{p}$  future frames. Let  $\mathbf{M}_{\mathcal{I}} \in \{0,1\}^{N_p \cdot L}$  be a binary mask indicating which patch tokens in the  $N_{p}$  future frames are masked (1) or visible (0) for each modality  $\mathcal{I}$ . To create a mask  $\mathbf{M}$ , we first sample a masking ratio  $r \in (0,1)$  (selected uniformly) and adjust it with a scheduling function  $\gamma(r)$ . The final number of masked tokens for the future frames is  $\lfloor \gamma(r) \cdot N_p \cdot L \rfloor$ .
+
+To enhance masked visual modeling, we allow masking to occur across different modalities for each future frame token. We explored the following multimodal masking strategies, illustrated in Figure 4:
+
+- Fully-independent: Each modality  $\mathcal{I}$  generates its own independent mask. We explore two variants: one with independently chosen masking ratios  $r$  per modality and another with a shared masking ratio  $r$  across modalities.  
+- Fully-shared: All modalities share a single, randomly-sampled, mask M, meaning the same tokens are masked for each modality.  
+- Partially-shared + Exclusive: First, a common initial mask M is sampled for all modalities. Then, to create
+
+![](images/c0fa421b5427868d9a12280357e628012876e57b302a3dcd41842a13fd056afc.jpg)  
+Figure 4. Masking strategies. We explored four strategies for masking future-frame tokens across modalities: Fully Masked (all tokens masked), Fully Independent (independently masked tokens per modality), Fully Shared (shared mask across modalities), and Partially Shared + Exclusive (shared mask for some tokens, with others masked exclusively per modality).
+
+per-modality masks  $\mathbf{M}_{\mathcal{I}}$ , each future frame token marked as visible in  $\mathbf{M}$  is set to be visible in only one of the  $K$  modalities, while remaining masked in the others.
+
+- Fully-masked: All future-frame tokens are masked simultaneously across all modalities. This baseline strategy differs from the others in that it is not random, masking all tokens in the future frames without sampling a subset.
+
+For each modality  $\mathcal{I}$ , the future-frame tokens in  $\mathbf{Z}_{\mathcal{I}}$  indicated as masked in  $\mathbf{M}_{\mathcal{I}}$  are replaced with a modality-specific learnable mask embedding  $[\mathrm{MASK}]_{\mathcal{I}} \in \mathbb{R}^{d_{\mathcal{I}}}$ .
+
+Inference Time At this phase, all future-frame tokens are treated as masked tokens and are predicted with single step.
+
+# 3.3. Spatio-Temporal Transformer with Decomposed Attention
+
+After the per-modality masking process, the transformer processes the fused multimodal token embeddings  $\mathbf{Z}$  across all frames, treating future-frame tokens as masked during inference. To begin, we add learnable position embeddings to the token embeddings  $\mathbf{Z}$ , which are then passed through alternating layers of bidirectional self-attention and MLPs, producing the output token embeddings  $\tilde{\mathbf{Z}}$ .
+
+To address the quadratic complexity of Multi-Head Self Attention (MSA) with respect to the number of tokens [71], we decompose attention into temporal and spatial components, similar to [1, 24]. Temporal attention is applied to tokens at the same spatial position across frames, while spatial attention is applied to tokens within the same frame. Both the MSAs and MLPs are implemented using Pre-LN [77].
+
+# 3.4. Multimodal Decoder
+
+After the final transformer layer, we use  $K$  prediction heads, one for each modality, to decode the transformer's output token embeddings  $\tilde{\mathbf{Z}}$  into  $K$  sets of pixel-wise predictions.
+
+Per-Modality Decoder For each modality  $\mathcal{I}$ , decoding from the transformer's output embeddings  $\tilde{\mathbf{Z}}$  to pixel-wise predictions follows a two-stage approach that mirrors the hierarchical structure of the per-modality embedder. First, a linear layer projects the token embeddings  $\tilde{\mathbf{Z}} \in \mathbb{R}^{(N \cdot L) \times d}$  from  $d$  dimensions to  $P^2 \cdot C_{\mathcal{I}}$  dimensions, producing intermediate embeddings  $\tilde{\mathbf{X}}_{\mathcal{I}}^E \in \mathbb{R}^{(N \cdot L) \times (P^2 \cdot C_{\mathcal{I}})}$ .
+
+Next, we reshape  $\tilde{\mathbf{X}}_{\mathcal{I}}^{E}$  to dimensions  $N\times H\times W\times C_{\mathcal{I}}$  and apply a weight matrix  $\tilde{W}_{\mathcal{I}}\in \mathbb{R}^{C_{\mathcal{I}}\times |\mathcal{L}_{\mathcal{I}}|}$  followed by a softmax operation, yielding the final per-pixel predictions  $\tilde{\mathbf{X}}_{\mathcal{I}}\in \mathbb{R}^{N\times H\times W\times |\mathcal{L}_{\mathcal{I}}|}$ . Following common practices in language modeling, we tie  $\tilde{W}_{\mathcal{I}}$  to the transpose of the embedding matrix  $W_{\mathcal{I}}\in \mathbb{R}^{|\mathcal{L}_{\mathcal{I}}|\times C_{\mathcal{I}}}$  from the embedder, i.e.,  $\tilde{W}_{\mathcal{I}} = W_{\mathcal{I}}^{\top}$ .
+
+Like the embedder, our decoding approach avoids VAEs and is fully integrated within the transformer, enabling end-to-end training of the full video prediction pipeline.
+
+# 3.5. End-to-End Training for Masked Multimodal Visual Modeling
+
+To effectively learn the multimodal next-frame prediction task, we introduce a novel masked visual modeling objective tailored for multimodal data. Building on traditional masked visual modeling methods designed for single-modality data [6, 8, 24, 26], our method integrates multiple modalities into a unified, end-to-end trainable framework.
+
+Per-Modality Masked Modeling Loss. To simplify the loss description, we define  $\tilde{\mathbf{X}}_{\mathcal{I}}^{F} \in \mathbb{R}^{(N_{p} \cdot L) \times P^{2} \times |\mathcal{L}_{\mathcal{I}}|}$  and  $\mathbf{X}_{\mathcal{I}}^{F} \in \mathcal{L}_{\mathcal{I}}^{(N_{p} \cdot L) \times P^{2}}$  as the per-modality model predictions and targets for the  $N_{p}$  future frames. These are reshaped so that the first two dimensions represent the number of tokens  $(N_{p} \cdot L)$  and the number of pixels  $(P^{2})$  within each token, respectively. The per-modality loss  $\mathcal{L}_{\mathcal{I}}(\mathbf{X}_{\mathcal{I}}, \mathbf{M}_{\mathcal{I}})$  is computed as the cross-entropy loss between the predictions and the targets for the future-frame tokens that are masked:
+
+$$
+\mathcal {L} _ {\mathcal {I}} \left(\mathbf {X} _ {\mathcal {I}}, \mathbf {M} _ {\mathcal {I}}\right) = \sum_ {n} ^ {N _ {p} \cdot L} \mathbf {M} _ {\mathcal {I}} (n) \sum_ {p} ^ {P ^ {2}} \mathcal {L} _ {C E} \left(\tilde {\mathbf {X}} _ {\mathcal {I}} ^ {F} (n, p), \mathbf {X} _ {\mathcal {I}} ^ {F} (n, p)\right) \tag {1}
+$$
+
+where  $\mathcal{L}_{CE}(\cdot, \cdot)$  is the cross-entropy loss function,  $(n,p)$  indexes the values in  $\tilde{\mathbf{X}}_{\mathcal{I}}^{F}$  and  $\mathbf{X}_{\mathcal{I}}^{F}$  corresponding to the  $p$ th pixel within the  $n$ th token, and  $(n)$  indexes the masking value of the  $n$ th token in  $\mathbf{M}_{\mathcal{I}}$ .
+
+End-to-End Multimodal Training Our multimodal video transformer is trained end-to-end using the following multimodal masked visual modeling objective:
+
+$$
+\mathcal {L} _ {\mathrm {M V M}} = \underset {\left. \left. \mathbf {X} _ {\mathcal {I} _ {i}}, \mathbf {M} _ {\mathcal {I} _ {i}} \right. \right\} _ {i = 1} ^ {K} \sim \mathcal {D}} {\mathbb {E}} \sum_ {i = 1} ^ {K} w _ {\mathcal {I} _ {i}} \mathcal {L} _ {\mathcal {I}} \left(\mathbf {X} _ {\mathcal {I} _ {i}}, \mathbf {M} _ {\mathcal {I} _ {i}}\right), \tag {2}
+$$
+
+where  $w_{\mathcal{I}_i}$  is the weight coefficient for the loss of the  $\mathcal{I}_i$  modality. Unlike most transformer-based generative models that rely on pre-trained tokenizers, our framework trains all modules—the embeddings (Sec. 3.1), the masked transformer backbone (Sec. 3.3), and the decoder heads (Sec. 3.4)—together using the objective defined in Eq. (2). This end-to-end approach ensures that the entire model is optimized jointly, making our multimodal visual modeling framework both simple and effective.
+
+# 4. Experiments
+
+# 4.1. Experimental Protocol
+
+Data. To evaluate our method, we use the Cityscapes dataset [14], which contains video sequences of a car driving in urban environments. The dataset includes 2,975 training sequences, 500 validation sequences, and 1,525 test sequences, each with 30 frames at 16 fps and a resolution of  $1024 \times 2048$  pixels. The 20th frame in each sequence has semantic segmentation annotations for 19 classes. We train on the training split and evaluate on the validation split. We also validate our approach on SYNTHIA-Seq [60] dataset. For more details regarding evaluation and results on SYNTHIA-Seq refer to Suppl. Sec. 7.4.
+
+Implementation details. For our models we set  $C_{\mathcal{I}} = 10$  for the pixel-wise embeddings. We use patch size of  $P = 16$ , which on frames of  $256 \times 512$  resolution produces  $16 \times 32 = 512$  patch tokens per frame. The transformer has 12 layers with a hidden dimension of  $d = 1536$ . We train both multimodal models (segmentation and depth modalities) and single-modality variations for these two tasks. Unless stated otherwise, we use the CONCAT fusion strategy, the "Partially-shared + Exclusive" multimodal masking strategy, and a sequence length  $N = 5$  (with  $N_c = 4$  context frames and  $N_p = 1$  future frame). For end-to-end training, we use the Adam optimizer [35] with momentum parameters  $\beta_1 = 0.9$ ,  $\beta_2 = 0.99$ , and a learning rate of  $1.6 \times 10^{-4}$  with cosine annealing. Training is conducted on 8 A100 40Gb GPUs with an effective batch size of 64. The longest training run was 3200 epochs (147,200 iterations) over 32 hours. For most experiments, we use 800 epochs.
+
+Evaluation Metrics. To assess our method's performance in predicting future semantic segmentation and depth maps, we evaluate on full-resolution using the following evaluation metrics. For semantic segmentation, we use two mean Intersection over Union (mIoU) metrics: mIoU (ALL) for all classes and MO-mIoU (MO) for movable objects (person, rider, car, truck, bus, train, motorcycle, bicycle). For depth prediction, we use two standard evaluation metrics [16, 21, 41]: the mean Absolute Relative Error (AbsRel, scaled by 100) and the threshold-based accuracy metric  $\delta_{1}$ .
+
+Evaluation Scenarios. Following prior work [43, 47], we consider two evaluation scenarios: short-term prediction (3 frames ahead, 0.18s) and mid-term prediction (9 frames ahead, 0.54s). In both cases, the 20th frame is the forecasting target. We temporally subsample sequences by a factor of 3 before processing them with our model. This means that, for short-term prediction, a model with a context length of four frames (i.e.,  $N_{c} = 4$  and  $N_{p} = 1$ ) uses frames 8, 11, 14, and 17 as context to predict frame 20. For mid-term prediction, the model uses frames 2, 5, 8, and 11 as context and predicts frame 20 auto-regressively (first frame 14, then 17, and finally frame 20).
+
+<table><tr><td rowspan="2">METHOD</td><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td></tr><tr><td>ALL</td><td>MO</td><td>ALL</td><td>MO</td></tr><tr><td>3Dconv-F2F [11]</td><td>57.0</td><td>-</td><td>40.8</td><td>-</td></tr><tr><td>Dil10-S2S [43]</td><td>59.4</td><td>55.3</td><td>47.8</td><td>40.8</td></tr><tr><td>F2F [44]</td><td>-</td><td>61.2</td><td>-</td><td>41.2</td></tr><tr><td>DeformF2F [61]</td><td>65.5</td><td>63.8</td><td>53.6</td><td>49.9</td></tr><tr><td>LSTM M2M [68]</td><td>67.1</td><td>65.1</td><td>51.5</td><td>46.3</td></tr><tr><td>F2MF [62, 63]</td><td>69.6</td><td>67.7</td><td>57.9</td><td>54.6</td></tr><tr><td>PFA [40]</td><td>71.1</td><td>69.2</td><td>60.3</td><td>56.7</td></tr><tr><td>Oracle [65]</td><td>78.6</td><td>80.8</td><td>78.6</td><td>80.6</td></tr><tr><td>Copy-Last</td><td>55.5</td><td>52.7</td><td>40.5</td><td>32.2</td></tr><tr><td>VISTA Fine-tuned [18]</td><td>46.3</td><td>44.9</td><td>41.0</td><td>36.7</td></tr><tr><td>FUTURIST Segm.-Only (ours)</td><td>73.4</td><td>74.2</td><td>62.4</td><td>60.5</td></tr><tr><td>FUTURIST (ours)</td><td>73.9</td><td>74.9</td><td>62.7</td><td>61.2</td></tr></table>
+
+Table 1. Comparison results with future semantic segmentation methods on Cityscapes validation set using MIoU metric. ALL: mIoU of all classes. MO: mIoU of movable objects.
+
+We calculate segmentation metrics using the ground truth annotations for the 20th frame in Cityscapes. For depth, since Cityscapes lacks true depth annotations, we use pseudo-annotations from DepthAnythingV2 for evaluation.
+
+# 4.2. Quantitative Results
+
+Here, we quantitatively evaluate our model, FUTURIST, on predicting future semantic segmentation and depth maps.
+
+Baselines. We compare our method against three baselines. The first is the Oracle baseline, which applies the image segmentation model (Segmenter [65]) or the monocular depth prediction model (DepthAnythingV2 [82]) directly on the target future frame. Since these models are the same ones used to compute segmentation and depth maps for the context frames, the Oracle baselines serve as an upper bound for our method's performance.
+
+The second baseline, Copy-Last, simply copies the segmentation or depth maps from the last available context frame to the target future frame, providing a lower bound for our method's performance.
+
+The third baseline uses the state-of-the-art driving world model, VISTA [18], which generates future RGB frames conditioned on three context frames through a video diffusion model. VISTA is a large-scale model with 2.5 billion parameters, trained on 1,740 hours of driving videos from YouTube. In this baseline, we finetune VISTA on Cityscapes and use it (with action-free conditioning) to generate future RGB frames, then apply the Segmenter and DepthAnythingV2 models to these frames to produce future-frame segmentation and depth maps. This comparison allows us to assess our method, which directly predicts future segmentation and depth maps, against the state-of-the-art in generative-based future prediction. More details regarding Vista finetuning in Suppl. Sec. 7.1.
+
+Comparison with Prior Work on Segmentation Forecasting. In Table 1, we compare our model with previous semantic future prediction methods on the Cityscapes dataset. We report results for both the default multimodal
+
+<table><tr><td rowspan="3">TRAINING MODALITY</td><td colspan="4">SEGMENTATION</td><td colspan="4">DEPTH</td></tr><tr><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td></tr><tr><td>ALL</td><td>MO</td><td>ALL</td><td>MO</td><td>δ1</td><td>ABSREL</td><td>δ1</td><td>ABSREL</td></tr><tr><td>SEGMENTATION</td><td>72.5</td><td>73.3</td><td>61.1</td><td>58.6</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DEPTH</td><td>-</td><td>-</td><td>-</td><td>-</td><td>95.4</td><td>5.923</td><td>90.6</td><td>10.194</td></tr><tr><td>MULTIMODAL</td><td>72.9</td><td>73.8</td><td>61.6</td><td>59.9</td><td>95.8</td><td>5.606</td><td>91.5</td><td>9.490</td></tr></table>
+
+![](images/0c48c303d1cdee56bbeae0e56acaa4194589ddde23b96fbda38a62b855ecb8f2.jpg)  
+Figure 5. Scaling Training Epochs. Model performance for segmentation forecasting (all classes and movable objects) and depth forecasting, as a function of the number of training epochs. Results for (a) short-term prediction and (b) mid-term prediction.
+
+version (using segmentation and depth modalities) and a segmentation-only variant. Both versions outperform prior methods in short- and mid-term predictions, with the multimodal version achieving the best performance and setting a new state-of-the-art. Our model shows significant improvements over the previous state-of-the-art method, PFA [40], especially for movable object (MO) classes, which are typically more difficult to predict.
+
+Comparison with VISTA. We also provide results for the VISTA-based baseline in Table 1. VISTA performs notably worse, even lower than the Copy-Last baseline. As shown in Figure 6, this is due to VISTA's inability to maintain the semantic structure of the scene in future frames. Despite generating visually realistic frames, VISTA's future predictions often suffer from issues such as object disappearance and artifacts that lead to inaccurate results from the oracle segmentation and depth models. These limitations highlight the advantage of our approach, which models future predictions directly in semantic space. Complete quantitative results, including depth metrics, are provided in Suppl. Sec. 7.
+
+Multi-modal vs Single-modality models. In Table 2, we compare our model's default multimodal version (segmentation plus depth) to single-modality versions using only segmentation or only depth. Results for both segmentation and depth forecasting show that the multimodal model outperforms the single-modality versions, demonstrating that it captures synergistic effects between the two modalities, enabling more accurate future predictions.
+
+Scaling Training Epochs. Building on research into scal
+
+Table 2. Multi-modal vs. single-modality approaches. Trained for 800 epochs. ABSREL is multiplied by 100 for readability.  
+
+<table><tr><td rowspan="3">SEQUENCE LENGTH</td><td colspan="4">SEGMENTATION</td><td colspan="4">DEPTH</td></tr><tr><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td></tr><tr><td>ALL</td><td>MO</td><td>ALL</td><td>MO</td><td>δ1</td><td>ABSREL</td><td>δ1</td><td>ABSREL</td></tr><tr><td>3</td><td>72.3</td><td>73.2</td><td>60.5</td><td>58.9</td><td>95.5</td><td>5.883</td><td>91.0</td><td>9.835</td></tr><tr><td>4</td><td>73.0</td><td>74.0</td><td>61.5</td><td>59.9</td><td>95.7</td><td>5.597</td><td>91.4</td><td>9.507</td></tr><tr><td>5</td><td>72.9</td><td>73.8</td><td>61.6</td><td>59.9</td><td>95.8</td><td>5.606</td><td>91.5</td><td>9.490</td></tr><tr><td>7</td><td>72.9</td><td>73.8</td><td>62.2</td><td>60.6</td><td>95.8</td><td>5.594</td><td>91.7</td><td>9.309</td></tr></table>
+
+Table 3. Sequence Length Impact. Models trained for 800 epochs with sequence lengths  $N = 4, 5$ , and 7, with  $N_p = 1$ .  
+
+<table><tr><td rowspan="3">MASKING STRATEGY</td><td colspan="4">SEGMENTATION</td><td colspan="4">DEPTH</td></tr><tr><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td></tr><tr><td>ALL</td><td>MO</td><td>ALL</td><td>MO</td><td>δ1</td><td>ABSREL</td><td>δ1</td><td>ABSREL</td></tr><tr><td>Indep. (Same r)</td><td>72.5</td><td>73.3</td><td>60.9</td><td>58.9</td><td>95.7</td><td>5.745</td><td>91.1</td><td>9.634</td></tr><tr><td>Indep. (Diff. r)</td><td>71.9</td><td>72.8</td><td>59.9</td><td>57.9</td><td>95.5</td><td>5.862</td><td>90.7</td><td>9.888</td></tr><tr><td>Fully Shared</td><td>72.5</td><td>73.3</td><td>61.2</td><td>59.2</td><td>95.6</td><td>5.731</td><td>91.2</td><td>9.586</td></tr><tr><td>Part. Shared+Excl.</td><td>72.9</td><td>73.8</td><td>61.6</td><td>59.9</td><td>95.8</td><td>5.607</td><td>91.5</td><td>9.491</td></tr><tr><td>Fully Masked</td><td>71.2</td><td>71.6</td><td>59.5</td><td>56.9</td><td>95.3</td><td>6.139</td><td>90.6</td><td>10.122</td></tr></table>
+
+Table 4. Comparison of multimodal masking training strategies. Models trained for 800 epochs. During inference, next-frame tokens are masked and predicted with a single inference step.  
+
+<table><tr><td rowspan="3">MODALITY FUSION STRATEGY</td><td colspan="4">SEGMENTATION</td><td colspan="4">DEPTH</td></tr><tr><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td><td colspan="2">SHORT-TERM</td><td colspan="2">MID-TERM</td></tr><tr><td>ALL</td><td>MO</td><td>ALL</td><td>MO</td><td>δ1</td><td>ABSREL</td><td>δ1</td><td>ABSREL</td></tr><tr><td>ADD</td><td>72.2</td><td>72.8</td><td>60.7</td><td>58.5</td><td>95.5</td><td>5.793</td><td>91.0</td><td>9.763</td></tr><tr><td>CONCAT</td><td>72.5</td><td>73.3</td><td>60.9</td><td>58.9</td><td>95.7</td><td>5.745</td><td>91.1</td><td>9.634</td></tr></table>
+
+Table 5. Comparison of modality fusion strategies. All models were trained for 800 epochs with sequence length 5.
+
+ing laws for transformer-based architectures [34, 85], we investigate how our model's performance scales with the number of training epochs. As shown in Figure 5, extending the training duration results in significant improvements in both segmentation and depth prediction. These results suggest that our model can continue to enhance its predictive capabilities with more training, even when trained on limited datasets like Cityscapes.
+
+Modality Fusion Strategies. In Table 5, we compare the ADD and CONCAT strategies for multimodal fusion. Both strategies are effective, with CONCAT yielding slightly better results, making it our default choice.
+
+Masking Strategies. In Table 4, we compare various multimodal training masking strategies discussed in subsection 3.2. The Partially-shared + Exclusive strategy achieves the best results across all metrics. This strategy restricts future-frame masking during training such that each future-frame token is either fully masked (both modalities are hidden) or partially masked (only one modality is visible). Importantly, no future-frame token has both modalities visible at the same time. We believe this approach helps the model better learn the synergistic effects between the two modalities. In contrast, the Fully-Masked strategy yields the worst results, despite matching the masking approach used during inference. We hypothesize this is because the strategy is too aggressive and less effective in promoting the
+
+![](images/f9708c29d11705a86bcb49131d9e00327c8d2fe852c5a89c2db3aa91662fd683.jpg)  
+Future Frame
+
+![](images/8433ae3af9d43d0ae88c38d7c0d0e910b179d238b6d7317479faf04f3877cbd4.jpg)  
+Scene Munster (0)
+
+![](images/d46e2826f6c762e4f5d9d7b63925fca83eb5e922b3cf12574b9c24e5232fa98f.jpg)  
+Vista (Output)
+
+![](images/38a67998c2f9d381e8b3440afa7e43eaf41a83ebf7eccb3170cd394da0bb075a.jpg)  
+Scene Munster (160) Future Frame Vista (Output)
+
+![](images/8eb8445efbac966005e4e2f17b61180034517d2be903e4581fa34409939e7818.jpg)  
+Segmentation
+
+![](images/871192183ec9565663816b98f43fc297203a39ed760ec09e2ff4cc7138a56fda.jpg)  
+Depth  
+(a) Short-Term
+
+![](images/538bf2f161af5a1e3fcc109953cf58ca9ea1b7ad37b91d2e435ebe85a71f3018.jpg)  
+Segmentation
+
+![](images/5c54d499050899f1abe93d97467ce0fafd62832821162e6f8e1e68afc5c1cf8c.jpg)  
+Depth
+
+![](images/578fc917ad26bfd932c88778f0b7024f0cc61766d09566c41136236fac664fcc.jpg)  
+Future Frame
+
+![](images/e32a7af13ca7265119751f0ddefead46be247890376ef0fde84d74fa70941b3d.jpg)  
+Vista (Output)
+
+![](images/c5704797c9c7cf5b2b3d34dc8091921d224d6c79a800d4a68bd8e00d2f4a8999.jpg)  
+Future Frame
+
+![](images/8a516550cd6b7c74427466ff1acac2eebe1e942b2a0281ca0f0483d5835aee28.jpg)  
+Vista (Output)
+
+![](images/57938baf4bf812fc6efe3cdd63a25aaac6514b53d0abf124cacfa70c99cdc26c.jpg)  
+Segmentation
+
+![](images/c795b3de5802e8a9c0477c340cb97240397d58b724775c56b76860d7ec0c5f18.jpg)  
+Segmentation
+
+![](images/206e2b0a4ecdd4b7b4e0b5d174cb995902fbb652738a00411b3cdf33f6b1b51a.jpg)  
+Depth
+
+![](images/a5e0952573a3a6df1cf1d09a547a090a5f75ab040adde70fa134521069e5e752.jpg)
+
+![](images/5fb715ec58025039671fb00663e9798b998e8b34986b3fb9890051df3ea1c3e7.jpg)
+
+![](images/657a5be01a36adb5f58bbb3c25127c717fb1a86127ed7b4e2b7b8b89dd17f465.jpg)
+
+![](images/3d73c7189d2ed5c4232773d2e1c91d203c78a209d41f64fd383dd4f79dbd6c65.jpg)  
+(b) Mid-Term  
+Figure 6. Qualitative comparison of future semantic segmentation and depth prediction. Oracle results are derived from Segmenter [65] (segmentation) and DepthAnythingV2 [82] (depth). We compare against the state-of-the-art method VISTA [18], which generates future RGB frames via video diffusion, followed by Segmenter and DepthAnythingV2 for predictions.
+
+![](images/7df6aab398f90d560d4487469eaafc70159569a925b246ef400558c92fb86119.jpg)
+
+![](images/801dee2dc289d3dc1469bbce36d20a779188aebe11242943237d2e5e7974fbab.jpg)
+
+model's learning of interactions between the modalities.
+
+Sequence Length Impact. In Table 3 we compare models with sequence lengths  $N$  of 4, 5, and 7 frames (with  $N_p = 1$ ). While all models perform similarly, the 7-frame model achieves slightly better results for mid-term segmentation and all depth prediction metrics. However, we use the 5-frame context by default in this paper due to the higher computational cost of the 7-frame model.
+
+Additional Experiments. In the Suppl. Sec. 7, we present additional experiments validating our design choices. First, in Suppl. Sec. 7 we demonstrate that our VAE-free tokenization approach significantly outperforms alternative tokenization methods using pretrained and finetuned VQ-VAE models. Second, in Suppl. Sec. 8 we examine our multi-modal fusion strategy against a separable tokens approach, showing that under equal compute budgets, our method achieves superior performance on most metrics.
+
+# 4.3. Qualitative Results
+
+We present qualitative results for our method in Figure 1
+
+![](images/3ec8b50814629e46fe41c836bf269fc3d4c2386a1c51a9370b29b9b3d4f7eba3.jpg)
+
+![](images/1e0f7e56a0537e52f9b5b1040358d1b906f6703d490d7cb0219f954411296b76.jpg)
+
+![](images/f49fa771cea5cd9f5f5269f53d34e2de5ace9f82ab4baeb72a09799622ea9076.jpg)
+
+![](images/b9bc48572312ae5df045759ff660476350675c454880326ddec03a8191107ad1.jpg)
+
+![](images/4f3eda4656466a05077126fdc94b1a2b7f558638a253a4e486ae60e3e2115605.jpg)
+
+![](images/6bd654055fa06ac8fea71ed79267ae3156e142eebeea71c6e336623d6f1101e4.jpg)
+
+![](images/57ee73404f71b7bd7e7d6951386a0dffc126501f3fbd1f6209ea312461fd56d2.jpg)
+
+![](images/4895ca60eb8f500ff92b6c62f013037eac921abbf3a89549d6ac70f817aaa5e4.jpg)
+
+![](images/556ebc94210348bac390ac9d28695a94562940815f4fdb56297f419597433df4.jpg)  
+Figure 7. Long-term semantic segmentation and depth predictions. Our method uses autoregressive rollouts to predict future semantic and depth maps over long horizons. Starting from four context frames ( $X_{t-9}$  to  $X_t$ ), it generates coherent predictions up to 48 frames (2.88 seconds) with a frame-wise step of 3, accurately capturing both static elements and dynamic changes. Due to space constraints, we present only frames  $X_{t+3}$ ,  $X_{t+18}$ , and  $X_{t+48}$ .
+
+![](images/78248d23e3071f7bef0f03c0bcf9a5d621b26ec99fe8b378ba7c4d5bf7d1e763.jpg)
+
+![](images/9059d5da74563e2d8748485a575824e2b2e1334841a4c69cef4398a454f382d4.jpg)
+
+![](images/847f20b13e3b7b04664a3bdf5707359ecaecf7a0b78af1daf2a19e51a288f0f8.jpg)
+
+and Figure 6 on semantic segmentation and depth prediction forecasting, comparing it to the Oracle baseline. Additionally, Figure 6 includes a comparison with the VISTA baseline. Our method effectively forecasts the scene's semantic structure, producing future predictions closely aligned with the Oracle and outperforming the VISTA baseline. In Figure 7, we show long-horizon rollouts of the semantic segmentation and depth maps generated by consecutive frames-wise autoregressive predictions from our model. Starting from four context frames ( $X_{t-9}$  to  $X_t$ ), it produces consistent predictions up to 48 frames ahead, accurately capturing both static elements and dynamic changes. Additional visualizations are provided in Suppl. Sec. 8.
+
+# 5. Conclusion
+
+This work advances semantic future prediction with FUTURIST, a multimodal visual sequence transformer featuring: a VAE-free hierarchical tokenization strategy for efficient end-to-end multimodal training; a novel multimodal masked visual modeling objective; and an efficient cross-modality fusion mechanism that improves per-modality predictions by learning cross-modal synergies.
+
+We evaluated FUTURIST on the Cityscapes dataset for semantic segmentation and depth prediction. Our results show accurate short-term and mid-term predictions, outperforming single-modality models and setting a new state-of-the-art in future semantic segmentation. These findings demonstrate FUTURIST's effectiveness in extending masked transformers for multimodal future prediction. We discuss the limitations of our method and directions for future work in Suppl. Sec. 9.
+
+Acknowledgements This work has been partially supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.
+
+Hardware resources were granted with the support of GRNET. Also, this work was performed using HPC resources from GENCI-IDRIS (Grants 2023-A0141014182, 2023-AD011012884R2, and 2024-AD011012884R3).
+
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\ No newline at end of file
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+# Adventurer: Optimizing Vision Mamba Architecture Designs for Efficiency
+
+Feng Wang $^{1}$  Timing Yang $^{1}$  Yaodong Yu $^{2}$  Sucheng Ren $^{1}$  Guoyizhe Wei $^{1}$  Angtian Wang $^{1}$  Wei Shao $^{3}$  Yuyin Zhou $^{4}$  Alan Yuille $^{1}$  Cihang Xie $^{4}$ $^{1}$ Johns Hopkins University  $^{2}$ UC Berkeley  $^{3}$ University of Florida  $^{4}$ UC Santa Cruz
+
+# Abstract
+
+In this work, we introduce the Adventurer series models where we treat images as sequences of patch tokens and employ uni-directional language models to learn visual representations. This modeling paradigm allows us to process images in a recurrent formulation with linear complexity relative to the sequence length, which can effectively address the memory and computation explosion issues posed by high-resolution and fine-grained images. In detail, we introduce two simple designs that seamlessly integrate image inputs into the causal inference framework: a global pooling token placed at the beginning of the sequence and a flipping operation between every two layers. Extensive empirical studies highlight that compared with the existing plain architectures such as DeiT [46] and Vim [57], Adventurer offers an optimal efficiency-accuracy trade-off. For example, our Adventurer-Base attains a competitive test accuracy of  $84.3\%$  on the standard ImageNet-1k benchmark with 216 images/s training throughput, which is  $3.8\times$  and  $6.2\times$  faster than Vim and DeiT to achieve the same result. As Adventurer offers great computation and memory efficiency and allows scaling with linear complexity, we hope this architecture can benefit future explorations in modeling long sequences for high-resolution or fine-grained images. Code is available at https://github.com/wangf3014/Adventurer.
+
+# 1. Introduction
+
+We start introducing our method with a thought experiment: An adventurer holding a torch is exploring an ancient relic located in a dark cave deep in the mountains. A huge mural painted inside the cave has caught his attention. However, the cave is narrow and pitch-dark, with the torch serving as the only source of light, illuminating only a small part of the mural at a time. To figure out what is depicted on the mural, the adventurer has to "scan" it from top left to bottom right. By repeating this process several times, do you think it is sufficient for him to understand the content of the mural?
+
+In fact, even under good lighting conditions, the area that
+
+![](images/78e2c18535a0a9c288f7433d1f60bf8f0c44e0fe7500a308befa9e599f3a4ae2.jpg)
+
+![](images/49b6de4d652a7d7c85492b9b945fab7321ea0d314159ca4b1c7a9511a7da3fab.jpg)  
+Figure 1. Time and memory efficiency at different resolutions. (a): Training time for one image (second/image) on an A100 GPU. At the input size of  $1280^2$ , our Adventurer-Base is  $11.7 \times$  faster than ViT-Base. (b): The memory requirement (GB/image) of Adventurer also grows slowly when input resolution increases, achieving a  $14.0 \times$  superior memory efficiency than ViT at  $1280^2$ .
+
+the human eye can focus on at one time is very limited. For example, when forcing your eyesight to focus on this word, you cannot count how many words there are in this line. The understanding of complex visual scenes actually relies on the rapid movement of the eyes, known as the Saccade Mechanism [26, 32]. Under this mechanism, the human eye perceives only a very small visual area at a time, and then the eyesight rapidly scans between areas to gain a comprehensive understanding of the whole scene.
+
+This visual understanding mechanism inspires us to con
+
+![](images/5db69bf244f387db2f9ba61e69f1088af3abe3ab354fe7e36658f46974a639ea.jpg)
+
+![](images/7832e24f3cf9f61be5814f1190f010192d9e5f2b342c72c5ad3bf7a8acaca2fe.jpg)
+
+![](images/b706d6be806eac8d9cb65644ee952e316dbcbfd86a9088b577cc36768f04a210.jpg)  
+(a) Attention masks
+
+![](images/f76134d49bde6fbdc5f1c8b3046bbc30dfd5ec119d1011075368030acac21634.jpg)  
+Figure 2. Comparison of causal attention formulations. We compare our causal ViT with the standard ViT where all tokens are fully visible to others and the naive causal ViT with half visibility. (a): Comparison of attention masks. Positions of  $\square$  denote "invisible".  $x_{\mathrm{A}}$  and  $x_{\mathrm{C}}$  denote the heading average token and class token respectively. (b): Comparison of accuracy on ImageNet.
+
+![](images/b76c5286d37c6a7d8b3ce418b1148540565602495aa6121e853119c7fa9c0442.jpg)  
+(b) Accuracy comparison
+
+sider the possibility of modeling images as 1D sequences of patches. However, in contrast to vision transformers [10] that require referring all other tokens when understanding each patch token and thereby result in quadratic complexity with respect to sequence length, we aim to employ a more efficient causal modeling approach, which scales linearly with the number of patches and better aligns with the low power consumption characteristic of the human vision.
+
+To this end, a very straightforward way is dividing the image into non-overlapping patches, flattening them as a 1D token sequence, and then processing them simply by a unidirectional language model. Nonetheless, this naive causal modeling approach is not directly applicable to image understanding because in a uni-directional sequence, each token can only receive information from the tokens before it, which results in tokens at the start of the sequence having poor representations due to the lack of global context.
+
+But interestingly, we find that this issue can be effectively addressed with just two simple designs: first, we place an average pooling token at the beginning of the sequence, which is computed by the average of all other tokens in the sequence. This allows tokens at the start of the sequence to access sufficient global information, thus enhancing the quality of their representations. Second, we introduce sequence flipping operations between layers of the model to counteract the information imbalance caused by positional differences among tokens. We term this two simple designs heading average and inter-layer flipping, respectively. The overall framework of this Causal Image Modeling (CIM) paradigm is shown in Figure 3.
+
+To validate the efficiency and effectiveness of our CIM framework, we first integrate it with Vision Transformer (ViT) architectures, with Figure 2a showing the difference
+
+in attention masks compared to the standard ViT and a naive causal ViT. As we analyzed earlier, causal models can easily impact the representation of tokens at the beginning of the sequence and thereby degrade predictive performance. In Figure 2b, we observe a  $1.16\%$  and  $1.13\%$  accuracy decrease on ImageNet [9] when employing a naive causal ViT-Small and Base respectively. However, this issue is well addressed by our reformed causal framework, while our causal ViTs can seamlessly match the performance of the standard ones with full token visibility. This experiment can directly demonstrate the following three points:
+
+1. Causal modeling is sufficient for image encoding. We find that when equipped with the heading average token and sequence flipping operations, the uni-directional language models can be directly used for image encoding and achieve results competitive with standard ViTs. We will further elaborate in the following sections that this modeling approach is also applicable to various visual understanding tasks such as semantic segmentation, object detection, and instance segmentation.  
+2. Standard ViTs involve redundant computations. As shown in Figure 2, causal modeling ignores around half of the computation in self-attention but can attain almost the same accuracy of standard ViTs. With appropriate parallel processing mechanisms [8], causal modeling can substantially accelerate self-attention. For instance, when processing a sequence of 2,000 tokens, causal attention can achieve a speed increase of about  $50\%$  compared to the fully-visible attention.  
+3. Visual backbones can be much more efficient. Besides being able to speed up self-attention, the greater advantage of causal modeling lies in the ability to incorporate RNN-like token mixers such as Mamba [7, 12], whose
+
+computation scales linearly with sequence length. Compared to the quadratic complexity of transformers, this
+
+unique advantage can effectively solve the problems of computational and memory explosion when processing high-resolution and fine-grained images.
+
+We term our causal image models Adventurer to echo the thought experiment at the beginning. As shown in Figure 3, the Adventurer models consist of a number of causal token mixers and channel mixers, incorporating our newly introduced mechanisms of heading average and inter-layer sequence flipping to process image tokens. By default, we use the latest Mamba-2 [7] structure as the token mixer and SwiGLU MLP [48] blocks as the channel mixer. Empirically, our Adventurer models exhibit strong capabilities in image understanding, showcasing highly competitive results in classification, segmentation, and detection tasks. In dealing with long sequences, our model demonstrates a significant speed advantage. For example, with an input size of  $448 \times 448$  and a patch size of  $8 \times 8$ , i.e., a sequence of over 3,000 tokens, our Base-sized model achieves a competitive test accuracy of  $84.8\%$  on ImageNet [9] with 5.3 times faster training speed compared with ViT-Base at the same input scale.
+
+# 2. Related Work
+
+Generic vision backbones. Convolutional Neural Networks (CNNs) [25] have long been the dominant backbone architecture for various vision tasks. Over time, the CNN structures have experienced a series of major innovations [18, 20, 24, 31, 41, 45] and now remain competitive to modern visual architectures. Vision transformers [10], on the other hand, has recently represented a paradigm shift from CNNs' hierarchical feature extraction to patch-by-patch visual encoding. Since the introduction of ViTs, the research community has made substantial strides in developing more robust and efficient training approaches [46, 47], optimizing model designs [5, 30, 54], and advancing the frontiers of self-supervised and weakly supervised learning [1, 4, 6, 19, 37, 49, 56].
+
+Mamba and state space models. State Space Models (SSMs) have long been utilized in control systems, primarily to handle continuous inputs [22]. Advancements in discretization methods [13, 16, 35, 44] have expanded the application of SSMs to deep learning, particularly in modeling sequential data [14, 15, 42]. SSMs broadly include any recurrent models that utilize a latent state, ranging from traditional models like Hidden Markov Models [11] and RNNs to more modern approaches such as Linear Attention [23], RetNet [43], and RWKV [36]. Recently, [12] introduce Mamba, a novel SSM block that leverages structured SSMs along with state expansion optimized for hardware efficiency.
+
+Mamba in visual applications. Similar to the Transformer's success in NLP and its adoption in vision tasks, Mamba has also been extended to vision fields. For example, [57] stack forward and backward scanning blocks to capture bidirectional information, addressing the directionality issue inherent in causal models. [29] introduce a hybrid architecture that integrates Mamba with 2D convolution, enabling the capture of contextual information from multiple directions and dimensions. [17] utilize a framework that integrates Mamba with self-attention, enhancing the model's capability to capture long-range spatial relationships. [40] proposes the Visual State Space Duality (VSSD) model, which enhances the performance and efficiency of state space models in sequential modeling tasks by incorporating non-causality and multi-scan strategies. Mamba-based architectures have extended to a wide range of various vision domains [21, 27, 28, 38, 50, 53].
+
+# 3. Method
+
+# 3.1. Building Causal Image Models
+
+Overall, we follow the practice of vision transformers [10] that incorporate patch embedding, positional embedding, token mixers and channel mixers to build our Adventurer models. Formally, given an input image  $\mathbf{I} \in \mathbb{R}^{3 \times h \times w}$ , we first divide it into non-overlapping patches of size  $p \times p$  flattening them to form a token sequence  $X \in \mathbb{R}^{hw / p^2 \times d}$  where  $d$  denotes the number of hidden channels. For easy notations, here we assume  $h = w$  and denote  $n = h^2 / p^2$ . Similar to language models, we append the class token at the end of sequence to represent global features. For positional embeddings, here we simply use a learnable matrix  $P \in \mathbb{R}^{(n + 1) \times d}$  that is added to the patch and class tokens. We leave the exploration of position encoding more suitable for causal models to future works.
+
+As shown in Figure 3, each layer of our Adventurer model consists of a causal token mixer and a channel mixer. In this work, we discuss two variants of Adventurer models: Transformer-based and Mamba-based. For the former, we use causal self-attention as token mixer and follow the original Vision Transformers [10] by leveraging a simple Multi-Layer Perceptron (MLP) as channel mixer. For the Mamba-based models, we employ Mamba-2 [7] as token mixer and MLP with SwiGLU [39] activation as channel mixer. Unless otherwise specified, the term Adventurer by default refers to its Mamba-based variant in this paper.
+
+We present detailed configurations of our Adventurer models in Table 1. As mentioned above, Mamba [12] is a RNN-like state space model that has incorporated very efficient hardware-aware designs to support parallel computation. Due to its recurrent formulation, Mamba's computational complexity scales linearly with sequence length, offering an efficient modeling approach that allows us to in-
+
+![](images/109a1969c6d29ead7cb870aa825bac80aa65e1d7801cbdd7f26f3b484c337dbd.jpg)  
+Figure 3. Causal image modeling framework of Adventurer. We learn visual representations simply by a uni-directional language model comprising causal token mixers and channel mixers. Two simple designs are introduced to integrate this framework into image inputs: a global pooling token placed at the start of the sequence and a flipping operation between every two causal blocks.
+
+crease input resolution or reduce patch size to obtain more detailed visual information. For Mamba-2 blocks, we adopt a  $2 \times$  expand ratio and set the feature dimension to be a multiple of 256 to better leverage its parallel efficiency [7]. Following the recent advances of large language models [48], we opt to use an improved MLP block with SwiGLU activation as channel mixer. We set the hidden dimension of MLP to  $2.5 \times$  input/output dimension to appropriately reduce the computational load.
+
+<table><tr><td>Model</td><td>Blocks</td><td>Dimension</td><td>Parameters</td></tr><tr><td>Adventurer-Tiny</td><td>12</td><td>256</td><td>12 M</td></tr><tr><td>Adventurer-Small</td><td>12</td><td>512</td><td>44 M</td></tr><tr><td>Adventurer-Base</td><td>12</td><td>768</td><td>99 M</td></tr><tr><td>Adventurer-Large</td><td>24</td><td>1024</td><td>346 M</td></tr></table>
+
+Table 1. Configurations of our Adventurer models. Each Adventurer block consists of a Mamba-2 [7] token mixer and an MLP channel mixer with SwiGLU activation [48].
+
+# 3.2. Adapting Images into Causal Inference
+
+As discussed in Section 1, when we use a causal model to process image tokens, it can easily incur the problem of information imbalance. That is, tokens at the end of the sequence can effectively aggregate information from other tokens, while those at the beginning of the sequence struggle to access the global context of the image. To address this issue, existing causal models typically employ a method of multiple scans and average the multi-way outputs [29, 50, 57]. While this method does not significantly increase the number of model parameters, the computation cost and actual inference time are multiplied. Instead, we address the information imbalance problem effectively under the condition of using only one-way scanning in each layer, through two simple mechanisms: Heading Average and Inter-Layer Flipping.
+
+Heading Average denotes placing a global average pooling token at the beginning of the input sequence for
+
+each Adventurer layer. Formally, given the input for the  $i$ -th Adventurer block:
+
+$$
+\boldsymbol {X} ^ {i} = \left\{\boldsymbol {x} _ {1} ^ {i}, \boldsymbol {x} _ {2} ^ {i}, \dots , \boldsymbol {x} _ {n} ^ {i}, \boldsymbol {x} _ {\mathrm {C L S}} ^ {i} \right\}, \quad \boldsymbol {x} _ {j} ^ {i} \in \mathbb {R} ^ {d}, \tag {1}
+$$
+
+we form an augmented sequence by putting an average token at the beginning:
+
+$$
+\boldsymbol {X} _ {\mathrm {a u g}} ^ {i} = \{\boldsymbol {x} _ {\mathrm {A V G}} ^ {i}, \boldsymbol {x} _ {1} ^ {i}, \boldsymbol {x} _ {2} ^ {i}, \dots , \boldsymbol {x} _ {n} ^ {i}, \boldsymbol {x} _ {\mathrm {C L S}} ^ {i} \}, \qquad (2)
+$$
+
+$$
+\boldsymbol {x} _ {\mathrm {A V G}} ^ {i} = \frac {1}{n + 1} \sum_ {j} \boldsymbol {x} _ {j} ^ {i}. \tag {3}
+$$
+
+This operation forces the average token which contains sufficient global information to be the starting point, enabling the patch tokens at the beginning of the sequence to also access the global context. To ensure that the heading average token accurately represents the global feature for each layer, we discard the output of  $x_{\mathrm{AVG}}$  at the end of each Adventurer block and recalculate it by Equation 3 as the next layer's input.
+
+Inter-Layer Flipping, instead of inner-layer multi-way scanning, provides with a more efficient strategy to overcome the information imbalance issue. Specifically, our token mixers scan the input sequence only once, and between every two Adventurer blocks, we reverse the order of patch tokens and leave the positions of the class token and average token unchanged. We illustrate different scanning strategies in Figure 4. As is shown, additional scans typically increase the computational load and inference latency proportionally, while our one-way scanning approach possesses optimal efficiency but similar performance compared with multi-way scans. For a clearer understanding of the Adventurer models' computational process, we present a PyTorch-like pseudo code in Algorithm 1.
+
+# 3.3. Speed and Memory Comparison
+
+We quantitatively compare the differences in training speed and GPU memory overhead between Adventurer, ViT, and
+
+![](images/0faa7831ec5b16be45b47794e06be5a22f6e36d4d24a6c18d6ab37582a82df26.jpg)  
+(a) Different scanning strategies
+
+![](images/62e14a690df6d29be546fd2e009a4bae60a780bb20a56bf2615c2d4cea7dcb98.jpg)  
+(b) Throughput-accuracy trade-off  
+Figure 4. Do we really need multi-way scans for causal image models? Here we illustrate and compare various scanning strategies, finding that the multi-way approaches hardly offer further performance improvements relative to our models. Please also note that for causal image models involving multi-way scanning, the number of model parameters does not directly reflect its computing cost and actual inference speed as the multiple scans can share most parameters in one layer.
+
+an existing vision Mamba architecture [57]. As shown in Figure 1, ViT, due to its quadratic complexity relative to sequence length, experiences a rapid increase in processing time and memory requirements as input resolution increases. In contrast, Mamba-based visual backbones, with their linear complexity, exhibit clear advantages in speed and memory efficiency at high resolutions. Remarkably, at an input size of  $1280 \times 1280$ , our Adventurer-Base achieves a speed improvement of 11.7 times and a memory savings of 14.0 times compared to ViT-Base. We also note that compared to Vim-Base, our model shows significant speed superiority, a result of our series of structural optimizations: we have implemented efficient one-way scanning, introduced hardware-friendly channel mixers, and adopted the latest Mamba-2 structure.
+
+# 4. Experiments
+
+# 4.1. Experimental Setups
+
+We primarily evaluate the Adventurer models on the standard ImageNet-1k classification benchmark [9]. The dataset consists of around 1.28 million training images and 50,000 validation images across 1,000 categories. We follow the recent multi-stage training recipe [50] for Mamba models, which comprises 300 epochs pretraining with an input size of  $128 \times 128$ , followed by 100 epochs training in  $224 \times 224$  and 20 more finetuning epochs in  $224 \times 224$  with stronger data augmentation and higher drop path rates. This strategy involves only  $\sim 230$  effective training epochs at  $224 \times 224$  but outperforms the commonly used 300-epoch schedules [46, 57]. More details can be found in Appendix.
+
+We also evaluate our models in downstream semantic
+
+Algorithm 1 PyTorch-like Pseudocode of Adventurer  
+```python
+patch_embedding: [B, 3, W, H] -> [B, N, C]
+# pos_embedding: learnable parameters, [N+1, C]
+# token_mixers: a list of L causal token mixers
+# channel_mixers: a list of L channel mixers
+def forward_feature/images):
+    x = patch_embedding/images) # [B, N, C]
+    x = concatenate([x, clf_token], dim=1) # end clf
+    x = x + pos_embedding # [B, N+1, C]
+    for i in range(L): # a total of L blocks
+        # heading average token
+        avg = x.mean(dim=1, keepdim=True)
+        x = concatenate([avg, x], dim=1) # [B, N+2, C]
+        # forward token Mixer and channel mixer
+        x = x + token_mixers[i](x)
+        x = x + channel_mixers[i](x)
+        x = x[:, 1:] # discard avg output: [B, N+1, C]
+        # flip sequence, leaving clf at the end
+        x = concatenate([x[:, :, -1].flip(1), x[:, -1:]], dim=1)
+    return x
+```
+
+segmentation, object detection, and instance segmentation tasks. For semantic segmentation, we fine-tune our models with an UperNet [52] decoder head on the ADE20k dataset [55], featuring 150 detailed semantic categories within 20K training images, 2K validation images, and 3K test images. Consistent with earlier baselines [46, 57], we train the models with a total batch size of 16 across 160,000 iterations, using an AdamW optimizer [33] with 5e-5 learning rate and 0.01 weight decay.
+
+We conduct object detection and instance segmentation tasks on the COCO 2017 dataset [2], which consists of
+
+<table><tr><td>Model</td><td>Token mixer</td><td>Input size</td><td>Parameters</td><td>Throughput (↑)</td><td>Memory (↓)</td><td>Accuracy (%)</td></tr><tr><td>DeiT-Tiny [46]</td><td>Self-Attention</td><td>224</td><td>5M</td><td>3480</td><td>3.4G</td><td>72.2</td></tr><tr><td>DeiT-Small [46]</td><td>Self-Attention</td><td>224</td><td>22M</td><td>1924</td><td>6.8G</td><td>79.8</td></tr><tr><td>Adventurer-Tiny (ours)</td><td>Mamba</td><td>224</td><td>12M</td><td>2757</td><td>4.2G</td><td>78.2</td></tr><tr><td>Adventurer-Small (ours)</td><td>Mamba</td><td>224</td><td>44M</td><td>1405</td><td>8.3G</td><td>81.8</td></tr><tr><td>DeiT-Base [46]</td><td>Self-Attention</td><td>224</td><td>86M</td><td>861</td><td>14.4G</td><td>81.8</td></tr><tr><td>Vim-Tiny [57]</td><td>Mamba</td><td>224</td><td>7M</td><td>750</td><td>4.8G</td><td>76.1</td></tr><tr><td>MambaReg-T [50]</td><td>Mamba</td><td>224</td><td>9M</td><td>746</td><td>5.1G</td><td>77.4</td></tr><tr><td>ConvNeXt-T [31]</td><td>2D Conv.</td><td>224</td><td>29M</td><td>635</td><td>8.3G</td><td>82.1</td></tr><tr><td>EfficientNet-B3 [45]</td><td>2D Conv.</td><td>300</td><td>12M</td><td>546</td><td>19.7G</td><td>81.6</td></tr><tr><td>Adventurer-Base (ours)</td><td>Mamba</td><td>224</td><td>99M</td><td>856</td><td>13.0G</td><td>82.6</td></tr><tr><td>ConvNeXt-S [31]</td><td>2D Conv.</td><td>224</td><td>50M</td><td>412</td><td>13.1G</td><td>83.1</td></tr><tr><td>Vim-Small [57]</td><td>Mamba</td><td>224</td><td>26M</td><td>395</td><td>9.4G</td><td>80.5</td></tr><tr><td>MambaReg-S [50]</td><td>Mamba</td><td>224</td><td>28M</td><td>391</td><td>9.9G</td><td>81.4</td></tr><tr><td>ConvNeXt-B [31]</td><td>2D Conv.</td><td>224</td><td>89M</td><td>305</td><td>17.9G</td><td>83.8</td></tr><tr><td>VMamba-B [29]</td><td>Mamba + 2D Conv.</td><td>224</td><td>89M</td><td>246</td><td>37.1G</td><td>83.9</td></tr><tr><td>DeiT-Base [46]</td><td>Self-Attention</td><td>384</td><td>86M</td><td>201</td><td>63.8G</td><td>83.1</td></tr><tr><td>MambaReg-B [50]</td><td>Mamba</td><td>224</td><td>99M</td><td>196</td><td>20.3G</td><td>83.0</td></tr><tr><td>Adventurer-Large (ours)</td><td>Mamba</td><td>224</td><td>346M</td><td>301</td><td>35.5G</td><td>83.4</td></tr><tr><td>Adventurer-Base (ours)</td><td>Mamba</td><td>448</td><td>99M</td><td>216</td><td>45.2G</td><td>84.3</td></tr><tr><td>DeiT-Base/P14 (our impl.)</td><td>Self-Attention</td><td>448</td><td>86M</td><td>86</td><td>&gt;80G</td><td>83.5</td></tr><tr><td>MambaReg-L [50]</td><td>Mamba</td><td>224</td><td>341M</td><td>67</td><td>55.5G</td><td>83.6</td></tr><tr><td>MambaReg-B [50]</td><td>Mamba</td><td>384</td><td>99M</td><td>63</td><td>51.4G</td><td>84.3</td></tr><tr><td>EfficientNet-B7 [45]</td><td>2D Conv.</td><td>560</td><td>66M</td><td>61</td><td>&gt;80G</td><td>84.3</td></tr><tr><td>DeiT-Base/P14 (our impl.)</td><td>Self-Attention</td><td>560</td><td>87M</td><td>41</td><td>&gt;80G</td><td>84.0</td></tr><tr><td>MambaReg-L [50]</td><td>Mamba</td><td>384</td><td>342M</td><td>23</td><td>&gt;80G</td><td>84.5</td></tr><tr><td>Adventurer-Base/P8 (ours)</td><td>Mamba</td><td>448</td><td>100M</td><td>57</td><td>&gt;80G</td><td>84.8</td></tr></table>
+
+Table 2. ImageNet classification Results. We report training throughput and GPU memory to reflect the actual time and space complexity of the models. We group the baselines by throughput with best results bolded. Our results are highlighted in blue. It shows that Adventurer is significantly faster than other Mamba-based models while achieving accuracies comparable to ViT and CNN baselines. As resolution increases, Adventurer exhibits superior efficiency-accuracy trade-offs over both Mamba and ViT models.
+
+118K training images, 5K validation images, and 20K test images. Following the previous work [57], we employ a Cascade Mask R-CNN [3] decoder head and train the model using the AdamW optimizer with 1e-4 learning rate, 0.05 weight decay, and a total batch size of 16 for 12 epochs.
+
+# 4.2. Main Results
+
+Image classification. We evaluate our models on the ImageNet-1k classification benchmark and summarize the results in Table 2. As is shown, our Adventurer models consistently achieve the best predictive performance at each level of training costs, demonstrating the significant efficiency and effectiveness of our one-way causal image modeling paradigm. Remarkably, by increasing the input size and decreasing the patch size, we obtain a competitive  $84.8\%$  test accuracy with a base-sized model (100M parameters), which showcases the significant impact of scaling up input resolution and reducing receptive granularity on image understanding. This observation also directly underscores the importance of introducing causal image models with linear complexity — while increasing resolution or reducing granularity substantially aids visual encoding, scaling inputs is particularly challenging for transformers. For example, if we double the width and height of an input image, the length of the token sequence becomes  $4\times$
+
+as large. For self-attention, this approximately leads to a  $16 \times$  computation demand and can easily exceed the limits of existing hardware.
+
+It is equally noteworthy that the Adventurer models are significantly faster than other vision Mamba counterparts such as Vim [57], Mamba-Reg [50], and VMamba [29], while this speed improvement primarily originates from our one-way scanning strategy. For example, compared with the previous pure Mamba architecture Vim-Base (98M parameters), our Adventurer-Base (99M parameters) is  $4.2 \times$  faster yet achieves  $0.7\%$  higher test accuracy on ImageNet. More importantly, while most Mamba-based architectures demonstrate a theoretical acceleration over transformers in processing long sequences, their actual speed often falls short when training with the common 196-length short sequences (i.e., the  $224 \times 224$  input with  $16 \times 16$  patch size). However, our Adventurer framework makes the first Mamba-based structure whose training speed is comparable to vision transformers in processing such short sequences, and this speed advantage expands as the sequence length increases, achieving about a  $15 \times$  acceleration over transformers when dealing with sequences at the 3,000-token level.
+
+Semantic Segmentation. We further conduct semantic segmentation experiments to validate Adventurer's effectiveness in dense prediction. As summarized in Table 3, our
+
+<table><tr><td>Backbone</td><td>Params</td><td>Latency (↓)</td><td>mIoU (%)</td></tr><tr><td>ResNet-50 [18]</td><td>64M</td><td>0.69×</td><td>42.0</td></tr><tr><td>DeiT-Tiny [46]</td><td>33M</td><td>0.62×</td><td>40.1</td></tr><tr><td>DeiT-Small [46]</td><td>51M</td><td>0.68×</td><td>44.0</td></tr><tr><td>Adventurer-Tiny (ours)</td><td>20M</td><td>0.50×</td><td>42.1</td></tr><tr><td>Adventurer-Small (ours)</td><td>56M</td><td>0.64×</td><td>45.8</td></tr><tr><td>ResNet-101 [18]</td><td>83M</td><td>0.74×</td><td>43.8</td></tr><tr><td>Vim-Tiny [57]</td><td>16M</td><td>0.77×</td><td>41.2</td></tr><tr><td>Vim-Small [57]</td><td>48M</td><td>0.85×</td><td>45.0</td></tr><tr><td>MambaReg-S [50]</td><td>56M</td><td>0.86×</td><td>45.3</td></tr><tr><td>Adventurer-Base (ours)</td><td>115M</td><td>0.86×</td><td>46.6</td></tr><tr><td>DeiT-Base [46]</td><td>119M</td><td>1.00×</td><td>45.5</td></tr><tr><td>MambaReg-B [50]</td><td>132M</td><td>1.42×</td><td>47.7</td></tr><tr><td>MambaReg-L [50]</td><td>377M</td><td>2.12×</td><td>49.1</td></tr><tr><td>Adventurer-Base/P8 (ours)</td><td>115M</td><td>2.04×</td><td>49.4</td></tr></table>
+
+Table 3. ADE20k semantic segmentation results. All backbones are pretrained on ImageNet and employ an UperNet decoder head for dense prediction. We group the models by their training latency relative to DeiT-Base. Our results are marked in blue. The best result for each group is bolded.  
+
+<table><tr><td>Backbone</td><td>APb</td><td>APb50</td><td>APb75</td><td>APm</td><td>APm50</td><td>APm75</td></tr><tr><td>ResNet-50 [18]</td><td>41.2</td><td>59.4</td><td>45.0</td><td>35.9</td><td>56.6</td><td>38.4</td></tr><tr><td>ReNet-101 [18]</td><td>42.9</td><td>61.0</td><td>46.6</td><td>37.3</td><td>58.2</td><td>40.1</td></tr><tr><td>DeiT-Tiny [46]</td><td>44.4</td><td>63.0</td><td>47.8</td><td>38.1</td><td>59.9</td><td>40.5</td></tr><tr><td>DeiT-Small [46]</td><td>44.7</td><td>65.8</td><td>48.3</td><td>39.9</td><td>62.5</td><td>42.8</td></tr><tr><td>DeiT-Base [46]</td><td>47.2</td><td>66.3</td><td>51.5</td><td>41.8</td><td>64.7</td><td>44.9</td></tr><tr><td>Vim-Tiny [57]</td><td>45.7</td><td>63.9</td><td>49.6</td><td>39.2</td><td>60.9</td><td>41.7</td></tr><tr><td>Adventurer-Tiny</td><td>46.5</td><td>65.2</td><td>50.4</td><td>40.3</td><td>62.2</td><td>43.5</td></tr><tr><td>Adventurer-Small</td><td>47.8</td><td>66.7</td><td>51.8</td><td>41.5</td><td>63.9</td><td>44.5</td></tr><tr><td>Adventurer-Base</td><td>48.4</td><td>67.2</td><td>52.4</td><td>42.0</td><td>64.8</td><td>45.0</td></tr></table>
+
+models achieve higher mIoU than the baselines at different levels of training speed. As dense prediction tasks favor higher input resolutions than classification, the speed disadvantage of transformers when processing long sequences becomes evident. Under the default  $512 \times 512$  input size and  $16 \times 16$  patch size setup, out Adventurer-Base becomes  $1.2 \times$  faster than DeiT-Base ( $2.1 \times$  faster if only comparing encoding time) and outperforms it by  $1.1\%$  mIoU. Notably, in semantic segmentation task, we are the first to successfully scale the sequence length to 6,400 and achieves a competitive mIoU of  $48.5\%$ , which significantly outperforms MambaReg's  $47.7\%$  that consumes similar training cost.
+
+Object detection and instance segmentation. We also benchmark the performance of our model on object detection and instance segmentation tasks to further demonstrate its generalizability. Similar to the semantic segmentation task, here our Adventurer models consistently exhibit superior efficiency than CNN, Transformer, as well as Mamba-based models. For example, to attain a bounding-box average precision of  $48.4\%$ , the existing SoTA of pure Mamba architecture (MambaReg-Base [50]) requires  $3.9 \times$  training
+
+Table 4. COCO object detection and instance segmentation results. All backbones are pretrained on ImageNet and employ a Cascade Masked R-CNN [3] decoder head for the two downstream tasks. Our results are marked in blue. The best results are bolded.  
+
+<table><tr><td>Model</td><td>Causal</td><td>Head avg.</td><td>ILF</td><td>Accuracy (%)</td></tr><tr><td>DeiT-Small</td><td>✓</td><td>✗</td><td>✗</td><td>78.8</td></tr><tr><td>DeiT-Small</td><td>✓</td><td>✓</td><td>✗</td><td>79.1 (+0.3)</td></tr><tr><td>DeiT-Small</td><td>✓</td><td>✗</td><td>✓</td><td>79.6 (+0.8)</td></tr><tr><td>DeiT-Small</td><td>✓</td><td>✓</td><td>✓</td><td>79.9 (+1.1)</td></tr><tr><td>DeiT-Small</td><td>✗</td><td>✗</td><td>✗</td><td>79.9 (+1.1)</td></tr><tr><td>Adventurer-Small</td><td>✓</td><td>✗</td><td>✗</td><td>80.3</td></tr><tr><td>Adventurer-Small</td><td>✓</td><td>✓</td><td>✗</td><td>80.8 (+0.5)</td></tr><tr><td>Adventurer-Small</td><td>✓</td><td>✗</td><td>✓</td><td>81.2 (+0.9)</td></tr><tr><td>Adventurer-Small</td><td>✓</td><td>✓</td><td>✓</td><td>81.8 (+1.5)</td></tr></table>
+
+Table 5. Ablation study of Causal Image Modeling. We ablate the effect of Heading Average and Inter-Layer Flipping (ILF), which serve as two key components of our causal image modeling framework. We make causal DeiT models by applying the attention mask discussed in Figure 2a. The accuracy denotes ImageNet classification results. Our default setup is highlighted in blue.  
+
+<table><tr><td>Mode</td><td>Latency</td><td>Tiny</td><td>Small</td><td>Base</td></tr><tr><td>24 × Mamba layers</td><td>1.3×</td><td>78.0</td><td>81.6</td><td>82.3</td></tr><tr><td>12 × Mamba + 12 × MLP</td><td>1.0×</td><td>78.0</td><td>81.7</td><td>82.4</td></tr><tr><td>12 × Mamba + 12 × SwiGLU</td><td>1.0×</td><td>78.2</td><td>81.8</td><td>82.6</td></tr></table>
+
+Table 6. Ablation study of channel mixers. Here we compare three different choices: a simple MLP with a  $4 \times$  hidden dimension, a SwiGLU MLP with a  $2.5 \times$  hidden dimension, and no channel mixer but doubled Mamba layers. The reported results are ImageNet test accuracy (\%). "Latency" denotes required training time relative to our default setup which is highlighted in blue.
+
+time. By now, the Adventurer models have obtained favorable results in four different visual understanding tasks, showcasing that our causal image modeling framework facilitates both image-level and pixel-level inference. With significant speed advantages, these experimental results demonstrate the good potential of Adventurer to serve as a foundational visual backbone for future applications, particularly in meeting the practical demands for increasingly high-resolution and fine-grained images.
+
+# 4.3. Ablation Studies
+
+Components of causal image modeling. We first ablate the effect of the key components of our causal image modeling framework. As summarized in Table 5, the heading average and inter-layer flipping mechanisms consistently benefit both Transformer and Adventurer models. The table shows that a naive causal modeling is not sufficient to match the baseline performance of existing models, yet our simple designs can effectively address this problem with quite minimal costs. We also observe that the flipping operation typically contributes more to the performance improvement than heading average, which is possibly because flipping not only addresses the information imbalance issue but also facilitates learning direction-invariant features.
+
+Choices of channel mixers. As is introduced above, the Adventurer models by default use Mamba as token mixers and SwiGLU MLP as channel mixers. In previous experience, using only Mamba layers [7, 50], or employing
+
+<table><tr><td>#Tokens</td><td>Acc. (%)</td><td>Token</td><td>Acc. (%)</td><td>Reca.</td><td>Acc. (%)</td></tr><tr><td>1</td><td>79.5</td><td>Duplicate [cls]</td><td>81.4</td><td>X</td><td>81.4</td></tr><tr><td>4</td><td>79.5</td><td>new token</td><td>81.5</td><td></td><td></td></tr><tr><td>9</td><td>79.3</td><td>average</td><td>81.8</td><td>✓</td><td>81.8</td></tr><tr><td colspan="2">(a) #Heading tokens</td><td colspan="2">(b) Design choices</td><td colspan="2">(c) Recalculation</td></tr></table>
+
+Table 7. Ablation study of heading tokens. We use an Adventurer-Small and report ImageNet test accuracy. Results are based on  $192^{2}$  sized inputs for (a) and  $224^{2}$  for (b) and (c). (a): We divide all patch tokens into  $N$  parts, averaging them as heading tokens. (b): We compare the effect of duplicating the class token or learning a new one as the heading token. (c): By default, we recalculate the heading average token at the beginning of each token mixer and ablate its impact here.
+
+simple MLPs like those in the original vision transformers [10, 37], has also yielded competitive performance on both visual and language tasks. Here we compare these three different designing choices and summarize the results in Table 6. Compared to the Mamba-only architecture, our model shows an overall accuracy improvement of around  $0.2\%$ , demonstrating the significant role of introducing a dedicated channel mixers in enhancing model representational capabilities. In addition, since linear layers have better compatibility with hardware, incorporating MLP-like channel mixers also results in a considerable speed increase.
+
+Designing the heading token. To develop Adventurer models, we have tried many different types of heading tokens to facilitate our one-way scanning approach. Here we present these ablation studies in Table 7. First, instead of using a single heading token that is calculated by globally pooling all patches, we can employ relatively finer-grained tokens to represent the global context. In detail, we attempt to equally divide all patch tokens into  $N$  grids in the 2D space, averaging the features within each grid to form more and finer heading tokens. However, as summarized in Table 7a, this strategy does not improve performance and may disrupt the original feature distribution, leading to accuracy degradation when there are too many heading tokens.
+
+In Table 7b, we also try two more variants that duplicate the class token or train a new learnable token as the heading token, yet both fall short when comparing with our default setup. Additionally, Table 7c proves that it is necessary to recalculate the heading average token at the beginning of each Adventurer layers. These experiments validate our initial hypothesis about the functionality of the heading average mechanism: we need a token that compresses as much global context as possible to serve as the starting point of the sequence. This helps address the issue of tokens at the beginning of the sequence receiving insufficient information. Calculating an average token before the start of each layer proves to be the most straightforward and effective method to accomplish this objective.
+
+![](images/621007a662bebdbb934fb7fc64092e85d68dc0fe699af30064e245f8ab49017a.jpg)  
+Figure 5. Results of patch size scaling. We reduce the patch size to form very long vision sequences and observe that Adventurer can consistently obtain performance gains. Here we test on  $128 \times 128$  inputs with a maximum sequence length of 16,384.
+
+# 4.4. Discussions
+
+In this paper, we construct a highly efficient causal image model by optimizing vision Mamba's architectural designs. The significance of this advancement does not lie in the amount of performance improvement under current testing standards, but rather in providing a practical model that can be used to explore the scaling potentials of modern visual architectures for super-long visual sequences. It is noteworthy that such scaling is very challenging for transformers due to their quadratic complexity. For example, the recent Pixel Transformer [34] attempts to reduce the patch size of ViT to  $1 \times 1$  to assess the impact of inductive bias on the model, but they can only resize ImageNet images to  $28 \times 28$  to meet hardware constraints. In contrast, with Adventurer, this scaling experiment becomes feasible with manageable resources, and here we show the corresponding results for a  $128 \times 128$  input size in Figure 5. For future works, we are utilizing Adventurer's great computational efficiency and linear complexity to further explore the model's predictive performance on super-long visual sequences [51].
+
+# 5. Conclusion
+
+In this work, we are motivated to build a simple and efficient visual backbone by causal image modeling. Through extensive empirical studies, we find that by employing two simple mechanisms—Heading Average and Inter-Layer Flipping—causal models can well integrate with visual inputs, matching or even surpassing the predictive performance of traditional vision transformers. Compared to existing vision Mamba architectures (e.g., Vim and MambaReg), our Adventurer framework achieves a significant speed improvement of  $4\sim 5$  times by simplifying the structure, greatly enhancing the practicality of causal models in vision tasks. We hope this work can inspire future explorations in super-long visual sequence modeling.
+
+# Acknowledgment
+
+This work is supported by NEI Award ID R01EY037193 and ONR: N00014-21-1-2690.
+
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\ No newline at end of file
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+# Adversarial Diffusion Compression for Real-World Image Super-Resolution
+
+Bin Chen $^{1,4,*}$  Gehui Li $^{1,*}$  Rongyuan Wu $^{3,4,*}$  Xindong Zhang $^{4}$   
+Jie Chen $^{1,\dagger}$  Jian Zhang $^{1,2,\dagger}$  Lei Zhang $^{3,4}$
+
+$^{1}$ School of Electronic and Computer Engineering, Peking University  
+ $^{2}$ Guangdong Provincial Key Laboratory of Ultra High Definition Immersive Media Technology, Shenzhen Graduate School, Peking University  
+ $^{3}$ The Hong Kong Polytechnic University  $^{4}$ OPPO Research Institute
+
+{chenbin, ligehui921}@stu.pku.edu.cn rong-yuan.wu@connect.polyu.hk zhangxindong1@oppo.com
+
+{jiechen2019,zhangjian.sz}@pku.edu.cn cslzhang@comp.polyu.edu.hk
+
+# Abstract
+
+Real-world image super-resolution (Real-ISR) aims to reconstruct high-resolution images from low-resolution inputs degraded by complex, unknown processes. While many Stable Diffusion (SD)-based Real-ISR methods have achieved remarkable success, their slow, multi-step inference hinders practical deployment. Recent SD-based one-step networks like OSEDiff and S3Diff alleviate this issue but still incur high computational costs due to their reliance on large pretrained SD models. This paper proposes a novel Real-ISR method, AdcSR, by distilling the one-step diffusion network OSEDiff into a streamlined diffusion-GAN model under our Adversarial Diffusion Compression (ADC) framework. We meticulously examine the modules of OSEDiff, categorizing them into two types: (1) Removable (VAE encoder, prompt extractor, text encoder, etc.) and (2) Prunable (denoising UNet and VAE decoder). Since direct removal and pruning can degrade the model's generation capability, we pretrain our pruned VAE decoder to restore its ability to decode images and employ adversarial distillation to compensate for performance loss. This ADC-based diffusion-GAN hybrid design effectively reduces complexity by  $73\%$  in inference time,  $78\%$  in computation, and  $74\%$  in parameters, while preserving the model's generation capability. Experiments manifest that our proposed AdcSR achieves competitive recovery quality on both synthetic and real-world datasets, offering up to  $9.3 \times$  speedup over previous one-step diffusion-based methods. Code and models are available at https://github.com/Guaishou74851/AdcSR.
+
+![](images/94c673f1e980870341e072653678ed95f89b9f9a391dcb2f1cca8ac1e9dd6d27.jpg)  
+Figure 1. Comparison between our proposed AdcSR and typical one-step diffusion-based Real-ISR methods. (a) The state-of-the-art one-step diffusion network OSEDiff [96] employs complete SD [80] models for Real-ISR, suffering from high computational costs. (b) We distill OSEDiff (ADC-teacher) into a smaller diffusion-GAN hybrid model, AdcSR (ADC-student), under the proposed ADC framework, achieving significantly improved efficiency while maintaining competitive recovery performance.
+
+# 1. Introduction
+
+Image super-resolution (ISR) [17, 49, 54, 84, 120] is a fundamental and long-standing problem in computer vision. It aims to reconstruct the high-resolution (HR) image from a low-resolution (LR) counterpart. One line of ISR research assumes that the LR image  $\mathbf{x}_{\mathrm{LR}}$  is a bicubic-downsampled version of the HR image  $\mathbf{x}_{\mathrm{HR}}$ . However, deep ISR networks trained using this assumption often struggle to generalize to real-world scenarios, where degradations are more complex and typically unknown. Another increasingly popular line of ISR research, known as real-world ISR (Real-ISR) [90, 114], employs random shufflings of degradation operations and high-order degradation processes to synthesize LR-HR training pairs. These approaches have improved the performance of deep ISR networks in real-world scenarios.
+
+In the field of ISR and Real-ISR, generative adversarial networks (GANs) [3, 22, 25, 50, 63, 89, 105, 122] like SR-
+
+![](images/38e459749193796fa99b548918be7e4c4c0021bf0915fcafd549f9c4e93bac2b.jpg)  
+Figure 2. Comparison of our proposed AdcSR with other existing one-step diffusion-based Real-ISR methods [91, 96, 112] in terms of visual quality of super-resolution images (top) and model efficiency (bottom). The proposed AdcSR model shows competitive performance in recovering photo-realistic details, while providing the highest inference speed on an NVIDIA A100 GPU, the lowest computational cost, and the second-fewest parameters.
+
+GAN [42], BSRGAN [114], and Real-ESRGAN [90] have shown greater effectiveness than non-generative models [6–9, 11, 24, 43, 46, 85, 119, 121] in producing realistic details. In addition to GANs, diffusion [12, 15, 36, 77]-based methods such as SR3 [71], StableSR [88], and SeeSR [97] have enhanced the quality of super-resolved images by training powerful diffusion networks [14, 44, 60, 83, 110, 111] and leveraging pretrained text-to-image (T2I) diffusion models [20, 53, 68, 81, 88, 106, 109] such as Stable Diffusion (SD) [67, 70, 75, 80]. However, these GANs and diffusion-based Real-ISR approaches suffer from limited recovery quality or slow inference with tens to hundreds of sampling steps.
+
+Recently, efforts [26, 37, 45, 65, 100] have been made to improve the inference speed of diffusion models for RealISR. For instance, SinSR [91] distills the 15-step ResShift [111] into a one-step student ISR model. However, it does not utilize large pretrained T2I models and tends to produce oversmoothed results [13, 96, 112]. Building on pretrained SD models, OSEDiff [96] applies variational score distillation (VSD) [94] to ensure the realism of super-resolution images with a one-step diffusion sampling. S3Diff [112] designs a degradation-guided Low-Rank Adaptation (LoRA) [30] module and an online negative sample generation strategy to improve the perceptual quality of images. Nevertheless, the complexity of these approaches in terms of parameter number and inference time can still be too high for real deployments, especially on resource-limited edge devices.
+
+To reduce complexity while maintaining recovery quality, in this paper, we propose a novel diffusion-based RealISR model AdcSR, which is obtained by applying our proposed adversarial diffusion compression (ADC) framework to OSEDiff. Our main idea is based on the hypothesis that, given LR input  $\mathbf{x}_{\mathrm{LR}}$  containing abundant information about the target HR image  $\mathbf{x}_{\mathrm{HR}}$ , a structurally compressed version of SD-based one-step diffusion networks like OSEDiff [96] has a sufficient capacity to learn an effective Real-ISR mapping. As illustrated in Fig. 1, we remove the variational
+
+autoencoder (VAE) encoder, prompt extractor, text encoder, cross-attention (CA), and time embedding layers in the SD UNet which we find less important than other modules like self-attention (SA) layers to develop the architecture of AdcSR. Then, we compress the remaining denoising UNet and VAE decoder using channel pruning for improved efficiency. To preserve the model's generative recovery ability while ensuring training efficiency, inspired by the success of diffusion GANs [32, 35, 52, 59, 74, 93, 98, 102, 107], we pretrain our pruned VAE decoder and introduce adversarial distillation in the feature space of VAE decoder. This enables AdcSR to utilize the information from pretrained SD and OSEDiff models, as well as the ground truth (GT) images. By doing so, we significantly reduce the complexity of OSEDiff while maintaining competitive recovery quality, as shown in Fig. 2. In summary, our contributions are:
+
+(1) We introduce ADC, a novel framework that combines structural compression (module removal and pruning) with adversarial distillation (knowledge distillation with adversarial loss) to streamline SD-based one-step Real-ISR models into smaller diffusion-GAN hybrid networks.  
+(2) By applying ADC to a state-of-the-art SD-based one-step network [96], we propose AdcSR model, a structurally compressed diffusion GAN that effectively achieves a  $3.7 \times$  inference acceleration and a  $74\%$  reduction in parameters.
+
+# 2. Related Work
+
+Real-ISR based on LR-HR Pair Synthesis. To make ISR networks applicable to real scenarios, BSRGAN [114] and Real-ESRGAN [90] pioneer the use of shuffled and high-order degradations to synthesize LR-HR pairs for training Real-ISR GANs. They inspire a lot of works [10, 50, 99, 118] that develop new degradation prediction mechanisms [51, 63] and network structures [11, 49, 55]. However, these approaches often suffer from artifacts and oversmoothing.
+
+The success of diffusion models in high-quality generation has prompted researchers to explore leveraging powerful diffusion priors like SD [70, 80] for Real-ISR. Most SD-based methods [53, 81, 109] train adapter modules [64, 116] that use the LR image as control signal to guide the superresolution processes. For example, StableSR [88] finetunes a time-aware encoder and introduces a controllable feature warping module to balance quality and fidelity. PASD [106] extracts both low-level and high-level features from the LR image and inputs them into the pretrained SD model with a pixel-aware CA module. SeeSR [97] enhances model's semantic awareness by using degradation-robust tag-style text prompts and soft prompts to guide diffusion sampling. In addition to these, ResShift [111] introduces a new residual shifting-based diffusion model to improve the efficiency of the transition from  $\mathbf{x}_{\mathrm{LR}}$  to  $\mathbf{x}_{\mathrm{HR}}$ . However, these approaches require tens to hundreds of iterative steps for diffusion sam
+
+pling, which increases inference latency and limits their application in real deployments where fast inference is critical.
+
+Diffusion Distillation for One-Step Inference. To accelerate the generation process of diffusion models, numerous techniques [23, 27, 57, 62, 69, 72, 101, 103, 124] have been proposed to distill a multi-step diffusion sampling process into a student model with fewer steps. Recent methods [2, 125] further reduce the required number of steps to just one. For instance, InstaFlow [56] distills an ordinary differential equation (ODE) sampling trajectory into a one-step network. Consistency models [58, 78] learn to output consistent results at any timestep. Subsequent works like CTM [35], SDXL-Lightning [52], UFOGen [102], LADD [74], DMD2 [108], and Diffusion2GAN [32] leverage adversarial distillation to improve the quality of generated images using pretrained networks as discriminators. For Real-ISR, SinSR [91] shortens ResShift [111] via bidirectional distillations. OSEDiff [96] introduces VSD [94] approach in latent space to enhance the realism of super-resolved images. Building upon the distilled SD-Turbo [73] models, S3Diff [112] designs a degradation-guided LoRA module and an online negative prompting strategy for improved ISR quality. However, the complexity of existing SD-based one-step diffusion networks remains too high for real deployment on mobile and edge devices due to their large-scale parameters and heavy computation. To mitigate this problem, we structurally compress and distill OSEDiff into a smaller diffusion GAN, enhancing efficiency while maintaining performance.
+
+Structural Compression for Latent Diffusion Models. To achieve photo-realistic image generation, large-scale latent diffusion models [67, 70, 80] are widely employed due to their powerful generative priors. However, the deployment of these models is hindered by their high computation costs. To address this issue, a lot of works [5, 21, 113, 123, 125] have explored compression techniques for efficiency. For example, BK-SDM [34] applies block removal for SD models. SnapFusion [48] designs block-removed UNet and efficient VAE decoder with an improved distillation approach, achieving 8-step T2I inferences. To our knowledge, no existing compression techniques are specifically designed for diffusion-based Real-ISR. In this work, we propose a novel method based on introduced adversarial diffusion compression (ADC). Moving beyond previous one-step approaches [13, 45, 91, 96, 112], we demonstrate that, given LR image as a starting point of super-resolution, the latent encoding, prompt extraction, text-conditioned denoising, and decoding can be compressed into an optimized diffusion GAN.
+
+# 3. Method
+
+# 3.1. Preliminary
+
+OSEDiff, and Its Limitations. OSEDiff [96] is a typical state-of-the-art one-step diffusion-based Real-ISR method
+
+that employs a LoRA-finetuned SD VAE encoder  $\mathcal{E}_{\mathrm{OSEDiff}}$ , a LoRA-finetuned SD UNet  $\epsilon_{\mathrm{OSEDiff}}$ , a pretrained SD VAE decoder  $\mathcal{D}_{\mathrm{SD}}$ , and a pretrained prompt extractor  $\mathcal{C}$  [97] to perform super-resolution through the following process:
+
+$$
+\mathbf {z} _ {\mathrm {L R}} = \mathcal {E} _ {\text {O S E D i f f}} \left(\mathbf {x} _ {\mathrm {L R}}\right), \quad \mathbf {c} = \mathcal {C} \left(\mathbf {x} _ {\mathrm {L R}}\right), \tag {1}
+$$
+
+$$
+\hat {\mathbf {z}} _ {\mathrm {H R}} = \left[ \mathbf {z} _ {\mathrm {L R}} - \sqrt {1 - \bar {\alpha} _ {T}} \boldsymbol {\epsilon} _ {\mathrm {O S E D i f f}} (\mathbf {z} _ {\mathrm {L R}}; T, \mathbf {c}) \right] / \sqrt {\bar {\alpha} _ {T}}, \tag {2}
+$$
+
+$$
+\hat {\mathbf {x}} _ {\mathrm {H R}} = \mathcal {D} _ {\mathrm {S D}} \left(\hat {\mathbf {z}} _ {\mathrm {H R}}\right). \tag {3}
+$$
+
+In Eq. (1), the LR image  $\mathbf{x}_{\mathrm{LR}}$  is encoded into the VAE latent space, and text prompts  $\mathbf{c}$  are extracted from  $\mathbf{x}_{\mathrm{LR}}$  in parallel. In Eq. (2), one-step diffusion denoising is executed using the noise schedule  $\{\bar{\alpha}_t\}$  [29] at the  $T$ -th timestep. Finally, in Eq. (3), the denoised latent code is decoded back into image space to obtain the super-resolution image  $\hat{\mathbf{x}}_{\mathrm{HR}}$ . However, OSEDiff has a total parameter number of 1775M and an inference latency of 0.11s on an NVIDIA A100 GPU for a  $512 \times 512$  target HR image, which can still be too expensive for real deployment environments where both computational and storage resources are limited. Similar challenges persist in other one-step diffusion-based methods utilizing large-scale pretrained SD models [13, 45, 65, 82, 100, 112].
+
+# 3.2. Structural Compression Strategy
+
+To improve the efficiency of SD-based Real-ISR methods, we propose an Adversarial Diffusion Compression (ADC) framework. Its key insight is that ISR differs from T2I tasks, which rely solely on text inputs for generation, while the LR image in Real-ISR provides rich information about the target HR image. Thus, unlike previous SD-based one-step approaches that employ complete SD model structures, we hypothesize that competitive Real-ISR performance does not require these full architectures, which have been validated to possess sufficient capacity for one-step T2I and Real-ISR (see Sec. 2). Taking OSEDiff [96] as example in this work, we propose that the modules used in Eqs. (1)-(3) contain redundancy and can be removed or pruned for efficiency. To be specific, as shown in Fig. 1, we categorize the modules into two types: (1) Removable (VAE encoder, prompt extractor, text encoder, CA layers, and time embeddings) and (2) Prunable (denoising UNet and VAE decoder). Based on this categorization, in ADC, we design a structural compression strategy that includes two modifications for SD-based one-step methods: (1) Removal of unnecessary modules, and (2) Pruning of remaining compressible modules. In the following, we detail and justify these modifications.
+
+# 3.2.1. Removal of Unnecessary Modules
+
+Eliminating VAE Encoder. In previous SD-based one-step Real-ISR approaches, the VAE encoder maps  $\mathbf{x}_{\mathrm{LR}}$  to a latent code  $\mathbf{z}_{\mathrm{LR}}$ , as shown in Eq. (1). This process involves multiple downsampling operations, which can lead to the loss of information important for Real-ISR. To preserve the complete information of the LR input without loss, we eliminate
+
+![](images/03217449ec9d8a34bbbe2a5339a510edad35720cb4b6629805edb912ee0fd678.jpg)  
+Figure 3. Illustration of the training and inference processes of AdcSR, an instantiation of our ADC framework applied to OSEDiff. (a) In Stage 1, we pretrain a pruned VAE decoder that shares the latent space with SD and OSEDiff. (b) In Stage 2, we distill the knowledge from OSEDiff (ADC-teacher) into AdcSR (ADC-student) by aligning features in the pretrained decoder. An adversarial loss encourages the student to generate features that can fool a LoRA-finetuned SD UNet (ADC-discriminator), utilizing the corresponding real features of GT images. Since all supervisions perform in the feature space, there is no need to decode images as in previous approaches [96, 112]. (c) During inference, the LR image is directly fed into our trained compressed UNet and VAE decoder to obtain the super-resolution result.
+
+![](images/38ed522cfc7197c84e523e17eed15b3ba1b14e27d1d35dfdf73d62839ad979a5.jpg)
+
+![](images/61951f3da690c8e2649adb94d3c6b6aed507a79c07510ec4990371433a63407b.jpg)
+
+the VAE encoder entirely. Instead, we apply a PixelUnshuffle [76] operation to  $\mathbf{x}_{\mathrm{LR}}$  , rearranging its spatial pixels into channel dimension while maintaining the same spatial size as  $\mathbf{z}_{\mathrm{LR}}$  . Correspondingly, the first convolution of UNet is adjusted to match the increased channel number, and the output of PixelUnshuffle is then directly input into the UNet.
+
+Removing Text and Time Modules. In models like OSEDiff, a prompt extractor generates textual prompts from  $\mathbf{x}_{\mathrm{LR}}$ , which are then used in text encoder and CA layers within the denoising UNet, as shown in Eqs. (1) and (2). Additionally, time embeddings are included to condition the UNet on different timesteps. While the text prompts are generally important for guiding T2I synthesis, in the specific context of Real-ISR, we have empirically observed that they contribute less significantly to enhance quality, compared to the other remaining modules. Furthermore, since OSEDiff performs only one-step diffusion sampling, time embeddings are unnecessary, as there is no need to differentiate between timesteps. Therefore, we remove the prompt extractor, text encoder, CA layers, and time embeddings from the UNet, retaining only its SA, linear, and convolutional layers.
+
+# 3.2.2. Pruning of Remaining Modules
+
+Optimizing UNet-VAE Decoder Connection. Before decoding the output image, traditional SD-based methods like OSEDiff map the high-capacity feature (often hundreds of channels) in UNet to a 4-channel latent code  $\hat{\mathbf{z}}_{\mathrm{HR}}$ . This dimensionality reduction can potentially result in a loss of feature information and constrain the model's representation ability. To mitigate this and fully leverage the rich feature representations learned by the UNet, we enhance the information flow between UNet and VAE decoder. Specifically, we remove the output layer of UNet and the input layer of VAE decoder, which reduce and then increase the feature channels. Instead, we introduce a convolution layer that directly connects the high-dimensional feature in UNet to the
+
+first blocks of the VAE decoder, improving the model's recovery quality while reducing its overall inference latency.
+
+Pruning Feature Channels. We hypothesize that the current one-step model, compressed by the above three operations, still contains redundancy and has sufficient capacity to learn an effective Real-ISR mapping with even fewer parameters. Although previous works [5, 34, 61, 79, 113] compress SD-based models by removing network blocks or layers, we find that this can noticeably degrade the performance of one-step diffusion networks, where the depth of UNet and VAE decoder is already relatively shallow. Further decreasing the depth may impair the ability of model to extract hierarchical features and learn complex transformations for high-quality Real-ISR. To avoid this issue and strike a balance between recovery quality and efficiency, we opt for channel pruning. Concretely, we retain  $75\%$  of the feature channels in the UNet and  $50\%$  channels in the VAE decoder. This reduces the model's complexity while alleviating performance loss by preserving network depth.
+
+The resulting structurally compressed model, which we name AdcSR, incorporates the proposed two modifications in ADC and consists of three modules: (1) a PixelUnshuffle layer that prepares the LR input image  $\mathbf{x}_{\mathrm{LR}}$  for processing by rearranging its pixels without information loss; (2) a channel-pruned SD UNet without text encoder, CA layers, and time embeddings, processing the rearranged LR image while keeping the original depth; and (3) a channel-pruned VAE decoder which receives the high-dimensional features from UNet and generates the super-resolution image  $\hat{\mathbf{x}}_{\mathrm{HR}}$ .
+
+# 3.3. Training Scheme
+
+Direct removal and pruning can degrade the model's generative capabilities due to reduced capacity and altered network structure. To mitigate this, as Fig. 3 shows, our ADC uses a two-stage training scheme: (1) pretraining VAE de
+
+Table 1. Quantitative comparison of different methods on DRealSR. Efficiency metrics are tested on an NVIDIA A100 GPU. Throughout this paper, the best, second-best, and third-best results are highlighted in bold red, underlined blue, and italic green, respectively.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>DISTS↓</td><td>NIQE↓</td><td>MUSIQ↑</td><td>CLIPIQA↑</td><td>#Steps↓</td><td>Time (s)↓</td><td>MACs (G)↓</td><td>#Param. (M)↓</td></tr><tr><td>StableSR [88]</td><td>28.03</td><td>0.7536</td><td>0.3284</td><td>0.2269</td><td>6.52</td><td>58.51</td><td>0.6356</td><td>200</td><td>11.50</td><td>79940</td><td>1410</td></tr><tr><td>DiffBIR [53]</td><td>26.71</td><td>0.6571</td><td>0.4557</td><td>0.2748</td><td>6.31</td><td>61.07</td><td>0.6395</td><td>50</td><td>2.72</td><td>24234</td><td>1717</td></tr><tr><td>SeeSR [97]</td><td>28.17</td><td>0.7691</td><td>0.3189</td><td>0.2315</td><td>6.40</td><td>64.93</td><td>0.6804</td><td>50</td><td>4.30</td><td>65857</td><td>2524</td></tr><tr><td>PASD [106]</td><td>27.36</td><td>0.7073</td><td>0.3760</td><td>0.2531</td><td>5.55</td><td>64.87</td><td>0.6808</td><td>20</td><td>2.80</td><td>29125</td><td>1900</td></tr><tr><td>ResShift [111]</td><td>28.46</td><td>0.7673</td><td>0.4006</td><td>0.2656</td><td>8.12</td><td>50.60</td><td>0.5342</td><td>15</td><td>0.71</td><td>5491</td><td>119</td></tr><tr><td>SinSR [91]</td><td>28.36</td><td>0.7515</td><td>0.3665</td><td>0.2485</td><td>6.99</td><td>55.33</td><td>0.6383</td><td>1</td><td>0.13</td><td>2649</td><td>119</td></tr><tr><td>OSEDiff [96]</td><td>27.92</td><td>0.7835</td><td>0.2968</td><td>0.2165</td><td>6.49</td><td>64.65</td><td>0.6963</td><td>1</td><td>0.11</td><td>2265</td><td>1775</td></tr><tr><td>S3Diff [112]</td><td>27.39</td><td>0.7469</td><td>0.3129</td><td>0.2108</td><td>6.17</td><td>64.16</td><td>0.7156</td><td>1</td><td>0.28</td><td>2621</td><td>1327</td></tr><tr><td>AdcSR (Ours)</td><td>28.10</td><td>0.7726</td><td>0.3046</td><td>0.2200</td><td>6.45</td><td>66.26</td><td>0.7049</td><td>1</td><td>0.03</td><td>496</td><td>456</td></tr></table>
+
+![](images/74446ab2011dc66333c3bc6ffe3bcd03c4d9c7968d3fe250840eca9e4fb717f2.jpg)  
+Figure 4. Efficiency comparison using a bubble plot, showing the inference time, computation, and parameter number (see Tab. 1) for super-resolving a  $128 \times 128$  LR image on an NVIDIA A100 GPU. AdcSR achieves the fastest inference, lightest computation, and second-fewest parameters. Bubble colors represent approach types: green for multi-step, blue for one-step, and red for AdcSR.
+
+coder, and (2) adversarial distillation to compensate for potential performance loss and ensure high-quality Real-ISR.
+
+Stage 1: Pretraining Channel-Pruned VAE Decoder. In the first stage, we pretrain a pruned VAE decoder [19, 86] to restore its ability to decode images. As shown in Fig. 3 (a), we freeze the parameters of the pretrained SD VAE encoder and train only the VAE decoder from scratch. Given an input image  $\mathbf{x}$ , the encoder produces latent codes, which are then decoded back into an image  $\hat{\mathbf{x}}$  by the decoder. To train the decoder, following [70], we adopt a reconstruction loss consisting of a pixel-level  $L_{1}$  loss  $\| \hat{\mathbf{x}} - \mathbf{x} \|_{1}$ , an LPIPS loss [117], and a patch-based adversarial loss [18, 19, 31] to encourage the reconstructed  $\hat{\mathbf{x}}$  to be visually similar to  $\mathbf{x}$ .
+
+Stage 2: Knowledge Distillation with Adversarial Loss. In the second stage, we distill the knowledge from the pretrained OSEDiff (teacher) into our compressed AdcSR (student). Specifically, as illustrated in Fig. 3 (b), we connect the pruned UNet and all the first blocks of pruned decoder at
+
+the level with the smallest spatial size, and jointly finetune them. The student is initialized using the pretrained SD and VAE decoder from Stage 1. Distillation is performed in the feature space by aligning the student's features  $\mathbf{f}_{\mathrm{student}}$  with the teacher's corresponding features  $\mathbf{f}_{\mathrm{teacher}}$  using an  $L_{1}$  loss:
+
+$$
+\mathcal {L} _ {\text {d i s t i l l}} = \left\| \mathbf {f} _ {\text {s t u d e n t}} - \mathbf {f} _ {\text {t e a c h e r}} \right\| _ {1}. \tag {4}
+$$
+
+Here,  $\mathbf{f}_{\mathrm{teacher}}$  is obtained by passing the LR image through the teacher's VAE encoder, prompt extractor, UNet, and all first blocks of the pretrained decoder, while  $\mathbf{f}_{\mathrm{student}}$  is produced from the student's pruned UNet and all first blocks of the pruned decoder. This distillation in feature space is both effective and efficient without the need to decode images.
+
+To further enhance the visual quality of super-resolution outputs, we introduce an adversarial loss on  $\mathbf{f}_{\mathrm{student}}$ , encouraging it to follow the same distribution as the corresponding features of GT images. Specifically, we obtain the real features  $\mathbf{f}_{\mathrm{GT}}$  by encoding  $\mathbf{x}_{\mathrm{HR}}$  using SD encoder and processing them with the first blocks of pruned decoder at the smallest spatial size. We reuse a pretrained SD UNet as the discriminator, where the first convolution layer is adjusted to match the channel number of  $\mathbf{f}_{\mathrm{student}}$  and  $\mathbf{f}_{\mathrm{GT}}$ . In addition, we integrate LoRA modules, ensuring that only the LoRA and the first convolution layer remain trainable, while all other parameters are frozen to efficiently finetune the pretrained SD UNet. The discriminator is conditioned on the text prompts c extracted by the teacher, with timestep fixed at  $T$ . Following [107], we employ the non-saturating adversarial loss:
+
+$$
+\mathcal {L} _ {\mathrm {a d v}} = \text {S o f t p l u s} (- \text {D i s c r i m i n a t o r} (\mathbf {f} _ {\text {s t u d e n t}})), \tag {5}
+$$
+
+which provides fine-grained feedback as the discriminator's output shares the same spatial dimension as input features. The total training loss is defined as  $\mathcal{L} = \mathcal{L}_{\mathrm{distill}} + \lambda_{\mathrm{adv}}\mathcal{L}_{\mathrm{adv}}$
+
+# 4. Experiment
+
+# 4.1. Experimental Setting
+
+Implementation Details. Following [13, 45, 53, 81, 88, 91, 96, 97, 100, 106, 111, 112], we conduct experiments on the Real-ISR task with scaling factor 4. The sizes of LR and HR
+
+![](images/5057b80584d234bb4a4c5468d62ef5c699b221098c8865c1f89cae7326eb0862.jpg)  
+Figure 5. Qualitative comparison on images named "0835_pch_00035" from DIV2K-Val (top) and "Nikon_045" from RealSR (bottom).
+
+images are set to  $128 \times 128$  and  $512 \times 512$  by default. We initialize our pruned SD UNet using the pretrained weights of SD2.1-base [75], reusing only the parameters corresponding to the first  $75\%$  of intermediate feature channels while removing the rest. To match the  $64 \times 64$  spatial size of latent codes in SD, we set the scaling factor of PixelUnshuffle layer to 2. The convolutional kernels and biases in the first and last UNet layers are repeated in the channel dimension to align with the rearranged LR image and the intermediate features of the first blocks in our pruned SD VAE decoder.
+
+In Stage 1, we employ the code of latent diffusion models [41, 70] to pretrain a  $50\%$  channel-pruned SD VAE decoder from scratch on OpenImage [66] for 250K steps, followed by 250K steps on LAION-Face [40] and LAION-Aesthetic [39]. The weighting factors of  $L_{1}$  loss and LPIPS loss are both set to 1, while the weighting factor of the patch-based adversarial loss is set to 0 for the first 50K steps and 1 for the remaining steps. The learning rate is fixed at 1.3e-6.
+
+In Stage 2, we jointly finetune the  $25\%$  channel-pruned UNet and all first blocks at the smallest spatial size of the pretrained VAE decoder from Stage 1 on LSDIR [47] with  $\lambda_{\mathrm{adv}} = 1$  for 200K steps. The learning rate is initialized at 1e-4 and halved for every 100K steps. The learning rate and LoRA rank for the discriminator are set to 1e-6 and 4, respectively. The high-order degradation pipeline of RealESRGAN [90] is used to synthesize LR-HR pairs. In both two stages, we employ the Adam [38] optimizer and a batch size of 96 for training on 8 NVIDIA A100 (80GB) GPUs.
+
+Test Datasets. Following [96, 97, 112], we test AdcSR and compare it with other methods using the 3K synthesized test images from DIV2K-Val [1, 88] and the center-cropped real images from RealSR [4] and DRealSR [95].
+
+Compared Methods. We compare the proposed AdcSR model against eight diffusion-based approaches: StableSR [88], DiffBIR [53], SeeSR [97], PASD [106], ResShift
+
+[111], SinSR [91], OSEDiff [96], and S3Diff [112].
+
+Evaluation Metrics. We adopt both full- and no-reference metrics for performance evaluation. For reference-based fidelity, we use PSNR and SSIM [92], calculated on the Y channel in the YCrCb space. For reference-based perceptual quality, we apply LPIPS [117] and DISTS [16]. FID [28] is also employed to measure the distance between the distributions of GT and super-resolution images. In addition, we utilize no-reference metrics including NIQE [115], MUSIQ [33], MANIQA [104], and CLIPIQA [87].
+
+# 4.2. Comparison with State-of-the-Arts
+
+Image Quality Comparison. The first 8 columns of Tab. 1 manifest that our AdcSR achieves promising results across multiple metrics. Firstly, it ranks in top 3 for full-reference quality metrics SSIM, LPIPS, and DISTS, surpassing most other approaches. Secondly, it attains competitive results in PSNR and no-reference metrics NIQE, MUSIQ, and CLIP-IQA, performing on par with many state-of-the-art methods. Thirdly, compared to the previous one-step diffusion-based models SinSR and particularly its teacher OSEDiff, AdcSR yields superiority in most of the perceptual quality metrics, and remains competitive with S3Diff across various cases.
+
+Figs. 2 (top) and 5 exhibit the competitive performance of AdcSR in recovering sharp and photo-realistic images. We observe that StableSR, DiffBIR, SeeSR, and PASD can bring unnatural artifacts and blurriness at the intersection of the rocky landscape and the water, along with noise and distortions in the regions of leaves. ResShift and SinSR suffer from noticeable blurry artifacts. OSEDiff and S3Diff could generate fewer details on the surfaces of rocks and water, introducing an additional slight highlight effect on the cluster of leaves. In comparison, AdcSR effectively reconstructs vivid details and natural textures in the regions of parrot's feathers, building, rocky landscape, still water, and leaves.
+
+Table 2. Ablation study of eliminating VAE encoder on DRealSR.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>LPIPS↓</td><td>DISTS↓</td><td>#Param. (M)↓</td><td>Time (s)↓</td></tr><tr><td>w/o Elimination</td><td>27.97</td><td>0.3077</td><td>0.2239</td><td>490</td><td>0.05</td></tr><tr><td>w/ Elim. (Ours)</td><td>28.10</td><td>0.3046</td><td>0.2200</td><td>456</td><td>0.03</td></tr></table>
+
+Table 3. Ablation study of optimizing the connection between the denoising UNet and the VAE decoder on DRealSR.  
+
+<table><tr><td>Method</td><td>FID↓</td><td>MUSIQ↑</td><td>MANIQA↑</td><td>CLIPIQA↑</td><td>FPS↑</td></tr><tr><td>w/o Optimization</td><td>140.09</td><td>65.18</td><td>0.5807</td><td>0.6756</td><td>34.66</td></tr><tr><td>w/ Opt. (Ours)</td><td>134.05</td><td>66.26</td><td>0.5927</td><td>0.7049</td><td>34.79</td></tr></table>
+
+![](images/1139ec32d876c311cce295f04a30b0a079ddd1c6d2b295873d1d06682c3d77c1.jpg)  
+Figure 6. Ablation study of our two structural optimizations: eliminating VAE encoder, and optimizing the connection between the denoising UNet and the VAE decoder on "0886_pch_00025" (top) and "0892_pch_00015" (bottom) from DIV2K-Val.
+
+![](images/5dc1edd3a3c58734ab379746d665997d81565c3302ea3b6829815709adb35030.jpg)  
+Figure 7. Ablation study of eliminating VAE encoder on "0815_pch_00001" (left) and "0847_pch_00033" (right) from DIV2K-Val.
+
+Efficiency Comparison. The last 4 columns of Tab. 1 and Fig. 2 (bottom) demonstrate the superior efficiency of proposed AdcSR in step number, inference time, and computational cost. By distilling the SD-based one-step teacher [96] into a structurally compressed diffusion GAN, AdcSR offers substantial speedups:  $383.3 \times$ ,  $90.7 \times$ ,  $143.3 \times$ ,  $93.3 \times$ , and  $23.7 \times$  over previous multi-step approaches StableSR, DiffBIR, SeeSR, PASD, and ResShift, respectively. Compared to the one-step model SinSR, it achieves a  $4.3 \times$  acceleration. Compared to its teacher, the previously fastest method OSEDiff, it achieves a  $3.7 \times$  acceleration, a  $78\%$  reduction in computation, and a  $74\%$  decrease in total parameters. This allows for a real-time speed of 34.79 frames per second (FPS) in diffusion-based Real-ISR. Notably, it attains a significant  $9.3 \times$  speedup over S3Diff, which suffers from slower inferences due to its use of complete SD models and degradation-guided LoRA module. Fig. 4 further visualizes this efficiency comparison using a bubble plot, exhibiting the effective compression and substantial efficiency gains of AdcSR while maintaining recovery quality.
+
+Due to page limitations, please refer to our Supplementary Material for more comparison results and analyses.
+
+Table 4. Ablation study of removing the prompt extractor, text encoder, time embeddings, and related modules on RealSR.  
+
+<table><tr><td>Method</td><td>DISTS↓</td><td>#Param.↓</td><td>Time↓</td></tr><tr><td>w/ Extractor, CA, etc., w/ Time Embeddings</td><td>0.2116</td><td>1311</td><td>0.07</td></tr><tr><td>w/o Extractor, CA, etc., w/ Time Embeddings</td><td>0.2130</td><td>471</td><td>0.03</td></tr><tr><td>w/o Extr., CA, etc., w/o Time Emb. (Ours)</td><td>0.2129</td><td>456</td><td>0.03</td></tr></table>
+
+Table 5. Ablation study of pruning feature channels on RealSR.  
+
+<table><tr><td>Pruning Ratio (UNet / VAE Decoder)</td><td>LPIPS↓</td><td>FID↓</td><td>#Param.↓</td><td>Time↓</td></tr><tr><td>0% / 0% (No Channel Pruning)</td><td>0.2883</td><td>116.74</td><td>839</td><td>0.06</td></tr><tr><td>0% / 50% (Less Channel Pruning)</td><td>0.2839</td><td>118.73</td><td>801</td><td>0.04</td></tr><tr><td>25% / 50% (Ours)</td><td>0.2885</td><td>118.41</td><td>456</td><td>0.03</td></tr><tr><td>50% / 50% (More Channel Pruning)</td><td>0.2897</td><td>125.10</td><td>210</td><td>0.03</td></tr></table>
+
+![](images/e2c6b11c0ddefcaa82e8a62377b745ba637cff7e52bde7f4e36bbe257ebb76d4.jpg)  
+Figure 8. Ablation study of pruning channels with various ratios on "Nikon_027" (top) and "Nikon_043" (bottom) from RealSR.
+
+# 4.3. Ablation Study
+
+Effect of Eliminating the VAE Encoder, and Optimizing the UNet-VAE Decoder Connection. Tab. 2 exhibits that eliminating the encoder of VAE decreases total parameter number and inference time by  $9\%$  and  $40\%$ , while achieving improvements of 0.13dB, 0.0031, and 0.0039 in PSNR, LPIPS, and DISTS metrics, respectively. Tab. 3 validates the effectiveness of optimizing the UNet-decoder connection, which brings improvements of 6.04, 1.08, 0.0120, and 0.0293 in FID, MUSIQ, MANIQA, and CLIPIQA, as well as a 0.13 FPS gain in the inference speed. Fig. 6 visually demonstrates that omitting either of these two operations leads to noticeable blurriness in the regions of parrot's body and the intersecting lattice beams. In particular, as exhibited in Fig. 7, using the VAE encoder to compress the LR input into a latent code causes the loss of key characteristics like the clear separation between tree trunks and branches from the background, the details on the left side of the tire, the subtle shadows, and the fine textures on the car headlights. This may be attributed to the information-lossy processing of the VAE encoder. Overall, these findings indicate that directly feeding the LR image into denoising UNet, and connecting the UNet's features before its final layer to the VAE decoder, without passing through the VAE encoder or compressing into a latent code, can effectively enhance both the fidelity and perceptual quality of super-resolved images.
+
+Table 6. Ablation study of knowledge distillation on RealSR.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>NIQE↓</td><td>CLIPIQA↑</td></tr><tr><td>w/o Dist. (Replacing L/distill with ||fstudent - fGT||1)</td><td>26.75</td><td>8.59</td><td>0.5329</td></tr><tr><td>w/ Distillation in Image Space</td><td>25.80</td><td>6.74</td><td>0.4742</td></tr><tr><td>w/ Dist. in Feature Space of Level 4</td><td>25.54</td><td>6.51</td><td>0.6168</td></tr><tr><td>w/ Dist. in Feature Space of Level 3</td><td>25.49</td><td>5.91</td><td>0.6591</td></tr><tr><td>w/ Dist. in Feature Space of Level 2</td><td>25.43</td><td>5.83</td><td>0.6635</td></tr><tr><td>w/ Dist. in Feature Space of Level 1 (Ours)</td><td>25.47</td><td>5.35</td><td>0.6731</td></tr></table>
+
+![](images/55cc590dd0698acdecada8df906b55b55e55829bccbe36c5f4c7244ff641a737.jpg)  
+Figure 9. Ablation study of knowledge distillation in a feature space vs. image space (IS) and the effect of adversarial loss on "Canon_006" (top) and "Nikon_046" (bottom) from RealSR.
+
+Effect of Removing the Text and Time Modules. Tab. 4 manifests the efficiency gains brought by removing these modules. Concretely, removing extractor, text encoder, and CA layers reduces parameters by  $64\%$  and time by  $57\%$ , with a 0.0014 increase in DISTS. Furthermore, the removal of time embeddings results in a 0.0001 boost in DISTS and an extra  $3\%$  reduction in parameters. Considering the significant decrease in complexity with minor recovery quality drops, these removals are incorporated into our approach.
+
+Effect of Pruning Feature Channels. Tab. 5 presents the results of channel pruning. Our method (pruning  $25\%$  channels in the UNet and  $50\%$  in the VAE decoder) achieves notable reductions of  $46\%$  in parameter number and  $50\%$  in inference time compared to the baseline (no channel pruning), with minor drops of 0.0002 in LPIPS and 1.67 in FID. However, more aggressive pruning ( $50\%$  in both UNet and VAE decoder) leads to a further  $54\%$  reduction in parameters but results in a higher increase of 6.69 in FID and no gains in speed. Fig. 8 shows that more pruning significantly impairs the ability of model to recover textures. Therefore, we choose pruning ratios  $25\%$  and  $50\%$  as default settings.
+
+Effect of Knowledge Distillation in Feature Space. Tab. 6 studies the effect of distilling at various decoder levels, from level 1 (smallest spatial size) to 4 (largest size), and in image space. Firstly, we observe that replacing  $\mathbf{f}_{\mathrm{teacher}}$  with  $\mathbf{f}_{\mathrm{GT}}$  in loss  $\mathcal{L}_{\mathrm{distill}} = \| \mathbf{f}_{\mathrm{student}} - \mathbf{f}_{\mathrm{teacher}}\|_1$  significantly degrades the perceptual quality, leading to a deterioration of 3.24 in NIQE and 0.1402 in CLIPIQA. This confirms the effectiveness of knowledge distillation. Secondly, conducting distillation in the feature space with smallest spatial size achieves the best perceptual quality, yielding improvements of 1.39
+
+Table 7. Ablation study of using adversarial loss on DRealSR.  
+
+<table><tr><td>Method</td><td>LPIPS↓</td><td>DISTS↓</td><td>MUSIQ↑</td><td>MANIQA↑</td></tr><tr><td>w/o Adversarial Loss</td><td>0.3261</td><td>0.2392</td><td>62.14</td><td>0.5650</td></tr><tr><td>w/ Adv. (Real Feature: fteacher)</td><td>0.3208</td><td>0.2376</td><td>66.03</td><td>0.5916</td></tr><tr><td>w/ Adv. (Real Feat.: fGT) (Ours)</td><td>0.3046</td><td>0.2200</td><td>66.26</td><td>0.5927</td></tr></table>
+
+in NIQE and 0.1989 in CLIPIQA compared to distillation in image space. Fig. 9 visually demonstrates that omitting the distillation or performing it in image domain introduces distortions and blurriness in the super-resolved results, validating the effectiveness of our distillation scheme in ADC.
+
+Effect of Adversarial Loss. Tab. 7 shows the impact of various settings for  $\mathcal{L}_{\mathrm{adv}}$ . Omitting  $\mathcal{L}_{\mathrm{adv}}$  significantly degrades perceptual quality by 0.0115, 0.0192, 4.12, and 0.0277 in LPIPS, DISTS, MUSIQ, and CLIPIQA, respectively. Using  $\mathcal{L}_{\mathrm{adv}}$  with real features  $\mathbf{f}_{\mathrm{teacher}}$  as in [32] without leveraging  $\mathbf{f}_{\mathrm{GT}}$  results in non-negligible performance drops of 0.0162, 0.0176, 0.23, and 0.0011 in these four metrics. Fig. 9 further illustrates that, compared to omitting  $\mathcal{L}_{\mathrm{adv}}$ , our scheme enhances details in the boats and the woman's face, making textures in the cabin, eyelashes, and iris more natural. These results validate that our adversarial learning scheme effectively utilizes GT to improve the realism of super-resolved images, enabling the model to learn beyond its teacher.
+
+# 5. Conclusion
+
+In this paper, we proposed a novel method, AdcSR, based on our Adversarial Diffusion Compression (ADC) framework, for real-world image super-resolution (Real-ISR). To be specific, we structurally compressed a typical state-of-the-art SD-based one-step diffusion network, OSEDiff, into a smaller diffusion GAN. We identified and removed unnecessary modules (VAE encoder, prompt extractor, etc.) from OSEDiff, and pruned its remaining compressible modules (denoising UNet and VAE decoder). Since direct removal and pruning can degrade the model's generative capability, we developed a two-stage training scheme that first pretrains a pruned SD VAE decoder and then performs adversarial distillation to compensate for performance loss. Experiments on both synthetic and real-world datasets demonstrated that our AdcSR model delivered competitive image quality and superior computational efficiency compared to existing diffusion-based Real-ISR approaches.
+
+While ADC and AdcSR have demonstrated effectiveness in compressing SD-based one-step Real-ISR network and achieving real-time inference, they face challenges in accurately recovering fine textures and heavily degraded details, as shown in Fig. 6. Moreover, although this work focuses on streamlining the state-of-the-art Real-ISR model OSEDiff, our ADC framework could be extended to other SD-based methods. We plan to explore such extensions and integrate additional generative priors for Real-ISR in future work.
+
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\ No newline at end of file
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+# Adversarial Domain Prompt Tuning and Generation for Single Domain Generalization
+
+Zhipeng Xu $^{1*}$ , De Cheng $^{1†}$ , Xinyang Jiang $^{2*}$ , Nannan Wang $^{1}$ , Dongsheng Li $^{2}$ , Xinbo Gao $^{3}$ $^{1}$ Xidian University,  $^{2}$ Microsoft Research Asia,  $^{3}$ Chongqing University of Posts and Telecommunications  
+xu_zhipeng@stu.xidian.edu.cn, {dcheng, nnwang}@xidian.edu.cn  
+{xinyangjiang, dongsli}@microsoft.com, gaoxb@cqupt.edu.cn
+
+# Abstract
+
+Single domain generalization (SDG) aims to learn a robust model, which could perform well on many unseen domains while there is only one single domain available for training. One of the promising directions for achieving single-domain generalization is to generate out-of-domain (OOD) training data through data augmentation or image generation. Given the rapid advancements in AI-generated content (AIGC), this paper is the first to propose leveraging powerful pre-trained text-to-image (T2I) foundation models to create the training data. However, manually designing textual prompts to generate images for all possible domains is often impractical, and some domain characteristics may be too abstract to describe with words. To address these challenges, we propose a novel Progressive Adversarial Prompt Tuning (PAPT) framework for pre-trained diffusion models. Instead of relying on static textual domains, our approach learns two sets of abstract prompts as conditions for the diffusion model: one that captures domain-invariant category information and another that models domain-specific styles. This adversarial learning mechanism enables the T2I model to generate images in various domain styles while preserving key categorical features. Extensive experiments demonstrate the effectiveness of the proposed method, achieving superior performances to state-of-the-art single-domain generalization approaches.
+
+# 1. Introduction
+
+Recent machine learning models (e.g., deep neural network) have achieved remarkable performances on various tasks, under the key assumption that the training and testing data are independently and identically distributed (i.e., iid). However, this assumption often does not hold in many real-world scenarios due to the domain shift, especially when
+
+![](images/583d6ebecc8fc6a7484523f32874736f3a98c558893f9e0559f0a8ea3e8d6135.jpg)  
+Figure 1. Comparison between our method with existing single domain generalization approaches: Left: the traditional domain augmentation-based method; Middle: the simple T2I foundation model with text description as prompt for domain augmentation; Right: our proposed method, which learns two sets of abstract prompts (i.e., category and domain) instead of the static textual domains, to instruct the diffusion-based T2I foundation model for generating images of a wide range of domain styles.
+
+testing on out-of-distribution (OOD) or previously unseen datasets. To mitigate the issue of domain shift, various approaches have been proposed, including domain adaptation (DA) [9, 10, 20, 39, 44, 48, 50] and domain generalization (DG) methods [11, 24, 37, 38, 66, 68, 69, 73, 76]. These methods typically involve incorporating data from multiple training domains (e.g., multi-domain generalization), or the target domain data. Despite showing encouraging performances on the OOD data, it may not always be applicable due to data acquiring budget or privacy issue. Therefore, we aim to address the more challenging but more useful task, i.e., single domain generalization (SDG).
+
+SDG aims to train a model on a labeled source domain and perform well on multiplied unseen target domains. This learning paradigm presents significant challenges because only one source domain is given and the target domains are usually unseen/out-of-distribution and unavailable during training. Existing works have made considerable suc
+
+cesses by employing data augmentation to extend the distribution of the source domain [4, 57] or learning adaptive data normalization [18] typically. However, it remains challenging how to construct diverse domains to achieve a provable generalization performance on target domains. Namely, it is challenging to guarantee a mitigated distribution discrepancy between the generated domains and target domains. Recent research provides strong evidence that Text-to-Image (T2I) foundation models have a powerful ability to generate images from text descriptions. Given that text inherently conveys rich semantic information, these models can produce a wide variety of images across different domains using text prompts. However, there still contains the following key issues that need to be addressed: 1) How to generate images from domains whose characteristics that are too abstract to describe with language? 2) How to enable T2I models to automatically generate a sufficiently diverse range of images across different domains?
+
+To address these challenges, this paper proposes to automatically learn a group of abstract prompts for out-of-distribution image generation with T2I models, eliminating the need for manually crafted descriptions. As shown in Fig. 1, our method applies prompt-tuning to diffusion-based T2I models, learning two types of abstract prompts: category prompts, which capture domain-invariant category information that remains consistent across domains, and domain prompts, which represent diverse domain styles, including those too abstract to express in words (e.g., "a photo of [class_prompt] in the style of [domain_prompt]"). Furthermore, to ensure both diversity in domain styles and consistency in key categorical features of generated images, we propose a novel Progressive Adversarial Prompt Tuning (PAPT) framework. In this framework, we first learn category prompts from the source domain data, then progressively learn new domain prompts, which are stored in a domain-specific memory bank. This framework reduces style similarity between newly generated domains and those already in the memory bank while enhancing semantic consistency between generated images and their corresponding category prompts.
+
+The main contributions can be summarized as follows:
+
+- We propose the first work that leverages the text-to-image foundation model for single-domain generalization (SDG). To obtain a wider range of domain styles beyond manual language description, we propose to learn a group of abstract learnable prompts representing diverse domains instead of static textual domains.  
+- We propose a novel Progressive Adversarial Prompt Tuning (PAPT) framework to balance the trade-off between generating images in diverse domain styles and preserving key categorical features.  
+- Through generating images with high domain diversity, the proposed method achieves superior performances to
+
+state-of-the-art SDG methods, illustrated by extensive experiments on mainstream SDG datasets.
+
+# 2. Related work
+
+# 2.1. Domain Generalization
+
+Over the last decade, many efforts have been devoted to domain generalization (DG) to address the OOD issue. Currently, DG methods can mainly be categorized into five dimensions, including domain alignment [11, 20], meta-learning [17, 65, 74], data augmentation [4, 57], disentangled representation learning [30, 46], and capturing causal relations. Despite showing encouraging performances on OOD data, their real-world applications are still limited due to the necessity of having data from other domains. In this work, we focus on an extreme case in DG: single domain generalization (SDG).
+
+# 2.2. Data augmentation for SDG
+
+SDG focuses on generalizing a model learned from only one source domain to multiple unseen target domains. Current methods often employ data augmentation strategies to enrich training data diversity. In particular, some works [47, 63, 64, 77] have demonstrated that the method of adversarial domain augmentation (ADA) can be highly effective in enhancing the generalization ability and robustness of the model by synthesizing virtual images during the training process. [70, 78] operate in the style space defined with style statistics, which can be simply applied to any tasks/models. [18] proposes a generic normalization approach (ASR-Norm) to adapt the data originating from diverse domains when trained with ADA. Nevertheless, these existing works remain constrained in their ability to generate domains with extreme distributional shifts relative to the source. To address this limitation, we leverage the T2I foundation model to generate a wider variety of domain images, aiming for larger diversity.
+
+# 2.3. Text-to-Image model
+
+T2I model has been widely studied in the context of GANs [21], with the key developments including models like DALL-E [53] and CogView [16], which allows users to synthesize novel scenes with unseen compositions and produce vivid images in a myriad of styles. Recently, remarkable visual results have been achieved by leveraging large-scale auto-regressive [53] or diffusion models [42]. [54] proposes the latent diffusion model, which applies diffusion model in the latent space of powerful pre-trained autoencoders and uses text with rich semantic information as a condition to guide the generation of images. Some work [13, 71] fit a neural network reward function using human scores or relative preferences and then finetune the latent diffusion model. However, re-training a model with
+
+![](images/d2dc24880f4c1240c7cf2d45159beeb5c76c6d5c93af82896bb25048da064ed2.jpg)  
+Figure 2. The framework of our proposed method. We first train a set of category prompts  $\mathbf{E}_k^c$  for each class to capture domain-invariant category information in step (a). Subsequently, we train domain prompts  $\mathbf{E}_o^d$  that represent abstract domain styles instead of rigid textual domains through adversarial domain prompt tuning in step (b). As new domain prompts are learned, they are added to a domain-specific memory bank. We then minimize the style similarity between the newly generated domain and previous domains in the memory bank, while maximizing the semantic consistency between generated images and the corresponding category in step (c).
+
+an expanded dataset for each new concept is prohibitively expensive. Thus, [19] proposes a method that does not alter the parameters of the latent diffusion model. Instead, they optimize conditional input prompts.
+
+# 3. Methodology
+
+# 3.1. Problem Definition
+
+Let  $\mathcal{D}^{\mathcal{S}}$  be one labeled source domain and  $\mathcal{D}^{\mathcal{T}} = \{\mathcal{D}_1^{\mathcal{T}},\mathcal{D}_2^{\mathcal{T}},\dots ,\mathcal{D}_{N^{\mathcal{T}}}^{\mathcal{T}}\}$  be the multiple target domains, where  $N^{\mathcal{T}}$  is the total number of target domains. We denote  $\mathcal{D}^{\mathcal{S}} = \{(\mathbf{x}_i,y_i)\}_{i = 1}^{N^s}$ , where  $\mathbf{x}_i\in \mathcal{X}$  is the  $i_{th}$  training example sampled from the input space  $\mathcal{X}$ , and  $y_{i}\in \mathcal{V}$  is the corresponding label. In particular, we consider  $K$  classes in each domain. The  $m_{th}$  unseen target domain can also be defined as  $\mathcal{D}_m^T = \{(\mathbf{x}_i,y_i)\}_{i = 1}^{N_m^T}$ , where  $N_{m}^{\mathcal{T}}$  is the number of training samples from the  $m_{th}$  domain  $\mathcal{D}_m^T$ . Single-domain generalization (SDG) aims to build a model that can perform well on all unseen target domains, through generating images in diverse domain styles to address the domain distribution shift problem. Note that, this study is verified on solving the image classification problem.
+
+# 3.2. Overall Framework of our Method
+
+This paper proposes a novel Progressive Adversarial Prompt Tuning (PAPT) framework for the pre-trained T2I model, to generate images of a wide range of domain styles, for SDG. Our approach aims to learn two sets of abstract prompts instead of the textual description to instruct the
+
+diffusion-based T2I foundation model. Specifically, the Category Prompt Tuning is first adopted to capture categorical features from the source domain data. Then, Adversarial Domain Prompt Tuning is utilized to learn domain prompts, which model domain styles different from some predefined or previously learned ones in the domain-specific memory bank. To generate a sufficiently diverse range of images across different domains automatically, we propose the Progressive Training Scheme. This mechanism designs a memory bank to store the learned domain prompts, which is iteratively updated by adding the new domain prompt. Specifically, the new domain prompt is progressively and adversarially learned to be different from existing ones. Finally, by leveraging source domain and the multiple generated domain images together, we can learn a powerful SDG model.
+
+# 3.3. Preliminaries
+
+We implement our method over Latent Diffusion Models (LDMs) [54], which consist of two core components. Firstly, an auto-encoder is pre-trained on a large dataset. An encoder  $\mathbf{f}_E$  learns to map the input images  $\mathbf{x}$  into the spatial latent representation  $\mathbf{z}_0 = \mathbf{f}_E(\mathbf{x})$ . The decoder  $\mathbf{f}_D$  reconstructs the image from the latent representation, such that  $\mathbf{f}_D(\mathbf{f}_E(\mathbf{x})) \to \mathbf{x}$ . The amount of noise added varies according to the timestep  $t$  following a variance schedule of  $\{\beta_t \in (0,1)\}_{t=1}^T$ , with  $T$  being the total timestep. Then we can add noise  $\epsilon$  to the latent representation  $\mathbf{z}_0$  as follows:
+
+$$
+\mathbf {z} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {z} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \epsilon \in \mathcal {N} (0, 1), \tag {1}
+$$
+
+where  $\epsilon$  is sampled from Gaussian distribution and  $\alpha_{t} = 1 - \beta_{t}$ ,  $\overline{\alpha}_{t} = \prod_{i=1}^{t} \alpha_{i}$ . The second component is a conditional denoising module, which learns a reverse diffusion process that predicts the noise  $\hat{\epsilon}$ :
+
+$$
+\hat {\epsilon} = \epsilon_ {\theta} (\mathbf {z} _ {t}, t, \Phi (\mathbf {w})), \tag {2}
+$$
+
+where  $\mathbf{w}$  is the text embedding vector containing the image content descriptions (i.e., the class name), and  $\Phi(\cdot)$  is an encoder that maps the condition input of some text description into an intermediate representation  $\Phi(\mathbf{w})$ . Following [54], it is mapped to the intermediate layers of the UNet [55]  $\epsilon_{\theta}(\cdot)$  in Eq. 2 via a cross-attention layer implemented as Attention  $(\mathbf{Q}, \mathbf{K}, \mathbf{V}) = \mathrm{Softmax}(\frac{\mathbf{Q}\mathbf{K}^{\top}}{\sqrt{d}}) \cdot \mathbf{V}$ , with:
+
+$$
+\mathbf {Q} = \mathbf {W} _ {Q} ^ {(i)} \cdot \varphi_ {i} (\mathbf {z} _ {t}), \mathbf {K} = \mathbf {W} _ {K} ^ {(i)} \cdot \Phi (\mathbf {w}), \mathbf {V} = \mathbf {W} _ {V} ^ {(i)} \cdot \Phi (\mathbf {w}). \tag {3}
+$$
+
+Here,  $\varphi_{i}(\mathbf{z}_{t})$  denotes an intermediate representation of the UNet implementing  $\epsilon_{\theta}$ ,  $\mathbf{W}_Q^{(i)}$ ,  $\mathbf{W}_V^{(i)}$ ,  $\mathbf{W}_K^{(i)}$  are projection matrices, and  $\Phi (\mathbf{w})$  is the conditional input for the diffusion model. The LDM loss can be written as:
+
+$$
+\mathcal {L} _ {L D M} = \mathbb {E} _ {\mathbf {f} _ {E} (\mathbf {x}), y, \epsilon \in \mathcal {N} (0, 1), t} \left[ \| \epsilon - \hat {\epsilon} \| _ {2} ^ {2} \right], \tag {4}
+$$
+
+where  $\| \cdot \|$  is  $L2$  norm [26] and both  $\Phi(\cdot)$  and  $\epsilon_{\theta}$  are jointly optimized via Eq. 4.
+
+# 3.4. Category Prompt Tuning
+
+The Category Prompt Tuning aims to capture domain-invariant category information from the source domain data. In real-world scenarios, some concepts/categories are difficult for the diffusion model to understand through a single class label/name. So in the first stage, we use LDMs to train a set of prompts for each category, serving as an abstract representation for the corresponding class. Specifically, we denote  $\mathbf{t}_k^c$  as the input string to facilitate the domain-invariant category description of the  $k_{th}$  class as follows,
+
+$$
+\mathbf {t} _ {k} ^ {c} = \text {" a p h o t o o f a * "} , k \in [ 1, K ]. \tag {5}
+$$
+
+In Eq. 5,  $K$  is the total number of classes, and  $*$  is defined as a 'placeholder' indicating the position of class name within the input string. Subsequently, the input string  $\mathbf{t}_k^c$  follows tokenization and then each token is transformed into the embedding vector. Suppose  $M_c$  is the length of the tokens corresponding to the input string  $\mathbf{t}_k^c$  after the exclusion of the placeholder  $*$ , then the corresponding tokenized vector can be defined as  $\hat{\mathbf{t}}_k^c = [\hat{\mathbf{t}}_{k,1}^c,\dots ,\hat{\mathbf{t}}_{k,j}^c,\dots ,\hat{\mathbf{t}}_{k,M_c}^c]$ . Following the embedding function  $\varepsilon (\cdot)$  for all the tokens, we then add a learnable category prompt  $\mathbf{E}_k^c$  for the  $k_{th}$  domain-invariant category description at the position of the placeholder in the embedding space:
+
+$$
+\mathbf {w} _ {k} ^ {c} = \left[ \varepsilon \left(\hat {\mathbf {t}} _ {k, 1} ^ {c}\right), \dots , \varepsilon \left(\hat {\mathbf {t}} _ {k, j} ^ {c}\right), \dots , \varepsilon \left(\hat {\mathbf {t}} _ {k, M _ {c}} ^ {c}\right), \mathbf {E} _ {k} ^ {c} \right]. \tag {6}
+$$
+
+Afterward, we use  $\Phi(\mathbf{w}_k^c)$  as the category condition input to the cross-attention layer of the UNet  $\epsilon_{\theta}(\cdot)$ , directing the prediction of noise while optimizing only  $\mathbf{E}_k^c$  with  $\mathcal{L}_{LDM}$  in Eq. 4. To be specific,  $\Phi(\cdot)$  is the text encoder of CLIP [51] in our experiment. Finally, we can learn  $K$  category prompts with each for one class.
+
+# 3.5. Adversarial Domain Prompt Tuning
+
+Image Sampling with Domain Prompt. In this paper, we aim to learn a set of abstract domain prompts, where each prompt in the domain-specific memory bank  $\mathcal{P}$  is used to instruct the pre-trained diffusion model to generate images in a specific domain style:
+
+$$
+\mathcal {P} = \left\{E _ {1} ^ {d}, E _ {2} ^ {d}, \dots , E _ {N} ^ {d} \right\}, \mathcal {P} \in \mathbb {R} ^ {N \times D}, \tag {7}
+$$
+
+where  $N$  in Eq. 7 represents the number of learned domains in  $\mathcal{P}$ , and D represents the prompts dimension. Given the  $i_{th}$  domain prompt  $\mathbf{E}_i^d$  in  $\mathcal{P}$ , we compose a text description to generate an image belonging to  $k$ -th category as follows:
+
+$$
+\begin{array}{l} \mathbf {t} _ {k, i} ^ {c - d} = \text {" a p h o t o o f a * i n t h e s t y l e o f ＂}, \tag {8} \\ w h e r e k \in [ 1, K ], i \in [ 1, N ], \\ \end{array}
+$$
+
+where the token embedding of  $*$  and  $\dagger$  will be replaced by our learnable category prompt  $\mathbf{E}_k^c$  and domain prompt  $\mathbf{E}_i^d$ , respectively. Similar to Eq. 6,  $\mathbf{t}_{k,i}^{c - d}$  is defined as a set of tokens corresponding to the input string  $\mathbf{t}_{k,i}^{c - d}$ . As a result, the overall token embedding of  $\mathbf{w}_{k,i}^{c - d}$  is formulated as:
+
+$$
+\mathbf {w} _ {k, i} ^ {c - d} = \left[ \varepsilon \left(\hat {\mathbf {t}} _ {k, i, 1} ^ {c - d}\right), \dots , \mathbf {E} _ {k} ^ {c}, \dots , \varepsilon \left(\hat {\mathbf {t}} _ {k, i, M _ {c - d}} ^ {c - d}\right), \mathbf {E} _ {i} ^ {d} \right], \tag {9}
+$$
+
+where  $M_{c-d}$  is the length of the tokens in  $\hat{\mathbf{t}}_{k,i}^{c-d}$ . Finally, we use the pre-trained diffusion model to generate the image belonging to  $k_{th}$  category with  $i_{th}$  domain style, by feeding the obtained token embedding  $\mathbf{w}_{k,i}^{c-d}$  into the diffusion denoiser in Eq. 2 at every Denoising Diffusion Probabilistic Models (DDPMs) [27] sampling step.
+
+Domain Prompt Tuning. Next, we elaborate on how to learn the domain prompt by our proposed Adversarial Domain Prompt Tuning module. The goal of this module is to ensure that the domain style of the image generated with the currently learned domain prompt is different from the domain styles stored in the memory bank  $\mathcal{P}$ .
+
+First, we set up an initial memory bank of prompts by manually selecting several textual domains and using their corresponding token embeddings as the initial domain prompts in the memory bank. In order to learn a new domain prompt  $\mathbf{E}_o^d$ , we first use the diffusion model to generate an original latent representation  $\mathbf{z}_0$  from the  $k_{th}$  category by composing the text description following Eq. 8. Then, the domain similarity between the generated  $\mathbf{z}_0$  and
+
+![](images/4866e8ebf10a148d81f6de49fc2cba841ef458231e865ea8b1541dc54fbeeb67.jpg)  
+(a) w/o Progressive Training Scheme
+
+![](images/66be0a46ed5a290006f9afce7e814ef12b9ffb5e24efdacc67305114f5e0edf7.jpg)  
+(b) w/ Progressive Training Scheme
+
+![](images/3279fa0e2ccba07898d3a7cb7f1f8d2f4879f837d1e6b1d586aeb15e4d387c8b.jpg)  
+Figure 3. This figure shows the impact of the Progressive Training Scheme. By comparing the two figures, we found that after using the Progressive Training Scheme, the areas of classification errors have decreased. This observation indicates that the more diverse abstract domains we learn, the more likely we are to generate OOD images that are close to the classification boundary.
+
+the  $i$ -th domain style in  $\mathcal{P}$  is formulated as the probability that  $\mathbf{z}_0$  belongs to the  $i_{th}$  domain:
+
+$$
+\mathbf {p} _ {i} ^ {d} \left(\mathbf {z} _ {0}; \Phi \left(\mathbf {w} _ {i} ^ {d}\right)\right) = \frac {\exp \left(<   \mathbf {z} _ {0} , \Phi \left(\mathbf {w} _ {i} ^ {d}\right) > / \tau\right)}{\sum_ {i = 1} ^ {N} \exp \left(<   \mathbf {z} _ {0} , \Phi \left(\mathbf {w} _ {i} ^ {d}\right) > / \tau\right)}, \tag {10}
+$$
+
+where we can define  $\mathbf{p}^d = [\mathbf{p}_1^d,\dots ,\mathbf{p}_i^d,\dots ,\mathbf{p}_N^d ]$  as the collection of probabilities for domain classification.  $\tau$  is a hyper-parameter to control the sharpness of the output, and  $<  \cdot ,\cdot >$  is the dot product which can be termed as the cosine similarity as the features are normalized.
+
+The  $\mathbf{w}_i^d$  in Eq. 10 represents the token embedding corresponding to the domain-specific textual description  $\mathbf{t}_i^d$  in Eq. 11 of the  $i_{th}$  domain style in the  $\mathcal{P}$ :
+
+$$
+\begin{array}{l} \mathbf {t} _ {i} ^ {d} = \text {" i n t h e s t y l e o f} \dagger \text {"}, i \in [ 1, N ], \\ \mathbf {w} _ {i} ^ {d} = \left[ \varepsilon \left(\hat {\mathbf {t}} _ {i, 1} ^ {d}\right), \dots , \varepsilon \left(\hat {\mathbf {t}} _ {i, j} ^ {d}\right), \dots , \varepsilon \left(\hat {\mathbf {t}} _ {i, M _ {d}} ^ {d}\right), \mathbf {E} _ {i} ^ {d} \right], \tag {11} \\ \end{array}
+$$
+
+where  $\hat{\mathbf{t}}_i^d$  can be defined as a set of tokens corresponding to the domain-specific textual description  $\mathbf{t}_i^d$  and  $M_{d}$  is the length of the tokens in  $\hat{\mathbf{t}}_i^d$ . As a result, the adversarial domain loss is formulated to minimize the total style similarity between the  $\mathbf{z}_0$  and all the previous domains in  $\mathcal{P}$ .  $\mathbf{w}_i^d$  corresponds to each learnable domain prompt  $\mathbf{E}_i^d$  in  $\mathcal{P}$ . In other words, we want the newly generated domain  $\mathbf{E}_o^d$  to be distributionally different from the previous domain in  $\mathcal{P}$ :
+
+$$
+\mathcal {L} _ {\text {d o m a i n}} = - \sum_ {i = 1} ^ {N} - \log \mathbf {p} _ {i} ^ {d} \left(\mathbf {z} _ {0}; \Phi \left(\mathbf {w} _ {i} ^ {d}\right)\right). \tag {12}
+$$
+
+To ensure  $\mathbf{z}_0$  still maintains the category semantics after optimizing with the adversarial domain loss, we further propose a category consistency loss, which maximizes the semantic consistency between  $\mathbf{z}_0$  and the categorical embedding  $\mathbf{w}_k^c$  in Eq. 6:
+
+$$
+\mathcal {L} _ {\text {c l a s s}} = - \log \mathbf {p} _ {k} ^ {c} \left(\mathbf {z} _ {0}; \Phi \left(\mathbf {w} _ {k} ^ {c}\right)\right)), \tag {13}
+$$
+
+where the  $\mathbf{p}_k^c$  represent the probability of  $\mathbf{z}_0$  belonging to the  $k_{th}$  category. We calculate the  $\mathbf{p}_k^c$  with the same as Eq. 10 by  $\mathbf{z}_0$  and  $\Phi (\mathbf{w}_k^c)$ . The final adversarial domain prompt tuning loss is written as:
+
+$$
+\mathcal {L} _ {\text {a l l}} = \mathcal {L} _ {\text {c l a s s}} + \lambda \mathcal {L} _ {\text {d o m a i n}}, \tag {14}
+$$
+
+where  $\lambda$  in Eq. 14 is a hyper-parameter. It balances the trade-off between training the new domain prompt distributionally different from existing ones and preserving its key categorical semantic information. Optimizing Eq. 14 requires sampling  $\mathbf{z}_0$  and back-propagating the gradient through the entire sequence of sampling steps, which is impractical. As a result, we propose using a one-step approximation of  $\mathbf{z}_0$ . Specifically, we first sample an intermediate state  $\mathbf{z}_t$  with a relatively low noise level, and then conduct a one-step approximation of  $\mathbf{z}_0$  with  $\mathbf{z}_t$ , and the loss gradient is only back-propagated from the  $t$ -th to the 0-th step:
+
+$$
+\mathbf {z} _ {0} = \frac {1}{\sqrt {\bar {\alpha} _ {t}}} \left(\mathbf {z} _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, \Phi \left(\mathbf {w} _ {k, i} ^ {c - d}\right)\right)\right). \tag {15}
+$$
+
+# 3.6. Progressive Training Scheme
+
+To automatically generate images with diverse domain styles, we need to progressively update  $\mathcal{P}$  by continuously adding new domain prompts. To achieve this, we propose a Progressive Training Scheme: after a certain number of prompt tuning iterations, the currently learned domain prompt  $\mathbf{E}_o^d$  is added to  $\mathcal{P}$ , allowing  $\mathcal{P}$  to be gradually updated with new styles as follows:
+
+$$
+\mathcal {P} \leftarrow \mathcal {P} \cup \left\{\mathbf {E} _ {o} ^ {d} \right\}. \tag {16}
+$$
+
+Fig. 3 provides a sample illustration. The purpose of this training scheme is to ensure that each time when we train the new domain  $\mathbf{E}_o^d$  using adversarial domain loss in Eq. 12, we can also increase the distance between the new domain  $\mathbf{E}_o^d$  and the previously added domain  $\mathbf{E}_i^d$  in  $\mathcal{P}$ . In this way, each training domain will be distributionally different from previous ones. Thus, we have a higher probability of learning more challenging abstract domains.
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Protocols
+
+Following previous works [49, 58], we adopt five commonly used benchmark datasets in DG tasks for evaluation: PACS [32], VLCS [32], OfficeHome [62], DomainNet [45] and TerraIncognita [2]. To ensure reliable results, we calculate the average performance across multiple experiments.
+
+# 4.2. Implementation details
+
+In our implementation, we adopt the ResNet-18 [23] for PACS and VLCS and ResNet-50 [23] for OfficeHome pretrained on ImageNet [15] as backbone for the SDG setting,
+
+Table 1. SDG results (\%) on PACS. One domain is used as the source domain and the others are used as the target domain.  
+
+<table><tr><td>Method</td><td>Venue</td><td>P</td><td>A</td><td>C</td><td>S</td><td>Avg.</td></tr><tr><td>Augmix [25]</td><td>ICLR&#x27;20</td><td>38.30</td><td>66.54</td><td>70.16</td><td>52.48</td><td>56.87</td></tr><tr><td>RSC [29]</td><td>ECCV&#x27;20</td><td>41.60</td><td>73.40</td><td>75.90</td><td>56.20</td><td>61.80</td></tr><tr><td>L2D [70]</td><td>ICCV&#x27;21</td><td>52.29</td><td>76.91</td><td>77.88</td><td>53.66</td><td>65.18</td></tr><tr><td>RSC+ASR [29]</td><td>CVPR&#x27;21</td><td>54.60</td><td>76.70</td><td>79.30</td><td>61.60</td><td>68.10</td></tr><tr><td>pAdaln [43]</td><td>CVPR&#x27;21</td><td>33.66</td><td>64.96</td><td>65.24</td><td>32.04</td><td>49.98</td></tr><tr><td>ERM [61]</td><td>ICLR&#x27;21</td><td>33.65</td><td>65.38</td><td>64.20</td><td>34.15</td><td>49.34</td></tr><tr><td>Mixstyle [78]</td><td>ICLR&#x27;21</td><td>37.44</td><td>67.60</td><td>70.38</td><td>34.57</td><td>52.50</td></tr><tr><td>EFDMix [75]</td><td>CVPR&#x27;22</td><td>42.50</td><td>63.20</td><td>73.90</td><td>38.10</td><td>54.40</td></tr><tr><td>DSU [35]</td><td>ICLR&#x27;22</td><td>42.10</td><td>71.54</td><td>74.51</td><td>47.75</td><td>58.97</td></tr><tr><td>ACVC [14]</td><td>CVPRW&#x27;22</td><td>48.05</td><td>73.68</td><td>77.39</td><td>55.30</td><td>63.61</td></tr><tr><td>MAD [49]</td><td>CVPR&#x27;23</td><td>52.95</td><td>75.51</td><td>77.25</td><td>57.75</td><td>65.87</td></tr><tr><td>P-RC [12]</td><td>CVPR&#x27;23</td><td>57.11</td><td>76.98</td><td>78.54</td><td>62.89</td><td>68.88</td></tr><tr><td>Meta-Casual [6]</td><td>CVPR&#x27;23</td><td>59.60</td><td>77.13</td><td>80.14</td><td>62.55</td><td>69.86</td></tr><tr><td>ITTA [7]</td><td>CVPR&#x27;23</td><td>56.50</td><td>78.40</td><td>79.80</td><td>60.70</td><td>68.80</td></tr><tr><td>Prompt-Driven [34]</td><td>CVPR&#x27;24</td><td>60.09</td><td>78.77</td><td>82.69</td><td>62.94</td><td>71.12</td></tr><tr><td>PAPT (Ours)</td><td>-</td><td>62.12</td><td>69.84</td><td>78.57</td><td>80.34</td><td>72.72</td></tr></table>
+
+Table 2. SDG results  $(\%)$  on VLCS. One domain is used as the source domain and the others are used as the target domain.  
+
+<table><tr><td>Method</td><td>Venue</td><td>V</td><td>L</td><td>C</td><td>S</td><td>Avg.</td></tr><tr><td>Augmix [25]</td><td>ICLR&#x27;20</td><td>75.25</td><td>59.52</td><td>45.90</td><td>57.43</td><td>59.53</td></tr><tr><td>ERM [61]</td><td>ICLR&#x27;21</td><td>76.72</td><td>58.86</td><td>44.95</td><td>57.71</td><td>59.56</td></tr><tr><td>pAdaIn [43]</td><td>CVPR&#x27;21</td><td>76.03</td><td>65.21</td><td>43.17</td><td>57.94</td><td>60.59</td></tr><tr><td>Mixstyle [78]</td><td>ICLR&#x27;21</td><td>75.73</td><td>61.29</td><td>44.66</td><td>56.57</td><td>59.56</td></tr><tr><td>EFDMix [75]</td><td>CVPR&#x27;22</td><td>72.35</td><td>61.41</td><td>52.34</td><td>63.28</td><td>62.33</td></tr><tr><td>DSU [35]</td><td>ICLR&#x27;22</td><td>76.93</td><td>69.20</td><td>46.54</td><td>58.36</td><td>62.76</td></tr><tr><td>ACVC [14]</td><td>CVPRW&#x27;22</td><td>76.15</td><td>61.23</td><td>47.43</td><td>60.18</td><td>61.25</td></tr><tr><td>MAD [49]</td><td>CVPR&#x27;23</td><td>76.15</td><td>69.36</td><td>48.04</td><td>61.74</td><td>63.82</td></tr><tr><td>PAPT (Ours)</td><td>-</td><td>73.16</td><td>74.69</td><td>69.66</td><td>75.96</td><td>73.37</td></tr></table>
+
+follows [49, 58] for a fair comparison. The models are trained for 50 epochs using a batch size of 64 and a learning rate of 0.001 for each stage. We utilize the SGD optimizer and conduct the training on a single NVIDIA RTX3090 GPU. In our proposed method, the parameter  $N$  in Eq. 7 is set to 5. The parameter  $\lambda$  in Eq. 14 is set to 10. To ensure the reliability of our method, we independently repeat all experiments five times and report the average results.
+
+# 4.3. Results on Single Domain Generalization
+
+We compare our method with baseline method [61], the data augmentation based method [8, 14, 25, 35, 43, 49, 75, 78], the domain invariant representation based method [1, 3, 20, 29, 31, 36, 59], the feature disentanglement based method [41], the distributionally robust optimization based method [56], the gradient operation based method [29, 52] and the flatness-aware based methods [36, 58, 67, 79].
+
+Tab. 1, Tab. 2, and Tab. 3 show the comparison results on PACS, VLCS, and OfficeHome, respectively. Notably, our proposed method outperforms the state-of-the-art method by  $1.60\%$ ,  $9.55\%$ , and  $3.73\%$  on Avg-acc on all benchmark datasets. Especially when taking "Sketch" (PACS), "Caltech101" (VLCS), "SUN09" (VLCS), and "Clipart" (OfficeHome) as the source domain, our PAPT leads to  $17.40\%$ ,  $21.62\%$ ,  $14.22\%$  and  $12.60\%$  improvement in Avg-acc. It is important to highlight that the domain shift in the VLCS dataset mainly comes from background and viewpoint changes. In other words, the domain label does not
+
+Table 3. SDG results (\%) on OfficeHome. One domain is used as the source domain and the others are used as the target domain.  
+
+<table><tr><td>Method</td><td>Venue</td><td>A</td><td>C</td><td>P</td><td>R</td><td>Avg.</td></tr><tr><td>DANN [20]</td><td>IJCAI&#x27;16</td><td>55.20</td><td>49.30</td><td>48.40</td><td>58.40</td><td>52.80</td></tr><tr><td>CORAL [59]</td><td>ICCV&#x27;16</td><td>55.60</td><td>52.80</td><td>50.30</td><td>59.40</td><td>54.50</td></tr><tr><td>IRM [1]</td><td>-</td><td>54.90</td><td>53.20</td><td>48.60</td><td>59.20</td><td>54.00</td></tr><tr><td>Mixup [72]</td><td>-</td><td>55.50</td><td>54.10</td><td>49.40</td><td>59.40</td><td>54.60</td></tr><tr><td>GroupDRO [56]</td><td>ICLR&#x27;20</td><td>55.10</td><td>52.00</td><td>50.30</td><td>59.30</td><td>54.20</td></tr><tr><td>MTL [3]</td><td>JMLR&#x27;21</td><td>55.30</td><td>53.30</td><td>49.00</td><td>60.40</td><td>54.50</td></tr><tr><td>VReX [31]</td><td>ICML&#x27;21</td><td>55.50</td><td>52.60</td><td>49.10</td><td>59.30</td><td>54.10</td></tr><tr><td>Mixstyle [78]</td><td>ICLR&#x27;21</td><td>44.30</td><td>29.80</td><td>33.60</td><td>48.50</td><td>39.00</td></tr><tr><td>ERM [61]</td><td>ICLR&#x27;21</td><td>55.60</td><td>52.80</td><td>50.30</td><td>59.40</td><td>54.50</td></tr><tr><td>SAM [36]</td><td>ICLR&#x27;21</td><td>56.90</td><td>53.80</td><td>50.90</td><td>61.50</td><td>55.80</td></tr><tr><td>SagNet [41]</td><td>CVPR&#x27;21</td><td>56.90</td><td>53.40</td><td>50.80</td><td>61.20</td><td>55.60</td></tr><tr><td>Fishr [52]</td><td>ICML&#x27;22</td><td>55.10</td><td>51.20</td><td>49.20</td><td>59.90</td><td>53.90</td></tr><tr><td>RIDG [8]</td><td>ICCV&#x27;23</td><td>56.80</td><td>55.40</td><td>50.50</td><td>60.90</td><td>55.90</td></tr><tr><td>SAGM [67]</td><td>CVPR&#x27;23</td><td>57.70</td><td>54.80</td><td>51.50</td><td>61.40</td><td>56.30</td></tr><tr><td>ITA [7]</td><td>CVPR&#x27;23</td><td>56.00</td><td>51.50</td><td>50.50</td><td>61.60</td><td>54.90</td></tr><tr><td>UDIM [58]</td><td>ICLR&#x27;24</td><td>58.50</td><td>55.70</td><td>54.50</td><td>64.50</td><td>58.30</td></tr><tr><td>PAPT (Ours)</td><td>-</td><td>59.81</td><td>68.30</td><td>59.12</td><td>60.87</td><td>62.03</td></tr></table>
+
+convey any semantic information. Since the result on VLCS  $(63.82\% \rightarrow 73.37\%)$  further proves our proposed method does not rely on the domain labels from the source domain, it can be applied to other robustness tasks that do not contain domain labels (VLCS and TerraInc). To sum up, our proposed method has two main advantages: (1) We fully leverage the flexibility of learnable domain prompts to represent abstract and challenge domains instead of relying on rigid textual domains. (2) Unlike existing data augmentation methods, We propose a novel progressive training scheme to harness the potential of the T2I model to generate diverse images automatically. Further mitigating the domain discrepancies between source and target domains.
+
+# 4.4. Results on Multiple Domain Generalization
+
+We extend our proposed method to multi-source DG setting by extracting the same images as input from various source domains to train class prompt  $\mathbf{E}_k^c$ . Then keep the subsequent training process consistent with the SDG setting. We compare our method with several popular DG methods.
+
+Tab. 4 shows the multi-source DG results on all the DG benchmark datasets with ResNet-50 [23] as the backbone. Notably, our proposed method outperforms the state-of-the-art method SMOS by  $1.34\%$  on Avg-acc. (1) This further demonstrates that our proposed method not only benefits single-domain generalization but also enhances multi-source domain generalization; (2) In the challenging case with large style discrepancies, such as DomainNet, our PAPT can even gain significant performance than SMOS by  $4.88\%$ . (3) The representative data augmentation method, e.g. Mixstyle, shows the limited performance with ERM on VLCS  $(77.30\% \rightarrow 77.90\%)$  and TerraInc  $(43.80\% \rightarrow 34.00\%)$  dataset. We speculate that this may result from the distinct types of domain shifts, which typically manifest as differences in viewpoint and background in VLCS and TerraInc, rather than as variations in texture and style commonly observed in other DG datasets.
+
+Table 4. Multi-source DG results (%) on PACS, VLCS, OfficeHome, TerraInc, and DomainNet benchmark datasets.  
+
+<table><tr><td>Method</td><td>Venue</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>Avg.</td></tr><tr><td>DANN [20]</td><td>IJCAI&#x27;16</td><td>83.60±0.40</td><td>78.60±0.40</td><td>65.90±0.60</td><td>46.70±0.50</td><td>38.30±0.40</td><td>62.60</td></tr><tr><td>MLDG [33]</td><td>AAAI&#x27;18</td><td>84.90±1.00</td><td>77.20±0.40</td><td>66.80±0.60</td><td>47.70±0.90</td><td>41.20±0.10</td><td>63.60</td></tr><tr><td>GroupDRO [56]</td><td>ICLR&#x27;20</td><td>84.40±0.80</td><td>76.70±0.60</td><td>66.00±0.70</td><td>43.20±1.10</td><td>33.30±0.20</td><td>60.70</td></tr><tr><td>RSC [29]</td><td>ECCV&#x27;20</td><td>85.20±0.90</td><td>77.10±0.50</td><td>65.50±0.90</td><td>46.60±1.00</td><td>38.90±0.50</td><td>62.70</td></tr><tr><td>VREx [31]</td><td>ICML&#x27;21</td><td>84.90±0.60</td><td>78.30±0.20</td><td>66.40±0.60</td><td>46.40±0.60</td><td>33.60±2.20</td><td>61.90</td></tr><tr><td>Mixstyle [78]</td><td>ICLR&#x27;21</td><td>85.20±0.30</td><td>77.90±0.50</td><td>60.40±0.20</td><td>44.00±0.70</td><td>34.00±0.10</td><td>60.30</td></tr><tr><td>ERM [61]</td><td>ICLR&#x27;21</td><td>85.50±0.20</td><td>77.30±0.40</td><td>66.50±0.30</td><td>46.10±1.80</td><td>43.80±0.10</td><td>63.90</td></tr><tr><td>SAM [36]</td><td>ICLR&#x27;21</td><td>85.80±0.20</td><td>79.40±0.10</td><td>69.60±0.10</td><td>43.30±0.70</td><td>44.30±0.00</td><td>64.50</td></tr><tr><td>SagNet [41]</td><td>CVPR&#x27;21</td><td>86.30±0.20</td><td>77.80±0.50</td><td>68.10±0.10</td><td>48.60±1.00</td><td>40.30±0.10</td><td>64.20</td></tr><tr><td>Miro [5]</td><td>ECCV&#x27;22</td><td>85.40±0.40</td><td>79.00±0.00</td><td>70.50±0.40</td><td>50.40±1.10</td><td>44.30±0.20</td><td>65.90</td></tr><tr><td>GSAM [79]</td><td>ICLR&#x27;22</td><td>85.90±0.10</td><td>79.10±0.20</td><td>69.30±0.00</td><td>47.00±0.80</td><td>44.60±0.20</td><td>65.10</td></tr><tr><td>SAGM [67]</td><td>CVPR&#x27;23</td><td>86.60±0.20</td><td>80.00±0.30</td><td>70.10±0.20</td><td>48.80±0.90</td><td>45.00±0.20</td><td>66.10</td></tr><tr><td>DomainDrop [22]</td><td>ICCV&#x27;23</td><td>87.90±0.30</td><td>79.80±0.30</td><td>68.70±0.10</td><td>51.50±0.40</td><td>44.40±0.50</td><td>66.50</td></tr><tr><td>GMDG [60]</td><td>CVPR&#x27;24</td><td>85.60±0.30</td><td>79.20±0.30</td><td>70.70±0.20</td><td>51.10±0.90</td><td>44.60±0.10</td><td>66.30</td></tr><tr><td>SMOS [40]</td><td>CVPR&#x27;24</td><td>89.40±0.30</td><td>79.80±0.10</td><td>71.60±0.10</td><td>55.40±0.40</td><td>45.30±0.00</td><td>68.30</td></tr><tr><td>RES [28]</td><td>ECCV&#x27;24</td><td>90.00±0.30</td><td>79.80±0.20</td><td>71.80±0.30</td><td>51.40±0.60</td><td>46.70±0.20</td><td>67.90</td></tr><tr><td>PAPT (Ours)</td><td>-</td><td>91.69±0.44</td><td>80.84±0.32</td><td>71.21±0.53</td><td>54.27±1.01</td><td>50.18±0.47</td><td>69.64</td></tr></table>
+
+Notably, our proposed PAPT substantially improves the ERM of  $3.54\%$  and  $6.38\%$  on two datasets, respectively. This observation indicates that compared to the existing data augmentation-based methods, our PAPT not only alleviates the negative impacts of style shifts but also guarantees a provable generalization performance under varying viewpoint conditions.
+
+# 4.5. Ablation Study
+
+To validate the effectiveness of each component of our proposed PAPT, we conduct ablation studies in Tab. 5 and Tab. 6. Our baseline (see  $1^{st}$  row) only uses the source domain as training data. In  $2^{nd}$  row, we use a simple description ("a photo of a [class]") as the input of T2I model to generate additional training images. In  $3^{rd}$  row, we train category prompt  $\mathbf{E}_k^c$  using the Category Prompt Tuning (CPT), and generate images with some textual domains. In  $4^{th}$  row, we train a domain prompt  $\mathbf{E}_i^d$  using the Adversarial Domain Prompt Tuning (AD) and generate images with only one  $\mathbf{E}_i^d$  and textual domains. In  $5^{th}$  row, we incorporate the Progressive Training Scheme (PTS) to generate images with diverse domain prompts in  $\mathcal{P}$ .
+
+Table 5. Ablation studies on individual components of our proposed method on PACS dataset with SDG setting.  
+
+<table><tr><td>T2I</td><td>CPT</td><td>AD</td><td>PTS</td><td>P</td><td>A</td><td>C</td><td>S</td><td>Avg.</td></tr><tr><td>X</td><td>X</td><td>X</td><td>X</td><td>34.00</td><td>58.60</td><td>66.40</td><td>27.50</td><td>46.60</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>X</td><td>40.23</td><td>59.17</td><td>68.80</td><td>66.91</td><td>58.78</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>55.55</td><td>68.87</td><td>71.56</td><td>69.36</td><td>66.34</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>58.72</td><td>69.00</td><td>75.61</td><td>77.55</td><td>70.22</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>62.12</td><td>69.84</td><td>78.57</td><td>80.34</td><td>72.72</td></tr></table>
+
+The Effectiveness of Adversarial Domain Prompt Tuning (AD). Our Adversarial Domain Prompt Tuning substantially improves the model performance of  $0.13\% \sim 8.19\%$  across each domain and  $3.88\%$  on Avg-acc (see  $3^{rd}$  and  $4^{th}$  row in Tab. 5) on PACS dataset. In contrast, the manually designed textual domain demonstrates limited perfor
+
+Table 6. Ablation studies on individual components of our proposed method on VLCS dataset with SDG setting.  
+
+<table><tr><td>T2I</td><td>CPT</td><td>AD</td><td>PTS</td><td>V</td><td>L</td><td>C</td><td>S</td><td>Avg.</td></tr><tr><td>X</td><td>X</td><td>X</td><td>X</td><td>71.81</td><td>61.06</td><td>52.60</td><td>62.32</td><td>61.95</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>X</td><td>72.08</td><td>69.31</td><td>60.75</td><td>70.95</td><td>68.28</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>72.68</td><td>70.44</td><td>61.54</td><td>71.70</td><td>69.09</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>72.94</td><td>73.95</td><td>67.94</td><td>75.20</td><td>72.51</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>73.16</td><td>74.69</td><td>69.66</td><td>75.96</td><td>73.37</td></tr></table>
+
+Table 7. The impact of manually designed textual domain initialization in  $\mathcal{P}$  on PACS, VLCS, and OfficeHome with SDG setting.  
+
+<table><tr><td>Idx</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>Avg.</td></tr><tr><td colspan="5">Initialization with watercolor, oil painting and pixlate.</td></tr><tr><td>1</td><td>72.72±0.32</td><td>73.37±0.21</td><td>62.03±0.38</td><td>73.05</td></tr><tr><td colspan="5">Initialization with ink drawing, cyber art and realism.</td></tr><tr><td>2</td><td>72.13±0.19</td><td>73.05±0.28</td><td>61.99±0.44</td><td>72.59</td></tr><tr><td colspan="5">initialization with printmaking, line art and pastel.</td></tr><tr><td>3</td><td>72.57±0.24</td><td>73.12±0.15</td><td>62.08±0.36</td><td>72.85</td></tr></table>
+
+mance as some domain characteristics are too abstract to describe with words. Unlike relying on rigid textual input, our AD fully leverages the flexibility of learnable domain prompts to more effectively characterize the diverse abstract styles, resulting in a generalization performance gain. Meanwhile, existing data augmentation methods that mainly introduce diverse styles obtain relatively slight performance gains on VLCS dataset compared to PACS ones. However, our AD significantly improves the model performance of  $0.28\% \sim 6.40\%$  across each domain and  $3.42\%$  on Avg-acc (see  $3^{rd}$  and  $4^{th}$  row in Tab. 6). This observation indicates our AD can better model the changes in background and viewpoint and mitigate the distributional difference under these conditions with the powerful pre-trained T2I model. The results basically indicate the advantage of AD across different domain shifts. Fig. 4 also shows some images generated by our proposed method.
+
+The Effectiveness of Progressive Training Scheme
+
+![](images/7ded75b7032c51a3553d6ebdbdadab240936fd932c9b680058f4ebe7b8dc8326.jpg)  
+Art painting
+
+![](images/86ac9dab8688ca2d4cbd699a26a3aa12bcde300d3bdfc85bad21184b83c68a0f.jpg)  
+PACS dataset
+
+![](images/7b43f0bf9a56e02dd1ccd7b8389b25bc89ed190b692d5548ff7d33f66209ee54.jpg)
+
+![](images/f3c99e15e53b1f1183b7c0046ce8c37f8cf5a60244b643095d68b43cbe76da5b.jpg)
+
+![](images/c354b77a714f1e681c5d5deca4215fba93e26717568d5885cbc9819628e5dd4a.jpg)  
+Sketch  
+Prompt: A photo of a house
+
+![](images/94bce23e5b06df73c7490e5644b96633c48796c4e23a4e63de50d6fd61cfa5c0.jpg)  
+Figure 4. This figure shows the training data generated by the T2I model under different input conditions, corresponding to each row in the Tab. 5 and Tab. 6. It can be observed that our proposed method learns some abstract domains that are difficult to describe with language after replacing the manually designed textual domains with the domain prompt  $\mathbf{E}_i^d$ . Furthermore, after applying the Progressive Training Scheme, the T2I model generates a sufficiently diverse range of images across different domains.
+
+![](images/245adc84def19bd6b302dcc5af89e6f666f39c98de4697e86e545f5ab423f194.jpg)
+
+![](images/512aa57afcfe0b41161451390047bbfe9c178403ea39f20fb5de09ba607d3f89.jpg)  
+Prompt: A photo of a  $E_{k}^{c}$  in the style of watercolor (basic domain in  $P$
+
+![](images/91e35222f35c6c070abe74e68437f7eeb68bc484c48600019fa245d7e96bef05.jpg)
+
+![](images/3fdab32a62540ef12e804f8cf433bd495aae80b8a93240c8c7c7f33f26c6f75c.jpg)
+
+![](images/2241ac0768b49d7ba902a2872eaf9bc9d205340c49a8d0bf769d4c96c4520dea.jpg)
+
+![](images/600f5ed7867cb3b65a2e3f0a17b9d64a957152cc95006ec9a5fae8171f20041f.jpg)  
+Prompt: A photo of a  $E_k^c$  in the style of  $E_i^d$
+
+![](images/3a49faa46e0b11d890922c7f1aa6c804e420550676cbd28132cfa78a8dff31b3.jpg)
+
+![](images/672e35db29e54f5de33f32e53aa192d57e99edf57d2fc2059b17d6af0078acf8.jpg)
+
+![](images/5b56a8f3ff8ab7d71ba1f5a2d761db4bc7ebc8283ab270e72cf2e564bbe5c702.jpg)
+
+![](images/8b5ab76dbeb8cafeee5ad8fa925208f6334781c28169b2b927c25b483c2365d7.jpg)  
+Prompt: A photo of a  $E_k^c$  in the style of  $E_l^d$  (with  $P$ )
+
+![](images/128ce67a1d7d29f0d5446eca7cee045cfc9820f5f438dba3267a6b4043e53e92.jpg)
+
+![](images/45a412b55b2868ae8bddad923c0c4f17e3e0b94fced20faed060f12fe74fbc96.jpg)
+
+![](images/20d5a358193ef47e91107d97d64c7e91691010662d7f8f0cb2ae845ca7e4cfdc.jpg)
+
+![](images/8c8fb333e63d31f7649bff05e1d96b55088c96fe2211476ba592a98efdde0a51.jpg)
+
+![](images/9ff144ab3313beeab4abb49f9b30bf9638ab6897f180191187c44807b8972fa6.jpg)
+
+![](images/3d6deea9dcf0efbba81439bd2957dc1daa95df3964b130f0f06cf6acce1e9f44.jpg)  
+Impact of N on SDG setting  
+Figure 5. Impact of domain prompt number in Eq.  $7N$  on PACS and VLCS dataset on SDG setting and multi-source DG setting.
+
+![](images/31f699204a042c0af08360da5a2de6897d865a3dced0de359431cdc25d30e153.jpg)  
+Impact of N on multi-source DG setting
+
+(PTS). Our Progressive Training Scheme achieves improvements of  $0.84\% \sim 3.40\%$  across each domain and  $2.50\%$  on Avg-acc (see  $4^{th}$  row and  $5^{th}$  row in Tab. 5) on PACS dataset and  $0.22\% \sim 1.72\%$  across each domain and  $0.83\%$  on Avg-acc (see  $4^{th}$  row and  $5^{th}$  row in Tab. 6) on VLCS dataset. This observation indicates that by ensuring uniformly well performance across sufficiently diverse domains, our PAPT can further shrink the distribution discrepancies between source and target domains. To visualize the effectiveness of our PTS, we conduct experiments to assess the impact of domain prompt number  $N$  in Eq. 7 on SDG and multi-source DG setting, respectively, as shown in Fig. 5. Even under the multi-source DG setting with more source domains, PTS can still improve the model's generalization performance as the number of  $N$  increases. To further demonstrate the stability of our PTS, we studied the impact of different initialization of the manually designed textual domains in  $\mathcal{P}$ , as shown in Tab. 7. It is observable that our PTS shows slight fluctuations in individual benchmark datasets, demonstrating the insensitive to the initialization of  $\mathcal{P}$ .
+
+# 4.6. Parameter Analysis
+
+We conduct experiments to analyze the impact of the hyperparameters in our method on PACS dataset, including  $\lambda$  in Eq. 14. The results are shown in Fig. 6.  $\lambda$  is a parameter to balance the trade-off between generating images in diverse domain styles and preserving key categorical features.
+
+![](images/e879074df378b0e650e620d6824479dfbf88ce6d5ee73654f72d0ae632769f74.jpg)
+
+![](images/3a30524a4bc979ff81af66a957a62d4161356991b126e078b0b57b85545e5c5b.jpg)
+
+![](images/107d250d4f916e63cf5ba0cf647be045a416db8220d7e1e664a78f67d7b9b11c.jpg)  
+Figure 6. Parameter analysis of  $\lambda$  in Eq. 14 on PACS dataset.
+
+![](images/4df363595093c2a59cc555ce65b134e04ed5d4f9f008bed857dbbad5703dfdc2.jpg)
+
+Based on Fig. 6, we set  $\lambda = 10$  for all datasets.
+
+# 5. Conclusion
+
+In this paper, we propose the Progressive Adversarial Domain Prompt Tuning framework based on the pre-trained T2I foundation model on SDG. Our method leverages adversarial training to learn two sets of abstract prompts, one that captures domain-invariant category information and another that models domain-specific styles. Furthermore, we employ the Progressive Training Scheme to enhance the diversity of domain styles. Extensive experiments on multiple DG datasets have demonstrated that our framework outperforms existing state-of-the-art SDG methods.
+
+Acknowledgements: This work was supported in part by the National Key R&D Program of China under Grant No.2023YFA1008600, in part by NSFC under Grant NO.62176198, U22A2096, and 62036007, in part by the Key R&D Program of Shaanxi Province under Grant 2024GX-YBXM135, in part by the Shaanxi Province Core Technology Research and Development Project under Grant 2024QY2-GJHX-11.
+
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+# AeSPa : Attention-guided Self-supervised Parallel imaging for MRI Reconstruction
+
+Jinho Joo $^{1*}$  Hyeseong Kim $^{1,2*}$  Hyeyeon Won $^{1}$  Deukhee Lee $^{1,2}$  Taejoon Eo $^{1\dagger}$  Dosik Hwang $^{1,2\dagger}$
+
+$^{1}$  Yonsei University  $^{2}$  Korea Institute of Science and Technology
+
+{jinho381, hyeseongkim, dosik.hwang}@yonsei.ac.kr
+
+hywon4825@gmail.com dkylee@kist.re.kr ship9136@naver.com
+
+# Abstract
+
+This study introduces a novel zero-shot scan-specific self-supervised reconstruction method for magnetic resonance imaging (MRI) to reduce scan times. Conventional supervised reconstruction methods require large amounts of fully-sampled reference data, which is often impractical to obtain and can lead to artifacts by overly emphasizing learned patterns. Existing zero-shot scan-specific methods have attempted to overcome this data dependency but show limited performance due to insufficient utilization of  $k$ -space information and constraints derived from MRI forward model. To address these limitations, we introduce a framework utilizing all acquired  $k$ -space measurements for both network inputs and training targets. While this framework suffers from training instability, we resolve these challenges through three key components: an Attention-guided  $K$ -space Selective Mechanism (AKSM) that provides indirect constraints for non-sampled  $k$ -space points, Iteration-wise  $K$ -space Masking (IKM) that enhances training stability, and a robust sensitivity map estimation model utilizing cross-channel constraint that performs effectively even at high reduction factors. Experimental results on the FastMRI knee and brain datasets with reduction factors of 4 and 8 demonstrate that the proposed method achieves superior reconstruction quality and faster convergence compared to existing zero-shot scan-specific methods, making it suitable for practical clinical applications. The implementation of our proposed method is publicly available at https://github.com/joojinho97/AeSPa.git.
+
+# 1. Introduction
+
+Magnetic Resonance Imaging (MRI) has transformed medical imaging and diagnostics by providing detailed anatomical visualization without radiation exposure, ensuring pa
+
+![](images/bb8288016812606c73aa8b2384617b4b702bac8b2cf26ad7f3f4818fcad1148c.jpg)  
+Figure 1. Experimental results on the FastMRI knee dataset using 1D Gaussian sampling with  $\mathbf{R} = 8$  with 16 ACS lines.
+
+tient safety and comfort. However, long scan times remain a major challenge in MRI, often resulting in patient discomfort and degraded image quality due to motion artifacts or contrast washout [14, 22]. To address this limitation, k-space undersampling has emerged as an effective approach, although this incomplete data acquisition inevitably leads to aliasing artifacts and degraded image quality. To overcome these reconstruction challenges, various methods have been proposed, ranging from conventional compressed sensing (CS) or parallel imaging [5, 9, 19, 23, 25, 27, 32] to deep learning approaches [3, 11, 18, 20, 21, 26, 35]. Deep learning-based methods have emerged as the state-of-the-art, typically combining image priors, learned through training, with data consistency to solve the ill-posed inverse problem [7, 16, 17]. For instance, Supervised U-Net [39] implements an image-to-image framework with a data consistency layer, while KIKI-Net [6], Deep Cascade [30], and E2E-VarNet [33] employ multiple iterations of reconstruction refinement with repeated data consistency steps.
+
+While supervised learning approaches can learn robust image priors for accurate MRI reconstruction, they require extensive training datasets encompassing various contrast types (e.g., T1, T2, T1-pre, T1-post, FLAIR) and imaging regions (e.g., brain, musculoskeletal, heart, abdomen). The acquisition of such comprehensive datasets is often impractical and time-consuming, which ultimately limits the clinical applicability of conventional supervised deep learning methods [1, 24, 31, 38-40]. To address this challenge, recent research has focused on approaches that do not require fully-sampled data, zero-shot scan-specific self-supervised learning methods [36, 37]. These approaches enable training without fully-sampled reference data, expanding the applicability of deep learning reconstruction to a wider range of MRI applications.
+
+Despite the progress, the zero-shot scan-specific methods primarily suffer from two limitations [8, 15, 36, 37], leading to increasingly ill-posed reconstruction at relatively high acceleration factors and compromised reconstruction performance. First, these methods divide k-space measurements into two mutually exclusive sets, where only a portion of k-space points is used as input data for both network and data consistency units while the remaining portion serves as training targets. This fixed division scheme can restrict the utilization of k-space measurements to approximately half of the available points for each purpose, potentially limiting the exploitation of k-space information. Second, these methods learn limited image representations since a single undersampled scan contains less information than extensive fully-sampled scans used in supervised learning. These limitations frequently result in training instability and convergence to local minima. To overcome these limitations, we propose a framework that eliminates the need for k-space division by utilizing all undersampled k-space points in a unified manner. Our approach uses all acquired k-space measurements in two ways: as network inputs to estimate the coil-combined image and coil sensitivity maps, and as reference points to calculate loss by comparing them with the forward model outputs. Moreover, we introduce several key components that ensure stable training and guide the framework toward more accurate solutions in this unified approach. These techniques enable better exploitation of k-space domain information and MRI forward model constraints, achieving superior state-of-the-art reconstruction performance. The key contributions of this work are as follows:
+
+- Attention-guided K-space Selective Mechanism (AKSM). AKSM selects pixels from non-sampled k-space that significantly influence image quality and utilizes them for final inference, thereby improving reconstruction quality in no-reference environments.  
+- Iteration-wise K-space Masking (IKM). We introduce IKM to stabilize training and prevent the model from get-
+
+ting trapped in local minima. This masking guides the network to focus on regions with reliable information, enabling stable model training.
+
+- Robust Sensitivity Map Estimation Model with Cross-Channel constraint. We propose a model that reliably infers sensitivity maps under high reduction factors by utilizing a cross-channel constraint.
+
+We validate our approach on the FastMRI [39] dataset. As shown in Fig. 1, our model (AeSPa, red star) outperforms both conventional parallel imaging methods and existing zero-shot deep learning-based methods in terms of SSIM, while achieving significantly faster reconstruction time. This demonstrates that AeSPa provides high-quality MRI reconstruction with excellent computational efficiency, making it practical for clinical applications.
+
+# 2. Related work
+
+# 2.1. Conventional Parallel Imaging
+
+Parallel imaging techniques have significantly advanced MRI by utilizing multiple receiver coils to accelerate image acquisition and improve image quality. This acceleration is achieved by exploiting the distinct spatial sensitivities of multiple coils, allowing for reduced k-space sampling without compromising image reconstruction. Among these techniques, Sensitivity Encoding (SENSE) [27] uses sensitivity maps to resolve aliasing artifacts from undersampling, while GRAPPA [9] operates in k-space by estimating missing data from neighboring points. ESPIRiT [34] unifies SENSE and GRAPPA approaches through eigenvalue decomposition, while L1-SPIRiT [25] integrates compressed sensing with parallel imaging. Additionally, Total Generalized Variation (TGV) [19] has been proposed to minimize artifacts by considering both first and second-order derivatives of the reconstructed image.
+
+# 2.2. Supervised MRI Reconstruction
+
+In recent years, supervised deep learning methods for MRI reconstruction have been developed to learn the reconstruction process from paired undersampled and fully-sampled data [1, 2, 4, 28, 31, 38]. Methods like Deep Cascade [30] and KIKI-Net [6] focus on single-coil reconstruction with data consistency layers, demonstrating improved reconstruction quality. Further extending to multi-coil reconstruction, approaches such as the original U-Net [29] adaptation for MRI [39], Variational Network (VN) [12], and its extension E2E-VarNet [33], have shown promising results on the FastMRI dataset [39]. However, these methods require paired training data and may perform poorly on data outside their training distribution.
+
+# 2.3. Scan-Specific MRI Reconstruction
+
+Building upon these parallel imaging advances, recent work in self-supervised learning has aimed to overcome the limitations of supervised MRI reconstruction methods, particularly the need for fully-sampled reference data. Yaman et al. [36] proposed the Self-Supervision via Data Undersampling (SSDU) framework, which enables physics-guided deep learning reconstruction to be trained on undersampled data only. This was further advanced by their Zero-Shot Self-Supervised Learning (ZS-SSL) approach [37], which performs subject-specific reconstruction by training on measurements from a single undersampled scan. SPICER [15] proposes a method for estimating sensitivity maps in scan-specific self-supervised MRI reconstruction, enabling rapid acquisition of high-resolution images without reference data by combining the spatial sensitivities with coil images.
+
+While these self-supervised methods offer promising directions for accelerated MRI reconstruction without fully-sampled training data, they face certain limitations. The partitioning of k-space data in [36] may lead to suboptimal use of available information, potentially affecting reconstruction quality in highly accelerated scenarios. [37], while addressing subject-specific reconstruction, can be computationally intensive as it requires training a new model for each scan. These limitations in existing self-supervised methods motivate the development of more efficient and effective approaches for scan-specific MRI reconstruction.
+
+# 3. Method
+
+Preliminary. In magnetic resonance imaging, the goal is to reconstruct an image  $\mathbf{x}$  from the acquired k-space measurements  $\mathbf{k}_{\mathrm{acq}}$ , with non-acquired k-space points filled with zeros. The basic forward model for this process can be described as
+
+$$
+\mathbf {k} _ {a c q} = \mathbf {A x} + \varepsilon , \tag {1}
+$$
+
+where  $\mathbf{A}$  denotes the encoding operator that maps from image space to k-space, and  $\varepsilon$  represents measurement noise. In the multi-coil setting, data is acquired simultaneously from multiple receiver coils, each with a different spatial sensitivity profile. The forward model becomes
+
+$$
+\mathbf {k} _ {(a c q, i)} = \mathbf {A} _ {i} \mathbf {x} + \varepsilon_ {i}, \quad i = 1, \dots , N _ {c}, \tag {2}
+$$
+
+where  $\mathbf{k}_{(acq,i)}$  represents the k-space data from the  $i$ -th coil,  $\mathbf{A}_i$  is the encoding operator for the  $i$ -th coil (incorporating the coil sensitivity profile), and  $N_{c}$  is the number of coils. The encoding operator  $\mathbf{A}_i$  can be decomposed as
+
+$$
+\mathbf {A} _ {i} = \mathbf {P F S} _ {i}, \tag {3}
+$$
+
+where  $\mathbf{P}$  is the undersampling mask operator,  $\mathbf{F}$  is the Fourier transform, and  $\mathbf{S}_i$  is the sensitivity map for the  $i$ -th coil. To reconstruct the image  $\mathbf{x}$  from the undersampled
+
+multi-coil images, we formulate an optimization problem that balances data consistency (DC) with prior knowledge about the image. This can be expressed as
+
+$$
+\mathbf {x} ^ {\prime} = \underset {\mathbf {x}} {\operatorname {a r g m i n}} \left(\frac {1}{2} \sum_ {i = 1} ^ {N _ {c}} \| \mathbf {A} _ {i} \mathbf {x} - \mathbf {k} _ {(a c q, i)} \| _ {2} ^ {2} + \lambda R (\mathbf {x})\right), \tag {4}
+$$
+
+where  $\mathbf{x}'$  represents the optimized image of the  $\mathbf{x}$ ,  $\|\cdot\|_2^2$  denotes the squared  $\ell_2$ -norm,  $R(\mathbf{x})$  is a regularization term designed to reflect prior knowledge about the image properties, and  $\lambda$  is a regularization parameter that balances the DC term with the regularization term.
+
+Overall architecture. We propose Attention-guided Self-supervised Parallel imaging for MRI Reconstruction (AeSPa), which reconstructs high-quality MR images exclusively from multi-coil undersampled k-space data, as illustrated in Fig. 2. The framework consists of two main reconstruction modules: a coil combined image estimation model (ccm) and a coil sensitivity map estimation model (csm). In addition, it includes two regularization components: Attention-guided K-space Selective Mechanism (AKSM) and Iteration-wise K-space Masking (IKM), which are designed to enhance the training stability and reconstruction quality by leveraging k-space information effectively.
+
+The overall workflow is as follows. The coil combined image estimation model uses the coil combined image from undersampled k-space as its initial input to produce initial coil combined MR images. Subsequently, the sensitivity map estimation model receives multi-coil MR images from undersampled k-space as inputs at initial to reconstruct sensitivity maps. These coil combined MR images and sensitivity maps are used to reconstruct k-space. By applying an  $\mathbf{F}^{-1}$  to the reconstructed k-space, multi-coil MR images can be reconstructed, and by applying a coil combination process with the reconstructed k-space and the sensitivity maps, coil combined images can be obtained. These two datasets are updated as inputs to the sensitivity map estimation and coil combined image estimation models, respectively. We train our framework for 2,000 iterations  $(T)$ . More details are provided in the supplementary material. The parameters of the three models are described as
+
+$$
+\xi^ {(t)} = \left\{\theta^ {(t)}, \psi^ {(t)}, \phi^ {(t)} \right\}, \tag {5}
+$$
+
+where  $\xi^{(t)}$  denotes the parameters at iteration  $t$  of the coil-combined image model  $\theta^{(t)}$ , the sensitivity map estimation model  $\psi^{(t)}$ , and Mamba [10] for AKSM  $\phi^{(t)}$ .
+
+$$
+\xi^ {(t)} = \underset {\xi^ {(t)}} {\operatorname {a r g m i n}} \mathcal {L} \left(\mathbf {k} _ {a c q}, f \left(\mathbf {k} _ {a c q}, \hat {\mathbf {S}} ^ {(t - 1)}, \hat {\mathbf {x}} ^ {(t - 1)}; \xi^ {(t)}\right)\right). \tag {6}
+$$
+
+Here,  $f$  represents a single iteration step in the forward reconstruction process, as illustrated in Fig. 2. In each iter-
+
+ation, the model refines the coil combined image and sensitivity maps using the previous estimates.  $\xi^{\prime}$  represents the optimized image  $\xi^{(t)}$  when  $t = T$ . Then, we can express reconstructed coil combined image as follow:
+
+$$
+\hat {\mathbf {x}} ^ {(t)} = f \left(\mathbf {k} _ {a c q}, \hat {\mathbf {S}} ^ {(t - 1)}, \hat {\mathbf {x}} ^ {(t - 1)}; \xi^ {(t)}\right), \tag {7}
+$$
+
+where  $\hat{\mathbf{x}}^{(t)}$  represents the estimated coil combined image at iteration  $t$ , with  $\hat{\mathbf{x}}^{(0)}$  being the initial coil combined image obtained from the  $\mathbf{k}_{acq}$ , and the final reconstructed image  $\mathbf{x}'$  is defined as  $\hat{\mathbf{x}}^{(t)}$  at  $t = T$ .
+
+# 3.1. Attention guided K-space selective mechanism
+
+The key challenge in zero-shot scan-specific MRI reconstruction is the absence of guidance labels for the reconstructed non-sampled k-space during self-supervised learning without supervision. To address this, we propose AKSM, which calculates attention values for non-sampled k-space regions, guided by no-reference regularization in the image domain. AKSM is inspired by modern MRI data sampling techniques and the computational structure of attention mechanisms such as Mamba. It is designed to focus on frequency bases that enhance image quality in the k-space domain, aiming to achieve high-quality image reconstruction in zero-shot scan-specific MRI reconstruction.
+
+The training and reconstruction process of AKSM is detailed in Algorithm 1. As shown in Fig. 2, the Mamba layer of AKSM takes the k-space reconstructed from AeSPa as input and outputs attention values for each k-space pixel. Then, a sigmoid function is applied to the output attention values, which are elementwise multiplied by the k-space reconstructed from AeSPa to create an attention-weighted k-space. This attention-weighted k-space is used to create the coil-combined image  $\hat{\mathbf{x}}_{AKSM}$  via  $A_{cc}$  in Eq. 8, which is then applied to Mamba's no-reference regularization loss. Then, the k-space indices with the highest attention values, categorized as top K based on the sampling direction, are selected, and their corresponding k-space values are stored in k-space repository  $(\mathbf{k}_{sel})$ .  $\hat{\mathbf{x}}_{AKSM}^{final}$  is the final coil-combined image for evaluation, generated by  $A_{cc}$  operator with  $\hat{\mathbf{S}}$  and  $\mathbf{k}_{sel}$ . For the  $\hat{\mathbf{x}}_{AKSM}^{final}$  evaluation, we perform post-processing in the following order: center crop, max normalization, magnitude calculation, and bandpass filtering. Further details can be found in the supplementary material.
+
+$$
+A _ {c c} \left(\hat {\mathbf {M}} ^ {(t - 1)}, \hat {\mathbf {k}} _ {A t t}\right) \triangleq c c \left(c s m \left(\hat {\mathbf {M}} ^ {(t - 1)}\right), \mathbf {F} ^ {- 1} \hat {\mathbf {k}} _ {A t t}\right), \tag {8}
+$$
+
+where  $cc$  denotes the coil combined operator, performing the coil combination operation on the multi-coil images and sensitivity map.  $\hat{\mathbf{k}}$  is reconstructed k-space from forward model,  $\tilde{\mathbf{M}}$  denotes the reconstructed multi coil images.
+
+Algorithm 1 AKSM in Training and Reconstruction
+
+Parameters:  $\mathbf{Att}_{sum}$  is the sum of the real and imaginary attention values at the same index along the channel-wise direction.  $\sigma$  is sigmoid function,  $\hat{\mathbf{k}}_{Att}$  is attention-weighted k-space.
+
+procedure
+
+When training  $AKSM$ ,  $\hat{\mathbf{k}}$  and  $\hat{\mathbf{S}}$  stop gradient.
+
+for  $t = 1,2,\dots T$  do
+
+$$
+\mathbf {A t t} _ {v a l u e} = M a m b a (\hat {\mathbf {k}})
+$$
+
+$$
+\mathbf {A t t} _ {\text {v a l u e}} = \sigma (\mathbf {A t t} _ {\text {v a l u e}})
+$$
+
+$$
+\mathbf {k} _ {A t t} = \mathbf {k} \odot \mathbf {A t t} _ {v a l u e}
+$$
+
+$$
+\hat {\mathbf {x}} _ {A K S M} = A _ {c c} (\dot {\mathbf {k}} _ {A t t})
+$$
+
+$$
+\operatorname {C o m p u t e} \mathcal {L} _ {A K S M} \left(A _ {c c} \left(\hat {\mathbf {M}} ^ {(t - 1)}, \hat {\mathbf {k}} _ {A t t}\right)\right)
+$$
+
+$$
+\text {U p d a t e} \quad M a m b a \text {f o r} A K S M.
+$$
+
+$$
+\mathbf {k} _ {s e l} = \{\hat {\mathbf {k}} \in \operatorname {T o p} K \text {f r o m} \mathbf {A t t} _ {s u m} \text {i n d i c e s} \}
+$$
+
+$$
+e n d \mathrm {f o r}
+$$
+
+$$
+\text {e n d p r o c u d u r e}
+$$
+
+Reconstruction
+
+procedure
+
+$$
+\hat {\mathbf {x}} _ {A K S M} ^ {f i n a l} = A _ {c c} (\hat {\mathbf {M}} ^ {(T)}, \mathbf {P k} _ {a c q} + (\mathbf {1} - \mathbf {P}) \mathbf {k} _ {s e l} ^ {(T)})
+$$
+
+Post-processing for evalutaion using  $\hat{\mathbf{x}}_{AKSM}^{final}$
+
+$$
+\text {e n d p r o c u d u r e}
+$$
+
+# 3.2. Iteration-wise K-space Masking
+
+He et al. [13] introduced a framework where strategic masking enables models to capture complex data patterns without labeled data. Inspired by this, we propose IKM, which applies iteration-varying uniform random masks to non-sampled k-space regions and performs DC on these masked regions. Through this iterative masking and consistency process, IKM facilitates effective learning of high-frequency information while jointly updating both the coil combined image estimation and sensitivity map estimation.
+
+Data consistency after IKM. After masking a certain percentage of the reconstructed k-space with zero values at random, DC is applied with the undersampled k-space. We create  $\hat{\mathbf{M}}^{(t)}$  using  $\hat{\mathbf{k}}_{IKM}$  with the  $\mathbf{F}^{-1}$ , and  $\hat{\mathbf{x}}^{(t)}$  using  $\hat{\mathbf{k}}_{IKM}$  with the coil combine operator  $A_{cc}$ . Each is then used to update the inputs of the sensitivity map and coil combined image estimation models.  $\hat{\mathbf{k}}_{IKM}$  is defined as follows:
+
+$$
+\hat {\mathbf {k}} _ {I K M} = \mathbf {P} _ {r m} ^ {(t)} (\mathbf {1} - \mathbf {P}) \hat {\mathbf {k}} ^ {(t)} + \mathbf {k} _ {a c q}, \tag {9}
+$$
+
+$$
+\mathbf {P} _ {r m} ^ {(t)} = \left\{ \begin{array}{l l} \mathbf {P} _ {r m} ^ {\text {n e w}} & \text {i f} t = 1 \text {o r} t \bmod 1 0 = 0, \\ \mathbf {P} _ {r m} ^ {(t - 1)} & \text {i f o t h e r w i s e}, \end{array} \right. \tag {10}
+$$
+
+where  $\mathbf{P}_{rm}^{(t)}$  denotes a random k-space mask that is updated with a new mask every 10 iterations and  $\mathbf{P}_{rm}^{new}$  denotes generated random k-space masking. Due to the coil sensitivity encoding process in parallel MRI, the desired
+
+![](images/ad35e1eae4efe285b9c48385c2a3e295e331800d8748baac361f4e764c58c312.jpg)  
+Figure 2. The overview of the proposed method. The blue text denotes the update input for the coil-combined image estimation model, while the green text represents the update input for the sensitivity map estimation model.
+
+![](images/4c242ab05f39c5288a142075422589d3a9f032143eafcccd1df98821de3afea9.jpg)
+
+coil-combined image information is inherently distributed across the k-space measurements obtained from multiple coils. By leveraging this distributed information through IKM, our approach effectively enhances the model's stability and generalization performance during training.
+
+# 3.3. Robust Sensitivity Map Estimation
+
+In parallel MRI, particularly in scan-specific reconstruction, external algorithms such as ESPIRiT have been used to estimate sensitivity maps. However, ESPIRiT is inefficient when the number of autocalibration signal (ACS) lines is small [15]. This issue leads to a degradation in the quality of the sensitivity map when fewer sampling lines are used for higher MRI acceleration, ultimately resulting in a decline in the final image quality. Therefore, this paper proposes a sensitivity map estimation model with a simple yet effective constraint function to generate high-quality sensitivity maps in sampled k-space with limited ACS lines.
+
+Cross-Channel constraint. In MRI reconstruction, Divide Root Sum of Squares (DSS) is a standard technique used commonly for sensitivity map normalization within sensitivity map estimation models [33, 36, 37]. Considering that each coil image is the product of the true MR image and its spatially varying sensitivity map, the DSS of sensitivity maps across channels should theoretically yield a ones matrix. However, DSS approach does not guarantee that the sum of squares across channels for each pixel in the sensitivity map equals 1. Therefore, we propose a cross-channel constraint that directly applies the constraint within the sensitivity map estimation model so that it follows Eq. 11,
+
+where  $\mathbf{1}$  denotes an all-ones matrix with the same dimension as  $\mathbf{S}_i$ . This physically-motivated cross-channel constraint strongly regularizes sensitivity estimates, resulting in a more accurate sensitivity map.
+
+$$
+\mathbf {1} - \sum_ {i = 1} ^ {N _ {c}} \left(\mathbf {S} _ {i} ^ {*} \mathbf {S} _ {i}\right) = 0. \tag {11}
+$$
+
+# 3.4. Objective Function
+
+In this section, we explain the objective functions used in the proposed model. Our model employs DC loss, total variation loss, cross-channel loss, and AKSM loss. Note that all variables in the following equations are functions of iteration step (t), but we omit this notation for simplicity.
+
+DC loss. For multi-coil MRI reconstruction, the DC loss ensures that the reconstructed k-space data remains consistent with the acquired k-space measurements across all coils. The DC loss can be expressed as
+
+$$
+\mathcal {L} _ {\mathrm {d c}} = \sum_ {i = 1} ^ {N _ {c}} \| \mathbf {P} \left(\hat {\mathbf {k}} _ {i} - \mathbf {k} _ {(a c q, i)}\right) \| _ {1} ^ {1}. \tag {12}
+$$
+
+Through empirical studies, we determined that  $\ell_1$ -norm performs better than  $\ell_2$ -norm.
+
+Total variation loss. To improve image quality, we calculate total variation loss on the reconstructed sensitivity map  $\mathcal{L}_{tv}^{\hat{S}}$  and coil combined image  $\mathcal{L}_{tv}^{\hat{x}}$ . Applying total variation loss to sensitivity maps and the coil-combined image enforces spatial smoothness, effectively suppressing high-frequency artifacts and preserving essential structures in
+
+both domains.
+
+Cross-channel loss. As discussed in 3.3, we use cross-channel loss to impose an additional constraint on the sensitivity map estimation model.
+
+$$
+\mathcal {L} _ {c c} = \mathbf {1} - \sum_ {i = 1} ^ {N _ {c}} \left(\hat {\mathbf {S}} _ {i} ^ {*} \hat {\mathbf {S}} _ {i}\right), \tag {13}
+$$
+
+AKSM loss. In the AKSM module, the total variation loss is computed on the coil combined image reconstructed as follows:
+
+$$
+\mathcal {L} _ {A K S M} = \sum_ {u, v} \sqrt {\left(\hat {\mathbf {x}} _ {A K S M} ^ {(u + 1 , v)} - \hat {\mathbf {x}} _ {A K S M} ^ {(u , v)}\right) ^ {2} + \left(\hat {\mathbf {x}} _ {A K S M} ^ {(u , v + 1)} - \hat {\mathbf {x}} _ {A K S M} ^ {(u , v)}\right) ^ {2}}, \tag {14}
+$$
+
+where  $u$  and  $v$  denote pixel indices in the spatial domain.
+
+Total loss. The total loss function for csm and ccm is defined as:
+
+$$
+\mathcal {L} _ {t o t a l} = \mathcal {L} _ {d c} + \lambda_ {1} \mathcal {L} _ {t v} ^ {\hat {S}} + \lambda_ {2} \mathcal {L} _ {t v} ^ {\hat {x}} + \lambda_ {3} \mathcal {L} _ {c c}, \tag {15}
+$$
+
+where we decided to set  $\lambda_{1},\lambda_{2}$ , and  $\lambda_{3}$  to 1 based on empirical studies.
+
+# 4. Experiments
+
+To evaluate the effectiveness of our proposed model, we conducted two sets of experiments. First, we performed comparative experiments with conventional parallel imaging methods [9, 19, 25] and scan-specific deep learning methods [15, 36, 37] on the FastMRI [39] knee and brain datasets. Additionally, through ablation studies, we analyzed the contribution of each component: AKSM, IKM, and sensitivity map estimation model with cross-channel constraint, in terms of reconstruction quality and speed for multi-coil MRI reconstruction.
+
+Dataset. In our experiments, we evaluated the proposed multi-coil MR reconstruction method using the FastMRI knee and brain datasets. From these datasets, we selected proton-density weighted images (PD) for the knee dataset and T1-weighted with contrast agent (T1-Post) for the brain dataset. The knee dataset was acquired with 15 receiver coils, while the brain dataset was acquired with either 20 or 16 receiver coils. A total of 25 patients' data were used, and two slices around the center were extracted from each subject, yielding a total of 50 slices. To train and evaluate the model, we used fully-sampled MR data that was retrospectively undersampled by applying four different undersampling masks. We conducted experiments with two reduction factors  $(\mathrm{R} = 4$  and 8). For  $\mathbb{R} = 4$  we used 28 ACS lines, and for  $\mathbf{R} = 8$  we used 16 ACS lines.
+
+# 4.1. Comparison Study
+
+Qualitative Comparison. Fig. 3 illustrates qualitative comparisons for accelerated MRI reconstruction on the
+
+FastMRI brain dataset, using 1D Gaussian sampling at  $R = 4$ . The results demonstrate that AeSPa achieves preserving finer anatomical details with greater clarity compared to other methods. The results on the FastMRI knee dataset are available in the supplementary material for comprehensive evaluation.
+
+Quantitative Comparison. The experimental results in Tables 1 and 2 demonstrate the superior performance of the proposed method across various sampling patterns and reduction factors. In the FastMRI knee dataset, with Gaussian sampling at  $R = 4$ , our model achieved the average PSNR of 35.99 dB and SSIM of 0.899, while in the brain dataset under the same conditions, it achieved a PSNR of 39.08 dB and SSIM of 0.956, outperforming all existing methods. This represents superior performance compared to both conventional parallel imaging methods and state-of-the-art deep learning-based methods. These results demonstrate the effectiveness of combining deep learning with parallel MRI reconstruction to improve image quality and robustness, and ablation studies have confirmed our methodology's efficiency.
+
+Reconstruction time. Table 3 presents a comparison of average reconstruction times for single-instance reconstruction methods. The table includes average reconstruction times for SSDU [36], ZS-SSL [37], SPICER [15], and the proposed method, AeSPa (Ours). Compared to existing methods, our proposed model AeSPa achieves a reconstruction time of 12 mins, showing a modest increase in computational cost relative to SPICER (10.5 mins) while maintaining significant computational advantages over ZS-SSL (44 mins) and SSDU (21.5 mins). These results demonstrate that AeSPa is efficient not only in terms of reconstruction performance but also in processing speed, suggesting its potential advantage in scenarios requiring real-time reconstruction or large-scale data processing.
+
+# 4.2. Ablation Study
+
+In this section, we provide an in-depth evaluation of our model's utility through ablation studies to assess the impact of each component on performance.
+
+Model components. To evaluate the effectiveness of the proposed model architecture, we conducted experiments on the FastMRI knee PD dataset with  $R = 8$ , ablating IKM, AKSM, and sensitivity map estimation with a cross-channel constraint. As shown in Table 4, each component incrementally boosted performance. Starting with the baseline (PSNR: 29.01dB), adding AKSM improved results (PSNR: 29.70 dB). Adding IKM further raised performance (PSNR: 31.24 dB). Finally, incorporating sensitivity map estimation with a cross-channel constraint achieved the best results (PSNR: 32.57 dB). These results demonstrate that each component effectively contributes to enhanced reconstruction quality.
+
+![](images/e4125f34d220f4a0f103a15963263770821fa1ebf10573635374bc9a2da1faa2.jpg)  
+Figure 3. Qualitative results for accelerated MRI reconstruction on the FastMRI brain data. Reconstruction was performed using 1D Gaussian random sampling with  $R = 4$ .
+
+<table><tr><td rowspan="3"></td><td colspan="4">1D Uniform</td><td colspan="4">1D Gaussian</td></tr><tr><td colspan="2">R = 4, ACS = 28</td><td colspan="2">R = 8, ACS = 16</td><td colspan="2">R = 4, ACS = 28</td><td colspan="2">R = 8, ACS = 16</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td></tr><tr><td>ZF</td><td>23.27 ± 4.37</td><td>0.775 ± 0.05</td><td>18.62 ± 4.26</td><td>0.673 ± 0.06</td><td>25.28 ± 4.29</td><td>0.815 ± 0.04</td><td>20.14 ± 3.98</td><td>0.708 ± 0.05</td></tr><tr><td>GRAPPA [9]</td><td>25.53 ± 3.71</td><td>0.758 ± 0.06</td><td>20.55 ± 3.91</td><td>0.654 ± 0.07</td><td>27.91 ± 3.77</td><td>0.806 ± 0.05</td><td>22.38 ± 3.74</td><td>0.709 ± 0.06</td></tr><tr><td>TGV [19]</td><td>29.01 ± 3.08</td><td>0.814 ± 0.06</td><td>24.37 ± 3.45</td><td>0.709 ± 0.07</td><td>30.18 ± 3.42</td><td>0.825 ± 0.06</td><td>24.95 ± 3.55</td><td>0.734 ± 0.07</td></tr><tr><td>CS-Wavelet [23]</td><td>29.70 ± 2.74</td><td>0.821 ± 0.05</td><td>24.89 ± 3.14</td><td>0.726 ± 0.06</td><td>31.57 ± 3.32</td><td>0.835 ± 0.06</td><td>26.41 ± 3.07</td><td>0.760 ± 0.06</td></tr><tr><td>L1-SPIRiT [25]</td><td>30.93 ± 2.84</td><td>0.811 ± 0.05</td><td>25.95 ± 2.61</td><td>0.717 ± 0.06</td><td>31.36 ± 3.40</td><td>0.826 ± 0.06</td><td>29.71 ± 2.52</td><td>0.777 ± 0.06</td></tr><tr><td>SSDU [36]</td><td>31.72 ± 3.98</td><td>0.839 ± 0.06</td><td>27.34 ± 2.30</td><td>0.721 ± 0.07</td><td>31.61 ± 4.17</td><td>0.829 ± 0.06</td><td>30.11 ± 3.27</td><td>0.799 ± 0.06</td></tr><tr><td>ZS-SSL [37]</td><td>31.71 ± 3.92</td><td>0.836 ± 0.06</td><td>27.06 ± 2.61</td><td>0.722 ± 0.07</td><td>32.23 ± 3.58</td><td>0.838 ± 0.06</td><td>30.47 ± 3.28</td><td>0.800 ± 0.06</td></tr><tr><td>SPICER [15]</td><td>32.88 ± 3.53</td><td>0.869 ± 0.04</td><td>27.61 ± 2.35</td><td>0.767 ± 0.05</td><td>32.92 ± 3.21</td><td>0.855 ± 0.05</td><td>29.50 ± 2.88</td><td>0.813 ± 0.05</td></tr><tr><td>AeSPa (Ours)</td><td>34.23 ± 3.91</td><td>0.874 ± 0.05</td><td>28.37 ± 3.28</td><td>0.795 ± 0.05</td><td>35.99 ± 3.04</td><td>0.899 ± 0.04</td><td>32.57 ± 3.24</td><td>0.853 ± 0.05</td></tr></table>
+
+Table 1. Quantitative results on FastMRI knee with reduction factors (R = 4 and 8) for both 1D Uniform and Gaussian sampling patterns. The best, second-best entries are marked in red, orange, respectively.  
+
+<table><tr><td rowspan="3"></td><td colspan="4">1D Uniform</td><td colspan="4">1D Gaussian</td></tr><tr><td colspan="2">R = 4, ACS = 28</td><td colspan="2">R = 8, ACS = 16</td><td colspan="2">R = 4, ACS = 28</td><td colspan="2">R = 8, ACS = 16</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td></tr><tr><td>ZF</td><td>27.42 ± 1.98</td><td>0.859 ± 0.03</td><td>25.30 ± 1.65</td><td>0.824 ± 0.04</td><td>29.31 ± 2.35</td><td>0.887 ± 0.03</td><td>27.04 ± 2.04</td><td>0.851 ± 0.04</td></tr><tr><td>GRAPPA [9]</td><td>29.16 ± 2.14</td><td>0.856 ± 0.03</td><td>25.24 ± 1.68</td><td>0.795 ± 0.04</td><td>31.64 ± 2.54</td><td>0.889 ± 0.03</td><td>29.82 ± 2.46</td><td>0.866 ± 0.03</td></tr><tr><td>TGV [19]</td><td>30.37 ± 2.07</td><td>0.898 ± 0.02</td><td>26.84 ± 1.61</td><td>0.843 ± 0.03</td><td>32.91 ± 2.42</td><td>0.925 ± 0.02</td><td>31.73 ± 2.53</td><td>0.913 ± 0.02</td></tr><tr><td>CS-Wavelet [23]</td><td>30.88 ± 2.12</td><td>0.911 ± 0.02</td><td>25.88 ± 1.68</td><td>0.825 ± 0.03</td><td>34.08 ± 2.32</td><td>0.945 ± 0.01</td><td>33.01 ± 2.65</td><td>0.932 ± 0.02</td></tr><tr><td>L1-SPIRiT [25]</td><td>32.03 ± 2.31</td><td>0.925 ± 0.01</td><td>27.42 ± 1.89</td><td>0.854 ± 0.03</td><td>34.34 ± 2.40</td><td>0.944 ± 0.01</td><td>34.03 ± 2.51</td><td>0.944 ± 0.01</td></tr><tr><td>SSDU [36]</td><td>35.70 ± 2.43</td><td>0.918 ± 0.02</td><td>30.48 ± 2.18</td><td>0.850 ± 0.04</td><td>33.16 ± 4.34</td><td>0.884 ± 0.07</td><td>33.72 ± 3.22</td><td>0.903 ± 0.04</td></tr><tr><td>ZS-SSL [37]</td><td>35.59 ± 2.49</td><td>0.935 ± 0.01</td><td>30.44 ± 2.16</td><td>0.863 ± 0.03</td><td>35.21 ± 2.76</td><td>0.921 ± 0.03</td><td>33.91 ± 2.71</td><td>0.918 ± 0.02</td></tr><tr><td>SPICER [15]</td><td>35.98 ± 2.25</td><td>0.944 ± 0.01</td><td>30.95 ± 2.68</td><td>0.876 ± 0.03</td><td>35.42 ± 2.89</td><td>0.950 ± 0.01</td><td>32.60 ± 3.06</td><td>0.919 ± 0.02</td></tr><tr><td>AeSPa (Ours)</td><td>36.24 ± 2.63</td><td>0.947 ± 0.01</td><td>30.49 ± 2.41</td><td>0.881 ± 0.03</td><td>39.08 ± 2.04</td><td>0.956 ± 0.01</td><td>34.96 ± 2.44</td><td>0.925 ± 0.02</td></tr></table>
+
+Table 2. Quantitative results on FastMRI brain with reduction factors (R = 4 and 8) for both 1D Uniform and Gaussian sampling patterns. The best, second-best entries are marked in red, orange, respectively.  
+
+<table><tr><td></td><td>SSDU [36]</td><td>ZS-SSL [37]</td><td>SPICER [15]</td><td>AeSPa (Ours)</td></tr><tr><td>Time</td><td>21.5 mins</td><td>44 mins</td><td>10.5 mins</td><td>12 mins</td></tr></table>
+
+Table 3. Average reconstruction times for single-instance reconstruction methods.
+
+We also investigated the frequency of input updates in the sensitivity map and the coil combined image estimate
+
+tion model, as presented in Table 5. This ablation study revealed that updating the inputs of sensitivity map estimation model every 10 iterations and the inputs of coil combined image estimation model every 1 iteration achieved the best reconstruction quality, achieving a balance between computational efficiency and image accuracy.
+
+In addition, we performed a performance ablation study
+
+![](images/3414b8b2b1e3611cdd90cb81075c54877795be9ccb94ba8878925bb576e443f5.jpg)  
+Figure 4. Comparison of training progress with AKSM, without AKSM, and with coil combined image estimation model.
+
+![](images/570a0fbdb562219e685415c99f52b5993435d001dc5212f3276758cf0c837fa1.jpg)
+
+<table><tr><td>sensitivity map</td><td>cross channel</td><td>IKM</td><td>AKSM</td><td>PSNR ↑</td><td>SSIM ↑</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>32.57 ± 3.24</td><td>0.853 ± 0.05</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>32.43 ± 3.08</td><td>0.852 ± 0.05</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>32.32 ± 3.31</td><td>0.843 ± 0.06</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>31.24 ± 2.26</td><td>0.845 ± 0.04</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>30.74 ± 4.75</td><td>0.812 ± 0.09</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>32.29 ± 3.27</td><td>0.842 ± 0.06</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>30.03 ± 4.39</td><td>0.805 ± 0.09</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>29.70 ± 2.53</td><td>0.803 ± 0.06</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>29.11 ± 4.93</td><td>0.798 ± 0.09</td></tr><tr><td></td><td></td><td></td><td></td><td>29.01 ± 2.73</td><td>0.791 ± 0.06</td></tr></table>
+
+Table 4. Results of ablation studies on our method, evaluated on the FastMRI knee PD dataset using 1D Gaussian sampling with  $\mathbf{R} = 8$ .  
+
+<table><tr><td>csm / ccm</td><td>1 / 1</td><td>1 / 10</td><td>10 / 1</td><td>10 / 10</td></tr><tr><td>PSNR ↑</td><td>23.37 ± 4.69</td><td>21.88 ± 4.79</td><td>32.57 ± 3.24</td><td>31.78 ± 2.86</td></tr><tr><td>SSIM ↑</td><td>0.751 ± 0.06</td><td>0.727 ± 0.06</td><td>0.853 ± 0.05</td><td>0.847 ± 0.05</td></tr></table>
+
+Table 5. An Ablation study on the update cycle (iterations) of the coil combined image (ccm) and the sensitivity map estimation (csm) models, conducted on the FastMRI knee dataset using 1D Gaussian sampling with  $\mathbf{R} = 8$ .  
+
+<table><tr><td>Parameter (K)</td><td>PSNR ↑</td><td>SSIM ↑</td></tr><tr><td>600 (93.75%)</td><td>32.55 ± 3.36</td><td>0.846 ± 0.06</td></tr><tr><td>400 (62.5%)</td><td>32.57 ± 3.24</td><td>0.853 ± 0.05</td></tr><tr><td>200 (31.25%)</td><td>32.45 ± 2.61</td><td>0.852 ± 0.04</td></tr><tr><td>100 (15.63%)</td><td>31.44 ± 2.55</td><td>0.846 ± 0.04</td></tr></table>
+
+Table 6. Ablation study results on the selection ratio of k-space in the training process for the FastMRI knee dataset using 1D Gaussian sampling with  $\mathbf{R} = 8$ .
+
+on the percentage of k-space data selected based on the sampling direction in each iteration within the AKSM framework, as shown in Table 6. These results show that selecting  $62.5\%$  of k-space data per iteration maximizes PSNR and SSIM, supporting our approach and validating optimal parameter settings for reconstruction.
+
+The Effect of AKSM. Fig. 4 demonstrates the impact of AKSM on training performance in three cases: with AKSM (red), without AKSM (blue), and using coil combined im
+
+age estimation model output (green). This evaluation was conducted on a single slice from the FastMRI knee PD dataset with  $R = 4$ . The case using coil combined image estimation model output showed the lowest performance. The case without AKSM demonstrated rapid initial improvement but unstable convergence. Finally, the case with AKSM achieved the most stable convergence and highest performance. These results highlight the effectiveness of AKSM in MRI reconstruction.
+
+# 5. Conclusion
+
+In this study, we propose a novel zero-shot self-supervised parallel imaging method for MRI reconstruction to reduce scan times and improve image quality without the need for fully-sampled reference data. Our model introduces several key components, including the Attention-guided K-space Selective Mechanism (AKSM), Iteration-wise K-space Masking (IKM) and Sensitivity Map Estimation Model with Cross-Channel constraint. These components collectively enable high-performance MR image reconstruction under high reduction factors by efficiently leveraging our proposed method. Experimental evaluations on FastMRI knee and brain datasets demonstrated that our approach outperforms conventional methods in both image fidelity and computational efficiency.
+
+Limitations and future work. A limitation of our method is that the fixed approach, while ensuring consistency in zero-shot scenarios, may compromise optimal reconstruction quality due to the lack of adaptive stopping criteria. Future work will explore no-reference image quality metrics for developing adaptive stopping criteria, which could enable scan-specific optimization while maintaining the training-data-free advantages.
+
+Acknowledgements. This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2021R1C1C2008773, 2022R1A2C2008983), Artifi
+
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+# AerialMegaDepth: Learning Aerial-Ground Reconstruction and View Synthesis
+
+Khiem Vuong Anurag Ghosh
+
+Deva Ramanan* Srinivasa Narasimhan* Shubham Tulsiani*
+
+Carnegie Mellon University
+
+https://aerial-megadepth.github.io
+
+![](images/b844678bca20c2176095345cd3b35044b57d588653fb90c21725be0dfeabd5cd.jpg)  
+Multi-view Geometry Prediction
+
+![](images/a60bf6054e9323a0c001a5403a2f1ea854b5b76ada7342dd407adf864adf56e0.jpg)  
+view 1
+
+![](images/dffe3d8f725eb043b79533a588f7f3819f47f9fa729d6e6292c6833980c5d4b3.jpg)  
+view 2
+
+![](images/1e8329b8027b2682e52fff00eb37c7e08772bfb0785716ae9650474069187c14.jpg)  
+DUSt3R
+
+![](images/256b198c655046d174a98e03961f8e81a8cbdeafbe8706b3cbc9634e5bfa6df7.jpg)  
+Ours  
+Figure 1. First row: Examples of our generated cross-view (aerial-ground) geometry data, including co-registered pseudo-synthetic (i.e., mesh-rendered) aerial and real ground-level images, with corresponding depth maps, point clouds, and camera intrinsics/extrinsics in a unified coordinate system, for a variety of scenes. Second row: Leveraging such data curated over 137 landmarks and 132K geo-registered images, we show significant improvements in learning-based methods on real unseen ground-aerial scenarios across two representative tasks: 1) multi-view geometry prediction using DUSt3R [64] finetuned on our data, and 2) novel view synthesis from a single image conditioned on a target pose by fine-tuning ZeroNVS [45] that was originally trained on MegaScenes [60].
+
+![](images/edc1f865af724350f354e0fdd7ab1d800053b453f5a7868efbd7625c46fa9afc.jpg)  
+ZeroNVS
+
+![](images/cd54e2b894a57e6bd49c4f692763fac776b798f8f436f2be75a4a193dd59faea.jpg)  
+Novel View Synthesis (input view  $1\to$  synthesize view 2)  
+Ours
+
+# Abstract
+
+We explore the task of geometric reconstruction of images captured from a mixture of ground and aerial views. Current state-of-the-art learning-based approaches fail to han
+
+dle the extreme viewpoint variation between aerial-ground image pairs. Our hypothesis is that the lack of high-quality, co-registered aerial-ground datasets for training is a key reason for this failure. Such data is difficult to assemble precisely because it is difficult to reconstruct in a scalable way. To overcome this challenge, we propose a scalable framework combining pseudo-synthetic renderings from 3D citywide meshes (e.g., Google Earth) with real, ground-level
+
+crowd-sourced images (e.g., MegaDepth [29]). The pseudosynthetic data simulates a wide range of aerial viewpoints, while the real, crowd-sourced images help improve visual fidelity for ground-level images where mesh-based renderings lack sufficient detail, effectively bridging the domain gap between real images and pseudo-synthetic renderings. Using this hybrid dataset, we fine-tune several state-of-the-art algorithms and achieve significant improvements on real-world, zero-shot aerial-ground tasks. For example, we observe that baseline DUSt3R [64] localizes fewer than  $5\%$  of aerial-ground pairs within 5 degrees of camera rotation error, while fine-tuning with our data raises accuracy to nearly  $56\%$ , addressing a major failure point in handling large viewpoint changes. Beyond camera estimation and scene reconstruction, our dataset also improves performance on downstream tasks like novel-view synthesis in challenging aerial-ground scenarios, demonstrating the practical value of our approach in real-world applications.
+
+# 1. Introduction
+
+The ability to register, reconstruct, or generally reason about multi-view images has been a cornerstone task in computer vision. While classical pipelines [50, 51] leveraged hand-designed features [3, 35, 44] and matching mechanisms, their subsequent incarnations [7, 39, 63] have incorporated several learning-based components e.g. learned features [13, 32] or learned "doppelganger" detectors [8]. More recently, approaches have departed from this classical pipeline to directly learn multi-view tasks such as 2D correspondences [33, 46, 58], camera estimation [30, 62, 72], pointmap prediction [26, 64] and novel-view synthesis [34, 45, 60] in an end-to-end manner. This shift towards learning-based components and approaches has led to impressive progress, particularly in challenging scenarios, e.g., sparsely sampled input, or varying illumination.
+
+Much of this progress has been fueled by large crowdsourced image collections like MegaDepth [29], which provides accurate 3D reconstructions built using structure-from-motion (SfM) from thousands of tourist-uploaded images at various landmarks. This 3D data offers valuable supervision for geometric tasks and has been transformative for multi-view learning algorithms. However, because these images are primarily captured by tourists, they mostly cover ground-level viewpoints, and in some cases, aerial viewpoints, but rarely both. As a result, methods like DUSt3R [64] and MASt3R [26], though trained on diverse "in-the-wild" datasets including MegaDepth, struggle with large viewpoint changes between handheld (ground-level) and drone-mounted (aerial) views, as shown in Figure 1. For example, in our evaluation, pre-trained DUSt3R achieves only a  $\sim 5\%$  success rate in registering cameras (under  $5^{\circ}$  rotational error) from ground-aerial pairs.
+
+Our central hypothesis is that this limitation stems from
+
+the lack of training data that contains co-registered ground-aerial image pairs. While independent ground and aerial camera poses are easy to obtain, merging them into a unified coordinate system often requires specialized sensors or manual effort, limiting scalability. To address this, we propose a flexible and scalable data generation framework leveraging geospatial platforms like Google Earth, which render 3D textured meshes of cities and landmarks – providing another vast data source. We refer to these mesh renderings as pseudo-synthetic since they are rendered from 3D meshes of actual landmarks textured with real photos. We construct pseudo-synthetic data by rendering aerial-ground viewpoints at varying altitudes from these textured meshes. While using these images alone show promising improvements, such mesh renderings from ground-level viewpoints are not as photorealistic, with a domain gap due to differences in lighting, texture, and other visual details compared to real images. To mitigate this, we propose to co-register abundantly available real ground images (e.g., from MegaDepth [29]) with the pseudo-synthetic images within the same coordinate frame. The pseudo-synthetic data, captured at varying altitudes, simulates a wide range of aerial viewpoints, while the real, crowd-sourced images help improve visual fidelity, especially for ground-level images where mesh renderings lack details. We call this hybrid dataset AerialMegaDepth, and Figure 1 shows some landmarks from our data, with 132,137 co-registered real and pseudo-synthetic images across 137 scenes.
+
+From this dataset, we generate over 1.5 million aerial-ground image pairs and fine-tune several state-of-the-art reconstruction algorithms, showing significant improvements on real-world mixed-altitude imagery (see Figure 1 for examples). Quantitatively, fine-tuning 3D prediction models like DUSt3R [64] and MAST3R [26] improves the camera registration success rate (with rotation error under  $5^{\circ}$ ) from just  $5\%$  to nearly  $56\%$ . In addition, our dataset also improves novel-view synthesis in challenging aerial-ground scenarios (see Figure 1). Finally, we emphasize that our framework is flexible and scalable, applicable not only to MegaDepth but also to other crowd-sourced datasets [6, 22, 36, 60] and geospatial platforms [9, 12, 24], making it possible to leverage a nearly unlimited source of data to learn aerial-ground 3D reconstruction.
+
+# 2. Related Works
+
+Datasets for Multiview 3D and Geometry. Several datasets released in the last decade have pushed the frontier of multiview 3D geometry. Internet-sourced datasets of landmarks like MegaDepth [29] and IMC-PT [23] mostly have ground-level views. But still, these datasets, whose ground-truth was built using SfM [50], have spurred monocular depth estimation [5, 68], multiview stereo [26, 64], learned feature matching [19, 46, 58, 76], learned pose
+
+![](images/4c1056385b3a53f93b7064f745d5e0f26521bca044ed51cc6c4ee640913419e4.jpg)  
+Example of cross-view (ground-aerial) geometric supervision data
+
+![](images/af7c5d3af6cca25a821af252d714e6719141f55719017007e9ecfb1bf2ad164d.jpg)
+
+![](images/c9b218f9de0ebdbe85fca29dc73c63696f2e284a230e3b99c01fd08c565d44f2.jpg)  
+Images with depth maps
+
+![](images/e03008c6d9c680313b142f13570e0e6d87be1add2106f1c795316502f9edd71e.jpg)  
+ground: real, aerial: pseudo-synthetic)  
+Aligned point clouds and cameras
+
+![](images/e13126283d9aa3108c0f2950a3332429d9480cdd900f8ed95d0dbec643f1af4a.jpg)  
+Sample 2D correspondences  
+Figure 2. Overview of the data generation framework. To address the challenges of ground-aerial camera registration and novel-view synthesis, we propose a flexible framework combining pseudo-synthetic renderings from 3D city-wide meshes (e.g. Google Earth) with real, ground-level images (e.g. MegaDepth [29]). The pseudo-synthetic data is captured at varying altitudes, while the real, crowd-sourced images help improve visual fidelity especially for ground-level images where mesh-based renderings lack detail. The pipeline generates pseudo-synthetic images from different altitudes, co-registers them with real images, and aligns ground-level images with aerial data for 3D reconstruction. This hybrid dataset of real and pseudo-synthetic images provides geometric supervision that helps improve performance on downstream tasks such as ground-aerial camera registration and novel view synthesis, particularly in ground-aerial settings.
+
+regression [62, 63, 72], etc. Datasets like BlendedMVS [69] generate training images by blending rendered images from textured 3D mesh with input real images. However, scenes in these datasets are solely captured from drones or ground, and not both simultaneously. This is because capturing data with drastic viewpoint changes is challenging and requires specialized sensors or manual effort. Instead, our pseudo-synthetic data, paired with real ground images, anchors scenes with simultaneous aerial and ground views.
+
+Datasets with 3D city meshes [12, 24] have also been proposed. In contrast, our dataset contains both real and pseudo-synthetic data of the same landmarks in a unified coordinate system. While purely synthetic data [14, 28, 42, 52, 74] have been used for various 3D learning tasks, these datasets are not anchored to real scenes, making it difficult to bridge the sim-to-real gap. Methods using 3D meshes with image queries have been explored for other tasks like visual place recognition [4, 61] and localization [40, 41].
+
+Learning for Multiview 3D. Driven by large-scale supervision, learning-based methods have resulted in more robust feature matching [10, 17-19, 33, 46, 58], pose estimation [62, 64, 71, 72] and direct regression of 3D pointmaps in a unified coordinate frame [26, 64]. Likewise, generating novel views from an input view conditioned on camera poses [34, 45, 56, 77] is enabled by large datasets like MegaScenes [60]. However, these methods struggle
+
+with extreme ground-aerial viewpoints due to limited supervision data. We show that our hybrid real and pseudosynthetic data significantly improves performance of such learning-based methods on real mixed-altitude imagery.
+
+Aerial-ground Registration. Prior work has addressed aerial-ground registration using specialized classical and learning-based methods [27, 31, 53, 78]. Our work is orthogonal, as we propose a hybrid dataset to potentially improve these methods among other tasks. In the same vein, very few co-registered ground-aerial datasets exist. MAVREC [16] and University1652 [75] provides no depth or pose information, and GrAco [79] has only monochrome imagery and is small-scale. We also distinguish our work from satellite-ground localization [20, 48, 54, 55, 66] as satellite viewpoint is orthographic and distant while viewpoints in our data are closer to a drone-view sharing common (albeit small) field-of-view with the ground-view.
+
+# 3. Generating Aerial-Ground 3D Data
+
+To address the scarcity of aerial-ground 3D data, we introduce an approach that combines renderings from 3D city-wide mesh models with real crowd-sourced images. The 3D meshes generate pseudo-synthetic renderings across varied altitudes and orientations, particularly aerial viewpoints, while real images complement this with ground-level cap
+
+tures, where pseudo-synthetic renderings often lack visual fidelity. An overview of our framework is in Figure 2.
+
+# 3.1. Pseudo-synthetic data generation
+
+We chose Google Earth as our primary data source for its quality and landmark coverage, allowing us to render images from any viewpoint. Our framework, however, is compatible with any geo-referenced 3D textured meshes [4, 9, 41]. These images are termed pseudo-synthetic as they are renderings of 3D meshes textured with real photos.
+
+Automatically generating query viewpoints. Our goal is to render images that have sufficient visual overlap, both with each other and with the real images from MegaDepth [29]. We start with scenes from MegaDepth which contains SfM reconstructions for 196 landmarks, each with thousands of internet-sourced images. While the EXIF GPS tags in these images are not precise enough for accurate co-registration or alignment, we use them to roughly sample Google Earth's rendering viewpoints, ensuring they correspond to the same building or landmark. This is achieved by geo-referencing the local 3D reconstruction into the global ECEF frame using a similarity transform computed from the noisy GPS data. To ensure co-visibility among rendered images, we sample 200 points from the geo-referenced point cloud to serve as look-at targets for generating query viewpoints. This ensures that our rendered pseudo-synthetic images maintain sufficient visual overlap with each other and also with MegaDepth's real images.
+
+Generating pseudo-synthetic 3D reconstruction. While users can specify and render images from any location and orientation, Google Earth unfortunately does not provide direct access to the underlying 3D mesh. Therefore, to recover scene geometry from the rendered pseudosynthetic images (for which camera extrinsics and intrinsicities are known), we extract keypoints [13] and match features [33] between the pseudo-synthetic rendered images to triangulate the 3D point cloud. With this process, we generated data from 137 sites or landmarks, each with 600 images taken from varying elevations, ranging from 1 meter to 350 meters, resulting in a total of 82,220 pseudo-synthetic images. We refer to this as pseudo-synthetic reconstruction.
+
+# 3.2. Co-registering real crowd-sourced images
+
+While pseudo-synthetic images from 3D textured meshes can directly improve geometry prediction tasks - as demonstrated in Section 5 - we make two key observations that help further improve the downstream performance. First, since these meshes are typically textured from aerial images, they tend to appear realistic from elevated, drone-like viewpoints but often lack visual fidelity at ground level, where low-viewing angles introduce artifacts on building facades [41]. A domain gap also exists between ground-level pseudo-synthetic and real images, such as the absence
+
+![](images/c9294f1cfbdbf007bfaf198ddd5e66c0df675e31b604ad8b567ce6e5e971f545.jpg)
+
+![](images/721d0618edc937a2de34788ebcfab48583c7887e171ff645b0a8634e19b05c8b.jpg)  
+Pseudo-synthetic image (from Google Earth)
+
+![](images/bc66e3e6371b8fc4fff5149ace247c20f2d630a5fb3ee8e900929beba05ab6a2.jpg)
+
+![](images/8f6bf8c69b4f7d2573fa989d17a8037d10bc511f6fc408756e575283f4aba92d.jpg)  
+Real image (from MegaDepth)  
+Figure 3. Feature matching between real and pseudo-synthetic images. The pseudo-synthetic rendering has a noticeable domain gap compared to the real MegaDepth image (e.g., no transients, simplistic lighting) but still enables reliable feature matching [46] to register real images into the pseudo-synthetic reconstruction.
+
+of transients and simplistic lighting model, which may limit generalization to real-world data. Second, despite these limitations, mesh-based visual localization methods [41] show that real images can still be registered accurately to pseudo-synthetic reconstructions with state-of-the-art feature matching [33, 46, 58] as shown in Figure 3. To combine the benefits of both real and pseudo-synthetic images, we thus register real, ground-level images into the pseudosynthetic reconstructions, resulting in aligned real (ground) MegaDepth and pseudo-synthetic (aerial) images.
+
+Specifically, we follow standard visual localization pipeline [47] by first retrieving top- $k$  most similar pseudosynthetic images for each real MegaDepth query image [2]. 2D correspondences [13, 33] are lifted to 2D-3D matches using the pseudo-synthetic 3D points, and each query image's 6-DoF pose is estimated with a RANSAC-based PnP solver [25]. We refine the alignment by optimizing the localized MegaDepth images while keeping pseudo-synthetic cameras fixed. Using COLMAP's MVS [51], we generate semi-dense depth maps for supervision. In total, we register 49,937 MegaDepth images with 82,200 pseudo-synthetic images across 137 scenes, forming AerialMegaDepth - a hybrid dataset of 132,137 images with diverse viewpoints and lighting variations, as shown in Figure 4.
+
+# 4. Learning Aerial-Ground 3D Reconstruction
+
+We explore our data's impact on supervised learning for multi-view 3D reconstruction and novel view synthesis.
+
+Selection of image pairs as supervision data. Our objective is to select image pairs that offer adequate overlap for effective supervision, particularly for ground-to-aerial pairs with altitude differences, ensuring the overlap is neither too high (making the task too easy) nor too low (making it too difficult). To achieve this, we compute an  $N \times N$  covisibility matrix  $\mathcal{C}$  for each scene, where each element
+
+![](images/e51b3e017783c9ba50040c59ec15260ec4959cdc36935d8788931dad31703c6e.jpg)  
+Figure 4. AerialMegaDepth data (top: MegaDepth, bottom: Google Earth) features diverse viewpoints & lighting conditions.
+
+$\mathcal{C}[i,j] \in [0,1]$  represents the percentage of points in image  $i$  that are visible in image  $j$ . For ground-to-aerial settings, we prioritize pairs with significant viewpoint differences, meaning the可视ability is asymmetrical: we select pairs  $(i,j)$  such that  $\mathcal{C}[i,j]$  is small and  $\mathcal{C}[j,i]$  is large, or vice-versa. We quantify this difference with a score  $s = \frac{\mathrm{AM}}{\mathrm{HM}}$ , where AM is the arithmetic mean and HM is the harmonic mean of  $\mathcal{C}[i,j]$  and  $\mathcal{C}[j,i]$ . A high score indicates pairs with a large viewpoint difference, ideal for challenging cross-view tasks, aligning with our goal of prioritizing ground-to-aerial pairs. Using this approach, we generate a varying-altitude dataset of 1.5M image pairs, each comes with camera intrinsics, camera poses, and depthmaps to be used as supervision for learning geometric tasks.
+
+Multi-view Pose and Geometry Estimation. We consider the problem of estimating intrinsic, extrinsic camera parameters, and 3D scene from a set of  $N$  unconstrained images. Following the architecture of DUSt3R [64], we regress pointmaps for image pairs, where each pixel is associated with a 3D point in the coordinate system of the first frame. This allows us to compute the per-camera focal length (under a pinhole model with centered principal point) and the 6-DoF relative pose  $\mathbf{T} = [\mathbf{R}|t]$  for each image pair using PnP [25]. For  $N > 2$  images, DUSt3R's global alignment (GA) step combines pointmaps across all images, optimizing a dense pairwise graph in 3D to align pointmaps within a global coordinate frame. We initialize with a DUSt3R checkpoint trained on millions of image pairs from eight datasets [11, 29, 37, 43, 49, 59, 69, 70] and fine-tune on our data, resulting in substantial improvements for ground-aerial camera registration. We also observe similar improvements by fine-tuning MAST3R [26] and using it as a front-end to provide 2D-2D correspondences, which are then fed into COLMAP for bundle adjustment (similar to the approach in MAST3R-SfM [15]).
+
+Novel View Synthesis. For single-image novel view synthesis (NVS), our goal is to synthesize a plausible target ground view from a reference aerial image. Tung et al. [60] fine-tuned ZeroNVS [45] on MegaScenes with over 2M image pairs from 32K scenes, achieving significant improvements on scene-level view synthesis compared to object-
+
+centric settings [1, 43]. By further fine-tuning ZeroNVS on our dataset with varying altitudes, we achieve significant improvements in aerial-to-ground view synthesis.
+
+# 5. Experiments
+
+# 5.1. Multiview Pose Estimation and Reconstruction
+
+Datasets. We fine-tune the baseline models [26, 64] on our data using pairwise 3D pointmaps as supervision. For evaluation, we focus on ground-aerial settings and include data from ULTRRA Challenge [67], which consists of images captured by ground-level cameras and drones, all calibrated using SfM constrained by RTK-corrected GPS coordinates for cm-level accuracy. Additionally, we use data from ACC-NVS1 [57] which captures various urban sites with ground-truth poses obtained via GNSS/IMU systems corrected by a stationary RTK base station. Overall, the evaluation data includes six sites with over 5,000 calibrated ground-aerial images.
+
+Evaluation Metrics. Following [23, 62], we evaluate camera pose using Relative Rotation Accuracy (RRA) and Relative Translation Accuracy (RTA). RRA measures the angular difference between the predicted and ground-truth relative rotations, and RTA calculates the angular difference between the predicted and ground-truth translation vectors. We report  $\mathrm{RTA}@\tau / \mathrm{RRA}@\tau$ , i.e., the percentage of camera pairs with RTA/RRA below a threshold  $\tau$ . We also evaluate reconstruction accuracy by aligning the predicted pointmap from DUSt3R with ground-truth from MVS [51] using a RANSAC-based optimal similarity transform. We report  $\delta @$ $[0.5\mathrm{m}, 1\mathrm{m}, 2\mathrm{m}]$ , representing the percentage of points with errors within  $0.5\mathrm{m}$ ,  $1\mathrm{m}$ , and  $2\mathrm{m}$ , respectively.
+
+Two-view pose and geometry estimation. We evaluate the impact of our data on ground-aerial registration in the two-view case (one aerial and one ground image). For DUSt3R [64], relative pose is computed from the predicted 2D-3D matches using PnP [25]. We also present baselines of 2D correspondence matching with SuperPoint [13] + SuperGlue [46]  $(\mathrm{SP} + \mathrm{SG})$ , semi-dense matching with LoFTR [58], and MASt3R [26], where for MASt3R, 2D correspondences are extracted via reciprocal nearest neighbor from its dense local feature maps. For these methods, we compute relative pose assuming known ground-truth intrinsics, using essential matrix estimated from 2D matches.
+
+Table 1 shows that all baseline methods, including SP+SG, LoFTR, DUSt3R and MASt3R, struggle with ground-aerial pairs. For example, baseline DUSt3R only recovers  $5.20\%$  of the total number of image pairs with good accuracy (RRA@5°). While fine-tuning on synthetic data like MatrixCity [28] notably improves baseline methods, fine-tuning on pseudo-synthetic renderings (with more realistic textures, containing varying-altitude mesh renderings from Google Earth, denoted as DUSt3R/MASt3R +
+
+![](images/5474d6bd0aea5e17b0605cc820b69faf6bf06423ef631d48f88ff4602df10195.jpg)  
+Figure 5. Zero-shot ground-aerial camera and geometry prediction results. Given two input images, one aerial and one ground, we compare the performance of the baseline DUSt3R [64] with the model fine-tuned on our varying-altitude data. The results demonstrate significant improvements over the baseline in unseen, challenging ground-aerial scenarios, showing the effectiveness of fine-tuning DUSt3R [64] with our data. Additionally, the last column presents qualitative results on a challenging ground-aerial pair from the WxBS [38] dataset, which involves significant viewpoint change.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Camera Rotation Accuracy</td><td colspan="3">Camera Translation Accuracy</td><td colspan="3">3D Pointmap Accuracy</td></tr><tr><td>RRA@5°</td><td>RRA@10°</td><td>RRA@15°</td><td>RTA@5°</td><td>RTA@10°</td><td>RTA@15°</td><td>δ@0.5m</td><td>δ@1m</td><td>δ@2m</td></tr><tr><td>LoFTR [58]</td><td>0.92</td><td>1.83</td><td>2.45</td><td>0.92</td><td>1.53</td><td>2.14</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SP+SG [46]</td><td>8.56</td><td>10.09</td><td>12.23</td><td>7.65</td><td>9.79</td><td>11.31</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MASt3R [26] (released)</td><td>3.36</td><td>3.36</td><td>4.59</td><td>2.45</td><td>3.36</td><td>4.28</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MASt3R + MatrixCity</td><td>19.78</td><td>30.88</td><td>38.17</td><td>10.67</td><td>25.72</td><td>29.43</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MASt3R + PSynth (Ours)</td><td>26.49</td><td>43.71</td><td>47.62</td><td>25.25</td><td>40.32</td><td>49.34</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MASt3R + Hybrid (Ours)</td><td>49.54</td><td>66.36</td><td>72.48</td><td>42.51</td><td>63.30</td><td>69.11</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DUSt3R [64] (released)</td><td>5.20</td><td>7.95</td><td>9.48</td><td>2.75</td><td>5.81</td><td>9.17</td><td>29.02</td><td>42.16</td><td>43.79</td></tr><tr><td>DUSt3R + MatrixCity</td><td>17.85</td><td>37.28</td><td>42.80</td><td>11.33</td><td>25.24</td><td>33.24</td><td>31.43</td><td>47.13</td><td>57.02</td></tr><tr><td>DUSt3R + PSynth (Ours)</td><td>31.28</td><td>47.63</td><td>51.61</td><td>28.78</td><td>45.66</td><td>51.47</td><td>32.77</td><td>53.42</td><td>61.45</td></tr><tr><td>DUSt3R + Hybrid (Ours)</td><td>55.96</td><td>71.25</td><td>76.15</td><td>46.48</td><td>68.20</td><td>72.78</td><td>38.24</td><td>62.33</td><td>74.52</td></tr></table>
+
+Table 1. Finetuning with our data significantly improves pairwise camera pose estimation in the ground-aerial setting. Baselines, including learned 2D correspondence matching (SP+SG [13, 46], LoFTR [58], MAST3R [26]) and 3D pointmap-based regression (DUSt3R [64]), struggle in this setting. For instance, DUSt3R localizes fewer than  $5\%$  of pairs within  $5^{\circ}$  rotation error (RRA@ $5^{\circ}$ ). Finetuning on MatrixCity improves performance, but using pseudo-synthetic ground-aerial pairs (DUSt3R + PSynth) boosts accuracy to  $31\%$ , and adding real ground data (DUSt3R + Hybrid) further increases it to  $55\%$ . This also significantly improves 3D pointmap accuracy. The first half of the table shows methods that predict 2D matches, with ground-truth intrinsics used to compute the relative poses.
+
+![](images/888da54dc52ef6a81a9ab7fdca909cf64e1dbf292f0adc5e908c2bf29f985236.jpg)  
+Figure 6. Challenging ground-aerial feature matching. Finetuned MASt3R [26] achieves accurate and robust feature matching across ground-aerial pairs with extreme viewpoint changes (correspondences extracted via reciprocal nearest neighbor from MASt3R's local feature maps). This highlights the effectiveness of our AerialMegaDepth data in improving matching performance.
+
+PSynth) is more effective, increasing accuracy to  $31.28\%$  at RRA@5°. But the largest improvement comes from training on hybrid data (that aligns pseudo-synthetic mesh
+
+renderings to real-world images for pair construction), denoted as DUSt3R/MASt3R + Hybrid, bringing the performance to more than  $55\%$ . This demonstrates that our novel framework of hybrid real and pseudo-synthetic data significantly improves ground-aerial camera registration. We note that while our primary evaluation focuses on the ground-aerial setting, additional results in the Supplementary show that DUSt3R and MASt3R still perform well on similar-viewpoint pairs (e.g., ground-ground and aerial-aerial) even after fine-tuning with our varying-altitude data.
+
+In addition to pose accuracy, we also observe substantial improvements in 3D geometry prediction, particularly in 3D pointmap accuracy from DUSt3R. As shown in Table 1, finetuning on our combined dataset (DUSt3R + Hybrid) improves the percentage of 3D points within a 1-meter error by  $20\%$  compared to the baseline DUSt3R. Since we align
+
+![](images/c7f0b7763859ccdc106d47580c8bf4b887d23190794248e06c65bed1ec527335.jpg)  
+Figure 7. 3D reconstruction from one aerial and four ground images with virtually no overlap. We use the global alignment process of DUSt3R [64] to merge pointmaps predictions. Despite the lack of overlap among the ground images, we find that incorporating a reference aerial image can effectively serve as a "map", significantly improving pose estimation accuracy when fine-tuned on our cross-view data.
+
+![](images/a946e1d3abc88ce95adab1ac83bed7dbf090cce9acb4eca2e2e76f0f7f28fb1a.jpg)
+
+![](images/38f9e94ebd6a66666dbb174d7fa265adb6d6216b3fe62e9a259aab3652806e4b.jpg)
+
+<table><tr><td># of ground images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>no aerial image (i.e., ground only)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DUSt3R-GA (released)</td><td>12.20</td><td>32.21</td><td>38.31</td><td>43.98</td><td>47.98</td></tr><tr><td>one aerial image</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DUSt3R-GA (released)</td><td>14.63</td><td>33.02</td><td>37.50</td><td>43.73</td><td>48.47</td></tr><tr><td>DUSt3R-GA + PSynth (Ours)</td><td>29.27</td><td>44.72</td><td>48.78</td><td>55.85</td><td>55.45</td></tr><tr><td>DUSt3R-GA + Hybrid (Ours)</td><td>56.10</td><td>55.28</td><td>57.72</td><td>59.27</td><td>60.65</td></tr><tr><td>MASt3R-SfM (released)</td><td>9.03</td><td>31.69</td><td>40.02</td><td>49.88</td><td>59.34</td></tr><tr><td>MASt3R-SfM + Psynth (Ours)</td><td>23.10</td><td>39.53</td><td>48.12</td><td>59.13</td><td>64.76</td></tr><tr><td>MASt3R-SfM + Hybrid (Ours)</td><td>51.07</td><td>52.21</td><td>61.31</td><td>63.92</td><td>67.45</td></tr></table>
+
+<table><tr><td># of ground images</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>no aerial image (i.e., ground only)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DUSt3R-GA (released)</td><td>9.76</td><td>27.96</td><td>31.40</td><td>40.80</td><td>43.13</td></tr><tr><td>one aerial image</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DUSt3R-GA (released)</td><td>9.76</td><td>27.15</td><td>31.40</td><td>41.78</td><td>43.62</td></tr><tr><td>DUSt3R-GA + PSynth (Ours)</td><td>31.27</td><td>43.09</td><td>46.82</td><td>55.72</td><td>56.10</td></tr><tr><td>DUSt3R-GA + Hybrid (Ours)</td><td>51.29</td><td>52.85</td><td>54.07</td><td>55.61</td><td>57.72</td></tr><tr><td>MASt3R-SfM (released)</td><td>9.28</td><td>23.91</td><td>29.01</td><td>46.91</td><td>51.45</td></tr><tr><td>MASt3R-SfM + Psynth (Ours)</td><td>25.80</td><td>41.09</td><td>44.52</td><td>58.79</td><td>61.22</td></tr><tr><td>MASt3R-SfM + Hybrid (Ours)</td><td>48.84</td><td>49.71</td><td>57.89</td><td>60.98</td><td>62.41</td></tr></table>
+
+Table 2. Including a single aerial image with  $N$  ground images notably improves pose estimation of the ground images, as shown in Ground Cameras Rotation Accuracy @  $15^{\circ}$  (RRA@15°) (left) and Translation Accuracy @  $15^{\circ}$  (RTA@15°) (right). Using DUSt3R's global optimization [64], Row 1 shows results for ground-only input images, while the rest includes an aerial image as input. Although pose estimation improves with more ground images, adding even one aerial reference image significantly boosts accuracy, especially when ground images have minimal overlap (e.g.,  $N \leq 3$ ) as this aerial view helps align the ground images within a shared coordinate frame.
+
+predicted and ground-truth pointmaps using a RANSAC-based similarity transform, baseline DUSt3R model could still achieve reasonable geometry accuracy by producing good depth estimates for at least one of the views, even if they struggle to register them together accurately (as shown in pose accuracy). By finetuning on our data, we see substantial improvements in both 3D pointmap accuracy and ground-aerial pose registration, highlighting the impact on both pose and geometry prediction. We show qualitative results in Fig. 5 and Fig. 6 and encourage readers to check the website for additional results. We emphasize that this is zero-shot performance on unseen data, as there is no overlap between our training and evaluation scenes.
+
+Co-registering ground images with aerial context. We evaluate multi-view ground-aerial camera registration, where one aerial image is matched with  $N$  ground im
+
+ages. To perform multiview pose estimation, we explore two approaches: 1) the global alignment (GA) process of DUSt3R [64] to merge all predicted pairwise pointmaps in the same coordinate frame, and 2) the MASt3R-SfM [15] approach, which uses MASt3R as a front-end to extract 2D correspondences followed by COLMAP [50] bundle adjustment. In Table 2, we report accuracy for ground images only. Perhaps unsurprisingly, when ground images are sparse ( $N \leq 3$ ), they often lack visual overlap, making pose estimation particularly challenging. In this case, we observe a significant improvement in performance (from  $14.63\%$  to  $56.10\%$  for RRA@ $15^{\circ}$  with  $N = 2$ ) when using the model finetuned with our data. The key reason for this improvement is, even with almost no overlap among ground images, a single aerial image can serve as an "overhead map", helping to "stitch" or align the ground images into a common
+
+![](images/551809f5169ea3cc71c909452425285b57f4e70ae59fb9459a62457458af53ba.jpg)
+
+![](images/5baf7de324db8b1bd38283c336893d4dbda81dacfef9222bdaf5e159c064d275.jpg)
+
+![](images/f545fd7bc7c82a6bf9d6cc9564a6255e66eb569437c684ad3a196175af97dc8d.jpg)  
+Figure 8. Results of extreme viewpoint change in novel-view synthesis with ZeroNVS [45] finetuned on MegaScenes [60] (ZeroNVS MS) & additionally finetuned on our data. Though by no means perfect, note the big improvement in visual quality and viewpoint accuracy.
+
+![](images/0a6f6d6189727e485f2bccc70bdc865693321f05d945f274d7a05c4ab5d6d85e.jpg)
+
+![](images/9a65fd86a40d7a1da5208d1146348687d2c144974c981b3efdf4641bdc47cda0.jpg)
+
+![](images/e1c7d042186a69428bc450db48393883dd3d606a5feef3fbf296101c8bd84f5d.jpg)
+
+![](images/4fd1a88f06ca901b0574c6b72b784160a7873336fb3015f0f691fada285ec09d.jpg)
+
+![](images/1b3b95ac3abc9f30e2725de7c0733584e26829afe667e5f629f543363ef874d6.jpg)
+
+<table><tr><td colspan="5">NVSSdreamSim ↓LPIPS ↓PSNR ↑SSIM ↑</td></tr><tr><td colspan="5">pseudo-synth. images</td></tr><tr><td>ZeroNVS (MS)</td><td>0.448</td><td>0.413</td><td>10.847</td><td>0.416</td></tr><tr><td>ZeroNVS (Ours)</td><td>0.377</td><td>0.359</td><td>12.381</td><td>0.484</td></tr><tr><td colspan="5">real images</td></tr><tr><td>ZeroNVS (MS)</td><td>0.550</td><td>0.639</td><td>7.478</td><td>0.183</td></tr><tr><td>ZeroNVS (Ours)</td><td>0.442</td><td>0.580</td><td>8.220</td><td>0.218</td></tr></table>
+
+Table 3. Quantitative results for aerial-ground novel-view synthesis comparing ZeroNVS model finetuned on MegaScenes (MS) and our data (Ours), with finetuning improves all metrics.
+
+frame. An example is shown in Figure 7 demonstrating the effectiveness of our approach in this scenario.
+
+# 5.2. Novel View Synthesis
+
+Datasets. We focus on the challenging aerial-to-ground synthesis task. We combine our dataset with MegaScenes [60], using a 3:1 ratio during finetuning to help prevent overfitting. For evaluation, we use both real-world aerial-ground pairs as well as pseudo-synthetic data from Google Earth that includes a wide range of images captured at varying altitudes, allowing us to assess the model's ability to synthesize views across diverse ground-aerial setups.
+
+Finetuning details. We follow ZeroNVS [45] for novel view synthesis, which takes the extrinsic matrix and field-of-view as inputs to generate novel views at the target pose. The translation vector is scaled based on the 20th depth quantile of the reference image (during evaluation we used MVS depth). Starting from ZeroNVS trained on MegaScenes, we fine-tune the model on our dataset, significantly improving novel views in ground-aerial contexts.
+
+Evaluation Metrics. We evaluate view synthesis quality using standard image reconstruction metrics, including LPIPS [73], PSNR, and SSIM [65]. Additionally, we also include the DreamSim [21] score, which aligns more closely with human perceptual judgments.
+
+Results and Discussions. Table 3 presents significant quan
+
+titative improvements for single image aerial-to-ground novel-view synthesis. From the qualitative results in Figure 8, we see that ZeroNVS (Ours), produces realistic and accurate images that follow the desired poses. In contrast, ZeroNVS (MS), which was finetuned solely on MegaScenes, struggles with such views, highlighting once again the effectiveness of incorporating ground-aerial data into the training process. We emphasize that this is still a very challenging task, as the viewpoint difference between the reference and target pose is large. The network must learn to retain the underlying scene structure while generating plausible images for unseen parts of the scene and/or demonstrate correct occlusions. Our results show that the model somewhat successfully addresses this challenge, but much research remains to be done in this task.
+
+# 6. Conclusion
+
+Despite notable advances in learning-based 3D reconstruction, large-area reconstruction from a sparse mix of drone and ground imagery remains a challenge. As shown over the last decade, adding significant data where little existed before improves the performance of supervised-learning-based networks. The key innovation in our work comes from understanding how geospatial platforms and crowdsourced imagery can be combined to provide a potentially unlimited amount of data for training large aerial-ground 3D models. Carefully finetuning existing 3D models with our data showed nearly  $15 \times$  improvement in camera estimation and registration, which is at the heart of the largescale reconstruction problem. We hope our hybrid data framework will help spur further research in the area.
+
+In the future, aerial drone views could serve as a bridge between ground and satellite views, where abundant data is widely available. Combining them all could bring us closer to the ambitious goal of planet-scale 3D reconstruction.
+
+Acknowledgements: This work was supported by Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.
+
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\ No newline at end of file
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+# AeroGen: Enhancing Remote Sensing Object Detection with Diffusion-Driven Data Generation
+
+Datao Tang $^{1,2}$  Xiangyong Cao $^{1,2*}$  Xuan Wu $^{1,2}$  Jialin Li $^{1,2}$  Jing Yao $^{5}$  Xueru Bai $^{6}$  Dongsheng Jiang $^{7}$  Yin Li $^{7}$  Deyu Meng $^{2,3,4}$
+
+$^{1}$  School of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049, China
+
+<sup>2</sup> Ministry of Education Key Laboratory of Intelligent Networks and Network Security, Xi'an Jiaotong University, Xi'an, 710049, China
+
+$^{3}$  School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China
+
+$^{4}$  Pengcheng Laboratory  $^{5}$  Chinese Academy of Sciences
+
+$^{6}$  Xidian University  $^{7}$  Huawei Technologies Ltd
+
+![](images/1ea76c88e0151157b1ce05373c63ec8c6cf0917d7327fc1e9a848578bd4690ca.jpg)  
+DIOR
+
+![](images/0e87facfef951c3845640a3aa8fff1052832fb78168c0af3e8543092a9a9294b.jpg)  
+DIOR-R  
+Figure 1. Generated images with our proposed AeroGen. AeroGen enables the input of both horizontal and rotated bounding box layout conditions, facilitating accurate remote sensing image layout generation.
+
+![](images/725975d85b2373f9d1125e4e3ed1aaf11ff3e85fef1d61be6b0b4fbea2041781.jpg)  
+HRSC
+
+# Abstract
+
+Remote sensing image object detection (RSIOD) aims to identify and locate specific objects within satellite or aerial imagery. However, there is a scarcity of labeled data in current RSIOD datasets, which significantly limits the performance of current detection algorithms. Although existing techniques, e.g., data augmentation and semi-supervised learning, can mitigate this scarcity issue to some extent, they are heavily dependent on high-quality labeled data and perform worse in rare object classes. To address this issue, this paper proposes a layout-controllable diffusion generative model (i.e. AeroGen) tailored for RSIOD. To our knowledge, AeroGen is the first model to simultaneously support horizontal and rotated bounding box condition generation, thus enabling the generation of high-
+
+quality synthetic images that meet specific layout and object category requirements. Additionally, we propose an end-to-end data augmentation framework that integrates a diversity-conditioned generator and a filtering mechanism to enhance both the diversity and quality of generated data. Experimental results demonstrate that the synthetic data produced by our method are of high quality and diversity. Furthermore, the synthetic RSIOD data can significantly improve the detection performance of existing RSIOD models, i.e., the mAP metrics on DIOR, DIOR-R, and HRSC datasets are improved by  $3.7\%$ ,  $4.3\%$ , and  $2.43\%$ , respectively. The code is available at here.
+
+# 1. Introduction
+
+Object detection is a key technology for understanding and analyzing remote sensing images. It enables efficient pro
+
+cessing of large-scale satellite data to extract and identify critical information, such as land cover changes [42], urban development status [16], and the impacts of natural disasters [45]. Through object detection, researchers can automatically extract terrestrial targets from complex remote sensing images, including buildings, vehicles, roads, bridges, farmlands, and forests. This information can be further applied in environmental monitoring, urban planning, land use analysis, and disaster emergency management.
+
+With the rapid development of deep learning, supervised learning-based object detection algorithms have made significant progress in remote sensing image analysis [49]. Although these algorithms can accurately locate and classify multiple objects in remote sensing images, they are heavily dependent on a large number of labelled training data. However, obtaining sufficient annotated data for remote sensing images is particularly challenging. Due to the presence of numerous and complex targets in remote sensing images, the manual annotation process is not only time-consuming and labour-intensive but also requires annotators to possess specialized knowledge, thus leading to high costs.
+
+Although traditional data augmentation methods [4] (e.g., rotation and scaling) and enhancement techniques suitable for object detection (e.g., image mirror [15], object-centric cropping [21], and copy-paste [7]) can increase data diversity to some extent, they do not address the fundamental issue of insufficient data. The emergence of generative models [11, 25] provides a new solution to this problem. Currently, in the field of natural images, numerous high-performance generative models [27, 31] have been developed, capable of generating high-quality images from text conditions and also achieving significant progress in layout control. For remote sensing images, the application of generative models is usually combined with specific tasks, such as change detection [46], semantic segmentation [34] and road extraction [33]. These studies have been highly successful in utilizing data obtained from generative models to augment real-world datasets, thereby enhancing the performance of target models in downstream tasks. Therefore, utilizing generative diffusion models to fit the distribution of existing datasets and generate new samples to enhance the diversity and richness of remote sensing datasets is a feasible solution.
+
+In this paper, we focus on the remote sensing image object detection (RSIOD) task and construct a layout generation model (i.e., AeroGen) specifically designed for this task. The proposed AeroGen model allows for the specification of layout prior conditions with horizontal and rotated bounding boxes, enabling the generation of high-quality remote sensing images that meet specified conditions, thus filling a gap in the research field of RSIOD. Based on the AeroGen model, we further propose a conditional generation-based end-to-end data augmentation framework.
+
+Unlike pipeline-style data augmentation schemes in the natural image domain [43], our proposed pipeline is implemented by directly synthesizing RSIOD data through conditional generative models, thus eliminating the need for additional instance-pasting procedures. By introducing a diversity-conditioned generator and generation quality evaluation, we further enhance the diversity and quality of the generated images, thereby achieving end-to-end data augmentation for downstream object detection tasks. Moreover, we also design a novel filtering mechanism in this data augmentation pipeline to select high-quality synthetic training images, thus further boosting the performance.
+
+In summary, the contributions of our work are threefold:
+
+- We propose a layout-controllable diffusion model (i.e., AeroGen) specifically designed for remote sensing images. This model can generate high-quality RSIOD training datasets that conform to specified categories and spatial positions. To our knowledge, AeroGen is the first generative model to support layout conditional control for both horizontal and rotated bounding boxes.  
+- We design a novel end-to-end data augmentation framework that integrates the proposed AeroGen generative model with a layout condition generator as well as an image filter. This framework can produce synthetic RSIOD training datasets with high diversity and quality.  
+- Experimental results show that the synthetic data can improve the performance of current RSIOD models, with improvements in mAP metrics by  $3.7\%$ ,  $4.3\%$ , and  $2.43\%$  on the DIOR, DIOR-R, and HRSC datasets, respectively. Notably, the performance in some rare object classes also significantly improves, e.g., achieving improvements of  $17.8\%$ ,  $14.7\%$ , and  $12.6\%$  in the GF, DAM, and APO categories, respectively.
+
+# 2. Related Work
+
+# 2.1. Diffusion Models
+
+Diffusion models [11, 25, 31], renowned for their stable training and superior generative quality, are increasingly supplanting Generative Adversarial Networks (GANs) [30, 40] in generative tasks. While text-guided diffusion models excel at producing realistic images, their reliance on brief text prompts often limits precise control over spatial composition and personalized generation. To overcome this, researchers have integrated diverse control mechanisms, expanding applications to layout-guided generation [17, 36, 39, 44, 47], style transfer [6, 37], image restoration [5], and video synthesis [12]. For layout-to-image tasks, methods like ReCo [39] enforce object relational constraints via cross-attention modulation, LayoutDiffusion [44] injects bounding box coordinates through adaptive layer normalization, and GLIGEN [17] employs gated self-attention to dynamically align layouts with text semantics. MIGC
+
+[47] further enhances compositional accuracy by decoupling object- and scene-level denoising. Built on the efficient latent diffusion framework (LDM) [31], these approaches demonstrate how diffusion models balance fine-grained control with computational efficiency, establishing them as versatile tools for complex generation tasks.
+
+# 2.2. Task-Oriented Data Generation
+
+Generative models are increasingly used to synthesize training data for tasks such as object detection [1, 18, 41, 48], semantic segmentation [34], and instance segmentation [43]. Beyond natural image synthesis, these models adapt to specialized domains like remote sensing and medical imaging via fine-tuning. For example, GeoDiffusion [1] employs text-guided geometric control to generate spatially aligned detection datasets, while DiffusionEngine [41] leverages diffusion models as scalable data engines for object detection. Domain-specific advancements include SSL-driven embedding generation for histopathology [9], joint image-segmentation synthesis in SatSynth [34], and hyperspectral image super-resolution [26]. Remote sensing applications further benefit from models like CRS-Diff [33] and DiffusionSat [14], which utilize multi-modal inputs for tasks like road extraction. However, remote sensing image object detection (RSIOD) lacks dedicated generative solutions. To address this, we propose a layout-controllable model supporting both rotated and horizontal bounding boxes for high-precision synthetic remote sensing imagery.
+
+# 2.3. Generative Data Augmentation
+
+Existing methods typically combine synthetic and real data directly for downstream training, though some approaches enhance data utility through quality filtering. For instance, Auto Cherry-Picker [2] optimizes synthetic data selection, while X-Paste [43] employs a copy-paste strategy with CLIP-based filtering to boost instance segmentation. DriverGen [8] further analyzes synthetic data distribution and proposes a multi-stage pipeline to improve diversity. Closest to our work, ODGEN [48] generates multi-object scenes via object-wise synthesis to mitigate domain gaps. However, our method focuses on remote sensing object detection, synthesizing images end-to-end using a conditional generator without manual instance pasting. We additionally introduce a diversity-conditioned generator coupled with a dual-criteria (diversity-quality) filtering mechanism, significantly enhancing data utility for downstream tasks.
+
+# 3. AeroGen
+
+In this section, we introduce AeroGen, a layout-conditional diffusion model for enhancing remote sensing image data. The model consists of two key components: (a) a remote sensing image layout generation model in Sec. 3.1 that allows users to generate high-quality RS images based on
+
+predefined layout conditions, such as horizontal and rotated boxes; (b) a generation pipeline in Sec. 3.2 that combines a diffusion-model-based diversity-conditional generator, which produces diverse layouts aligned with physical conditions, with a data-filtering mechanism to balance the diversity and quality of synthetic data, improving the utility of the generated dataset.
+
+# 3.1. Layout-conditional Diffusion Model
+
+The model weights, obtained through comprehensive fine-tuning on a remote sensing dataset based on LDM [31, 33], are adopted for RS study. In the original text-to-image diffusion model, the conditional position information is combined with the text control condition, and layout-based remote sensing image generation is achieved by establishing a unified position information encoding along with a corresponding dual cross-attention network, as shown in Fig. 2. Building on the latest research advances [17, 47], combined with the regional layout mask-attention strategy, control accuracy is improved, particularly for small target regions.
+
+Layout Embedding. As shown in Fig. 2(a), each object's bounding box or rotational bounding box is uniformly represented as a list of eight coordinates, i.e.,  $\mathbf{x} = [x_1, y_1, \ldots, x_4, y_4]$ , ensuring a consistent representation between horizontal and rotated bounding boxes. Building on this, Fourier [24] encoding is employed to convert these positional coordinates into a frequency domain vector representation, similar to GLIGEN [17]. We use a frozen CLIP text encoder [28] to obtain fixed codes  $\mathbf{c}$  for different categories, which serve as layout condition inputs. The Fourier-encoded coordinates are then fused with the category encodings using an additional linear layer to produce the layout control input:
+
+$$
+\mathbf {h} = \operatorname {L i n e a r} ([ \gamma (\mathbf {x}); \mathbf {c} ]), \tag {1}
+$$
+
+where  $[\gamma (\mathbf{x});\mathbf{c}]$  denotes the concatenation of Fourier-coded coordinates and category codes, and Linear  $(\cdot)$  represents the linear transformation layer. In this manner, spatial location and category information are effectively combined as layout control tokens.
+
+Layout Mask Attention. In addition to traditional token-based control [39, 44], recent studies [13, 47] indicate that direct semantic embedding based on feature maps is also an effective method for layout guidance. In the denoising process of a diffusion model, the injection of conditional information is gradual, enabling local attribute editing at the noise level. To this end, conditionally encoded noise region steering is employed and combined with a cropping step for improved layout precision. As shown in Fig. 2(b), each bounding box is first transformed into a  $0/1$  mask  $M$ , and category attributes are obtained through CLIP encoding. During each denoising step, the mask attention network provides additional layout guidance. The process is
+
+![](images/ba028fcf7a1f39323d69e5712c2781fe952e55748ec31ee0dec2ebf5eb2b2a0e.jpg)  
+Figure 2. AeroGen's overall architecture. (a) The layout embedding module combines bounding box coordinates with vectorized semantic information using Fourier and MLP layers. This encodes layout information to facilitate control, with the prompt description processed by a CLIP text encoder for global conditional guidance. (b) The injection of layout information at the noise level is demonstrated, where a local mask governs the injection position of the layout information, allowing for finer layout control. (c) The overall architecture and training process of AeroGen. At each timestep, the image being denoised first passes through a layout information injection module, which enhances layout conditional guidance.
+
+expressed as follows: for each denoised image  $Q$  and category encoding  $K, V$ , the mask  $M$  is used for attention computation according to the following equation:
+
+$$
+\mathcal {Q} = \sum_ {i = 1} ^ {n} M _ {i} \cdot \operatorname {s o f t m a x} \left(\frac {Q K _ {i} ^ {\top}}{\sqrt {d _ {k}}} + \mathcal {M} _ {i}\right) V _ {i}, \tag {2}
+$$
+
+where  $M$  represents the corresponding bounding box mask, and  $\mathcal{M}_i$  derived from  $M_{i}$  as the attention mask. This method enables precise manipulation of local noise characteristics during the diffusion generation process, offering finer control over the image layout.
+
+AeroGen Architecture. In AeroGen, the text prompt serves as a global condition and is integrated with layout control tokens via a dual cross-attention mechanism. The output is computed as:
+
+$$
+\operatorname {O u t} = \Psi (Q, K ^ {g}, V ^ {g}) + \lambda \cdot \Psi (Q, K ^ {l}, V ^ {l}), \tag {3}
+$$
+
+where  $\Psi$  represents the cross-attention mechanism.  $K^{g}$  and  $V^{g}$  are the keys and values of the global text condition, while  $K^{l}$  and  $V^{l}$  are the layout control tokens.  $\lambda$  balances the influence of global and layout conditions.
+
+The overall loss function for AeroGen combines both the global text condition and layout control, defined as:
+
+$$
+\mathcal {L} = \mathbb {E} \left[ \left\| \epsilon - \epsilon_ {\theta} \left(\mathbf {x} _ {t}, t, \mathbf {c} ^ {g}, \mathbf {c} ^ {l}\right) \right\| ^ {2} \right], \tag {4}
+$$
+
+where  $\mathbf{x}_t$  represents the noisy image at time step  $t$ ,  $\mathbf{c}^g$  is the global text condition, and  $\mathbf{c}^l$  is the layout control.
+
+# 3.2. Generative Pipeline
+
+The layout generative pipeline, as illustrated in Fig. 3, is divided into five stages: label generation, label filter, image generation, image filter, and data augmentation. Each generation step is followed by a corresponding screening step to ensure synthesis quality.
+
+Label Generation. Inspired by recent cutting-edge research [34], we adopt a denoising diffusion probabilistic model (DDPM [11]) to learn the conditional distribution and directly sample from it to obtain layout labels, thereby avoiding conflicts in layout conditions that may arise from random synthesis approaches. The specific method is illustrated in Fig. 3, where a labelling matrix  $\mathbf{M}_L$  is first constructed. This matrix contains all categories of conditions with dimensions  $H\times W\times N$ , where  $H$  and  $W$  represent
+
+![](images/4b02e955b5f2ec6fdfd7835d080ecdcdda4e9700aabf4270507ca76eafb606ad.jpg)  
+Figure 3. Overview of the pipeline based on AeroGen. By fitting the conditional distribution using a diffusion model, we expand a diverse set of layout conditions and combine them with AeroGen to generate synthetic data. Additionally, we introduce two filters to eliminate low-quality synthetic conditions and images, further ensuring the semantic consistency and layout consistency of the synthetic images. Finally, we incorporate synthetic images alongside real images in the training set to improve the performance of downstream tasks.
+
+![](images/0554cafc2fad0778022a8c52e612bbc32b404cb453c8686dcf6787a3ad7223dd.jpg)
+
+![](images/ed9719d9a3f0bdc789f5b0964e62de541ce7f43b81210865134d7a48371feb51.jpg)
+
+the height and width of the images, respectively, and  $N$  denotes the number of condition categories. For each condition corresponding to the target frame of the image, the value within the target frame region is set to 1, while the values in the remaining regions are set to -1. This process is formally represented as:
+
+$$
+\mathbf {M} _ {L} (i, j, k) = \left\{ \begin{array}{l l} 1, & \text {i f} (i, j) \in \mathcal {R} _ {k}, \\ - 1, & \text {i f} (i, j) \notin \mathcal {R} _ {k}, \end{array} \right. \tag {5}
+$$
+
+where  $i\in \{1,\dots ,H\}$ $j\in \{1,\ldots ,W\}$  and  $k\in$ $\{1,\dots ,N\}$  , with  $\mathcal{R}_k$  denoting the target area for the  $k$  -th category. Next, this conditional distribution is fitted using a DDPM-based generator  $G_{\theta}$  . The loss function is based on the mean square error (MSE):
+
+$$
+\mathcal {L} = \mathbb {E} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {M} _ {L} ^ {(t)}, t\right) \| ^ {2} \right], \tag {6}
+$$
+
+where  $\mathbf{M}_L^{(0)}$  represents the original layout matrix,  $\mathbf{M}_L^{(t)}$  represents the noise matrix at the  $t$ -th time step, and  $\epsilon_{\theta}(\mathbf{M}_L^{(t)}, t)$  denotes the model's predicted noise at step  $t$ .
+
+Label Filter and Enhancement. The label data sampled from the generator may not always align with real-world intuition or effectively guide image generation. Therefore, we propose a normal distribution-based filtering mechanism to screen the generated bounding box information, ensuring that the data conform to the distribution characteristics of real labels. The label filter assumes that the attributes of the bounding boxes (e.g., area) follow a normal distribution  $(\mathcal{N}(\mu_X,\sigma_X^2))$  and introduces the following constraint:  $\frac{(X - \mu_X)}{\sigma_X}\leq \epsilon$ , where  $\epsilon$  determines the filter's strictness,
+
+thereby ensuring that generated bounding boxes fall within a realistic and feasible range. Synthetic pseudo-labels and genuine a priori labels are filtered to form a comprehensive layout condition pool through additional enhancement strategies, including scaling, panning, rotating, and flipping.
+
+Image Generation. The synthetic bounding box labels are obtained based on the pool of layout conditions. The corresponding synthetic images are generated using the layout-guided diffusion model through the image generation process described in Sec. 3.1. The model uses these bounding box labels to guide the generation, ensuring that the image content matches the generated layout conditions.
+
+Image Filter. Since the images generated by the diffusion model do not consistently meet high-quality or predefined layout requirements, a screening mechanism is implemented to evaluate both the quality of the generation and the consistency of the layout. The consistency of the semantic and layout is evaluated using the CLIP model [20] and a ResNet101-based classifier [10]. Synthetic images are then filtered by calculating their CLIP scores and minimum classification accuracies, which are compared against predefined thresholds to select the final filtered images.
+
+Data Augmentation. The synthetic data serves as a complementary dataset alongside the real dataset, and both are utilized as training data for downstream target detection model training.
+
+# 4. Experiments
+
+In this section, we conducted extensive experiments to verify the generative capabilities of AeroGen and its auxiliary data augmentation ability to support downstream RSIOD
+
+![](images/83bc5f86dcd0a94f7c7696416da53bff4ef83fc0a87b5d82bd1295dd8e2c024a.jpg)  
+Figure 4. Visualization comparison of the generated image by different methods on the DIOR dataset.
+
+<table><tr><td>Dataset</td><td>Modality</td><td>Images</td><td>Objects</td><td>Categories</td></tr><tr><td>DIOR [16]</td><td>HBB</td><td>23,463</td><td>192,518</td><td>20</td></tr><tr><td>DIOR-R [3]</td><td>OBB</td><td>23,463</td><td>192,518</td><td>20</td></tr><tr><td>HRSC [22]</td><td>OBB</td><td>1,061</td><td>2,976</td><td>19</td></tr></table>
+
+Table 1. Statistical information of the benchmark RSIOD datasets.
+
+tasks. Specifically, we assessed the performance of our layout generation model AeroGen from both quantitative and qualitative perspectives. Subsequently, we performed data augmentation experiments on three datasets (i.e., DIOR, DIOR-R, and HRSC) to verify the effectiveness of synthetic data generated by our AeroGen model in improving the performance of downstream object detection tasks.
+
+# 4.1. Implementation Details
+
+Data Preparation. An overview of the three datasets is provided in Tab. 1. Notably, the DIOR and DIOR-R datasets [3] share the same image data but differ in annotation format, with DIOR using bounding boxes and DIOR-R using rotated bounding boxes. HRSC [22] is a Remote Sensing dataset for ship detection, with image sizes ranging from  $300 \times 300$  to  $1500 \times 900$  pixels.
+
+Training Details. We trained our AeroGen separately on each dataset for 100 epochs. During training, we used the
+
+AdamW optimizer [23] with a learning rate of 1e-5. Only the attention layers of UNet and the Layout Mask Attention (LMA) are updated, while the remaining weights are inherited from the fine-tuned LDM in RS data [33].
+
+Evaluation Metrics. For the quantitative analysis of generated images, we used the FID score to evaluate the visual quality of the generated images and employed Classification Score (CAS) [29] and YOLO Score [19] to measure the layout consistency of the generated images. In the data augmentation experiments, we assessed object detection model performance based on mAP50 and mAP50-95 (mAP) metrics to evaluate their overall quality.
+
+# 4.2. Image Quality Results
+
+Quantitative Evaluation. We used a bounding box condition defined by four extreme coordinates and conducted both training and testing on the DIOR dataset. We compared AeroGen with state-of-the-art layout-to-image generation methods, including LostGAN [32], ReCo [39], LayoutDiffusion[44], and GLIGEN [17]. The performance of these methods on three metrics is reported in Tab. 2. To ensure fairness, we initialized all methods with identical SD weights (Stable Diffusion 1.5) and trained them on the DIOR dataset for the same number of epochs. Our method outperformed other methods across all the metrics.
+
+Furthermore, we evaluated AeroGen and GLIGEN on
+
+<table><tr><td>Method</td><td>Dataset</td><td>Modality</td><td>FID ↓</td><td>CAS ↑</td><td>YOLO Score ↑</td></tr><tr><td>LostGAN [32]</td><td></td><td></td><td>57.10</td><td>46.02</td><td>14.3/27.3/15.2</td></tr><tr><td>Layout Diffusion [44]</td><td></td><td></td><td>45.31</td><td>56.98</td><td>20.0/37.4/19.3</td></tr><tr><td>ReCo [39]</td><td>DIOR [16]</td><td>HBB</td><td>42.56</td><td>55.42</td><td>21.1/40.7/23.1</td></tr><tr><td>GLIGEN [17]</td><td></td><td></td><td>41.31</td><td>63.50</td><td>25.8/44.4/27.8</td></tr><tr><td>AeroGen (Ours)</td><td></td><td></td><td>38.57</td><td>76.84</td><td>29.8/54.2/31.6</td></tr><tr><td>GLIGEN [17]†</td><td>DIOR-R [3]</td><td>OBB</td><td>48.43</td><td>58.89</td><td>24.6/41.6/25.1</td></tr><tr><td>AeroGen (Ours)</td><td></td><td></td><td>35.07</td><td>74.13</td><td>29.6/57.6/32.0</td></tr><tr><td>GLIGEN [17]†</td><td>HRSC [22]</td><td>OBB</td><td>66.69</td><td>43.35</td><td>23.4/44.7/26.3</td></tr><tr><td>AeroGen (Ours)</td><td></td><td></td><td>45.86</td><td>51.19</td><td>27.1/51.0/27.6</td></tr></table>
+
+Table 2. Quantitative results of the generated images by different methods. For the Oriented Bounding Box (OBB) modality, we replicated the GLIGEN† method to account for the rotated bounding box. The best results are in bold.
+
+the DIOR-R and HRSC datasets with rotated bounding boxes, where AeroGen consistently excelled. Notably, the original GliGen method does not support rotated bounding box conditions; therefore, we modified the layout encoding (as shown in Fig. 2 (a)) and retrained the model.
+
+Qualitative Evaluation. Fig. 4 compares the results of AeroGen with those of other methods. AeroGen shows superior layout consistency and an enhanced capability for generating small objects. Besides, we present experimental results on natural images in the supplemental material.
+
+# 4.3. Data Augmentation Experiments
+
+We synthesized augmented data on three RSIOD datasets to enhance model training. For the DIOR/DIOR-R datasets, we generated 10k, 20k, and 50k synthetic samples respectively for the RSIOD task. Following the same proportion, 2k, 4k, and 10k synthetic samples were created for the HRSC dataset. The experiments were conducted using the OBB branch configurations of two established RSIOD frameworks: the unified YOLOv8 [35] and Oriented R-CNN [38]. Table 3 demonstrations that incorporate synthetic data consistently enhance downstream task performance across all experimental settings.
+
+We visualize the mAP scores for different categories in detail, as shown in Fig. 5. In most categories, results incorporating enhancements significantly outperform those without them, particularly in rarer categories, achieving improvements of  $17.8\%$ ,  $14.7\%$ , and  $12.6\%$  in the GF, DAM, and APO categories, respectively. AeroGen, enhanced on YOLOv8 by leveraging original training data and 10k synthetic images, achieves superior performance over competitors on the DOTA dataset in Tab. 4.
+
+# 4.4. Ablation Study
+
+Ablation of Enhanced Methods. We compared synthetic data enhancement methods with traditional approaches, including the basic enhancement techniques of Flip and Copy-Paste [7] for target detection tasks, as shown in Tab. 5. The target detection model trained on synthetic data performs significantly better than when trained with traditional
+
+![](images/6afa8df64b7382ea6212bff6371aa320d76824da3edcd7cb873d90e509b2d1b5.jpg)  
+Figure 5. Comparison of mAP50 across each category on the DIOR-R dataset under the setting of data augmentation with 50k generation images (aug) and without augmentation (w/o aug).
+
+methods, demonstrating the effectiveness of the generative model for data enhancement.
+
+Ablation of Different Modules. We assessed the impact of different modules on image quality generated by AeroGen in Tab. 6. The contribution of each module to the enhancement of image quality is evaluated by incorporating additional components into the original SD model. Results show that Layout Mask Attention (LMA) effectively captures global semantic information and preserves layout consistency, while adding Dual Cross Attention (DCA) further enhances performance, particularly inYOLO Score, indicating improved regional target generation. Overall, the model performs best when both LMA and DCA are used.
+
+Ablation of Augment experiments. We further analyze the filtering strategies and data augmentation techniques in the generation pipeline, including diverse generation strategies, filtering strategies for layout conditions, and filtering strategies for layout and semantic consistency of images. We use the synthetic data generated in various ways as enhancement data and conduct enhancement experiments on
+
+<table><tr><td>Gen Data</td><td>mAP↑</td><td>mAP50↑</td></tr><tr><td>0</td><td>54.22</td><td>72.69</td></tr><tr><td>10k</td><td>55.62</td><td>74.79</td></tr><tr><td>20k</td><td>56.78</td><td>76.31</td></tr><tr><td>50k</td><td>57.92</td><td>77.10</td></tr></table>
+
+(a) DIOR  
+
+<table><tr><td>Gen Data</td><td>mAP↑</td><td>mAP50↑</td></tr><tr><td>0</td><td>37.39</td><td>60.21</td></tr><tr><td>10k</td><td>39.81</td><td>62.39</td></tr><tr><td>20k</td><td>41.12</td><td>63.33</td></tr><tr><td>50k</td><td>41.69</td><td>64.12</td></tr></table>
+
+(b) DIOR-R  
+
+<table><tr><td>Gen Data</td><td>mAP↑</td><td>mAP50↑</td></tr><tr><td>0</td><td>63.49</td><td>90.28</td></tr><tr><td>2k</td><td>64.12</td><td>91.79</td></tr><tr><td>4k</td><td>64.78</td><td>92.31</td></tr><tr><td>10k</td><td>65.92</td><td>93.10</td></tr></table>
+
+(c) HRSC  
+Table 3. The enhancement effects of various scales of synthetic data on downstream tasks across DIOR, DIOR-R, and HRSC datasets.  
+
+<table><tr><td>Dataset</td><td>Baseline</td><td>LostGAN</td><td>ReCo</td><td>LayoutD</td><td>GLIGEN</td><td>AeroGen</td></tr><tr><td>DIOR</td><td>72.69</td><td>69.49</td><td>72.89</td><td>73.07</td><td>73.39</td><td>74.79</td></tr><tr><td>DOTA1.0</td><td>70.31</td><td>60.52</td><td>68.56</td><td>68.91</td><td>70.22</td><td>71.38</td></tr></table>
+
+Table 4. Enhancement experiment on original train set and 10k synthetic images on YOLOv8 Model.  
+
+<table><tr><td>Strategy</td><td>mAP↑</td><td>mAP50↑</td></tr><tr><td>Flip</td><td>37.39</td><td>60.21</td></tr><tr><td>CopyPaste [7]</td><td>38.25</td><td>61.79</td></tr><tr><td>AeroGen</td><td>41.32</td><td>63.98</td></tr><tr><td>CopyPaste + Flip [7]</td><td>38.75</td><td>62.11</td></tr><tr><td>AeroGen + Flip</td><td>41.69</td><td>64.12</td></tr></table>
+
+Table 5. Comparison of different augmentation strategies on the DIOR-R dataset with 50k synthetic images.  
+
+<table><tr><td rowspan="2">LMA</td><td colspan="2">DCA</td><td rowspan="2">FID ↓</td><td rowspan="2">CAS ↑</td><td rowspan="2">YOLO Score ↑</td></tr><tr><td>Local</td><td>Global</td></tr><tr><td>X</td><td>X</td><td>X</td><td>82.11</td><td>18.48</td><td>1.3/3.9/1.1</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>61.50</td><td>50.11</td><td>25.3/46.5/27.2</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>66.29</td><td>40.71</td><td>16.5/29.2/17.7</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>51.42</td><td>55.26</td><td>25.8/46.9/27.3</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>40.76</td><td>73.89</td><td>28.5/52.7/29.3</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>38.57</td><td>76.84</td><td>29.8/54.2/31.6</td></tr></table>
+
+Table 6. Ablation study of different modules in the AeroGen model on the DIOR dataset.  
+
+<table><tr><td colspan="3">Layout Diversity</td><td colspan="2">Image Quality</td><td colspan="2">Metrics</td></tr><tr><td>Synthesis</td><td>Filter</td><td>Augment</td><td>Semantic</td><td>Layout</td><td>mAP↑</td><td>mAP50↑</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>41.69</td><td>64.12</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>41.31</td><td>63.47</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>40.92</td><td>62.41</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>39.62</td><td>61.32</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>40.27</td><td>62.13</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>37.05</td><td>60.03</td></tr></table>
+
+the DIOR-R datasets and the experimental results are shown in Tab. 7. As can be seen, each component in the generation
+
+Table 7. Ablation study results analyzing the impact of diverse generation and filtering strategies in the synthesis pipeline on layout labeling and image filtering consistency.  
+
+<table><tr><td>Train Set</td><td>Redet</td><td>F-RCNN</td><td>O-RCNN</td></tr><tr><td>DIOR</td><td>59.21</td><td>57.32</td><td>60.21</td></tr><tr><td>DIOR+10k Synthetic Data</td><td>62.03</td><td>60.11</td><td>62.39</td></tr></table>
+
+Table 8. Comparison of detection models with data augmentation.  
+
+<table><tr><td>Dataset</td><td>mAP</td><td>mAP50</td></tr><tr><td>HRSC-100</td><td>35.20 / 37.35</td><td>70.25 / 73.60</td></tr><tr><td>HRSC-100+2k</td><td>42.35 / 44.48</td><td>78.17 / 80.05</td></tr><tr><td>HRSC-100+5k</td><td>46.23 / 48.02</td><td>81.98 / 84.23</td></tr></table>
+
+Table 9. Few-shot experiment with 100 images (HRSC-100).
+
+pipeline contributes positively.
+
+To systematically evaluate the effectiveness of data augmentation strategies across diverse detection frameworks, we conducted comprehensive experiments on the DIOR dataset. As demonstrated in Tab. 8, the proposed AeroGen framework achieved significant and consistent performance improvements in all architectures evaluated. To further validate its utility in data-scarce scenarios, we constructed a simulated few-shot training subset (HRSC-100) augmented with AeroGen-generated synthetic samples. Experimental results in Tab. 9 reveal that AeroGen robustly enhances detection accuracy under limited training data conditions.
+
+# 5. Conclusion
+
+This paper introduces AeroGen, a layout-controllable diffusion model designed to enhance remote sensing image datasets for target detection. The model comprises two primary components: a layout generation model that creates high-quality remote sensing images based on predefined layout conditions, and a data generation pipeline that incorporates a diversity of condition generators for the diffusion model. The pipeline employs a double filtering mechanism to exclude low-quality generation conditions and images, thereby ensuring the semantic and layout consistency of the generated images. By combining synthetic and real images in the training set, AeroGen significantly improves model performance in downstream tasks. This work highlights the potential of generative modeling in enhancing the datasets of remote sensing image processing tasks.
+
+Acknowledgment. This work was supported by the National Natural Science Foundation of China under Grant 62192781, Grant 62272375, Grant 62272374, Grant 62250009, Grant 62137002, Grant 62276208, and Grant 62425113, in part by Natural Science Foundation of Shaanxi Province under Grant 2024JC-JCQN62, in part by Natural Science Basic Research Program of Shaanxi Province under Grant 2024JC-JCQN-02, in part by Project of China Knowledge Center for Engineering Science and Technology, in part by Project of Chinese academy of engineering "The Online and Offline Mixed Educational Service System for "The Belt and Road" Training in MOOC China," in part by the Major Key Project of PCL under Grant PCL2024A06, and in part by Tianyuan Fund for Mathematics of the National Natural Science Foundation of China under Grant 12426105.
+
+# References
+
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\ No newline at end of file
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+# AesthetiQ: Enhancing Graphic Layout Design via Aesthetic-Aware Preference Alignment of Multi-modal Large Language Models
+
+Sohan Patnaik*†
+
+Rishabh Jain*
+
+Balaji Krishnamurthy
+
+Mausoom Sarkar
+
+Media and Data Science Research, Adobe
+
+# Abstract
+
+Visual layouts are essential in graphic design fields such as advertising, posters, and web interfaces. The application of generative models for content-aware layout generation has recently gained traction. However, these models fail to understand the contextual aesthetic requirements of layout design and do not align with human-like preferences, primarily treating it as a prediction task without considering the final rendered output. To overcome these problems, we offer Aesthetic-Aware Preference Alignment (AAPA), a novel technique to train a Multi-modal Large Language Model (MLLM) for layout prediction that uses MLLM's aesthetic preferences for Direct Preference Optimization over graphic layouts. We propose a data filtering protocol utilizing our layout-quality heuristics for AAPA to ensure training happens on high-quality layouts. Additionally, we introduce a novel evaluation metric that uses another MLLM to compute the win rate of the generated layout against the ground-truth layout based on aesthetics criteria. We also demonstrate the applicability of AAPA for MLLMs of varying scales (1B to 8B parameters) and LLM families (Qwen, Phi, InternLM). By conducting thorough qualitative and quantitative analyses, we verify the efficacy of our approach on two challenging benchmarks - Crello and Webui, showcasing  $17\%$ , and  $16\%$  improvement over current State-of-The-Art methods, thereby highlighting the potential of MLLMs in aesthetic-aware layout generation. Results can be downloaded from Project Webpage
+
+# 1. Introduction
+
+The arrangement of visual elements for a graphic layout significantly impacts how users perceive and interact with digital content [25]. The growing demand for automated design solutions demonstrates broad impact across multiple domains, including poster design [20, 50], user interface de
+
+![](images/f2526035921a6c78ee1fa73fdac8803c8571651e9ea6e880742b9d73835a8543.jpg)  
+Figure 1. Existing cross-entropy loss based methods penalize element misalignment heavily while preferential tuning via AAPA better capture aesthetic nuances in layouts
+
+sign [11, 22], document layouts [50, 55], and presentation slides [14]. Designers expect layouts to achieve dual-level harmony, creating a seamless blend of fine-grained design elements - color, font, and layout - while ensuring they work cohesively with different types of elements in the overall design [18]. These fine-grained components must maintain aesthetic integrity and enhance the design's collective harmony. For instance, when examining basic design elements, colors must strike a delicate balance between contrast and cooperation, delivering visual style.
+
+As digital content creation accelerates, the field of automated layout generation has evolved across multiple directions. Research has progressed from unconditional generation [2, 16, 22, 28, 50] to more sophisticated approaches, including conditional generation based on user inputs (such as element types [23-25], sizes [24, 28], or relationships [23, 25]), conditional refinement using coarse attributes [41], and conditional completion with partially available elements [16]. Recently, Multi-modal Large Language Models (MLLMs) have demonstrated remarkable capabilities in spatial reasoning and visual-semantic understanding [9, 32, 38]. Their ability to process both textual and visual information enables them to capture com
+
+plex spatial relationships and translate challenging language concepts into coherent layout arrangements. Current approaches [43, 45, 51] primarily reduce the complex design problem to a numeric representation, where each design element is simplified to a tuple  $(x, y, w, h)$  encoding its center coordinates, width, and height. While both autoregressive models and diffusion models [1, 7, 54] approach layout generation differently-the former through sequential prediction and the latter through denoising-they share a fundamental limitation: both treat layouting as an optimization problem over position representations. As illustrated in Fig.1, when multiple layouts are aesthetically pleasing, optimizing based on the absolute numerical position through cross-entropy-based loss incorrectly penalizes other alternative layouts predicted by the model, thus enforcing incorrect understanding. Moreover, reducing visual elements to numerical values strips away critical design attributes, hierarchical relationships, and semantic context that human designers naturally consider. This reductionist approach fails to capture the aesthetics or visual appeal of the rendered layouts, particularly when dealing with complex layouts that require subtle aesthetic considerations and contextual awareness.
+
+To this end, we pose a fundamental research question: "Can we utilize aesthetic preferences to guide the training of MLLMs, thereby enhancing the visual impact of generated layouts?" While MLLMs demonstrate strong visual-semantic alignment capabilities, these are often underutilized when trained solely with supervised position loss per element, which enforces a single layout variation for each input. Although incorporating aesthetic awareness through rendered layouts and an aesthetic discriminator seems intuitive, creating a differentiable layout renderer and the discriminator is non-intuitive. Instead, we propose learning aesthetics by proxy through preference learning between multiple layouts, hypothesizing that this approach enables MLLMs to develop a deeper contextual and aesthetic understanding of design principles.
+
+In this paper, we introduce Aesthetic-Aware Preference Alignment (AAPA), a novel algorithm that extends Direct Preference Optimization (DPO) [40] for aesthetic-aware layout generation. AAPA creates multiple layout candidates and leverages an MLLM as a judge to rank them based on their aesthetics, thereby developing robust aesthetic preferences. To ensure reliable training, we implement a rigorous data filtering protocol using alignment and overlap metrics, guaranteeing the model learns preferences only from well-formed layouts. Additionally, we present a novel evaluation framework using MLLMs as aesthetic scorers, introducing the  $\%$  win rate metric that measures how often model-generated layouts outperform ground-truth layouts aesthetically. This approach offers more direct quality assessment than traditional metrics like Intersection over Union (IoU) or Boundary Displacement Error (BDE) [27], which fail to
+
+capture subtle aesthetic considerations. Our main contributions can be summarized as follows:
+
+- We demonstrate that VLMs can effectively utilize their real-world knowledge and visual-semantic alignment capabilities to enhance layout prediction tasks.  
+- We propose Aesthetic-Aware Preference Alignment, a novel method to improve aesthetics of generated layouts through preference-based learning.  
+- We highlight the importance of data filtering based on quality heuristics through alignment and overlap heuristics, ensuring robust training on high-quality samples.  
+- We develop a novel evaluation framework that assess layout aesthetics via MLLMs, providing more meaningful quality measurements than traditional metrics.  
+- We conduct extensive qualitative and quantitative analyses of each proposed component using two challenging benchmark datasets, Crello and WebUI, demonstrating the effectiveness of our approach across diverse settings.  
+- We showcase the versatility and effectiveness of our approach across MLLMs of varying scales and families, and perform several ablation studies to provide deeper insights into the contributions of each component.
+
+# 2. Related works
+
+Graphic Layout Generation: As digital content creation continues to grow rapidly, the automated generation of visually appealing layouts that meet users' needs has emerged as an important research problem. Early works employed rule-based [39] and energy optimization [25, 37] techniques to structure graphic layouts, providing a solid foundation but offering limited flexibility. GAN-based approaches [23, 29, 56] introduced frameworks for unconditional layout generation by capturing geometric relationships across elements and leveraging differentiable rendering in the image-space, while transformer models such as LayoutTransformer [16], VTN [1], and BLT [24] used autoregressive and bidirectional transformers to improve layout quality. With advancements in NLP, masking strategies, language models, and encoder-decoder architectures have been applied to layout generation. Approaches like CanvasVAE [50], FlexDM [20], and ICVT [5] integrate images and text to enhance content relevance, enabling conditional generation through multi-modal features extracted via transformer-based architectures [12, 26, 47]. However, these methods still face challenges in adaptability to diverse content and impose constraints that limit their practical usability in real-world design applications.
+
+Constraint-aware Layout Prediction: Recent works have leveraged diffusion models to improve layout generation quality across various conditions. PLay [10] uses a latent diffusion model conditioned on guidelines to align elements, while LayoutDM [7] and LDGM [19] employ the discrete diffusion framework [3] to build unified mod
+
+els without guidelines, using attribute-specific corruption strategies [15] to restrict variables of different attributes to their respective sample spaces. LDGM further applies discretized Gaussian noise to enable gradual coordinate changes. Following a similar design, LayoutDiffusion [54] and LACE [8] enhance visual quality by scaling up the transformer backbone and improving alignment and overlap metrics. However, these methods lack contextual understanding and fail to capture semantic relationships across elements, leading to designs that may be geometrically accurate but aesthetically incoherent. Other diffusion-based methods [6, 17] attempt to generate layouts in continuous space but still rely on quantized geometric attributes or conditional generation based on categorical attributes, limiting their flexibility. Training diffusion models with masked and unmasked layouts [48] has shown potential for unifying various tasks but still lacks the contextual understanding.
+
+LLMs Assisted Layout Generation: Recent works have explored large language models (LLMs) for layout generation, treating layouts as structured data formats like XML or JSON. LayoutNUWA [45] fine-tunes LLaMa [46] and CodeLLaMa [42] for content-agnostic layout generation, achieving state-of-the-art results across multiple datasets. LayoutPrompter [30] introduces a training-free approach by leveraging RAG (Retrieval-Augmented Generation) to enhance in-context learning in GPT [4], though it is limited to open-domain generation. These methods, however, translate visual domain features into hard tokens, potentially leading to significant information loss. To address this, recent works propose multi-modal techniques such as visual instruction tuning [33] with aligned visual adaptation heads, allowing models to process visual information directly. While these approaches show promise, they rely on cross-entropy loss for optimization, which penalizes aesthetically good layouts along with poor ones (as depicted in Fig.1), neglecting aesthetic preferences and leading to suboptimal design outcomes. This cross-entropy loss-based optimization fails to capture nuanced aesthetic considerations essential for high-quality layouts.
+
+# 3. Methodology
+
+Our approach to layout prediction focuses on generating aesthetically aligned designs, with a Multi-modal Large Language Model (MLLM) serving as an evaluator for layout quality. We want to capture design aesthetics in layout configurations by using another MLLM (judge). To address the challenges given by subjective design preferences, limited datasets, and high-dimensional variability, we use an Aesthetic-Aware Preference Alignment (AAPA) technique, which aligns our model's output with aesthetic evaluations from the judge MLLM. We begin by formalizing the layout prediction task, discussing the input and output representations, and the fine-tuning approach. We then introduce
+
+AAPA, which drives aesthetic sensitivity in layout generation (Fig 2). Finally, we present additional insights gained from scaling and pretraining on a large dataset of templates.
+
+# 3.1. Layout Prediction Task
+
+The goal of layout prediction involves placing design elements over a blank canvas to generate an aesthetically pleasing graphic template. Formally, consider a set of  $N$  design elements  $E = \{e_1,e_2,\dots ,e_N\}$  that need to be placed over a canvas of width  $W_{c}$  and height  $H_{c}$  to obtain a graphic layout  $G$ . We define the placement of an element  $e_i$  through bounding box attributes  $b_{i} = (x_{i},y_{i},w_{i},h_{i})$  that represent the graphic element's center coordinates, width, and height of the bounding box. Given the type of each element denoted by  $T(e_i)\in \mathcal{T}$ , where  $\mathcal{T} = \{\text{image},\text{text},\text{shape},\text{background}\}$ , we verbalise the input through a prompt template denoted by  $\mathcal{P}_{H_c,W_c}^E$  (Eq.1).
+
+$$
+\mathcal {P} _ {H _ {c}, W _ {c}} ^ {E} = \bigcup_ {i = 1} ^ {n} \left\{ \begin{array}{l l} \text {I m a g e T o k e n s} \left(e _ {i}\right) & \text {i f} T \left(e _ {i}\right) \in \mathcal {T} - \{\text {t e x t} \} \\ \text {T e x t T o k e n s} \left(e _ {i}\right) & \text {i f} T \left(e _ {i}\right) = \text {t e x t} \end{array} \right. \tag {1}
+$$
+
+Consider the layout MLLM  $\mathcal{M}_{\mathrm{layout}}$  with three components: a vision encoder  $f_{\mathrm{vision}}$ , a text encoder  $f_{\mathrm{text}}$ , and a large language model  $\mathcal{L}$ .  $\mathcal{M}_{\mathrm{layout}}$  takes as input the verbalized prompt,  $\mathcal{P}_{H_c,W_c}^E$ , by encoding each token in the prompt using either a vision encoder or a text encoder, depending on the type of the corresponding design element. For each token representing an element  $e_i$  where  $T(e_i) \in \mathcal{T} - \{\mathrm{text}\}$ , the vision encoder  $f_{\mathrm{vision}}$  produces an embedding  $z_i^{\mathrm{vision}} = f_{\mathrm{vision}}(\mathrm{ImageTokens}(e_i))$ . For tokens representing elements where  $T(e_i) = \mathrm{text}$ , the text encoder  $f_{\mathrm{text}}$  produces an embedding  $z_i^{\mathrm{text}} = f_{\mathrm{text}}(\mathrm{TextTokens}(e_i))$ . The final multi-modal embedding  $Z$  for  $\mathcal{P}_{H_c,W_c}^E$  is then represented as the union of all encoded tokens, combining vision and text embeddings based on each token's type (Eq.2).
+
+$$
+Z = \bigcup_ {i = 1} ^ {N} \left\{ \begin{array}{l l} z _ {i} ^ {\text {v i s i o n}} & \text {i f} T (e _ {i}) \in \mathcal {T} - \{\text {t e x t} \} \\ z _ {i} ^ {\text {t e x t}} & \text {i f} T (e _ {i}) = \text {t e x t} \end{array} \right. \tag {2}
+$$
+
+Once the multi-modal embedding  $Z$  is constructed, it is fed into the large language model component  $\mathcal{L}$  of  $\mathcal{M}_{\mathrm{layout}}$  to predict the position of each design element.
+
+# 3.2. Position-Aware Layout Instruction Tuning
+
+To facilitate accurate layout prediction, we discretize the bounding box coordinates  $b_{i} = (x_{i},y_{i},w_{i},h_{i})$ . These continuous attributes are mapped into discrete bins based on the width  $W_{c}$  and height  $H_{c}$  of the canvas. The binning function  $B(\cdot)$  depicted by Eq. 3 maps each continuous attribute into one of  $K$  bins, where  $K$  is the number of bins:
+
+$$
+B \left(a _ {i}\right) = \left\lfloor \frac {a _ {i}}{D} \times K \right\rfloor \quad \text {w i t h} \quad D = \left\{ \begin{array}{l l} W _ {c} & \text {i f} a _ {i} \in \left\{x _ {i}, w _ {i} \right\} \\ H _ {c} & \text {i f} a _ {i} \in \left\{y _ {i}, h _ {i} \right\} \end{array} \right. \tag {3}
+$$
+
+![](images/9ff11ffacb3b4181ff873363dabc6d4b229f2fa015dd5a356835654edccc9938.jpg)  
+Figure 2. The training for the aesthetic layout prediction task consists of the following steps: 1) Vision Encoder: Design elements (images and text) are processed to generate image and text embeddings. 2) AesthetiQ Model Prediction: Embeddings are passed to the AesthetiQ model, which predicts layout coordinates. 3) Training with Cross-Entropy Loss: The predicted layout is compared with the ground truth and trained using cross-entropy loss. 4) Sampling for Comparison: Multiple layout predictions are generated using AesthetiQ inference. 5) Pair Selection and Quality Filtering: We filter the data based on quality heuristics to ensure layout quality in samples. 6) Judging by ViLA: The ViLA model compares layout pairs and selects the better one based on aesthetic preferences. 7) Aesthetic Preference Optimization (AAPA): Feedback from ViLA is used to fine-tune the AesthetiQ model for aesthetic optimization.
+
+![](images/f4e0d48ec05a40281b4508d8f12044b163c6679080d1cb76ffc496ac90c2671f.jpg)
+
+For each of these binned values, we introduce position tokens  $\mathrm{pos}_k$ , where  $k \in \{0,1,\dots,K\}$ . Thus, each attribute  $x_i,y_i,w_i,h_i$  is assigned the tokens  $\mathrm{pos}_{B(x_i)}$ ,  $\mathrm{pos}_{B(y_i)}$ ,  $\mathrm{pos}_{B(w_i)}$ , and  $\mathrm{pos}_{B(h_i)}$  respectively. This discretization reduces the continuous spatial attributes to a fixed set of discrete position tokens, simplifying the layout prediction task. By quantizing the position, the model can more effectively learn the spatial relationships across design elements. Once the position tokens are integrated into the multi-modal embedding, the language model component  $\mathcal{L}$  predicts the layout by outputting the corresponding position tokens for each element, which are mapped back to approximate spatial coordinates using the function  $B^{-1}$ .
+
+Let  $Y = \{y_{1}, y_{2}, \ldots, y_{M}\}$  represent the ground truth sequence of position tokens corresponding to the predicted bounding box attributes of the design elements, where each  $y_{i} \in \{\mathrm{pos}_{0}, \mathrm{pos}_{1}, \ldots, \mathrm{pos}_{K}\}$ , and  $M$  is the number of output tokens.  $\mathcal{L}$  outputs policy  $\pi_{\mathcal{M}}(\mathcal{P}_{H_c, W_c}^E)$ , a sequence of logits  $\hat{y}_i$ , where  $\hat{y}_i \in \mathbb{R}^K$  represents the predicted probabilities for each position token of each design element  $e_i$ . We train  $\mathcal{M}_{\mathrm{layout}}$  through the cross-entropy loss (Eq. 4)
+
+$$
+\mathcal {L} _ {\mathrm {C E}} = - \frac {1}{S} \sum_ {i = 1} ^ {S} \sum_ {j = 1} ^ {M} \sum_ {k = 0} ^ {K} \mathbb {I} \left(y _ {j} = \operatorname {p o s} _ {k}\right) \log \hat {y} _ {j, k} \tag {4}
+$$
+
+where  $\mathbb{I}(y_i = \mathrm{pos}_k)$  is the indicator function and  $\hat{y}_{i,k}$  is the predicted probability (logit) for the  $k$ -th position token of the  $j$ -th element, and S is the size the dataset. Thus, during instruction tuning, the  $\mathcal{M}_{\mathrm{layout}}$  learns the correct spatial placement of each element through the alignment of the predicted position tokens with the ground truth tokens. However, cross-entropy loss is suboptimal as it requires an exact match (Fig 1). Additionally, if the ground-truth position token is  $pos_{32}$  and the model predicts  $pos_{33}$ , the cross-entropy loss penalizes this heavily despite the minimal difference between the two positions.
+
+# 3.3. Aesthetic-Aware Preference Alignment
+
+A significant challenge in layout prediction arises from the non-differentiable nature of rendering individual elements on a canvas, which prevents the model from directly "seeing" the rendered template for aesthetic evaluation. To address this, we introduce a judge model  $\mathcal{M}_{\mathrm{judge}}$  that performs a pairwise comparison of two graphic layouts to determine which one is aesthetically superior. Given two graphic lay
+
+outs, rendered on a canvas using a renderer  $\mathcal{R}$ , denoted as  $G^{i} = \mathcal{R}(E^{i},W_{c}^{i},H_{c}^{i})$ ,  $i = \{1,2\}$ , the goal of  $\mathcal{M}_{\mathrm{judge}}$  is to decide which layout is better based on aesthetic criteria.  $\mathcal{M}_{\mathrm{judge}}$  takes as input a judge prompt  $\mathcal{P}_{\mathrm{judge}}$ , which verbalizes the evaluation criteria for comparing the two layouts, and the two graphic layouts  $G^{1}$  and  $G^{2}$ , to produce a binary decision about which layout is better. Formally,
+
+$$
+d = \mathcal {M} _ {\text {j u d g e}} \left(\mathcal {P} _ {\text {j u d g e}}, G ^ {1}, G ^ {2}\right) \tag {5}
+$$
+
+where  $d \in \{1,2\}$  represents the decision of the  $\mathcal{M}_{judge}$ . If  $d = 1$ , then graphic layout  $G^1$  is considered better than graphic layout  $G^2$ , and vice versa. Thus, we define
+
+$$
+G ^ {\mathrm {w}} = \left\{ \begin{array}{l l} G ^ {1} & \text {i f} d = 1 \\ G ^ {2} & \text {i f} d = 2 \end{array} , \quad G ^ {\mathrm {r}} = \left\{ \begin{array}{l l} G ^ {2} & \text {i f} d = 1 \\ G ^ {1} & \text {i f} d = 2 \end{array} \right. \right. \tag {6}
+$$
+
+Through this pairwise comparison, the judging model  $\mathcal{M}_{\mathrm{judge}}$  selects the best  $(G^{w})$  and worst  $(G^{r})$  graphic layouts based on aesthetic quality without computing any explicit scores. Scoring individual layouts was found to be challenging, as MLLMs often assign similar scores across a range of layouts due to their limited exposure to the design space. Once we obtain the preferential data from  $\mathcal{M}_{\mathrm{judge}}$ ,  $\mathcal{M}_{\mathrm{layout}}$  is tuned further to prefer the better layout compared to the worse layout evaluated based on aesthetics. For this, we apply Aesthetic-Aware Preference Alignment (AAPA) to train the layout model  $\mathcal{M}_{\mathrm{layout}}$  using AAPA loss (Eq. 7)
+
+$$
+\mathcal {L} _ {\mathrm {A A P A}} = - \log \sigma \left(\beta \left(\log \frac {\pi_ {\mathcal {M}} \left(\mathcal {P} _ {H _ {c} , W _ {c}} ^ {E ^ {w}}\right)}{\pi_ {\hat {\mathcal {M}}} \left(\mathcal {P} _ {H _ {c} , W _ {c}} ^ {E ^ {w}}\right)} - \log \frac {\pi_ {\mathcal {M}} \left(\mathcal {P} _ {H _ {c} , W _ {c}} ^ {E ^ {r}}\right)}{\pi_ {\hat {\mathcal {M}}} \left(\mathcal {P} _ {H _ {c} , W _ {c}} ^ {E ^ {r}}\right)}\right)\right) \tag {7}
+$$
+
+where  $\pi_{\mathcal{M}}$  and  $\pi_{\hat{\mathcal{M}}}$  are the policies of layout prediction and reference model respectively, and  $\beta = 0.1$  is a hyperparameter to control divergence from the reference model. We initialize the reference model  $\hat{\mathcal{M}}$  to be the same as the layout prediction model  $\mathcal{M}_{\mathrm{layout}}$  at the start of the training.
+
+Quality Metrics-based Layout Filtering: To ensure high quality layouts are used to train  $\mathcal{M}_{\mathrm{layout}}$  through AAPA, we enforce a data filtration process based on quality metrics that evaluate the alignment and overlap of the predicted bounding boxes. The goal is to maximize alignment between design elements while minimizing overlap, ensuring that the selected layouts are aesthetically pleasing and well-structured. For each design element  $e_i$ , let  $\theta_i = (x_i^L, y_i^T, x_i^C, y_i^C, x_i^R, y_i^B)$  represents the top-left  $(x_i^L, y_i^T)$ , center  $(x_i^C, y_i^C)$ , and bottom-right  $(x_i^R, y_i^B)$  coordinates of the bounding box. We compute the minimum distance between the key coordinates of element  $e_i$  and all of those other elements  $e_j$  ( $j \neq i$ ), to find the adjacent element with respect to the key coordinates and compute alignment quality metric  $\mathcal{Q}_{\mathrm{align}}$ , depicted by Eq.8.
+
+$$
+\mathcal {Q} _ {\text {a l i g n}} (G) = \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {\min  \left(f \left(\Delta x _ {i} ^ {*}\right) , f \left(\Delta y _ {i} ^ {*}\right)\right) - 1}{e - 1} \tag {8}
+$$
+
+where  $f(x) = \exp (1 - x)$ ,  $\Delta x_{i}^{*}\in \{\Delta x_{i}^{L},\Delta x_{i}^{C},\Delta x_{i}^{R}\}$  and  $\Delta y_{i}^{*}\in \{\Delta y_{i}^{T},\Delta y_{i}^{C},\Delta y_{i}^{B}\}$ . The horizontal and vertical distances are computed as  $\Delta x_{i}^{*} = \min_{j\neq i}|x_{i}^{*} - x_{j}^{*}|$ , and  $\Delta y_{i}^{*} = \min_{j\neq i}|y_{i}^{*} - y_{j}^{*}|$  respectively. Similarly, we compute the average overlap of an element  $e_i$  with all other elements  $e_j$  and define  $\mathcal{Q}_{\mathrm{overlap}}$  using Eq. 9.
+
+$$
+\mathcal {Q} _ {\text {o v e r l a p}} (G) = \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {j \neq i} \left(1 - \frac {\operatorname {A r e a} \left(e _ {i} \cap e _ {j}\right)}{\operatorname {A r e a} \left(e _ {i}\right)}\right) \tag {9}
+$$
+
+where,  $\mathrm{Area}(e_i \cap e_j)$  denotes the area of intersection between element  $e_i$  and  $e_j$  and  $\mathrm{Area}(e_i)$  denotes the area of element  $e_i$ . Ideally, we want overlap to be less, and therefore higher  $\mathcal{Q}_{\mathrm{overlap}}$  denotes lesser overlap. We compute the overall quality metric  $\mathcal{Q}(G)$  for a graphic layout  $G$  by taking the average of the alignment score  $\mathcal{Q}_{\mathrm{align}}$  and the overlap score  $\mathcal{Q}_{\mathrm{overlap}}$ . For a given layout  $G_s$ , if its quality metric satisfies  $\mathcal{Q}(G_s) > \mu_{\mathcal{Q}} - \sigma_{\mathcal{Q}}$ , i.e., the quality metric exceeds one standard deviation below the mean quality metric across the entire dataset, we classify it as a higher-quality layout. By applying this data filtration process, we enhance the overall quality of the training data, which in turn helps to effectively train the layout model  $\mathcal{M}_{\mathrm{layout}}$ .
+
+Aesthetic-Aware Layout Evaluation: To evaluate the aesthetic quality of predicted layouts, we employ the judge model  $\mathcal{M}_{\mathrm{judge}}$  to perform pairwise comparisons between predicted layouts and their corresponding ground truth layouts. For a test dataset  $\mathcal{D}_{\mathrm{test}}$  containing  $S$  samples, let  $G_{p}^{i} = \mathcal{R}(\pi_{\mathcal{M}}(\mathcal{P}_{H_{c},W_{c}}^{E^{i}},W_{c}^{i},H_{c}^{i})$  be the predicted layout and  $G_{g}^{i} = \mathcal{R}(E^{i},W_{c}^{i},H_{c}^{i})$  be the ground truth layout for the  $i$ -th sample. The win rate  $\mathcal{W}$  is computed as:
+
+$$
+\mathcal {W} = \frac {1}{S} \sum_ {i = 1} ^ {S} \mathbb {I} \left\{\mathcal {M} _ {\text {j u d g e}} \left(\mathcal {P} _ {\text {j u d g e}}, G _ {p} ^ {i}, G _ {g} ^ {i}\right) = 1 \right\} \tag {10}
+$$
+
+where  $\mathbb{I}(\cdot)$  is the indicator function that returns 1 if the predicted layout wins over the ground truth layout in the aesthetic comparison, and 0 otherwise. A higher win rate indicates that the layout model  $\mathcal{M}_{\mathrm{layout}}$  generates layouts that are aesthetically superior to the ground truth layouts.
+
+# 3.4. Pre-training to Enhance Layout Understanding
+
+To further explore the role of data size for pretraining data hungry MLLM's, we trained our model on an 80,000 template dataset collected from an online design creation platform. This pretraining phase aims to imbue the model with foundational design principles, such as minimizing element overlap, enhancing alignment, and prioritizing salient regions for important elements. Our experiments reveal that pretraining before position-aware layout instruction tuning significantly boosts the model's aesthetic sensitivity, as evidenced by improvements in alignment with design principles when compared to models trained without pretraining.
+
+# 4. Experimental Details
+
+Datasets: We evaluate AesthetiQ on two benchmark graphic layout datasets: Crello [50] and WebUI [49], both posing unique challenges. Crello dataset contains 23,302 vector-based design templates across various formats (e.g., social media posts, banners), split into 19,479 training, 1,852 validation, and 1,971 test samples. Its primary challenge lies in handling diverse canvas sizes and aspect ratios while maintaining design consistency. WebUI dataset comprises 70k web page UIs, including visual screenshots and metadata. WebUI's challenges stem from variability in web page structures across domains. Both datasets test the model's ability to manage complex layouts and ensure semantic coherence across diverse design structures.
+
+Implementation Details: For our layout prediction model  $\mathcal{M}_{\mathrm{layout}}$ , we use InternVL [9] as the backbone, given its robust spatial understanding and visual reasoning capabilities across diverse tasks like DocVQA [36], TextVQA [44], MME [13], MMMU [53], and MMVET [52]. InternVL's multi-image training aligns well with layout prediction, where interpreting contextual relationships between multiple elements is crucial. For judging layouts based on aesthetics, we leverage VILA-7B [31] as  $\mathcal{M}_{\mathrm{judge}}$ . We train AesthetiQ for 20 epochs on an effective batch size of 128 using 8 80GB A100 GPUs. Position coordinates are discretized with  $K = 224$  tokens, and  $\mathcal{M}_{\mathrm{layout}}$  is optimized using a learning rate of  $4e^{-5}$ , weight decay of 0.01, and Cosine Annealing [34] with warmup ratio 0.03 through the AdamW optimizer [35]. Layout preferences for AAPA are obtained by randomly choosing between comparing two model-predicted layouts or comparing a model-predicted layout with the ground truth.
+
+Evaluation Protocol: To assess the effectiveness of AAPA, including pre-training and quality-metric-based filtering, we evaluate two key metrics: Mean Intersection over Union (mIoU) and  $\mathcal{M}_{\mathrm{judge}}$  win rate. The mIoU is computed across three different inference settings: All (predicting the position of all elements), Single (predicting the position of a single text element), and Multiple (predicting the position of all text elements). This allows us to evaluate the model's ability to accurately predict layout configurations under varying levels of complexity. The  $\mathcal{M}_{\mathrm{judge}}$  win rate is calculated in the All inference mode and evaluates the aesthetic quality of generated layouts by comparing them against ground truth using  $\mathcal{M}_{\mathrm{judge}}$ . This dual-metric evaluation ensures a comprehensive assessment of both spatial accuracy and subjective visual appeal.
+
+# 5. Results and Analysis
+
+Comparison of AesthetiQ with baselines: Table 1 compares layout generation methods on the Crello dataset, showcasing the superior performance of our AesthetiQ
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Mean IoU (%)</td><td rowspan="2">MjudgeWin Rate (%)</td></tr><tr><td>All</td><td>Single</td><td>Multiple</td></tr><tr><td>SmartText+[27]</td><td>-</td><td>4.7</td><td>2.3</td><td>-</td></tr><tr><td>Typography LMM[21]</td><td>-</td><td>40.2</td><td>17.2</td><td>-</td></tr><tr><td>FlexDM[20]</td><td>12.71</td><td>35.5</td><td>10.3</td><td>0.93</td></tr><tr><td>LACE [8]</td><td>23.18</td><td>41.96</td><td>21.49</td><td>3.51</td></tr><tr><td>PosterLLaVa[51]</td><td>25.18</td><td>42.74</td><td>23.58</td><td>5.03</td></tr><tr><td>LayoutNUWA[45]</td><td>25.74</td><td>43.83</td><td>24.16</td><td>5.58</td></tr><tr><td>AesthetiQ-1B</td><td>22.85</td><td>40.83</td><td>26.55</td><td>2.43</td></tr><tr><td>AesthetiQ-2B</td><td>28.19</td><td>45.92</td><td>30.44</td><td>6.13</td></tr><tr><td>AesthetiQ-4B</td><td>38.16</td><td>49.27</td><td>37.14</td><td>14.74</td></tr><tr><td>AesthetiQ-8B</td><td>42.83</td><td>52.67</td><td>40.64</td><td>17.19</td></tr></table>
+
+Table 1. Comparison of layout generation methods based on Mean IoU (\%) and Judge Win Rate (\%) on Crello Dataset. AesthetiQ models outperform baselines, achieving higher IoU and Judge Win Rate, with AesthetiQ-8B showing the best overall performance.  
+
+<table><tr><td>Method</td><td>Mean IoU (%)</td><td>Mjudge</td><td>Win Rate (%)</td></tr><tr><td>Desigen[49]</td><td>15.36</td><td>4.81</td><td></td></tr><tr><td>LACE[8]</td><td>17.88</td><td>5.27</td><td></td></tr><tr><td>PosterLLaVa[51]</td><td>30.19</td><td>14.73</td><td></td></tr><tr><td>LayoutNUWA[45]</td><td>32.16</td><td>15.28</td><td></td></tr><tr><td>AesthetiQ-1B</td><td>38.47</td><td>19.29</td><td></td></tr><tr><td>AesthetiQ-8B</td><td>48.29</td><td>24.48</td><td></td></tr></table>
+
+Table 2. Comparison of AesthetiQ with baseline methods based on Mean IoU (%) and Judge Win Rate (%) on WebUI Dataset, showcasing significantly superior performance of AesthetiQ.
+
+models across multiple metrics. AesthetiQ-8B achieves the highest Mean IoU scores, with  $42.83\%$  in the All setting,  $52.67\%$  in the Single setting, and  $40.64\%$  in the Multiple setting, significantly surpassing baselines like LACE [8] (23.18% in All) and LayoutNUWA [45] (25.74% in All). Additionally, AesthetiQ-8B achieves the best  $\mathcal{M}_{\mathrm{judge}}$  win rate of  $17.19\%$ , highlighting its ability to produce layouts that are both geometrically precise and aesthetically appealing. These consistent improvements in mIoU and judge win rate reflect AesthetiQ's capacity to model intricate design structures while integrating aesthetic constraints, resulting in layouts that better align with judge preferences compared to other methods like FlexDM [20] and SmartText+ [27], which perform poorly across both metrics. Moreover, multi-modal LLM-based methods such as PosterLLaVa [51] and LayoutNUWA also fall short of AesthetiQ-8B, underscoring the robustness of our approach in handling diverse layout configurations while maintaining high visual quality. We also train and evaluate AesthetiQ with Gpt4o as a judge to further highlight the robustness of our approach in supplementary.
+
+Table 2 further demonstrates that AesthetiQ models significantly outperform all baselines on the WebUI dataset across both metrics. For instance, AesthetiQ-8B achieves a remarkable Mean IoU of  $48.29\%$  and a judge win rate
+
+![](images/a682e4e691065a7baa209a4e5450d40b8f0548004b32f2385aef747f1b466b16.jpg)  
+Figure 3. Qualitative comparison of our model, AesthetiQ, against recent methods FlexDM, LACE, and LayoutNUWA. Despite the challenge of arranging numerous elements, AesthetiQ consistently achieves superior layout quality. In row (a), AesthetiQ effectively places text within salient regions, maintaining clear hierarchy and avoiding overlaps, which enhances readability and aesthetic appeal. In row (b), it achieves precise alignment across elements and optimally positions diverse shapes, preserving a cohesive visual structure. Row (c) showcases AesthetiQ's advanced semantic understanding, generating a visually balanced and aesthetically pleasing layout. Overall, AesthetiQ consistently outperforms competitors in creating coherent, well-structured designs that align with human aesthetic preferences.
+
+of  $24.48\%$ , well above LayoutNUWA, the top-performing baseline, which scores  $32.16\%$  in Mean IoU and  $15.28\%$  in win rate. Even smaller variants, like AesthetiQ-1B, exhibit strong performance with a Mean IoU of  $38.47\%$  and a judge win rate of  $19.29\%$ . In contrast, previous methods such as Desigen [49] (15.36% IoU, 4.81% win rate) and LACE (17.88% IoU, 5.27% win rate) perform significantly worse. These results highlight AesthetiQ's strength in producing layouts that are not only more accurate but also more aesthetically pleasing.
+
+Qualitative Results: Figure 3 presents a qualitative comparison of AesthetiQ against strong baselines. In row (a), AesthetiQ skillfully places text in prominent areas, establishing a clear hierarchy and avoiding overlaps, which improves readability and visual appeal. Row (b) highlights AesthetiQ's precise alignment of elements and optimal positioning of various shapes, resulting in a unified visual layout. In row (c), AesthetiQ demonstrates its advanced semantic understanding, producing a balanced and aesthetically pleasing design. Overall, AesthetiQ consistently surpasses baselines by generating coherent, well-structured layouts that align with human aesthetic preferences. A user study, detailed in the Appendix, shows that AesthetiQ was consistently the top choice for predicted layouts compared to FlexDM, LACE, and LayoutNUWA. Additionally, human preferences exhibit a high correlation of  $78\%$  and  $88\%$
+
+with the preference distribution of the judge models Vila and GPT-4o, respectively.
+
+Larger Models Capture Aesthetics Better: Scaling up model size significantly improves layout generation performance. As seen in Fig 4, larger models outperform smaller ones in the metrics All, Single, Multiple IoU, and Judge Win Rate. For example, moving from 1B to 8B parameters boosts the Judge Win Rate from  $2.43\%$  to  $17.19\%$ , suggesting larger models better capture aesthetic nuances and complex spatial relationships. This trend indicates a strong alignment between model scale and the ability to reflect aesthetic preferences, making larger models more suited for aesthetic-aware layout generation. Further, this also showcases the difficulty of the layout generation task.
+
+Pre-training Enhances Layout Understanding: Pretraining with a large dataset of 80,000 templates enhances the model's grasp of layout structuring, providing a strong foundation for fine-tuning and AAPA. Models pretrained on this dataset show improvements across metrics. For instance, pretraining raises the 8B model's IoU from  $37.64\%$  to  $40.81\%$ . This phase equips models with essential layout generation and understanding capabilities, which AAPA further refines to achieve aesthetic alignment.
+
+Quality-metrics Based Layout Filtering Improves AAPA Training: Quality filtering, guided by alignment maximization and overlap minimization heuristics, enhances model
+
+![](images/9987d1281c71e9e61398da225e31fffc5fc5f36a39f51386ea63dd232eeff995.jpg)  
+Figure 4. Performance improvement across scale (1B-8B parameters) for layout generation, showing effects of pretraining, quality filtering, and Aesthetic-Aware Preference Alignment (AAPA). Left: IoU progression under different training configurations. Middle:  $\mathcal{M}_{\mathrm{judge}}$  Win Rate improvements, emphasizing the impact of AAPA and pretraining. Right: Configuration table indicating settings for each experiment. The results underscore the impact of each design component in AesthetiQ, emphasizing their role in tackling layout generation challenges.
+
+performance by selecting high-quality layouts for training. Without filtering, aesthetic quality and layout coherence decline, as suboptimal samples impact learning. AAPA's performance drops without filtering, with decreases in IoU across scales. Quality filtering boosts the 4B model's IoU by  $4.97\%$  and Judge Win Rate by  $2.56\%$ , highlighting its importance in maintaining aesthetic standards.
+
+Effect of AAPA on Performance: AAPA considerably enhances the aesthetic quality of generated layouts by aligning them with preferences derived from Multi-modal Large Language Models (VLMs). This preference-based alignment improves the Judge Win Rate, guiding the model towards aesthetically pleasing layouts rather than exact ground truth matches. AesthetiQ-1B model shows limited gains, as it faces challenges in producing high-quality layouts during sampling, limiting the effectiveness of preference optimization. However, AAPA-trained larger models demonstrate superior performance on Crello and WebUI benchmarks across metrics, underscoring the value of preference-based training in aesthetic-sensitive tasks.
+
+Generating Layouts with Different Aspect Ratios: Layouts must adapt to various aspect ratios across platforms. Our model maintains stable performance across common aspect ratios like 4:3, 16:9, and square formats, effectively rearranging elements to fit different dimensions. As shown in Fig 5, the model consistently produces visually balanced layouts for diverse aspect ratios, demonstrating its flexibility and robustness in generating aesthetically coherent layouts across various screen requirements.
+
+# 6. Conclusion
+
+In this work, we introduced Aesthetic-Aware Preference Alignment (AAPA), a novel approach for training Multi-modal Large Language Models (MLLMs) in the
+
+![](images/ac022a1f2a83ba335a2532eefade204df26efbf9ac016b9f1ef08afa17bbdc02.jpg)
+
+![](images/b1c7df2535eef33b7f03540eaf3b0a81a8dfc7636b0ef08496912ad0f0ff0504.jpg)  
+Figure 5. Capability of AesthetiQ to generate templates in various aspect ratios by changing the canvas height and width
+
+task of aesthetic-driven layout prediction. By leveraging aesthetic preferences directly through a preference optimization mechanism, AAPA addresses critical limitations of existing generative models that lack contextual aesthetic understanding and alignment with human-like preferences. Our proposed data filtering protocol, based on layout-quality heuristics, ensures that only high-quality layouts contribute to training, further enhancing model performance. Additionally, we propose a novel metric to evaluate the aesthetic superiority of generated layouts over ground truth, enabling a more holistic assessment.
+
+# References
+
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\ No newline at end of file
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+# Aesthetic Post-Training Diffusion Models from Generic Preferences with Step-by-step Preference Optimization
+
+Zhanhao Liang $^{1}$ , Yuhui Yuan $^{5}$ , Shuyang Gu $^{5}$ , Bohan Chen $^{2}$ , Tiankai Hang $^{3}$ , Mingxi Cheng $^{4}$ , Ji Li $^{4}$ , Liang Zheng $^{1}$ $^{1}$ The Australian National University  $^{2}$ University of Liverpool  
+ $^{3}$ Southeast University  $^{4}$ Microsoft  $^{5}$ Microsoft Research Asia
+
+![](images/c987faf8253186de45dd3abf57f7b50bc5d2d2bcb68bbc62d9bf03b1505abef4.jpg)  
+Figure 1. Problem illustration of existing DPO methods. We show two denoising trajectories of a preferred image (a) and a dispreferred image (b) generated from prompt "A cat jumps on a dog". (1) Disagreement between generic preferences and aesthetic preference. While (a) is preferred due to its better layout, its details are poorer than (b). Red boxes show the erroneous fusion of the cat's leg and the dog's body. (2) Large sample differences between trajectories. This makes it difficult to identify subtle aesthetic-related differences at each step.
+
+# Abstract
+
+Generating visually appealing images is fundamental to modern text-to-image generation models. A potential solution to better aesthetics is direct preference optimization (DPO), which has been applied to diffusion models to improve general image quality including prompt alignment and aesthetics. Popular DPO methods propagate preference labels from clean image pairs to all the intermediate steps along the two generation trajectories. However, preference labels provided in existing datasets are blended with layout and aesthetic opinions, which would disagree with aesthetic preference. Even if aesthetic labels were provided (at substantial cost), it would be hard for the two-trajectory methods to capture nuanced visual differences at different steps. To improve aesthetics economically, this paper uses existing generic preference data and introduces step-by-step preference optimization (SPO) that discards the propagation strategy and allows fine-grained image details to be assessed. Specifically, at each denoising step, we 1) sample a pool of candidates by denoising from a shared noise latent, 2) use a step-aware preference model to find a suitable win-lose pair to supervise the diffusion model, and 3) randomly select one from the pool to initialize the next de
+
+noising step. This strategy ensures that diffusion models focus on the subtle, fine-grained visual differences instead of layout aspect. We find that aesthetics can be significantly enhanced by accumulating these improved minor differences. When fine-tuning Stable Diffusion v1.5 and SDXL, SPO yields significant improvements in aesthetics compared with existing DPO methods while not sacrificing image-text alignment compared with vanilla models. Moreover, SPO converges much faster than DPO methods due to the use of more correct preference labels provided by the step-aware preference model. Code and models are available at https://github.com/RockeyCoss/SPO.
+
+# 1. Introduction
+
+This paper aims to improve the ability of diffusion models in generating visually appealing images based on human preference data. That is, given a pool of image pairs and human preference within each pair, we fine-tune diffusion models so that they are more likely to generate images consistent with human aesthetic preference<sup>1</sup>.
+
+![](images/c71466b242bd7122ed7166a5392472f99108d32cbc20c1eae732d8b60b4166e1.jpg)  
+Figure 2. Qualitative comparison between Vanilla SDXL, Diffusion-DPO-SDXL and SPO-SDXL. SPO-SDXL exhibits very strong image aesthetics including more visual details and appealing styles. Prompts are provided in the supplementary material.
+
+Direct preference optimization (DPO) is shown to be effective for aligning diffusion models with human preferences in general aspects such as image-text alignment [29]. Given a pair of images generated from the same prompt, DPO methods encourage predictions to align with the preferred image while discouraging resemblance to the dispreferred one. A few existing studies use human preferences at timestep 0 with clean images  $\boldsymbol{x}_0^w$  and  $\boldsymbol{x}_0^l$ , where  $w$  and  $l$  are win and lose preference labels, respectively [21, 29, 32]. The labels are directly propagated to intermediate samples along the two trajectories, assuming all intermediate samples along the win trajectory are also preferred.
+
+However, for two problems existing systems are not best effective for aesthetic alignment. First, generic preferences provided in public datasets like Pick-a-Pic [11] are not aesthetics specific, and they often disagree. In Fig. 1, (a) is generally preferred because of the correctly generated dog, cat, and their spatial arrangement, but in terms of aesthetics, (a) should be dispreferred. More examples are provided in the supplementary material. This introduces noisy supervision signals and compromises the model improvement towards better aesthetics. Technically, this problem can be fixed by manually annotating an aesthetics-only preference dataset, but it is very expensive, because of layout influence and complexity of aesthetics. Second, in two-trajectory methods, the images within each pair at each denoising step look very different, as shown in Fig. 1. Even if accurate aesthetic preference was provided at each step (at great cost), it would still be very non-trivial to learn, because the large layout discrepancy would dominate over aesthetic nuances.
+
+To better align diffusion models with aesthetic preference, we introduce step-by-step preference optimization (SPO). SPO is new in that it completely discards the current preference propagation strategy, pushing for evaluating
+
+image details. Specifically, at each step beginning with a noisy image  $\boldsymbol{x}_t$ , we generate a pool of  $\boldsymbol{x}_{t-1}$  samples. We evaluate their quality using a step-aware preference model (SPM) and assign win/lose labels to the pair showing the largest quality difference. We then randomly select an image from the pool to initialize timestep  $t - 1$ . Because the win-lose pair 1) comes from the same image and 2) is generated in one or very few steps, the two samples would only exhibit small differences in details. SPM allows us to capture such detailed differences and guide the diffusion model to generate more visually pleasing images.
+
+We use SPO to fine-tune Stable Diffusion v1.5 (SD1.5) [23] and SDXL [18]. Although we use a training set with generic human perferences [11], we demonstrate significant improvement in aesthetics compared with those fine-tuned by popular DPO methods. Moreover, SPO converges much faster than Diffusion-DPO. This is because the step-by-step design makes it easier to focus on fine-grained visual details, and SPM produces more accurate preference labels. We summarize key points of this paper below.
+
+- We aim to improve image aesthetics of diffusion models.  
+- We point out that generic human preferences are often different from pure aesthetic preference and that obtaining aesthetic-only preference data is very expensive.  
+- We design SPO, where we determine win-lose pairs at each step in an online manner. We make sure win-lose pairs come from the same noisy sample, so after one or very few steps of denoising their differences are small and in fine-grained details, and can be captured by a preference model trained with generic preference data.  
+- When fine-tuning SD-1.5 and SDXL, SPO is more effective in enhancing image aesthetics compared with DPO methods, and converges faster than Diffusion-DPO [29].
+
+# 2. Related Work
+
+Recently, inspired by post-training methods that improve LLMs, e.g., reinforcement learning from human feedback (RLHF) [16, 35], various post-training methods are proposed to align pre-trained diffusion models with human preferences. For example, Chen et al. [2] leverage the PPO loss [26] to fine-tune the text encoder of diffusion models. AligningT2I [13] develops a reward model to evaluate the quality of generated images and fine-tunes the diffusion model using image-text pairs, weighted by assessment of the reward model. DPOK [7] and DDPO [1] use policy gradient to fine-tune diffusion models, aiming at maximizing reward signals. Furthermore, ReFL [31], DRaFT [3], and AlignProp [19] directly propagate the gradients through differentiable reward models to fine-tune the denoising steps. Recent methods are inspired by direct preference optimization (DPO) [21], which eliminates the need for explicit reward models when post-training LLMs. Diffusion-DPO [29] fine-tunes diffusion models on the Pick-a-Pic [11] dataset that contains image preference pairs. D3PO [32] generates pairs of images from the same prompt and uses a preference model to identify preferred and dispreferred images. DenseReward [33] improves the DPO scheme with a temporal discounting approach to emphasize initial denoising steps. These methods optimize the trajectory-level preference, where the accumulated image differences are too large to allow the network to focus on aesthetics subtleties. In comparison, SPO by its step-by-step mechanism can focus on nuanced visual differences in just a single or few steps.
+
+# 3. DPO Revisit and Diagnosis
+
+General formulation. Given a generation model  $\pi_{\theta}(\cdot)$  and a condition  $c$ , the probability of generating output  $o$  is  $\pi_{\theta}(o \mid c)$ . We use  $\pi_{\theta}(\cdot)$  to generate a set of output pairs  $S$ , where each pair comes from the same condition  $c$ . Human or preference model is employed to label the preference order of the output pairs as  $(o^w, o^l, c)$ , where  $o^w$  is the preferred output and  $o^l$  is dispreferred. According to Rafailov et al. [21], the DPO loss used to fine-tune  $\pi_{\theta}$  is defined as:
+
+$$
+\mathcal {L} _ {\mathcal {D P O}} = - \mathbb {E} _ {(o ^ {w}, o ^ {l}, c) \sim \mathcal {S}} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\theta} (o ^ {w} | c)}{\pi_ {\text {r e f}} (o ^ {w} | c)} - \beta \log \frac {\pi_ {\theta} (o ^ {l} | c)}{\pi_ {\text {r e f}} (o ^ {l} | c)}\right) \right]. \tag {1}
+$$
+
+$\pi_{\mathrm{ref}}(\cdot)$  and  $\sigma (\cdot)$  refer to the reference model and the sigmoid function, respectively.  $\beta$  is the strength of regularization.
+
+DPO for diffusion model post-training. We denote the text-to-image diffusion model with parameters  $\theta$  as  $p_{\theta}$  and text prompt as  $c$ . The denoising process generates intermediate states  $\{\pmb{x}_T, \pmb{x}_{T-1}, \dots, \pmb{x}_1, \pmb{x}_0\}$ . Existing works including Diffusion-DPO [29] and D3PO [32] measure preference based on the final image  $\pmb{x}_0$  and assign the preference for  $\pmb{x}_0$  directly to the entire generation trajectory, or all the in
+
+intermediate states. Let  $\mathcal{T}_w$  and  $\mathcal{T}_l$  denote the denoising trajectories which generate the preferred and dispreferred images, respectively. Using the Markov property of diffusion models and Jensen's inequality, they reformulate the general DPO loss in Eq. 1 into the following step-wise form:
+
+$$
+\mathcal {L} _ {\mathcal {D P O} - \mathcal {D}} = - \underset {\left( \begin{array}{l} \boldsymbol {x} _ {t - 1} ^ {w}, \boldsymbol {x} _ {t} ^ {w} \end{array} \right) \sim \mathcal {T} _ {w}} {\mathbb {E} _ {\left(\boldsymbol {x} _ {t - 1} ^ {l}, \boldsymbol {x} _ {t} ^ {l}\right) \sim \mathcal {T} _ {l}}} \left[ \log \sigma \left(\beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid \boldsymbol {x} _ {t} ^ {w} , c\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid \boldsymbol {x} _ {t} ^ {w} , c\right)} - \beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid \boldsymbol {x} _ {t} ^ {l} , c\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid \boldsymbol {x} _ {t} ^ {l} , c\right)}\right) \right], \tag {2}
+$$
+
+where  $\mathcal{L}_{\mathcal{DPO} - \mathcal{D}}$  encourages denoising steps to progress towards the preferred image and away from dispreferred one.
+
+Diagnosis on aesthetic alignment. Aligning diffusion models with human aesthetic preference is very challenging. From architecture, win-lose pairs in the two-trajectory methods usually differ significantly (primarily in layout), rendering it hard to focus on image detail comparisons. From data, existing aesthetic scoring datasets [15, 25] do not provide paired image data coming from the same prompt. Collecting a dedicated aesthetic preference dataset would be more costly compared with tasks like classification or prompt alignment preference. So a cost-efficient choice is existing generic preference datasets where annotators were asked to score images based on holistic opinions like prompt alignment and aesthetics. However as pointed out in Section 1, generic preferences may be contradictory to aesthetic preference. If we directly propagate them to all diffusion steps like Diffusion-DPO and D3PO do (see Fig. 3), noisy preferences will compromise fine-tuning.
+
+# 4. Proposed Approach
+
+# 4.1. Framework Overview
+
+To align diffusion models with aesthetic preference while still using generic preferences, we propose step-by-step preference optimization (SPO), an online reinforcement learning method. Fig. 3  $(c)$  depicts its workflow. Given an intermediate  $x_{t}$ , at timestep  $t$ , we sample a pool of denoised samples  $\{\pmb{x}_{t-1}^{1}, \pmb{x}_{t-1}^{2}, \dots, \pmb{x}_{t-1}^{k}\}$ . We apply a step-aware preference model (Section 4.2) to compare the quality of these candidate samples, and select the highest-quality sample and the lowest-quality sample as the win-sample and the lose-sample, respectively. SPO ensures the win-lose pair comes from the same  $x_{t}$  and thus have small differences in image details to reflect aesthetics. We then randomly select a sample from the candidate pool (Section 4.3), which is used to initialize the next iteration. SPO is optimized by a revised DPO loss function (Section 4.4) and can be extended to the SDXL model (Section 4.5).
+
+# 4.2. Step-Aware Preference Model (SPM)
+
+Overall use. SPM predicts preference order among the  $k$  sampled denoised samples  $\{\pmb{x}_{t - 1}^{1},\pmb{x}_{t - 1}^{2},\dots ,\pmb{x}_{t - 1}^{k}\}$ . Thus, SPM takes timestep  $t - 1$ , intermediate sample  $\pmb{x}_{t - 1}$ , and
+
+![](images/c8cba9afc64bbcebea4a5441cd26800621acef760b7b6ddbaea557cb4080e0bf.jpg)
+
+![](images/ec66e3ee7a284ead0cf8ef8b41b1c1d10ab654b245f5debe6a4097f07e5b6cac.jpg)  
+Figure 3. Comparing frameworks of SPO, Diffusion-DPO, and D3PO approaches. SPO does not adopt direct preference propagation as other DPO methods do. In SPO, a pool of samples are generated at each step, from which a proper win/lose pair is selected and used to fine-tune the diffusion model. Then, a single sample is randomly selected to initialize the next iteration.
+
+prompt  $c$  as input, and outputs a quality score. SPM is different from existing preference models. The latter uses clean images  $x_0$  and prompt  $c$  as input without time condition, because they are designed for assessing clean images. Following [11], we construct SPM based on CLIP [20].
+
+For SPM training, we initialize the model with PickScore [11] and fine-tune it following [4], making the model useful for noisy images. Specifically, we add the same amount of noise to a pair of clean images, assuming that their preference order can be kept. During training, for each pair of images and their human-labeled preference, we randomly sample a timestep  $t$  and add the same noise to both images to obtain  $\boldsymbol{x}_t^w$  and  $\boldsymbol{x}_t^l$ . Then we feed the noisy intermediate pair  $\{\boldsymbol{x}_t^w, \boldsymbol{x}_t^l\}$  and timestep  $t$  to SPM and train the model to correctly predict the preference, using loss function  $\mathcal{L}_{\mathrm{pref}} = (\log 1 - \log \hat{p}_w)$ , where  $\hat{p}_w$  is the probability of the win image being the preferred one, following [11].  $\hat{p}_w$  is computed using the following equation:
+
+$$
+\hat {p} _ {w} = \frac {\exp \left(\tau \cdot f _ {\mathrm {C L I P - V}} \left(\boldsymbol {x} _ {t} ^ {w} , t\right) \cdot f _ {\mathrm {C L I P - T}} (c)\right)}{\exp \left(\tau \cdot f _ {\mathrm {C L I P - V}} \left(\boldsymbol {x} _ {t} ^ {w} , t\right) \cdot f _ {\mathrm {C L I P - T}} (c)\right) + \exp \left(\tau \cdot f _ {\mathrm {C L I P - V}} \left(\boldsymbol {x} _ {t} ^ {l} , t\right) \cdot f _ {\mathrm {C L I P - T}} (c)\right)}, \tag {3}
+$$
+
+where  $c$  represents the text prompt,  $\tau \in \mathcal{R}$  is a temperature.  $f_{\mathrm{CLIP - V}}(\cdot)$  and  $f_{\mathrm{CLIP - T}}(\cdot)$  are the vision and text encoders of CLIP, respectively. To allow for timestep-conditional preference prediction, we modify the CLIP vision encoder using time-conditional adaptive layernorm [17]. To alleviate the domain gap between the noised image at the  $t$ -th timestep and images used to train the PickScore model, we estimate  $\hat{x}_0$  from the noisy sample directly, following DDIM [28].
+
+# 4.3. Random Selection of  $x_{t}$  to Start Next Step
+
+In SPO, we randomly sample  $\boldsymbol{x}_t$  from the candidate pool  $\{\boldsymbol{x}_t^1, \boldsymbol{x}_t^2, \dots, \boldsymbol{x}_t^k\}$ , which is then used to start the next denoising step. This ensures every win-loss pair comes from the same latent. Since  $\boldsymbol{x}_t$  is very noisy when  $t$  is large, we use the standard diffusion sampling process when  $t$  is greater than the threshold  $\kappa$ . Only when  $t \leq \kappa$  do we sample candidate pools and apply random selection. This random selection is shown in Fig. 3 (c): selection of  $\boldsymbol{x}_{t-1}$  is depicted and is consistent with the above discussion.
+
+# 4.4. Objective Function of SPO
+
+At the  $t$ -th denoising timestep, we sample a pool of candidates  $\{\pmb{x}_{t-1}^1, \pmb{x}_{t-1}^2, \dots, \pmb{x}_{t-1}^k\}$  and use the step-aware preference model to construct a preference pair  $(\pmb{x}_{t-1}^w, \pmb{x}_{t-1}^l)$ , where  $\pmb{x}_{t-1}^w$  and  $\pmb{x}_{t-1}^l$  are the most and least preferred in the pool. Using various prompts, we can obtain many preference pairs at  $t$ -th timestep. Using the general form of DPO loss in Eq. 1, the SPO objective at the  $t$ -th timestep is:
+
+$$
+\begin{array}{l} \mathcal {L} _ {t} (\boldsymbol {\theta}) = - \mathbb {E} _ {c \sim p (c), \boldsymbol {x} _ {t - 1} ^ {w}, \boldsymbol {x} _ {t - 1} ^ {l}} \sim_ {p \theta} (\boldsymbol {x} _ {t - 1} | c, t, \boldsymbol {x} _ {t}) \\ \left. \left[ \log \sigma \left(\beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid c , t , \boldsymbol {x} _ {t}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid c , t , \boldsymbol {x} _ {t}\right)} - \beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid c , t , \boldsymbol {x} _ {t}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid c , t , \boldsymbol {x} _ {t}\right)}\right) \right], \right. \tag {4} \\ \end{array}
+$$
+
+where  $c$  is the prompt and  $p(c)$  is the distribution of prompts. By combining the SPO objectives across all  $T$
+
+![](images/2df43043157df5f1d5fa476cc3a60294d274154b9c181ebef13d6167200ec7b3.jpg)  
+Figure 4. Framework of multi-step-by-step preference optimization (MSPO). From  $\pmb{x}_t$ , we first sample  $k$  latents  $\{\pmb{x}_{t-1}^1, \pmb{x}_{t-1}^2, \dots, \pmb{x}_{t-1}^k\}$  as SPO does. For each latent, we perform multiple (i.e.,  $j$ ) denoising steps to obtain  $\{\pmb{x}_{t-j}^1, \pmb{x}_{t-j}^2, \dots, \pmb{x}_{t-j}^k\}$ , from which a win-lose pair is selected by SPM. Then we apply random selection and iterations in the same manner as SPO.
+
+timesteps, we obtain the final SPO objective:
+
+$$
+\mathcal {L} (\theta) = - \mathbb {E} _ {t \sim \mathcal {U} [ 1, T - \kappa ]}, c \sim p (c), x _ {T} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), \boldsymbol {x} _ {t - 1} ^ {w}, \boldsymbol {x} _ {t - 1} ^ {t} \sim p _ {\theta} (\boldsymbol {x} _ {t - 1} | c, t, \boldsymbol {x} _ {t})
+$$
+
+$$
+\left. \left[ \log \sigma \left(\beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid c , t , \boldsymbol {x} _ {t}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {w} \mid c , t , \boldsymbol {x} _ {t}\right)} - \beta \log \frac {p _ {\theta} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid c , t , \boldsymbol {x} _ {t}\right)}{p _ {\text {r e f}} \left(\boldsymbol {x} _ {t - 1} ^ {l} \mid c , t , \boldsymbol {x} _ {t}\right)}\right) \right], \right. \tag {5}
+$$
+
+where  $\mathcal{U}$  and  $\mathcal{N}$  are the uniform distribution and Gaussian distribution, respectively.
+
+# 4.5. Extension to Multi-step Preference Optimization for SDXL
+
+For stronger models like SDXL, we observe that the difference between  $\pmb{x}_t$  and  $\pmb{x}_{t-1}$  is too small, so is the difference between the selected candidates  $\pmb{x}_{t-1}^w$  and  $\pmb{x}_{t-1}^l$ . While a relatively small difference allows SPM to focus on image details, that difference is too small would create ambiguities and confuse fine-tuning. To address this issue, we expand step-by-step preference optimization to multi-step preference optimization (MSPO), which uses multiple denoising steps to increase the diversity of the candidate set (see Fig. 4). This simple extension allows us to select more different samples and more clear preference signals.
+
+# 4.6. Discussions and Insights
+
+DPO for diffusion model vs. language model. Diffusion models involve many intermediate steps, each producing a latent feature/image. In contrast, language models typically predict the final result at each position with a single step without iterative refinement. This distinction necessitates specific DPO design in diffusion models.
+
+SPO is an implicit aesthetic optimizer and distiller. We do not use a dedicated aesthetic preference dataset. Aesthetic optimization is done implicitly through SPM, which is trained to perceive image quality from generic opinions. When the two images to be compared are relatively similar, the output from SPM thus mainly describes image details instead of significant layout differences. Sample win-lose
+
+![](images/d0a48eb8f7f3524d4464ecd753470bd0cde164922f9f5a8ad3278daf10854d0e.jpg)  
+Figure 5. Win-lose pairs identified by the SPM during fine-tuning. Top: Preferred images. Bottom: Dispreferred images. In SPO, these pairs look similar so image details can be focused on. From these pairs, SPM favors images with fewer artifacts in (a) and (b) and more refined details in (c) and (d). These images appear blurry because for visualization purpose we directly predict the clean image from the intermediate noisy latents.
+
+pairs selected by the SPM are shown in Fig. 5. In this way, we are able to distill aesthetic details from generic data.
+
+How often does generic preferences and aesthetic preference disagree? It is hard to quantify because it is non-trivial to annotate a validation set. Fig. 1 and supplementary material depict some disagreement scenarios based on careful manual inspection. In fact, because of the nuanced nature of aesthetics, an image may be superior in certain aesthetic aspects while its paired image is better in other aspects. So there are probably more disagreement scenarios than we can think of now.
+
+Limitations. First, SPO is not applicable to recent flow matching models, such as SD3 [6] and Flux [12] because SPO requires the intermediate steps to be stochastic which flow matching models do not satisfy. Second, SPO is specifically designed to improve aesthetics and offers limited help for improving image-text alignment. Third, we also limit ourselves to learning from crowd-sourced data without tapping into the subjective, political, and historical aspects of aesthetics. It is interesting to study these problems in future.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Datasets. For SPO, we train the step-aware preference model (SPM) on the Pick-a-Pic V1 dataset. This dataset has over 580k labeled image preference pairs, each generated by the same text prompt with various diffusion models [18, 22, 24]. Human annotators were asked to rate the general quality of each image, forming win-lose pairs. When fine-tuning diffusion models with SPO, DDPO or D3PO, we use a subset of 4k prompts (without images) randomly selected from Pick-a-Pic V1, where win-lose pairs are generated online. Note that these three methods do not use images or preference labels but use text prompts only. For DDPO and D3PO, PickScore trained on Pick-a-Pic V1 is used as their reward model to provide guidance. For Diffusion-DPO and MAPO [27], we use their online-available checkpoints for evaluation, which were trained on Pick-a-Pic V2 dataset with over 800k image preference pairs. So overall, SPO and the competitive models are trained on similar datasets and can be fairly compared.
+
+If not specified, we report quantitative results based on the 500 validation prompts, i.e., validation_uniquesplit of Pick-a-Pic [11], which is adopted in [29]. We also use GenEval [8] to evaluate image-text alignment, including rendering of single and two objects, counting, colors, position and attribute binding. There are 553 test prompts.
+
+Evaluation Protocol. This paper evaluates image quality with four automatic metrics. We use PickScore [11], HPSV2 [30] and ImageReward [31] for prompt-aware human preference estimation. These models are trained on human preference datasets and learn to replicate human decisions about which images are more favorable. We use Aesthetic score [25] to evaluate visual appeal. This score is prompt agnostic and employs a linear estimator on top of the vision encoder of CLIP [20] to predict the aesthetic quality of images. Note that PickScore, HPSV2, and ImageReward all assess aesthetics to some extent. Apart from these automatic metrics, we also use human studies. We invite 10 people to assess 300 pairs of images generated by two methods of interest. Their preferences are summarized into winning percentage from 0 to  $100\%$ . The text prompts are randomly selected from PartiPrompts (100 prompts) [34] and HPSV2 benchmark (200 prompts) [30].
+
+Implementation details. We apply DDIM [28] with  $\eta = 1.0$  and 20 timesteps as the sampler and use classifier free guidance [9] with scale 5.0 for sampling during online training. We use LoRA [10] for both SD-1.5 and SDXL, fine-tuning the models for 10 epochs. The LoRA rank is 4 and 64 for SD-1.5 and SDXL, respectively. We set the strength of regularization  $\beta = 10$ . For SD-1.5, we set the batch size as 40 and learning rate as  $6e^{-5}$ . For SDXL, we set the batch size as 8, gradient accumulation as 2, and
+
+Table 1. Method comparison on SDXL. SPO overall yields the best fine-tuning performance especially in aesthetics. Note PickScore, HPSV2, and ImageReward partially assess aesthetics.  
+
+<table><tr><td>Method</td><td>PickScore</td><td>HPSV2</td><td>ImageReward</td><td>Aesthetic</td></tr><tr><td>SDXL</td><td>21.95</td><td>26.95</td><td>0.5380</td><td>5.950</td></tr><tr><td>Diff.-DPO</td><td>22.64</td><td>29.31</td><td>0.9436</td><td>6.015</td></tr><tr><td>MAPO</td><td>22.11</td><td>28.22</td><td>0.7165</td><td>6.096</td></tr><tr><td>SPO</td><td>23.06</td><td>31.80</td><td>1.0803</td><td>6.364</td></tr></table>
+
+Table 2. Comparing different methods on SD-1.5.  
+
+<table><tr><td>Method</td><td>PickScore</td><td>HPSV2</td><td>ImageReward</td><td>Aesthetic</td></tr><tr><td>SD-1.5</td><td>20.53</td><td>23.79</td><td>-0.1628</td><td>5.365</td></tr><tr><td>DDPO</td><td>21.06</td><td>24.91</td><td>0.0817</td><td>5.591</td></tr><tr><td>D3PO</td><td>20.76</td><td>23.97</td><td>-0.1235</td><td>5.527</td></tr><tr><td>Diff.-DPO</td><td>20.98</td><td>25.05</td><td>0.1115</td><td>5.505</td></tr><tr><td>SPO</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr></table>
+
+Table 3. Method comparison on GenEval based on SDXL. †: results are reproduced with a classifier-free guidance scale of 5.0 and 50 inference steps. GenEval evaluates image-text alignment.  
+
+<table><tr><td>Method</td><td>Single Object</td><td>Two Object</td><td>Counting</td><td>Colors</td><td>Position</td><td>Attribute Binding</td><td>Overall</td></tr><tr><td>SDXL†</td><td>97.50</td><td>71.21</td><td>39.06</td><td>84.04</td><td>11.00</td><td>17.75</td><td>53.43</td></tr><tr><td>Diff.-DPO</td><td>99.06</td><td>80.81</td><td>46.56</td><td>88.30</td><td>13.25</td><td>29.50</td><td>59.58</td></tr><tr><td>SPO</td><td>97.81</td><td>73.48</td><td>41.25</td><td>85.64</td><td>13.00</td><td>20.00</td><td>55.20</td></tr></table>
+
+learning rate as  $1e^{-5}$ . Since very noisy images are difficult to compare, we do not use SPM to very early stages. That is, we only compute the preference of  $x_{t}$  when  $t \leq \kappa$  and consider all  $x_{t}$  with  $t > \kappa$  as tied. We empirically set  $\kappa$  as 750 and will evaluate  $\kappa$  in Section 5.4. When fine-tuning SDXL with the MSPO (Section 4.5), we set the number of inner steps to 4. We do not apply SDXL refiner [18] to ensure fair comparison. For SPM training, we adopt learning rates of 3e-6 and 1e-6 for SD-1.5 and SDXL, respectively. We use DDIM scheduler with classifier free guidance scale of 5 and 20 steps to perform inference on validation prompts.
+
+# 5.2. Main Evaluation on Aesthetic Alignment
+
+Automatic metrics. Using the four automatic scores (Section 5.1), we compare SPO with Diffusion-DPO, D3PO, etc., in Table 1 and Table 2 based on SDXL and SD-1.5, respectively. Note that ImageReward, PickScore, and HPSV2 assess overall image quality including aesthetics.
+
+We have two observations. First, compared with vanilla SDXL and SD-1.5, the DPO methods yield consistent improvement in these metrics, demonstrating their effectiveness. Second, we observe that SPO yields the best scores across the four metrics for both SDXL and SD-1.5. For example, for SDXL, we achieve 23.06, 31.80, 1.0803, and 6.364 in PickScore, HPSV2, ImageReward, and Aesthetics, respectively. The improvement over Diffusion-DPO
+
+![](images/5cf56c69e769c11d58cde185cd4e7fe6975c11952fe44e6c134654d2e29f725e.jpg)  
+Win Rate Percentage (%) on 300 prompts sampled from Partiprompt and HPSV2 benchmark  
+Figure 6. User study results comparing SPO with Diffusion-DPO and Vanilla SDXL. We sampled 100 and 200 prompts for evaluation from Participments [34] and HPSV2 benchmark [30], respectively. SPO yields clear improvement in visual appeal.
+
+Table 4. Comparing random sampling with Table 5. Comparing SPM with variants: no Table 6. Impact of number of sampled images other sampling strategies. time condition or the PickScore model [11].  $k$  at each step. We use  $k = 4$ .  
+
+<table><tr><td>Initial.</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>xw t-1</td><td>17.87</td><td>11.31</td><td>-2.2692</td><td>3.963</td></tr><tr><td>xt l t-1</td><td>19.36</td><td>18.63</td><td>-1.3743</td><td>5.338</td></tr><tr><td>random</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr></table>
+
+Table 7. Impact of #inner steps  $j$  when finetuning SDXL with MSPO. We set  $j = 4$ .  
+
+<table><tr><td>#inner steps j</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>1</td><td>22.85</td><td>31.37</td><td>1.0071</td><td>6.359</td></tr><tr><td>2</td><td>22.84</td><td>31.17</td><td>1.0118</td><td>6.268</td></tr><tr><td>3</td><td>22.94</td><td>31.55</td><td>1.0847</td><td>6.380</td></tr><tr><td>4</td><td>23.06</td><td>31.80</td><td>1.0803</td><td>6.364</td></tr><tr><td>5</td><td>23.03</td><td>31.23</td><td>0.9656</td><td>6.423</td></tr><tr><td>6</td><td>22.95</td><td>30.57</td><td>0.9770</td><td>6.390</td></tr></table>
+
+<table><tr><td>Prefer. model</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>SPM</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr><tr><td>w/o step con.</td><td>21.19</td><td>25.84</td><td>0.1365</td><td>5.678</td></tr><tr><td>PickScore</td><td>20.28</td><td>23.09</td><td>-0.2982</td><td>5.410</td></tr></table>
+
+Table 8. Impact of timestep range.  
+
+<table><tr><td>Timestep Range</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>[0-250]</td><td>20.61</td><td>23.34</td><td>-0.1823</td><td>5.413</td></tr><tr><td>[0-500]</td><td>20.69</td><td>25.67</td><td>0.0810</td><td>5.399</td></tr><tr><td>[0-750]</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr><tr><td>[0-1000]</td><td>19.77</td><td>22.72</td><td>-0.4529</td><td>5.111</td></tr><tr><td>[250-750]</td><td>21.19</td><td>26.23</td><td>0.2658</td><td>5.581</td></tr><tr><td>[500-750]</td><td>20.43</td><td>24.91</td><td>-0.1553</td><td>5.582</td></tr><tr><td>[250-500]</td><td>20.60</td><td>25.60</td><td>0.1037</td><td>5.336</td></tr></table>
+
+<table><tr><td>#samples k</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>2</td><td>21.37</td><td>26.56</td><td>0.3235</td><td>5.714</td></tr><tr><td>4</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr><tr><td>8</td><td>21.19</td><td>27.62</td><td>0.4199</td><td>5.605</td></tr></table>
+
+Table 9. Comparing win-lose pair choices. Choosing images of the highest and lowest quality is generally better than random selection. Note both strategies allow win-lose preference to align with aesthetic preference.  
+
+<table><tr><td>win-lose sample</td><td>P-S</td><td>HPSV2</td><td>I-R</td><td>AE</td></tr><tr><td>best &amp; worst</td><td>21.43</td><td>26.45</td><td>0.1712</td><td>5.887</td></tr><tr><td>random</td><td>21.21</td><td>26.51</td><td>0.1656</td><td>5.796</td></tr></table>
+
+is  $+0.42$ ,  $+2.49$ ,  $+0.1367$ , and  $+0.349$  on the four metrics, respectively. This again demonstrates the effectiveness of SPO in aesthetic improvement.
+
+User studies. We compare SPO with Diffusion-DPO and Vanilla SDXL through user studies. We ask annotators to compare three aspects: general preference, visual appeal, and prompt alignment and summarize the winning percentage in Fig. 6. Results indicate that SPO has consistently more winning votes from users in general preference and visual appeal, and it is apparent that its visual appeal has a greater winning margin. For example, in general preference alignment, SPO wins  $52.8\%$  of all cases, while in visual appeal, it wins  $58.27\%$  of the cases. Similar observation can be made in SPO vs. vanilla SDXL.
+
+Qualitative comparison. We show sample images in Fig. 2. Images generated by SPO are more visually appealing than those generated by SDXL and Diffusion-DPO.
+
+# 5.3. Evaluation on Image-Text Alignment
+
+SPO slightly improves vanilla models. From Table 1 and Table 2, PickScore metric indicates some improvement over SDXL and SD-1.5. User studies (Fig. 6), on prompt alignment has similar results. On GenEval, Table 3 shows SPO
+
+improves prompt alignment score by  $1.77\%$  over SDXL.
+
+SPO has mixed results compared with Diffusion-DPO. Table 1 and Table 2 demonstrate improvement over Diffusion-DPO, and yet our user studies support a performance tie or SPO's slight win in prompt alignment. Further, GenEval results indicate that SPO is not as good as Diffusion-DPO in improving image-text alignment, which we tend to agree with, because the SPO design does not fully capture layout changes. But an interesting insight is that image-text alignment and aesthetics are probably often blended. So while SPO is designed for aesthetic alignment, it still yields some prompt alignment improvement, but the improvement is not as much as Diffusion-DPO.
+
+# 5.4. Further Analysis
+
+If not specified, we use SD-1.5 and Pick-a-Pic val. set.
+
+Effectiveness of step-aware preference model (SPM). An important design of SPM is the addition of timestep conditioning. To verify its usefulness, we remove the timestep conditioning in SPM (SPM w/o step). A second variant is to simply use the PickScore model [11] which has no time condition and is trained on clean images only. Results in Table 5 show that both variants lead to performance drop,
+
+validating the SPM design.
+
+Effectiveness of random selection for initializing next iteration. At the end of each SPO iteration, we need to initialize the next iteration, where random selection is an option. Here we compare random selection with using the win sample  $\pmb{x}_{t-1}^{w}$  or the lose sample  $\pmb{x}_{t-1}^{l}$  for initialization. Results are presented in Table 4. We clearly find that random selection is better. If we only select  $\pmb{x}_{t-1}^{w}$  or  $\pmb{x}_{t-1}^{l}$ , training becomes biased towards the intermediate samples that are more preferred or more dispreferred, respectively. This prevents the network from learning from more diverse trajectories, deteriorating generalization ability.
+
+Impact of number of candidates sampled at each denoising step. To find useful win-lose pairs, we obtain a set of candidates  $\{\pmb{x}_{t - 1}^1,\pmb{x}_{t - 1}^2,\dots ,\pmb{x}_{t - 1}^k\}$  at each step, drawn from the conditional distribution  $p_{\theta}\left(\pmb{x}_{t - 1}\mid \pmb{x}_t,\pmb {c},t\right)$ . Table 6 presents results by varying  $k$ . We have two observations.
+
+First, when increasing  $k$ , the discrepancy within sampled pairs becomes larger (but still small enough to only reflect image detail differences). The larger contrast between the preferred and dispreferred samples helps the model learn human preferences. Second, when  $k$  is too large, quality of the most dispreferred sample would be lower than average of samples generated by the base model. As a result, the "push away" effect of the dispreferred image is weakened, causing performance degradation. We choose  $k = 4$ .
+
+Impact of the number of inner steps  $j$  in MSPO. A larger  $j$  allows the generated images to have higher diversity, which would be useful for strong diffusion models. In Table 7, we study how  $j$  impacts SPO. We observe that fin-tuning performance increases with  $j$  in the beginning and then becomes saturated. When  $j = 1$ , MSPO reduces to SPO. When  $j$  goes to infinite, MSPO would essentially reduce to Diffusion-DPO because there will only be one step. From the table, we choose  $j = 4$ .
+
+Impact of timestep range. SPO is only applied to timestep range  $[0 - \kappa ]$ . Table 8 summarizes the results of applying SPO to various timestep ranges. We have the following observations.
+
+First, discarding very large timesteps, i.e., [750-1000], yields better performance as these timesteps barely generate image details and are very noisy. Second, if we remove [0-250] and only use [250-750], there is a considerable performance drop, indicating that [0-250] is useful. Similarly, [0-500] is also useful. Third, if we compare [500-750], [250-500] and [0-250], we find that applying SPO to [250-500] achieves slightly better overall performance. We speculate [250-500] is a critical timestep range for SPO. Compared to larger timesteps, timesteps in [250-500] focus more on detail refinement. Moreover, compared to smaller timesteps, the denoising steps in [250-500] sample  $x_{t - 1}$  with a sufficiently large variance to construct win-loss pairs for training. Based on these findings, we set  $\kappa = 750$  and apply
+
+SPO to timestep range [0-750].
+
+Comparing ways of choosing win-lose pairs. In Table Table 9, we compare two ways. The proposed method uses a sample with highest quality and another sample with lowest quality. The other way is to randomly select two samples and use SPM to decide their win-lose preference. Results show that the proposed way is generally better. That said, both options allow for proper assessment of aesthetic preference because they ensure a sample pair comes from the same sample and has relatively small differences.
+
+Computational cost. We use  $4 \times$  A100 GPUs, which take 12 and 29.5 hours to fine-tune SD-1.5 and SDXL, respectively. We also spend 8 and 29 hours training SPM for SD-1.5 and SDXL, respectively. In comparison, the GPU hours used for fine-tuning SD-1.5 and SDXL using Diffusion-DPO are 384 and 4,800, respectively. As a result, the total training GPU hours of SPO-SD-1.5 and SPO-SDXL is about  $20.8\%$  and  $4.9\%$  of DPO-SD-1.5 and DPO-SDXL, respectively. This significant efficiency gain is probably because of the SPO design, where the image details are properly highlighted for the network to learn.
+
+# 6. Conclusion
+
+This paper studies how to align diffusion models with human aesthetic preference. This problem is challenging for two reasons. First, existing two-trajectory methods exhibit large image discrepancies, preventing models from focusing on aesthetic nuances. Second, it is very non-trivial to collect aesthetic-only preference data, while existing datasets record generic preferences that may conflict with image aesthetic preference. To improve aesthetic alignment, we propose an aesthetic alignment solution that distills aesthetics from generic preference data. Specifically, the proposed step-by-step preference optimization method allows a pair of samples to originate from the same image, so their differences are relatively small after one or very few steps, which would reflect their image details or aesthetics. Our preference model captures these differences, enabling the model to improve towards generating better image details. In experiments, we demonstrate that SPO better aligns SD-1.5 and SDXL with human aesthetic preference compared with other DPO methods and is efficient to train.
+
+# Acknowledgments
+
+We gratefully acknowledge the support of the ARC Future Fellowship (FT240100820), awarded to Liang Zheng.
+
+# References
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+# AffordDP: Generalizable Diffusion Policy with Transferable Affordance
+
+Shijie Wu† Yihang Zhu† Yunao Huang Kaizhen Zhu Jiayuan Gu Jingyi Yu Ye Shi* Jingya Wang* ShanghaiTech University, Shanghai, China
+
+{wushj12023,zhuyh2023,huangya2024,zhukzh2024,gujy1,yujingyi,shiye,wangjingya}@shanghaiitech.edu.cn
+
+https://afforddp.github.io/
+
+![](images/87d986a5e10425496de4922323d8f594bb809164064b972cbecf0a5248b3f360.jpg)
+
+Teleoperation Data showing task "Open Cabinet Door"
+
+![](images/9a13a920f48fb61e8af1784f30d82f9f71ba0e14716ba0c8c7b086809bb400b2.jpg)
+
+![](images/45056e9b1b63b4efc7b64c094f0dd509240c7bb99c881009799e363554b5984e.jpg)  
+Figure 1. We propose AffordDP, a novel diffusion-based imitation learning method for generalizable robotic manipulation. AffordDP leverages rich manipulation priors from transferable affordances to enhance generalization to unseen scenarios and incorporates affordance guidance to enable precise control.
+
+Affordance aspulation Prior
+
+![](images/590d652461585e3a28f6ccae8062de95255173d0d7d6659f9868ad5071e06d12.jpg)  
+Affordance
+
+![](images/9e9de76e05a4c536b7d425c8d5e54994314dfbb982916cacbdb9589ef4929045.jpg)
+
+![](images/b870e36d8a42940dcd7538160fcdacf06e6cc2eb32df051f316371856e618144.jpg)  
+Unseen Placement  
+Unseen Instance
+
+Generalize to
+
+![](images/738c81650cfb09a60d01d179eb622c2f16d95694900cb67a73d541bf857cc80d.jpg)
+
+Different Scenarios
+
+![](images/0692cc4270658ecaf3cd529f6d14b7abadc35cb65023e113e9cb40987bda9b6d.jpg)  
+#  
+Unseen Scene
+
+# Abstract
+
+Diffusion-based policies have shown impressive performance in robotic manipulation tasks while struggling with out-of-domain distributions. Recent efforts attempted to enhance generalization by improving the visual feature encoding for diffusion policy. However, their generalization is typically limited to the same category with similar appearances. Our key insight is that leveraging affordances—manipulation priors that define “where” and “how” an agent interacts with an object—can substantially enhance generalization to entirely unseen object instances and categories. We introduce the Diffusion Policy with transferable Affordance (AffordDP), designed for generalizable manipulation across novel categories. AffordDP models affordances through 3D contact points and post-contact trajectories, capturing the essential static and dynamic information for complex tasks. The transferable affordance from in-domain data to unseen objects is achieved by estimating a 6D transformation matrix using foundational vision models and point cloud registration techniques. More importantly, we incorporate affordance guidance during
+
+diffusion sampling that can refine action sequence generation. This guidance directs the generated action to gradually move towards the desired manipulation for unseen objects while keeping the generated action within the manifold of action space. Experimental results from both simulated and real-world environments demonstrate that AffordDP consistently outperforms previous diffusion-based methods, successfully generalizing to unseen instances and categories where others fail.
+
+# 1. Introduction
+
+Imitation learning offers an efficient solution for teaching robots a variety of skills by replicating behavior from experts without the need to explicitly program actions or model the environment. It has garnered significant interest across a wide range of fields, including autonomous driving [13, 16, 21], robotic manipulation [3, 6, 15, 17, 22, 34, 36], and legged locomotion [20, 25, 26]. Recently, diffusion-based imitation models [6, 14, 30] have gained significant attention within the field. These models conceptualize a robot's visuomotor policy as a conditional diffusion denoising process, facilitating the learning of conditional action distributions.
+
+Despite their high expressiveness and flexibility, diffusion-based imitation models [6, 14, 30] still struggle to generalize to out-of-domain distributions, which significantly limits their practical deployment. Recently, some pioneering works have sought to enhance the generalization ability of visual feature encoding and directly apply these advancements to diffusion policy [6]. For instance, Ze et al. [41] utilized 3D point cloud representations instead of 2D representations to improve feature encoding. Concurrently, Yang et al. [38] proposed integrating SIM(3)-equivariant networks to enhance generalization ability. Additionally, Wang et al. [35] introduced 3D semantic fields with multi-view input into diffusion policy to further improve its generalization ability. While these approaches may enable diffusion models to generalize to different initial locations, appearances, or poses, their generalization is typically limited to the same category with similar appearances. Subsequently, achieving the generalization of diffusion models to unseen instances and unseen categories remains challenging.
+
+As human beings, we, in contrast, can easily transfer skills to objects with different appearances or even different types of objects. For example, once we learn the skill of opening a cabinet, it is easy to apply this skill to opening a microwave or a refrigerator (just as learning to ride a bicycle makes it easy to ride a tricycle). This ability is due to the vast amount of task-specific interaction prior knowledge that humans possess. This interaction prior knowledge at the object level specifically manifests as knowing "where" and "how" an agent should interact with an object to complete a given task, which is often defined as affordances in many studies [1, 40]. However, current imitation learning methods typically define affordances as 2D contact points with trajectory, task-specific keyframes, or value maps [2, 28, 42]. This significantly limits the representation of affordances in terms of "how" an agent should interact with the object. To tackle this key issue, we design a general representation for both static and dynamic affordances and further propose a diffusion policy with affordance transfer, allowing for the transfer of interaction prior knowledge across different instances and categories.
+
+Specifically, we present a new Diffusion Policy with transferable Affordance that we call AffordDP to address complex manipulations of unseen objects and categories. The transferable affordance encompasses both static and dynamic affordances, capturing 3D contact points and postcontact trajectories, thus providing the "where" and "how" information crucial for manipulation tasks. The transferable affordance is derived from in-domain data and applied to unseen objects by estimating a 6D transformation matrix, utilizing foundational vision models and point cloud registration techniques. AffordDP employs the transferable affordance as an informative condition for the diffusion
+
+model, thereby enhancing its capability to generalize across varied manipulative scenarios. However, simply integrating transferable affordance as the diffusion condition may lack sufficient accuracy to achieve zero-shot adaptation for unseen robotic manipulation. To address this challenge, we introduce an affordance-guided sampling process for diffusion policy. In particular, the affordance guidance is defined as the distance between the robot's end-effector position and the static affordance. This guidance during the diffusion sampling process enables the generated action sequence to gradually move toward the desired manipulation for unseen objects while keeping the generated action within the manifold of action space. We adaptively apply the affordance guidance for fine-grained control. The novelty and contributions of this paper are outlined as follows.
+
+- We introduce AffordDP that leverages transferable affordance for enhanced generalization to unseen objects and categories that cannot be completed by existing diffusion-based methods.  
+- Our framework enables the transfer of both static and dynamic affordances by utilizing foundational vision models, making it possible to represent complex manipulations with limited in-domain data.  
+- We integrate adaptive affordance guidance to our AffordDP that can direct the generated action sequence to gradually move towards the desired manipulation for unseen objects within the manifold of action space.
+
+# 2. Related work
+
+# 2.1. Diffusion-based Imitation Learning
+
+As one of the first works [6, 14, 30] that introduce diffusion into imitation learning, the Diffusion Policy [6] leverages a diffusion denoising process to model conditional action distributions. Despite its advantages in modeling multimodal data and providing stable training, the Diffusion Policy still faces limitations in generalizing to out-of-domain distributions. When the position or shape of objects changes, the Diffusion Policy struggles to adapt successfully. 3D Diffusion Policy [41] addresses this to some extent by using point clouds for visual representation, which improves spatial generalization. Equibot [38] further advances this by combining SIM(3)-equivariant neural network architectures with diffusion policies, enhancing generalization to SIM(3)-equivariant scenes. Another approach, Im2Flow2Act [37], combines self-supervised 2D flow prediction with a flow-based Diffusion Policy. However, its reliance on 2D flow limits its effectiveness, failing to capture object movements in the 3D space accurately and leading to less precise actions. Concurrent with our work, GenDP [35] and G3Flow [4] employ 3D semantic fields to enhance point cloud observations used in Diffusion Policy. However, these approaches require a multi-view setup to generate semantic
+
+![](images/065a341f2d9c7865e20092fee33fd4a40562610cbbe1a2ebbd259ff05ff4d351.jpg)  
+Static and Dynamic Affordance Transfer
+
+![](images/1345680cfe59385b9bd2dc3fb74ab028f2cf077216c579784762c0383686420c.jpg)  
+Affordance-Guided Diffusion Policy
+
+![](images/4402f9245a937f62f800859d53895267916797782672484aace307891a337b5c.jpg)  
+Figure 2. Overview of AffordDP. The left part demonstrates static and dynamic affordance transfer. Given the target scene RGB-D image, AffordDP retrieves a similar object in the affordance memory and transfers its static and dynamic affordance to the target object. The right part illustrates the key components of affordance-guided diffusion policy. Conditioned on 3D affordance, point cloud observation, and robot proprioception, AffordDP utilizes the Diffusion Policy and adaptive affordance guidance for precise control.
+
+fields and are limited to category-level generalization. In contrast, our method uniquely conditions diffusion on 3D affordance trajectories, allowing our model to generalize more effectively to objects with similar affordance trajectories, regardless of their category.
+
+# 2.2. Generalizable Manipulation for Robotics
+
+Generalizable manipulation is a principal focus in the field of imitation learning. To encourage policies to concentrate on task-relevant factors while minimizing irrelevant distractions, previous methods typically extract object-centric features from images, like object poses [8], task-specific region proposals [9], keypoints [23] and segmented point clouds [46]. A further trend in this field is the integration of affordance into policy learning. Mainstream works [2, 12, 24] tend to learn affordance from large datasets or through intensive reinforcement learning, which can entail significant overhead. To address these limitations, recent advancements have leveraged semantic information from foundational vision models to enable zero-shot affordance transfer. Pioneering methods such as Robo-ABC [18] and RAM [19] allow affordance transfer in a training-free manner. However, they are limited to predicting affordances either as 2D contact points or 3D contact points with direction. Additionally, they rely on grasp generators [10] and motion planners [7, 32] to perform manipulation tasks, which face
+
+challenges in high-dimensional action spaces and complex manipulation tasks. This reliance often results in unimodal actions, limiting effectiveness in environments with significant uncertainty. Our method advances these developments by combining 2D semantic correspondences with 3D geometrical correspondences, significantly enhancing the capability for effective trajectory-level transfer.
+
+# 3. Transfer of Static and Dynamic Affordances
+
+AffordDP generates 3D affordances denoted by  $\Phi = (c, \tau)$ , where  $c \in \mathbb{R}^3$  represents the static affordance as 3D contact point and  $\tau \in \mathbb{R}^{3 \times N}$  represents the dynamic affordance as post-contact trajectory in the form of an ordered list of 3D points. Affordance transfer is defined as generating the affordance for the target object given a source object with its affordance. Upon specifying a target object, AffordDP retrieves the most similar object from the object memory. The static affordance  $c$  is transferred using the semantic correspondence, and the dynamic affordance  $\tau$  is transferred using a 6D transformation matrix, whose translation and rotation components are derived independently. An overview is shown in Fig. 3.
+
+![](images/d5a6a83cc04ccedee21f52a0c3558f91f1b06d13eaad664fb1ad731f4eb6c13c.jpg)  
+Static Affordance Transfer  
+Dynamic Affordance Transfer  
+Figure 3. Overview of Static and Dynamic Affordance Transfer. The left part is static affordance transfer, and the right part is dynamic affordance transfer. The source and target images are processed through SD-DINOv2 [43] to generate feature maps  $F^S$  and  $F^T$ . The similarity is computed and used to find the corresponding target image points using an argmax operation. These points are projected back to obtain point clouds. Point-SAM [45] is then used to obtain the source and target part point clouds. The Iterative Closest Point (ICP) algorithm is applied to the point clouds to determine the transformation matrix  $T = [\mathbf{R}|\mathbf{t}]$  for dynamic affordance transfer.
+
+# 3.1. Affordance memory and similarity retrieval
+
+To build the affordance memory, we utilize Grounded-SAM [29] to crop the object from the image and employ the CLIP [27] image encoder to extract the feature vector  $z$ . Additionally, we record the contact point as the static affordance  $c$ , and the trajectory of the robot end-effector after contacting the object (in world coordinates) as the dynamic affordance  $\tau$ . We define the affordance memory  $\mathcal{M}$ , which includes the task name  $T$ , the affordance  $\Phi = \{c, \tau\}$ , the appearance feature  $z$ , and the point cloud of the manipulable object  $\mathcal{P}$  recovered from RGB-D images as follows,
+
+$$
+\mathcal {M} = \{(T, \Phi , z, \mathcal {P}) \}. \tag {1}
+$$
+
+The cosine similarity between the source and target cropped image feature vectors serves as a proximity metric for retrieval. In practical terms, for an object with task  $T$ , we perform retrieval within the subset of the memory corresponding to the same task  $T$ .
+
+# 3.2. Static affordance transfer
+
+Static affordance transfer involves finding the contact point of the target object in 3D world coordinates, given the contact point of the source object. This task is challenging because the two objects may differ in appearance, shape, rotation, or even category. We leverage the rich semantic information provided by foundation vision models to mitigate these variances. We upsample SD-DINOv2 [43] features to generate pixel-level image features. By matching the features of the source static affordance in the 2D image  $c_{2D}^{S}$  with all features of the target image pixels, we can identify
+
+the target static affordance in the 2D image  $c_{2D}^{\mathcal{T}}$ . We then back-project the target static affordance  $c_{2D}^{\mathcal{T}}$  to 3D world coordinates as  $c_{3D}^{\mathcal{T}}$ .
+
+# 3.3. Dynamic affordance transfer
+
+To transfer dynamic affordances, we utilize a 6D transformation matrix. Previous alignment-based methods that rely on instance-level registration between source and target objects [47] often yield unreliable results due to shape and scale discrepancies. For example, transferring a top drawer affordance from a tall closet to a central drawer in a square closet can lead to inaccuracies. To address this issue, we independently estimate the rotation matrix and translation vector, better accommodating structural differences and enhancing the accuracy of affordance transfer.
+
+The translation vector  $\mathbf{t}$  is obtained by computing the difference between the source and target 3D contact points. To determine the rotation matrix  $\mathbf{R}$ , we perform point cloud registration on source and target point clouds. We employ a state-of-the-art promptable 3D segmentation model [45], using  $c_{3D}$  as a prompt to segment manipulable parts. This approach reduces sensitivity to structural variance, as part point clouds exhibit less variability than complete objects. We then use the iterative closest point (ICP) algorithm [5] to register the 3D parts by minimizing the objective function:
+
+$$
+E (\mathbf {T}) = \sum_ {(\mathbf {p}, \mathbf {q}) \in \mathcal {K}} \left[ (\mathbf {p} - \mathbf {T q}) \cdot \mathbf {n _ {p}} \right] ^ {2}, \tag {2}
+$$
+
+where  $\mathbf{T}$  is the transformation,  $\mathcal{K} = \{(\mathbf{p},\mathbf{q})\}$  is the correspondence set between the target point cloud  $\mathbf{P}$  and the
+
+source point cloud  $\mathbf{Q}$ , and  $\mathbf{n_p}$  is the normal of point  $\mathbf{p}^*$ .
+
+After deriving the rotation matrix  $\mathbf{R}$  from the registration results, we combine it with the translation vector  $\mathbf{t}$  obtained earlier to compute the 6D transformation matrix:
+
+$$
+\tau^ {\mathcal {T}} = \mathbf {R} \tau^ {\mathcal {S}} + \mathbf {t}. \tag {3}
+$$
+
+This 6D transformation matrix maps the dynamic affordance of the source object to the target object.
+
+# 4. Affordance Guided Diffusion Policy
+
+To enhance the generalization capacity, we design a conditional diffusion model that takes in the transferable affordance as an additional condition, which treats this manipulation prior as a bridge to narrow the gap between training and practical deployment. However, simply adding affordance as a diffusion condition does not fully leverage its potential, as the diffusion model is inherently focused on modeling the overall action distribution, prioritizing alignment with the distribution rather than adherence to specific task constraints. To address this, we introduce an adaptive affordance-guided sampling process to direct the policy toward static affordance (contact point), enhancing task focus and precision.
+
+# 4.1. Conditions for AffordDP
+
+The overall conditions of our diffusion model are:
+
+$$
+\mathcal {C} = \left\{O _ {t}, S _ {t}, \Phi \right\}, \tag {4}
+$$
+
+where  $O_{t}$  represents the scene point cloud,  $S_{t}$  denotes robot proprioception, and  $\Phi$  represents the affordance, which is composed of static affordance  $c$  (contact point) and dynamic affordance  $\tau$  (trajectory). Our diffusion model builds upon Denoising Diffusion Implicit Models (DDIMs) [31] and aims to approximate affordance-guided conditional distribution  $p(a_{t}|O_{t},S_{t},\Phi)$ , to capture the action distribution through a gradual denoising process from a Gaussian distribution.
+
+To extract the overall conditioning feature  $f_{t}$  from each element in  $\mathcal{C}$ , we use distinct encoders. Since only a small region surrounding the robot and target object offers meaningful contextual information, we crop and downsample the scene point cloud before applying an MLP for scene feature extraction, following a similar approach to the 3D Diffusion Policy [41]. To capture the full dynamics of the trajectory sequence  $\tau$ , we utilize a transformer encoder [33] with a [CLS] token to represent the trajectory feature. The contact point  $c$  and robot proprioception  $S_{t}$  features are extracted using separate MLPs. We define the conditioning feature  $f_{t}$  as follows,
+
+$$
+f _ {t} = \left\{f _ {t} ^ {O}, f _ {t} ^ {S}, f ^ {\Phi} \right\}, \tag {5}
+$$
+
+where  $f_{t}^{O}$  denotes the scene feature,  $f_{t}^{S}$  represents the robot state feature, and  $f^{\Phi}$  integrates both the static and dynamic affordance features for simplicity.
+
+# 4.2. Conditional diffusion model training
+
+Starting from an initial noise vector  $a_{t}^{k}$ , AffordDP uses a noise prediction network  $\epsilon_{\theta}$  to iteratively denoise the noise vector conditioned on the conditioning feature  $f_{t}$  till a noise-free action  $a_{t}^{0}$  is formed. This process can be described using the following equations:
+
+$$
+a _ {t} ^ {k - 1} = \sqrt {\alpha_ {k - 1}} \left(a _ {t} ^ {k} - \sqrt {1 - \alpha_ {k}} \epsilon_ {\theta} ^ {k}\right) / \sqrt {\alpha_ {k}} + \tag {6}
+$$
+
+$$
+\sqrt {1 - \alpha_ {k - 1} - \sigma_ {k} ^ {2}} \epsilon_ {\theta} ^ {k} + \sigma_ {k} \epsilon^ {k},
+$$
+
+$$
+\sigma_ {k} = \sqrt {\left(1 - \alpha_ {k - 1}\right) / \left(1 - \alpha_ {k}\right)} \sqrt {1 - \alpha_ {k} / \alpha_ {k - 1}}, \tag {7}
+$$
+
+where  $\epsilon^k$  is random noise,  $\alpha_{k}$  is the noise schedule and  $k$  is the number of denoising iterations. Similar to previous diffusion-based policies [6, 41], we train the noise prediction network  $\epsilon_{\theta}$  to predict the noise  $\epsilon^k$  added at  $k$ -th iteration,
+
+$$
+\mathcal {L} = \left\| \epsilon_ {k} - \epsilon_ {\theta} \left(a _ {t} ^ {k}, k, f _ {t}\right) \right\| ^ {2}. \tag {8}
+$$
+
+# 4.3. Diffusion sampling with affordance guidance
+
+However, while the standard diffusion formulation is designed to capture the comprehensive action distribution, it may generate actions that remain within this distribution but fail to meet specific task conditions, particularly in high-precision tasks such as grasping a door handle to open it. To this end, we add additional guidance to steer its output distribution towards specific properties  $y$ . With the Bayes Theorem, we can introduce the given condition with an additional likelihood term  $p(a_t|y)$ :
+
+$$
+\nabla_ {a _ {t} ^ {k}} \log p \left(a _ {t} ^ {k} \mid y\right) = \nabla_ {a _ {t} ^ {k}} \log p \left(a _ {t} ^ {k}\right) + \nabla_ {a _ {t} ^ {k}} \log p \left(y \mid a _ {t} ^ {k}\right). \tag {9}
+$$
+
+By utilizing a differentiable loss function  $L(a_{t}^{0},y)$  for sampling guidance, we eliminate the need to train the classifier or retrain the whole network. We can use the estimated likelihood of  $L(a_{t}^{0},y)$  for the additional correction step:
+
+$$
+a _ {t} ^ {k - 1} = \operatorname {D D I M} \left(a _ {t} ^ {k}, \epsilon_ {\theta} \left(a _ {t} ^ {k}, k, f _ {t}\right)\right) - \gamma \nabla_ {a _ {t} ^ {k}} L \left(\hat {a} _ {t} ^ {0} \left(a _ {t} ^ {k}\right), y\right), \tag {10}
+$$
+
+where  $\hat{a}_t^0 (a_t^k)$  is an estimate based on  $a_{t}^{k}$  and  $\gamma$  is guidance weight.
+
+During inference, given the robot's current joint positions  $q_{pos}$ , we use the forward kinematics to compute the 3D position of the robot's end-effector  $p_{ee}$ . We then use the distance between the end-effector's position  $p_{ee}$  and the static affordance  $c_{3D}$  as the adaptive loss function  $\mathcal{L}_g$  for the adaptive affordance guidance. This loss function is adaptive because it is only utilized when the end-effector approaches
+
+the static affordance  $c_{3D}$  within a predefined range. This prevents it from being applied when the gripper is far from or has already grasped the target object. If the gripper is approaching the target object, then the adaptive loss function can be represented as:
+
+$$
+\mathcal {L} _ {g} = \left\{ \begin{array}{l l} \| p _ {e e} - c _ {3 D} \| _ {2}, & \| p _ {e e} - c _ {3 D} \| _ {2} <   \theta , \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {11}
+$$
+
+Here  $\theta$  is a predefined threshold to control the actuating range of the affordance guidance. Motivated by DSG [39], we introduce an analytical solution to the sampling process of the diffusion model, which can guide the generation process to the direction of gradient descent while preserving the generated  $a^0$  within the manifold:
+
+$$
+a _ {t} ^ {k - 1 ^ {*}} = \mu_ {\theta} \left(a _ {t} ^ {k}\right) - \sqrt {n} \delta_ {k} \nabla_ {a _ {t} ^ {k}} \mathcal {L} _ {g} / | | \nabla_ {a _ {t} ^ {k}} \mathcal {L} _ {g} | | _ {2}, \tag {12}
+$$
+
+$$
+\begin{array}{l} \mu_ {\theta} \left(a _ {t} ^ {k}\right) = \sqrt {\alpha_ {k - 1}} \left(a _ {t} ^ {k} - \sqrt {1 - \alpha_ {k}} \epsilon_ {\theta}\right) / \sqrt {\alpha_ {k}} + (13) \\ \sqrt {1 - \alpha_ {k - 1} - \sigma_ {k} ^ {2}} \epsilon_ {\theta}, (13) \\ \end{array}
+$$
+
+where  $n$  represents the action dimensions. By incorporating affordance loss guidance into the standard diffusion formulation, AffordDP can generate action sequences directed toward the target manipulation positions for unseen objects, thereby enhancing its generalization capabilities.
+
+# 5. Experiments
+
+# 5.1. Experiment Setup
+
+We evaluate our approach on multiple tasks, including both simulations and real-world scenarios. For the simulation scenario, we use IsaacGym as the simulation platform, leveraging objects from GAPartnet [11] and point clouds generated by depth cameras within the simulation for observations. We use the Franka arm and a side-mounted camera setting for both simulation and real-world scenarios.
+
+Expert demonstrations. We use CuRoBo [32] as the motion planner for expert demonstration collection in the simulation. To ensure diversity in the collected trajectories, we introduce random noise to the initialization parameters, including the 6D object position, the robot arm's base position, and the initial DOF of the robot arm. Using part bounding boxes annotated by GAPartnet, we can collect expert demonstrations specific to part manipulation. In the real-world scenario, we collect expert demonstrations through teleoperation.
+
+Baseline methods. We selected two state-of-the-art diffusion-based policies as our baselines for comparison: 1) Diffusion Policy (DP) [6], which utilizes images as observations to generate actions via diffusion; and 2) DP3 [41], which replaces image inputs in the Diffusion Policy with point clouds. We evaluate different policies by the success rate.
+
+Training settings. DP [6] and DP3 [41] adopt a single-object training approach, involving only one object during the training process. This setup encourages the policy to learn object-specific features, potentially limiting its generalization ability to adapt to unseen instances, which can be a common requirement in practical applications. To this end, we design two training settings: object-specific policy training and unified policy training. The former retains the original single-object training setup used in DP and DP3, while the latter employs a multi-object training approach that promotes learning task-relevant strategies for broader generalization.
+
+# 5.2. Simulation Performance
+
+We evaluate our method on two tasks for the simulation scenario: PullDrawer and OpenDoor. For a fair comparison, we assess all methods under both training settings—object-specific policy training and unified policy training—to highlight our method's consistent advantage over baselines.
+
+In the object-specific policy training, we collect 30 expert demonstrations for each task. To analyze how variability in training data impacts algorithm performance, we construct datasets with differing levels of variance, reflected in the initial 6D placements of the objects and the initial joint positions of the robot arm. Our method and the baselines are evaluated across each variance level to assess robustness. The quantitative results are summarized in Tab. 2. Our approach significantly outperforms the baselines across different variance levels on both tasks. Notably, while baseline methods are comparable to ours under low variance conditions, our method demonstrates a substantial advantage over baselines as variance levels increase.
+
+For the unified policy training, we carefully choose 5 distinct objects for each task and collect 20 demonstrations for each object. To evaluate generalization capabilities, we introduce three types of test objects: seen instances, unseen instances within the same category, and instances from unseen categories. The quantitative results presented in Tab. 3 show that our approach achieves superior performance across all three object types. Even for some categories that are not involved during training, our method still demonstrates strong generalization capabilities and exceptional performance. In contrast, the baseline methods exhibit very low success rates with unseen categories. By leveraging transferable affordance, AffordDP can capture the inherent properties of both seen and unseen objects, significantly enhancing the policy's learning and adaptability.
+
+# 5.3. Real-world Performance
+
+We evaluate our method on three tasks for the real-world scenario: OpenDoor, PullDrawer, and Pick&Place. We use the unified policy training setting for real-world experiments. Using teleoperation, we collect 25 demonstrations
+
+![](images/bbaab3dc788407e6c991dfefc732f01b89c38ba2efcb6125f87edc990e8ab0f1.jpg)  
+Figure 4. Policy rollouts in the real world. The left part is an intuitive demonstration of three real-world task processes, involving PullDrawer, OpenDoor, and Pick&Place. The right part represents the policy rollout results. Without spatial perception and a lack of adequate training data, which can be over 200 demonstrations [6, 41], DP fails to target the object correctly, often resulting in random and potentially unsafe actions. Lacking comprehensive static and dynamic affordance information, DP3 struggles to grasp the target accurately, even if it moves the gripper close to the target. In contrast, our method effectively grasps the target object and completes the task, demonstrating accurate spatial targeting.
+
+![](images/1b3955c7164d04833ee82fbef0650a4ca55c8297a402d2f5656d8558b8a05b1c.jpg)
+
+![](images/1f1b7771484d2dfcc0aa8275b6e0d1e6b55d6745b1f0757b013084d7fefc7c32.jpg)  
+Table 1. Instance and Category Generalization on PullDrawer task. We evaluate the generalization capacities by replacing the target object with unseen instances and unseen categories. Each object undergoes three evaluation trials, and a green checkmark is awarded if the task succeeds in at least one out of the three trials.
+
+per object, with a total of 4 objects for each task, resulting in 100 demonstrations per task.
+
+Consistent with the unified policy training experiments for the simulation scenario, we evaluate our method on three types of test objects: seen instances, unseen instances within the same category, and instances from unseen categories. The results, shown in Tab. 4, highlight the effectiveness of our method in real-world scenarios. Fig. 4 shows policy deployment results, showcasing our methods'supe
+
+<table><tr><td colspan="7">Simulation results of object-specific policy for seen instance</td></tr><tr><td>Tasks</td><td colspan="3">Pull Printer</td><td colspan="3">Open Door</td></tr><tr><td>Methods</td><td>Easy</td><td>Median</td><td>Hard</td><td>Easy</td><td>Median</td><td>Hard</td></tr><tr><td>DP</td><td>80.0%</td><td>16.7%</td><td>13.3%</td><td>76.7%</td><td>26.7%</td><td>30.0%</td></tr><tr><td>DP3</td><td>80.0%</td><td>13.3%</td><td>16.7%</td><td>66.7%</td><td>36.7%</td><td>20.0%</td></tr><tr><td>Ours</td><td>80.0%</td><td>33.3%</td><td>26.7%</td><td>90.0%</td><td>53.3%</td><td>50.0%</td></tr></table>
+
+Table 2. Simulation performance of different methods under the object-specific policy training setting for seen instance. We categorized datasets into varying difficulty levels based on variance levels. The variance level is directly related to the random noise (position, rotation) introduced during the data collection process, the details of variance levels can be found in supplementary.  
+
+<table><tr><td colspan="7">Simulation results of the unified policy training setting</td></tr><tr><td>Tasks</td><td colspan="3">Pull Printer</td><td colspan="3">Open Door</td></tr><tr><td>Methods</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td></tr><tr><td>DP</td><td>20.7%</td><td>6.7%</td><td>3.3%</td><td>23.3%</td><td>17.5%</td><td>3.3%</td></tr><tr><td>DP3</td><td>41.3%</td><td>10.0%</td><td>3.3%</td><td>41.1%</td><td>5.0%</td><td>5.6%</td></tr><tr><td>Ours</td><td>90.0%</td><td>55.6%</td><td>73.3%</td><td>74.4%</td><td>52.5%</td><td>26.7%</td></tr></table>
+
+Table 3. Simulation performance of different methods under the unified policy training setting. We compare our method with the baseline across three types of test objects, involving seen objects, unseen instances within the same category, and instances from unseen categories.
+
+<table><tr><td colspan="10">Real-World Results</td></tr><tr><td>Tasks</td><td colspan="3">Pull Printer</td><td colspan="3">Open Door</td><td colspan="3">Pick &amp; Place</td></tr><tr><td>Methods</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td></tr><tr><td>DP</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td><td>0.0%</td></tr><tr><td>DP3</td><td>10.0%</td><td>0.0%</td><td>10.0%</td><td>20.0%</td><td>0.0%</td><td>30.0%</td><td>40.0%</td><td>30.0%</td><td>15.0%</td></tr><tr><td>Ours</td><td>67.5%</td><td>45.0%</td><td>40.0%</td><td>80.0%</td><td>50.0%</td><td>50.0%</td><td>52.5%</td><td>65.0%</td><td>50.0%</td></tr></table>
+
+riority over baselines. And Tab. 1 gives some results on the PullDrawer task to showcase the instance and category generalization capacity of our method. Experimental outcomes demonstrate that our method successfully generalizes to unseen instances, even those from unseen categories. In the most challenging scenarios, our method continues to exhibit strong zero-shot capabilities, significantly outperforming baseline approaches.
+
+Table 4. Real-World performance of different methods for all three types of test objects for three tasks. Our method consistently outperforms DP and DP3 in all scenarios, especially in tasks with unseen instances and categories. Notably, DP fails in all tasks, while DP3 achieves limited success in certain unseen categories. DP may require over 200 demonstrations for training before showing reliable performance [6, 41]. Observations from policy rollouts indicate that DP3 has overfitted to specific positions, allowing successful grasps only when the test object is located in those specific areas. Additionally, DP3 often produces highly overlapping action sequences across different object placements in task scenarios involving unseen instances and categories. In contrast, our method demonstrates a stable superiority. We can conclude from the task results of the seen instance that static and dynamic affordance provides a bridge across action distributions associated with different objects—something DP3 struggles to model due to the complexity of such distributions.  
+
+<table><tr><td>Contact Point</td><td>Trajectory</td><td>Affordance Guidance</td><td>Seen Instance</td><td>Unseen Instance</td><td>Unseen Category</td></tr><tr><td>✓</td><td></td><td></td><td>72.2%</td><td>42.5%</td><td>17.8%</td></tr><tr><td>✓</td><td>✓</td><td></td><td>71.6%</td><td>50.0%</td><td>22.2%</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>74.4%</td><td>52.5%</td><td>26.7%</td></tr></table>
+
+Table 5. Ablation study in simulation. Success rates are shown across three scenarios: seen objects, unseen instances, and unseen categories. The combination of contact point, trajectory, and affordance guidance yields the highest success rates in both seen and unseen scenarios, particularly excelling in unseen categories.
+
+# 5.4. Ablation Study
+
+To validate the efficacy of our proposed technique, we conducted ablation studies in a simulated environment under the unified policy training setting. In these experiments, we selectively omitted two critical components, trajectory and affordance guidance, in our method while maintaining other modules unchanged, to evaluate the importance of these components.
+
+As illustrated in Tab. 5, the performance of AffordDP markedly decreases when only the contact point is included, and the dynamic affordance is excluded. The integration of dynamic affordance leverages prior knowledge of object manipulation, thereby enhancing the model's performance, particularly for tasks with significant variability in object manipulation trajectories.
+
+Moreover, adaptive affordance guidance substantially boosts the performance of AffordDP in previously unseen categories. When the model encounters objects with appearances that differ considerably from those in the training set, adaptive affordance guidance steers the generated action to gradually move toward the desired manipulation for unseen objects while keeping the generated action within the manifold of action space, effectively mitigating the impact of covariance shift.
+
+# 6. Conclusion and Discussion
+
+In conclusion, the Generalizable Diffusion Policy with transferable Affordance (AffordDP) significantly advances the generalization capabilities of diffusion-based robotic manipulation policies. By modeling affordances through 3D contact points and post-contact trajectories, and incorporating affordance guidance during diffusion sampling, AffordDP effectively generalizes across entirely unseen object instances and categories. The estimation of the 6D transformation matrix using foundational vision models and point cloud registration techniques allows for the transferability of these affordances. Experimental results in both simulated and real-world environments validate the superiority of AffordDP over previous methods, marking a substantial step forward in the robotic community.
+
+Despite these advancements, AffordDP does have some limitations that need to be addressed in future work. Current foundational models have limitations in understanding spatial information, which can restrict AffordDP's ability to specify affordance transfers for particular parts. Additionally, AffordDP's effectiveness is limited in scenarios where modeling or extracting affordances is challenging. Future work should focus on enhancing the spatial understanding of foundational models and improving affordance extraction techniques to overcome these limitations.
+
+# 7. Acknowledgement
+
+This work was supported by the Shanghai Local College Capacity Building Program (23010503100), National Natural Science Foundation of China (No.62406195), MoE Key Laboratory of Intelligent Perception and Human-Machine Collaboration (ShanghaiTech University), HPC Platform of ShanghaiTech University and Shanghai Engineering Research Center of Intelligent Vision and Imaging.
+
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+# AirRoom: Objects Matter in Room Reidentification
+
+Runmao Yao Yi Du Zhuoqun Chen Haoze Zheng Chen Wang Spatial AI & Robotics (SAIR) Lab, University at Buffalo
+
+{yaorunmao，zhz19231211}@gmail.com，{yid，chenw}@sairlab.org，zhc057@ucsd.edu
+
+# Abstract
+
+Room reidentification (ReID) is a challenging yet essential task with numerous applications in fields such as augmented reality (AR) and homecare robotics. Existing visual place recognition (VPR) methods, which typically rely on global descriptors or aggregate local features, often struggle in cluttered indoor environments densely populated with man-made objects. These methods tend to overlook the crucial role of object-oriented information. To address this, we propose AirRoom, an object-aware pipeline that integrates multi-level object-oriented information—from global context to object patches, object segmentation, and keypoints—utilizing a coarse-to-fine retrieval approach. Extensive experiments on four newly constructed datasets—MPReID, HMReID, Gibson-ReID, and ReplicaReID—demonstrate that AirRoom outperforms state-of-the-art (SOTA) models across nearly all evaluation metrics, with improvements ranging from  $6\%$  to  $80\%$ . Moreover, AirRoom exhibits significant flexibility, allowing various modules within the pipeline to be substituted with different alternatives without compromising overall performance. It also shows robust and consistent performance under diverse viewpoint variations. Project website: https://sairlab.org/airroom/.
+
+# 1. Introduction
+
+With the rapid development of spatial computing, room re-identification (ReID) has become a key area of interest, enabling advancements in applications like augmented reality (AR) [37] and homecare robotics [33]. It plays a crucial role in enhancing user experiences across various scenarios. For instance, on devices like the Apple Vision Pro, accurate room ReID enables smooth transitions between virtual and real-world elements. Similarly, in AR-guided museum tours, precisely identifying a user's position within specific rooms is essential for delivering location-sensitive content.
+
+Unlike outdoor environments, where visual place recognition (VPR) methods have matured and perform reliably [2, 13, 16], indoor room ReID remains a challenging prob
+
+![](images/f966fca87abaeb23a61954c09066ea1e071d0aad75076464eb2e841c63db5945.jpg)  
+Figure 1. AirRoom leverages multi-level, object-oriented features, including global context, object patches, object segmentation, and keypoints, to perform coarse-to-fine room reidentification.
+
+lem. A primary reason for this difficulty is the cluttered nature of indoor scenes, which are often densely packed with man-made objects [45]. These densely distributed objects often pose significant challenges to existing methods, which were originally designed for city-style and distinct structures [23]. Consequently, these methods struggle to fully capture the intricate details and varied spatial layouts of indoor environments. For instance, foundation models like DINO [9] and DINOV2 [25] can generate global descriptors that capture broad scene-level features. However, these descriptors may struggle in semantically similar environments, such as adjacent rooms with similar layouts or decorations, where distinguishable features are minimal [7]. In contrast, methods like Patch-NetVLAD [13], AirLoc [3] and AnyLoc [16] create a global descriptor by aggregating local features, which can enhance discriminative power. Yet, in indoor settings densely populated with similar and repetitive objects, these approaches may still face difficulties in distinguishing between highly similar features, reducing their effectiveness in such contexts [35].
+
+Additionally, different from room categorization [18], which relies on identifying object types to classify spaces into semantic categories, room ReID requires accurately retrieving the same room instance from a reference database
+
+based on a given query image. For instance, reidentifying a particular kitchen demands a combination of global functional contexts and fine-grained matching of specific object attributes. Moreover, room ReID must handle viewpoint variations, which necessitates tolerance for partial mismatches in object arrangement and appearance. These requirements often result in the failure of algorithms based solely on object categorization, as they lack the precision needed to reidentify unique room instances accurately [39].
+
+This raises an important question: "What kinds of object attributes are truly essential for room ReID?" To address this, we conduct the first comprehensive study exploring multi-level object-oriented information and its impact on room ReID. As shown in Figure 1, our experiments show that all four levels of object-oriented information, i.e., global context, object patches, object segmentation, and keypoints, are essential. Specifically, we find that each level plays a unique role in room ReID. Global context, such as the combination of objects like a couch and television, conveys essential semantic information for categorizing a room as a living room. Object patches provide finer details, enabling differentiation within a room, such as distinguishing a bedside table in a bedroom from a desk in a workspace. Object segmentation offers further granularity by isolating individual items, like separating a dining table from surrounding chairs to clarify the room layout. Finally, keypoints on objects, such as handles on a dresser, enhance room ReID by filtering out visually similar furniture in other rooms. Moreover, integrating multi-level object-oriented information adds robustness to viewpoint variations.
+
+Based on these observations, we propose AirRoom, a simple yet highly effective room reidentification (ReID) system consisting of three stages: Global, Local, and Fine-Grained. In the Global stage, a Global Feature Extractor is used to capture global context features, which are then employed to coarsely select five functionally similar candidate rooms. In the Local stage, instance segmentation is applied to identify individual objects, followed by the Receptive Field Expander to extract object patches. An Object Feature Extractor is then used to obtain both object and patch features, which are utilized in Object-Aware Scoring to narrow the selection down to two candidate rooms. Finally, in the Fine-Grained stage, feature matching is employed to precisely identify the final room.
+
+In summary, our contributions include:
+
+- We introduce AirRoom, an object-aware room ReID pipeline with two novel modules: the Receptive Field Expander and Object-Aware Scoring, effectively leveraging multi-level object-oriented information to overcome the limitations observed in previous methods.  
+- We have curated four comprehensive room reidentification datasets—MPReID, HMReID, GibsonReID, and ReplicaReID—providing diverse benchmarks for
+
+evaluating room reidentification methods.
+
+- Extensive experiments demonstrate that AirRoom outperforms SOTAs, maintaining robust and reliable performance even under significant viewpoint variations.
+
+# 2. Related Work
+
+In this section, we review areas mostly related to our work, i.e., image retrieval and visual place recognition.
+
+# 2.1. Image Retrieval
+
+Image retrieval is a fundamental and well-established task in computer vision that involves searching for images similar to a given query within a large database. The process of image retrieval typically consists of two stages: global retrieval and re-ranking. In the first stage, a global descriptor that aggregates local features is used to retrieve  $k$  candidates from a large database. This is followed by spatial verification through local feature matching to re-rank these  $k$  candidates. Early research relied on handcrafted features [5, 22], while current methods utilize deep networks to learn informative representations [8, 28].
+
+Most image retrieval methods focus on selecting diverse relevant images to help users discover options that align with their interests or needs in real-world applications [43]. Although these methods are effective in retrieving similar images, they often lack the emphasis on distinguishing between categories or achieving precise ReID [11]. In contrast, our approach prioritizes achieving accurate ReID. Following a "global retrieval and re-ranking" pipeline, we first use global context features to identify the top five room candidates. Our object-aware mechanism then refines the search in a coarse-to-fine manner, progressively distinguishing among candidates until the most similar room is identified, yielding accurate results.
+
+# 2.2. Visual Place Recognition
+
+Visual place recognition (VPR) is often framed as a special image retrieval problem, aiming to match a view of a location with an image of the same place taken under different conditions. Previous methods fall into two categories: those that directly use global descriptors and those that aggregate local features into a global descriptor. Earlier approaches that relied on global descriptors primarily used CNN-based backbones, such as ResNet [14], to generate these descriptors. More recent methods, however, leverage foundation models like DINOv2 [25] for enhanced feature representation. In the aggregation category, early techniques employed handcrafted features like SIFT [22], SURF [4], and ORB [31]. Later advancements, including the NetVLAD series [2, 13] and AnyLoc [16], adopted learning-based models to extract feature maps and combine local features into comprehensive global descriptors.
+
+![](images/08a9260cb227234567fd5012b25a7dd2c6390a93d8cbee91279dfa733b4ca6e9.jpg)  
+Figure 2. The AirRoom coarse-to-fine pipeline. The pipeline begins with the Global Feature Extractor, which captures global context features to retrieve the top-5 reference images. Instance segmentation then generates object masks, followed by the Receptive Field Expander, which extracts object patches. The Object Feature Extractor processes both object and patch features. The Object-Aware Scoring module narrows the selection to the top-2 candidates, and Fine-Grained Retrieval identifies the most suitable reference image.
+
+However, the high performance of most VPR approaches is largely attributed to large-scale training on VPR-specific datasets [16]. Collecting extensive data for outdoor scenes is relatively straightforward due to natural variations in daylight, weather, and seasons. However, such data collection is more challenging in indoor rooms, making large-scale training on indoor datasets difficult and potentially limiting their effectiveness. Our approach effectively tackles this challenge by focusing on object-oriented feature representations, allowing us to leverage mature, pre-trained models for object feature learning. This design enables AirRoom to deliver robust performance without requiring any additional training or fine-tuning on specific datasets.
+
+# 3. Proposed Approach
+
+We propose a simple yet highly effective pipeline, AirRoom, for room reidentification that leverages multi-level object-oriented information, as shown in Figure 2. We will now systematically introduce each module of the pipeline, following the sequence of stages in which they are executed.
+
+# 3.1. Global Stage
+
+In this stage, we utilize the Global Feature Extractor to capture global context features, which are derived from the collective presence of objects within the room. These features are then used for Global Retrieval, coarsely selecting semantically similar candidate rooms from the database.
+
+# 3.1.1. Global Feature Extractor
+
+Indoor rooms exhibit fewer variations compared to outdoor environments. They lack diverse topographies, such as aerial, subterranean, or underwater features, and do not experience temporal changes like day-night or seasonal variations. Consequently, collecting large datasets for each indoor room is challenging, complicating large-scale training as seen in many VPR methods [1, 2, 13].
+
+However, indoor rooms are inherently rich in objects,
+
+each contributing to the room's overall semantic context. By leveraging this global context information, we can refine the reference search to specifically focus on rooms with similar semantic features to those in the query image. For this purpose, we prefer backbones pretrained on large image datasets, as they provide strong generalizability and effectively capture informative global context features [17]. Our model selections, therefore, include pretrained CNN-based models such as ResNet [14] and transformer-based self-supervised models like DINOv2 [25].
+
+# 3.1.2. Global Retrieval
+
+Using the Global Feature Extractor, we extract global context features for  $M$  query and  $N$  reference images. Let  $\mathbf{Q} \in \mathbb{R}^{M \times D_g}$  and  $\mathbf{R} \in \mathbb{R}^{N \times D_g}$  denote the query and reference features, respectively, where  $D_g$  is the feature dimension. The cosine similarity matrix  $\mathbf{S}$  is then computed as:
+
+$$
+\mathbf {S} _ {i j} = \frac {\mathbf {Q} _ {i} \cdot \mathbf {R} _ {j}}{\| \mathbf {Q} _ {i} \| \| \mathbf {R} _ {j} \|.} \tag {1}
+$$
+
+For each query, we select the top-5 most similar reference candidates using the following formula:
+
+$$
+\operatorname {T o p} _ {5} \left(\mathbf {S} _ {i,:}\right) = \operatorname {a r g s o r t} \left(- \mathbf {S} _ {i,:}\right) [: 5 ], \tag {2}
+$$
+
+where  $\mathbf{S}_{i,:}$  represents the cosine similarity for the  $i$ -th query.
+
+# 3.2. Local Stage
+
+Global context features provide valuable semantic information that helps narrow down the candidate list. However, when faced with many semantically similar rooms, relying solely on global context is insufficient, and local features become increasingly essential. In this stage, we adopt a local perspective by first applying instance segmentation and the Receptive Field Expander to identify objects and patches. We then use the Object Feature Extractor to extract features from both objects and patches, followed by Object-Aware Scoring to further refine the candidate list.
+
+# 3.2.1. Instance Segmentation
+
+For each query image and its corresponding five candidates, we employ instance segmentation methods, such as Mask R-CNN [15] and Semantic-SAM [20], to identify and delineate individual objects. This process generates each object's mask and bounding box. Next, we calculate the center point  $c$  of each object using its bounding box, as shown below:
+
+$$
+c = \left(\frac {x + W}{2}, \frac {y + H}{2}\right). \tag {3}
+$$
+
+In this equation,  $x$  and  $y$  represent the pixel coordinates of the top-left corner of the bounding box, while  $W$  and  $H$  denote the width and height of the bounding box, respectively.
+
+# 3.2.2. Receptive Field Expander
+
+Single object information alone is not sufficiently discriminative. For example, although different desks may have distinct appearances, they can be found in both dining halls and offices. However, when an object is connected with its neighboring items—such as a desk alongside a computer, keyboard, or notebook—it suggests that the room is more likely to be an office rather than a dining hall. This insight motivates us to expand the receptive field from a single object to a patch containing multiple objects.
+
+Given the center points of all objects in an image, we employ Delaunay triangulation [6] to generate a triangulated graph of object relationships. Specifically, Delaunay triangulation is applied to the set of object centers, ensuring that no object centers are inside the circumcircle of any triangle. This method maximizes the minimum angle of the triangles, preventing narrow, elongated triangles and ensuring more uniform object adjacency. By analyzing the adjacency relationships among the resulting triangles, we can construct the object adjacency matrix, which encodes the spatial and relational proximity of objects within the room.
+
+![](images/df7bc5d9c31a7c5deffc8f940c9a7b9ef0da91afcff561a4445283ed4e46ac30.jpg)  
+Figure 3. The Receptive Field Expander broadens the receptive field from individual objects to patches rich in contextual information. Leveraging the object adjacency matrix and each object's bounding box, it expands single objects such as a cupboard, window pane, and chair into object patches like a modular kitchen, multi-pane window, and dining set, respectively.
+
+Given the object adjacency matrix and bounding boxes in an image, for each object, we consider the bounding boxes of its neighboring objects and enlarge the current object's
+
+bounding box to encompass all adjacent objects. This expansion increases the receptive field, enabling us to capture richer contextual information, as illustrated in Figure 3. We then apply Non-Maximum Suppression (NMS) to select the highest confidence bounding boxes, removing overlapping ones based on their Intersection over Union (IoU) scores. This results in a set of clean, informative object patches.
+
+# 3.2.3. Object-Aware Refinement
+
+The Object-Aware Refinement module is composed of three key submodules: Object Feature Extractor, Mutual Nearest Neighbors, and Object-Aware Scoring.
+
+Object Feature Extractor To effectively leverage object patches and object segmentation information, we prioritize global features over local feature aggregation. The latter approach may fail to capture object characteristics effectively and can significantly increase computational complexity and storage demands [49]. As discussed in Section 3.1.1, we continue to rely on models pre-trained on large image datasets. Using the Object Feature Extractor, we obtain features for both query and reference patches and objects. Let  $Q_{p} = \{\mathbf{p}_{\mathbf{i}}^{\mathbf{q}}\}_{i = 1}^{n_{qp}}$  and  $Q_{o} = \{\mathbf{o}_{\mathbf{i}}^{\mathbf{q}}\}_{i = 1}^{n_{o0}}$  represent the query patch and object feature sets, respectively. For each reference image among the query's five candidates, we define the reference patch and object feature sets as  $R_{p} = \{\mathbf{p}_{\mathbf{i}}^{\mathbf{r}}\}_{i = 1}^{n_{rp}}$  and  $R_{o} = \{\mathbf{o}_{\mathbf{i}}^{\mathbf{r}}\}_{i = 1}^{n_{ro}}$ .
+
+Mutual Nearest Neighbors Given a set of query features  $\{\mathbf{f}_{\mathbf{i}}^{\mathbf{q}}\}_{i = 1}^{n_q}$  and reference features  $\{\mathbf{f}_{\mathbf{i}}^{\mathbf{r}}\}_{i = 1}^{n_r}$ , we obtain feature pairs by identifying mutual nearest neighbor matches through exhaustive comparison of the two sets. Let  $P$  denote the set of cosine similarity scores for these mutual nearest neighbor matches, then we have
+
+$$
+P = \left\{\cos \left(\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}}, \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}}\right) \mid i = \mathrm {N N} _ {r} \left(\mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}}\right), j = \mathrm {N N} _ {q} \left(\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}}\right) \right\} \tag {4}
+$$
+
+where
+
+$$
+\mathrm {N N} _ {q} \left(\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}}\right) = \arg \max  _ {j} \left(\frac {\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}} \cdot \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}}}{\| \mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}} \| \| \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}} \|}\right), \tag {5}
+$$
+
+$$
+\mathrm {N N} _ {r} \left(\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {r}}\right) = \arg \max  _ {j} \left(\frac {\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {r}} \cdot \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {q}}}{\| \mathbf {f} _ {\mathbf {i}} ^ {\mathbf {r}} \| \| \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {q}} \|}\right), \tag {6}
+$$
+
+$$
+\cos \left(\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}}, \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}}\right) = \frac {\mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}} \cdot \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}}}{\| \mathbf {f} _ {\mathbf {i}} ^ {\mathbf {q}} \| \| \mathbf {f} _ {\mathbf {j}} ^ {\mathbf {r}} \|}. \tag {7}
+$$
+
+By utilizing mutual nearest neighbors, we can significantly improve retrieval accuracy, simultaneously narrowing the search space and enhancing overall retrieval efficiency [50].
+
+Object-Aware Scoring The object-aware score  $s$  is the sum of the global score  $s_{\mathrm{global}}$  (calculated in Equation 1), the patch score  $s_{\mathrm{patch}}$ , and the object score  $s_{\mathrm{object}}$ :
+
+$$
+s = s _ {\text {g l o b a l}} + s _ {\text {p a t c h}} \left(Q _ {p}, R _ {p}\right) + s _ {\text {o b j e c t}} \left(Q _ {o}, R _ {o}\right). \tag {8}
+$$
+
+![](images/4d9094fb562177fde0da12ca309b11e0548b2289d43b9e197d22f770106bed52.jpg)  
+Figure 4. Illustration of four newly constructed room reidentification datasets: MPReID, HMReID, GibsonReID, and ReplicaReID. Each room provides only one reference image in the database, while query images for each room capture varied viewpoints.
+
+Here,  $s_{\mathrm{patch}}$  and  $s_{\mathrm{object}}$  can either be  $s_{\mathrm{mean}}$  or  $s_{\mathrm{max}}$ , where
+
+$$
+s _ {\text {m e a n}} \left(Q _ {t}, R _ {t}\right) = \frac {1}{\left| P \left(Q _ {t} , R _ {t}\right) \right|} \sum_ {x \in P \left(Q _ {t}, R _ {t}\right)} x, \tag {9a}
+$$
+
+$$
+s _ {\max } \left(Q _ {t}, R _ {t}\right) = \max  _ {x \in P \left(Q _ {t}, R _ {t}\right)} x. \tag {9b}
+$$
+
+In these equations,  $P$  denotes the set of cosine similarity scores for mutual nearest neighbor matches, with  $Q_{t}$  representing either  $Q_{p}$  or  $Q_{o}$ , and  $R_{t}$  representing either  $R_{p}$  or  $R_{o}$ . The global score  $s_{\mathrm{global}}$  serves as a prior, indicating that the initial five candidates vary in relevance. Thus, we retain this term to account for their differing levels of relevance.
+
+Object-Aware Refinement For each query, we select the top-2 most similar reference candidates from the initial five using the Object-Aware Scoring:
+
+$$
+\operatorname {T o p} _ {2} \left(\mathbf {s} _ {i}\right) = \operatorname {a r g s o r t} \left(- \mathbf {s} _ {i}\right) [: 2 ], \tag {10}
+$$
+
+where  $\mathbf{s}_i$  is the object-aware scores for the  $i$ -th query.
+
+# 3.3. Fine-Grained Stage
+
+Patch and object features provide valuable information for understanding the room layout; however, they may be insufficient when distinguishing highly visually similar rooms, particularly in the presence of viewpoint variations and occlusions. Keypoints on objects, by contrast, exhibit strong robustness to texture and appearance variations, enabling them to effectively handle partial occlusions and reject outliers [24]. This allows keypoints to offer a more refined approach, capturing finer details for more accurate room identification. In this stage, we use Fine-Grained Retrieval to select the final top-1 result.
+
+# 3.3.1. Fine-Grained Retrieval
+
+Deep matchers, such as SuperGlue [34], perform well in visual localization tasks under challenging conditions, both
+
+indoors and outdoors. However, they tend to face efficiency issues. In contrast, LightGlue [21] offers high efficiency without compromising matching accuracy, making it an ideal choice for our Fine-Grained Retrieval.
+
+For each query image and its two candidate reference images, we match the query to each candidate and record the number of matching keypoint pairs. A higher number of matches typically indicates greater overlap and consistency between the features of the two images, suggesting a higher degree of similarity in their content [22]. The candidate with more matches is selected as the final result.
+
+# 4. Experimental Results
+
+# 4.1. Datasets
+
+No existing indoor scene datasets are ideally suited for room reidentification tasks, as none fully satisfy the requirements. Datasets like ScanNet++ [46] and MIT Indoor Scenes [27] lack room-level segmentation, resulting in multiple rooms sharing a single scene label. The 17 Places [32] dataset includes uniquely labeled rooms but offers limited viewpoint variations, and the images are often vague. While this dataset also includes day-night changes, these are not particularly relevant for most indoor scenarios. The Reloc110 [3] dataset is likely the most suitable option; however, its quality is insufficient, with many images containing only solid-colored walls or floors due to random sampling, resulting in minimal contextual information.
+
+Several high-quality indoor 3D datasets—such as Matterport3D [10], Habitat-Matterport3D [30], the Gibson Database of 3D Spaces [44], and Replica [38]—offer real-world indoor scenes. Building on these resources and utilizing the interactive Habitat Simulator [26, 36, 40], we created four new datasets: MPReID, HMReID, GibsonReID, and ReplicaReID, as shown in Figure 4.
+
+Using the Habitat Simulator, we configured an agent for each room and manually selected 5 to 10 key poses to guide its exploration. The agent captured  $640 \times 480$  RGB-D images from various angles, resulting in 300 to 800 images
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">MPReID</td><td colspan="4">HMReID</td><td colspan="4">GibsonReID</td><td colspan="4">ReplicaReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>CVNet</td><td>17.45</td><td>29.52</td><td>17.45</td><td>19.34</td><td>11.71</td><td>25.42</td><td>11.95</td><td>13.86</td><td>12.04</td><td>24.06</td><td>12.07</td><td>14.27</td><td>15.93</td><td>20.53</td><td>15.74</td><td>16.64</td></tr><tr><td>DINOv2</td><td>59.36</td><td>64.68</td><td>59.36</td><td>58.91</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td><td>61.01</td><td>65.88</td><td>61.78</td><td>61.71</td><td>78.06</td><td>79.68</td><td>77.97</td><td>77.44</td></tr><tr><td>Patch-NetVLAD</td><td>64.32</td><td>70.47</td><td>64.36</td><td>65.53</td><td>64.86</td><td>68.78</td><td>64.32</td><td>65.16</td><td>61.47</td><td>66.90</td><td>62.04</td><td>62.51</td><td>63.77</td><td>64.97</td><td>63.86</td><td>63.87</td></tr><tr><td>AnyLoc</td><td>92.34</td><td>93.23</td><td>92.36</td><td>92.32</td><td>89.69</td><td>90.25</td><td>89.53</td><td>89.62</td><td>85.85</td><td>87.42</td><td>86.15</td><td>86.21</td><td>88.57</td><td>89.89</td><td>88.46</td><td>88.42</td></tr><tr><td>AirRoom</td><td>93.96</td><td>94.52</td><td>93.98</td><td>93.91</td><td>93.80</td><td>94.01</td><td>93.55</td><td>93.62</td><td>91.68</td><td>92.41</td><td>91.79</td><td>91.63</td><td>87.18</td><td>89.39</td><td>87.08</td><td>87.24</td></tr></table>
+
+Table 1. Overall performance comparison between AirRoom and baseline models on four newly constructed room ReID datasets.
+
+per room, depending on the number of key poses. However, many randomly sampled images were of low quality, often containing only walls or floors with minimal context. To address this, we carefully filtered the images for each room, retaining those that accurately represented the space and provided valuable information for room ReID.
+
+In total, the datasets are as follows: MPReID includes 15 scenes, 105 rooms, and 16,231 RGB-D images; HMReID consists of 21 scenes, 105 rooms, and 15,781 RGB-D images; GibsonReID contains 24 scenes, 45 rooms, and 6,743 RGB-D images; and ReplicaReID includes 12 scenes, 19 rooms, and 2,862 RGB-D images.
+
+# 4.2. Database Preprocess
+
+In the room reidentification setting, we have multiple query images and a reference database. For each dataset, we select only one image per room to build the database. Specifically, for all the images of each room, we first use CLIP [29] to extract feature embeddings. Then, we apply K-means clustering with the number of clusters set to 1. The image closest to the cluster center is chosen as the reference image, as it best represents the room's visual characteristics [42].
+
+After building the reference database, we preprocess features. First, we use the Global Feature Extractor to obtain and save the global context features. Next, we apply the instance segmentation module to segment the objects. Then, we use our Receptive Field Expander to obtain object patches and the Object Feature Extractor to extract and save the features of both the objects and the patches.
+
+# 4.3. Experimental Overview
+
+We conducted five primary experiments: overall performance comparison, group-wise performance comparison, pipeline flexibility evaluation, ablation studies, and runtime analysis. For evaluation, we used accuracy, precision, recall, and the F1 score as metrics. Per-class precision, recall, and F1-score were computed using a multi-class confusion matrix, followed by macro averaging. Accuracy was measured as the ratio of correctly matched queries to the total number of queries. A detailed runtime analysis and additional experimental results are provided in the appendix.
+
+# 4.4. Overall Performance Comparison
+
+In this section, we present a performance comparison between the best-performing version of our approach and several state-of-the-art methods, allowing us to benchmark our pipeline against established room reidentification models across different feature extraction and retrieval strategies.
+
+We selected three categories of baseline methods: image retrieval (CVNet [19]), global descriptor-based visual place recognition (VPR) (DINOv2 [25]), and VPR using aggregated local features (Patch-NetVLAD [13] and AnyLoc [16]). Specifically, we used the Base version of DINOv2, configured CVNet with a ResNet50 [14] backbone and a reduction dimension of 2048, selected the performance version of Patch-NetVLAD, and set up AnyLoc with AnyLoc-VLAD-DINOv2 using 32 VLAD clusters.
+
+![](images/7db6f80a7c20eea9a599e4f4a78923e3214910ce8762485175cdf6c3dec2bb93.jpg)  
+Figure 5. Given a bedroom query, AirRoom accurately retrieves the target image by leveraging object relevance for room reidentification. In contrast, CVNet retrieves visually similar images without preserving scene accuracy, DINOv2 captures semantic content but overlooks color details, Patch-NetVLAD, using aggregated local features to form global descriptors, retrieves images with mismatched semantic information, and AnyLoc considers semantic and color attributes but neglects object importance within rooms.
+
+Table 1 presents a quantitative comparison between AirRoom and baseline methods, showing that AirRoom outperforms all baselines on nearly all metrics and datasets. In room reidentification tasks, image retrieval methods generally exhibit lower classification metrics due to their focus not being on top-1 precision, while VPR methods yield better results. Global descriptor-based VPR methods capture only high-level semantic information, often retrieving rooms with similar semantics but lacking detailed features. In contrast, VPR methods using aggregated local features, such as Patch-NetVLAD, emphasize low-level encodings but may overlook global context, resulting in less accurate retrievals. Figure 5 illustrates failure cases for CVNet, DINOv2, Patch-NetVLAD, and AnyLoc, highlighting these limitations. Although AnyLoc, known for its robust performance in "anywhere, anytime, anyview" VPR, performs
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">MPReID</td><td colspan="4">HMReID</td><td colspan="4">GibsonReID</td><td colspan="4">ReplicaReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>ResNet50</td><td>76.14</td><td>79.21</td><td>76.20</td><td>76.58</td><td>69.03</td><td>73.21</td><td>68.61</td><td>69.07</td><td>68.84</td><td>72.30</td><td>69.50</td><td>69.00</td><td>75.05</td><td>78.61</td><td>75.30</td><td>74.88</td></tr><tr><td>CVNet</td><td>17.45</td><td>29.52</td><td>17.45</td><td>19.34</td><td>11.71</td><td>25.42</td><td>11.95</td><td>13.86</td><td>12.04</td><td>24.06</td><td>12.07</td><td>14.27</td><td>15.93</td><td>20.53</td><td>15.74</td><td>16.64</td></tr><tr><td>AirRoom-ResNet50</td><td>86.16</td><td>87.69</td><td>86.19</td><td>86.16</td><td>81.23</td><td>83.90</td><td>80.76</td><td>81.23</td><td>82.53</td><td>84.91</td><td>82.86</td><td>82.54</td><td>83.51</td><td>84.85</td><td>83.54</td><td>83.17</td></tr><tr><td>NetVLAD</td><td>82.22</td><td>86.77</td><td>82.24</td><td>82.92</td><td>72.04</td><td>80.79</td><td>71.83</td><td>73.05</td><td>68.86</td><td>81.00</td><td>69.24</td><td>71.01</td><td>77.04</td><td>81.31</td><td>77.28</td><td>77.63</td></tr><tr><td>Patch-NetVLAD(4096)</td><td>64.32</td><td>70.47</td><td>64.36</td><td>65.53</td><td>64.86</td><td>68.78</td><td>64.32</td><td>65.16</td><td>61.47</td><td>66.90</td><td>62.04</td><td>62.51</td><td>63.77</td><td>64.97</td><td>63.86</td><td>63.87</td></tr><tr><td>Patch-NetVLAD(512)</td><td>66.62</td><td>71.85</td><td>66.67</td><td>67.62</td><td>65.63</td><td>69.28</td><td>65.01</td><td>65.57</td><td>60.95</td><td>69.16</td><td>61.43</td><td>62.46</td><td>66.00</td><td>68.75</td><td>66.25</td><td>66.22</td></tr><tr><td>Patch-NetVLAD(128)</td><td>65.04</td><td>70.84</td><td>65.09</td><td>66.15</td><td>61.17</td><td>66.71</td><td>60.69</td><td>61.42</td><td>58.31</td><td>66.15</td><td>58.69</td><td>59.66</td><td>61.88</td><td>66.29</td><td>62.12</td><td>62.05</td></tr><tr><td>AirRoom-NetVLAD</td><td>89.38</td><td>90.99</td><td>89.40</td><td>89.50</td><td>83.47</td><td>86.91</td><td>83.08</td><td>83.66</td><td>82.29</td><td>87.27</td><td>82.61</td><td>82.98</td><td>83.58</td><td>84.42</td><td>83.60</td><td>83.37</td></tr></table>
+
+Table 2. Group-wise performance comparison with baseline models to assess the effectiveness of the object-aware mechanism.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">MPReID</td><td colspan="4">HMReID</td><td colspan="4">GibsonReID</td><td colspan="4">ReplicaReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>ViT</td><td>81.90</td><td>85.27</td><td>81.96</td><td>81.71</td><td>76.47</td><td>79.37</td><td>76.04</td><td>75.91</td><td>76.46</td><td>78.51</td><td>77.00</td><td>76.88</td><td>77.99</td><td>81.41</td><td>78.15</td><td>77.46</td></tr><tr><td>AirRoom-ViT</td><td>89.70</td><td>90.97</td><td>89.72</td><td>89.35</td><td>86.58</td><td>88.13</td><td>86.12</td><td>86.23</td><td>87.08</td><td>88.24</td><td>87.33</td><td>87.19</td><td>84.84</td><td>86.85</td><td>84.79</td><td>84.45</td></tr><tr><td>DINO</td><td>80.66</td><td>84.32</td><td>80.73</td><td>81.14</td><td>73.54</td><td>77.73</td><td>73.13</td><td>73.79</td><td>72.28</td><td>74.92</td><td>72.92</td><td>72.89</td><td>86.58</td><td>87.77</td><td>86.60</td><td>86.49</td></tr><tr><td>AirRoom-DINO</td><td>88.00</td><td>89.59</td><td>88.05</td><td>88.09</td><td>83.62</td><td>85.43</td><td>83.14</td><td>83.40</td><td>84.62</td><td>86.23</td><td>84.95</td><td>84.83</td><td>87.49</td><td>88.56</td><td>87.41</td><td>87.25</td></tr><tr><td>DINOv2</td><td>59.36</td><td>64.68</td><td>59.36</td><td>58.91</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td><td>61.01</td><td>65.88</td><td>61.78</td><td>61.71</td><td>78.06</td><td>79.68</td><td>77.97</td><td>77.44</td></tr><tr><td>AirRoom-DINOv2</td><td>76.10</td><td>79.03</td><td>76.11</td><td>75.80</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td><td>78.63</td><td>80.44</td><td>79.00</td><td>78.45</td><td>85.57</td><td>86.58</td><td>85.45</td><td>85.19</td></tr><tr><td>AnyLoc(16)</td><td>90.22</td><td>91.18</td><td>90.25</td><td>90.17</td><td>84.63</td><td>86.40</td><td>84.56</td><td>84.91</td><td>82.20</td><td>83.77</td><td>82.59</td><td>82.74</td><td>85.64</td><td>87.52</td><td>85.59</td><td>85.67</td></tr><tr><td>AirRoom-AnyLoc(16)</td><td>93.05</td><td>93.66</td><td>93.08</td><td>92.99</td><td>91.55</td><td>92.12</td><td>91.32</td><td>91.47</td><td>89.04</td><td>89.97</td><td>89.21</td><td>89.13</td><td>86.83</td><td>89.03</td><td>86.76</td><td>86.90</td></tr><tr><td>AnyLoc(8)</td><td>88.03</td><td>89.33</td><td>88.08</td><td>88.01</td><td>81.93</td><td>83.89</td><td>81.94</td><td>82.25</td><td>79.27</td><td>81.29</td><td>79.72</td><td>79.71</td><td>84.98</td><td>86.19</td><td>85.03</td><td>84.88</td></tr><tr><td>AirRoom-AnyLoc(8)</td><td>92.37</td><td>93.14</td><td>92.40</td><td>92.32</td><td>90.24</td><td>90.85</td><td>90.01</td><td>90.13</td><td>88.37</td><td>89.38</td><td>88.56</td><td>88.52</td><td>85.81</td><td>87.67</td><td>85.77</td><td>85.80</td></tr></table>
+
+well, AirRoom further enhances performance, achieving a  $20\%$  to  $40\%$  improvement within the available margin compared to AnyLoc. For instance, AnyLoc achieves  $89.69\%$  accuracy on HMReID, leaving approximately  $10\%$  room for improvement. AirRoom, with an accuracy of  $93.80\%$ , demonstrates up to a  $40\%$  improvement within this remaining margin. These results highlight AirRoom's superior precision and refinement in room reidentification.
+
+# 4.5. Group-Wise Performance Comparison
+
+Many baseline methods adopt a "backbone + enhancement mechanism" paradigm, which our approach also follows. In this section, we compare the performance of our object-aware enhancement mechanism with that of several state-of-the-art methods, using the same backbone as each group's baseline. This setup allows us to directly assess the effectiveness of our object-aware enhancement mechanism.
+
+For the ResNet50 backbone group, we use CVNet [19] as the baseline. In the NetVLAD backbone group, we employ Patch-NetVLAD [13] as the baseline, testing it at three reduction dimensions: 4096, 512, and 128.
+
+Table 2 reveals that within each group, the single backbone outperforms the baseline methods that attempt to enhance performance through various mechanisms, indicating that these mechanisms do not effectively capture critical information in indoor rooms. In contrast, our object-aware enhancement mechanism significantly improves the backbone's performance by emphasizing the importance of objects in indoor environments.
+
+# 4.6. Pipeline Flexibility Evaluation
+
+In this section, we systematically evaluate the flexibility and adaptability of AirRoom by testing different configurations of its key modules. The results clearly demonstrate that AirRoom is not reliant on any specific model and can ef
+
+fectively integrate a diverse range of models.
+
+# 4.6.1. Global Feature Extractor
+
+We test various Global Feature Extractors, including ViT [12], DINO [9], DINOv2 [25], and AnyLoc-VLAD-DINOv2 [16] with VLAD cluster sizes of 16 and 8.
+
+As shown in Table 3, AirRoom consistently achieves over  $85\%$  across all metrics and datasets in nearly every case, regardless of the capabilities of the Global Feature Extractor used. Even in the single exception with DINOv2, AirRoom still improves performance by nearly  $15\%$ . This demonstrates that the effectiveness of our pipeline is not reliant on any specific Global Feature Extractor, highlighting AirRoom's adaptability to various backbone configurations and underscoring its robust flexibility.
+
+# 4.6.2. Instance Segmentation
+
+We compare traditional instance segmentation methods, such as Mask R-CNN [15], with more recent approaches, including Semantic-SAM [20], which leverage advanced techniques for more granular segmentation.
+
+Table 4 shows that AirRoom consistently outperforms the baseline by over  $15\%$ , regardless of the instance segmentation module used. This demonstrates that our pipeline is not dependent on any specific instance segmentation method, underscoring its adaptability in this component.
+
+Table 3. Global Feature Extractor Flexibility.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">HMReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>DINOv2</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td></tr><tr><td>AirRoom-MaskRCNN</td><td>69.44</td><td>72.23</td><td>69.08</td><td>69.07</td></tr><tr><td>AirRoom-SSAM</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td></tr></table>
+
+Table 4. Instance Segmentation Flexibility.
+
+# 4.6.3. Object Feature Extractor
+
+We experiment with both traditional backbones, such as ResNet50 [14], and more modern backbones, like DINOv2 [25], as the Object Feature Extractor.
+
+As shown in Table 5, AirRoom achieves substantial performance improvements over the baseline, with minimal performance variation between different Object Feature Extractors. This supports the flexibility of our pipeline in accommodating a range of feature extraction methods.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">HMReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>DINOv2</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td></tr><tr><td>AirRoom-ResNet50</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td></tr><tr><td>AirRoom-DINOv2</td><td>68.67</td><td>71.81</td><td>68.33</td><td>68.59</td></tr></table>
+
+# 4.6.4. Object-Aware Scoring
+
+We evaluate both the mean  $(s_{\mathrm{mean}})$  and max  $(s_{\mathrm{max}})$  strategies for computing the patch score  $(s_{\mathrm{patch}})$  and object score  $(s_{\mathrm{object}})$ , assessing their impact on the overall performance.
+
+Table 6 shows that AirRoom's performance remains stable regardless of the object-aware scoring method used. This underscores the robustness of object-oriented information in room reidentification and demonstrates AirRoom's flexibility in adapting to different scoring strategies.
+
+Table 5. Object Feature Extractor Flexibility.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">HMReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>DINOv2</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td></tr><tr><td>AirRoom-Max(patch)-Mean(object)</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td></tr><tr><td>AirRoom-Max(patch)-Max(object)</td><td>71.02</td><td>74.02</td><td>70.72</td><td>70.85</td></tr><tr><td>AirRoom-Mean(patch)-Max(object)</td><td>70.85</td><td>73.85</td><td>70.55</td><td>70.70</td></tr><tr><td>AirRoom-Mean(patch)-Mean(object)</td><td>70.90</td><td>73.78</td><td>70.62</td><td>70.73</td></tr></table>
+
+# 4.7. Ablation Studies
+
+In this section, we remove certain modules from our pipeline—including the global score  $s_{\mathrm{global}}$ , the patch score  $s_{\mathrm{patch}}$ , the object score  $s_{\mathrm{object}}$ , within object-aware scoring, and the entire Fine-Grained Retrieval (FGR)—to assess the importance and effectiveness of each component.
+
+Table 7 shows that removing any module from our pipeline leads to a performance drop. However, as long as at least one module remains, our pipeline still outperforms the baseline. Table 8 demonstrates that when the Global Feature Extractor (ViT) performs well, the global score  $s_{\mathrm{global}}$  significantly enhances performance. On the other hand, when the Global Feature Extractor (DINOv2) is less effective, the global score  $s_{\mathrm{global}}$  has a slight negative impact, causing a small drop in performance. This result aligns with our hypothesis in Section 3.2.3, where the global score acts as a prior to rank the priority of the five candidates. Overall, these ablation studies confirm that every module in our pipeline is both important and necessary.
+
+# 4.8. Limitations
+
+While AirRoom achieves state-of-the-art performance in room reidentification under various viewpoint variations, a limitation of our work is the inability to verify robustness to indoor object rearrangements caused by movable ob
+
+Table 6. Object-Aware Scoring Flexibility.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">HMReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>DINOv2 (AirRoom-w/o all)</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td></tr><tr><td>AirRoom-w/o spatch</td><td>66.68</td><td>70.04</td><td>66.42</td><td>66.68</td></tr><tr><td>AirRoom-w/o s_object</td><td>69.77</td><td>72.84</td><td>69.48</td><td>69.64</td></tr><tr><td>AirRoom-w/o FGR</td><td>66.11</td><td>70.85</td><td>65.80</td><td>66.41</td></tr><tr><td>AirRoom-w/o spatch &amp; s_object</td><td>62.26</td><td>66.43</td><td>62.03</td><td>62.46</td></tr><tr><td>AirRoom-w/o s_object &amp; FGR</td><td>59.39</td><td>65.25</td><td>59.14</td><td>59.97</td></tr><tr><td>AirRoom-w/o s_object &amp; FGR</td><td>63.44</td><td>68.68</td><td>63.14</td><td>63.84</td></tr><tr><td>AirRoom</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td></tr></table>
+
+Table 7. Ablation Studies (Excluding Global Score Experiments).  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">HMReID</td></tr><tr><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>ViT</td><td>76.47</td><td>79.37</td><td>76.04</td><td>75.91</td></tr><tr><td>AirRoom-ViT-w/o sglobal</td><td>84.86</td><td>86.82</td><td>84.34</td><td>84.61</td></tr><tr><td>AirRoom-ViT</td><td>86.58</td><td>88.13</td><td>86.12</td><td>86.23</td></tr><tr><td>DINOv2</td><td>53.91</td><td>60.52</td><td>53.73</td><td>54.69</td></tr><tr><td>AirRoom-DINOv2-w/o sglobal</td><td>71.73</td><td>74.97</td><td>71.44</td><td>71.64</td></tr><tr><td>AirRoom-DINOv2</td><td>70.95</td><td>73.86</td><td>70.66</td><td>70.78</td></tr></table>
+
+Table 8. Ablation Studies on Global Score.
+
+jects. Although our mutual nearest neighbors-based Object-Aware Scoring method is somewhat robust to such rearrangements, the datasets used in our experiments lack these cases. In contrast, recent advances in dynamic scene understanding [47] focus on recognizing scenes in the presence of moving objects, potentially offering greater robustness than our approach. Future work should consider constructing datasets that include object rearrangements and integrating new techniques to enhance robustness to movable objects, thereby improving room reidentification.
+
+# 5. Conclusion
+
+Room reidentification is a challenging yet crucial research area, with growing applications in fields like augmented reality and homecare robotics. In this paper, we introduce AirRoom, a training-free, object-aware approach for room reidentification. AirRoom leverages multi-level object-oriented features to capture both spatial and contextual information of indoor rooms. To evaluate AirRoom, we constructed four novel datasets specifically for room reidentification. Experimental results demonstrate its robustness to viewpoint variations and superior performance over state-of-the-art methods across nearly all metrics and datasets. Furthermore, the pipeline is highly flexible, maintaining high performance without relying on specific model configurations. Collectively, our work establishes AirRoom as a powerful and versatile solution for precise room reidentification, with broad potential for real-world applications.
+
+# Acknowledgments
+
+This work was supported by the DARPA award HR00112490426. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of DARPA.
+
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+[46] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes, 2023. 5  
+[47] Yanpeng Zhao, Yiwei Hao, Siyu Gao, Yunbo Wang, and Xiaokang Yang. Dynamic scene understanding through object-centric voxelization and neural rendering, 2024. 8  
+[48] Jia Zheng, Junfei Zhang, Jing Li, Rui Tang, Shenghua Gao, and Zihan Zhou. Structured3d: A large photo-realistic dataset for structured 3d modeling. In Proceedings of The European Conference on Computer Vision (ECCV), 2020. 2  
+[49] Lingxi Zheng, Yi Zheng, and Yi Yang. Sift meets cnn: A decade survey of instance retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(5):1224-1244, 2018. 4  
+[50] Zhun Zhong, Liang Zheng, Dengpan Cao, and Shaozi Li. Re-ranking person re-identification with k-reciprocal encoding. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1318–1327, 2017. 4
\ No newline at end of file
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+# Alias-Free Latent Diffusion Models: Improving Fractional Shift Equivalence of Diffusion Latent Space
+
+![](images/072e4a3e43be7a8a74f1f56cd65de3b7ed799db0f59f5b3fbbdff613f7e52b9c.jpg)  
+Figure 1. Visualization of AE and LDM latent shift experiments. Top: we shift the input of an  $8 \times$  upsampling VAE decoder by 1/8 pixel in each step. The intermediate output images from Stable Diffusion (SD) VAE appear increasingly blurry. Bottom: we shift the noisy latent of LDM by 1/8 pixel in each step. Without cross-frame attention, SD struggles to generate consistent results; even with it, we can observe a "bouncing effect", where textures initially stick but suddenly shift in subsequent steps. In contrast, our alias-free SD (AF-SD) produces shift-equivariant results in both experiments, maintaining consistency and clarity across steps.
+
+# Abstract
+
+Latent Diffusion Models (LDMs) are known to have an unstable generation process, where even small perturbations or shifts in the input noise can lead to significantly different outputs. This hinders their applicability in applications requiring consistent results. In this work, we redesign LDMs to enhance consistency by making them shift-equivariant. While introducing anti-aliasing operations can partially improve shift-equivariance, significant aliasing and inconsistency persist due to the unique challenges in LDMs, including 1) aliasing amplification during VAE training and multiple U-Net inferences, and 2) self-attention modules that inherently lack shift-equivariance. To address these issues, we redesign the attention modules to be shift-equivariant and propose an equivariance loss that effectively suppresses the frequency bandwidth of the features in the continuous domain. The resulting alias-free
+
+LDM (AF-LDM) achieves strong shift-equivariance and is also robust to irregular warping. Extensive experiments demonstrate that AF-LDM produces significantly more consistent results than vanilla LDM across various applications, including video editing and image-to-image translation. Code is available at: https://github.com/SingleZombie/AFLDM
+
+# 1. Introduction
+
+Latent Diffusion Models (LDMs) [34] achieve high-resolution image synthesis by performing the denoising diffusion process in a compressed latent space obtained via a VAE [23]. Thanks to the rich image prior learned in LDMs, they have been broadly adopted in a variety of downstream applications. For example, LDMs are widely used for video editing by processing each frame [5, 11, 22, 47, 49, 50, 56]. They can also be finetuned for image-to-image translation tasks such as super-resolution [45, 46, 57] and normal es
+
+timation [10, 28, 48, 52], etc. These tasks often require the results to be consistent, e.g., the texture details of consecutive video frames should be coherent without flickering, and the normal estimation results of the same region should remain stable regardless of random shifts of the input image.
+
+Despite the significant demand for ensuring such consistency, LDMs unfortunately fall short in this aspect due to the inherently unstable generation process from the Gaussian noise to the clean image. Even small perturbations, such as pixel shifts or flow warping applied to the initial noisy latent, can result in drastically different images [4, 49], as shown in Fig. 1 (SD and  $\mathrm{SD^{*}}$ ). While some attempts introduce additional sophisticated modules to alleviate the inconsistency [49], how to fundamentally address this issue from the design of LDM remains underexplored. This motivates us to investigate improving the shift-equivariance of LDMs, i.e., a shift to the latent noise (e.g., 1/8 pixel) should lead to a rescaled shift in the final generated image (e.g., 1 pixel), where the rescale is caused by the upsampling in the decoder. This useful property can facilitate various vision synthesis tasks that require high stability and consistency.
+
+Previous works have studied shift-equivariance for vanilla convolutional neural networks (CNNs) from the signal processing perspective [3, 19, 31, 55]. A common cause of the failure to preserve equivariance is aliasing effects, which means that when we consider the discrete features in the continuous domain, they contain high frequencies beyond what the discrete sampling rate can represent according to the Nyquist-Shannon sampling theorem [38]. This happens in CNNs because some operations, such as downsampling, upsampling, and non-linear layers, cannot correctly band-limit the features in the continuous domain. To address this issue, several anti-aliasing operations have been proposed, which constrain the output signal to be band-limited [19, 31, 55]. For example, StyleGAN3 [19] has successfully adopted this principle to build an alias-free and shift-equivariant generator.
+
+A natural question then arises: Can we simply adopt those anti-aliasing modules in LDMs to achieve shift-equivariance? Our preliminary study reveals that existing anti-aliasing modules alone are insufficient to achieve a highly shift-equivariant LDM. We identify several reasons: 1) Although a randomly initialized VAE with alias-free modules initially exhibits reduced aliasing, these effects intensify as training progresses (Fig. 2). This is likely because the VAE's learning process benefits from amplifying the remaining high-frequencies leaked from imperfect alias-free designs, such as the processing of boundary pixels [21] and nonlinearities [31]. 2) The iterative denoising process in LDMs requires multiple U-Net inferences, causing aliasing to accumulate across denoising steps (Fig. 5). 3) The self-attention operations in the U-Net, which are sen
+
+![](images/11185b18688b6a20db0ad16bde4873279029c13bb82e3d1b6afe3491abacc958.jpg)  
+(a)
+
+![](images/55c83dc1df17392b81d9b104116436d29a9890fbf47b9888aa30089cf0e65580.jpg)  
+Figure 2. Frequency map visualization of upsampled VAE latent. The upsampled latent serves as an approximation of a continuous signal. Left: Illustration of latent upsampling algorithm. For an encoder that downsamples the image by  $8 \times$ , we can leverage its shift-equivariance to achieve  $2 \times$  upsampling of the latent. By shifting the input image by 4 pixels, we create a 0.5-pixel shift in the latent. Combining these fractional shifted latents yields a higher-resolution latent. Right: Visualization of  $8 \times$  upsampled latent in both spatial and frequency domains. (a) AF-VAE with random weights, (b) AF-VAE without equivariance loss, (c) AF-VAE with equivariance loss. Ideally, a correctly band-limited latent would only use  $1/8$  of the frequencies in the upsampled frequency domain. During training, the aliasing effects in a randomly initialized VAE with alias-free modules become more prominent; however, our proposed equivariance loss helps suppress the aliasing during training.
+
+![](images/894c846baddd886de3c86a7822c1ac989bdda53241c6756aa508fd52700e224d.jpg)
+
+sitive to global translations, are not shift-equivariant.
+
+To overcome these unique challenges in LDMs, we re-design alias-free LDMs in two distinct aspects. First, given the aliasing amplification in both VAE and U-Net inferences, it is extremely challenging to address aliasing purely from model design. Instead, we introduce an effective but much less explored way, which is an equivariance loss that includes fractional shift-equivariance of LDM's VAE and U-Net as part of the training objective. This significantly reduces aliasing without sacrificing performance. Fig. 2 verifies that this loss effectively suppresses the bandwidth of the VAE latent space.
+
+Second, we demonstrate that in order to make self-attention shift-invariant, the pool of keys and values must be fixed, while queries should shift along with the input. To achieve this, we select a reference frame, and always use the keys and values of that frame in attention calculation to ensure shift-equivariance with respect to that frame. While this solution happens to have the same form as the cross-frame attention (CFA) [22], we are the first to disclose its
+
+significance in equivariance. In addition, while previous works often use CFA in test time [5, 22, 49, 50], we find it critical to use CFA in both training and inference to suppress aliasing.
+
+With these improvements, we present Alias-Free Latent Diffusion Model (AF-LDM). As shown in Fig. 1, our AF-LDM demonstrates high fractional shift-equivariance throughout the generation pipeline. Further experiments verify that AF-LDM is robust even for irregular pixel shifts, such as flow warping. This property motivates us to propose a simple warping-equivariant video editing method that models the deformation among frames without using additional mechanisms for temporal coherence. Beyond generation, AF-LDM generalizes effectively to other image-to-image tasks that benefit from consistency and stability, such as super-resolution and normal estimation.
+
+In summary, our contributions are as follows:
+
+- We take the first attempt to investigate the shift-equivalence in LDMs and introduce a novel alias-free LDM (AF-LDM), which effectively mitigates aliasing effects and ensures shift-equivalence.  
+- To address aliasing amplification in LDMs beyond the capabilities of existing techniques, we introduce an equivariance loss to constrain the bandwidth of the underlying continuous feature. Additionally, we ensure shift-equivariance in attention layers by employing consistent reference keys and values during shifting or warping, applying this strategy in both training and inference stages.  
+- We validate the effectiveness of AF-LDM in several downstream tasks that require consistent results, including video editing and image-to-image tasks, demonstrating its broad applicability and significant potential.
+
+# 2. Related Work
+
+# 2.1. Diffusion Models
+
+The diffusion model is a family of generative models that transform Gaussian noise into a clean image through a progressive denoising process. Early diffusion models [16, 41] operate the denoising process directly in image space, requiring up to a thousand denoising steps. While effective, the image diffusion models are criticized for their extremely long training and inference time. Inspired by previous two-stage generative models [8, 43], Latent Diffusion Models (LDMs) [34] accelerate the image diffusion models by decomposing the image generation process into latent generation followed by latent decoding. Although advancements in LDMs have introduced improvements from various perspectives, such as network backbone [9, 33] and training objectives [25, 27, 29], the two-stage generation structure remains integral. Our experiments reveal that all existing latent diffusion models suffer from instability caused by aliasing effects.
+
+# 2.2. Stability of Latent Diffusion Models
+
+Compared to GANs, LDMs exhibit notable instability, especially concerning smooth latent space and shift-equivalence. A smooth latent space, a concept well-developed in GAN literature, enables continuous changes in generated images when interpolating latents [17, 18]. This smoothness enhances image editing applications for diffusion models, such as inversion [32, 42] and interpolation [14, 39, 53]. The other property, shift-equivalence, ensures consistency in generated outputs as input objects shift within a scene. This property is crucial for achieving temporal coherence in video editing applications [4, 5, 11, 22, 49, 50]. Common practices that mitigate the instability of diffusion models include image overfitting [20, 40, 53], cross-frame attention [22], and regularization [12, 51]. Warped Diffusion [6] specifically identifies the issue of shifting inconsistency in LDMs and proposes equivariance self-guidance as a remedy. Despite these efforts, the shift-equivalence of LDMs is still an underexplored topic.
+
+# 2.3. Alias-Free Neural Networks
+
+Ailasing, the overlap of signals due to improper sampling, significantly affects neural networks by reducing their shift-equivalence and shift-invariance [1, 55]. Initial efforts to create alias-free neural networks focus on improving the shift-invariance of classification CNNs through optimized downsampling techniques [3, 36, 55]. Later, StyleGAN3 [19] reveals that the upsampling, downsampling, and nonlinear operations of neural networks are not alias-free and introduce Kaiser filtering as an approximation to ideal signal processing. Following this, Alias-Free Convnets (AFC) [31] expanded upon StyleGAN3's approach, replacing the Kaiser filters with FFT-based operations and implementing polynomial nonlinearities. While most previous works discuss the aliasing effects in classification CNNs and GANs, limited research has explored the aliasing effects in LDM.
+
+# 3. Method
+
+# 3.1. Preliminaries
+
+Stable Diffusion. Stable Diffusion (SD) [34] is a latent diffusion model that consists of a Variational autoencoder (VAE) [23] and a text-conditioned denoising U-Net [35]. First, given an input image  $x \in \mathbb{R}^{H \times W \times 3}$ , the encoder  $\mathcal{E}$  and decoder  $\mathcal{D}$  of the VAE are trained to minimize the distance between  $x$  and the reconstructed image  $\mathcal{D}(z)$ , where  $z = \mathcal{E}(x) \in \mathbb{R}^{H / k \times W / k \times 4}$  is the latent downsampled by  $k \times$ . Next, a latent denoising U-Net  $\epsilon_{\theta}(z_t, t)$  is trained to denoise the noisy latent  $z_t$  at timestep  $t$ . During sampling, a clean latent  $z$  is sampled via a reverse diffusion process and then decoded to obtain the final image  $\mathcal{D}(z)$ .
+
+Both VAE and U-Net are built on the encoder-decoder architecture that consists of similar modules. Specifically, the
+
+networks incorporate ResNet blocks [13] and self-attention blocks [44]. To rescale the feature, the networks employ the nearest downsample and bilinear upsample. Although the networks heavily rely on shift-equivariant convolution layers, the other modules, including nonlinearities, sampling, and self-attention, are not shift-equivariant.
+
+StyleGAN3 StyleGANs [17, 18] generate high-resolution images by gradually upsampling a constant low-resolution feature with a CNN-based synthesis network. Despite high generation quality, a "texture sticking" effect occurs in the original StyleGAN, where the details in the output image stick to the same position when shifting the input feature. StyleGAN3 [19] argues that the aliasing in the synthesis network causes this effect. The issue is analyzed by a continuous signal interpretation: each network feature is equivalent to a continuous signal. A discrete feature  $Z$  can be converted into a continuous signal  $z$  via interpolation filter and be converted back via Dirac comb. Similarly, each network layer  $F$  has its counterpart  $f$  in the continuous domain. If a network layer is shift-equivariant, then its effect in the discrete and continuous domain should be equivalent, i.e., the conversion between  $F(Z)$  and  $f(z)$  should still be invertible.
+
+Based on the continuous signal interpretation, StyleGAN3 makes several primary improvements:
+
+1. Fourier Latent: Transform the input of the synthesis network from the image feature to the Fourier feature.  
+2. Cropping Boundary Pixels: Crop the border pixels after each layer to stop leaking absolute position.  
+3. Ideal Resampling: Replace bilinear upsampling with Kaiser filters that better approximate an ideal low-pass filter.  
+4. Filtered Nonlinearity: Wrap nonlinearities between a  $2 \times$  upsampling and  $2 \times$  downsampling to suppress the high frequencies introduced by this operation.
+
+Fractional Shift Equivalence. Let  $T_{\Delta}$  be the shift operator that shifts an image  $x \in \mathbb{R}^{H \times W}$  by  $\Delta \in \mathbb{N}^2$  pixels, an operator  $f: \mathbb{R}^{H \times W} \to \mathbb{R}^{H \times W}$  is shift equivariant if it satisfies  $f(T_{\Delta}(x)) = T_{\Delta}(f(x))$ . The shift equivariance can be extended to fractional shift equivariance, i.e.,  $\Delta \in \mathbb{R}^2$ . In this work, we implement it as the Fourier shift, which shifts the phase of an image in the Fourier domain according to  $\Delta$ . With fractional shift, we can extend  $f$  to an operator that rescales the image. Assume  $f: \mathbb{R}^{H \times W} \to \mathbb{R}^{kH \times kW}$  is an operator that rescale the image by a factor of  $k$ , then it is fractional shift equivariant if  $f(T_{\Delta}(x)) = T_{k \cdot \Delta}(f(x))$ .
+
+Since the resolution of an image is limited, some pixels are moved out or missing after shifting. There are two common ways to process the edge pixels: circular shift  $T^{\mathrm{cir}}$  fills the missing pixels with pixels that just moved out. In constant, cropped shift  $T^{\mathrm{cro}}$  fills the missing pixels with a constant, and the shift-equivariance is only considered in valid regions. This paper uses cropped shift by default since it is closer to the default padding mode of convolutional layers.
+
+![](images/428d7acdf9a05a17f17fc58fe51c8aca085607b941e6c8f5fcf77bdeca9da890.jpg)  
+Figure 3. The architecture of AF-LDM. Both VAE and U-Net of SD can be represented by an encoder-decoder structure. We implement ideal upsample, ideal downsample and filtered nonlinearity following [19, 31].
+
+# 3.2. Alias-free Latent Diffusion Models
+
+In this work, we focus on improving the fractional shift-equivalence of SD [34] for its widespread applications in the community. While StyleGAN3 provides an effective methodology for designing alias-free CNNs, these alias-free mechanisms cannot be directly applied to SD. This is because the generation process of StyleGAN3 solely depends on the latent-to-image synthesis network, enabling extremely flexible latent-related design for equivariance, such as using Fourier latents and cropping border pixels as reviewed in Sec. 3.1. In contrast, the equivariance of LDMs depends jointly on AE encoder, decoder, and U-Net. Specifically, the latent is produced by AE encoder, leaving less room to redefine the latent, not to mention the self-attention operators that are sensitive to small changes.
+
+To this end, we propose Alias-Free LDM (AF-LDM) (Fig. 3), which has two significant improvements. 1) We propose a continuous latent representation (Sec. 3.3), which has a limited frequency bandwidth and naturally supports fractional shift. To ensure this representation, we modify network modules with anti-aliasing designs and regularize the learning process with an equivariance loss. 2) To enhance the equivariance of self-attention, we employ equivariant attention (Sec. 3.4) that fixes the key and value features of self-attention when processing the shifted latents. Some anti-aliasing techniques are inspired by StyleGAN3. The comparison between StyleGAN3 and our AF-LDM is summarized in Table 1.
+
+# 3.3. Continuous Latent Representation via Equiv-ariance Loss
+
+Based on the definition, a LDM pipeline is fractional shift-equivariant if
+
+Table 1. Comparison between StyleGAN3 and AF-LDM. Our main improvements are highlighted in bold.  
+
+<table><tr><td></td><td>StyleGAN3</td><td>AF-LDM</td></tr><tr><td>Latent Representation</td><td>Fourier feature</td><td>Continuous latent</td></tr><tr><td>Resampling</td><td>Kaiser filtering</td><td>FFT</td></tr><tr><td>Filtered Nonlinearity</td><td>✓</td><td>✓</td></tr><tr><td>Cropping Boundary Pixels</td><td>✓</td><td>✗</td></tr><tr><td>Equivariance Loss</td><td>✗</td><td>✓</td></tr><tr><td>Equivariant Attention</td><td>-</td><td>✓</td></tr></table>
+
+$$
+\epsilon_ {\theta} \left(T _ {\Delta} \left(z _ {t}\right), t\right) = T _ {\Delta} \left(\epsilon_ {\theta} \left(z _ {t}, t\right)\right), \tag {1}
+$$
+
+$$
+\mathcal {D} \left(T _ {\Delta} (z)\right) = T _ {k \cdot \Delta} (\mathcal {D} (z)), \tag {2}
+$$
+
+where  $k$  is the downsampling factor of VAE. Since we implement fractional shift as Fourier shift, each  $z$  should be a band-limited continuous latent that can be sampled everywhere by applying DFT, phase shift, and IDFT. For example, if the resolution of input image  $x$  is  $s \times s$ , then the maximum frequency of  $z$  should be less than  $s / (2k)$  based on sampling theorem [38].
+
+By incorporating anti-aliasing layers shown in Fig. 3, the shift-equivariance of a randomly initialized AE is significantly enhanced<sup>1</sup>, as verified in Table 2. However, as training progresses, shift-equivariance gradually deteriorates. We hypothesize that this is because of the imperfect anti-aliasing designs, such as the processing of boundary pixels and nonlinearities, which enable the network to introduce aliasing that undermines equivariance. These aliasing effects may inadvertently aid the networks' learning process, leading to their amplification over time.
+
+Recognizing that anti-aliasing modules alone are insufficient to fully resolve the equivariance issue, we shift our focus to regularizing network learning by directly optimizing the error between the outputs of shifted inputs and the corresponding shifted outputs. Specifically, we propose an equivariance loss for any network  $f$  that rescales the input by  $k \times$ :
+
+$$
+L = \left\| f \left(T _ {\Delta} (x)\right) - T _ {k \cdot \Delta} (f (x)) \right\| _ {2} ^ {2}. \tag {3}
+$$
+
+The loss is directly added to the original training loss of  $f$ . Since  $T$  is a Fourier shift, this loss forces the network to only use the low-frequency information that the discrete latent can represent. With all these modifications, the continuous latent of Alias-free VAE is nearly a band-limit signal as illustrated in Fig. 2. In practice, the equivariance loss is implemented as follows.
+
+VAE. We compute the equivariance loss for the VAE encoder and decoder separately. Formally, given input  $x \in \mathbb{R}^{H \times W \times C}$ , the equivariance loss is defined as
+
+$$
+L _ {\text {e n c}} = \left\| \left[ \mathcal {E} \left(T _ {\Delta} (x)\right) - T _ {\Delta / k} (\mathcal {E} (x)) \right] \cdot M _ {\Delta / k} \right\| _ {2} ^ {2}, \tag {4}
+$$
+
+$$
+L _ {\mathrm {d e c}} = \left\| \left[ \mathcal {D} \left(T _ {\Delta / k} (z)\right) - T _ {\Delta} (\mathcal {D} (z)) \right] \cdot M _ {\Delta} \right\| _ {2} ^ {2}, \tag {5}
+$$
+
+where  $z = sg(\mathcal{E}(x))$ ,  $sg$  is stop gradient operator, and  $M_{\Delta}$  denotes the valid mask for cropped shift  $T_{\Delta}$ . Since the fractional shift of an image is not well defined, the offsets are integers, i.e.,  $\Delta = (\Delta_x,\Delta_y)\in \mathbb{N}^2$ .
+
+U-Net. For latent  $z_{t} \in \mathbb{R}^{H / k \times W / k \times C'}$  at timestep  $t$ , the equivariance loss of U-Net is defined as
+
+$$
+L _ {\text {u n e t}} = \left\| \left[ \epsilon_ {\theta} ^ {\prime} \left(T _ {\Delta} ^ {\text {c i r}} \left(z _ {t}\right), t\right) - T _ {\Delta} \left(\epsilon_ {\theta} \left(z _ {t}, t\right)\right) \right] \cdot M _ {\Delta} \right\| _ {2} ^ {2}, \tag {6}
+$$
+
+where  $\Delta = (\Delta_x / k, \Delta_y / k)$ ,  $\Delta_x$  and  $\Delta_y$  are sampled in the same way as VAE.  $\epsilon_{\theta}'$  is the U-Net with equivariant attention (Sec. 3.4). We first compute  $\epsilon_{\theta}(z_t, t)$  and cache attention features and then compute  $\epsilon_{\theta}'(T_{\Delta}^{\mathrm{cir}}(z_t), t)$ . Considering U-Net is more easily affected by the padded pixels due to cropped shift in the iterative denoising process, we apply circular shift  $T^{\mathrm{cir}}$  when shifting the input latent to pad meaningful pixels. Note that we still use cropped valid mask  $M_{\Delta}$  to filter out the padded pixels when computing loss.
+
+# 3.4. Equivariant Attention
+
+Given an input image token sequence  $x\in \mathbb{R}^{HW\times d_m}$ , the self-attention operation [44] is defined as
+
+$$
+\mathrm {S A} (x) = \operatorname {s o f t m a x} \left(x W ^ {Q} \left(x W ^ {K}\right) ^ {\top}\right) x W ^ {V}, \tag {7}
+$$
+
+where  $W^{Q}, W^{K} \in \mathbb{R}^{d_{m} \times d_{k}}$  and  $W^{V} \in \mathbb{R}^{d_{m} \times d_{v}}$  are projection matrices. For simplicity, the scaling factor is omitted. While self-attention is inherently shift-equivariant under circular shifts, it fails to maintain equivariance under cropped shifts or non-rigid deformations (e.g., warping). That is because to achieve equivariance, we need
+
+$$
+\begin{array}{l} \operatorname {s o f t m a x} (T (x) W ^ {Q} (T (x) W ^ {K}) ^ {\top}) T (x) W ^ {V} = \tag {8} \\ T \left(\operatorname {s o f t m a x} \left(x W ^ {Q} \left(x W ^ {K}\right) ^ {\top}\right) x W ^ {V}\right), \\ \end{array}
+$$
+
+and  $T(\cdot)$  denotes shifting (reindexing rows). The right-hand side of the equation 8 reduces to  $\operatorname{softmax}(T(x)W^Q(xW^K)^\top)xW^V$  since softmax and matrix right multiplication are row-wise independent. The equation breaks since  $T(x)W^K$  and  $T(x)W^V$  are modified by cropping.
+
+To address this, we redefine self-attention as a point-wise operation, ensuring equivariance under any relative shifts to a reference frame. Formally, given a reference frame  $x_{r} \in \mathbb{R}^{HW \times d_{m}}$  and its shifted version  $x_{s}$ , we propose Equivariant Attention (EA), defined as:
+
+$$
+\operatorname {E A} \left(x _ {r}, x _ {s}\right) = \operatorname {s o f t m a x} \left(x _ {s} W ^ {Q} \left(x _ {r} W ^ {K}\right) ^ {\top}\right) x _ {r} W ^ {V}. \tag {9}
+$$
+
+Since matrix right multiplication is row-wise independent and each token is a row vector of  $x_{s}$ , the above equation is
+
+Table 2. AF-VAE reconstruction quality and shift-equivariance on  ${256} \times  {256}$  ImageNet validation set. Equiv. Loss refers to Equivariance Loss. †: Original SD VAE was trained on OpenImages [24]. This model is trained on ImageNet using our code.  
+
+<table><tr><td>Model Configuration</td><td>Rec. PSNR</td><td>rFID</td><td>Enc. SPSNR</td><td>Dec. SPSNR</td></tr><tr><td>SD VAE</td><td>26.94</td><td>0.69</td><td>25.07</td><td>22.31</td></tr><tr><td>SD VAE†</td><td>26.45</td><td>0.63</td><td>19.71</td><td>21.36</td></tr><tr><td>+ Ideal sampling</td><td>25.76</td><td>1.01</td><td>21.51</td><td>21.75</td></tr><tr><td>+ Filtered nonlinearity</td><td>25.42</td><td>0.86</td><td>29.49</td><td>24.61</td></tr><tr><td>+ Equiv. loss (AF-VAE)</td><td>25.53</td><td>1.00</td><td>45.10</td><td>33.88</td></tr><tr><td>SD VAE† + Equiv. loss</td><td>24.59</td><td>4.18</td><td>41.46</td><td>30.74</td></tr><tr><td>AF-VAE random weights</td><td>-</td><td>-</td><td>29.43</td><td>29.02</td></tr></table>
+
+Table 3. Unconditional AF-LDM sampling quality and shift-equivalence on  $256 \times 256$  FFHQ.  
+
+<table><tr><td>Model Configuration</td><td>FID</td><td>Latent SPSNR</td><td>Image SPSNR</td></tr><tr><td>LDM w/ SD VAE</td><td>14.91</td><td>27.47</td><td>12.38</td></tr><tr><td>+ CFA in Inference</td><td>14.91</td><td>38.22</td><td>21.69</td></tr><tr><td>LDM w/ AF-VAE</td><td>15.27</td><td>22.87</td><td>12.18</td></tr><tr><td>+ CFA in Inference</td><td>15.27</td><td>23.58</td><td>13.09</td></tr><tr><td>+ Ideal Sampling</td><td>17.03</td><td>24.44</td><td>14.03</td></tr><tr><td>+ Filtered Nonlinearity</td><td>14.28</td><td>24.53</td><td>14.15</td></tr><tr><td>+ Equiv. Loss w/o CFA</td><td>16.90</td><td>28.57</td><td>17.65</td></tr><tr><td>+ CFA in Equiv. Loss (AF-LDM)</td><td>19.05</td><td>40.94</td><td>28.06</td></tr><tr><td>LDM w/ AF-VAE + Equiv. loss</td><td>39.14</td><td>37.63</td><td>25.99</td></tr><tr><td>AF-LDM random weights</td><td>-</td><td>39.84</td><td>29.68</td></tr></table>
+
+a point-wise operation applied individually to each token in  $x_{s}$ . As a result, the operation is inherently equivariant for any relative deformation.
+
+Interestingly, we observe that this equivariant attention mechanism has the same form as Cross-Frame Attention (CFA) in video editing literature, which is primarily used as an inference-time technique. In our method, however, it is important to incorporate EA together with equivariance loss during training to effectively mitigate aliasing effects. This is because, without EA, the equivariance loss will focus on fixing the attention module rather than the aliasing. For ease of understanding, we refer to EA as CFA in the experiment section.
+
+# 4. Experiment
+
+# 4.1. Ablation Study
+
+In the ablation study, we first train the Alias-Free VAE (AF-VAE) on  $256 \times 256$  ImageNet [7], initializing weights from the Stable Diffusion VAE (kl-f8 model in [34]). We then train an unconditional AF-LDM in the latent space of AF-VAE on  $256 \times 256$  FFHQ [17] from scratch.
+
+To assess the fractional shift-equivariance of models, we compute shift PSNR (SPSNR) [19, 55] that positively correlates with shift-equivariance. Formally, for a model  $f$  that rescales the inputs by  $k$ , SPSNR for an input  $x$  is given by:
+
+$$
+\operatorname {S P S N R} _ {f} (x) = \operatorname {P S N R} \left(f \left(T _ {\Delta} (x)\right), T _ {k \cdot \Delta} (f (x))\right). \tag {10}
+$$
+
+In the following experiments, we evaluate both the quality and shift-equivariance of VAE and LDM. Our alias-free
+
+![](images/e291396dcb10be652d4ea33f37a4800d11436d33efbb0050c766d2c0bad8b66e.jpg)  
+Figure 4. Visualization of LDM latent fractional shifts. The latent is obtained by DDIM inversion. The difference map between outputs and shifted outputs is given in the bottom right corner.
+
+models are trained with an objective that balances enhancing equivariance with maintaining the original task quality. VAE. To evaluate VAE quality, we use reconstruction PSNR and FID [15]. Shift-equivariance is measured by encoder SPSNR and decoder SPSNR. The encoder SPSNR checks if the VAE latents are properly band-limited, while the decoder SPSNR evaluates output consistency under input shift. All metrics are computed on  $50,000 \times 256$  ImageNet validation images.
+
+Table 2 shows that ideal sampling and filtered nonlinearity improve VAE shift-equivariance. However, both encoder and decoder SPSNR decrease compared to a randomly initialized model (last row), possibly due to imperfect anti-aliasing modules. Adding an equivariance loss as a regularization term balances task fidelity with high shift-equivariance. Note that applying equivariance loss without anti-aliasing modules significantly lowers the reconstruction quality (second-to-last row), highlighting that alias-free architecture is necessary for adding equivariance loss.
+
+LDM. For LDM quality evaluation, we use FID computed on 50,000 samples generated with 50 DDIM steps. Shift-equivalence of LDM is measured by latent SPSNR and image SPSNR, with the former only considering the denoising process and the latter encompassing both denoising and VAE encoding. The SPSNR is computed on 10,000 randomly sampled noisy latents. Unless otherwise specified, CFA is enabled by default during inference, as disabling it would result in significant changes to the image's identity.
+
+The quantitative results are shown in Table 3, and partial
+
+![](images/4daa8a6c0b7c1edf693efd2e0ba875123994120fb65ab056c491d3e0e8c64f45.jpg)  
+Figure 5. Shift-equivariance during denoising process. We perform two denoising processes: one with Gaussian noise and the other with a  $1/2$  pixel-shifted version of the same noise, computing the SPSNR after each denoising step. The experiment is conducted on 10,000 samples over 20 denoising steps.
+
+![](images/f37211dbf5c6bd47a94a28f4b556b1ae5badea4ebf9ad832b566b357f21a2dee.jpg)  
+Figure 6. Quantitative comparison of fractional shift consistency. We horizontally shift latents by  $1/8$  pixels per step and compute the average SPSNR for the VAE decoder and LDM pipeline for each step. The VAE is tested on 500 ImageNet validation images, and LDM is tested on 500 FFHQ images.
+
+![](images/79f7e4ba8ddd1b2458e7e5356a81c1b47d2686ba4a6edaea03be7a1ccc5e69da.jpg)
+
+visualization results are shown in Fig. 4. Although LDM with SD VAE has good SPSNR, we can observe severe quality degradation in fractional shift results (Fig. 4(a)). Using AF-VAE can improve the quality of shifted frames, but "texture sticking" still occurs (Fig. 4(b)). This issue can be addressed by adding equivariance loss (Fig. 4(c)). By applying CFA in equivariance loss, the final model, AF-LDM, has the best overall shift-equivariance.
+
+To further demonstrate the improvements of our AF-LDM over standard LDM, we evaluate SPSNR at each step of the denoising process, as shown in Fig. 5. In standard LDM, shift-equivariance degrades progressively due to error accumulation throughout the denoising process. In contrast, our AF-LDM mitigates this degradation, maintaining higher shift-equivariance across denoising steps.
+
+Fractional Shift Consistency. To verify consistent shift-equivalence under fractional shifts, we horizontally shift a set of images and compute the averaged SPSNR for each step (Fig. 6). Baseline models exhibit high shift-equivalence only for integer shifts, causing the blur outputs of the VAE decoder and the "bouncing effect" of LDM. In contrast, alias-free models achieve higher average SPSNR and lower variance, resulting in more stable AF-LDM outputs.
+
+![](images/f8be00b7f9f193de4a23517e2e8c9efd62862dc9f4cc515e12c12e588f23c75b.jpg)  
+Figure 7. Warping consistency experiments. Given neighboring frames and their ground truth optical flow, we can warp the inverted latents and compute the inversion warping error. We then reconstruct an inverted latent and its warped version to test the generation warping error. Cross-Frame attention (CFA) is enabled in both inversion and generation. The input warping error is computed as a reference.
+
+![](images/498941ae91ca658c4233f9ecd371af8a87e4509ec46029797473e9c679b2fb09.jpg)  
+Figure 8. Qualitative comparison of video editing consistency between SD and AF-SD using warping-equivariant video editing. Texture flickering can be observed in SD's results. More results are available in the supplementary.
+
+# 4.2. Warping-Equivariant Video Editing
+
+With a more stable generation process, our AF-LDM can enhance video editing by improving temporal consistency. To showcase this application, we implement an alias-free Stable Diffusion (AF-SD) by integrating AF-VAE, anti-alias U-Net modifications, and retraining the text-conditional LDM on LAION Aesthetic  $6.5+$  dataset [37]. We then propose a simple and elegant Warping-equivariant video editing algorithm.
+
+Although our AF-SD is designed for pixel shift-equivariance, it performs well under irregular pixel shifts, such as flow warping. We verify this through the experiment shown in Fig. 7. Quantitative results in Table 4 demonstrate superior inversion and generation warping-equivariance in AF-SD over SD, indicating that AF-SD can better pre
+
+Table 4. Warping error (defined in Fig. 7) computed on Sintel [2].  
+
+<table><tr><td>Model</td><td>Input Warping PSNR</td><td>Inversion Warping PSNR</td><td>Generation Warping PSNR</td></tr><tr><td>SD</td><td rowspan="2">22.77</td><td>17.53</td><td>21.95</td></tr><tr><td>AF-SD</td><td>19.68</td><td>26.10</td></tr></table>
+
+![](images/6c024fe8d7f33d045b82b4537005d8f3b232969455b7f6f7aa020426a559a551.jpg)
+
+![](images/2dad366361fdeb267fc22d9b466d6c5dfc6a6c21bbf2462fcfaa788687fa735e.jpg)
+
+![](images/2c0e9c9e2005bd20286561c3541839410ead065a7250c4d1322e10e167ebe44d.jpg)
+
+![](images/a111c0ca4dfbce0a48676b243e3340cd72bffca388beddf80a8bb1a56f6b30ab.jpg)
+
+![](images/04121cbd05af62fb7d2ddbf51f2b62fa558aac8d9b88961353483c3e0b41e814.jpg)
+
+![](images/817a7fbe110820387314d976d9f320e3b74c4d4c72ff99cefa3e1664a600c602.jpg)
+
+![](images/dfa5bcd88a8383af659321640f958c17b21fe75b2ee582f6d06ee87f82307750.jpg)
+
+![](images/b8242549b8c536f9b14eac7263787f7888387a04039e7fa5b7695604dcf9bec0.jpg)
+
+![](images/dd701f186e544f0ccf6514ff721b6358e701f9fb14778d13cf6eda584049242f.jpg)  
+Figure 9. Qualitative comparison of shift-equivalence in latent  $\mathrm{I}^2\mathrm{SB}4\times$  super-resolution results.
+
+![](images/3f629f2b279e1bf5885b1bf187501b4ccba850c68bde1412c01a05ad1acb465d.jpg)
+
+![](images/7b31343162065d5dc45c4f866a0de1b3643473da4d86c4099cd06ef44ff55e52.jpg)
+
+![](images/0fbea3051f67d28938a689efc95db26e22b21176f9945103b221201decebda07.jpg)
+
+serve deformation information. Higher inversion warping-equivalence is especially advantageous in inversion-based video editing because even if the reconstruction process is changed (for example, using another prompt), the diffusion model can still generate consistent results by utilizing the deformation information from latents.
+
+Based on these observations, we propose a novel warping-equivariant video editing method. First, we apply DDIM inversion to input video to an intermediate denoising timestep (similar to SDEdit [30]) with an empty prompt. Then, we regenerate a video from the inverted latents with a new prompt. CFA is enabled in both processes. This method implicitly deforms noisy latents without the need for explicit latent warping [4, 5, 49, 50]. As illustrated in Fig. 8, AF-SD's robust inversion and generation ensure more consistent edited videos than SD.
+
+# 4.3. Image-to-image Translation
+
+Super-resolution with Latent  $\mathbf{I}^2\mathbf{SB}$ . Image-to-Image Schrodinger Bridge  $(\mathrm{I}^2\mathrm{SB})$  [26] is a conditional diffusion model that directly maps one image distribution to another without going through Gaussian noise. Originally,  $\mathrm{I}^2\mathrm{SB}$  operates in image space, with model weights initialized from an unconditional diffusion model. In our experiments, we implement two variants of  $\mathrm{I}^2\mathrm{SB}$  for  $4\times$  super-resolution in latent space: one based on LDM and the other on AF-LDM. As shown in Fig. 9, the standard latent  $\mathrm{I}^2\mathrm{SB}$  exhibits severe flickering and quality degradation when input shifts. In contrast, the alias-free variant demonstrates strong shift-equivalence, providing consistent outputs.
+
+Normal Estimation with YOSO. Normal Estimation is another image-to-image task that requires the model to produce consistent outputs across shifts. We implement a one-step conditional diffusion model [48], You-Only-SampleOnce (YOSO), following StableNormal [52]. YOSO lever
+
+![](images/776d44634d6d651495ef055a6f2b127b00705d55b4619959ffbf024b1073ddf6.jpg)
+
+![](images/72124ef19bd80d57725d1dd0c662fddb18aa5920cd0711781d935e1df5c18bec.jpg)
+
+![](images/ee2dee5a7446a4442362d44d6a2a137d771f875ec8bf7c9638feb240e8a225ed.jpg)
+
+![](images/4f91f5894245b32d1f47f105c2f203a986b11f1039942652a3ae5637b3086f5c.jpg)
+
+![](images/23a94907bc5de9a54f2ac72ce4f5d4595af5154c979689fd84bf610f9494f2f3.jpg)
+
+![](images/b24389bbd774ccba073963104c6166cc798bd68ed9ffe1bed0b87cee6ff1a1b7.jpg)
+
+![](images/9c8e1a6e8f7ead87656d34c4f62c2b3df22401c830226412ca410de4909a373e.jpg)
+
+![](images/243da1bdca91d29f5b5a31848c3ce2a7da5b64b06ca667aa2a6dfd5cd5ae2546.jpg)
+
+![](images/215ffbae1763b913b4ef947d6b8890f2008ba2ceec83d70b2469179c80e3010b.jpg)
+
+![](images/897e214be5266f974092f24276a6fc99f65a72902afce9339986a2f1ffa466fc.jpg)
+
+![](images/842867a4cca48e5438cabda8dd19b7fdada881d03484b07764858b54ecb9d4fd.jpg)
+
+![](images/8cc57eff78fea3e62b4ee778f9646f98986a8928c6ac974249680dcd35f71031.jpg)
+
+![](images/2e9c312d4c270ec29a4ff8689070e9178758b6ed490b56a04862d0e4c3e335a7.jpg)  
+Figure 10. Qualitative comparison of shift-equivariance in YOSO normal estimation. The contrast of local regions is enhanced. Please refer to the supplementary for a clearer video comparison.
+
+![](images/572efdcb054256b7f6d639e7b04b45c1f03b78fbba8a4743509bc7dcf0fd3906.jpg)
+
+![](images/3c019474f7d9f22f06c9961ecf27f0cf0c7c4feb045dc7d251d9c4bf5f12c31f.jpg)
+
+![](images/2eada2d3cb4e651ba8b2b84d43f5b0d2b9030b0adb48de6b7793dc3c91430d68.jpg)
+
+ages ControlNet [54] to adapt a pre-trained SD into a normal map prediction model conditioned on input RGB images. For our implementation, we use  $x_0$  parameterization instead of  $x_{t}$  parameterization used in [52]. We first train a baseline YOSO initialized from SD. We then enhance the ControlNet of YOSO with our anti-alias designs and train an alias-free YOSO (AF-YOSO) based on AF-SD.
+
+We compare the shift-equivariance of vanilla YOSO and AF-YOSO in Fig. 10. Although the baseline model produces largely consistent outputs, some flickering remains, particularly around high-frequent textures. In contrast, AF-YOSO delivers fully consistent results across the entire image, effectively mitigating flickering.
+
+# 5. Conclusion
+
+We present Alias-Free Latent Diffusion Models, a novel framework designed to eliminate the instability of LDMs when input shifts occur. By incorporating equivariance loss and equivariant attention along with anti-aliasing modules, our model achieves significantly improved shift-equivalence. Experimental results demonstrate that our model can facilitate various editing tasks, such as inversion-based video editing, providing consistent and stable outputs. Additionally, the approach can be extended to other tasks that leverage a pre-trained latent diffusion model, such as super-resolution and normal estimation, substantially enhancing consistency over spatial shifts.
+
+Acknowledgments. This research is supported by NTU SUG-NAP. This study is also supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).
+
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+# Align-A-Video: Deterministic Reward Tuning of Image Diffusion Models for Consistent Video Editing
+
+Shengzhi Wang $^{1}$ , Yingkang Zhong $^{2}$ , Jiangchuan Mu $^{1}$ , Kai Wu $^{3}$ , Mingliang Xiong $^{2}$ , Wen Fang $^{2}$ , Mingqing Liu $^{2}$ , Hao Deng $^{2}$ , Bin He $^{1}$ , Gang Li $^{1}$ , and Qingwen Liu  $^{*1,2}$
+
+$^{1}$ Shanghai Research Institute for Autonomous Intelligent Systems, Tongji University  $^{2}$ School of Computer Science and Technology, Tongji University  $^{3}$ ByteDance
+
+# Abstract
+
+Due to control limitations in the denoising process and the lack of training, zero-shot video editing methods often struggle to meet user instructions, resulting in generated videos that are visually unappealing and fail to fully satisfy expectations. To address this problem, we propose Align-A-Video, a video editing pipeline that incorporates human feedback through reward fine-tuning. Our approach consists of two key steps: 1) Deterministic Reward Fine-tuning. To reduce optimization costs for expected noise distributions, we propose a deterministic reward tuning strategy. This method improves tuning stability by increasing sample determinism, allowing the tuning process to be completed in minutes; 2) Feature Propagation Across Frames. We optimize a selected anchor frame and propagate its features to the remaining frames, improving both visual quality and semantic fidelity. This approach avoids temporal consistency degradation from reward optimization. Extensive qualitative and quantitative experiments confirm the effectiveness of using reward fine-tuning in Align-A-Video, significantly improving the overall quality of generated videos.
+
+# 1. Introduction
+
+The rapid advancement of diffusion models [11, 28, 31, 47] has significantly enhanced image generation technologies, enabling precise manipulation of various image attributes [2, 14]. However, diffusion models have yet to achieve high-quality performance in video generation. Due to the complexity of temporal motion in videos, training a video diffusion model requires substantial data and computational
+
+![](images/797116fa8a08b896be7d4d2df628f5d57645081195d00507ec3ad34c06484e9f.jpg)
+
+![](images/9bb6e32d0580ade1b035dcfcd2f776f4bda620323286e0456b7eefee4f879fbd.jpg)  
+Input Video
+
+![](images/0f709e0334363aa021f4615922e915ce7ce035e2c3c89fed997194deef6f20fa.jpg)  
+To "Superman is skiing"
+
+![](images/05ce5a86ba2ff3ad132dba1fbbd011f3190433ae34a8e1600277e8f70c70b674.jpg)  
+Flatten
+
+![](images/936fa5eb470a4aac6d06cded2cf2edba6b1787a0b86f929bcb5a97d0bd2de399.jpg)
+
+![](images/29acbe004f302cdc06347e2531f28e979bee47a627b8dcbb6b3dc3b35cd760b6.jpg)  
+TokenFlow  
+Figure 1. Given a source input video and a text prompt, we utilize a pre-trained image diffusion model [24] to edit the video. State-of-the-art zero-shot video editing methods, such as Flatten [5] and TokenFlow [10], struggle to generate content that is align with the text prompt. Our proposed method achieves improved text alignment and better visual quality.
+
+![](images/ed4527fe457223256300529a0224c8f88f5533fb97aafa28b7e47af89056ef2f.jpg)
+
+![](images/57ca91b6f40a52390ad5ddaeb6eff1954323f7e3d2e4d6cb2f75d5b05e14b59a.jpg)  
+Align-A-Video(Ours)
+
+resources [37, 45]. To avoid learning temporal dynamics from scratch, zero-shot video editing methods leverage pre-trained image diffusion models to transform source videos into new ones while preserving the original motion [5, 10, 18, 22, 44, 49]. However, successfully applying image diffusion models to the video domain is a challenging task. It requires addressing the following key aspects: 1) Temporal consistency : cross-frame constraints for motion consistency; 2) Semantic fidelity: generated content matches the input text descriptions; 3) Visual quality: aligns with the user's aesthetic preferences.
+
+Current state-of-the-art methods [5, 10, 41, 44, 49] achieve temporal consistency by imposing strict control conditions, such as DDIM inversion [31], attention feature injection [35], depth guidance [46], and optical-flow constraints [43]. While these techniques successfully stabilize
+
+inter-frame coherence, their heavy reliance on fixed priors introduces two critical limitations: semantic fidelity degradation and visual quality compromise, as shown in Fig. 1. This reveals a fundamental challenge in video editing: Existing approaches treat temporal consistency as a primary optimization target, yet inadvertently suppress the flexibility required for high-fidelity semantic preservation and visual refinement.
+
+![](images/3d6a4f8e00d8a7135d58198199c59c9ffdfd05ac9e53146ed8ed209d3703a5f4.jpg)  
+Figure 2. Overview of the Align-A-Video Framework.
+
+In this paper, we introduce a novel method for video editing tasks, comprising two key components: image reward optimization and video editing inference, as shown in Fig. 2. Directly applying image-based reward optimization to video content could compromise temporal consistency (i.e., the smooth continuity between frames in a video) [45]. To address this issue, rather than optimizing the entire video at once, our method begins by refining an anchor frame (a key frame in the video). This approach enhances the anchor frame while preserving both semantic accuracy and visual quality. The features of the optimized anchor frame are then used as a reference to adjust the remaining frames. To better propagate the optimized features while ensuring appearance consistency across the entire video, we adapt the spatial-temporal attention mechanism from [41] into a cross-frame attention mechanism. This adaptation prioritizes the relationship between the anchor frame and the other frames. By integrating these two components, our framework achieves significant improvements in the overall quality of the edited videos. In summary, our main contributions are as follows:
+
+- A novel one-shot tuning paradigm for text-guided video-to-video generation tasks, effectively improving visual quality and semantic fidelity of generated videos while maintaining temporal consistency.  
+- A fast reward tuning method that aims to achieve stable and rapid alignment of a text-image pair in terms of shape, texture, and color.  
+- A feature propagation method allows the reward optimization results to propagate across frames.
+
+# 2. Related Work
+
+Our work lies at the intersection of text-guided V2V synthesis and image reward fine-tuning. In this section, we provide a concise overview of the key research in these areas, highlighting the connections and distinctions between our work and previous studies.
+
+# 2.1. Text-Guided V2V Synthesis
+
+Gen-1 displayed a structure and content-driven approach [6]. However, it required significant computational resources and was limited by the duration of videos it could process. Recently, some promising work has utilized pretrained image diffusion models for text-driven V2V synthesis tasks [5, 10, 13, 17, 22, 26, 27, 38, 41, 49, 50], either in one-shot or zero-shot training methods. Tune-A-Video [41] utilizes a one-shot approach that expands the latent space into the spatial-temporal domain and incorporates a temporal attention module to assimilate motion priors. Despite these innovations, issues with temporal consistency persist. To address this, several training-free methods have been developed: ControlVideo [49] calculates a depth map from the source video, enhancing the editing quality via ControlNet; TokenFlow [10] maintains temporal consistency by aligning inter-frame correspondences in the diffusion feature space; Flatten [5] leverages optical flow to direct the attention module during diffusion. Although these methods are effective, they often overload the diffusion process with pixel information to maintain consistency, causing the output to overly resemble the source video and diverge from textual prompts and intended edits. Our research seeks to refine the output quality and text alignment of edited videos without compromising their temporal consistency.
+
+# 2.2. Image Reward Tuning
+
+Reinforcement learning with human feedback when applied to large language models, enhances their capability to produce text outputs that align with human preferences [19, 32]. From this perspective, image and video generation tasks share the same target [1, 7, 20, 36, 45]. In the realm of image generation, DDPO [1] and DPOK [7] conceptualize the denoising steps of diffusion models as a series of decision-making processes, introducing the technique of denoising diffusion policy optimization. They demonstrated improvements in image compression, aesthetics, and text alignment using reward functions such as the JPEG compression algorithm, LAION aesthetics predictor [25], and BERTScore [48]. Furthermore, DRaFT [4] and AlignProp [20] implement gradient clipping and checkpointing during the sampling phase to efficiently propagate the gradients from differentiable reward functions. In video generation, InstructVideo [45] and VADER [21] use reward fine-tuning to optimize text-to-video (T2V) diffusion models. They utilize gradient clipping and checkpointing methods to
+
+backpropagate reward gradients during the diffusion model sampling process. Considering the challenges of training a video-specific reward model, both methods initially use image reward models as the reward function. Due to the degradation of temporal consistency caused by directly applying dense image rewards to video outputs, InstructVideo introduced Segmented Video Rewards, which strategically evaluates video quality based on a set of sparsely sampled frames. The efforts of InstructVideo and VADER revolve around using extensive data to train general-purpose text-to-video models, a process that typically requires a substantial amount of time. Conversely, our approach concentrates on swift, precise reward optimization with a single prompt for text-guided V2V synthesis, capable of completing optimization within several minutes.
+
+# 3. Methodology
+
+# 3.1. Preliminaries
+
+Diffusion models [11, 28] learn to approximate the probability distribution  $p(x)$  by reversing a noise-adding process, which gradually corrupts the sample  $x$ . The forward process, in which noise is progressively added to a clean image  $x_0$  according to  $x_{t} = \sqrt{\bar{\alpha}_{t}} x + \sqrt{1 - \bar{\alpha}_{t}}\epsilon$ , where  $\epsilon \sim N(0,1)$  and  $\bar{\alpha}_t$  are the noise schedule that controls the rate of the diffusion process. The model then learns a reverse diffusion process to predict the noise  $\hat{\epsilon}$  given  $x_{t}$  and  $t$  as inputs. The denoising process is achieved by a neural network  $\hat{\epsilon} = \epsilon_{\theta}(x_t;t)$ . By adding an additional conditional signal  $c$  (such as text) to the denoising neural network  $\epsilon_{\theta}$ , the probability distribution can be extended to  $p(x|c)$ . Training the parameters  $\theta$  of the denoising network  $\epsilon_{\theta}$  with a large number of image-text pairs using the following objective [11, 30]:
+
+$$
+\mathcal {L} _ {D M} = \mathbb {E} _ {x, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \hat {\epsilon} \| _ {2} ^ {2} \right]. \tag {1}
+$$
+
+DDIM enables the conversion of random noise into a deterministic outcome during sampling. Assuming that the ordinary differential equation can be reversed in the small-step limit, the deterministic DDIM reverse transformation [29, 31] can be expressed as:
+
+$$
+z _ {t} = \sqrt {\frac {\bar {\alpha} _ {t}}{\bar {\alpha} _ {t - 1}}} z _ {t - 1} + \sqrt {\bar {\alpha} _ {t}} \left(\sqrt {\frac {1}{\bar {\alpha} _ {t}} - 1} - \sqrt {\frac {1}{\bar {\alpha} _ {t - 1}} - 1}\right) \epsilon_ {\theta} (z _ {t}, t). \tag {2}
+$$
+
+where  $z_{t}$  is the latent variable at timestep  $t$ ;  $\bar{\alpha}_{t}$  is the cumulative scaling factor at timestep  $t$ .
+
+# 3.2. Overall Framework
+
+Given an input video  $\mathcal{I} = [I^1, \ldots, I^n]$  and an editing prompt  $\mathcal{P}$ , we aim to generate an edited video  $\mathcal{J} = [J^1, \ldots, J^n]$  that aligns with the text prompt  $\mathcal{P}$ . However, discrepancies may arise between  $\mathcal{J}$  and  $\mathcal{P}$  due to various conditional constraints during the sampling process.
+
+Therefore, we introduce image reward fine-tuning within the video editing pipeline to align the edited video with the textual prompts. As shown in Fig. 3, our framework, named Align-A-Video, consists of two steps: during fine-tuning, we use image reward scores to update the projection matrix in the attention blocks. During inference, we sample a new video from the inverted latent noise of the input video, guided by the editing prompt.
+
+# 3.3. Deterministic Reward Tuning
+
+The goal of image reward tuning is to train the parameters  $\theta$  of  $\epsilon$  to maximize a reward function  $\mathcal{R}$  for the generated images:
+
+$$
+\mathcal {L} _ {\mathcal {R}} (\theta) = \mathbb {E} _ {\mathbb {P} (\boldsymbol {\mathcal {P}})} \mathbb {E} _ {\mathbb {P} (x | \boldsymbol {\mathcal {P}}, z)} [ - \mathcal {R} (x, \boldsymbol {\mathcal {P}}) ], \tag {3}
+$$
+
+where  $\mathbb{E}_{\mathbb{P}(\mathcal{P})}$  denotes the expected distribution of prompts  $\mathcal{P}$ , and  $\mathbb{E}_{\mathbb{P}(x|\mathcal{P},z)}$  is the expected distribution of the generated images  $x$  given the prompts  $\mathcal{P}$  and the sampled noise  $z \sim \mathcal{N}(0,\mathbf{I})$ . Directly applying image rewards to edited videos compromise temporal consistency due to the misalignment between frame-wise optimization and overall video coherence [45]. Given that video is a natural extension of images, we believe that human preferences for images can be extended to video. Therefore, we consider performing single-frame optimization and then propagating the results to the remaining frames.
+
+For an given editing prompt  $\mathcal{P}$ , our goal is to maximize the reward scores of generated images  $x$ . A natural idea is to optimize the expected distribution of the generated images  $x$  given the prompts  $\mathcal{P}$  and the sampled noise  $z$ :
+
+$$
+\mathcal {L} _ {\mathcal {R}} (\theta) = \mathbb {E} _ {\mathbb {P} (x \mid \boldsymbol {\mathcal {P}}, z)} [ - \mathcal {R} (x, \boldsymbol {\mathcal {P}}) ]. \tag {4}
+$$
+
+However, this approach encounters difficulties in achieving training convergence. When minimizing the expected loss across different sampled noise inputs, the variability in the noise  $z_{i}$  results in noticeable changes in the model output  $x_{i}$ , which in turn leads to substantial fluctuations in the reward scores. These fluctuations contribute to instability in the gradient  $\nabla_{\theta}\mathcal{L}_{\mathcal{R}}$  (See Fig. 4, first row). Additionally, this optimization process is not sufficiently targeted, as it lacks a clear focus on specific objectives or constraints that could guide the training more effectively for subsequent video editing inference.
+
+To address these challenges, we introduce deterministic reward tuning. For a given anchor frame  $I_{anc} \in [I^1, \dots, I^n]$ , we apply DDIM inversion [31] to obtain a deterministic initial noise  $z$ , which is then reused in each training iteration. Keeping the initial noise constant eliminates the variance introduced by randomness, resulting in more consistent outputs and stable parameter updates. This allows the model to concentrate on refining the input-output relationship, thereby reducing volatility in gradient descent and facilitating reliable convergence (See Fig. 4).
+
+![](images/cf0cf2a3ffb81f0746de66d01abc6f95a4b75039a9757b46c48b6d6a890a95db.jpg)  
+Figure 3. Align-A-Video pipeline.
+
+![](images/867d6e892969587c9fac9468a0505e04421302811ccd9d539b585aad180b0b18.jpg)  
+Figure 4. Observations on single-prompt reward optimization. Directly optimizing the noise distribution for a single prompt led to training collapse (see first row). In contrast, sampling and fixing a single noise (i.e., using a constant random seed so that each iteration receives the same noise input) stabilizes the training process (see second row).
+
+In the generation process, the initial steps are crucial for shaping the rough structure of the image, while the subsequent steps refine this initial image. The essence of reward tuning is not to drastically change the model's output, but to subtly adjust it to align with human preferences. Guided by this concept, we extract inversion features during the last  $k$  steps of the deterministic DDIM inversion process. These features are then reused in the initial  $k$  steps of the denoising process [35]. This approach helps shape the rough structure of the generated images, thereby increasing their determinism. For the remaining denoising steps, we randomize the truncation of gradients, varying the time steps at which backpropagation occurs to subtly adjust the generated images while mitigating the short-term dependency
+
+bias introduced by gradient updates over a limited number of steps [20, 34]. Specifically, we define a hyperparameter  $l \sim \mathrm{Uniform}(K)$ , where  $K = \{k, \dots, T\}$  and  $T$  denotes the total number of DDIM steps. This hyperparameter serves as the starting point for reward tuning at the beginning of each training iteration, with gradients being truncated during the backpropagation process at  $l$ .
+
+Finally, since  $x$ ,  $\mathcal{P}$ , and  $z$  are all deterministic values, the expectation term  $\mathbb{E}_{\mathbb{P}(x|\mathcal{P},z)}$  is omitted. Thus, our reward loss is redefined as:
+
+$$
+\mathcal {L} _ {\mathcal {R}} (\theta) = - \mathcal {R} (x, \mathcal {P}). \tag {5}
+$$
+
+The proposed method fine-tunes the model exclusively on anchor frame generation, effectively eliminating the need to optimize the entire video or image set. This strategy significantly reduces the training cost while improving the precision of the optimization process.
+
+# 3.4. Feature Propagation of Anchor Frame
+
+Our method first sampling a set of keyframes, followed by feature propagation between anchor frames and keyframes, and finally using the keyframes to guide the generation of the remaining frames. Specifically, at each generation step, we sample a set of keyframes  $\{\mathcal{K}^i\}_{i\in \kappa}$ . To encourage visual consistent between these keyframes, we extend the self-attention to cross-frame attention, allowing simultaneous processing of keyframes [41]. The cross-frame attention features of all keyframes can be represented as  $\{\mathbf{Q}^i\}_{i\in \kappa},\{\mathbf{K}^i\}_{i\in \kappa},\{\mathbf{V}^i\}_{i\in \kappa}$ , where  $\mathbf{Q}^i,\mathbf{K}^i$  and  $\mathbf{V}^i$  are the query, key, and value for frame  $i\in \kappa$ , and  $\kappa =$
+
+![](images/a03fbd30301ccda60a803fbef03f82aaf3546a856187b99b6a93212284ffc533.jpg)  
+Figure 5. Qualitative comparisons between our method and baselines. Our approach achieves superior visual quality and semantic fidelity, while effectively preserving the structural integrity and motion consistency of the source frames. We recommend that readers consult the supplementary materials for more detailed results.
+
+![](images/f2db39b3d6cb720f56a85c438d0573362b9b8b6ce010420089802d5d36081ce3.jpg)
+
+![](images/59272dfa7638b494410bf92a43f94cfaf7065b52b2817480552ab91728733ae6.jpg)
+
+$\{i_1,\dots i_k\}$  . To facilitate the propagation of anchor frame features, we derive the query features  $\mathbf{Q}_{curr}$  from the current frame and derive the key  $\mathbf{K}_{anc}$  and value  $\mathbf{V}_{anc}$  from the anchor frame. Therefore, the cross-frame attention is formulated as:
+
+$$
+\phi (\mathcal {K} ^ {i}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {\text {c u r r}} \mathbf {K} _ {\text {a n c}} ^ {T}}{\sqrt {d}}\right) \mathbf {V} _ {\text {a n c}} \tag {6}
+$$
+
+Intuitively, each keyframe queries the anchor frame and aggregates information from it. This allows the keyframes to have a stronger dependency on the anchor frame, resulting in a roughly consistent appearance between the keyframes and the anchor frame.
+
+Given  $\{\phi (\mathcal{K}^i)\}$ , we propagate across the entire video based on the features correspondence extracted from the original video [10]. We fuse the remaining frames with the key frame based on the attention results, using a weighted average. The weights  $w_{i}$  are determined by the distance be
+
+tween the current frame and the key frames:
+
+$$
+w _ {s} = | s - p ^ {-} | / \left(| s - p ^ {-} | + | s - p ^ {+} |\right), \tag {7}
+$$
+
+where  $s = \{1, \dots, n\}$  is the index of the current frame,  $p^{-} \in \kappa$  represents the index of the nearest key frame before  $s$ , and  $p^{+} \in \kappa$  represents the index of the nearest key frame after  $s$ . The fused result for frame  $s$ , denoted by  $F_{s}$ , can be expressed as:
+
+$$
+F _ {s} = w _ {s} \cdot \phi \left(\mathcal {K} ^ {p ^ {-}}\right) + \left(1 - w _ {s}\right) \cdot \phi \left(\mathcal {K} ^ {p ^ {+}}\right). \tag {8}
+$$
+
+Feature propagation of the optimized anchor frame significantly improves prompt alignment performance and visual quality, while preserving motion consistency between edited and source videos.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We evaluate our method on the V2VBench dataset [33], a comprehensive benchmark specifically designed to assess video editing techniques. The dataset consists of 50 standardized videos, grouped into various categories. Each video is accompanied by 3 unique editing prompts, which collectively span 4 different editing tasks: foreground, stylization, a combination of foreground and background, and a combination of foreground and stylization.
+
+Implementation Details. Our method leverages a pretrained text-to-image model alongside existing image control techniques for video editing. We utilize Stable Diffusion (version 1.5) [24] as the image generator, together with the DDIM scheduler for reverse steps and sampling across a defined number of iterations. We adopt the PnP-diffusion [35] to guide the sampling process of keyframes. we employ HPSv2 [42] as the reward function. Directly backpropagating the reward loss into the diffusion model is computationally intensive and risks catastrophic forgetting [8, 9]. To mitigate these challenges and further accelerate fine-tuning, we integrate LoRA [12].
+
+Evaluation Metrics. We evaluate the performance of Align-A-Video from three key perspectives: 1)Visual Quality, which examines the overall visual appeal of the generated video; 2)Semantic Fidelity, assessing whether the edited video adheres accurately to user instructions; and 3)Temporal Consistency, assessing smooth continuity across frames. To evaluate semantic fidelity: we used the CLIP score [23] to assess the feature similarity between generated frames and their target prompts. The original CLIP score may not always accurately reflect video-level alignment. To address this, we also computed ViCLIP score [39], which is trained on video-text pairs, the ViCLIP score evaluates the spatiotemporal alignment between the video's content and the target prompts, providing a more comprehensive measure of alignment at the video level. For visual quality, we utilized the Aesthetic score [25], which is calibrated with human rankings, to assess the visual appeal and aesthetic quality of the edited video frames. Additionally, we considered the Pick score [16], a CLIP-based scoring function trained on extensive human preference labels, which simultaneously evaluates image and text inputs to reflect content quality and alignment. In addition to frame-by-frame evaluations, we employed the DOVER score [40], an advanced video quality assessment metric. Trained on a large-scale dataset of human-ranked videos, DOVER effectively evaluates artifacts, distortions, and blurriness in video content. For temporal consistency, we consider three metrics: CLIP Consistency, DINO Consistency, and Endpoint Error (EPE). Specifically, CLIP Consistency is obtained by
+
+calculating the cosine similarity between CLIP embeddings [23] of adjacent frames, primarily to assess inter-frame consistency and video smoothness. We use DINO [3] to check whether the object-level appearance in the edited video remains consistent by calculating the object-level inter-frame similarity, denoted as DINO Consistency. Additionally, we calculate the optical flow for each source-edited video pair using GMFlow [43] and measure the EPE to evaluate their consistent motion alignment.
+
+Baselines. We compare our method to the state-of-the-art methods: Tune-A-Video [41], TokenFlow [10], Flatten [5], Text2Video-Zero [15], ControlVideo [49]. We categorize these methods based on generation control conditions into three classes: 1) attention feature injection, which uses PnP diffusion [35] as a control mechanism to guide video generation, with methods such as TokenFlow and Flatten; 2) diffusion latents manipulation, which involves controlling or adjusting latents in the diffusion model's generation process to influence the generated content, including methods like Text2Video-Zero and ControlVideo; and 3) learning paradigm, which applies training to learn motion priors from the source video for generation control, with methods such as Tune-A-Video. We reimplemented these 5 methods using their officially released code repositories.
+
+# 4.2. Main Results
+
+Qualitative Evaluation. Figure 5 shows the comparison results between our method and the baselines. Text2VideoZero relies on random initial noise, leading to a heavy dependence on extended attention mechanisms to implicitly encourage consistency. Tune-A-Video encounters difficulties in learning motion consistency, especially when motion complexity increases. TokenFlow and Flatten perform well in three temporal consistency metrics; however, they fall short in adhering to textual instructions. Although attention feature injection aligns source frame structure and maintains motion consistency, it can impede the model's ability to follow prompt instructions accurately, sometimes resulting in meaningless edits. ControlVideo performs well in terms of visual quality and semantic fidelity but lacks alignment with the motion of source videos. In contrast, our method generates frames that simultaneously adhere to editing prompts, preserve the source frame structure, and achieve superior visual quality, whereas other methods struggle to meet all three objectives at once. Notably, although our method also employs attention feature injection, it successfully aligns the injected features with text instructions after just a few reward fine-tuning steps.
+
+Quantitative Evaluation. We present quantitative evaluation results in Table 1. No method consistently outperforms all others across all metrics. Baselines with attention feature injection (TokenFlow and Flatten) show a clear advantage in temporal consistency. On the EPE metric, even the
+
+Table 1. Quantitative evaluation results. Red and blue indicate the best and second-best result. S.: score; C.: consistency.  
+
+<table><tr><td></td><td colspan="3">Visual Quality</td><td colspan="2">Semantic Fidelity</td><td colspan="3">Temporal Consistency</td></tr><tr><td></td><td>Aesthetic S.</td><td>Pick S.</td><td>Dover S.</td><td>Clip S.</td><td>V-Clip S.</td><td>Clip C.</td><td>Dino C.</td><td>EPE</td></tr><tr><td>TokenFlow</td><td>5.035</td><td>20.594</td><td>0.695</td><td>0.264</td><td>0.238</td><td>0.957</td><td>0.956</td><td>-1.762</td></tr><tr><td>Flatten</td><td>4.847</td><td>20.391</td><td>0.680</td><td>0.265</td><td>0.242</td><td>0.931</td><td>0.940</td><td>-2.187</td></tr><tr><td>Tune-A-Video</td><td>5.299</td><td>20.959</td><td>0.697</td><td>0.282</td><td>0.263</td><td>0.873</td><td>0.824</td><td>-13.667</td></tr><tr><td>ControlVideo</td><td>5.520</td><td>21.039</td><td>0.708</td><td>0.282</td><td>0.259</td><td>0.956</td><td>0.937</td><td>-9.309</td></tr><tr><td>Text2Video-Zero</td><td>4.960</td><td>20.476</td><td>0.596</td><td>0.280</td><td>0.263</td><td>0.909</td><td>0.889</td><td>-15.611</td></tr><tr><td>Ours</td><td>5.512</td><td>21.847</td><td>0.761</td><td>0.284</td><td>0.265</td><td>0.955</td><td>0.944</td><td>-1.874</td></tr></table>
+
+lowest-performing feature injection method surpasses the best scores from other baselines. However, feature injection operations retain substantial pixel information from the source video, emphasizing temporal consistency at the expense of visual quality and semantic fidelity. Tune-A-Video excels at accurately following editing instructions (high semantic fidelity), but its output sometimes exhibits noticeable visual artifacts (lower temporal consistency). ControlVideo performs well overall but still falls short in maintaining consistent motion alignment with the input source video. Text2Video-Zero uses random noise instead of noise reversed from the source frames, resulting in generated frames that differ from the source frames and leading to unsatisfactory performance. Our method achieves superior performance in visual quality. It significantly outperforms other methods in the Dover score (0.761, compared to the second-best score of 0.708). It also achieves competitive performances in both semantic fidelity and temporal consistency. By employing reward tuning, our approach strikes a balance among these three aspects.
+
+# 4.3. Ablation study
+
+Effectiveness of Deterministic Reward Tuning. We ablated the training process to analyze its impact. The results shown in Fig. 6 indicate that the model without training replicates the motion from the input video (i.e., surfing) but fails to follow the input text instruction (edit "A man" to "Captain America"). Our method achieves optimal performance by aligning with textual instructions through deterministic reward tuning, without sacrificing temporal consistency. Additionally, using feature injection [35] to guide the denoising process enforces strict adherence to the structural layout of the source video, making it challenging to balance temporal consistency with structural editing [5, 10]. Our method employs reward training, guiding the edited results to gradually align with textual instructions. This process
+
+allows for relatively simple structural editing while maintaining temporal consistency. As shown in the second row of Fig. 7, the injected diffusion features are aligned with the textual instructions after the reward training and denoising processes.
+
+![](images/458cdb6e06b99e98c973788f9cf1a17b97c4be98ddbdd7d6cf2b9565390f930c.jpg)  
+Figure 6. Ablation study of reward tuning. RT: Reward Tuning.
+
+![](images/2ee48866965da66012c35e0eee417e3e9ccf8a4022dad9118d8915199f25d272.jpg)  
+Figure 7. Visualization of diffusion features. Given the input video, we apply DDIM inversion to each frame and extract features from the highest-resolution decoder layer. We apply PCA to the extracted features and visualize the top three components.
+
+Effectiveness of Cross Frame Attention. We conducted
+
+an ablation study on cross-frame attention, replacing it with the extended attention from [10]. The ablation results are shown in Fig. 8. Directly applying extended attention can retain some effects of reward optimization, but it makes the generated frames blurry, whereas our cross-frame self-attention preserves the quality of the generated frames. Most existing methods achieve cross-frame attention by extending self-attention to include multiple frames, thereby producing better coherence. Our approach continues this line of thought, sharing anchor frame features between key frames to ensure that optimization results propagate more effectively across frames.
+
+![](images/e1deca237559ae44c8992be028267bd8312f9051fc7164002803bc2d9c0c12e7.jpg)  
+Figure 8. Ablation study of cross-frame attention.
+
+![](images/3d44b8ff1e0b61f6b334665641aa57373a247bfe0de335731b4f48a3d44635f2.jpg)  
+Figure 9. Comparison of Editing Efficiency. We considered both time efficiency (the time required to perform one edit) and space efficiency (the maximum GPU memory allocated during editing). Tests were conducted on a single NVIDIA RTX 6000 ADA.
+
+# 4.4. Editing Efficiency
+
+In Fig. 9, we compare the editing efficiency of different methods on a 40-frame video. TokenFlow and ControlVideo demonstrate advantages in memory consumption and running speed. Due to the absence of DDIM inversion, Text2Video-Zero achieves a faster editing speed. However, its editing quality declines, with occasional artifacts and jitter. Our method effectively reduces memory consumption and significantly shortens training time through deterministic training, achieving competitive editing efficiency compared to other methods.
+
+# 4.5. Adaptation to Other Reward Models
+
+In this work, we focus on using HPSv2 [42]. To further validate the generalization capability of our method
+
+with respect to other reward functions, we explored using PickScore [16] and the LAION aesthetic predictor [25] as our reward models. We conducted the same reward finetuning as with HPSv2 and presented the results in Fig. 10. We observed that, although different in style from HPSv2, the quality of the results generally improved in terms of structure, colors, and detail. The LAION aesthetic predictor is solely used to evaluate the aesthetic quality of an image and thus does not possess text alignment capabilities.
+
+![](images/35b479608dff171b15953442005667a010312cd28e80d8223da1923133f7772f.jpg)  
+Figure 10. Training with different reward models.
+
+# 5. Conclusion
+
+In this paper, we present Align-A-Video, a novel method that leverages human preferences to guide text-driven V2V synthesis. To accelerate and stabilize the training process, we propose deterministic reward tuning. To achieve consistent optimization across frames, we introduce anchor frame feature propagation. Extensive experiments demonstrate that our method achieves superior results in visual quality, semantic fidelity, and temporal consistency.
+
+# 6. Acknowledgments
+
+This work was supported in part by the Shanghai Municipal Science and Technology Major Project under Grant 2021SHZDZX0100; in part by the Shanghai Municipal Commission of Science and Technology Project under Grant 19511132101; in part by the National Key Research and Development Program of China under No.2022YFA1004700; in part by the National Natural Science Foundation of China under Grant 62305019, Grant 62301308, Grant 62371342, and Grant 62071334; in part by the China National Postdoctoral Program for Innovative Talents under Grant BX20230223; in part by the China Postdoctoral Science Foundation under Grant 2023M732262; in part by Aeronautical Science Foundation of China under Grant 20230007038001; and in part by the Fundamental Research Funds for the Central Universities under Grant 22120210543.
+
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+[47] Qinsheng Zhang, Molei Tao, and Yongxin Chen. gddim: Generalized denoising diffusion implicit models. arXiv preprint arXiv:2206.05564, 2022. 1  
+[48] Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q Weinberger, and Yoav Artzi. Bertscore: Evaluating text generation with bert. arXiv preprint arXiv:1904.09675, 2019. 2  
+[49] Yabo Zhang, Yuxiang Wei, Dongsheng Jiang, Xiaopeng Zhang, Wangmeng Zuo, and Qi Tian. Controlvideo: Training-free controllable text-to-video generation. arXiv preprint arXiv:2305.13077, 2023. 1, 2, 6  
+[50] Yuyang Zhao, Enze Xie, Lanqing Hong, Zhenguo Li, and Gim Hee Lee. Make-a-protagonist: Generic video editing with an ensemble of experts. arXiv preprint arXiv:2305.08850, 2023. 2
\ No newline at end of file
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+# Align-KD: Distilling Cross-Modal Alignment Knowledge for Mobile Vision-Language Large Model Enhancement
+
+Qianhan Feng $^{1,2*}$ , Wenshuo Li $^{2}$ , Tong Lin $^{1\dagger}$ , Xinghao Chen $^{2\dagger}$ $^{1}$ State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University, China  
+ $^{2}$ Huawei Noah's Ark Lab, China
+
+fengqianhan@stu.pku.edu.cn,lintong@pku.edu.cn，{liwenshuo,xinghao.chen}@huawei.com
+
+# Abstract
+
+Vision-Language Models (VLMs) bring powerful understanding and reasoning capabilities to multimodal tasks. Meanwhile, the great need for capable artificial intelligence on mobile devices also arises, such as the AI assistant software. Some efforts try to migrate VLMs to edge devices to expand their application scope. Simplifying the model structure is a common method, but as the model shrinks, the trade-off between performance and size becomes more and more difficult. Knowledge distillation (KD) can help models improve comprehensive capabilities without increasing size or data volume. However, most of the existing large model distillation techniques only consider applications on single-modal LLMs, or only use teachers to create new data environments for students. None of these methods takes into account the distillation of the most important cross-modal alignment knowledge in VLMs. We propose a method called Align-KD to guide the student model to learn the cross-modal matching that occurs at the shallow layer. The teacher also helps student learn the projection of vision token into text embedding space based on the focus of text. Under the guidance of Align-KD, the 1.7B MobileVLM V2 model can learn rich knowledge from the 7B teacher model with light design of training loss, and achieve an average score improvement of 2.0 across 6 benchmarks under two training subsets respectively.
+
+# 1. Introduction
+
+Vision Language Model (VLM) is an important Multimodal technology, which build a bridge between vision and text data, and facilitate many real world tasks and applications [14, 26]. Based on the success of Large Language Models (LLMs) [43, 44, 52], efforts have been done to integrate vi
+
+![](images/25ef892ce9766efa803be9191287a0dd3acccd738d3c6d62fe8b3038c726d63b.jpg)  
+Figure 1. Radar plot of MobileVLM V2 1.7B model' performances with Align-KD policy under different settings.  $L$  and  $S$  refer to different Long and Short subdatasets for training, and MVLM2 refers to MobileVLM V2 model.
+
+sion modal features with LLMs to extend models' capability and their application potential and build up new Vision-Language Models (VLMs) [12, 22, 25, 28, 56]. However, new issues rise up: as the input features become more complex, the structures of VLMs also become deeper and heavier, since they have to digest information from different modalities and face even more various scenes [2, 4]. The growing size and complexity of VLMs makes them difficult to be accessed outside the server or high-speed Internet, which limit the development of these cutting-edge artificial intelligence under different scenarios, especially their deployment in off-line devices like mobile phones and robots, or some confidential application devices.
+
+Growing attentions have been focused on compressing VLMs while maintaining their remarkable capability as better as possible. MobileVLM family models [8, 10] are the first works to scale down VLMs to be able to run on
+
+mobile devices. Both MobileVLM V1 and MobileVLM V2 model contain special designed lightweight downsample vision projector to embed tokens into text embedding dimensions. With novel training strategy, MobileVLM V2 1.7B model outperforms a bunch of VLMs at 7B scale. Even so, continue to scale down the model would encounter more tough situations, where more severe performance drop would occur. In this case, new strategies are in need to aid the development of mobile VLMs.
+
+In contrast to cutting down the scale of mobile VLMs with the risk of significant performance drop, we are motivated to boost the model without enlarging the scale of data amount. Knowledge distillation (KD) method is widely used to increase the capability of neural networks, aims to instruct smaller student model with a larger and stronger teacher model, thus learning teacher's behaviors or hidden representations [19]. Previous knowledge distillation method for large model are mainly designed for single NLP modality [18, 20, 24]. In the field of vision-language multimodal models, most works are done before the large model era, focusing on aligning the vision proposals at the front side [13], which are no longer used in VLM technologies. Other works apply MSE loss on every transformer layers between models, but is not suitable for VLMs with significantly more layers with even different structures.
+
+Among these works, we notice that the alignment of vision and text inputs, the most important aspect of VLMs, is not considered in distillation. Poorly aligned cross-modal features could lead to difficulties in comprehending or reasoning. In this paper, we propose a lightweight knowledge distillation method, namely Align-KD, to let 1.7B student model learn the alignment knowledge from much stronger teachers. Firstly, we conduct several experiments on well-trained VLMs, and find that the first and last Transformer layer brings the largest shift on the features, similar as the trends in LLMs [42]. This contributes helps us to develop our belief that the alignment of modalities mainly happens at the shallow layers, where the input embeddings are projected to high dimension space for comprehending and reasoning. Then, given that the natural cross-modal querying mechanism of Attention block, we let student mimic teacher's text-query-vision attention distribution at the first layer. What's more, considering that the importance of vision tokens in the queue are different according to different text prompts, we inject teacher's informative vision embeddings unbalancedly into student's vision projector's output. Finally, we follow latest LLM research [18] to calculate reversed Kullback-Leibler divergence (R-KLD) between outputs to aid more general mean-seeking learning.
+
+We apply Align-KD policy to distill MobileVLM V2 1.7B, the state-of-the-art open-source VLM for mobile devices, from MobileVLM V2 7B teacher. We formulate two different subdatasets with increasing limitation of prompt
+
+maximum length, thus testing the effectiveness of Align-KD and VLMs under resource-limited scenarios. Following the multi-step training strategy of MobileVLM V2, Align-KD helps MobileVLM V2 1.7B model obtains universal promotion across 6 different benchmarks. The results show that Align-KD has great potential to help mobile VLMs to get enhancement with limited computation resource.
+
+The main contributions of our work are the followings:
+
+- We propose a knowledge distillation method Align-KD for mobile VLMs, which is the first work to distill the key cross-modal alignment knowledge.  
+- Align-KD helps cutting-edge MobileVLM V2 1.7B model obtains stable enhancement across different settings and benchmarks, largely facilitates the application of VLMs on edge devices.  
+- Align-KD doesn't rely on specific design of VLMs, and only requires light training designs, which gives it great potential to expand to various resource limited scenes.
+
+# 2. Related Works
+
+# 2.1. Large Models and Their Boosting
+
+In recent years, Large Language Models (LLMs) like GPT-3 [3], OPT [53] and LLaMA [43] significantly break through the borderline of deep learning and its applications. ChatGPT [36] set off a new wave and inspired follow-up work such as Vicuna [7]. Besides, some works try to introduce multimodal knowledge into the large model [2, 4, 6, 35, 49, 50, 56]. LLaVA [28] feed visual tokens into LLM and build up a comprehensive reasoning between visual and text contents, and many other works [12, 22, 25, 48] also approach to balance between vision and text understanding. However, the growing size of LLMs leads to a high demand on computing resources, which limits their applications. TinyLLaMA [52] and MobileLLaMA [9] scale down the architectures and maintain relatively good performance. Meanwhile in vision-language model field, MobileVLM family [8, 10] is the first open source work to facilitate the Vision-Language Model on mobile devices. Except for the development of training strategy and special architectures for large model, model compression techniques including quantization and pruning [15, 16] also thrive and provide solutions to relief burden of the computation resources. Equipped with these methods, LLMs are able to inference faster and lighter with little drop in accuracy.
+
+# 2.2. Large Language Model Distillation
+
+While former techniques are trying to do the subtraction, knowledge distillation (KD) [19] techniques are trying to do adding. In KD, weaker student model tries to learn from a stronger teacher model from different aspects, like the output or hidden representations. MiniLLM [18] studies the Kullback-Leibler divergence (KLD) loss on the output dis
+
+![](images/68bd2e8aa44cc76b0ccf3dae611e5e93dd9e916043fe737fbc979d99c08339ec.jpg)  
+(a)  
+Figure 2. Exploration of feature changing trend at different layers of MobileVLM V2 model families. (a) Cosine similarity of features from every two adjacent layers. (b) Cosine similarity of features from original vision and text embedding positions within each same layer. The data is presented in an order of magnitude to highlight the trend of change. (c) Normalized Euclidean distance of features from original vision and text embedding positions within each same layer. The experiments are conducted on ShareGPT4V-PT dataset, and all the calculations are averaged after conducted on each tokens.
+
+![](images/a10b8d7d2fec292961f29d340f81bbcbd69f5ac6a20e2c7fbcc5b5d6b078fe36.jpg)  
+(b)
+
+![](images/372123e4e80cbe6ef7f5710998465b572bbcdf272d62ad193f39972de5e5942e.jpg)  
+(c)
+
+tillation, and suggests that reverse KLD teaches LLM student better on mean-seeking than forward KLD. Other researchers pay attention to the hidden features, training a task-aware filter to distill knowledge from teacher to student at different middle layers [24]. Teachers can also be used to create a more suitable data environment for student model, especially in LLM background where data are diverse and sometimes polluted. Hsieh et al. [20] device a step-by-step distillation strategy to use teacher model's inference ability to provide training data for student, thus injecting both label noise and text inference into the data. Meta delves deeply into black-box systems [51], distilling high-quality outputs generated by System 2 techniques, such as Chain-of-Thought, Rephrase and Respond, etc., back into the standard large language model generation.
+
+# 2.3. Distillation for Vision-Language Model
+
+Most distillation methods for Vision-Language Model (VLM) are designed before Large Model Era. Considering that traditional VLMs rely on vision proposals, Fang et al. [13] propose to align the input proposals between teacher and student, and enable following transformer blocks to align their attention distributions. To compress VLM, Wang et al. [47] combine pruning with distillation, conducting easy output logits imitation and distillation on attention and hidden states. Although these works provide a thinking of VLM distillation, they are restrained within the field outside Vision-Language Model (VLM), which usually consists of more transformer layers and more complex alignment between vision and language modalities. In VLM-KD [54], researchers use VLM like LLaVA-NeXT [30] to generate text prompts and using contrastive learning to promote long-tail recognition ability of vision mod
+
+els. LLaVA-MoD [39] minimizes the Kullback-Leibler divergence between output distributions and utilizes Direct Preference Optimization (DPO) to enhance the ability of the s-MLLM to discern high-quality from low-quality samples. But LLaVA-MoD relies on integrating the Sparse Mixture of Experts (MoE) architecture into language model, and also neglects the gap of alignment knowledge in distillation, which leaves a huge space for further explorations.
+
+# 3. Align-KD
+
+In Vision-Language Models (VLMs), vision and text embeddings comprise the input of the large model. However, it is obvious that the embedding mechanisms are different for the two modalities, which means the embeddings have to go through cross-modal alignment in the feature space. The cross-modal alignment ability is crucial for VLMs, but previous works mainly focus on single modal LLMs distillation and neglect the importance of teaching student about the alignment knowledge. Here we first explore the cross-modal alignment in VLMs, and then propose our Align-KD method step by step based on MobileVLM family.
+
+# 3.1. Where Does the Alignment Happen?
+
+Most VLMs like MobileVLM [8, 10] design special vision projectors to project the vision embeddings, but this operation mainly aligns the dimension of embedded tokens. The alignment of vision and text embeddings into the same high dimension space is almost a black box system.
+
+Sun et al. [42] try to figure out the internal working mechanism of Transformer layers in LLMs. The researchers perform both skip and switch operations on every Transformer layer in LLaMA 2 7B, 13B and 70B [44] mod
+
+![](images/e69e980de40b29d841a36ccae208baf081960bf0637b5d03bdf05aa4dd8d1ea4.jpg)  
+Figure 3. Left: The overall framework of Align-KD. Align-KD utilizes the text-query-vision attention of teacher model's first layer to extract the knowledge of cross-modal alignment, then injects this knowledge into the cross-modal attention matrix of student's first layer. Besides, the projected vision tokens are dynamically enhanced according to text's focusing, also based on teacher's first layer cross-modal attention. Right: The schematic diagram of vision-language models' (VLMs) first layer attention matrix.  $A_{v - v}$ ,  $A_{t - v}$  and  $A_{t - t}$  attention refer to vision-query-vision, text-query-vision and text-query-text attention.
+
+els, and find out that the change in the first and last layer brings the largest drop in performance, while middle layers only give slight fluctuation. What's more, the parameter weight of middle layers shows high similarity while the first and last layer are quite different. They conclude that the first and last layer take up special responsibilities.
+
+This inspire us to explore whether the first and last layer in LLM of VLMs have similar functions to project input embeddings into/out of the high dimension space where the features mix. If so, the alignment of modalities should also happen simultaneously. Given the well trained MobileVLM V2 models with different sizes, we conduct 3 simple experiments to explore the feature change trend in different Transformer layers. First, we calculate the cosine similarity of every two adjacent features, including the input features. As shown in Figure 2(a), the similarities in middle layers are much higher than the first and last layers, which implies dramatic change in feature space in the two layers. Then, we locate the positions of vision tokens and text tokens in the input embeddings, and calculate the feature cosine similarity as well as the Euclidean distance of these two segments within every layers, and the results are shown in Figure 2(b) and Figure 2(c). The experimental results further confirm our conjecture that the head layer of LLM maps the input to the high-dimensional space for deep processing, and the last layer maps it to the output space. This means that the first layer is also responsible for mapping text and vision embeddings from different domains into the same high-dimensional space, or alignment. Note that the LLMs in MobileVLM V2 1.7B model and 3B model are from MobileLLaMA family, and the LLM in 7B model is Vicuna-7B [55], so the results are not structure-related.
+
+Except for the first layer in LLM of VLMs, models like
+
+MobileVLM also design vision projectors to downsample the vision embeddings, thus reducing the calculation. The projectors learn to maintain and enhance important information, and align the vision embeddings with the input text embeddings from the aspect of dimension. It also receives guidance from the backward gradient from downstream LLM to learn basic cross-modal knowledge.
+
+Based on the discussion, we propose to distill the knowledge of cross-modal alignment from two aspects of VLMs: the first layer of LLM in VLMs, and the output embeddings of vision projectors as shown in the left of Figure 3.
+
+# 3.2. First Layer Text-Query-Vision Attention Only
+
+The first layer of LLM in VLMs is the important place where the cross-modal alignment happens. Almost all of recent LLMs are built based upon the architecture of Transformer [45], an efficient parallel attention structure. While some works have been done to improve the Transformer block [31, 38, 41], the basic attention mechanism remains as: project the input features into query  $Q$ , key  $K$  and value  $V$ , and then use them to generate Attention values to help self-adaptive fusion among different feature tokens.
+
+Attention values imply tokens' unbalanced focusing degree on others and determine how the input features are going to be projected. This nature of attention mechanism makes it the perfect information carrier about the cross-modal alignment in VLMs. The attention matrix of VLMs are always in the similar mode as the right of Figure 3, where the input embeddings are the concatenated vision and text tokens. Since VLMs mainly use decoder transformer layers, the attention matrix is a lower triangular matrix and half masked. The lower part of the matrix consists of three parts: vision-query-vision attention  $A_{v - v}$ , text-query-text
+
+attention  $A_{t - t}$  and text-query-vision attention  $A_{t - v}$ .
+
+Previous knowledge distillation methods usually teach student model to learn from the whole attention values of teacher's different layers. On the contrary, we propose to let student model mimic the first layer's text-query-vision attention  $(A_{1,t - v})$  only. Given a knowledgeable teacher model  $T$ , we pick out its attention matrix  $A_1^T$  from its first layer, then split out the text-query-vision part to form  $A_{1,t - v}^{T}$  and do the same to get student  $S$  's first layer's text-query-vision attention  $A_{1,t_v}^S$ . Then, we apply an  $1\times 1$  convolution projector  $P_{attn}$  to align the dimension of these two, followed by a simple mean square error (MSE) loss to get the first layer  $A_{1,t - v}$  only KD loss:
+
+$$
+\mathcal {L} _ {A _ {1, t - v}} = M S E \left(P _ {\text {a t t n}} \left(A _ {1, t - v} ^ {T}\right), A _ {1, t - v} ^ {S}\right). \tag {1}
+$$
+
+This first layer  $A_{1,t - v}$  only KD has several advantages. (1) First and foremost, thanks to the cross-attention mechanism, the text-query-vision attention matrix of the first layer naturally implies how the input tokens of two modalities perceive each other, as well as the alignment projection scheme that tokens are going to take to project into more aligned feature space. On the contrary, it is difficult to extract useful knowledge from  $A_{1,t - t}$  when then text tokenizer of VLMs are usually fixed, while distilling  $A_{1,v - v}$  only lead to more vision-only enhancement, which has already been reinforced by front vision projector. And both of them lack the key cross-modal knowledge. (2) Secondly, first layer  $A_{1,t - v}$  only KD significantly reduces computing workload, making the whole method efficient. Some works distill attention matrices at multiple layers, and some of them even device special downstream tasks to help the student learning, which can cause excessive computational pressure. Even within the first attention matrix, first layer  $A_{1,t - v}$  only KD also saves up to  $50\%$  calculation compared with full distillation. This lightweight design enable potential chances to conduct training with limited computation resources. (3) What is more, considering that the design of different VLMs could be different in both the model depth and the block details, first layer  $A_{1,t - v}$  only KD exhibits greater flexibility and can be easily migrated to different models regardless of their particular structural design or the meaning of different depth transformer layers.
+
+# 3.3. Vision Enhancement Based on Text's Focusing
+
+The vision projector that generates the input vision tokens also takes up the responsibility to do rudimentary cross-modal alignment. For example, the LDP in MobileVLM model downsample the embeddings while extracting both detail and semantic features, and project the embeddings into less tokens with same dimension as text embeddings. This rough alignment lacks the perception of text modal information, only receiving backward gradients from downstream Transformer layers' cross-attention to get in touch
+
+![](images/92e98d23d7acd4bdb66a258120f4880d37a4c611f27deaedc32ab5241ee6404d.jpg)
+
+# Text Prompts
+
+['What are the key elements in this picture?', 'What does the bus screen show?',
+
+'Is there any plants in the picture?'  
+'Is the bus full of people?', 'Is the bus in a rural place o in the city?',  
+'Is the line of sight blocked?', 'What is the color of the building behind the bus?'
+
+![](images/00503223acd709c14c9184395ca389d83030d79a9967ad61b1f1fc4e969ccb8e.jpg)  
+Vision Tokens  
+Figure 4. Different text prompts cause different attention on vision tokens of the picture. The vision tokens with high attention activation also distribute sparsely.
+
+with another modality.
+
+To mitigate this shortage, we propose to leverage the cross-modal attention to help the projector get more exposure to cross-modal information. Although the vision tokens are already refined by the projector, the text's attention on different vision tokens is still rather sparse because of the directional indication of text prompts. The  $A_{1,t - v}$  not only contains information about cross-modal aligning projection, but also reveals which vision tokens the text prompts pay most attention to. Different prompts may focus on different embeddings, but some of the tokens are significantly left behind. Instead of inhibiting the learning of temporarily unpopular vision tokens, we propose to enhance most popular tokens at current based on teacher model's  $A_{1,t - v}$ , thus preventing hurting the learning of others. Having the text-query-vision attention from the first layer of teacher model, we add-up the attention value  $A_{1,t - v}^{T}$  along the text dimension to get the attention score  $Score_{n}$  of vision token  $n$ ,
+
+$$
+\operatorname {S c o r e} _ {n} = \sum^ {M} A _ {1, t - v, (n, m)} ^ {T}, m \in M, \tag {2}
+$$
+
+$M$  is the number of text tokens. Then, the indexes of tokens whose attention score  $Score_{n}$  if the top-  $K$  are sorted out, namely  $Idx_{K}$ . Finally, we conduct knowledge injection from teacher to student on vision tokens listed in  $Idx_{K}$ :
+
+$$
+\mathcal {L} _ {V - f o c u s} = M S E \left(P _ {V} \left(E m b _ {I d x _ {K}} ^ {T}\right), E m b _ {I d x _ {K}} ^ {S}\right), \tag {3}
+$$
+
+where  $Emb_{Idx_K}^T$  and  $Emb_{Idx_K}^S$  are teacher's and student's vision token embeddings within the range of  $Idx_K$ , and  $P_V$  is an  $1 \times 1$  convolution projector.
+
+Except for the knowledge injection on current popular tokens, the rest should not be overlooked. Low-ranked attention from the current text prompt does not mean the stable low popularity under other scenes. The focus on vision
+
+tokens may dramatically shift, e.g., when from 'What's the name of book's author on the cover?' to 'What is the color of the desk under the book?'. What is more, the teacher vision token naturally contains stronger knowledge because of the instruction of stronger LLM and higher dimension in most cases. In this case, we add the general knowledge distillation on all vision tokens from teacher to student, i.e.,
+
+$$
+\mathcal {L} _ {V - a l l} = M S E \left(P _ {V} \left(E m b _ {T}\right), E m b _ {S}\right), \tag {4}
+$$
+
+which prevents harmful suppression of other tokens. And we combine two losses using a weight  $\lambda$  to form the vision token enhancement loss based on text's focusing as
+
+$$
+\mathcal {L} _ {V} = \mathcal {L} _ {V - a l l} + \lambda \mathcal {L} _ {V - f o c u s}. \tag {5}
+$$
+
+# 3.4. Overall Knowledge Distillation Strategy
+
+Except for alignment distillation in the front of VLM, we follow MiniLLM to add reverse Kullback-Leibler divergence (RKLD) loss, which uses the predicted distribution of student model as target, between the outputs of student and teacher. Since the text prompts and input images are varied, RKLD loss is more suitable than forward Kullback-Leibler divergence (FKLD) for VLM to learn about the mean-seeking instead of mode-seeking, preventing from overfitting on specific scene. Extract the output prediction distribution  $p_T$ ,  $p_S$  from teacher and student, the reverse Kullback-Leibler divergence loss can be formulated as
+
+$$
+\mathcal {L} _ {R K L D} = p _ {S} \log \frac {p _ {S}}{p _ {T}}. \tag {6}
+$$
+
+The alignment loss and RKLD loss work together with the original supervised loss  $\mathcal{L}_{Sup}$ , and our overall Align-KD loss on student model can be formulated as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {S u p} + \mathcal {L} _ {A _ {1, t - v}} + \mathcal {L} _ {V} + \mathcal {L} _ {R K L D}. \tag {7}
+$$
+
+# 4. Experiments
+
+# 4.1. Basic Experiment Settings
+
+MobileVLM family [8, 10] is the latest and cutting-edge Vision-Language Model for mobile devices. The MobileVLM V2 1.7B model shows remarkable performance with lightweight design. Considering the limitation of further compression of the model, we propose to apply Align-KD on MobileVLM V2 1.7B to help obtain better performance on edge devices. We choose the well trained MobileVLM V2 7B model as the teacher to conduct the knowledge distillation. Align-KD is used as an extra strategy working together with the common student training.
+
+We use 8 NVIDIA V100 GPUs to conduct our distillation training. We follow MobileVLM V2's work to divide the training stage into pre-training and multi-task finetuning. Because of the limited memory space, we use gradient
+
+accumulation to achieve a global batch size of 256 for the pre-training stage and 128 for the multi-task fintuning stage. For both stage, we use the ZeRO2 strategy of DeepSpeed [1], and run all experiments under half-precision floating-point. We follow MobileVLM V2 to freeze the vision encoder and tokenizer while training, only train rest of the whole network. The maximum learning rate for the projector and other components are set to  $1e^{-3}$  and  $2e^{-5}$  respectively during pretraining and  $4e^{-5}$  during multi-task finetuning, using a cosine schedule. The convolutional projector for dimension alignment are randomly initialized and trained together. The weight  $\lambda$  in vision token loss  $\mathcal{L}_V$  is set to 0.1 to adapt to unstable changing of the tokens been focused. For top- $K$  selection in text-focus-based vision token knowledgeable distillation, we select the top 16 tokens with highest attention score. We follow the original MobileVLM V2 work on the rest of settings.
+
+# 4.2. Data and Dataset Reforming
+
+Align-KD follows MobileVLM V2 to train on various datasets. During the pretraining stage, ShareGPT4V-PT [4] is used to give the student a brief knowledge of vision and text. It is a caption dataset and comprises 1.2 million image-text pairs. In the multi-task training stage, more data from different tasks like conversation and VQA are provided: COCO[5], SBU[37], Visual Dialog[11], ShareGPT4V[4], SQA[34], IConQA[33], TextVQA[40], VSR[27], VIGC[46]. Note that SBU is a re-collected dataset and is updated from time to time, therefore some of the original data might have been removed. In this case, we washed the data list in the dataset, which is different from the original MobileVLM training. To evaluate the effectiveness of our Align-KD method, we test the performance on different benchmarks, including GQA[21], SQA[34], TextVQA[40], MME[17], MMBench[32] and POPE[23].
+
+While mobile VLMs are designed for mobile devices deployment with limited resources, the training of VLMs also faces challenges when the computational resources is not that adequate. The computation workload can be extremely high when the input text prompts are too long, which sometimes causes 'Out of Memory' error during training. We formulate two different subdatasets based on the original data listed above, each contains data with different maximum prompt lengths: Short with maximum lengths of 512 embedded tokens, and Long of 2048. Considering that the training data comprises many Visual Question Answering (VQA) tasks, we drop the overlong data instead of truncating them, making two subsets also vary in the data amount. This setting is different from the original MobileVLM work, but can help examine the effectiveness of Align-KD strategy under different resource-limited scenarios, and also helps extend the application scenarios of VLMs. The subset details are shown in Table 2.
+
+<table><tr><td>Method</td><td>LLM</td><td>#Samples</td><td>\(MMEP^P\)</td><td>GQA</td><td>\(VQAT^T\)</td><td>POPE</td><td>\(MMB^{dev}\)</td><td>\(SQAI^I\)</td><td>Avg.</td></tr><tr><td>MiniGPT-4</td><td>Vicuna-7B</td><td>5.0M</td><td>581.7</td><td>32.2</td><td>-</td><td>-</td><td>23.0</td><td>-</td><td>-</td></tr><tr><td>LLaVA-1.5[29]</td><td>Vicuna-7B</td><td>1.2M</td><td>1510.7</td><td>62.0</td><td>58.2</td><td>85.9</td><td>64.3</td><td>66.8</td><td>68.8</td></tr><tr><td>ShareGPT4V</td><td>Vicuna-7B</td><td>1.9M</td><td>1567.4</td><td>63.3</td><td>60.4</td><td>85.7</td><td>68.8</td><td>68.4</td><td>70.8</td></tr><tr><td>MoE-LLaVA-1.6B×4</td><td>StableLM-1.6B</td><td>2.2M</td><td>1300.8</td><td>60.4</td><td>47.8</td><td>84.3</td><td>59.4</td><td>62.6</td><td>63.3</td></tr><tr><td>MoE-LLaVA-2.7B×4</td><td>Phi-2.7B</td><td>2.2M</td><td>1396.4</td><td>61.1</td><td>50.2</td><td>85.0</td><td>65.5</td><td>68.7</td><td>66.7</td></tr><tr><td>MobileVLM 1.7B</td><td>MobileLLaMA 1.4B</td><td>3.6M</td><td>1196.2</td><td>56.1</td><td>41.5</td><td>84.5</td><td>53.2</td><td>57.3</td><td>58.7</td></tr><tr><td>MobileVLM 3B</td><td>MobileLLaMA 2.7B</td><td>3.6M</td><td>1288.9</td><td>59.0</td><td>47.5</td><td>84.9</td><td>59.6</td><td>61.2</td><td>62.8</td></tr><tr><td>MobileVLM V2 3B</td><td>MobileLLaMA 2.7B</td><td>3.6M</td><td>1440.5</td><td>61.1</td><td>57.5</td><td>84.7</td><td>63.2</td><td>66.7</td><td>68.1</td></tr><tr><td>MobileVLM V2 7B</td><td>Vicuna-7B</td><td>3.6M</td><td>1559.0</td><td>62.6</td><td>62.3</td><td>86.6</td><td>69.2</td><td>74.7</td><td>72.2</td></tr><tr><td>Subset / #Samples</td><td>Student Model</td><td>Align-KD</td><td>\(MMEP^P\)</td><td>GQA</td><td>\(VQAT^T\)</td><td>POPE</td><td>\(MMB^{dev}\)</td><td>\(SQAI^I\)</td><td>Avg.</td></tr><tr><td rowspan="2">Short / 3.6M</td><td>MobileVLM V2 1.7B</td><td>-</td><td>1246.3</td><td>55.1</td><td>51.2</td><td>85.3</td><td>57.6</td><td>63.2</td><td>62.4</td></tr><tr><td>MobileVLM V2 1.7B</td><td>✓</td><td>1288.4</td><td>58.9</td><td>52.4</td><td>86.5</td><td>57.8</td><td>66.6</td><td>64.4</td></tr><tr><td rowspan="2">Long / 3.6M</td><td>MobileVLM V2 1.7B</td><td>-</td><td>1289.2</td><td>59.0</td><td>52.2</td><td>86.1</td><td>55.9</td><td>64.5</td><td>63.7</td></tr><tr><td>MobileVLM V2 1.7B</td><td>✓</td><td>1303.8</td><td>60.1</td><td>53.1</td><td>87.0</td><td>57.5</td><td>67.7</td><td>65.1</td></tr></table>
+
+Table 1. Test of Align-KD strategy's effectiveness on MobileVLM V2 1.7B model. Long and Short refer to two subsets with different maximum prompt lengths limitations.  $\mathbf{MME}^{\mathrm{P}}$  refers to MME Perception,  $\mathbf{MMB}^{\mathrm{dev}}$  refers to MMBench-dev,  $\mathbf{SQA}^{\mathrm{I}}$  refers to SQA-IMG. The score of  $\mathbf{MME}^{\mathrm{P}}$  is divided by 20 when calculating the average performance.  
+
+<table><tr><td>Datasets</td><td>Long Samples</td><td>Short Samples</td></tr><tr><td colspan="3">Pretraining</td></tr><tr><td>ShareGPT4V-PT</td><td>1.25M</td><td>1.24M</td></tr><tr><td colspan="3">Multi-task Finetuning</td></tr><tr><td>COCO</td><td>592K</td><td>589k</td></tr><tr><td>SBU</td><td>837K*</td><td>822k*</td></tr><tr><td>Visual Dialog</td><td>123K</td><td>115K</td></tr><tr><td>ShareGPT4V</td><td>665K</td><td>655K</td></tr><tr><td>SQA</td><td>13K</td><td>5K</td></tr><tr><td>IConQA</td><td>107K</td><td>107K</td></tr><tr><td>TextVQA</td><td>35K</td><td>33K</td></tr><tr><td>VSR</td><td>13K</td><td>13K</td></tr><tr><td>VIGC</td><td>37K</td><td>35K</td></tr><tr><td>Total</td><td>3.67M</td><td>3.61M</td></tr></table>
+
+Table 2. Details of datasets used in different stages. *SBU dataset is re-collected, some datas are removed from the original links.
+
+# 4.3. Effectiveness of Align-KD
+
+After formulating our Long and Short subdatasets, we use them to train MobileVLM V2 1.7B model with proposed Align-KD strategy. Note that we use fully-trained and open-sourced MobileVLM V2 7B model provided by MobileVLM work as our knowledge distillation teacher. The results across 6 different benchmarks and two subsets are shown in Table 1. Trained with Long set, MobileVLM V2 1.7B model achieves an average score of 63.7. When trained with Align-KD policy, the student model witnesses a universal promotion across all benchmarks, achieving and average score of 65.1. To be more specific, Align-KD helps improve the MobileVLM V2 1.7B model to obtain an im
+
+provement of 3.2 on SQA benchmark, as well as 1.6 on MMBench. Under resource-limited scenarios, Align-KD gives MobileVLM V2 1.7B model an even better average improvement of 2 across all benchmarks, from 62.4 to 64.4. On GQA, Align-KD gives a promotion of 3.8. And it also brings notable promotion of 1.2 on POPE, which is a rather challenging hallucination testing benchmark.
+
+The comprehensive results are visualized in a radar plot in Figure 1. Our Align-KD brings stable and good bonus under different vision-language tasks. What's more, when the student suffers from the performance drop brought by the absence of long prompts, Align-KD successfully injects the knowledge into the model and makes student model after knowledge distillation achieve performances comparable with the model trained with long texts.
+
+# 4.4. Ablation Study
+
+We take a step forward to conduct ablation studies to testify the effectiveness of each method in Align-KD. We run all ablation experiments on Short subdataset for fairness, and the results are shown in Table 3. The reverse Kullback-Leibler divergence (RKLD) loss helps student learn to mimic the outputs of stronger teacher model, but brings somehow biased improvement. On the contrary, applying first layer  $A_{1,t - v}$  only loss provides notable and more balanced promotion to an average of 63.6. The combination of distillation on focused and all vision tokens further increase the performance by 0.8 on average.
+
+During cross-modal alignment learning, we apply the knowledge distillation only on the text-query-vision part of the first layer's attention. We further testify the rationality of this design by comparing with other methods, and the re
+
+<table><tr><td>Method</td><td>MME^P</td><td>GQA</td><td>VQAT</td><td>POPE</td><td>MMB^dev</td><td>SQAI</td><td>Avg.</td></tr><tr><td>MVLM2 1.7B</td><td>1246.3</td><td>55.1</td><td>51.2</td><td>85.3</td><td>57.6</td><td>63.2</td><td>62.4</td></tr><tr><td>+L_RKLD</td><td>1223.2</td><td>55.9</td><td>52.5</td><td>85.5</td><td>58.5</td><td>64.7</td><td>63.0</td></tr><tr><td>+L_{A1,t-v}</td><td>1263.6</td><td>57.8</td><td>53.1</td><td>85.7</td><td>57.2</td><td>64.6</td><td>63.6</td></tr><tr><td>+L_V-all</td><td>1288.2</td><td>57.7</td><td>52.3</td><td>86.2</td><td>57.8</td><td>64.3</td><td>63.8</td></tr><tr><td>+L_V-focus</td><td>1288.4</td><td>58.9</td><td>52.4</td><td>86.5</td><td>57.8</td><td>66.6</td><td>64.4</td></tr></table>
+
+sults are shown in Table 4. Replacing first layer  $A_{1,t - v}$  only KD strategy with distillation of vision-query-vision attention triggers extreme drop in performances. We suggest that this is because the self-attention of vision tokens is not helpful for initial cross-modal alignment, and could lead to very unstable fluctuation in the attention embedding. However, changing into text-query-text attention is remarkably better than vision-query-vision training, with a slight drop from 64.4 to 63.2. We believe this phenomenon can be attributed to the fixed text tokenizer while training, and this leads to indirect stable learning of projection of cross-modal attention. What's more, the learning on full attention performs better than learning only  $A_{1,v - v}$  and  $A_{1,t - t}$ , which further improves our conjectures above: the cross-modal  $A_{1,t - v}$  is the most important factor while learning  $A_{1,t - t}$  helps mitigate the negative influence brought by  $A_{1,v - v}$  distilling.
+
+In Figure 2, we infer that the first and last layer act as the most outstanding characters. Align-KD mainly focuses on the first layer, since it is exposed the most to the inputs that need to be aligned, while the last layer is mainly in charge of projecting into output space. However, we also testify how the student would behave with the knowledge of output attention. As it is shown in the last row of Table 4, after adding the distillation of the last attention to Align-KD, student model witnesses a drop in performance. A possible explanation is that the deep feature is already well mixed and extracted, and there is some overlap with functionality of the RKLD on outputs. Besides, the distillation on extra attention would lead to significant growth in the calculation, which is a burden for resource-limited scenarios, and the first layer  $A_{1,t - v}$  only KD in Align-KD demonstrates huge advantage in both effectiveness and efficiency.
+
+# 4.5. Discussions and Limitations
+
+Align-KD strategy brings benefit to MobileVLM V2 model under both long and short prompt limitations. Align-KD is relatively light designed, which enable possible expansion to resource-limited scenarios. We provide the working expense comparisons in Table 5, including the total training time and maximum memory occupied during training. The experiments are conducted on 8 Nvidia V100 GPUs. It costs around 296 GPU hours and 676 GPU hours to train Align-KD MVLM2 1.7B on Short and Long subdatasets.
+
+Table 3. The ablation results of testing each component in AlignKD. MVLM2 refers to MobileVLM V2 model.  
+
+<table><tr><td>Method</td><td>\(MME^P\)</td><td>GQA</td><td>\(VQAT^T\)</td><td>POPE</td><td>\(MMB^{dev}\)</td><td>\(SQA^I\)</td><td>Avg.</td></tr><tr><td>\(A_{1,t-v}\)</td><td>1288.4</td><td>58.9</td><td>52.4</td><td>86.5</td><td>57.8</td><td>66.6</td><td>64.4</td></tr><tr><td>\(A_{1,v-v}\)</td><td>1036.5</td><td>52.0</td><td>27.3</td><td>81.1</td><td>13.8</td><td>36.1</td><td>43.7</td></tr><tr><td>\(A_{1,t-t}\)</td><td>1228.2</td><td>61.0</td><td>49.7</td><td>86.2</td><td>56.4</td><td>64.3</td><td>63.2</td></tr><tr><td>\(A_{1,all}\)</td><td>1265.0</td><td>59.8</td><td>52.7</td><td>86.3</td><td>54.4</td><td>64.6</td><td>63.5</td></tr><tr><td>\(+A_{last,all}\)</td><td>1281.1</td><td>58.7</td><td>53.8</td><td>86.1</td><td>57.7</td><td>64.1</td><td>64.1</td></tr></table>
+
+Table 4. The ablation of attention distillation strategy.  $A_{1,t - v}$  is our first layer  $A_{1,t - v}$  only KD, and  $A_{1,v - v}$ ,  $A_{1,t - t}$  are in the same way.  $A_{1,all}$  refers to applying attention distillation on full attention of the first layer.  $+A_{last,all}$  refers to adding an extra KD loss on full attention of the last layer.  
+
+<table><tr><td>Settings</td><td>Total Training Time</td><td>Max Memory Occupied</td></tr><tr><td>Short MVLM2 1.7B</td><td>176 GPU hours</td><td>-</td></tr><tr><td>Long MVLM2 1.7B</td><td>228 GPU hours</td><td>-</td></tr><tr><td>Short w/ Align-KD</td><td>296 GPU hours</td><td>22.3 GB/device*</td></tr><tr><td>Long w/ Align-KD</td><td>676 GPU hours</td><td>30.7 GB/device†</td></tr></table>
+
+Table 5. The comparison of training time and memory workload. 'w/ Align-KD' refers to training with Align-KD policy. *Set batch size to 4 per iteration. †Set batch size to 1 per iteration.
+
+For some examples that would cause instantaneous overload due to the gradient accumulation, we save the output representations from teacher and let them join training later when we can remove the teacher model from the device. When dealing with Short, Align-KD can achieve training with maximum memory workload of 22.3 GB per GPU, which is acceptable for commercial devices like RTX 3090. As for Long subset, the workload of 30.7 GB per GPU is also acceptable for devices like NVIDIA V100. The memory load of vanilla MobileVLM V2 1.7B is not presented here since it can be flexibly tuned. Despite the extra workload brought, Align-KD still enables universal improvements across different vision-language tasks.
+
+# 5. Conclusion
+
+We propose a knowledge distillation method for MobileVLM V2 model, namely Align-KD in this paper. Based on the conjecture that the alignment mainly happens at the front layer of LLM in VLMs, Align-KD proposes to conduct knowledge distillation only on the text-query-vision part of the first attention. The vision tokens are also unbalancedly enhanced according to the text tokens' focusing. Using MobileVLM V2 7B model as teacher, Align-KD enables universal improvements across benchmarks under both regular training setting and resource-limited setting.
+
+# Acknowledgment
+
+This work was supported by Sichuan Science and Technology Program (No.2024YFHZ0026).
+
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+# Align3R: Aligned Monocular Depth Estimation for Dynamic Videos
+
+Jiahao Lu $^{1*}$  Tianyu Huang $^{2*}$  Peng Li $^{1}$  Zhiyang Dou $^{3}$  Cheng Lin $^{3}$  Zhiming Cui $^{4}$  Zhen Dong $^{5}$  Sai-Kit Yeung $^{1}$  Wenping Wang $^{6}$  Yuan Liu $^{1,7\dagger}$ ${}^{1}\mathrm{HKUST}$ ${}^{2}\mathrm{CUHK}$ ${}^{3}\mathrm{HKU}$ ${}^{4}\mathrm{ShanghaiTech}$ ${}^{5}\mathrm{WHU}$ ${}^{6}\mathrm{TAMU}$ ${}^{7}\mathrm{NTU}$
+
+* Equal contribution. Project page: https://igl-hkust.github.io/Align3R.github.io/
+
+![](images/eb3538240bf43d610ecec4ea0cfb2664a1e53d25c244819e8db2380d2e04fdfb.jpg)  
+Figure 1. Align3R estimates temporally consistent video depth, dynamic point clouds, and camera poses from monocular videos.
+
+# Abstract
+
+Recent developments in monocular depth estimation methods enable high-quality depth estimation of single-view images but fail to estimate consistent video depth across different frames. Very recent works address this problem by applying a video diffusion model to generate video depth conditioned on the input video, which is training-expensive and can only produce scale-invariant depth values without camera poses. In this paper, we propose a novel video-depth estimation method called Align3R to estimate temporally consistent depth maps for a dynamic video. Our key idea is to utilize the recent DUSt3R model to align estimated monocular depth maps of different timesteps. First, we fine-tune the DUSt3R model with additional estimated monocular depth as inputs for the dynamic scenes. Then, we apply optimization to reconstruct both depth maps and camera poses. Extensive experiments demonstrate that Align3R estimates consistent video depth and camera poses for a monocular
+
+video with superior performance than baseline methods.
+
+# 1. Introduction
+
+Monocular depth estimation for monocular videos or image sequences is a crucial problem in computer vision and robotics with applications in various downstream tasks, e.g., camera localization, scene reconstruction, and so on [3, 15, 35]. Traditional depth estimation methods [37] rely on strong camera motions with a large baseline to estimate dense depth maps with stereo matching. Despite its wide applications, estimating monocular depth is challenging due to its ill-posed nature.
+
+Recent works [2, 4, 9, 16, 18, 56, 57, 61] address this ill-posed problem in a data-driven manner, which enables relative or metric depth estimation on single-view images after training on large-scale datasets. Though impressive performance is achieved on the depth estimation for a single image, estimating temporally consistent video depth for a dynamic video is still challenging. All these single-view depth estimators have difficulty maintaining a consis
+
+tent scale factor of the estimated depth maps for different frames, which results in flickering artifacts in the estimated depth sequences.
+
+To align the depth maps of different frames, early-stage works [19, 26] mainly apply inference time optimization by aligning the depth maps with the correspondence constraints across different frames built from flow estimation or image matching. However, these methods can hardly handle large dynamic motions or camera motions due to the vulnerable flow estimation or image matching and their optimization process is extremely time-consuming taking more than several hours. Recent concurrent works [17, 38] take advantage of powerful video diffusion models to maintain the cross-frame consistency for direct video depth generation. However, such video diffusion models often require large computation resources and dataset volume for training. Due to their computation complexity, these methods can only process video clips of a predefined length and struggle to maintain consistency across different clips [38]. Moreover, they only produce scale-invariant depth without camera poses [17, 38], which are not sufficient for downstream tasks like 4D reconstruction [20, 24, 25, 46] or 3D tracking [52]. Thus, estimating a consistent depth sequence from a monocular video is still challenging.
+
+In this work, we propose a novel method called Align3R for consistent video depth estimation from a monocular video as shown in Fig. 1. The key idea of Align3R is to combine the monocular depth estimators with the recent DUSt3R [47] model. Monocular depth estimators enable high-quality depth estimation for each frame with fine details but cannot maintain cross-frame consistency while the DUSt3R model can predict coarse 3D pairwise point maps to align two frames. Thus, Align3R combines the best of two models for accurate and high-quality video depth estimation, which shows the following three characteristics. First, in comparison with the video diffusion-based methods [17, 38] that generates a depth video directly, Align3R only needs to learn to predict pairwise point maps, which is much easier for learning. Second, in comparison with the original DUSt3R model, Align3R can predict more details in depth maps due to the utilization of the high-quality monocular depth estimation methods [4, 57]. Third, Align3R further naturally supports camera pose estimation of dynamic videos, which is challenging for traditional Structure-from-Motion (SfM) pipelines [36]. The estimated camera poses further support various downstream tasks like dynamic novel-view synthesis.
+
+Combining the monocular depth estimation with DUSt3R is non-trivial. A straightforward way is a post-optimization strategy that utilizes the pairwise point map prediction of DUSt3R as constraints to directly align the monocular depth estimation from different frames as early-stage works [19, 26]. However, we find that this leads to
+
+sub-optimal results even after fine-tuning the DUSt3R on the dynamic videos. Instead of this post-optimization strategy, we propose a better combination strategy that utilizes the monocular depth estimation in fine-tuning DUSt3R. This pre-combination strategy effectively makes the finetuned DUSt3R model aware of the monocular depth maps to be aligned. Specifically, we unproject the estimated monocular depth maps to get 3D point maps, then apply an additional Transformer to encode the point maps, and finally add the encoded features into the decoder of DUSt3R. In this strategy, we inject the monocular depth estimation into the point map prediction of the DUSt3R model in fine-tuning, which not only results in more detailed point map prediction but also makes the fine-tuned model informed about the scale difference of input depth maps. After that, we only need to follow the optimization process of DUSt3R to predict the depth maps of different frames.
+
+We have conducted comprehensive experiments on 6 synthetic and real-world dynamic video datasets. The results show that Align3R is able to estimate temporal consistent video depth maps and outperforms all baseline methods by a large margin. Meanwhile, our method is also able to estimate accurate camera poses for the dynamic videos, showing better or comparable performance as our concurrent work MonST3R and pose estimation methods.
+
+# 2. Related works
+
+Monocular Depth Estimation. Traditional methods [14, 21, 23, 37] for depth estimation generally rely on explicit feature matching and epipolar constraints, thus having difficulty dealing with complex and low-textured scenes. In recent years, deep learning-based methods [1, 30, 54, 58, 62] have presented superior performance and become mainstream. However, their generalization ability to unseen domains could be challenging due to the limited training data. To address this problem, some methods are proposed to employ affine-invariant loss functions [33] for training on large-scale mixed datasets and achieve impressive accuracy and robustness regarding scale-shift-invariant relative depth estimation [11, 13, 56, 57]. Another stream of methods focuses on directly learning metric depth by leveraging camera parameters or careful network designs [2, 4, 16, 32, 61]. Besides, with the success of diffusion-based generative models [34], new attempts are made to leverage the diffusion priors for high-quality and zero-shot depth estimation [9, 18]. Nevertheless, all these methods focus on static monocular images and struggle to maintain cross-frame consistency for video depth estimation.
+
+Video Depth Estimation. To achieve consistent video depth estimation, early-stage approaches generally employ inference time optimization that takes camera poses or optimal flow as constraints to align the depth maps across differ
+
+ent frames [7, 19, 26, 49, 53, 66]. The performance of these methods largely depends on the accuracy of vulnerable camera pose or flow estimation, therefore struggling to deal with large camera motions or dynamic components. Recently, some feed-forward methods are proposed to directly predict depth sequences from videos [22, 41, 50, 51, 55, 59]. While achieving impressive accuracy, their generalization ability to open-world videos with diverse content could be constrained by the limited model capacity. In addition, some methods are developed to utilize the powerful video diffusion models to directly generate high-quality video depth [17, 38]. Despite the impressive performance, their video diffusion models often require large computation resources for training. Due to the computation complexity, these methods can only process video clips with a predefined length. In contrast, our method Align3R only needs to learn to predict pairwise point maps, which is much easier to learn and more flexible.
+
+Cocurrent Work. MonST3R [63] is a concurrent work that also finetunes DUSt3R on dynamic videos for both video depth and camera pose estimation, which achieves very impressive results. The major difference is that Align3R is initially motivated by consistent video depth estimation so Align3R incorporates an estimated monocular depth in the DUSt3R model while MonST3R directly finetunes the original DUSt3R model without any additional modules. Other concurrent works [45, 60] also adopt a DUSt3R-like framework for poseless Gaussian Splatting in static scenes.
+
+# 3. Method
+
+Overview. Given a video consisting of  $N$  frames  $\{\mathbf{I}_k\in$ $\mathbb{R}^{\mathrm{H}\times \mathrm{W}\times 3}|k = 1,\dots,N\}$  , our target is to estimate the corresponding depth maps  $\{\mathbf{D}_k\in \mathbb{R}^{\mathrm{H}\times \mathrm{W}}\}$  and camera poses  $\{\pi_k\in \mathbb{S}\mathbb{E}(3)\}$  . Align3R achieves this by first applying a monocular depth estimator, e.g. Depth Pro [4] and DepthAnything V2 [57], to estimate depth maps  $\{\hat{\mathbf{D}}_k\}$  for all frames. Then, we apply a modified DUSt3R model [47] to predict pairwise point maps for some frame pairs in the video using both the image  $\mathbf{I}_k$  and the estimated depth map  $\hat{\mathbf{D}}_k$  . Finally, we solve for globally consistent depth maps  $\{\mathbf{D}_k\}$  and camera poses  $\{\pi_k\}$  for all frames using these predicted pairwise point maps. In the following, we first introduce the DUSt3R [47] model.
+
+# 3.1. Recap of DUSt3R
+
+Given a set of images  $\{\mathbf{I}_k\}$  of a static scene, DUSt3R [47] can estimate depth maps and camera poses for all frames by pairwise point map prediction and global alignment.
+
+Pairwise prediction. In the point map prediction, DUSt3R applies a ViT-based network that takes a pair of image frames  $\mathbf{I}_n$ ,  $\mathbf{I}_m \in \mathbb{R}^{\mathrm{H} \times \mathrm{W} \times 3}$  as inputs, and outputs point maps of both frames  $\mathbf{X}_n^e$ ,  $\mathbf{X}_m^e \in \mathbb{R}^{\mathrm{H} \times \mathrm{W} \times 3}$  with respect to the coordinate of frame  $n$ , where  $e = (m,n)$ , and
+
+the corresponding confidence maps  $\mathbf{C}_n^e$ ,  $\mathbf{C}_m^e \in \mathbb{R}^{H \times W}$ . For the given image set  $\{\mathbf{I}_k\}$ , DUSt3R constructs a connectivity graph  $\mathcal{G}(\mathcal{V}, \mathcal{E})$  for selecting pairwise images, where the vertices  $\mathcal{V}$  represent  $N$  images and each edge  $e \in \mathcal{E}$  is an image pair.
+
+Global alignment. After predicting all the pairwise point maps, DUSt3R introduces a global alignment optimization to solve for the depth maps  $\mathbf{D} := \{\mathbf{D}_k\}$  and camera poses  $\pi := \{\pi_k\}$  by
+
+$$
+\underset {\mathbf {D}, \pi , \sigma} {\arg \min } \sum_ {e \in \mathcal {E}} \sum_ {v \in e} \mathbf {C} _ {v} ^ {e} \| \mathbf {D} _ {v} - \sigma_ {e} P _ {e} \left(\pi_ {v}, \mathbf {X} _ {v} ^ {e}\right) \| _ {2} ^ {2}, \tag {1}
+$$
+
+where  $\sigma = \{\sigma_{e}\}$  are the scale factors defined on the edges,  $P_{e}(\pi_{v},\mathbf{X}_{v}^{e})$  means projecting the predicted point maps  $\mathbf{X}_v^e$  to view  $v$  using poses  $\pi_v$  to get a depth map. The objective function in Eq. (1) explicitly constrains the geometry alignment between frame pairs, therefore after the optimization process, cross-view consistency can be maintained in the estimated depth maps.
+
+Motivation. Since DUSt3R enables the estimation of globally consistent depth maps while monocular depth estimators [4, 57] struggle to maintain cross-frame consistency, we can utilize the prediction and optimization of DUSt3R to enforce the cross-frame consistency for these monocular depth estimators. However, directly applying DUSt3R here presents two main challenges. First, DUSt3R is designed specifically for static scenes, limiting its applicability to dynamic videos. Second, DUSt3R's point map predictions tend to yield less detailed depth maps compared to pixel-aligned monocular depth estimators, reducing accuracy. To address these limitations, we propose to integrate monocular depth estimation within the DUSt3R framework and fine-tune DUSt3R for dynamic scenes.
+
+# 3.2. Incorporating Monocular Depth Estimation
+
+In this section, we aim to design a mechanism to incorporate the predicted monocular depth maps from Depth Pro [4] or Depth Anything V2 [57] into the DUSt3R model. A straightforward approach to incorporating monocular depth maps is to directly concatenate depth maps with the input RGB images. However, as shown in experiments, this approach destructively breaks the feature distributions of the pre-trained DUSt3R encoder. Instead, inspired by ControlNet [65], we adopt a new vision transformer to extract features from the depth maps and inject these features into the decoder of DUSt3R without ruining the original prediction before fine-tuning, as illustrated in Fig. 2.
+
+Depth to points. Since the predictions of the DUSt3R model are point maps for two images, we transform the estimated depth into point maps of the modality for better convergence. We unproject the estimated depth maps into 3D space to generate 3D point maps  $\hat{\mathbf{X}}_n,\hat{\mathbf{X}}_m\in \mathbb{R}^{\mathrm{H}\times \mathrm{W}\times 3}$
+
+![](images/49121d9c84b76a1d3c22bc9ec48238d0b3ed75474a555563bf1313d8c520353a.jpg)  
+Figure 2. Architecture of Align3R. Given two frames of a video, we apply the ViT-based encoder and decoder to predict pairwise point maps from them. In this process, we apply the external monocular depth estimator to estimate depth maps for these two images, process the estimated depth with a new ViT-based encoder, and finally inject the extracted features from this new encoder into the decoder of the original DUSt3R decoder with zero convolution layers. During inference, we apply global alignment to ensure consistent depth maps, camera poses and point clouds across each frame.
+
+This unprojection process requires the invariants of the input images. In models with focal length prediction, like Depth Pro [4], we utilize the predicted focal length to construct the intrinsic matrix. Meanwhile, for models without focal length prediction, like Depth Anything V2 [57], we set the focal length to a fixed value. Due to the large numerical ranges of predicted depth values, We normalize each axis  $(x,y,z)$  of the unprojected point maps separately to the range  $[-1,1]$ , ensuring stable model training.
+
+Point map ViT. Next, for each point map  $\hat{\mathbf{X}}_i$  with  $i = n$  or  $i = m$ , we apply a standard patch embedding method to divide the point maps into patches
+
+$$
+\hat {\mathbf {X}} _ {i} ^ {\prime} = \operatorname {P a t c h E m b e d} \left(\hat {\mathbf {X}} _ {i}\right), \tag {2}
+$$
+
+where  $\hat{\mathbf{X}}_i^{\prime}\in \mathbb{R}^{\mathrm{H}^{\prime}\times \mathrm{W}^{\prime}\times \mathrm{C}}$  is the patchified point map. Subsequently, we apply the self-attention mechanism to  $\hat{\mathbf{X}}_i^\prime$  to generate multi-level features  $\hat{\mathbf{F}}_i^{(1)},\hat{\mathbf{F}}_i^{(2)},\dots ,\hat{\mathbf{F}}_i^{(s)}$ , which will be injected into the DUSt3R decoder for information aggregation. At this stage, to avoid ruining the prediction of the original DUSt3R model, we use zero convolution [64] for feature fusion
+
+$$
+\hat {\mathbf {E}} _ {i} ^ {(l)} = \operatorname {Z e r o C o n v} \left(\hat {\mathbf {F}} _ {i} ^ {(l)}\right) + \mathbf {E} _ {i} ^ {(l)}, l = 1, 2, \dots , s, \tag {3}
+$$
+
+where  $\mathbf{E}_i^{(l)}$  is the feature map generated by the DUSt3R decoder on the  $l$ -th layer and  $\hat{\mathbf{E}}_i^{(l)}$  is the feature map with the injected point map features.
+
+# 3.3. Fine-tuning on Dynamic Videos
+
+The original DUSt3R model is only trained on static scenes and cannot correctly process dynamic videos. To improve the performance, we fine-tune the DUSt3R model along with the additional point map transformer on dynamic videos with ground-truth depth maps. To maintain DUSt3R's robust feature extraction capabilities, the encoder is frozen while only the decoder and the additional point map transformer are fine-tuned. The fine-tuning loss following DUSt3R is defined as follows
+
+$$
+L _ {d u s t 3 r} = \left\| \frac {1}{z} \mathbf {X} _ {v} ^ {e} - \frac {1}{\bar {z}} \overline {{\mathbf {X}}} _ {v} ^ {e} \right\| _ {2}, \qquad (4)
+$$
+
+where  $v \in \{n, m\}$  denotes the view index,  $\mathbf{X}$  and  $\overline{\mathbf{X}}$  are the predicted and ground-truth point maps, and  $z$  and  $\overline{z}$  are scaling factors used to normalize the predicted and ground-truth point maps. Notably,  $z$  and  $\overline{z}$  are computed from all valid pixels within a single image.
+
+Datasets. We apply 5 synthetic datasets for fine-tuning, including Sceneflow [27], VKITTI [10], TartanAir [48], Spring [28], PointOdyssey [69], as shown in Tab. 1. Among all these 5 datasets, we also include a diverse static dataset TartanAir to keep the performances on static regions. Among all scenes in the SceneFlow dataset, we use Monkaa, Driving, and a part of FlyingThings3D for training and we adopt the remaining part of FlyingThings3D as the test set. The large-scale synthetic dataset PointOdyssey
+
+<table><tr><td>Name</td><td>#Scene</td><td>Avg. #Img</td><td>Total #Img</td><td>Type</td></tr><tr><td>SceneFlow [27]</td><td>8k</td><td>10</td><td>80k</td><td>Dynamic</td></tr><tr><td>VKITTI [10]</td><td>100</td><td>425</td><td>42k</td><td>Dynamic</td></tr><tr><td>TartanAir [48]</td><td>500</td><td>900</td><td>450k</td><td>Static</td></tr><tr><td>Spring [28]</td><td>37</td><td>135</td><td>5k</td><td>Dynamic</td></tr><tr><td>PointOdyssey [69]</td><td>131</td><td>1.8k</td><td>240k</td><td>Dynamic</td></tr></table>
+
+Table 1. Statistics of datasets for fine-tuning.
+
+contains a training set and a validation set so we adopt the training set for fine-tuning and the validation set in the evaluation. On all these datasets, we sample two frames with temporal strides ranging from 1 to 10 as the training image pairs, which leads to reasonable overlap regions between the image pairs.
+
+Depth filtering. A noticeable problem in fine-tuning DUSt3R is that the numerical ranges of ground-truth point maps are very large. Far-away points with large depth values will dominate the training loss of Eq. (4). However, for an image pair with a limited baseline length, it is hard to predict points with large depth values exactly due to their small disparities and these far-away points are not as important as nearby objects. Thus, we filter out depth regions beyond 400 meters, which reduces the impact of distant objects (such as the sky) on prediction accuracy. This approach enables our model to better adapt to open-world dynamics by emphasizing depth prediction of objects near to camera.
+
+# 3.4. Inference on Long Videos
+
+After fine-tuning the model on dynamic videos, we apply the model to predict pairwise point maps for the given dynamic video. Then, we follow the DUSt3R to enforce the constraint in Eq. (1) to solve for the consistent depth maps and camera poses for each frame. However, we find that for long videos with more than 30 frames, the original optimization strategy in DUSt3R consumes too much memory and causes out-of-memory on a 4090 GPU. We adopt a hierarchical optimization to reduce memory consumption.
+
+Hierarchical optimization. Given a long video sequence, we divide the video into  $K$  clips of a predefined length of  $M = 10$  or  $M = 20$ . For each clip, we take one image as the key frame and construct a keyframe clip of length  $K$ . By conducting global alignment on the keyframe clip, we initialize the depth maps, camera poses, and focal lengths of these keyframes. Then, for each divided clip, we apply a local alignment to compute the depth maps, camera poses, and focal lengths for the remaining frames. Such a global-local hierarchical optimization ensures that we only optimize a short clip with limited frames every time, which effectively reduces memory and time consumption while keeping consistency.
+
+# 4. Experiments
+
+# 4.1. Implementation details
+
+We train our model on six RTX 4090 GPUs with a batch size of 12, requiring approximately 20 hours for 50 epochs. We use the AdamW optimizer with a learning rate of 0.00005. Input images are resized randomly to one of three resolutions:  $512 \times 288$ ,  $512 \times 336$ , or  $512 \times 256$ . Each epoch consists of 27,750 sampled image pairs, which contain 5,000 pairs from SceneFlow, 3,000 from VKITTI, 6,250 from TartanAir, 1,000 from Spring, and 12,500 from PointOdyssey. We use  $s = 6$  layers of features in Eq. (3). We adopt the flow losses proposed in MonST3R [63] to introduce the RAFT [42] flow in inference optimization, which influences the depth quality a little but is important for accurate camera pose estimation. More implementation details can be found in the supplementary material.
+
+# 4.2. Video depth estimation
+
+Evaluation datasets. We evaluate our model on both real-world datasets, including the Bonn [29] and TUM dynamics [40] datasets, and synthetic datasets, including the Sintel [5] dataset, the PointOdyssey [69] validation set, and the test set FlyingThings3D of Sceneflow [27]. Additionally, we report the qualitative results on the DAVIS [31] dataset.
+
+The Bonn dataset is a real-world RGB-D SLAM dataset containing 24 dynamic sequences, where people are doing different tasks such as manipulating boxes or playing with balloons. We evaluate our model on five videos with an average of 110 frames per video, the same as the setting used in DepthCrafter [17]. The TUM dynamics dataset is also a real-world dataset with 8 dynamic scenes and we select 50 frames from each scene for evaluation. The Sintel dataset is a synthetic dynamic dataset with 23 videos and approximately 50 frames per video. The PointOdyssey validation set is a synthetic dataset with 15 dynamic scenes with numerous moving foreground objects. We evaluate our model on the first 110 frames of each video. The FlyingThings3D test set is also a synthetic dataset with many moving foreground objects, containing around 900 dynamic scenes with approximately 10 frames per scene. We select 44 scenes with a stride of 20 for evaluation.
+
+Evaluation metrics. Following previous methods [17, 63], we evaluate our model by aligning the estimated depth maps with the ground truth using a single scale and shift before calculating the metrics. To ensure a fair comparison of temporal consistency across methods, we calculate a shared scale and shift for the entire video sequence, rather than computing individual scale and shift values for each frame as done in monocular depth estimation. We mainly report two metrics, i.e. Abs Rel  $\downarrow$  (absolute relative error) and percentage of inlier points  $\delta < 1.25\uparrow$ .
+
+Baselines. We compare our Align3R with single-frame
+
+<table><tr><td rowspan="3">Category</td><td rowspan="3">Method</td><td colspan="6">Indoors &amp; outdoors (Hard)</td><td colspan="4">Indoors (Easy)</td></tr><tr><td colspan="2">Sintel</td><td colspan="2">PointOdyssey val</td><td colspan="2">Flying Things3D test</td><td colspan="2">Bonn 5 scenes</td><td colspan="2">TUM dynamics</td></tr><tr><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td></tr><tr><td rowspan="2">Single-frame depth</td><td>Depth Anything V2 [57]</td><td>0.348</td><td>0.592</td><td>0.214</td><td>0.688</td><td>0.267</td><td>0.616</td><td>0.118</td><td>0.882</td><td>0.184</td><td>0.750</td></tr><tr><td>Depth Pro [4]</td><td>0.418</td><td>0.559</td><td>0.167</td><td>0.779</td><td>0.322</td><td>0.537</td><td>0.067</td><td>0.974</td><td>0.106</td><td>0.887</td></tr><tr><td rowspan="2">Video depth</td><td>ChronoDepth [38]</td><td>0.687</td><td>0.486</td><td>0.210</td><td>0.707</td><td>0.288</td><td>0.633</td><td>0.100</td><td>0.911</td><td>0.151</td><td>0.825</td></tr><tr><td>DepthCrafter [17]</td><td>0.292</td><td>0.697</td><td>0.229</td><td>0.675</td><td>/</td><td>/</td><td>0.075</td><td>0.971</td><td>0.176</td><td>0.744</td></tr><tr><td rowspan="2">Joint video depth</td><td>DUSt3R [47]</td><td>0.422</td><td>0.542</td><td>0.184</td><td>0.743</td><td>0.140</td><td>0.817</td><td>0.154</td><td>0.839</td><td>0.202</td><td>0.775</td></tr><tr><td>MonST3R [63]</td><td>0.335</td><td>0.586</td><td>0.089</td><td>0.909</td><td>0.132</td><td>0.836</td><td>0.082</td><td>0.953</td><td>0.140</td><td>0.841</td></tr><tr><td rowspan="2">depth &amp; pose</td><td>Ours (Depth Anything V2)</td><td>0.253</td><td>0.681</td><td>0.078</td><td>0.929</td><td>0.106</td><td>0.890</td><td>0.075</td><td>0.972</td><td>0.109</td><td>0.915</td></tr><tr><td>Ours (Depth Pro)</td><td>0.263</td><td>0.641</td><td>0.077</td><td>0.930</td><td>0.102</td><td>0.895</td><td>0.068</td><td>0.969</td><td>0.112</td><td>0.884</td></tr></table>
+
+Table 2. Video depth estimation results. We evaluate our model on both real-world datasets, Bonn and TUM dynamics, and synthetic datasets, Sintel, PointOdyssey validation set, and Sceneflow test set. Best and second best results are highlighted.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">ScanNetV2 (Static)</td><td colspan="2">NYU-v2 (Static)</td><td colspan="2">KITTI (AD)</td></tr><tr><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td><td colspan="2">Abs Rel ↓ δ &lt; 1.25 ↑</td></tr><tr><td>DUSt3R [47]</td><td>0.037</td><td>0.980</td><td>0.089</td><td>0.903</td><td>0.135</td><td>0.823</td></tr><tr><td>MonST3R [63]</td><td>0.042</td><td>0.972</td><td>0.102</td><td>0.883</td><td>0.103</td><td>0.874</td></tr><tr><td>Ours (Depth Anything V2)</td><td>0.035</td><td>0.983</td><td>0.080</td><td>0.918</td><td>0.110</td><td>0.909</td></tr><tr><td>Ours (Depth Pro)</td><td>0.034</td><td>0.983</td><td>0.084</td><td>0.907</td><td>0.104</td><td>0.910</td></tr></table>
+
+Table 3. More depth estimation results on static and autonomous driving scenes. "AD" refers to Autonomous Driving.
+
+and video depth estimation methods, i.e. Depth Anything V2 [57], Depth Pro [4], ChronoDepth [38] and DepthCrafter [17]. We also compare with methods for joint video depth and pose estimation methods, i.e. DUSt3R [47] and MonST3R [63]. For all baseline methods, we adopt their official implementation and re-evaluate their performance using a per-sequence scale and shift alignment on our evaluation datasets.
+
+Comparison with existing methods. In Tab. 2, we compare our results using Depth Anything V2 and Depth Pro as monocular depth input with all baseline methods. We summarize the results of Tab. 2 in the following.
+
+1. Our method achieves superior video depth estimation results compared to previous joint video depth and pose estimation methods DUSt3R and the concurrent work MonST3R on all metrics of all datasets.  
+2. Furthermore, with the assistance of global alignment, we can effectively align the predictions of monocular depth estimation models like Depth Anything V2 and Depth Pro, achieving better temporal consistency on three challenging outdoor datasets, including Sintel, PointOdyssey, and FlyingThings3D, which contain significant dynamic object motions or camera motions.  
+3. On the relatively simpler scenarios, like the Bonn and TUM dynamics datasets, which are indoor scenes with smooth camera motions and fewer dynamic objects, the original predictions of Depth Pro are already high-quality and consistent due to the relatively small and slow motions. We find that our method achieves comparable results as Depth Pro and may lose some details in the global alignment.
+
+We visualize the qualitative comparison on the DAVIS and TUM dynamics datasets in Fig. 3. As shown by the figure, our method achieves more consistent video depth than other baseline methods. Additionally, by incorporating monocular depth, our approach reconstructs more details on the depth maps than MonST3R.
+
+More depth estimation results on static and autonomous driving scenes. Our method is fine-tuned not only on dynamic datasets but also on the static dataset TartanAir [48]. Therefore, our method retains strong performance on static scenes with competitive results in static scenes and autonomous driving scenarios. In Table 3, we present the depth results on ScanNetV2 [8], NYU-v2 [12] and KITTI [39]. For the ScanNetV2 dataset, we sample the first 30 frames with the stride of 3 to save compute.
+
+# 4.3. Camera pose estimation
+
+Evaluation datasets. We evaluate the camera pose estimation on three real-world datasets, i.e. TUM dynamics, Bonn and ScanNetV2, and a synthetic dataset, i.e. Sintel. The TUM dynamics dataset consists of 8 sequences. We evaluate all methods on 30 and 90 frames of each sequence. For the ScanNetV2 dataset, we sample the first 30 frames with the temporal stride of 3 to save compute. For the Bonn dataset, we evaluate our model on five videos and also select 30 frames from each scene. For the Sintel dataset, we follow the evaluation protocol of previous methods [6, 68] to exclude scenes that are static or only contain straight motions, resulting in 14 sequences for evaluation.
+
+Evaluation metrics. We follow previous works [6, 44, 68] to report three metrics, i.e. ATE  $\downarrow$  (absolute translation error), RTE  $\downarrow$  (relative translation error) and RRE  $\downarrow$  (relative rotation error). ATE computes the deviation of estimated trajectories from the ground truth trajectories after alignment. RPE and RPE are the averaged local translation and rotation errors respectively over consecutive poses.
+
+Baselines. We compare our method with both pure camera pose estimation methods including DROID-SLAM [43], DPVO [44], COLMAP [36] and also joint depth and pose
+
+<table><tr><td rowspan="2">Category</td><td rowspan="2">Method</td><td colspan="2">TUM dynamics1</td><td rowspan="2">(Dynamic) RRE↓</td><td colspan="2">TUM dynamics2</td><td rowspan="2">(Dynamic) RRE↓</td><td colspan="3">Bonn 5 scenes (Dynamic)</td><td colspan="3">Sintel (Dynamic)</td><td colspan="3">ScanNetV2 (Static)</td></tr><tr><td>ATE ↓</td><td>RTE↓</td><td>ATE ↓</td><td>RTE↓</td><td>ATE(10-2) ↓</td><td>RTE(10-2) ↓</td><td>RRE↓</td><td>ATE ↓</td><td>RTE↓</td><td>RRE↓</td><td>ATE ↓</td><td>RTE↓</td><td>RRE↓</td></tr><tr><td rowspan="3">Pose only</td><td>DROID-SLAM† [43]</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>0.175</td><td>0.084</td><td>1.912</td><td>/</td><td>/</td><td>/</td></tr><tr><td>DPVO‡ [44]</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td><td>0.115</td><td>0.072</td><td>1.975</td><td>/</td><td>/</td><td>/</td></tr><tr><td>COLMAP [36]</td><td>/</td><td>/</td><td>/</td><td>0.076</td><td>0.059</td><td>7.689</td><td>3.43</td><td>0.927</td><td>0.905</td><td>0.559</td><td>0.325</td><td>7.302</td><td>/</td><td>/</td><td>/</td></tr><tr><td rowspan="6">Joint depth &amp; pose</td><td>Robust-CVD [19]</td><td>/</td><td>/</td><td>/</td><td>0.153</td><td>0.026</td><td>3.528</td><td>/</td><td>/</td><td>/</td><td>0.360</td><td>0.154</td><td>3.443</td><td>/</td><td>/</td><td>/</td></tr><tr><td>CasualSAM [67]</td><td>/</td><td>/</td><td>/</td><td>0.071</td><td>0.010</td><td>1.712</td><td>/</td><td>/</td><td>/</td><td>0.141</td><td>0.035</td><td>0.615</td><td>/</td><td>/</td><td>/</td></tr><tr><td>DUSt3R [47]</td><td>0.093</td><td>0.035</td><td>1.708</td><td>0.083</td><td>0.017</td><td>3.567</td><td>2.166</td><td>0.650</td><td>1.169</td><td>0.601</td><td>0.214</td><td>11.426</td><td>0.029</td><td>0.019</td><td>0.604</td></tr><tr><td>MonST3R [63]</td><td>0.020</td><td>0.014</td><td>0.478</td><td>0.063</td><td>0.009</td><td>1.217</td><td>0.686</td><td>0.595</td><td>0.593</td><td>0.111</td><td>0.044</td><td>0.780</td><td>0.019</td><td>0.013</td><td>0.386</td></tr><tr><td>Ours (Depth Anything V2)</td><td>0.011</td><td>0.010</td><td>0.321</td><td>0.031</td><td>0.010</td><td>1.014</td><td>0.646</td><td>0.588</td><td>0.585</td><td>0.163</td><td>0.062</td><td>0.419</td><td>0.017</td><td>0.012</td><td>0.348</td></tr><tr><td>Ours (Depth Pro)</td><td>0.012</td><td>0.010</td><td>0.327</td><td>0.027</td><td>0.018</td><td>0.446</td><td>0.673</td><td>0.570</td><td>0.576</td><td>0.128</td><td>0.042</td><td>0.432</td><td>0.017</td><td>0.013</td><td>0.352</td></tr></table>
+
+Table 4. Camera pose estimation results. We evaluate our model on three real-world datasets: TUM dynamics, Bonn and ScanNetV2, as well as the synthetic Sintel dataset. Best and second best results are highlighted.  $\ddagger$  means using ground truth camera intrinsics as input.  $^{1}$  and  $^{2}$  represents selecting 30 and 90 frames from each scene, respectively.
+
+![](images/ea4815c7cd658176799f0369af3b65afc5839db009b737df7453bf76511e849b.jpg)  
+Figure 3. Qualitative comparison on the DAVIS and TUM dynamics dataset. The red boxes show highlighted regions.
+
+estimators including Robust-CVD [19], CasualSAM [67], DUSt3R [47], and MonST3R [63]. For DROID-SLAM, DPVO, Robust-CVD, and CasualSAM, we use the re
+
+sults reported in MonST3R while re-evaluating COLMAP, DUSt3R, and MonST3R using their official codes.
+
+Comparison with existing methods. Tab. 4 shows the
+
+<table><tr><td rowspan="3">Setting</td><td colspan="4">Depth estimation</td><td colspan="6">Pose estimation</td></tr><tr><td colspan="2">Sintel</td><td colspan="2">TUM dynamics</td><td colspan="2">Sintel</td><td colspan="4">TUM dynamics</td></tr><tr><td>Abs Rel↓</td><td>δ&lt;1.25↑</td><td>Abs Rel↓</td><td>δ&lt;1.25↑</td><td>ATE↓</td><td>RPE Trans↓</td><td>RPE Rot↓</td><td>ATE↓</td><td>RPE Trans↓</td><td>RPE Rot↓</td></tr><tr><td>F.t. all</td><td>0.310</td><td>0.619</td><td>0.153</td><td>0.811</td><td>0.257</td><td>0.098</td><td>0.801</td><td>0.025</td><td>0.020</td><td>0.757</td></tr><tr><td>F.t. last 4 layers</td><td>0.319</td><td>0.603</td><td>0.159</td><td>0.805</td><td>0.191</td><td>0.086</td><td>1.293</td><td>0.016</td><td>0.016</td><td>0.514</td></tr><tr><td>F.t. decoder</td><td>0.306</td><td>0.613</td><td>0.135</td><td>0.864</td><td>0.227</td><td>0.117</td><td>0.865</td><td>0.017</td><td>0.012</td><td>0.435</td></tr><tr><td>w/o depth</td><td>0.306</td><td>0.613</td><td>0.135</td><td>0.864</td><td>0.227</td><td>0.117</td><td>0.865</td><td>0.017</td><td>0.012</td><td>0.435</td></tr><tr><td>Concat depth</td><td>0.399</td><td>0.537</td><td>0.182</td><td>0.794</td><td>0.338</td><td>0.246</td><td>1.823</td><td>0.034</td><td>0.025</td><td>0.776</td></tr><tr><td>ViT encoder</td><td>0.263</td><td>0.641</td><td>0.112</td><td>0.884</td><td>0.128</td><td>0.042</td><td>0.432</td><td>0.012</td><td>0.010</td><td>0.327</td></tr></table>
+
+quantitative results of our method and all baselines. The results show that the proposed Align3R achieves consistently better performance than all baseline methods on RTE and RRE metrics. For the ATE, our method achieves the best results on the real-world TUM Dynamics, Bonn and ScanNetV2 datasets but is slightly worse than MonST3R on the synthetic Sintel dataset. More qualitative comparisons of camera pose estimation are reported in the supplementary material.
+
+# 4.4. Ablation study
+
+We conduct analyses on fine-tuning strategy, how to incorporate monocular depth maps, and memory reduction of our hierarchical optimization strategy. More analyses are provided in the supplementary material.
+
+Finetuning strategy. In the top part of Tab. 5, we show the results of three different fine-tuning settings. From the results, it can be seen that fine-tuning the full model results in lower performance because such full fine-tuning disrupts the encoder features from DUSt3R. Then, we observe that fine-tuning all decoder layers leads to better performance than fine-tuning only a subset of decoder layers because fine-tuning the full decoder enhances the ability of the model to adapt to dynamic videos.
+
+Depth incorporation. We conduct an ablation study on whether to incorporate the monocular depth and how to incorporate it. The results are shown in the bottom part of Tab. 5. As shown by the results, discarding the input monocular depth degenerates the quality of depth maps because such estimated monocular depth maps often contain more details and thus help predict details on the point maps. Then, we compare an alternative strategy to concatenate the depth map with the input RGB images. Directly concatenating the depth maps disrupts the distribution of the pretrained DUSt3R encoder, leading to a degenerated performance. In contrast, the proposed strategy extracts features from the depth maps with a transformer and injects the features into the decoder of DUSt3R, which significantly improves the results. A qualitative comparison between these
+
+![](images/ac5771f68a41a5c82166b05059d60b96a703b78bfa3ac52280ab08c57811ff44.jpg)  
+Figure 4. Qualitative ablation study on estimated depth.
+
+Table 5. Ablation study on the Sintel and TUM dynamics dataset. “F.t. all” means fine-tuning the whole model of DUSt3R. “F.t. last 4 layers” means fine-tuning the last 4 layers of the decoder while “F.t. decoder” means fine-tuning the whole decoder. “w/o depth” means discarding the estimated depth in the model. “Concat depth” means concatenating the depth with the input RGB images as inputs to the DUSt3R model. “ViT encoder” means converting the depth maps into point maps, applying the new ViT to process the point maps, and finally injecting the extracted features into the decoder with zero convolution layers.  
+
+<table><tr><td>Setting</td><td>Abs Rel↓</td><td>δ&lt;1.25↑</td><td>Avg. time (min)↓</td><td>Memory (GB)↓</td></tr><tr><td>base</td><td>0.054</td><td>0.975</td><td>2.9</td><td>24.0</td></tr><tr><td>w. HO</td><td>0.056</td><td>0.974</td><td>1.1</td><td>5.9</td></tr><tr><td>w. WP</td><td>0.055</td><td>0.974</td><td>1.5</td><td>14.6</td></tr></table>
+
+Table 6. Ablation study on hierarchical optimization ("HO"). "WP" refers to the window frame processing of MonST3R.
+
+three settings is shown in Fig. 4.
+
+Hierarchical optimization. To validate our design of hierarchical optimization, we conduct an experiment on the Bonn dataset by selecting 30 frames for each video. In our hierarchical optimization, we set the predefined clip length  $M = 10$ . The results in Tab. 6 show that in comparison with the original DUSt3R optimization strategy and the window frame processing of MonST3R, our hierarchical optimization strategy effectively reduces memory and time consumption while maintaining quality.
+
+# 5. Conclusion
+
+In this paper, we introduce a new method called Align3R to simultaneously estimate depth maps and camera poses of dynamic videos. The key idea of Align3R is to combine a monocular depth estimator with the DUSt3R model. We propose a novel strategy to apply a transformer to extract features from the monocular depth and inject the extracted features of monocular depth into the decoder of the DUSt3R model. Then, we finetune the DUSt3R model on the dynamic videos. Finally, we can predict pairwise point maps and utilize these point maps to effectively solve for consistent video depth and camera poses. Extensive experiments on 6 synthetic and real-world datasets demonstrate the superior performances of our method.
+
+# References
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\ No newline at end of file
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+# AlignMamba: Enhancing Multimodal Mamba with Local and Global Cross-modal Alignment
+
+Yan Li $^{12}$ , Yifei Xing $^{1}$ , Xiangyuan Lan $^{1}$ , Xin Li $^{1}$ , Haifeng Chen $^{3}$ , Dongmei Jiang $^{12*}$ $^{1}$ Pengcheng Laboratory, Shenzhen, China  
+ $^{2}$ Northwestern Polytechnical University, Xi'an, China  
+ $^{3}$ Shaanxi University of Science and Technology, Xi'an, China
+
+liyan4ai@gmail.com, {xingyf, lanxy, lix07, jiangdm}@pcl.ac.cn, chenhaifeng@sust.edu.cn
+
+# Abstract
+
+Cross-modal alignment is crucial for multimodal representation fusion due to the inherent heterogeneity between modalities. While Transformer-based methods have shown promising results in modeling inter-modal relationships, their quadratic computational complexity limits their applicability to long-sequence or large-scale data. Although recent Mamba-based approaches achieve linear complexity, their sequential scanning mechanism poses fundamental challenges in comprehensively modeling cross-modal relationships. To address this limitation, we propose AlignMamba, an efficient and effective method for multimodal fusion. Specifically, grounded in Optimal Transport, we introduce a local cross-modal alignment module that explicitly learns token-level correspondences between different modalities. Moreover, we propose a global cross-modal alignment loss based on Maximum Mean Discrepancy to implicitly enforce the consistency between different modal distributions. Finally, the unimodal representations after local and global alignment are passed to the Mamba backbone for further cross-modal interaction and multimodal fusion. Extensive experiments on complete and incomplete multimodal fusion tasks demonstrate the effectiveness and efficiency of the proposed method. For instance, on the CMU-MOSI dataset, AlignMamba improves classification accuracy by  $0.9\%$ , reduces GPU memory usage by  $20.3\%$ , and decreases inference time by  $83.3\%$ .
+
+# 1. Introduction
+
+In recent years, multimodal representation fusion has emerged as a critical technology for integrating and understanding information across different modalities (e.g., audio, video, language). This capability is fundamental to
+
+a wide range of applications such as visual-language understanding [18, 42, 48] and audio-visual analysis [19, 21, 45, 46]. However, due to the inherent heterogeneity between modalities - each with its distinct statistical properties and feature distributions - achieving effective cross-modal alignment and fusion remains a significant challenge.
+
+Traditional approaches to this challenge have primarily relied on Transformer-based [38] architectures, which can be broadly categorized into two paradigms. Single-stream methods concatenate features from different modalities into a unified sequence and process them through a shared Transformer layer [13, 17, 28]. In contrast, multi-stream approaches employ separate encoders for each modality with cross-modal Transformers to facilitate information exchange [30, 36, 37, 56]. While these methods have demonstrated promising results in capturing dynamic cross-modal interactions, they suffer from a fundamental limitation: the quadratic computational complexity of attention mechanisms makes them inefficient for processing long-sequence or large-scale data common in real-world multimodal applications.
+
+Recent advances in sequence modeling have introduced the Mamba [5] architecture, based on State Space Models (SSMs) [6, 7], which achieves linear computational complexity while maintaining strong modeling capabilities. By incorporating selection mechanisms and hardware-aware parallel algorithms into SSMs, Mamba effectively captures long-range dependencies without the computational burden of attention mechanisms. This breakthrough has sparked considerable interest in adapting Mamba for multimodal fusion tasks, with approaches ranging from direct feature concatenation [29, 33, 44, 54] to multi-stream architectures [3, 10, 24]. However, our analysis reveals a critical limitation. As shown in Fig. 1, Mamba's sequential scanning mechanism, while computationally efficient, struggles to capture comprehensive cross-modal relationships, particularly with unscanned tokens. This inherent limitation
+
+![](images/b1f19ab0ad05fdb7cd4d67ff4b397fedf904300c68b8814160b5fdec75d842e1.jpg)  
+Figure 1. Transformer leverages attention mechanisms to model relationships across different modalities (top left), whereas Mamba struggles to achieve this due to its sequential scanning mechanism (top right). In contrast, the proposed AlignMamba utilizes both local (OT-based) and global (MMD-based) cross-modal alignment information to achieve efficient and effective multimodal fusion (bottom).
+
+leads to suboptimal alignment between modalities and consequently affects the quality of learned multimodal fusion representations.
+
+To address these issues, we propose AlignMamba, which integrates local and global cross-modal alignment information into Mamba for efficient and effective multimodal fusion. Specifically, we introduce a local alignment module based on Optimal Transport (OT), which learns a transport plan to align features across different modalities by minimizing the cost of feature transportation. While local alignment captures token-level cross-modal relationships, it does not account for distributional differences between modalities. Therefore, we also propose a global alignment loss based on Maximum Mean Discrepancy (MMD). Leveraging the theoretical advantages of reproducing kernel Hilbert space, MMD maps the feature distributions of different modalities into a high-dimensional space and achieves implicit alignment by minimizing their distributional differences. After local and global cross-modal alignment, all unimodal features are combined and fed into the Mamba backbone for further multimodal fusion. This dual alignment strategy ensures that Mamba can exploit both local and global relationships between modalities, thereby learning more comprehensive multimodal representations.
+
+In summary, the contributions of this paper are threefold:
+
+- We observe the limitation of directly applying Mamba to multimodal fusion tasks, which ignores more comprehensive cross-modal alignment information, and propose the AlignMamba framework to achieve efficient and effective multimodal fusion.  
+- We introduce an OT-based local alignment module for explicit learning of token-level correspondences, complemented by an MMD-based global alignment loss for im
+
+plicit distribution alignment. These two types of alignment information complement each other, achieving comprehensive cross-modal alignment.
+
+- Extensive experiments on both complete and incomplete multimodal fusion tasks demonstrate that AlignMamba achieves state-of-the-art results in terms of both effectiveness and efficiency.
+
+# 2. Related Work
+
+# 2.1. Transformer-based Multimodal Fusion
+
+Transformer [38], with its powerful modeling capabilities, has become the cornerstone architecture in modern neural networks. Existing multimodal fusion methods mainly rely on Transformers to model relationships between different modalities and learn multimodal fusion representations. These approaches can be categorized into two main types: multi-stream and single-stream methods.
+
+Multi-stream methods employ cross-modal Transformers to model interactions between any two modalities [15, 23]. For vision-language pre-training tasks, models like ViLBERT [30] and LXMERT [36] utilize two co-attention Transformer layers to model bidirectional relationships between visual and textual modalities. For audio-visual-textual trimodal fusion tasks, MulT [37] leverages cross-modal Transformers to model pairwise modal interactions, and then concatenate all bimodal fusion representations to obtain trimodal fusion representations. Similarly, CMA [37], based on cross-modal attention mechanisms, was proposed to fuse features from three modalities. More recently, BLIP-2 [16] introduced Q-Former, a lightweight querying Transformer architecture, to align vision-language modalities and learn multimodal fusion representations.
+
+Single-stream methods adopt a more straightforward strategy by concatenating features from different modalities and feeding them into a Transformer encoder for cross-modal interaction and multimodal fusion [22, 43]. For instance, in vision-language pre-training tasks, VisualBERT [17] extracts features from key regions using object detectors and concatenates these region feature sequences with text token embeddings before feeding them into a Transformer. In contrast, ViLT [13] replaces region feature sequences with image patch embedding sequences, discarding the object detection backbone and improving efficiency. Recent multimodal pre-training models, such as LLaVA [28], have adopted similar approaches to model cross-modal correspondences and learn multimodal fusion representations for downstream tasks.
+
+Existing methods achieve cross-modal interaction and fusion through cross-attention or self-attention mechanisms, learning comprehensive and effective multimodal fusion representations. However, the quadratic time complexity of Transformers limits their efficiency when processing
+
+large-scale or long-sequence data. This limitation necessitates the development of novel multimodal fusion methods that balance effectiveness and efficiency.
+
+# 2.2. Mamba-based Multimodal Fusion
+
+As a novel architectural paradigm, Mamba [5] incorporates selection mechanisms and hardware-aware parallel algorithms into SSMs [6, 7], achieving efficient and effective sequence modeling in the language domain. Inspired by its success, recent studies have explored adapting Mamba for multimodal fusion tasks. For instance, Pan-mamba [10] and Fusion-mamba [3] incorporate features from other modalities as inputs to unimodal Mamba to enable cross-modal interaction and fusion. Similarly, MambaDFuse [24] and MTMamba [26] utilize multimodal representations as inputs to unimodal Mamba for cross-modal interaction and fusion. In contrast, some approaches adopt a simpler strategy: VL-Mamba [33] and Cobra [54], for example, concatenate visual and textual representation sequences before feeding them into Mamba for sequence modeling and multimodal fusion.
+
+While these Mamba-based approaches demonstrate significant computational advantages compared to Transformer-based multimodal fusion methods, they face inherent limitations due to Mamba's sequential scanning mechanism. This mechanism makes it challenging to effectively learn cross-modal correspondences, particularly with unscanned tokens. The resulting loss in cross-modal alignment information may constrain the effectiveness of learned multimodal fusion representations. Therefore, how to effectively leverage cross-modal relationships within the Mamba framework to learn more comprehensive multimodal fusion representations remains an open research challenge.
+
+# 3. Method
+
+# 3.1. Overview
+
+Fig. 2 presents the framework of our proposed AlignMamba. Using audio-visual-language trimodal data as a case study, the framework first processes raw signals from each modality through modality-specific encoders to generate corresponding unimodal embedding sequences  $X_{a}$ ,  $X_{v}$ , and  $X_{l}$ . The framework then employs two complementary alignment mechanisms: an OT-based local alignment module that captures token-level correspondences, and an MMD-based global alignment loss that ensures distribution-level consistency. These mechanisms yield aligned embedding sequences  $\tilde{X}_{a}$  and  $\tilde{X}_{v}$  (illustrated here by aligning audio and visual modalities to the language modality as the anchor). The aligned unimodal embeddings, which now incorporate cross-modal correspondence information, are subsequently processed by the Mamba back
+
+bone for multimodal fusion. The following sections provide a detailed description of each component.
+
+# 3.2. OT-based Local Cross-modal Alignment
+
+Optimal Transport provides a principled framework for comparing and aligning probability distributions by finding the optimal way to transform one distribution into another while minimizing the transportation cost [39]. In our multimodal alignment context, OT offers a natural way to establish token-level correspondences between different modalities by treating feature sequences as discrete distributions.
+
+Given the unimodal feature sequences  $X_{a}\in \mathbb{R}^{T_{a}\times d}$ ,  $X_{v}\in \mathbb{R}^{T_{v}\times d}$ , and  $X_{l}\in \mathbb{R}^{T_{l}\times d}$  from audio, video, and language modalities respectively, where  $T_{a},T_{v}$ , and  $T_{l}$  denote the sequence lengths of different modalities and  $d$  is the feature dimension, we aim to learn the transport matrix  $M$  that capture fine-grained correspondences between different modalities. Take video-to-language alignment as an example, the classical optimal transport problem can be formulated as follows:
+
+$$
+\min  _ {T _ {v 2 l}} \sum_ {i = 1} ^ {T _ {v}} \sum_ {j = 1} ^ {T _ {l}} M _ {v 2 l} (i, j) C _ {v 2 l} (i, j). \tag {1}
+$$
+
+The optimization is constrained by:
+
+$$
+\left\{ \begin{array}{l l} \sum_ {j = 1} ^ {T _ {l}} M _ {v 2 l} (i, j) = \frac {1}{T _ {v}}, & \forall i \in [ 1, T _ {v} ] \\ \sum_ {i = 1} ^ {T _ {v}} M _ {v 2 l} (i, j) = \frac {1}{T _ {l}}, & \forall j \in [ 1, T _ {l} ] \\ M _ {v 2 l} (i, j) \geq 0, \quad \forall i, j \end{array} \right. \tag {2}
+$$
+
+where  $C_{v2l} \in \mathbb{R}^{T_v \times T_l}$  is the cost matrix. Given that the cosine distance emphasizes angular relationships between feature vectors while providing numerical stability through its bounded range, we use cosine distance as the cost matrix:
+
+$$
+C _ {v 2 l} (i, j) = 1 - \frac {X _ {v} ^ {i} \cdot X _ {l} ^ {j}}{| | X _ {v} ^ {i} | | _ {2} | | X _ {l} ^ {j} | | _ {2}}. \tag {3}
+$$
+
+However, solving this OT problem is extremely computationally expensive. Following [14], we adopt a relaxed version by removing the incoming sum constraint:
+
+$$
+\left\{ \begin{array}{l} \sum_ {j = 1} ^ {T _ {l}} M _ {v 2 l} (i, j) = \frac {1}{T _ {v}}, \quad \forall i \in [ 1, T _ {v} ] \\ M _ {v 2 l} (i, j) \geq 0, \quad \forall i, j \end{array} \right. \tag {4}
+$$
+
+This relaxed formulation allows each textual feature to be matched with multiple video features without constraining the total incoming flow, significantly reducing the computational complexity while maintaining the ability to capture meaningful cross-modal correspondences. The corresponding solution is defined as:
+
+$$
+M _ {v 2 l} (i, j) = \left\{ \begin{array}{l l} \frac {1}{T _ {v}}, & j = \arg \min  _ {j} C _ {v 2 l} (i, j), \\ 0, & j \neq \arg \min  _ {j} C _ {v 2 l} (i, j). \end{array} \right. \tag {5}
+$$
+
+![](images/8e5ea76594002270bf8eda1552532847d4b6baa8bb83c0781eef3fcd6ffe2c44.jpg)  
+Figure 2. AlignMamba enhances multimodal Mamba by incorporating token-level alignment and distribution-level alignment, enabling more effective multimodal fusion.
+
+Similarly, we compute the transport matrix  $M_{a2l}$  for audio-to-language alignment. Finally, the aligned video and audio features can then be obtained through:
+
+$$
+\left\{ \begin{array}{l} \tilde {X} _ {v} = M _ {v 2 l} ^ {\top} X _ {v} \in \mathbb {R} ^ {T _ {l} \times d}, \\ \tilde {X} _ {a} = M _ {a 2 l} ^ {\top} X _ {a} \in \mathbb {R} ^ {T _ {l} \times d}. \end{array} \right. \tag {6}
+$$
+
+This relaxed OT-based alignment process provides an efficient way to capture fine-grained cross-modal correspondences while maintaining computational tractability. The resulting transport matrices provide interpretable alignment information between different modalities. However, while this token-level alignment effectively captures local correspondences, ensuring global distribution-level consistency across modalities requires additional consideration, which we address through our MMD-based global alignment mechanism in the following section.
+
+# 3.3. MMD-based Global Cross-modal Alignment
+
+To ensure distribution-level consistency across modalities, we employ Maximum Mean Discrepancy as the global alignment metric [4]. MMD measures the statistical discrepancy between different modalities in a high-dimensional Reproducing Kernel Hilbert Space (RKHS) by
+
+comparing all orders of their statistics. For two feature sequences  $X$  and  $Y$ , the squared MMD distance is defined as:
+
+$$
+\mathrm {M M D} ^ {2} (X, Y) = \left\| \frac {1}{T} \sum_ {i = 1} ^ {T} \phi \left(x _ {i}\right) - \frac {1}{T} \sum_ {j = 1} ^ {T} \phi \left(y _ {j}\right) \right\| _ {\mathcal {H}} ^ {2}, \tag {7}
+$$
+
+where  $\phi (\cdot)$  is a feature mapping to a RKHS  $\mathcal{H}$ . Using the kernel trick, this can be computed as:
+
+$$
+\begin{array}{l} \mathrm {M M D} ^ {2} (X, Y) = \frac {1}{T ^ {2}} \sum_ {i = 1} ^ {T} \sum_ {i ^ {\prime} = 1} ^ {T} k \left(x _ {i}, x _ {i ^ {\prime}}\right) + \frac {1}{T ^ {2}} \sum_ {j = 1} ^ {T} \sum_ {j ^ {\prime} = 1} ^ {T} k \left(y _ {j}, y _ {j ^ {\prime}}\right) \\ - \frac {2}{T ^ {2}} \sum_ {i = 1} ^ {T} \sum_ {j = 1} ^ {T} k \left(x _ {i}, y _ {j}\right), \tag {8} \\ \end{array}
+$$
+
+where  $k(\cdot, \cdot)$  is a positive definite kernel function. In our implementation, we adopt the Gaussian kernel:
+
+$$
+k (x, y) = \exp \left(- \frac {\| x - y \| _ {2} ^ {2}}{2 \sigma^ {2}}\right), \tag {9}
+$$
+
+where  $\sigma$  is the kernel bandwidth parameter.
+
+For the aligned audio features  $\tilde{X}_a$ , the aligned video features  $\tilde{X}_v$ , and the language features  $X_l$ , the global alignment loss is defined as the sum of MMD distances between each pair of modalities:
+
+$$
+\mathcal {L} _ {\text {a l i g n}} = \mathrm {M M D} ^ {2} \left(\tilde {X} _ {v}, X _ {l}\right) + \mathrm {M M D} ^ {2} \left(\tilde {X} _ {a}, X _ {l}\right). \tag {10}
+$$
+
+By minimizing this loss during training, we encourage the feature distributions of different modalities to be aligned in the RKHS. While OT establishes token-level correspondences, MMD ensures the consistency of overall feature distributions, providing complementary alignment signals at different granularities. This dual-alignment strategy facilitates more effective multimodal fusion in subsequent processing stages.
+
+# 3.4. Mamba-based Fusion and Optimization
+
+Mamba-based Multimodal Fusion. Following the local and global alignment processes, we employ Mamba to facilitate efficient multimodal fusion while maintaining its inherent linear computational complexity. Unlike traditional Transformer-based methods that process all tokens simultaneously through self-attention mechanisms, our approach implements a time-priority scanning strategy that preserves Mamba's sequential nature while enabling effective cross-modal interactions. Given the aligned audio features  $\tilde{X}_a$ , the aligned video features  $\tilde{X}_v$ , and the language features  $X_l$ , we construct a unified multimodal feature sequence  $X_{mm}$  by interleaving features from different modalities at each timestep:
+
+$$
+X _ {m m} = \left[ \tilde {X} _ {a} ^ {1}, \tilde {X} _ {v} ^ {1}, X _ {l} ^ {1}, \tilde {X} _ {a} ^ {2}, \tilde {X} _ {v} ^ {2}, X _ {l} ^ {2}, \dots , \tilde {X} _ {a} ^ {T}, \tilde {X} _ {v} ^ {T}, X _ {l} ^ {T} \right], \tag {11}
+$$
+
+where the superscript denotes the temporal index. This temporal-priority organization ensures that features from different modalities at the same timestep are processed sequentially, allowing the selective scan mechanism of Mamba to effectively capture both intra- and inter-modal dependencies. The fused representations are obtained by processing the constructed sequence through multiple Mamba layers.
+
+Training Objective. The framework is optimized end-to-end using a composite loss function that combines the task-specific objective with the alignment constraints:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {t a s k}} + \lambda \mathcal {L} _ {\text {a l i g n}}, \tag {12}
+$$
+
+where  $\mathcal{L}_{task}$  is determined by the downstream task (e.g., cross-entropy loss for classification or mean squared error for regression),  $\mathcal{L}_{\text{align}}$  is the MMD-based alignment loss, and  $\lambda$  is a hyperparameter that balances the two objectives. During training, minimizing  $\mathcal{L}_{task}$  drives the model to learn task-relevant multimodal representations, while  $\mathcal{L}_{\text{align}}$  ensures consistent feature distributions across modalities.
+
+# 4. Experiment
+
+We evaluate our proposed method on two distinct multimodal fusion scenarios: complete multimodal fusion and incomplete multimodal fusion. In the complete fusion setting, all modalities are available during both training and inference, which tests the model's ability to effectively integrate complementary information across modalities. The incomplete fusion scenario, where certain modalities may be missing during inference, presents a more challenging yet practical setting that evaluates the model's robustness and adaptability to partial observations. Through extensive experiments on these two scenarios, we demonstrate the effectiveness of our approach in both ideal conditions and more challenging practical situations.
+
+# 4.1. Datasets and Evaluation Metrics
+
+We conduct experiments on two multimodal representation fusion benchmarks: CMU-MOSI [52] and CMU-MOSEI [53]. Both datasets consist of video segments collected from online platforms, containing visual (facial expressions), acoustic (voice), and textual (transcribed speech) modalities. Each segment in both datasets is annotated with a sentiment score ranging from -3 (highly negative) to +3 (highly positive). These scores are binarized into positive and negative sentiments for classification. To evaluate the effectiveness of our method, we adopt the following metrics based on previous works [25, 41]: binary accuracy and binary  $\mathrm{F_1}$  score.
+
+# 4.2. Comparison with SoTA Methods
+
+# 4.2.1. Results on Complete Multimodal Fusion Tasks
+
+<table><tr><td>Method</td><td>CMU-MOSI</td><td>CMU-MOSEI</td></tr><tr><td>ICCN [35]</td><td>83.0 / 83.0</td><td>84.2 / 84.2</td></tr><tr><td>MISA [9]</td><td>83.4 / 83.6</td><td>85.5 / 85.3</td></tr><tr><td>MulT [37]</td><td>84.1 / 83.9</td><td>82.5 / 82.3</td></tr><tr><td>MAG-BERT [34]</td><td>84.3 / 84.6</td><td>84.8 / 84.7</td></tr><tr><td>CM-BERT [50]</td><td>84.5 / 84.5</td><td>83.6 / 83.6</td></tr><tr><td>ULGM [11]</td><td>84.5 / 84.5</td><td>85.0 / 85.1</td></tr><tr><td>FDMER [47]</td><td>84.6 / 84.7</td><td>86.1 / 85.8</td></tr><tr><td>Self-MM [51]</td><td>84.8 / 84.9</td><td>85.0 / 84.9</td></tr><tr><td>MMIM [8]</td><td>85.1 / 85.0</td><td>85.1 / 85.0</td></tr><tr><td>HyCon [31]</td><td>85.2 / 85.1</td><td>85.4 / 85.6</td></tr><tr><td>ConFEDE [49]</td><td>85.5 / 85.5</td><td>85.8 / 85.8</td></tr><tr><td>AOBERT [12]</td><td>85.6 / 86.4</td><td>86.2 / 85.9</td></tr><tr><td>DMD [20]</td><td>85.8 / 85.8</td><td>86.0 / 86.1</td></tr><tr><td>MTMD [27]</td><td>86.0 / 86.0</td><td>86.1 / 85.9</td></tr><tr><td>AlignMamba</td><td>86.9 / 86.9</td><td>86.6 / 86.5</td></tr></table>
+
+Table 1. Performance comparison on CMU-MOSI and CMU-MOSEI datasets. Results are reported as Accuracy /  $F_1$  (\%).
+
+<table><tr><td>Dataset</td><td>MR</td><td>DCCA [1]</td><td>DCCAE [40]</td><td>MCTN [32]</td><td>MMIN [55]</td><td>GCNet [25]</td><td>IMDer [41]</td><td>AlignMamba</td></tr><tr><td rowspan="9">MOSI</td><td>10%</td><td>72.1 / 72.2</td><td>74.5 / 74.7</td><td>78.4 / 78.5</td><td>81.8 / 81.8</td><td>82.3 / 82.3</td><td>84.9 / 84.8</td><td>85.7 / 85.6</td></tr><tr><td>20%</td><td>69.3 / 69.1</td><td>71.8 / 71.9</td><td>75.6 / 75.7</td><td>79.0 / 79.1</td><td>79.4 / 79.5</td><td>83.5 / 83.4</td><td>84.3 / 84.1</td></tr><tr><td>30%</td><td>65.4 / 65.2</td><td>67.0 / 66.7</td><td>71.3 / 71.2</td><td>76.1 / 76.2</td><td>77.2 / 77.2</td><td>81.2 / 81.0</td><td>82.2 / 82.2</td></tr><tr><td>40%</td><td>62.8 / 62.0</td><td>63.6 / 62.8</td><td>68.0 / 67.6</td><td>71.7 / 71.6</td><td>74.3 / 74.4</td><td>78.6 / 78.5</td><td>80.0 / 79.6</td></tr><tr><td>50%</td><td>60.9 / 59.9</td><td>62.0 / 61.3</td><td>65.4 / 64.8</td><td>67.2 / 66.5</td><td>70.0 / 69.8</td><td>76.2 / 75.9</td><td>77.6 / 77.3</td></tr><tr><td>60%</td><td>58.6 / 57.3</td><td>59.6 / 58.5</td><td>63.8 / 62.5</td><td>64.9 / 64.0</td><td>67.7 / 66.7</td><td>74.7 / 74.0</td><td>75.8 / 75.1</td></tr><tr><td>70%</td><td>57.4 / 56.0</td><td>58.1 / 57.4</td><td>61.2 / 59.0</td><td>62.8 / 61.0</td><td>65.7 / 65.4</td><td>71.9 / 71.2</td><td>73.8 / 73.2</td></tr><tr><td>Avg.</td><td>63.8 / 63.1</td><td>65.2 / 64.8</td><td>69.1 / 68.5</td><td>71.9 / 71.5</td><td>73.8 / 73.6</td><td>78.7 / 78.4</td><td>79.9 / 79.6</td></tr><tr><td>Δ</td><td>14.7 / 16.2</td><td>16.4 / 17.3</td><td>17.2 / 19.5</td><td>19.0 / 20.8</td><td>16.6 / 16.9</td><td>13.0 / 13.6</td><td>11.9 / 12.4</td></tr><tr><td rowspan="9">MOSEI</td><td>10%</td><td>77.4 / 77.3</td><td>78.4 / 78.3</td><td>81.8 / 81.6</td><td>81.9 / 81.3</td><td>82.3 / 82.1</td><td>84.8 / 84.6</td><td>85.4 / 85.4</td></tr><tr><td>20%</td><td>73.8 / 74.0</td><td>75.5 / 75.4</td><td>79.0 / 78.7</td><td>79.8 / 78.8</td><td>80.3 / 79.9</td><td>82.7 / 82.4</td><td>83.6 / 83.3</td></tr><tr><td>30%</td><td>71.1 / 71.2</td><td>72.3 / 72.2</td><td>76.9 / 76.2</td><td>77.2 / 75.5</td><td>77.5 / 76.8</td><td>81.3 / 80.7</td><td>82.5 / 81.0</td></tr><tr><td>40%</td><td>69.5 / 69.4</td><td>70.3 / 70.0</td><td>74.3 / 74.1</td><td>75.2 / 72.6</td><td>76.0 / 74.9</td><td>79.3 / 78.1</td><td>81.7 / 80.5</td></tr><tr><td>50%</td><td>67.5 / 65.4</td><td>69.2 / 66.4</td><td>73.6 / 72.6</td><td>73.9 / 70.7</td><td>74.9 / 73.2</td><td>79.0 / 77.4</td><td>80.1 / 78.7</td></tr><tr><td>60%</td><td>66.2 / 63.1</td><td>67.6 / 63.2</td><td>73.2 / 71.1</td><td>73.2 / 70.3</td><td>74.1 / 72.1</td><td>78.0 / 75.5</td><td>79.4 / 78.2</td></tr><tr><td>70%</td><td>65.6 / 61.0</td><td>66.6 / 62.6</td><td>72.7 / 70.5</td><td>73.1 / 69.5</td><td>73.2 / 70.4</td><td>77.3 / 74.6</td><td>78.8 / 76.9</td></tr><tr><td>Avg.</td><td>70.2 / 68.8</td><td>71.4 / 69.7</td><td>75.9 / 75.0</td><td>76.3 / 74.1</td><td>76.9 / 75.6</td><td>80.3 / 79.0</td><td>81.6 / 80.6</td></tr><tr><td>Δ</td><td>11.8 / 16.3</td><td>11.8 / 15.7</td><td>9.1 / 11.1</td><td>8.8 / 11.8</td><td>9.1 / 11.7</td><td>7.5 / 10.0</td><td>6.6 / 8.5</td></tr></table>
+
+Table 2. Performance comparison on CMU-MOSI and CMU-MOSEI datasets. Results are reported as Accuracy /  ${\mathrm{F}}_{1}\left( \% \right)$  .
+
+Table 1 presents a comprehensive comparison between our approach and various state-of-the-art methods on the complete multimodal representation fusion task, which can be categorized into three main groups according to the network architecture: (1) LSTM methods, including ICCN [35], MISA [9], and MMIM [8]; (2) Cross-modal Transformer methods: MulT [37], Self-MM [51], and DMD [20]; (3) Contrastive learning methods: HyCon [31], ConFEDE [49], and MTMD [27]. It should be noted that although some methods have explored cross-modal alignment within the context of Transformer or LSTM architectures [20, 35, 37, 49], this paper specifically investigates the alignment issue within the Mamba architecture.
+
+On one hand, AlignMamba additionally incorporates token-level alignment to enhance multimodal fusion compared to contrastive learning approaches. On the other hand, AlignMamba's advantage over cross-modal Transformer methods lies in its consideration of distributional alignment relationships. Consequently, AlignMamba attains the best performance on all metrics in both datasets. For example, on the CMU-MOSI dataset, AlignMamba achieves a binary classification accuracy of  $86.9\%$ , representing a  $0.9\%$  improvement over previous methods. These results can be ascribed to AlignMamba's capacity to conduct extensive cross-modal alignment by leveraging its local alignment module and global alignment loss, thereby adeptly exploiting cross-modal correlations across different granularities and enabling the learning of more effective multimodal fusion representations.
+
+# 4.2.2. Results on Incomplete Multimodal Fusion Tasks
+
+Table 2 presents experimental results on incomplete multimodal representation fusion tasks. We compare AlignMamba with various state-of-the-art methods, which can be categorized into two main groups: (1) modality recovery approaches, including MCTN [32], MMIN [55], GCNet [25], and IMDer [41], which attempt to reconstruct missing modalities from available ones; and (2) non-recovery approaches, such as DCCA [1] and DCCAE [40], which directly learn from available modalities.
+
+The results demonstrate that AlignMamba consistently outperforms existing methods across different missing rates (MR), achieving an average accuracy of  $79.9\%$  on the CMU-MOSI dataset, a  $1.2\%$  improvement over previous methods. More importantly, AlignMamba demonstrates stronger robustness to increasing modality missing rates. For instance, on the CMU-MOSI dataset, while MMIN and IMDer experience significant performance degradation with accuracy drops of  $19.0\%$  and  $13.0\%$  respectively, AlignMamba shows better resilience with only an  $11.9\%$  decrease in binary classification accuracy.
+
+In conclusion, these improvements on both complete and incomplete multimodal fusion tasks can be attributed to the proposed dual alignment strategy: the local token-level alignment and global distribution-level alignment mechanisms work together to capture comprehensive cross-modal correspondences. This dual alignment strategy, combined with Mamba's efficient sequence modeling capabilities, not only enables learning more comprehensive and accurate
+
+multimodal fusion representations in complete multimodal scenarios, but also improves the robustness of learned representations in incomplete multimodal settings.
+
+# 4.3. Efficiency Analysis
+
+We conduct comprehensive efficiency analysis for Align-Mamba and compare them against both single-stream and multi-stream Transformer methods. Our evaluation metrics consist of GPU memory usage, inference time, and computational complexity. For a fair comparison, we specifically focus on the cross-modal interaction and fusion components, excluding the computational costs of unimodal encoders. All experiments are performed under identical conditions.
+
+# 4.3.1. GPU Memory Usage
+
+First, we report the GPU memory usage of each method with respect to varying input sequence lengths in Fig. 3. We exclude multi-stream Transformers on the  $12.8\mathrm{k}$ -token setting as they encounter an out-of-memory error. AlignMamba consistently achieves the best trade-off between sequence length and memory usage across all settings, surpassing other Transformer-based approaches by a nontrivial margin. For instance, when processing  $6.4\mathrm{k}$  tokens, AlignMamba requires only  $8.53\mathrm{GB}$  of memory, achieving  $20.3\%$  and  $58.0\%$  memory reduction compared to single-stream (10.7 GB) and multi-stream (20.3 GB) Transformers, respectively. This significant advantage in memory consumption is particularly valuable for processing longer sequences and deploying models on resource-constrained devices.
+
+![](images/b066ad43a2c62fd9545722d0a555ba6021879ff7d430b3015ab5e61cb2cc713b.jpg)  
+Figure 3. GPU memory usage comparison with varying lengths.
+
+# 4.3.2. Inference Time
+
+Next, we report the inference time of each method with respect to varying input sequence lengths in Fig. 4. To ensure fairness, we aggregate the running time of 50 inference passes for each model. AlignMamba again demonstrates consistent and substantial speed advantages over Transformer-based approaches across all settings. For instance, when processing 6.4k tokens, AlignMamba takes only 6.05 seconds, achieving  $83.3\%$  and  $87.6\%$  reduction in inference time compared to single-stream (36.13s) and multi-stream (48.61s) Transformers, respectively.
+
+![](images/5813b6cfc3f5d51b0c563f6c3e13df162558bb78c5446fc5c3b962121ae166cc.jpg)  
+Figure 4. Inference time comparison with varying lengths.
+
+# 4.3.3. Computational Complexity
+
+Finally, we analyze the FLOPs required by each method to quantify their computational efficiency. Without loss of generality, we fix the input sequence length to 1024 for each model. AlignMamba demonstrates superior efficiency with only 46.7G FLOPs, compared to 101.6G FLOPs for single-stream Transformer and 203.2G FLOPs for multistream Transformer. This represents a reduction of more than  $54\%$  compared to single-stream and  $77\%$  compared to multi-stream approaches, highlighting AlignMamba's computational advantages in cross-modal alignment and multimodal fusion tasks. This also justifies the lower memory consumption and swift inference speed as presented in the previous sections.
+
+# 4.4. Ablation Study
+
+We conduct comprehensive ablation studies from three aspects to evaluate our proposed method, as shown in Table 3.
+
+Component analysis. First, we evaluate the effectiveness of the OT-based local alignment module and MMD-based global alignment loss. Removing either component led to performance degradation across both datasets. For instance, on the CMU-MOSI dataset, accuracy dropped by  $2.3\%$  and  $1.1\%$  respectively. Notably, the OT-based alignment module demonstrated superior performance compared to the MMD-based alignment loss, likely because OT-based alignment provides explicit alignment plans while MMD-based alignment only imposes implicit alignment constraints.
+
+Mamba-based fusion. Furthermore, we ablate Align-Mamba with regular single-stream [54] and multi-stream Mamba-based fusion methods [3] to show the effectiveness of our method in terms of multimodal fusion. Results demonstrate reduced performances in these two Mamba-based methods, suggesting their lack of explicit consideration of inter-modal correspondences, which makes it difficult to learn comprehensive cross-modal relationships. This shows that naive Mamba architecture alone does not suffice in effective multimodal fusion and highlights both the limitations of Mamba's original scanning mechanism and the necessity of our proposed cross-modal alignment.
+
+Modality ablation. Lastly, we conduct modality ablation
+
+![](images/8a110fb2c0015d8dadb9124ea1a7f90738ca1d40074f82b36892969c919d077a.jpg)  
+Figure 5. The learned optimal transport plan. We only show the transport plan between video and language modalities for brevity.
+
+experiments by removing one modality at a time. When the text modality is removed, we only align the audio modality with the video modality. This results in significant performance degradation, likely due to the strong correlation between language and emotions. In contrast, removing the audio modality results in a smaller performance drop, possibly due to the sizable presence of irrelevant information in the audio modality such as background noise, reducing its impact on the overall performance.
+
+<table><tr><td></td><td>CMU-MOSI</td><td>CMU-MOSEI</td></tr><tr><td>AlignMamba</td><td>86.9 / 86.9</td><td>86.6 / 86.5</td></tr><tr><td colspan="3">Alignment</td></tr><tr><td>w/o Local</td><td>84.6 / 84.4</td><td>84.1 / 84.0</td></tr><tr><td>w/o Global</td><td>85.8 / 85.7</td><td>85.7 / 85.5</td></tr><tr><td>w/o both</td><td>82.5 / 82.3</td><td>82.8 / 82.6</td></tr><tr><td colspan="3">Fusion</td></tr><tr><td>Single-stream</td><td>82.3 / 82.1</td><td>81.8 / 81.4</td></tr><tr><td>Multi-stream</td><td>83.7 / 83.5</td><td>83.5 / 83.2</td></tr><tr><td colspan="3">Modality</td></tr><tr><td>w/o Audio</td><td>84.4 / 84.6</td><td>83.9 / 83.5</td></tr><tr><td>w/o Video</td><td>83.7 / 83.8</td><td>83.3 / 82.8</td></tr><tr><td>w/o Language</td><td>65.3 / 63.4</td><td>64.6 / 62.2</td></tr></table>
+
+# 4.5. Further Analysis
+
+# 4.5.1. Cross-modal Alignment
+
+To quantitatively assess our dual alignment strategy, we measure the  $\mathcal{A}$ -distance between modality pairs in Table 4. The  $\mathcal{A}$ -distance  $\in [0,2]$  is a common metric for domain discrepancy, with higher values indicating greater modality differences [2].  $\mathcal{A}_{al}$  and  $\mathcal{A}_{vl}$  represents the audio-language and video-language distances respectively. The results reveal significant and consistent reductions in inter-modal distances through our dual alignment strategy in both CMU-MOSI and CMU-MOSEI. These improvements
+
+demonstrate the effectiveness of our strategy in bridging the modality gap by learning meaningful cross-modal correlations, leading to more robust fusion representations.
+
+Table 3. Ablation studies on CMU-MOSI and CMU-MOSEI datasets. Results are reported as Accuracy  $/{\mathrm{F}}_{1}\left( \% \right)$  .  
+
+<table><tr><td></td><td colspan="2">CMU-MOSI</td><td colspan="2">CMU-MOSEI</td></tr><tr><td></td><td>Al</td><td>Vl</td><td>Al</td><td>Vl</td></tr><tr><td>w/Dual-align</td><td>1.59</td><td>1.49</td><td>1.61</td><td>1.53</td></tr><tr><td>w/o Dual-align</td><td>1.68</td><td>1.57</td><td>1.72</td><td>1.65</td></tr></table>
+
+Table 4.  $\mathcal{A}$  -distance between different modalities.
+
+# 4.5.2. Optimal Transport Plan
+
+Here, we qualitatively present the learned optimal transport plan. Fig. 5 illustrates an example from the CMUMOSI dataset. Notice that modalities exhibit temporal misalignment: the sentiment correspondence between different modalities may appear at different timesteps, which poses a challenge for multimodal representation fusion. For instance, the visual modality exhibits negative expressions at the beginning, while the textual modality introduces negative words toward the end. The original Mamba model struggles to explicitly learn these correspondences due to its sequential scanning mechanisms. In contrast, our proposed method leverages optimal transport to explicitly transform and align features in different temporal stages across modalities, reducing the modality gap and improving the effectiveness of multimodal fusion.
+
+# 5. Conclusion
+
+In this paper, we proposed AlignMamba, an efficient and effective method for multimodal representation fusion. By integrating OT-based local alignment and MMD-based global alignment, our method captures comprehensive cross-modal relationships while maintaining lower computational complexity. Extensive experiments on both complete and incomplete multimodal fusion tasks demonstrate that AlignMamba achieves state-of-the-art performance with significantly reduced computational costs.
+
+Acknowledgment. This work is supported in part by the National Natural Science Foundation of China
+
+(62236006) and in part by the Key Research and Development Program of Shaanxi (2022ZDLGY06-03).
+
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+# Alignment, Mining and Fusion: Representation Alignment with Hard Negative Mining and Selective Knowledge Fusion for Medical Visual Question Answering
+
+Yuanhao Zou  
+University of Michigan, Ann Arbor  
+yuanhaoz@umich.edu
+
+Zhaozheng Yin*  
+Stony Brook University  
+zyin@cs.stonybrook.edu
+
+# Abstract
+
+Medical Visual Question Answering (Med-VQA) is a challenging task that requires a deep understanding of both medical images and textual questions. Although recent works leveraging Medical Vision-Language Pre-training (Med-VLP) have shown strong performance on the MedVQA task, there is still no unified solution for modality alignment, and the issue of hard negatives remains underexplored. Additionally, commonly used knowledge fusion techniques for Med-VQA may introduce irrelevant information. In this work, we propose a framework to address these challenges through three key contributions: (1) a unified solution for heterogeneous modality alignments across multiple levels, modalities, views, and stages, leveraging methods like contrastive learning and optimal transport theory; (2) a hard negative mining method that employs soft labels for multi-modality alignments and enforces the hard negative pair discrimination; and (3) a Gated Cross-Attention Module for Med-VQA that integrates the answer vocabulary as prior knowledge and selects relevant information from it. Our framework outperforms the previous state-of-the-art on widely used Med-VQA datasets like RAD-VQA, SLAKE, PathVQA and VQA-2019. The code is available at https://github.com/AlexCold/AMiF
+
+# 1. Introduction
+
+Medical Visual Question Answering (Med-VQA) is a task that requires a joint understanding of both medical texts and images, aiding in clinical decision-making [34]. While deep learning models have made significant strides in general visual question answering tasks [39], Med-VQA presents unique challenges, such as the presence of obscure objects in images and relatively smaller scale of annotated medical datasets for training models [16, 50]. To address these challenges, many existing works [9, 10, 15, 22, 29, 30, 52] utilize Vision-Language Pre-training (VLP), achieving re
+
+markable success in the medical domain (i.e., Medical Vision-Language Pre-training, Med-VLP). These methods employ self-supervised learning to pre-train models on large unannotated medical datasets (e.g., MIMIC-CXR [24]), initializing their models with the ability to extract medical visual-language representations. The models are then fine-tuned for downstream tasks like Med-VQA.
+
+Among Med-VLP research, self-supervised techniques such as Contrastive Learning [6, 46, 58] are widely used to train visual and textual encoders to align representations between images and texts. While some works [5, 15, 29, 30, 54, 57-59] perform the global-level alignment (i.e., align only the [CLS] token of images and texts), other works [12, 22, 40, 52] attempt the local-level alignment, matching the similarity between image tokens and text tokens. However, these works focus on the inter-modality information (aligning images with texts), ignoring that medical datasets for Med-VLP (e.g., MIMIC-CXR [24]) contain valuable intra-modality similarities within images and reports. Though works like MUMC [29] attempt to align features within uni-modality, they do not perform local-level alignment and overlook the multi-view attribute of radiology imaging, which can naturally be used for intra-modality alignment. A unified approach that simultaneously addresses global-level alignment for both inter-modality (image-text) and intra-modality (image-image & text-text), and local-level alignment remains under-explored.
+
+Additionally, contrastive learning methods like CLIP [46] treat image-text pairs (image-text from the same patient) as positive samples, with unpaired images and texts as negative samples. However, in the medical domain, because of similar clinical manifestations of the same diseases, consistent anatomical imaging patterns, and standardized reporting practices, high similarities exist between unpaired images and texts, resulting in numerous hard negatives. While most of the prior CLIP-based works [5, 15, 22, 30, 52, 57-59] employ one-hot labels for contrastive learning, they overlook the issue of hard negatives in the medical domain. Though prior works [7, 29, 33, 54] use soft labels for hard negatives, their methods primarily
+
+![](images/b0c74a8b71eaffb68872df5b66e72f19c9129c670744ec0952a02419d3300ae6.jpg)  
+Figure 1. Motivations on: (a) unified modality alignment, (b) hard negative mining, and (c) selective knowledge fusion for Med-VQA.
+
+![](images/aa17d715eb60245b22fdb178eaf8d2ab8aa8046d8db16d8225655ff35513d184.jpg)
+
+![](images/1d32badc431ae220e65ada663d0c2c154506321804e6b466c032dd4f974dff28.jpg)
+
+consider hard negatives derived from image-text similarity (i.e., inter-modality), neglecting that the tight relationships within images and reports (i.e., intra-modality) could also be leveraged to explore hard negatives. Moreover, these soft label approaches calculate non-zero or even high similarity scores for hard negative pairs, making it hard to explicitly distinguish them from positive pairs. Thus, hard negative mining, i.e., distinguishing hard negative pairs from positive pairs for both inter-modality and intra-modality could be significantly improved in the medical domain.
+
+For fine-tuning downstream tasks like Med-VQA, fusing prior knowledge with the input image-question representation is a common practice to enhance the model's question-answering capability [10, 13, 16, 36, 41, 44, 53]. For example, many methods introduce knowledge graph matrices from Unified Medical Language System (UMLS, [3]) as prior knowledge. This prior knowledge contains terminology that covers a comprehensive scope of the medical domain, while a downstream task may only focus on a specific medical imaging modality or a specific human organ. Therefore, fusing untrimmed knowledge may introduce irrelevant or unnecessary information. For Med-VQA, a method that can selectively fuse appropriate prior knowledge with the joint image-question representation will lead to a better question-answering ability for the model.
+
+In this paper, to unify heterogeneous modality alignments and address the challenges of hard negatives and knowledge fusion in Medical Visual Question Answering, we propose a systematic framework named AMiF: Representation Alignment with Hard Negative Mining and Selective Knowledge Fusion. Our detailed contributions are:
+
+- We unify various modality alignments (Fig. 1 (a)) for medical representation learning at Multi-level: we use contrastive learning method for global-level alignment and optimal transport theory for local-level alignment; Multi-modality: we align not only the inter-modality (I2T: image-text) but also the intra-modality (I2I: image-image, T2T: text-text); Multi-view: we leverage the
+
+unique multi-view attribute in the medical datasets for the intra-modality I2I alignment; and Multi-stage: we focus on the global-level alignment in the first stage of pre-training, and then focus on local-level alignment and hard negative mining in the second stage.
+
+- We propose a hard negative mining method (Fig. 1 (b)) that operates across multiple modalities during pretraining. Specifically, for both inter-modality and intramodality alignments, we employ soft labels that assign non-zero values to negative pairs, which reflect the nuanced similarities between their representations due to similar disease characteristics. Subsequently, hard negative pairs mistakenly with high similarities are enforced to be identified and differentiated from positive pairs, helping AMiF learn discriminative image-text joint feature representations.  
+- For the Med-VQA task (Fig. 1 (c)), we extract the answer vocabulary from the task-specific dataset as prior knowledge. We introduce a Gated Cross-Attention Module to fuse the prior knowledge into the image-text joint representation. Then, the gated operation in the module selects useful information from the knowledge-fused representation to enhance model performance on VQA tasks.  
+- By applying the above techniques, our proposed AMiF shows its effectiveness on the Med-VQA tasks, evaluated on widely-used benchmark datasets including RAD-VQA [27], SLAKE [36], PathVQA [18] and VQA-2019 [2].
+
+# 2. Related Works
+
+# 2.1. Modality Alignment for Med-VLP
+
+While global-level alignment [5, 15, 29, 30, 54, 57-59] aligns the high-level [CLS] token of the modality representations, local-level alignment attempts to match all tokens of the representations. Numerous works have investigated the local-level alignment in the medical domain. Notably, Liao et al. compute the mutual information between local tokens [31], while GLoRIA [22], LRCLR [47], LoVT
+
+[40] and LIMITR [12] explore using contrastive learning to align image patch tokens and report tokens at local-level [48]. MGCA [52] uses a cross-attention module for local alignment. Unlike the idea of contrastive learning, UNITER [8] and ViLT [26] apply the Optimal Transport (OT) theory and IPOT algorithm [55] to optimize a transport plan for local-level alignment in the natural domain. The OT theory has not been used for Med-VLP yet. For multi-modality alignment, MUMC [29] introduces uni-modality alignment within images or texts. While LIMITR [12] compares both the frontal view and lateral view with the text representations. Our approach, which also explores multi-view images, focuses on alignment within the multi-view representations and unifies heterogeneous local-level alignment and global-level alignment on both inter- and intra-modalities.
+
+# 2.2. Hard Negatives for Med-VLP
+
+For Med-VLP, CLIP-based methods use the one-hot label for image-text pairs [5, 15, 29, 30, 54, 57-59], ignoring the hard negatives caused by the similarity between unpaired image-text representations in the medical domain. Many efforts attempt to solve the hard negative problem by applying soft label supervision for contrastive learning [1, 14, 20, 28, 35, 45]. In the medical domain, Jang et al. relax the similarity function by clipping the upper bound [23], ReCO [33] applies less penalty for the negative pairs, while MedCLIP [54] and KoBo [7] use soft label from external knowledge. In addition, MUMC [29] uses the self-distillation technique [28] to learn from the soft label generated itself. Different from the above studies, our approach explores hard negative mining in the medical domain. We not only use soft labels for hard-negative pairs of both intermodality and intra-modality alignments but also attempt to further distinguish the hard negatives from the positives.
+
+# 2.3. Med-VQA and Knowledge Fusion
+
+For Med-VQA, prior works like MEVF [41] and MMQ [13] attempt to train a meta-model using additional data besides the Med-VQA dataset to facilitate VQA performance. Other methods [9, 10, 15, 29, 30, 57] employ Med-VLP to initialize the model weight on large unlabeled datasets via self-supervised learning. Besides, without pre-training, other approaches introduce structured prior knowledge. For instance, LaPA [16] utilizes a knowledge graph [51] with well-stored medical information as its prior knowledge, integrating auxiliary information for more relevant answer prediction. Our approach uses answer vocabulary from the specific Med-VQA datasets as prior knowledge and enables selective knowledge fusion via a Gated Cross-Attention Module. Moreover, most prior works [9, 10, 16, 30] treat Med-VQA as a multi-labels classification task, using a fixed number of answers for prediction, while our model generates open-form answers like [28, 38].
+
+# 3. Methodology
+
+# 3.1. Overview
+
+As illustrated in Fig. 2, we divide the training process of AMiF into two phases: (a) pre-training and (b) fine-tuning.
+
+In pre-training phase, we use the medical pre-training dataset  $\{(I_i,W_i)\}_{i = 1}^N$ , where  $N$  is the dataset sample number and  $I_{i} = \{I_{i}^{(1)},\ldots ,I_{i}^{(v_{i})}\}$  is one imaging study case corresponding to one patient. We randomly sample multiple views from  $I_{i}$ , which corresponds to a single report  $W_{i}$ . If the case  $I_{i}$  does not have multiple views (i.e.,  $v_{i} = 1$ ), we augment the identical view multiple times. These multiview images are then encoded by a visual encoder, resulting in multi-view representations  $V_{i}^{(1)},V_{i}^{(2)}$  (the number of multi-view is chosen as 2 in this paper), while the corresponding report is encoded as report representation  $R_{i}$ . We split the pre-training into two stages: (1) Global-Level Alignment with soft labels, and (2) Tokens are further matched between  $V_{i}$  and  $R_{i}$ , where  $V_{i}$  is a random selection between  $V_{i}^{(1)}$  and  $V_{i}^{(2)}$ .
+
+In the fine-tuning phase, our AMiF utilizes the initialized weights (i.e., visual encoder, textual encoder, and Modality Co-Attention Module) from the pre-training phase, and is then adapted to the Med-VQA task via a Gated Knowledge Fusion Decoder, which takes answer vocabulary from the specific Med-VQA dataset as the prior knowledge and generates answers via an auto-regressive decoder.
+
+# 3.2. Unified Modality Alignment
+
+# 3.2.1 Global-Level Alignment
+
+Given the multi-view representations  $V_{i}^{(1)}, V_{i}^{(2)}$  and text representation  $R_{i}$  extracted by the visual and textual encoders, their [CLS] tokens are denoted as  $\mathbf{v}_{i}^{(1)}, \mathbf{v}_{i}^{(2)}, \mathbf{r}_{i} \in \mathbb{R}^{d}$  respectively ( $d$  is the token embedding dimension), which are used for the following inter-modality alignment (image-text) and intra-modality alignment (split as multi-view alignment and text-text alignment).
+
+Inter-Modality (Image-Text) First, we project the image and text embeddings  $\pmb{v}_i$  and  $\pmb{r}_i$  via a projection function  $\mathrm{proj}(\cdot)$ , where  $\pmb{v}_i \in \{\pmb{v}_i^{(1)}, \pmb{v}_i^{(2)}\}$ . Then, we compute the cosine similarity between the  $i$ -th image sample and the  $j$ -th text sample as:
+
+$$
+s _ {i j} ^ {\mathrm {i 2 t}} = \operatorname {p r o j} \left(\boldsymbol {v} _ {i}\right) ^ {\top} \operatorname {p r o j} \left(\boldsymbol {r} _ {j}\right). \tag {1}
+$$
+
+The probability of aligning (or matching) image i with text report j is computed as:
+
+$$
+P _ {i j} ^ {\mathrm {i 2 t}} = \frac {\exp \left(s _ {i j} ^ {\mathrm {i 2 t}} / \tau_ {1}\right)}{\sum_ {k = 1} ^ {N} \exp \left(s _ {i k} ^ {\mathrm {i 2 t}} / \tau_ {1}\right)}, \tag {2}
+$$
+
+where  $\tau_{1}$  is a temperature parameter. The similar computation is applied to  $P_{ij}^{\mathrm{t2i}}$ .
+
+![](images/8561668e20e1dd698e725759667ee05c1efb1f81130d422e2a30d1712bd1a8e1.jpg)  
+Figure 2. Architecture of AMiF: (a) Pre-Training Phase, (b) Fine-Tuning Phase, and (c) Modality Co-Attention Module.
+
+Intra-Modality (Multi-View & Text-Text) For the multi-view images, the probability of aligning image  $\boldsymbol{v}_i^{(1)}$  and  $\boldsymbol{v}_i^{(2)}$  is computed as:
+
+$$
+s _ {i j} ^ {\mathrm {i} 1, \mathrm {i} 2} = \operatorname {p r o j} \left(\boldsymbol {v} _ {i} ^ {(1)}\right) ^ {\top} \operatorname {p r o j} \left(\boldsymbol {v} _ {j} ^ {(2)}\right),
+$$
+
+$$
+P _ {i j} ^ {\mathrm {i} 1, \mathrm {i} 2} = \frac {\exp \left(s _ {i j} ^ {\mathrm {i} 1 , \mathrm {i} 2} / \tau_ {2}\right)}{\sum_ {k = 1} ^ {N} \exp \left(s _ {i k} ^ {\mathrm {i} 1 , \mathrm {i} 2} / \tau_ {2}\right)}. \tag {3}
+$$
+
+Similarly we obtain  $P_{ij}^{\mathrm{i2,i1}}$ . For text-text alignment, the probability of aligning report  $i$  and report  $j$  is computed as:
+
+$$
+s _ {i j} ^ {\mathrm {t 2 t}} = \operatorname {p r o j} (\boldsymbol {r} _ {i}) ^ {\top} \operatorname {p r o j} (\boldsymbol {r} _ {j}),
+$$
+
+$$
+P _ {i j} ^ {\mathrm {t 2 t}} = \frac {\exp \left(s _ {i j} ^ {\mathrm {t 2 t}} / \tau_ {3}\right)}{\sum_ {k = 1} ^ {N} \exp \left(s _ {i k} ^ {\mathrm {t 2 t}} / \tau_ {3}\right)}. \tag {4}
+$$
+
+The  $\tau_{2}$  and  $\tau_{3}$  are temperature parameters.
+
+Soft Label Generation We leverage a CLIP-based model [57] that is pre-trained on medical data to generate soft la
+
+bels for the inter-modality and intra-modality alignment. Denoting the multi-view image and text representations of the  $i$ th sample from the pre-trained CLIP-based model  $\mathcal{E}$  as  $V_{\mathcal{E},i}^{(1)}, V_{\mathcal{E},i}^{(2)}$  and  $R_{\mathcal{E},i}$ , we use the embeddings of their [CLS] tokens as the global-level representations, yielding  $\pmb{v}_{\mathcal{E},i}^{(1)}, \pmb{v}_{\mathcal{E},i}^{(2)}, \pmb{r}_{\mathcal{E},i} \in \mathbb{R}^d$ . Afterward, following the same routines as Eqs. (2) to (4), we compute the softmax cosine similarities  $Q_{ij}^{i2t}, Q_{ij}^{t2i}, Q_{ij}^{i1,i2}, Q_{ij}^{i2,i1}, Q_{ij}^{t2t} \in \mathbb{R}$  based on  $\pmb{v}_{\mathcal{E},i}^{(1)}, \pmb{v}_{\mathcal{E},i}^{(2)}$  and  $\pmb{r}_{\mathcal{E},i}$ . To add flexibility to the influence of positive image-text pairs and avoid classifying hard negatives as positive, we augment the soft labels by adding a flexibility weight  $\lambda$  for the positive pairs. Taking the soft label for inter-modality  $Q_{ij}^{i2t}$  as an example, we have the soft label computed as:
+
+$$
+H _ {i j} ^ {\mathrm {i} 2 \mathrm {t}} = Q _ {i j} ^ {\mathrm {i} 2 \mathrm {t}} + \lambda \cdot \mathbf {1} _ {\{i = j \}}, \tag {5}
+$$
+
+The same augmentation applies to all other soft labels, generating  $H_{ij}^{\mathrm{t2i}}, H_{ij}^{\mathrm{i1,i2}}, H_{ij}^{\mathrm{i2,i1}}$  and  $H_{ij}^{\mathrm{t2t}}$ .
+
+Alignment with Soft Labels In contrastive learning, hard negatives are defined as negative image-text pairs with high similarities mistakenly. Since the one-hot label focuses on the positive image-text pair within the batch, the hard negatives are often overlooked. Instead of using one-hot labels and InfoNCE loss [42] as CLIP-based methods, we use soft labels for both inter-modality and intra-modality alignment. Specifically, We employ the knowledge distillation [19], comparing the similarity gained in Eqs. (2) to (4) with the corresponding soft labels from the pre-trained CLIP-based model  $H_{ij}^{i2t}, H_{ij}^{t2i}, H_{ij}^{i1,i2}, H_{ij}^{i2,i1}, H_{ij}^{t2t} \in \mathbb{R}$ . The knowledge distillation is achieved by minimizing the KL-divergence loss, computed as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {i n t e r}} = \frac {1}{2} \left(\mathcal {L} _ {\text {i n t e r}} ^ {\mathrm {i 2 t}} + \mathcal {L} _ {\text {i n t e r}} ^ {\mathrm {t 2 i}}\right) \\ = \frac {1}{2 N} \sum_ {i = 1} ^ {N} \left(\mathrm {K L} \left(H _ {i} ^ {\mathrm {i} 2 \mathrm {t}} \| P _ {i} ^ {\mathrm {i} 2 \mathrm {t}}\right) + \mathrm {K L} \left(H _ {i} ^ {\mathrm {t} 2 \mathrm {i}} \| P _ {i} ^ {\mathrm {t} 2 \mathrm {i}}\right)\right), \tag {6} \\ \end{array}
+$$
+
+where  $P_{i}^{\mathrm{i2t}} = \left[P_{i1}^{\mathrm{i2t}},\dots ,P_{ij}^{\mathrm{i2t}},\dots ,P_{iN}^{\mathrm{i2t}}\right]$  denotes the probability distribution of aligning image  $i$  with all  $N$  possible reports, and the similar representation applies for  $P_{i}^{\mathrm{t2i}}$ ,  $H_{i}^{\mathrm{i2t}}$  and  $H_{i}^{\mathrm{t2i}}$ . The loss for intra-modality alignment is:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {i n t r a}} = \frac {1}{2} \left(\mathcal {L} _ {\text {i n t r a}} ^ {\mathrm {i 1 , i 2}} + \mathcal {L} _ {\text {i n t r a}} ^ {\mathrm {i 2 , i 1}}\right) + \mathcal {L} _ {\text {i n t r a}} ^ {\mathrm {t 2 t}} \\ = \frac {1}{2 N} \sum_ {i = 1} ^ {N} \left(\mathrm {K L} \left(H _ {i} ^ {\mathrm {i} 1, \mathrm {i} 2} \| P _ {i} ^ {\mathrm {i} 1, \mathrm {i} 2}\right) + \mathrm {K L} \left(H _ {i} ^ {\mathrm {i} 2, \mathrm {i} 1} \| P _ {i} ^ {\mathrm {i} 2, \mathrm {i} 1}\right)\right) \tag {7} \\ + \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {K L} \left(H _ {i} ^ {\mathrm {t} 2 \mathrm {t}} \| P _ {i} ^ {\mathrm {t} 2 \mathrm {t}}\right). \\ \end{array}
+$$
+
+For the first stage of pre-training, we conduct the global-level alignment with the following total loss:
+
+$$
+\mathcal {L} _ {\text {g l o b a l}} = \mathcal {L} _ {\text {i n t e r}} + \mathcal {L} _ {\text {i n t r a}}. \tag {8}
+$$
+
+# 3.2.2 Local-Level Alignment
+
+In the second stage of pre-training, we first pass the multimodal representations  $V_{i}$  and  $R_{i}$  through a Modality CoAttention Module (Fig. 2 (c)) that fuse each other's information, yielding the mutually-aware feature representations  $V_{\mathcal{F},i}$  and  $R_{\mathcal{F},i}$ . Next, we align the  $p$  token embeddings of the image representation  $V_{\mathcal{F},i} = \{\pmb{v}_{\mathcal{F},i}^{1},\pmb{v}_{\mathcal{F},i}^{2},\dots,\pmb{v}_{\mathcal{F},i}^{p}\}$  with the  $t$  token embeddings of the report representation  $R_{\mathcal{F},i} = \{\pmb{r}_{\mathcal{F},i}^{1},\pmb{r}_{\mathcal{F},i}^{2},\dots,\pmb{r}_{\mathcal{F},i}^{t}\}$ .
+
+Our objective is to compute an optimal transport plan  $\mathbf{T} \in \mathbb{R}^{p \times t}$  that minimizes the following loss function:
+
+$$
+\mathcal {L} _ {\text {l o c a l}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \min  _ {\mathbf {T}} \sum_ {j = 1} ^ {p} \sum_ {k = 1} ^ {t} \mathbf {T} _ {j k} \cdot \mathrm {C} \left(\boldsymbol {v} _ {\mathcal {F}, i} ^ {j}, \boldsymbol {r} _ {\mathcal {F}, i} ^ {k}\right), \tag {9}
+$$
+
+where  $C(\cdot)$  is the cost function between two embeddings:
+
+$$
+\mathrm {C} \left(\boldsymbol {v} _ {\mathcal {F}, i} ^ {j}, \boldsymbol {r} _ {\mathcal {F}, i} ^ {k}\right) = 1 - \left(\boldsymbol {v} _ {\mathcal {F}, i} ^ {j}\right) ^ {\top} \boldsymbol {r} _ {\mathcal {F}, i} ^ {k}. \tag {10}
+$$
+
+Since minimizing the transport plan  $\mathbf{T}$  directly is intractable, we use the inexact proximal point method (IPOT, [4, 8, 55]) to approximate an optimal transport plan  $\mathbf{T}^*$ . The resulting optimal plan  $\mathbf{T}^*$  captures how each image patch token is associated with a word token, based on the elements of the matrix.
+
+# 3.3. Hard Negative Mining
+
+The soft labels used for global-level alignment might compute high similarities to both hard negative pairs and positive pairs, which may lead to difficulties in distinguishing hard negative pairs from positive ones. We pair the representations of hard negatives from both inter-modality and intra-modality alignments, passing them through the Modality Co-Attention Module to generate mutually-aware representation pairs and enforce the classification on these representation pairs to be negative pairs, as illustrated in the lower-right of Fig. 2 (a).
+
+Specifically, take the  $i$ -th sample for example, which consists of an image-text pair  $(V_{i},R_{i})$  used for its multimodality alignment. The distribution of I2T (image-text) soft labels for  $V_{i}$  is  $H_{i}^{\mathrm{i}2\mathrm{t}} = \left[H_{i1}^{\mathrm{i}2\mathrm{t}},\dots ,H_{ij}^{\mathrm{i}2\mathrm{t}},\dots ,H_{iN}^{\mathrm{i}2\mathrm{t}}\right]$ . We sample a hard negative pair  $(V_{i},R_{m})$  from  $H_{i}^{\mathrm{i}2\mathrm{t}}$ . The sampling rule is that a negative pair with higher similarity has a higher chance of being chosen. Based on the index pair  $(i,m)$  of the hard negative pair, where  $m\neq i$ , we pair  $(V_{i},R_{m})$  together, passing them to the Modality Co-Attention Module, resulting in a mutually-aware representation pair  $(V_{\mathcal{F},i},R_{\mathcal{F},m})$ . Similarly, for intra-modality alignment, we consider hard negative pairs within multi-view images and texts. For multi-view images, suppose that  $V_{i}$  of the  $i$ -th sample and  $V_{n}$  of the  $n$ -th sample  $(n\neq i)$  form a hard negative pair. For texts, we have  $R_{i}$  and  $R_{k}$  forming a hard negative pair similarly, where  $i\neq k$ . Therefore, for the  $i$ -th sample, we build a hard negative set:
+
+$$
+\mathcal {S} _ {i} ^ {\mathrm {H N}} = \left\{\left(\boldsymbol {V} _ {\mathcal {F}, i}, \boldsymbol {R} _ {\mathcal {F}, m}\right), \left(\boldsymbol {V} _ {\mathcal {F}, i}, \boldsymbol {V} _ {\mathcal {F}, n}\right), \left(\boldsymbol {R} _ {\mathcal {F}, i}, \boldsymbol {R} _ {\mathcal {F}, k}\right) \right\}. \tag {11}
+$$
+
+Next, we formulate a classification problem to enforce the discrimination between hard negative pairs and positive pairs. Given representations of any hard negative pair  $(\mathbf{a},\mathbf{b})\in S_i^{\mathrm{HN}}$ , we first concatenate (Concat) these two representations, forming a joint representation. Then, a linear classification head (LH) is applied to this joint representation, which outputs a prediction logits:
+
+$$
+\boldsymbol {p} _ {(\boldsymbol {a}, \boldsymbol {b})} = \mathrm {L H} (\operatorname {C o n c a t} (\boldsymbol {a}, \boldsymbol {b})). \tag {12}
+$$
+
+A cross-entropy (CE) loss is applied on classifying hard negative pairs using Eq. (12):
+
+$$
+\mathcal {L} _ {\mathrm {H N}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {(a, b) \in \mathcal {S} _ {i} ^ {\mathrm {H N}}} \operatorname {C E} \left(\boldsymbol {p} _ {(a, b)}; y _ {(a, b)}\right), \tag {13}
+$$
+
+where  $y_{(a,b)}$  is a one-hot label (the hard negative pair is assigned with label 1 while the positive pair with label 0).
+
+![](images/77caf4ac9016558ab504346b0d1b87edb6181ca153616d0c1e960b7275e599f1.jpg)  
+Figure 3. Architecture of Gated Knowledge Fusion Decoder, which consists of a Gated Cross-Attention Module and an Auto-Regressive Decoder.
+
+# 3.4. Gated Knowledge Fusion Decoder
+
+To fine-tune the model pre-trained by the alignment and hard negative mining for specific downstream tasks such as Med-VQA (Fig. 2 (b)), we design a Gated Knowledge Fusion Decoder (Fig. 3), which consists of (1) a Gated Cross-Attention Module to select related knowledge from the generic prior knowledge and fuse it into the domain-specific downstream task; and (2) an auto-regressive decoder to generate open-form answers.
+
+# 3.4.1 Gated Cross-Attention Module
+
+Generic prior knowledge usually contains comprehensive information covering a wide range of medical topics, so irrelevant information is involved when applied to a specific-field Med-VQA task. Thus, we propose a Gated Cross-Attention Module (Fig. 3), which fuses the prior knowledge into the input image-question representation and uses a gate operation to select relevant information from the knowledge-fused representation.
+
+Given an image-text joint representation  $F_{i}\in \mathbb{R}^{(p + t)\times d}$  where  $p,t$  are the token numbers for image and text representations. We input it into the Gated Cross-Attention Module. The generic prior knowledge is represented by an answer vocabulary extracted from the Med-VQA dataset for fine-tuning, which is passed through a self-attention and a feed-forward sub-module, yielding  $F_{p}\in \mathbb{R}^{M\times d}$ , where  $M$  is the total token length of the knowledge. We use cross-attention for fusing the prior knowledge  $F_{p}$  and joint representation  $F_{i}$ . Specifically, the knowledge-fused representation is computed as:
+
+$$
+F _ {p, i} = \mathrm {C A} \left(F _ {i}, F _ {p}\right) + F _ {i}, \tag {14}
+$$
+
+where  $\mathrm{CA}(\cdot)$  represents the cross-attention mechanism, with the first argument as the query (Q), and the second as the key (K) and value (V).
+
+Next, to select related information from prior knowledge for accurate answer prediction, we have:
+
+$$
+G _ {p, i} = \operatorname {S i g m o i d} \left(\operatorname {P r o j e c t i o n} \left(F _ {p, i}\right)\right), \tag {15}
+$$
+
+where  $\operatorname{Sigmoid}(\cdot)$  is an activation function and  $\operatorname{Projection}(\cdot)$  is a mapping function in the  $d$ -dimensional space. The resulting  $G_{p,i} \in \mathbb{R}^{(p + t)\times d}$  is a weight matrix with all values between 0 and 1, indicating the portion of information selected from knowledge fused representation  $F_{p,i}$ . To balance information from the knowledge-fused representation  $F_{p,i}$  and the image-text joint representation  $F_{i}$ , we have the gated operation in Fig. 3 formulated as:
+
+$$
+\operatorname {G a t e} \left(F _ {p, i}, F _ {i}\right) = G _ {p, i} \odot F _ {p, i} + \left(1 - G _ {p, i}\right) \odot F _ {i}, \tag {16}
+$$
+
+where  $\odot$  is the element-wise product. The representation  $\operatorname{Gate}(F_{p,i}, F_i)$  is then passed through a feed-forward submodule, yielding a final knowledge-fused image-question representation  $F_i'$  for the answer generation below.
+
+# 3.4.2 Auto-Regressive Decoder
+
+Different from prior methods like [9, 10, 30] that predict answers by classifying from a fixed answer list, we utilize an auto-regressive decoder [11, 28] to generate open-form answers. Given the selected knowledge-fused image-question representation  $F_{i}^{\prime}$  from Sec. 3.4.1, the decoder is trained to generate answers auto-regressively via a conditional language modeling loss.
+
+# 4. Experiment
+
+# 4.1. Datasets
+
+Pre-training Datasets For pre-training AMiF, we use three medical datasets that are widely used for Med-VLP: MIMIC-CXR [24] is the largest publicly available radiology dataset that contains 377110 X-ray chest images and 227827 corresponding reports; ROCO [43] is a radiology dataset that has over 81,000 radiology images from various imaging modalities and their corresponding captions; and MedICaT [49] is a medical figure-caption dataset that contains over 217,000 image-caption pairs.
+
+Multi-view Images For MIMIC-CXR, there are existing multi-view images for each radiology study, so we randomly sample two different views. For ROCO and Med-ICaT datasets, which lack the multi-view information for each sample, we apply strong random data augmentation [6] for generating multi-views from one image. Ultimately we ensure all samples from the datasets have two multi-view images for intra-modality (image-image) alignment.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">VQA-RAD</td><td colspan="3">SLAKE</td><td colspan="3">PathVQA</td><td>VQA2019</td></tr><tr><td>Open</td><td>Closed</td><td>Overall</td><td>Open</td><td>Closed</td><td>Overall</td><td>Open</td><td>Closed</td><td>Overall</td><td>Overall</td></tr><tr><td>MMQ [13]</td><td>53.70</td><td>75.80</td><td>67.00</td><td>-</td><td>-</td><td>-</td><td>13.40</td><td>84.0</td><td>48.80</td><td>-</td></tr><tr><td>MEVF-BAN [41]</td><td>49.20</td><td>77.20</td><td>66.10</td><td>77.80</td><td>79.80</td><td>78.60</td><td>-</td><td>-</td><td>-</td><td>77.86</td></tr><tr><td>CPRD [35]</td><td>52.50</td><td>77.90</td><td>67.80</td><td>79.50</td><td>83.40</td><td>81.10</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MMBERT [25]</td><td>63.10</td><td>77.90</td><td>72.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.20</td></tr><tr><td>ARL [10]</td><td>65.10</td><td>85.96</td><td>77.50</td><td>79.70</td><td>89.30</td><td>84.00</td><td>-</td><td>-</td><td>-</td><td>80.32</td></tr><tr><td>M3AE [9]</td><td>67.23</td><td>83.46</td><td>77.01</td><td>80.31</td><td>87.82</td><td>83.25</td><td>-</td><td>-</td><td>-</td><td>79.87</td></tr><tr><td>PubMedCLIP [15]</td><td>60.10</td><td>80.00</td><td>72.10</td><td>78.40</td><td>82.50</td><td>80.10</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CPCR [37]</td><td>60.50</td><td>80.40</td><td>72.50</td><td>80.50</td><td>84.10</td><td>81.90</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>M2I2 [30]</td><td>61.80</td><td>81.60</td><td>73.70</td><td>74.70</td><td>91.10</td><td>81.20</td><td>36.30</td><td>88.00</td><td>62.20</td><td>-</td></tr><tr><td>MUMC [29]</td><td>71.50</td><td>84.20</td><td>79.20</td><td>-</td><td>-</td><td>84.90</td><td>39.00</td><td>90.40</td><td>65.10</td><td>-</td></tr><tr><td>RAMM [56]</td><td>-</td><td>-</td><td>78.27</td><td>-</td><td>-</td><td>86.05</td><td>-</td><td>-</td><td>-</td><td>82.13</td></tr><tr><td>PeFoMed [17]</td><td>62.60</td><td>87.10</td><td>77.40</td><td>77.80</td><td>88.70</td><td>82.10</td><td>35.70</td><td>91.30</td><td>63.60</td><td>-</td></tr><tr><td>LaPA [16]</td><td>68.72</td><td>86.40</td><td>79.38</td><td>82.17</td><td>88.70</td><td>84.73</td><td>-</td><td>-</td><td>-</td><td>81.60</td></tr><tr><td>BiomedCLIP [57]</td><td>67.60</td><td>79.80</td><td>75.20</td><td>82.50</td><td>89.70</td><td>85.40</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AMiF(Ours)</td><td>72.00</td><td>87.25</td><td>80.49</td><td>84.84</td><td>90.23</td><td>86.71</td><td>40.33</td><td>90.18</td><td>65.33</td><td>83.20</td></tr></table>
+
+Table 1. Accuracy comparison with existing methods on various VQA datasets, evaluated for Open and Closed sets and the Overall performances. Open represents a question set with open-form answers while Closed represents the question set with yes/no as the answer. The best and second-best results are bolded and underlined respectively.
+
+Med-VQA Datasets for Fine-tuning For fine-tuning the model for the Med-VQA task, we use VQA-RAD [27], SLAKE [36], VQA-2019 [2] and PathVQA[18]. VQA-RAD has 315 radiology images with 3064 question-answer pairs. SLAKE has 14,028 pairs of samples. VQA-2019 comprises 15,292 question-answer pairs. PathVQA contains 32,799 question-answer pairs. All datasets contain Open set (open-form answers) and Closed set (yes/no answers), and we follow the official splits for all datasets.
+
+# 4.2. Implementation Details
+
+For the pre-training phase, we apply CLIP-ViT/B-16 [46] as the initialized visual encoder, and ClinicalBERT [21] as the initialized textual encoder and decoder. For the finetuning phase, the Modality Co-Attention Module uses  $L = 6$  layers. The temperature parameters  $\tau_{1}, \tau_{2}, \tau_{3}$  are set to 0.07. The flexibility weight of the positive pair  $\lambda$  is set to 0.01. The total trainable model size is 326M, while the size of Gated Cross-Attention Module are 14.8M.
+
+Our pre-training phase contains 20 epochs for stage one, and 10 epochs for stage two, with 256 as batch size. The model uses AdamW optimizer with a learning rate of 4e-6.
+
+For more details about the implementation and training, please refer to the Supplement.
+
+# 4.3. Comparison with the State-of-the-Art
+
+As shown in Tab. 1, our method outperforms other methods across all Med-VQA datasets for Overall accuracy, and for the Open type questions, which is more challenging than Closed type, we also achieve the best performance. Notably, compared with BiomedCLIP [57], which is the pretrained model we utilize to generate soft labels, our method
+
+surpasses it on VQA-RAD and SLAKE datasets by  $5.29\%$  and  $1.31\%$  separately. For the PathVQA dataset, which is the largest one with challenging open-form question-answer pairs, we outperform the second best by  $1.33\%$ . These results show that our method has a better understanding ability on the Med-VQA tasks, with room for improvements.
+
+# 4.4. Ablation Study
+
+Ablation for Unified Modality Alignment To explore the impact of different components for pre-training, we conduct systematic ablative experiments for unified modality alignments in Tab. 2. Notably, our baseline (#1) only uses global inter-modality alignment. To prove the significance of intra-modality alignment to our AMiF, we conduct ablations #3, #7, and #8, which show improvements in average accuracy compared with #1, #5, and #6, respectively. When applying intra-modality alignment, we also evaluate the effectiveness of multi-view alignment via #3, which elevates the average accuracy by  $0.78\%$  compared with only text-text alignment (#2). To demonstrate that local-level alignment improves the model's ability, we compare #4 with #3, which shows a  $0.90\%$  increase in accuracy. Moreover, We also evaluate the impact of different weight combination in stage 2 of pre-training (i.e., local-level alignment loss and hard-negative mining loss), as shown in Tab. 3. Based on the ablative results we choose to balance those two losses.
+
+Ablation for Hard Negative Mining To show that our approach of hard negative mining benefits model performance on Med-VQA tasks, we first investigate the necessity of using soft labels for global-level alignment. As shown in
+
+<table><tr><td>#</td><td>G-inter</td><td>G-intra</td><td>Local</td><td>Soft Label</td><td>HN</td><td>RAD-VQA</td><td>SLAKE</td><td>Path-VQA</td><td>VQA-2019</td><td>Avg</td></tr><tr><td>1</td><td>✓</td><td></td><td></td><td></td><td></td><td>76.68</td><td>82.4</td><td>61.23</td><td>79.06</td><td>74.84</td></tr><tr><td>2</td><td>✓</td><td>*</td><td></td><td></td><td></td><td>77.06</td><td>82.47</td><td>61.92</td><td>79.70</td><td>75.28</td></tr><tr><td>3</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>77.92</td><td>82.64</td><td>63.78</td><td>79.88</td><td>76.06</td></tr><tr><td>4</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>78.44</td><td>83.83</td><td>64.66</td><td>80.92</td><td>76.96</td></tr><tr><td>5</td><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td>79.04</td><td>85.98</td><td>65.24</td><td>81.34</td><td>77.90</td></tr><tr><td>6</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>79.77</td><td>86.20</td><td>65.30</td><td>81.83</td><td>78.28</td></tr><tr><td>7</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>79.82</td><td>86.07</td><td>65.21</td><td>82.21</td><td>78.33</td></tr><tr><td>8</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>80.49</td><td>86.71</td><td>65.33</td><td>83.20</td><td>78.93</td></tr></table>
+
+Table 2. Ablation study for pre-training using different components (✓). G-inter and G-intra denote global inter- and intra-modality alignments, respectively. For intra-modality, * denotes only text-text alignment, while ✓ denotes both multi-view and text-text alignments. Local denotes local-level alignment. Soft Label denotes soft label for global-level alignment and HN denotes hard negative mining.
+
+<table><tr><td>#</td><td>\( {\mathcal{L}}_{\text{local }} \)</td><td>\( {\mathcal{L}}_{\mathrm{{HN}}} \)</td><td>RAD-VQA</td><td>SLAKE</td><td>Path-VQA</td><td>VQA-2019</td><td>Avg</td></tr><tr><td>1</td><td>1.0</td><td>1.0</td><td>80.49</td><td>86.71</td><td>65.33</td><td>83.20</td><td>78.93</td></tr><tr><td>2</td><td>1.0</td><td>0.2</td><td>78.32</td><td>84.92</td><td>63.30</td><td>82.15</td><td>77.17</td></tr><tr><td>3</td><td>0.2</td><td>1.0</td><td>79.57</td><td>84.82</td><td>64.93</td><td>82.53</td><td>77.96</td></tr><tr><td>4</td><td>1.0</td><td>3.0</td><td>79.16</td><td>85.17</td><td>64.46</td><td>82.26</td><td>77.76</td></tr><tr><td>5</td><td>3.0</td><td>1.0</td><td>78.61</td><td>84.59</td><td>65.42</td><td>83.14</td><td>77.94</td></tr></table>
+
+Table 3. Ablation study for pertaining with different weight combinations of Hard Negative Mining Loss (HN) and Local-Level Alignment Loss (local).  
+
+<table><tr><td>#</td><td>Pre-training</td><td>Knowledge</td><td>RAD-VQA</td><td>SLAKE</td><td>Path-VQA</td><td>VQA-2019</td><td>Avg</td></tr><tr><td>1</td><td>-</td><td>-</td><td>75.64</td><td>81.09</td><td>60.92</td><td>78.14</td><td>73.95</td></tr><tr><td>2</td><td>CLIP-based</td><td>-</td><td>77.65</td><td>82.92</td><td>61.30</td><td>79.92</td><td>75.45</td></tr><tr><td>3</td><td>Ours</td><td>-</td><td>79.03</td><td>84.32</td><td>63.53</td><td>81.03</td><td>76.98</td></tr><tr><td>4</td><td>Ours</td><td>Q</td><td>79.55</td><td>85.04</td><td>63.93</td><td>82.13</td><td>77.36</td></tr><tr><td>5</td><td>Ours</td><td>A</td><td>80.26</td><td>85.37</td><td>63.96</td><td>81.26</td><td>77.71</td></tr><tr><td>6</td><td>Ours</td><td>A&amp;G</td><td>80.49</td><td>86.71</td><td>65.33</td><td>83.20</td><td>78.93</td></tr></table>
+
+Table 4. Ablation study for fine-tuning on Med-VQA task. Q and A denotes introducing question and answer vocabulary as prior Knowledge, respectively. G denotes using the Gated operation in the Gated Cross-Attention Module.
+
+![](images/38313862bc8e32c4ae478549d6ac2e4eac9f960ee08e8c56216d14a2cc4cdfcd.jpg)  
+Figure 4. Visualization of the local-level alignment related to underlined words for the ablative study of hard negative mining.
+
+Tab. 2, the comparison between #7 and #4 indicates that using soft labels boosts the average model performance by  $1.37\%$ . We also show that soft labels for global intra-modality alignment facilitates the model's representation ability by comparing #7 with #5. Moreover, to prove the significance of hard negative pair discrimination, we compare #6 with #5 and #8 with #7. Besides, we also conduct a qualitative ablation study for hard negative mining as shown in Fig. 4, comparing ablations #8 and #4. After hard negative mining, the patch tokens related to the underlined words are more concentrated on regions with possible semantic information, showing that our mining method leads to a more robust modality co-attention module, which yields more interpretable results for local-level alignment.
+
+Ablation for Fine-tuning Med-VQA In Tab. 4, we show that compared with training our model from scratch (#1), our pre-training method (#3) greatly improves the average accuracy by  $3.03\%$ . The comparison between #3 and #2 shows that our pre-training method outperforms the CLIP-based model [57] used for generating soft labels. Besides the pre-training method, we study how selective knowledge fusion facilitates Med-VQA tasks. Comparing #4
+
+![](images/ff3ebfaf1f6641e3683ca8b2f9d7cf9813081887efd04b2cf44759feb7b25e4d.jpg)  
+Figure 5. Attention map related to underlined words for the ablative study of selective knowledge fusion.
+
+with #3, we find that fusing question vocabulary to image-question representation improves the model performance for question-answering by  $0.38\%$ . When we fuse the answer vocabulary instead (#5), we find the average performance is raised by  $0.35\%$ . These results are further enhanced when we apply the gated operation in our Gated Cross-Attention Module (#6), improving the average accuracy by  $1.22\%$  based on #5, which is the best result we currently have. Additionally, we visualize the attention map in Fig. 5. From regions denoted with red boxes, we see that the gated operation selects relevant information and filters out unnecessary ones.
+
+# 5. Conclusion
+
+In this paper, we introduced AMiF to address the challenges in Medical Visual Question Answering (Med-VQA). Specifically, we propose solutions for unified modality Alignment, hard negative Mining, and selective knowledge Fusion. We unify heterogeneous modality alignments across multiple levels, modalities, views, and stages. Our hard negative mining method employs soft labels for both inter-modality and intra-modality alignments and explores hard negative pairs to distinguish them from positive ones via enforced discrimination. For the Med-VQA task, we introduce a Gated Cross-Attention Module that integrates the answer vocabulary as prior knowledge and selects relevant information from it. Our experiments demonstrate the effectiveness of our approach on MedVQA tasks, compared with the previous state-of-the-art.
+
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\ No newline at end of file
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+# All Languages Matter: Evaluating LMMs on Culturally Diverse 100 Languages
+
+Ashmal Vayani $^{1,2}$ , Dinura Dissanayake $^{2}$ , Hasindri Watawana $^{2}$ , Noor Ahsan $^{2}$ , Nevasini Sasikumar $^{2}$ , Omkar Thawakar $^{2}$ , Henok Biadglign Ademtew $^{7}$ , Yahya Hmaiti $^{1}$ , Amandeep Kumar $^{8}$ , Kartik Kuckreja $^{2}$ , Mykola Maslych $^{1}$ , Wafa Al Ghallabi $^{2}$ , Mihail Mihaylov $^{2}$ , Chao Qin $^{2}$ , Abdelrahman M Shaker $^{2}$ , Mike Zhang $^{9}$ , Mahardika Krisna Ihsani $^{2}$ , Amiel Esplana $^{10}$ , Monil Gokani $^{11}$ , Shachar Mirkin $^{12}$ , Harsh Singh $^{2}$ , Ashay Srivastava $^{13}$ , Endre Hamerlik $^{14}$ , Fathinah Asma Izzati $^{2}$ , Fadillah Adamsyah Maani $^{2}$ , Sebastian Cavada $^{2}$ , Jenny Chim $^{15}$ , Rohit Gupta $^{1}$ , Sanjay Manjunath $^{2}$ , Kamila Zhumakhanova $^{2}$ , Feno Heriniaina Rabevohitra $^{16}$ , Azril Amirudin $^{17}$ , Muhammad Ridzuan $^{2}$ , Daniya Kareem $^{2}$ , Ketan More $^{2}$ , Kunyang Li $^{1}$ , Pramesh Shakya $^{1}$ , Muhammad Saad $^{2}$ , Amirpouya Ghasemaghaei $^{1}$ , Amirbek Djanibekov $^{2}$ , Dilshod Azizov $^{2}$ , Branislava Jankovic $^{2}$ , Naman Bhatia $^{11}$ , Alvaro Cabrera $^{2}$ , Johan Obando-Ceron $^{18}$ , Olympiah Otieno $^{19}$ , Fabian Farestam $^{20}$ , Muztoba Rabbani $^{21}$ , Sanoojan Baliah $^{2}$ , Santosh Sanjeev $^{2}$ , Abduragim Shtanchaev $^{2}$ , Maheen Fatima $^{22}$ , Thao Nguyen $^{2}$ , Amrin Kareem $^{2}$ , Toluwani Aremu $^{2}$ , Nathan Xavier $^{23}$ , Amit Bhatkal $^{2}$ , Hawau Toyin $^{2}$ , Aman Chadha $^{3}$ , Hisham Cholakkal $^{2}$ , Rao Muhammad Anwer $^{2,4}$ , Michael Felsberg $^{6}$ , Jorma Laaksonen $^{4}$ , Thamar Solorio $^{2}$ , Monojit Choudhury $^{2}$ , Ivan Laptev $^{2}$ , Mubarak Shah $^{1}$ , Salman Khan $^{2,5}$ , Fahad Shahbaz Khan $^{2,6}$
+
+<sup>1</sup>University of Central Florida, <sup>2</sup>Mohamed bin Zayed University of AI, <sup>3</sup>Amazon, <sup>4</sup>Aalto University, <sup>5</sup>Australian National University, <sup>6</sup>Linköping University, <sup>7</sup>Ehtiopian AI Institute, <sup>8</sup>Johns Hopkins University, <sup>9</sup>Aalborg University, <sup>10</sup>University of the West of England, <sup>11</sup>IIT Hyderabadabad, <sup>12</sup>Alpinference, <sup>13</sup>University of Maryland, <sup>14</sup>HUN-REN Institute for CS and Control, <sup>15</sup>Queen Mary University of London, <sup>16</sup>Chongqing University, <sup>17</sup>University of the People, <sup>18</sup>University of Montreal, <sup>19</sup>KUAT, <sup>20</sup>ETH Zurich, <sup>21</sup>University of California, Merced, <sup>22</sup>Air University, <sup>23</sup>Universidade Federal de Minas Gerais
+
+![](images/30af4bb0ffd22a1658d83fdaf76a58947a207aade30da695711cba46980dea22.jpg)  
+Figure 1. ALM-bench comprises a diverse set of 100 languages with manually verified annotations by respective native language experts. Here, qualitative examples highlight the comprehensive set of 13 cultural aspects covered in the benchmark, such as heritage, customs, architecture, literature, music, and sports. It also evaluates visual understanding for six generic aspects. The ALM-bench focuses on low-resource languages and different regions, spanning 73 countries across five continents and 24 distinct scripts. ALM-bench covers diverse questions, such as multiple choice questions (MCQs), true/false (T/F), short and long visual question answers (VQAs).
+
+# Abstract
+
+Existing Large Multimodal Models (LMMs) generally focus on only a few regions and languages. As LMMs continue to improve, it is increasingly important to ensure they understand cultural contexts, respect local sensitivities, and support low-resource languages, all while effectively integrating corresponding visual cues. In pursuit of culturally diverse global multimodal models, our proposed All Languages Matter Benchmark (ALM-bench) represents the largest and most comprehensive effort to date for evaluating LMMs across 100 languages. ALM-bench challenges existing models by testing their ability to understand and reason about culturally diverse images paired with text in various languages, including many low-resource languages traditionally underrepresented in LMM research. The benchmark offers a robust and nuanced evaluation framework featuring various question formats, including true/false, multiple choice, and open-ended questions, which are further divided into short and long-answer categories. ALM-bench design ensures a comprehensive assessment of a model's ability to handle varied levels of difficulty in visual and linguistic reasoning. To capture the rich tapestry of global cultures, ALM-bench carefully curates content from 13 distinct cultural aspects, ranging from traditions and rituals to famous personalities and celebrations. Through this, ALM-bench not only provides a rigorous testing ground for state-of-the-art open and closed-source LMMs but also highlights the importance of cultural and linguistic inclusivity, encouraging the development of models that can serve diverse global populations effectively. Our benchmark is publicly available at https://mbzuai-oryx.github.io/ALM-Bench/.
+
+# 1. Introduction
+
+In recent years, large multimodal models (LMMs) have seen significant progress across a variety of vision-language tasks [2, 5, 9, 27, 35, 41]. Despite these advances, a major limitation remains in the models' capacity to understand and respond accurately to cultural and linguistic diversity [36]. Current LMMs perform well in widely spoken languages with substantial training data but struggle with low-resource languages and nuanced cultural contexts, limiting their effectiveness on a global scale [28].
+
+Existing benchmarks for evaluating multilingual and multicultural capabilities in LMMs are limited in scope, often representing only a small subset of cultures and languages. Such benchmarks generally focus on high-resource languages and overlook the cultural richness of low-resource languages, which hinders the development and evaluation of models that can serve diverse populations across the globe. For instance, CulturalVQA [31]
+
+and GD-VCR [44] focus on culturally specific content in English and do not reflect global cultural diversity. Similarly, the Henna benchmark [4] includes cultural information from 11 countries but is restricted to the Arabic language. In terms of multilingualism, existing benchmarks [11, 14, 26, 40, 42, 47] include multilingual data but remain constrained by limited cultural diversity and are often restricted to only single question type. This gap highlights the need for a more comprehensive benchmark that addresses both linguistic and cultural inclusivity in LMMs.
+
+To address these challenges, we introduce a culturally and linguistically diverse multimodal benchmark: All Languages Matter Benchmark (ALM-bench). ALM-bench is specifically designed to evaluate LMMs across a diverse set of 100 languages, including many low-resource ones, with a strong emphasis on cultural depth. The complete list of these languages is presented in the Tab. A. 3. (suppl. material). In comparison to the recent CVQA benchmark [36], ALM-bench offers 3x more languages, more diverse question types, and  $\sim 2\mathrm{x}$  more image domains and samples with an extensive focus on fine-grained cultural aspects (Fig. 1). With these enhancements, ALM-bench aims to assess the next generation of massively multilingual multimodal models in a standardized way, pushing the boundaries of LMMs towards better cultural understanding and inclusivity.
+
+Our evaluations with 16 recent state-of-the-art LMMs show that existing models suffer from low-resource languages and cultures (Fig. 2). The analysis also shows a significant gap between the open and closed-source models in understanding cultural and linguistic nuances in a multimodal setting; e.g., GPT4o performs  $27\%$  better than the best open-source model (GLM-4V). Our evaluations across scripts and language groups highlight the need to improve the understanding of underrepresented regions, such as Southeast Asia and West Africa. We also show how simple prompting techniques can help improve LMM performance.
+
+Our contributions can be summarized as follows:
+
+- We introduce ALM-bench, a culturally diverse multilingual and multimodal VQA benchmark covering 100 languages with 22.7K question-answers. ALM-bench encompasses 19 generic and culture-specific domains for each language, enriched with four diverse question types.  
+- ALM-bench is meticulously curated and verified with native-language experts (over 800 hours of human annotators), ensuring cultural relevance and accuracy across low- and high-resource languages alike.  
+- We benchmark existing LMMs on ALM-bench, identifying performance gaps and areas for improvement, especially in culturally complex multilingual scenarios.
+
+![](images/133688872931829d17bb856be378ab1840c1faf1e77bc3ffd9a3a7ae9f86ac0f.jpg)  
+Figure 2. Benchmarking LMMs on diverse languages & cultures: (a) Performance of various open versus closed-sourced LMMs on ALM-bench. For each LMM, we also report performance on low versus high-resource languages. All these carefully selected models were released after 2023. (b) Performance of high-performing LMMs on our culturally curated 13 categories available in our ALM-bench.
+
+![](images/3373d1938eef4a94ff40555d75ff145f71abb412a274c0bfe3724d51dd4b13b7.jpg)
+
+# 2. Related Work
+
+To align large language models (LLMs) with human preferences, various approaches have been developed [34, 38, 48]. Over time, these methods are extended to enable LLMs to be sensitive to geo-diverse cultural values [1, 23, 30, 39]. This evolution has broadened their applicability to both multilingual and multimodal LLMs, enabling greater engagement with users from diverse linguistic and cultural backgrounds. Despite this progress, LMM benchmarks often fail to adequately address cultural aspects, especially for low-resource languages. Models such as GPT-4V [2] and Gemini 1.5 Pro [41] performs well on existing multimodal benchmarks, but these evaluations often lack in capturing the intricacies of multilingual and culturally diverse interactions. Open-source models, in particular, face challenges in accurately representing geodiverse values (e.g., local beliefs, rituals, and traditions), underscoring the need for a culturally aware evaluation framework for LMMs (see Tab. 1).
+
+Several recent benchmarks have been developed to evaluate the cultural aspects of multilingual LMMs, such as, the Henna benchmark [4] representing cultural information from 11 countries with nearly 1,132 samples. However, it is restricted to the Arabic language, covering only five domains while being closed-source. Other benchmarks, such as CulturalVQA [31] and GD-VCR [44] are also small-scale and focus only on culturally specific content. These benchmarks are limited to English and struggle to encompass the full spectrum of global cultural diversity. Their samples are unevenly distributed across countries and domains, which may lead to skewed assessment.
+
+Benchmarks such as SEED-Bench [20, 21] and MMStar [8] extend the CC3M dataset [32] to cover an extended set of domains. Despite their broader scope, these benchmarks
+
+lack cultural nuance and are constrained to multiple-choice questions (MCQ) which only assess the LMMs in one dimension. Although MM-Vet [45] and MMMU [46] offer a variety of question types, they primarily address basic perceptual abilities without demanding in-depth cultural reasoning or expert-level domain knowledge.
+
+For multilingual LMM benchmarking, CVQA [36] represents a recent effort, collecting cultural samples across 31 languages. However, it is limited to a single question type, MCQ, and features only a small proportion of samples on traditions and rituals. Similarly, MaRVL [24] covers five languages but lacks probing into cultural common sense and primarily focuses on non-Western cultural information, resulting in limited diversity. Other benchmarks, including MMMB [40], MMBench [26], Exams-V [11], M3Exam [47], M4U [42], and MME [14], do include multilingual evaluation samples. However, they are constrained by a lack of cultural diversity in their datasets, cover fewer languages, and are restricted to a single question type (e.g., MCQs).
+
+Our proposed benchmark, ALM-bench, bridges the aforementioned gaps (see Tab. 1) by introducing a culturally diverse dataset covering Western and non-Western regions, low and high-resource languages (100 in total), and specific regional dialects (e.g., Emirati Arabic, Egyptian Arabic). ALM-bench provides a robust evaluation framework for Multilingual LMMs, enabling a comprehensive assessment of their generic and cultural adaptability and promoting inclusivity in multilingual multimodal AI research.
+
+# 3. ALM Benchmark
+
+ALM-bench provides global coverage, featuring both generic and culture-specific image samples that preserve the nuances of native languages in VQAs (Fig. 4). It includes diverse QA formats such as MCQs, True/False, and open-ended VQA (long and short) under 19 domains, grouped
+
+<table><tr><td>Benchmark</td><td>Multilingual</td><td># of Languages</td><td># of Scripts</td><td>Total Domains</td><td>Total Samples</td><td>Question Types</td><td>Question Forms</td><td>Annotation Type</td><td>Cultural Specific Content</td><td>Open-Source</td><td>Bias Correction</td><td>Diversity</td></tr><tr><td>Henna [4]</td><td>X</td><td>1</td><td>1</td><td>5</td><td>1132</td><td>SVQA, LVQA</td><td>-</td><td>Auto+Manual</td><td>✓</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>CulturalVQA [31]</td><td>X</td><td>1</td><td>1</td><td>5</td><td>2378</td><td>SVQA</td><td>-</td><td>Manual</td><td>✓</td><td>X</td><td>-</td><td>X</td></tr><tr><td>GD-VCR [44]</td><td>X</td><td>1</td><td>1</td><td>1</td><td>886</td><td>MCQ</td><td>Fixed</td><td>Manual</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>SEED-Bench [20]</td><td>X</td><td>1</td><td>1</td><td>12</td><td>19242</td><td>MCQ</td><td>Diverse</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>SEED-Bench2 [21]</td><td>X</td><td>1</td><td>1</td><td>34</td><td>24371</td><td>MCQ</td><td>Diverse</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>MMStar [8]</td><td>X</td><td>1</td><td>1</td><td>18</td><td>1500</td><td>MCQ</td><td>Fixed</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>MM-Vet [45]</td><td>X</td><td>1</td><td>1</td><td>16</td><td>218</td><td>SVQA, LVQA</td><td>Fixed</td><td>Manual</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>MMMU [46]</td><td>X</td><td>1</td><td>1</td><td>30</td><td>11550</td><td>MCQ, SVQA</td><td>Fixed</td><td>Manual</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>CVQA [36]</td><td>✓</td><td>31</td><td>13</td><td>10</td><td>10000</td><td>MCQ</td><td>Fixed</td><td>Manual</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>MMMB [40]</td><td>✓</td><td>6</td><td>4</td><td>15</td><td>12000</td><td>TF, MCQ</td><td>Fixed</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>MMBench [26]</td><td>✓</td><td>2</td><td>2</td><td>20</td><td>2974</td><td>MCQ</td><td>Fixed</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>EXAMS-V [11]</td><td>✓</td><td>11</td><td>4</td><td>20</td><td>20932</td><td>MCQ</td><td>Diverse</td><td>Manual</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>MaRVL [24]</td><td>✓</td><td>5</td><td>3</td><td>11</td><td>7630</td><td>TF</td><td>Fixed</td><td>Manual</td><td>✓</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>M3Exam [47]</td><td>✓</td><td>9</td><td>3</td><td>4</td><td>12317</td><td>MCQ</td><td>Diverse</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>MaXM [7]</td><td>✓</td><td>7</td><td>5</td><td>-</td><td>2142</td><td>SVQA</td><td>Fixed</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>xGQA [33]</td><td>✓</td><td>8</td><td>5</td><td>-</td><td>12578</td><td>Y/N, SVQA</td><td>Fixed</td><td>Manual</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>M4U [42]</td><td>✓</td><td>3</td><td>2</td><td>64</td><td>8931</td><td>MCQ</td><td>Fixed</td><td>Auto+Manual</td><td>X</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>MME [14]</td><td>✓</td><td>2</td><td>2</td><td>14</td><td>2370</td><td>Y/N</td><td>Fixed</td><td>Manual</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Ours</td><td>✓</td><td>100</td><td>24</td><td>19</td><td>22763</td><td>MCQ, SVQA, LVQA, TF</td><td>Diverse</td><td>Auto+Manual</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+Table 1. Comparison of various LMM benchmarks with a focus on multilingual and cultural understanding. The Domains indicate the range of aspects covered by the dataset for each language. Question Form is categorized as "Diverse" if the questions phrasing varies, and "Fixed" otherwise. Annotation Types are classified as "Manual" if questions were originally in the local language, "Manual+Auto" if questions were generated or translated using GPT-4/Google API and subsequently validated by human experts, and "Auto" if generated or translated automatically without human validation. Bias Correction reflects whether the dataset is balanced across cultures and countries, while Diversity indicates whether the dataset includes both Western and non-Western minority cultures.  $\ddagger$  means information not available.
+
+into generic and cultural categories Tab. A. 1. (suppl. material).
+
+The generic category includes six domains: indoor and outdoor scenes, memes, paintings, food items, and sketches following [25]. The cultural category spans 13 comprehensive domains—Architecture, Customs, Economy, Festivals, Food, Heritage, Lifestyle, Literature, Media, Music, Notable Figures, Religion, and Sports—adding depth to cultural representation across languages. While some of these domains have been previously explored [3, 29, 31, 36], they are investigated in limited languages and do not fully capture the depth of cultural nuances. Our work introduces six unique domains, including literature, music, festivals, economy, media, and notable key figures to better capture cultural richness across diverse languages. More details are in Sec. A (suppl. material)
+
+ALM-bench comprises of 22,763 diverse questions across all subsets in 100 languages (see Fig. 4). The dataset spans 73 countries across five continents, capturing the cultural nuances of both underrepresented and predominant languages from different regions. We include 24 language scripts (Fig. 7) and 15 language families, with Latin being the most prevalent script, covering 53 languages, followed by Cyrillic with 10 languages; and Arabic with 9 languages. In terms of language families, Indo-European is the largest group, encompassing 55 languages, with Afro-Asiatic and Austronesian each representing eight languages (Fig. 9).
+
+# 3.1. Data Collection and Annotation
+
+Country-Language pairs. Our cultural data samples are curated from the country with the most prominent presence
+
+of each specific culture. We carefully selected 100 languages across 73 countries and five continents, striking a balance between low- and high-resource languages and between Western and non-Western cultures to ensure linguistic and cultural diversity. The selection criteria also consider the number of native speakers and the availability of speakers to validate and annotate the curated samples.
+
+To accurately capture the cultural nuances of each language, we follow [31] and link each language to a country based on the World Values Survey [16] to cover social, ritualistic, and cultural values. For multilingual countries like India, multiple languages are associated to capture their cultural diversity. For each country-language pair, we collect cultural samples for all 19 generic and cultural domains.
+
+Generic VQA Curation. Our ALM-bench has both generic and cultural questions. To evaluate visual understanding in 100 languages on generic scenes, e.g., indoor and outdoor images, we source examples from a well-known English-only LMM benchmark  $LLaVA-Bench$  (In-the-Wild) [25]. These English instructions are extended to the remaining 99 languages using GPT-4o followed by manual correction from native speakers. In some cases where the GPT-4o translations are poor, the annotators also translate the instructions from scratch. It results in a total of 6,000 open-ended samples across 100 languages for generic VQA.
+
+Cultural Image Curation. To curate diverse cultural image-QA pairs, we collect open-licensed images and their corresponding metadata from the Internet, focusing on specific country-language pairs across various cultural domains. For each domain, we go through several filtration steps, e.g., removing low-resolution images and removing
+
+![](images/f536cf332712933eee7a955126d2e00cf964cfe10c29bd4d36961896c3b90bbd.jpg)  
+Figure 3. Data collection and verification pipeline. Our benchmark features both cultural specific content sourced from the web (left) and generic image understanding collection sourced from existing LMM benchmark. The cultural part is carefully filtered to remove noisy samples and private information. We use GPT4o for translations which are manually verified and corrected with over 800 hours of human annotators (native speakers). Our ALM-bench has diverse question types and features approximately 23K QA pairs in total in 100 languages.
+
+![](images/153b95cc0374a3f2d9b93aefd56d62976a54f251a1dad2461b4f9bd4a9a74a15.jpg)  
+Figure 4. Data statistics of our ALM-bench showing the diversity of the scripts, global coverage, comprehensive categories, and various question types. Our dataset contains 22.7K high-quality question-answers in total, covering 100 languages and 24 scripts. All the samples are manually verified by native speakers.
+
+redundant samples to ensure diversity. To maintain high-quality and cultural relevance, we ask expert native speakers of each language to manually verify the quality and cultural diversity of these images. Images lacking cultural relevance are removed from the dataset. This manual filtration process discarded nearly  $10.7\%$  of the images. To ensure privacy, we blur any personally identifiable details (PIDs) and textual information in image that may directly leak the answer. Fig. 3 shows our data collection and verification pipeline.
+
+Cultural QA Generation. ALM-bench dataset covers different question types. To generate high-quality cultural questions, we utilize GPT-4o to create QA pairs based on the provided images and their metadata. Notably, images and QAs are not shared across languages in the cultural set. For each image, we generate two MCQs, two short questions, a long question, and a true/false question in English. We instruct GPT-4o to emphasize the cultural concepts depicted in each image, generate questions that require a visual understanding of an image, and not perpetuate bias and stereotypes. To mitigate the randomness in multiple choice and true/false, we ensure that these questions can also be answered when converted to open-ended questions [36]. We also evaluate with shuffled orders, predicting the entire cho
+
+![](images/73a09c2f8f220a6eaee658bdb4586e1dba9f4fdf9e6ffee35d665539f9b97950.jpg)  
+Figure 5. Analysis of the type of mistakes GPT-4o made while language translations via human-feedback. GPT-4o encounters more issues with respect to semantic and grammatical errors.
+
+sen option rather than just the leading alphabet. The detailed instructions are presented in Sec. I (suppl. material.) Filtration and Translation Errors. Given the QA pairs, we translate them to remaining 99 languages using GPT4o, followed by manual correction from native speakers. Similar to image filtering, native speakers assess translation quality and make detailed corrections to provide culturally grounded answers focusing on core cultural aspects. They also discard redundant and culturally irrelevant QAs.
+
+We note several challenges in GPT-4o's translations across 100 languages. Specifically, GPT-4o demonstrates difficulty in generating culturally grounded QA pairs across diverse languages. To analyze these issues, mistakes from the GPT-4o model in translations are categorized into four types: semantic error, cultural error, language error, and grammatical error. We sample 57 question-answer pairs from 51 randomly selected languages and plotted error distribution in Fig. 5. Notably, GPT-4o encounters more issues with semantic and grammatical accuracy when translating into different languages. We show examples of such errors in Fig. A.2. (suppl. material).
+
+# 4. Benchmarking LMMs on ALM-bench
+
+As discussed earlier, ALM-bench comprises four different question types: MCQs, T/F, Short and Long VQA. Therefore, we employ different prompts for each type of question. We use GPT-4o as a judge and prompt it to score responses of various question types with different criterion.
+
+![](images/b4e361e589058da42151ea6470bae24f978e88bda7719540f08c91f28fecfd42.jpg)  
+Figure 6. ALM-bench Performance comparison of different open and closed-sourced models (y-axis) on the 100 languages (x-axis) of our ALM-bench. The performance is represented as an average accuracy across all questions in a language. The actual performance of a model on a language is shown in each respective box, where the higher accuracy is highlighted with a high color intensity. The closed-source propriety models generally perform better across languages compared to their open-sourced counterparts. The performance on several high-resource languages (e.g., English, French, Chinese, and Spanish) is generally higher throughout different models, whereas all open-source models struggle on low resource languages (e.g., Amharic, Kinyarwanda, Burmese) fs QAW a Overall, GPT-4o and GLM-4V-9B performs better in terms of closed-source and open-source models, respectively. Best viewed zoomed in.
+
+We use accuracy for MCQs and T/F, correctness for short VQAs (SVQAs), and consistency, fluency, and relevance for long VQAs (LVQAs). Here, correctness refers to how closely the model's output aligns with the ground-truth [25]. For LVQAs, the consistency assesses whether the predicted answer is coherent across the entire generated output [18]. The fluency metric measures the naturalness and readability of model prediction [37], whereas the relevancy metric determines whether model prediction provides answers directly related to ground truth [6]. To ensure fair evaluation for decision-making questions (T/F and MCQs) using GPT-4o as a judge, we also show consistent performance using LLaMA-3.8.1B-Instruct [13] in Tab. A.2. (suppl. material).
+
+Overall Results: Fig. 6 presents the per-language performance of 16 recent LMMs on the ALM-bench. The results offer a number of insights: (a) the closed-source propriety models (GPT-4o [2] and Gemini-1.5-Pro [41]) generally perform better across the 100 languages, compared to their open-source counterparts. The best closed-source model, GPT-4o, achieves an overall accuracy of  $78.8\%$  compared to  $51.9\%$  overall accuracy obtained by the best performing open-source model GLM-4V-9B [15]. Both closed-source models struggle with several low-resource languages (e.g., Amharic, Kinyarwanda, Burmese, and Sanskrit). For instance, the performance of GPT-4o significantly drops from  $88.4\%$  for the English language to  $50.8\%$  for the Amharic language. (b) Several open-source models (GLM-4V-9B [15], Qwen2-VL [43], Molmo [12], LLaVA-OneVision [22]) achieve comparable overall performance. Similar to their closed-source counterparts, open-source models also struggle with low-resource languages. For instance, the performance of GLM-4V-9B [15] dramatically drops from  $80.3\%$  for the English language to  $15.6\%$  for the Amharic language. Fig. 2a presented earlier further shows the overall performance breakdown in terms of high-and low-resource languages across different models. It is worth mentioning that our ALM-bench comprises 50 high-resource and 50 low-resource languages following the definition of low-resource languages as in [10]. (c) Fig. 2a reveals a sub
+
+![](images/3832a097de8e7e093ba93b03e4fca4c7ae37e90f8c48f26df8adcd4af859db68.jpg)  
+Figure 7. Performance comparison of GPT-4o and Qwen2-VL on different language scripts. The count above each bar indicates the number of languages present in that script.
+
+stantial performance gap between high-resource and low-resource languages consistent across different models, with GPT-4o showing a  $6\%$  drop. This performance gap extends to more than  $8\%$  in case of some open-source models (e.g., GLM-4V-9B [15], Qwen2-VL [43]). A notable exception is the performance of closed-source Gemini-1.5-Pro [41], which does not deteriorate significantly for low-resource languages. Next, we present further results analysis.
+
+How important is visual context? To investigate this question, we ran an experiment with only the base LLM of various LMMs used in our evaluation. We randomly sample 50 languages and prompt the respective LLM with a textual question without the visual input. Our results demonstrate that the visual context is important to answer several questions in our benchmark and the LLMs struggle without input images. For instance, GPT-4o [2] performance drops by absolute  $27.3\%$  when prompted with textual questions alone. Specifically, it shows a significant performance gain in languages such as Sinhala  $(38.7\%)$ , Sanskrit  $(50\%)$ , and Dutch  $(40\%)$  when images are included. Similarly, Qwen2-7B gives a  $13\%$  absolute and  $24.8\%$  relative drop in performance without image inputs. This substantial performance drop underscores the robustness of our visual benchmark, revealing that without images, even the best-performing proprietary and open-source models LLMs struggle to answer accurately.
+
+Comparison across scripts: We further group the 100 lan
+
+![](images/a19c19f8b38e3a1644025c83cf6b45dbe45bf7bbb84ba0f8dd79e9500b441a60.jpg)  
+Figure 8. Error analysis across 4 diverse language scripts, including Bengali, Sinhalese, Latin and Cyrillic on GPT-4o results, demonstrates significant challenges for even the top-performing closed-source models, particularly in cultural and reasoning comprehension. The ALM-bench highlights these gaps, especially in languages with complex dialectal variations.
+
+![](images/ae9c7a7d3d5ad35d691edadb4cf59aa59b9ae87d86277ea4adf0e2b170585278.jpg)
+
+![](images/40341c88b94f4c3e4820713c9d947a7466f44d77870744794206400ec49c1ac4.jpg)
+
+![](images/336154cac16081ba7ff53e4aa0b8c4aceab814cc8cbbf32aea42ae85fea485e7.jpg)
+
+![](images/44f81ea4d27b738c10f732a30ce6d76e96e429c02aa6b0f543dc7ba8ada3deb8.jpg)  
+Figure 9. Performance comparison of GPT-4o and Qwen2-VL on different language families. The count above each bar indicates the number of languages present in that script.
+
+guages in ALM-bench by script [10]. We use data from Ethnologue [19] and the Glottolog database [17] on language scripts, origins, and families. This resulted in 24 distinct script groups. Fig. 7 shows GPT-4o and Qwen2-VL performance across these scripts, with both models struggling particularly on low-resource scripts such as, Ge'ez (Amharic), Sinhalese (Sinhala), Oriya (Odia), and Myanmar (Myanmar-Burmese). While the results are not surprising as they highlight that existing models are being predominantly trained on high-resource languages, the extent of decline for low-resource scripts is noteworthy.
+
+We conduct an error analysis on the cultural examples from ALM-bench by selecting one language per script and having native speakers review GPT-4o (best-performing model) responses. Errors were categorized into six types: lack of knowledge, reasoning error, perceptual error [46], language error, translation error, and lack of cultural understanding. Fig. 8 summarizes these error types across four scripts, showing that the primary issues involve knowledge gaps, reasoning errors, and cultural misunderstandings. Fig. 10 further illustrates specific errors across scripts. One such example in Sinhala asks about the type of music group that uses two traditional drums, the Thammattama and Dhawula, which are commonly played by Hewisi music groups associated with traditional Buddhist festivals. Although GPT-4o correctly answered Hewisi and recognized
+
+its role in Buddhist festivals, the response is incorrectly written in the Sinhala language. This highlights GPT-4o's language error with the Sinhalaese script, demonstrating a gap in script proficiency despite grasping cultural context.
+
+Comparison across language families: We also analyze the performance of LMMs by grouping the different languages with respect to 15 families taken from Britannica* as shown in Fig. 9. Results show that performance on several African (Atlantic-Congo) languages such as Igbo, Kinyarwanda, Shona, Swahili, and Yoruba is inferior compared to several Asian (e.g., Chinese, Korean, Vietnamese) and Western languages (e.g., English, French, German).
+
+Effect of question types: We perform this analysis on two closed-source (GPT-4o [2] and Gemini-1.5-Pro [41]) and two open-source (GLM-4V-9B [15], Qwen2-VL [43]) models, as shown in Fig. 11. Overall, we observe that all models fare better on decision-making questions (MCQs and T/F questions). Closed-source models perform better on long VQAs (LVQAs) than short VQAs (SVQA). We observe this trend to be the opposite in open-source models as they struggle to generate accurate and fluent long responses in a multilingual setting with 100 languages.
+
+Are LMMs Culturally Aware? We study the cultural understanding of LMMs on our 13 domains and report results in Fig. 2b. Overall, GPT-4o achieves the best results with an overall score of  $80.3\%$ . However, we observe a significant variation in performance across different cultural domains. For instance, GPT-4o achieves  $83.7\%$  on Education and heritage but drops to  $72.7\%$  on Notable key figures category. We conjecture this variation in performance likely arises since the higher-performing categories are covered in LMM training datasets, leading to better representation learning. In contrast, categories like Notable Key Figures and Customs are often culturally specific and nuanced across languages and regions.
+
+Impact of location-aware information in prompts: We show the performance of LMMs when evaluated with addi
+
+![](images/1bd6daa41c2edf6684d49f62dcb79ecd5b67cf0917d6b2c9b1e8f73b9f1e448a.jpg)  
+Figure 10. We present the qualitative examples of the success cases in the first row and failure cases of GPT-4o in the second row on different languages & domains in ALM-bench. For the failure cases, we specify different error types. For instance, the Urdu language question asks about the festival depicted in the image. The image specifically refers to Mela Chiraghan (Festival of Lights), a celebration held in honor of the Sufi saint Shah Jamal's shrine. Since the decoration in the image closely resembles that of Eid Milad un Nabi — another religious festival—the model erroneously associates it with this wrong event. This constitutes a lack of cultural understanding since the model fails to distinguish between the theme behind the decorations. Eid Milad un Nabi typically features more modest, reverential lighting with green lights, whereas the lighting in Mela Chiraghan is brighter and more colorful. Additionally, people typically dress for the Eid Milad un Nabi event in a traditional outfit which is absent in the image. These examples highlight the model's gap in cultural knowledge and its limitations in terms of accurately interpreting the cultural context of the given sample. Additional results are in the suppl. material.
+
+![](images/1f3ad20635c3355bd4d28ae7478b8b2b77f5023993ab642a4f1c24af569b5b18.jpg)  
+Figure 11. Performance of top-performing VLMs on ALM-bench according to different question types. Compared to open-ended questions, VLMs perform better on MCQs and T/F questions.
+
+tional country-specific information in Tab. 2. We randomly select 50 languages from the ALM-bench and include country information in the prompts to assess any potential performance gains. Here, we observe that closed-source models, including GPT-4o and Gemini-1.5-Pro, better utilize the added geographic context and indicate higher cultural specificity across languages than the open-source models.
+
+# 5. Ethical Consideration
+
+Data. Our cultural images in ALM-bench are sourced from the internet. Therefore, there may be potential biases in un
+
+<table><tr><td>Models</td><td>With Country Info.</td><td>Without Country Info.</td></tr><tr><td>GPT-4o</td><td>83.57%</td><td>80.96%</td></tr><tr><td>Gemini-1.5-Pro</td><td>81.52%</td><td>76.19%</td></tr><tr><td>GLM-4V-9B</td><td>56.78%</td><td>56.41%</td></tr><tr><td>Qwen2-VL</td><td>53.97%</td><td>52.57%</td></tr></table>
+
+Table 2. Performance of LMMs with and without additional country location information. Proprietary models show a notable performance boost of  $2.6\%$  to  $5\%$  when location-aware prompts are used, while open-source models exhibit a marginal improvement.
+
+derpresented domains. However, we believe ALM-bench represents a step forward in standardized multilingual-LMM evaluation, paving the way for greater inclusion of diverse cultural domains, languages, scripts, and origins.
+
+Translations. We use GPT-4o [2] for translations in 100 languages. The initial translations generated by GPT-4o undergo a thorough review by native speakers to ensure linguistic accuracy and cultural relevance to maintain high-quality standards across all language pairs. This combined approach enables consistent and accurate translations.
+
+Human Annotations. To ensure high-quality image filtering and language annotation, we collaborated with linguistic groups and finalized over 60 volunteers for bench
+
+mark curation. For most languages, annotators were required to be either native or bilingual speakers. However, for certain low-resource languages like Igbo, Hungarian, and Afrikaans, proficiency was also acceptable. Annotators were required to be familiar with the cultural context of the specific country-language pair they were working with. Demographic details about the expert annotators are provided in Sec. B (suppl. material). Among them,  $80.3\%$  are native speakers, and  $87.9\%$  have lived for over 15 years in countries where the target language is spoken, thereby ensuring a deeper cultural insight. Furthermore,  $46.7\%$  of annotators both male and female, fall within the 18-25 age bracket.
+
+# 6. Conclusion
+
+In this paper, we introduce ALM-bench, a novel multilingual multimodal cultural benchmark for evaluation with over 22.7k humanly verified samples across 19 domains. Our benchmark encompasses cultural nuances from 73 countries in 24 language scripts and 15 language families. We conduct empirical analysis on 16 vision-language models with various question types (MCQs, T/F, SVQA, and LVQAs) and highlight notable disparities in their performance.
+
+The performance difference between the best-performing open-source model and the proprietary model, GPT-4o, is  $27\%$ . Our results also highlight that the models perform superior on predominant language scripts such as Latin, Cyrillic, and Devanagari and under-performs on underrepresented scripts such as Ge'ez, Lao, Sinhalese, and Oriya. Moreover, cultural understanding of prominent language families such as Indo-European, Austronesian and Afro-Asiatic are well represented by GPT-4o as compared to Atlantic-Congo and Turkic families. Our work highlights the limitations of state-of-the-art LMMs in multilingual and multicultural settings, showing key areas for improvement.
+
+# 7. Acknowledgment
+
+We would like to thank Tafar Mab for providing high-quality annotations for Afrikaans and Kinyarwanda languages, Georgios Ioannides for verifying Greek language, Marek Suppa for annotating and verifying Czech, Slovak and Polish language, and Feno Heriniaina Rabevohitra for annotating Malagasy language. We also thank Yuhao Li for reviewing and assisting with the annotations for Chinese Simplified language. Finally, we extend our gratitude to the anonymous reviewers for their invaluable suggestions and feedback, which helped improve this paper. The computations were enabled by resources provided by NAISS at Alvis partially funded by Swedish Research Council through grant agreement no. 2022-06725, LUMI hosted by CSC (Finland) and LUMI consortium, and by Berzelius resource provided by the Knut and Alice Wallenberg Foundation at the NSC. This work was partially supported by
+
+by the Swedish Research Council (2022-04266) and from KAW (DarkTree project; 2024.0076).
+
+# References
+
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+# All-Day Multi-Camera Multi-Target Tracking
+
+Huijie Fan $^{1,3}$ , Yu Qiao $^{1}$ , Yihao Zhen $^{1,3}$ , Tinghui Zhao $^{1,3}$ , Baojie Fan $^{4}$ , Qiang Wang $^{2*}$ $^{1}$ State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences  
+ $^{2}$ Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University  
+ $^{3}$ University of Chinese Academy of Sciences  
+ $^{4}$ Nanjing University of Posts and Telecommunications  
+{fanhuijie,qiaoyu,zhenyihao,wangqiang}@sia.cn, zhaotinghui22@mails.ucas.ac.cn, jobfbj@gmail.com
+
+# Abstract
+
+The capability of tracking objects in low-light environments like nighttime is crucial for numerous real-world applications. However, previous Multi-Camera Multi-Target(MCMT) tracking methods are primarily focused on tracking during daytime with favorable lighting, overlooking the challenge posed by low-light conditions. The main difficulty of tracking under low-light condition is the lack of detailed visible appearance features. To address this issue, we incorporate the infrared modality into MCMT tracking framework to provide more useful information. We constructed the first Multi-modality (RGBT) Multi-camera Multi-target tracking dataset named M3Track, which contains sequences captured in low-light environments, laying a solid foundation for all-day multi-camera tracking. Based on the proposed dataset, we propose All-Day Multi-Camera Multi-Target tracking network, termed as ADM-CMT. Specifically, we propose an All-Day Mamba Fusion(ADMF) module to fuse information from different modalities adaptively. Within ADMF, the Lighting Guidance Model(LGM) extracts lighting relevant information to guide the fusion process. Furthermore, the Nearby Target Collection(NTC) strategy is designed to enhance tracking accuracy by leveraging information derived from surrounding objects of targets. Experiments conducted on M3Track demonstrate that ADMCMT exhibits strong generalization across different lighting conditions. The code will be released at https://github.com/QTRACKY/ADMCMT.
+
+# 1. Introduction
+
+Multi-Camera Multi-Target (MCMT)[21, 22] tracking aims to locate and associate the same targets between different frames and camera views with substantial overlaps. Compared with single-camera tracking, using multiple cameras
+
+![](images/6e614246d08cc102afe01ffc0247e382eec2ebc668302242d6ee4dedbb86fe99.jpg)  
+Figure 1. All-day tracking is dedicated to achieving robust tracking at any time of a day. Our approach to achieve all-day MCMT tracking is introducing infrared modality to MCMT framework, employing the complementary nature of infrared and visible light information to empower tracker with capability of tracking objects under different lighting conditions.
+
+to track the same target can effectively address the occlusion problem and improve tracking consistency. MCMT tracking has significant implications for a number of areas, including urban reconnaissance[20], crowd behavior analysis[28], and traffic scene understanding[32].
+
+Previous MCMT tracking methods[3, 12, 29, 30] focused primarily on tracking at daytime with favorable lighting, overlooking the challenge posed by low-light (night-time) conditions, which is inevitable in those aforementioned applications. A main limitation that obstructs previous MCMT methods to perform low-light tracking is the lack of detailed visible features. Inspired by multi-modality single-camera tracking methods[2, 14, 34, 48, 50], we incorporate infrared modality into MCMT tracking framework to introduce more detailed information, as the in
+
+![](images/53749d624c437b2827162c8c7afc36f071d856d603fc4f6cf741259e417ed9f5.jpg)  
+Figure 2. Example of the M3Track. M3Track is composed of well-aligned RGB and infrared sequences captured in different times of a day. From left to right: noon, afternoon, night.
+
+frared modality is hardly affected by lighting conditions. As shown in Fig.1, our core idea is using visible light (RGB) and infrared (Thermal) information as complementary to promote tracking performance under low-light condition, so as to realize all-day tracking.
+
+To address the limitation of existing MCMT datasets[8, 39], we constructed a high-quality Multi-modality (RGBT) Multi-camera Multi-target dataset, named M3Track. As shown in Fig 2, the proposed M3Track consists of well aligned RGB and infrared sequences captured at different times of a day and various weather conditions. To the best of our knowledge, our M3Track is the first MCMT tracking dataset that incorporates both infrared modality and low-light sequences. Furthermore, we present All-Day Multi-camera Multi-target tracking network termed as ADMCMT, which can jointly perform modality fusion, target detection, and target tracking at any time of a day. Specifically, we propose a modality fusion module based on mamba[10], named All-Day Mamba Fusion (ADMF). Within the ADMF, the Lighting Guidance Model (LGM) is used to extract lighting relevant information from visible light input, then the extracted lighting relevant information is sent into mamba-based fusion channels to guide the fusion of visible and infrared features. After that, the fused feature is sent to CenterNet[6] for detection and a transformer-based network for tracking. During the tracking stage, we employ the Nearby Target Collection strategy (NTC) that leverages information from surrounding objects of target to enhance both single-camera and multi-camera tracking capabilities of our model. Experiments demonstrate that ADMCMT exhibits strong generalization capabilities under different lighting conditions.
+
+Our main contributions are summarized as follows:
+
+- We construct the first Multi-modality (RGBT) Multi-camera Multi-target tracking dataset, named M3Track. It
+
+contains sequences captured at different times of a day, laying a solid foundation for all-day MCMT tracking.
+
+- We propose an All-Day Multi-Camera Multi-Target tracking network, termed as ADMCMT, which can adaptively fuse features from different modalities.  
+- We propose an All-Day Mamba Fusion module which use lighting relevant information to guide feature fusion and a Nearby Target Collection strategy to better utilize background information of targets.
+
+# 2. Related Work
+
+# 2.1. MCMT Tracking
+
+Multi-camera multi-target [21, 22] tracking aims to locate and associate targets between frames and cameras with substantial overlaps. Current MCMT tracking methods [3, 12, 13, 29, 31, 39, 40] can be broadly classified into two categories. One approach is to calculate the transformation matrix between images captured by different cameras through point-matching methods. The transformation matrix enables the matching of targets across images. MIA-Net [26] employs SIFT to perform point-matching, enhancing the efficiency of tracking small targets with limited visible features. The main limitation of this type of method is its reliance on similarity between the images, which can degrade performance when there are substantial angular differences between camera viewpoints.
+
+Another approach focuses on matching the appearance features of targets. CrossMOT[11] introduces both single-camera Re-ID embeddings and cross-camera Re-ID embeddings to match features between frames and cameras. GMT[7] constructs features with target appearance and contextual information such as location and time. Features are then used to generate global correlation via a transformer-based model in one-stage manner. Both the point-matching method and target matching method rely on visible infor
+
+![](images/80ffe8e7c06020f3f45cc7a4f6206c76aef2e6772350d2469a8aebaa2d0bfcd6.jpg)  
+Figure 3. M3Track is collected in diverse scenes under various lighting conditions. (a) represents the proportion of frames for each scene. (b) shows the number and average area of targets each scene, illustrate that M3Track has a high diversity in target dense and size.
+
+![](images/08979a0027eb7eee58711e0440f2cddfaafa34bc05f3267fd66a215c2f1f1e2d.jpg)
+
+<table><tr><td>Dataset</td><td>Scenes</td><td>Views</td><td>Frames</td><td>Boxes</td><td>Moving camera</td><td>Low-light</td><td>UAV view</td><td>Multimodality</td></tr><tr><td>EPFL</td><td>5</td><td>4</td><td>97K</td><td>625K</td><td>×</td><td>×</td><td>×</td><td>×</td></tr><tr><td>CAMPUS</td><td>4</td><td>4</td><td>83K</td><td>490K</td><td>×</td><td>×</td><td>×</td><td>×</td></tr><tr><td>MvMHAT</td><td>1</td><td>4</td><td>31K</td><td>208K</td><td>✓</td><td>×</td><td>×</td><td>×</td></tr><tr><td>WILDTRACK</td><td>1</td><td>7</td><td>3K</td><td>40K</td><td>×</td><td>×</td><td>×</td><td>×</td></tr><tr><td>DIVOTrack</td><td>10</td><td>3</td><td>54K</td><td>560K</td><td>✓</td><td>×</td><td>one</td><td>×</td></tr><tr><td>M3Track</td><td>19</td><td>2</td><td>118K×2</td><td>1188K</td><td>✓</td><td>✓</td><td>two</td><td>✓</td></tr></table>
+
+Table 1. Comparison with previous MCMT datasets. M3Track significantly surpassing previous datasets in both scene diversity and volume.
+
+mation, this dependency may seriously affect the tracking performance under low-light conditions.
+
+# 2.2. Tracking under low-light condition
+
+Tracking objects in low-light scenes poses a significant challenge owing to the absence of detailed visible features. Approaches to uncover more information in visible light images such as low-light enhancement and domain transfer[5] have been largely explored. LTrack [36] achieves low-light tracking by extracting invariant features from low-light videos utilizing the adaptive low-pass downsample module and the degradation suppression learning strategy. LDEnhancer [42] learns light distribution information to suppress image enhancement and refine image content.
+
+Using extra modalities such as event[45], depth[41], and thermal[35] gives a more direct approach for tracking objects at nighttime by introducing more information. Many multi-modality tracking datasets with low-light sequences have been established[15-19, 47] and played key roles in the generalization of single-target tracking. Methods with low-light tracking ability have also been widely researched on the basis of the rich dataset. BAT[2] uses bi-directional adapter to fuse multi-modality information in an adaptive manner. CMD[48] utilizes a three-stage frame
+
+work to bridge the performance gap between a compact student RGBT tracking model and a powerful teacher model.
+
+# 2.3. RGBT Fusion
+
+Infrared and visible light (RGB) data can serve as complementary to provide more useful information, which is essential for a range of downstream tasks, including target detection and tracking. The current methods of modality fusion can be broadly categorized into three types: pixel-level fusion[4], feature-level[2, 24, 27, 38, 46, 51] fusion and decision-level fusion[33]. Pixel-level fusion preserved more detailed information of the input images, but at the cost of high computational complexity. Feature-level fusion fuses features of detected targets, and yields an optimal equilibrium between performance and efficiency. Decision-level fusion processes different modality separately and only fuse the final decision, has high requirements for single modal algorithms. Recently, Mamba has been shown to outperform the transformer in long-term dependency modeling tasks owing to its selective structured state space and has shown competitive results in computer vision tasks. In the field of RGBT fusion, methods based on the Mamba approach[23] are also being actively applied and have shown remarkable performance.
+
+![](images/5b16e9bff101e771fdd7fb23e870a87950e683db7eab23b28eb98e6d6e4f1686.jpg)  
+Figure 4. The ADMCMT model first utilizes All-Day Mamba Fusion to fuse infrared and visible light feature under the guidance of lighting relevant information. Fused feature is used for target detection. After obtaining the detection result, Nearby Target Collection is used to help build Re-ID features of targets. Finally, Re-ID features are sent into a transformer based tracking model to obtain the tracking result.
+
+# 3. M3Track Dataset
+
+# 3.1. Previous MCMT Datasets
+
+Existing MTMC tracking datasets with overlapping fields of view include: EPFL[8], CAMPUS[39], WILDTRACK[9], MvMHAT[9] and DIVOTrack[11]. Each of these datasets suffers from issues like lack of scene diversity and varying annotation quality. Moreover, all of these datasets are collected at daytime with acceptable lighting, which poses tremendous challenges in conducting MCMT tracking research under low-light conditions.
+
+To address the limitations and enrich the diversity of MCMT datasets, we constructed the first multi-modality MTMC dataset with low-light sequences, named M3Track, which includes aligned RGB and infrared videos collected at different times of a day and in different weather. We hope data with diverse lighting conditions will promote visible light tracking, meanwhile RGB and infrared modalities can serve as complementarity to empower the model with the ability to track under low-light condition, thereby achieving all-day tracking. Comparison with previous MCMT datasets in Table 1 shows that M3Track surpasses previous datasets by nearly two times in terms of frame number, target number, and scenes. It is also noteworthy that previous RGBT tracking datasets are primarily built for single-object tracking, and our M3Track could also serve as a valuable single-camera multi-object RGBT tracking dataset.
+
+# 3.2. Data Collection
+
+The proposed M3Track dataset was collected with two drones, each equipped with both an RGB camera and an infrared camera. The drones were moving irregularly while recording. We collected 88 sequences across 19 distinct real-world scenarios with diverse surrounding environments
+
+and varying target densities, as illustrated in Fig. 3. To obtain diverse lighting conditions, we also collected the data under various weather conditions and different times of a day. These aforementioned efforts ensure that our dataset has sufficient diversity.
+
+After recording, we manually aligned the timestamps and the spatial relationships between the RGB and infrared cameras on each drone. Due to the difference in FOV and resolution between RGB and infrared cameras, we cropped and down-sampled all images to the resolution of  $640 \times 512$  for better alignment. The dataset is split by approximately 1:1 as the train set and the test set. Previous MCMT tracking datasets usually split one sequence into two for training and testing. However, this approach may result in correlation between the training and testing data, thereby affecting the reliability of test results. To address this issue, the test set of M3Track comprises novel scenes that are not present in the train set, along with scenes that are included in the train set but have distinct targets and varying target densities.
+
+# 3.3. Data Annotation
+
+M3Track dataset is annotated based on single-modality, we use RGB video as the reference for sequences recorded under preferable lighting conditions, and infrared video for sequences recorded under low-light conditions. The annotation process of M3Track involves two primary steps. First, we labeled all targets from different views at a given time  $t$  and assigned a unique ID to each target in the overlapping fields of view of the two cameras. After that, we use the semi-automatic object tracking software DarkLabel to label the targets with the same ID across consecutive frames. The above steps were repeated until all targets in the video are labeled and assigned IDs. The annotation results are carefully checked and adjusted for better accuracy.
+
+# 4. Method
+
+# 4.1. Overview
+
+The overall architecture of ADMCMT is illustrated in Fig. 4. The input of ADMCMT consists of visible and infrared image pairs of each view  $V_{t}^{n} = \{I_{t}^{ir}, I_{t}^{vi}\}$  at time  $t$ ,  $n$  represents the  $n_{th}$  view. Given the input images, we extract inter-modality features  $F_{t}^{ir}$  and  $F_{t}^{vi}$  and fuse them through All-Day Mamba Fusion module. The fused feature is then used as the input of the target detector. After acquiring the detection results, the Nearby Target Collection strategy is utilized to find surrounding objects for each target. For the  $i_{th}$  target, we use different Re-ID decoder to extract target feature  $F_{i}$  and nearby target features  $F_{n}$ .  $F_{i}$  and  $F_{n}$  are concatenated to get the final target feature  $F_{t}^{i}$ . The set of features in frame  $t$  and  $t - 1$  are sent into a single-stage MCMT tracker to obtain the tracking result.
+
+# 4.2. All-Day Mamba Fusion
+
+The richness of information contained in different modalities varies under different lighting conditions. RGB images usually contain more detailed appearance feature than infrared images (e.g color) under preferable lighting condition, while the reverse is true under low-light condition. To more effectively fuse multi-modality information, we proposed All-Day Mamba Fusion (ADMF) model which uses lighting relevant information to guide the fusion progress. The overall architecture of ADMF is illustrated in Fig. 5.
+
+Lighting relevant information. We divided sequences in M3Track into two categories according to their lighting conditions: {Daytime (optimal lighting), Nighttime (poor lighting)}. We send the feature map extracted by the first layer of the visible backbone[44] to the Lighting Guidance Module (LGM), which comprises a stack of four convolution layers and an MLP head to predict the lighting category. The lighting category prediction is constrained by the cross-entropy loss function, which is defined as follows:
+
+$$
+\mathcal {L} _ {\text {l i g h t}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \left(y _ {i} \log \left(\hat {y} _ {i}\right) + \left(1 - y _ {i}\right) \log \left(1 - \hat {y} _ {i}\right)\right) \tag {1}
+$$
+
+where  $N = 2$ ,  $y_{i}$  is the ground truth for sample  $i$ , and  $\hat{y}_i$  is the predicted probability. We process the feature extracted by the first convolution layer of LGM with another convolution layer to obtain  $F_{t}^{light}$ . Since the features in LGM are used to predict the lighting category,  $F_{t}^{light}$  should contain information related to lighting condition, thus reflecting the quality of features in RGB image.
+
+Feature fusion. With visible feature  $F_{t}^{vi}$  and infrared feature  $F_{t}^{ir}$  as input, we first fuse them with pixel-level averaging to obtain an initial cross-modality feature  $F_{t}^{fuse}$ . Considering that visible light information is more easily affected by lighting conditions, we add  $F_{t}^{light}$  acquired from
+
+![](images/94f9385d1f875f0cbb6d02f06f32ae101c84392c13bb53d9cca7a1a7b9c103ca.jpg)  
+Figure 5. The All-Day Mamba Fusion module consists of the VI, IR, LI channels, and the Lighting Guidance Module(LGM). LGM extracts lighting relevant information  $F_{t}^{light}$  from visible feature  $F_{t}^{vi}$  to guide the fusion process.
+
+LGM to  $F_{t}^{vi}$ . Since  $F_{t}^{light}$  contains information that reflects the quality of features in RGB images, this integration could adjust the weight of information in  $F_{t}^{vi}$  at pixel level. These aforementioned features are further processed by different channels respectively. The VI  $(F_{t}^{vi})$ , IR  $(F_{t}^{ir})$ , and LI  $(F_{t}^{light})$  channel consist of layer normalization operation and the MCS block, while the FU  $(F_{t}^{fuse})$  channel is a complete VSS block[25]. The outputs of the VI and IR channels are adjusted by the gating factor derived from the FU channel. Subsequently, all processed features are added and aggregated with an MLP layer. In this process, the lighting relevant information from LI plays a guiding role by indicating the quality of visible information in each pixel. After that,  $F_{t}^{fuse}$  is added to the aggregated feature as residual to obtain the final fusion result.
+
+# 4.3. Object Detection
+
+We utilize the CenterNet[6] as detector in ADMCMT. CenterNet takes the feature maps derived from ADMF as input and directly predicts the score map of the center of the object, as well as regressing on the size and offset of the object. This approach offers a streamlined and precise solution, making it particularly well-suited to tracking tasks. The location information of the target to be tracked is obtained following the utilization of the CenterNet, which in turn facilitates the extraction of features of the target. The loss function of the target detection model is as follows:
+
+$$
+\mathcal {L} _ {\text {d e t}} = \mathcal {L} _ {\text {h e a t m a p}} + \lambda_ {\text {s i z e}} \mathcal {L} _ {\text {s i z e}} + \lambda_ {\text {o f f}} \mathcal {L} _ {\text {o f f}} \tag {2}
+$$
+
+where  $\lambda_{\mathrm{size}} = 0.1$ ,  $\lambda_{\mathrm{off}} = 1.0$ ,  $\mathcal{L}_{\mathrm{heatmap}}$  denotes the heatmap centroid loss,  $\mathcal{L}_{\mathrm{off}}$  denotes the centroid offset loss, and  $\mathcal{L}_{\mathrm{size}}$  denotes the target aspect loss.
+
+![](images/1e0bed3fe990913492e4aa3c0f08dd913dc9b3f5d14e9bcb66771bd20b77e129.jpg)  
+Figure 6. Surrounding objects of target have a high consistency between different views and could be used to improve tracking performance.
+
+# 4.4. Nearby Targets Collection
+
+Utilizing background information of targets makes a crucial advancement for single-camera tracking[1] by providing the model with the location of the target. However, when it comes to multi-camera tracking, backgrounds of the same target captured by different cameras always have significant difference due to varying shooting angles, as shown in Fig. 6. Following the idea of utilizing background information, we notice that objects near the same target have a high degree of consistency between different cameras. Thus, we develop a Nearby Targets Collection(NTC) strategy to collect information about objects that are close to the target.
+
+After obtaining object detection results in the current frame from all cameras, for the  $ith$  target  $T_{i}$ , we expand its bboxes by two times. If there is overlap between the expended bbox and the bbox of another target  $T_{j}$ , we define  $T_{j}$  as a nearby target of  $T_{i}$ . Problem still occurs that objects in one view seem close to each other but are actually far away. To avoid this, we designed a simple area restriction. Specifically, the area of the current target is  $S$ , other objects with an area less than  $0.6S$  will not be considered as nearby targets. The  $ith$  target feature is denoted by  $F_{i}$  and the nearby target are denoted by  $F_{n}$ . Feature dim of each  $F_{n}$  is set to 32 and concatenated with  $F_{i}$  to obtain the final Re-ID feature of target  $F_{t}^{i}$ .
+
+# 4.5. Target tracking
+
+We use GMT[7] as tracker in ADMCMT. GMT is a strong transformer based MCMT tracker which can jointly conduct single-camera and cross-camera tracking. GMT takes the set of all target features in two consecutive frames  $F_{t}$  and  $F_{t-1}$  as input, output matrix  $M$ , where  $M_{ij}$  denotes the similarity score between the  $i_{th}$  target in  $F_{t}$  and the  $j_{th}$  target in  $F_{t-1}$ .  $M_{i0} = 0$  indicates target  $i$  in frame  $t$  is not associated with any trajectory in frame  $t$  and is therefore
+
+designated as  $p_i \sim p_0$ . For  $M_{i0} \neq 0$  and  $j > 0$ , the highest  $M_{ij}$  in row  $i$  indicates target  $i$  belongs to the trajectory  $j$  in frame  $t - 1$ , denoted as  $p_i \sim p_j$ . The association loss for GMT is as follows:
+
+$$
+X _ {i j} = \left\{ \begin{array}{l l} 1 & \text {i f} p _ {i} \sim p _ {j} \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {3}
+$$
+
+$$
+\mathcal {L} _ {\text {a s s i}} = - \frac {1}{N} \sum_ {t = 1} ^ {T} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} X _ {i j} \log \left(M _ {i j}\right) \tag {4}
+$$
+
+The loss of ADMCMT is the weighted sum of the losses of the LGM, the target detection module, and the target tracking module.
+
+$$
+\mathcal {L} _ {\text {T r a c k}} = \lambda_ {\text {l i g h t}} \mathcal {L} _ {\text {l i g h t}} + \lambda_ {\text {d e t}} \mathcal {L} _ {\text {d e t}} + \lambda_ {\text {a s s i}} \mathcal {L} _ {\text {a s s i}} \tag {5}
+$$
+
+where  $\lambda_{\mathrm{light}} = 0.1$ ,  $\lambda_{\mathrm{det}} = 2$ , and  $\lambda_{\mathrm{light}} = 5$ . Since  $\mathcal{L}_{\mathrm{light}}$  converges most easily, we assign it a minimal weight.
+
+# 5. Experiments
+
+# 5.1. Implementation Details
+
+The ADMCMT employs DLA-34 to extract image features and Centernet as the target detector. The model is trained on M3Track with a batch size of 40 (5 frames consist of 2 camera views and 2 modalities) for a total of 20,000 iterations using 4 NVIDIA RTX A6000 GPUs. We utilized Adam optimizer with a learning rate of  $10^{-4}$ . For nearby target collection, the current target is represented by a feature vector of dimension 1024, while each nearby target is represented by a feature vector of dimension 32. The inference is conducted on a single NVIDIA A6000 GPU. The confident threshold of the target detector has been set at 0.525 during inference. Which is the same as the previous works.
+
+# 5.2. Evaluation Metrics
+
+We evaluate the performance of ADMCMT on both single-camera and multi-camera metrics. We use MOTA, HOTA, IDF1, DetA, and MOTP as evaluation metrics for single-camera tracking and using Multi-Device target Association score (MDA)[26], Cross-View IDF1 (CVIDF1)[11], and Cross-View Matching Accuracy (CVMA) [11] to evaluate cross-camera tracking. MDA evaluates whether a tracker can accurately assign the same ID to the same target across different cameras and is defined as:
+
+$$
+\begin{array}{l} M D A = \frac {1}{C _ {N} ^ {2} * F} \sum_ {j = 1} ^ {N - 1} \sum_ {k = j + 1} ^ {N} \sum_ {i = 1} ^ {F} (6) \\ \times \left(\frac {T A _ {(j k , i)}}{G A _ {(j k , i)} + F A _ {(j k , i)} + M A _ {(j k , i)}}\right) \\ C _ {N} ^ {2} = \frac {N !}{(N - 2) ! \times 2 !} (7) \\ \end{array}
+$$
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Method</td><td colspan="5">Single camera tracking metrics</td><td colspan="3">Multi-camera tracking metrics</td></tr><tr><td>MOTA↑</td><td>HOTA↑</td><td>IDF1↑</td><td>DetA↑</td><td>MOTP↑</td><td>MDA↑</td><td>CVIDF1↑</td><td>CVMA↑</td></tr><tr><td rowspan="6">All</td><td>OSNet[49]</td><td>68.03</td><td>50.33</td><td>61.60</td><td>55.71</td><td>75.78</td><td>0.2756</td><td>48.50</td><td>28.60</td></tr><tr><td>CrossMOT[11]</td><td>65.30</td><td>44.84</td><td>59.91</td><td>48.62</td><td>75.54</td><td>0.2019</td><td>51.21</td><td>38.51</td></tr><tr><td>CT[37]</td><td>68.21</td><td>50.38</td><td>61.17</td><td>55.89</td><td>75.80</td><td>0.4340</td><td>53.65</td><td>44.71</td></tr><tr><td>MvMHAT[9]</td><td>66.39</td><td>48.60</td><td>58.96</td><td>54.99</td><td>75.77</td><td>0.2178</td><td>46.64</td><td>26.72</td></tr><tr><td>AGW[43]</td><td>67.62</td><td>50.44</td><td>62.02</td><td>55.54</td><td>71.54</td><td>0.4235</td><td>54.81</td><td>45.02</td></tr><tr><td>Ours</td><td>70.94</td><td>56.62</td><td>71.47</td><td>57.89</td><td>77.21</td><td>0.6169</td><td>68.77</td><td>61.81</td></tr><tr><td rowspan="6">Night</td><td>OSNet</td><td>66.43</td><td>49.95</td><td>63.25</td><td>54.29</td><td>75.86</td><td>0.2318</td><td>48.39</td><td>23.43</td></tr><tr><td>CrossMOT</td><td>53.94</td><td>42.00</td><td>58.62</td><td>40.43</td><td>71.83</td><td>0.1425</td><td>49.45</td><td>35.84</td></tr><tr><td>CT</td><td>66.83</td><td>51.04</td><td>65.33</td><td>54.44</td><td>75.88</td><td>0.2524</td><td>49.25</td><td>27.85</td></tr><tr><td>MvMHAT</td><td>63.23</td><td>48.82</td><td>61.03</td><td>53.03</td><td>75.95</td><td>0.2079</td><td>46.06</td><td>24.36</td></tr><tr><td>AGW</td><td>66.43</td><td>49.95</td><td>63.25</td><td>54.29</td><td>75.86</td><td>0.2318</td><td>48.39</td><td>23.43</td></tr><tr><td>Ours</td><td>69.71</td><td>51.19</td><td>66.02</td><td>56.40</td><td>76.50</td><td>0.4966</td><td>58.05</td><td>47.15</td></tr></table>
+
+Table 2. Comparison with previous SOTA MCMT trackers on M3Track. All presents results on full dataset and Night result presents results on nighttime scenes. The best results and the second best results are in are shown in red and blue.  
+
+<table><tr><td rowspan="2">V</td><td rowspan="2">I</td><td rowspan="2">FU</td><td rowspan="2">VI+IR</td><td rowspan="2">LGM</td><td rowspan="2">LI</td><td colspan="5">Single camera tracking metrics</td><td colspan="3">Multi-camera tracking metrics</td></tr><tr><td>MOTA</td><td>HOTA</td><td>IDF1</td><td>DetA</td><td>MOTP</td><td>MDA</td><td>CVIDF1</td><td>CVMA</td></tr><tr><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>58.98</td><td>51.84</td><td>65.25</td><td>50.24</td><td>76.92</td><td>0.6170</td><td>62.58</td><td>53.28</td></tr><tr><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>55.67</td><td>51.56</td><td>64.84</td><td>49.82</td><td>76.97</td><td>0.5132</td><td>61.63</td><td>48.01</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>68.23</td><td>53.94</td><td>67.87</td><td>56.96</td><td>76.41</td><td>0.5717</td><td>63.93</td><td>57.22</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>68.62</td><td>54.05</td><td>68.40</td><td>56.37</td><td>76.32</td><td>0.5728</td><td>64.15</td><td>57.34</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>69.16</td><td>54.76</td><td>69.06</td><td>57.01</td><td>77.15</td><td>0.5768</td><td>66.50</td><td>58.48</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>70.47</td><td>56.29</td><td>70.62</td><td>57.06</td><td>77.48</td><td>0.5866</td><td>67.09</td><td>61.02</td></tr></table>
+
+Table 3. Ablation study on different channels and LGM in ADMF. V presents visible light input and I presents infrared input. The best results and the second best results are in are shown in red and blue.
+
+Where  $i$  denotes the  $i$ -th frame,  $j$  and  $k$  represent different capture devices.  $T_{A(jk,i)}$  and  $F_{A(jk,i)}$  represent the number of pairs for which the MCMT tracker correctly and failed to associate a target ID, respectively.  $G_{A(jk,i)}$  represents the number of pairs for which the ground truth associates a target ID.  $M_{A(jk,i)}$  counts MCMT tracker's false associations that are valid in the ground truth.
+
+CVIDF1 is a cross-view version of IDF1 and is defines as:
+
+$$
+C V I D F 1 = \frac {2 \times C V I D P \times C V I D R}{C V I D P + C V I D R} \tag {8}
+$$
+
+Where CVIDP and CVIDR represent the Cross-View ID Precision and Cross-View ID Recall, respectively.
+
+CVMA is a cross-view version of MOTA and is defines as:
+
+$$
+C V M A = 1 - \frac {\sum_ {t} \left(m _ {t} + f p _ {t} + 2 m m e _ {t}\right)}{\sum_ {t} g _ {t}} \tag {9}
+$$
+
+Where  $m_t$  and  $g_t$  represent the missed detections at time  $t$  and the total true targets from all perspectives at that time,
+
+respectively.  $f p_{t}$  and  $mme_{t}$  are the counts of false positives and wrong matching pairs, respectively.
+
+# 5.3. Comparisons With State-of-The-Art Methods
+
+To demonstrate the effectiveness of our proposed ADM-CMT, we conducted experiments on M3Track against other SOTA MCMT trackers. Previous MCMT methods are all designed for single-modality tracking. For a fair comparison, we extract the multi-modality fusion results acquired from our ADMF model and use them as inputs to train other models. Moreover, we shared the detection results of our ADMCMT with other SOTA models. The result metrics are presented in Table 2. For single-camera tracking, our model achieved a performance of 70.94 MOTA and 71.47 IDF1, outperforming the second best model by 2.73 MOTA and 9.45 IDF1. For multi-view tracking, our model achieved 61.81 CVMA and 68.77 CVIDF1, reported a huge improvement of 16.79 CVMA, and 13.96 CVIDF1. We also conducted experiment on night scenes in M3Track, our model outperforms the second best model by 2.88
+
+<table><tr><td rowspan="2"></td><td rowspan="2">LGM</td><td rowspan="2">LI</td><td colspan="5">Single camera tracking metrics</td><td colspan="3">Multi-camera tracking metrics</td></tr><tr><td>MOTA↑</td><td>HOTA↑</td><td>IDF1↑</td><td>DetA↑</td><td>MOTP↑</td><td>MDA↑</td><td>CVIDF1↑</td><td>CVMA↑</td></tr><tr><td rowspan="3">Day</td><td rowspan="2">✓</td><td></td><td>69.55</td><td>55.47</td><td>69.78</td><td>57.11</td><td>76.54</td><td>0.5848</td><td>67.62</td><td>63.00</td></tr><tr><td></td><td>70.38</td><td>56.51</td><td>70.79</td><td>57.99</td><td>77.37</td><td>0.5934</td><td>68.34</td><td>63.82</td></tr><tr><td>✓</td><td>✓</td><td>71.75</td><td>58.44</td><td>72.92</td><td>59.06</td><td>77.82</td><td>0.6342</td><td>70.63</td><td>66.59</td></tr><tr><td rowspan="3">Night</td><td rowspan="2">✓</td><td></td><td>66.01</td><td>50.03</td><td>64.61</td><td>54.55</td><td>76.58</td><td>0.3930</td><td>54.30</td><td>43.01</td></tr><tr><td></td><td>66.46</td><td>50.21</td><td>64.84</td><td>54.50</td><td>75.76</td><td>0.4362</td><td>57.27</td><td>47.27</td></tr><tr><td>✓</td><td>✓</td><td>67.16</td><td>50.43</td><td>64.70</td><td>55.14</td><td>76.59</td><td>0.4436</td><td>58.52</td><td>47.04</td></tr></table>
+
+Table 4. Ablation study on and LGM and LI channel. Day presents results on daytime sequences and N presents results on nighttime scenes. The best results are shown in red.  
+
+<table><tr><td>Num</td><td>MOTA↑</td><td>IDF1↑</td><td>CVIDF1↑</td><td>CVMA↑</td></tr><tr><td>0</td><td>70.47</td><td>70.62</td><td>67.09</td><td>61.02</td></tr><tr><td>1</td><td>70.65</td><td>70.67</td><td>67.86</td><td>61.16</td></tr><tr><td>2</td><td>69.82</td><td>69.63</td><td>66.22</td><td>59.32</td></tr><tr><td>3</td><td>69.23</td><td>69.31</td><td>51.46</td><td>57.17</td></tr></table>
+
+Table 5. Ablation study on number of nearby targets. ADMCMT achieves best performance with 1 nearby target.  
+
+<table><tr><td>Area(S)</td><td>MOTA↑</td><td>IDF1↑</td><td>CVIDF1↑</td><td>CVMA↑</td></tr><tr><td>0.4</td><td>70.63</td><td>71.28</td><td>68.74</td><td>61.63</td></tr><tr><td>0.5</td><td>70.61</td><td>70.77</td><td>68.21</td><td>61.52</td></tr><tr><td>0.6</td><td>70.94</td><td>71.47</td><td>68.77</td><td>61.81</td></tr><tr><td>0.7</td><td>70.51</td><td>71.26</td><td>67.91</td><td>60.73</td></tr><tr><td>0.8</td><td>70.71</td><td>71.01</td><td>68.01</td><td>61.38</td></tr></table>
+
+Table 6. Ablation study on area threshold. ADMCMT achieves best performance with area threshold of 0.6.
+
+MOTA,0.69 IDF1, 8.6 CVIDF1 and 11.31 CVMA, exhibiting strong generalization across different lighting conditions.
+
+# 5.4. Ablation Study
+
+All-Day Mamba Fusion. The Ablation results of ADMF are shown in Table. 3. We first use single visible light and infrared modality as input to construct baseline. To verify the effectiveness of the proposed ADMF, we fuse RGB and infrared modality in a simple point-wise average manner and process the fused feature with FU, observe MOTA and DetA improvement and MDA, MOTP deterioration. The reason for this result may be that the simple fusion method introduces useless information. After adding IR and VI channels to the network, we obtain better performance than the simple point average fuse. The introduction of LGM led to comprehensive improvement. Overall results prove the effectiveness of ADMF and its internal units.
+
+We also conduct a detailed analysis of the experimental results under different lighting conditions. Results in Table. 4 indicates adding LGM and LI channels improves the tracking performance under low-light conditions (night) while maintaining reliability during the day, demonstrating that the LGM and LI channels meet our expectations to adaptively fuse information from different modalities.
+
+Nearby Target Collection. We conduct experiments to explore the effect of nearby target number and area threshold in NTC. Ablation results of nearby target number are shown in Table. 5 tells that ADMCMT achieve the best performance on M3Track with 1 nearby targets. We also conduct ablation on area threshold with one nearby target, results are shown in Table. 6. We consider the best targets number and area threshold depending on the camera pitching angle and object density. Specifically, scenes with dense objects and small camera pitching angle require more targets to contain useful information and lower thresholds to avoid distractors.
+
+# 6. Conclusion
+
+In this work, we implement all-day MCMT tracking by introducing the infrared modality. We have constructed the first Multi-modality (RGBT) MCMT tracking dataset, named M3Track, laying a solid foundation for all-day MCMT tracking. Based on the M3Track dataset, we present the All-Day Multi-Camera Multi-Target tracking network, termed as ADMCMT. We designed an All-Day Mamba Fusion model to adaptively fuse information from different modalities under the guidance of lighting-relevant information. Furthermore, we introduce the Nearby Target Collection strategy, which promotes tracking performance by effectively utilizing background information. Experiments demonstrate that ADMCMT exhibits strong generalization capabilities across different lighting conditions.
+
+Acknowledgements. This work is supported by the National Natural Science Foundation of China (62273339, U24A201397), the LiaoNing Revitalization Talents Program (XLYC2403128) and the fundamental research project of SIA.
+
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\ No newline at end of file
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+# All-Optical Nonlinear Diffractive Deep Network for Ultrafast Image Denoising
+
+Xiaoling Zhou $^{1*}$ , Zhemg Lee $^{2*}$ , Wei Ye $^{1\dagger}$ , Rui Xie $^{1}$ , Wenbo Zhang $^{2}$ , Guanju Peng $^{2}$ , Zongze Li $^{3\dagger}$ , Shikun Zhang $^{1\dagger}$
+
+$^{1}$ Peking University  $^{2}$ Tianjin University  $^{3}$ Pengcheng Laboratory
+
+xiaolingzhou@stu.pku.edu.cn, zhemglee@tju.edu.cn
+
+# Abstract
+
+Image denoising poses a significant challenge in image processing, aiming to remove noise and artifacts from input images. However, current denoising algorithms implemented on electronic chips frequently encounter latency issues and demand substantial computational resources. In this paper, we introduce an all-optical Nonlinear Diffractive Denoising Deep Network (N3DNet) for image denoising at the speed of light. Initially, we incorporate an image encoding and pre-denoising module into the Diffractive Deep Neural Network and integrate a nonlinear activation function, termed the phase exponential linear function, after each diffractive layer, thereby boosting the network's nonlinear modeling and denoising capabilities. Subsequently, we devise a new reinforcement learning algorithm called regularization-assisted deep Q-network to optimize N3DNet. Finally, leveraging 3D printing techniques, we fabricate N3DNet using the trained parameters and construct a physical experimental system for real-world applications. A new benchmark dataset, termed MIDD, is constructed for mode image denoising, comprising 120K pairs of noisy/noise-free images captured from real fiber communication systems across various transmission lengths. Through extensive simulation and real experiments, we validate that N3DNet outperforms both traditional and deep learning-based denoising approaches across various datasets. Remarkably, its processing speed is nearly 3,800 times faster than electronic chip-based methods.
+
+# 1. Introduction
+
+Image denoising is a crucial and challenging task across multiple fields, including signal processing [42, 46], computational imaging [5, 53, 58], and computer vision [50, 51, 60]. For instance, effective noise reduction in computational imaging is paramount to counteracting the detrimental effects of various noise sources and artifacts, such as
+
+those originating from image sensors, quantization, channel transmission, and environmental factors [38, 53]. Moreover, this task also holds considerable importance in fiber communication systems [4, 21]. As fiber communication links extend, the noise during mode communication inevitably degrades communication quality and increases the complexity of signal processing [14, 62].
+
+Considering the pivotal role of image denoising, substantial research has been undertaken on noise reduction utilizing electronic chip-based devices. These methods can be broadly categorized into two groups: traditional denoisers such as Wiener filtering [17] and block-matching and 3D filtering (BM3D) [13], and deep neural network (DNN)-based methods [35, 39], such as denoising convolutional neural network (DnCNN) [54], real image denoising network (RIDNet) [3], and masked training (MT) [11]. Despite being promising, these methods are time-consuming and impose substantial computational burdens [24, 40]. Consequently, exploring more efficient and effective computational platforms such as optical computing and quantum computing presents an intriguing avenue. Diffractive Deep Neural Network  $(\mathrm{D}^2\mathrm{NN})$  [33] is an all-optical diffractive neural network trained via deep learning, demonstrating impressive processing speed and performance. However, due to its oversight of noise filtering during training and its limited feature representation capability, the denoising performance of this architecture is considerably inferior to that of electronic chip-based methods [23, 36].
+
+This paper introduces a novel all-optical Nonlinear Diffractive Denoising Deep Network (N3DNet) designed to filter out image noise at the speed of light. To construct N3DNet, we first incorporate an image encoding and predenoising module into the original  $\mathrm{D}^2\mathrm{NN}$ , with the goal of achieving preliminary noise suppression and signal enhancement. Furthermore, we integrate a novel nonlinear activation function, termed the phase exponential linear (PEL) function, following each phase modulation layer within the network, thereby enhancing its feature representation capability and flexibility. The entire structure of the proposed N3DNet is depicted in Fig. 1, consisting of a sequence
+
+![](images/b78d6b68b2b4d4f4b30c3226b90da4a0d727073f53cb4fb72b991861ae46d717.jpg)  
+Figure 1. Schematic of the proposed N3DNet framework. We illustrate an example of utilizing N3DNet for mode image denoising, which is trained using the RA-DQN algorithm.
+
+of consecutive nonlinear phase modulation planes (layers), all of which are transmissive. This innovative diffractive architecture can achieve ultrafast image denoising by utilizing optical diffraction and the pixel-level global attention mechanism to eliminate noise-related optical modes while preserving the features of interest. By selectively diffracting each cell in N3DNet and employing the nonlinear layer to alter phase values, exquisite manipulation of the output image is achieved. Consequently, after computer-based training, N3DNet generates denoised images at the speed of light in real-world applications, eliminating the need for any digital computation. To optimize N3DNet, we design a new reinforcement learning algorithm called regularization-assisted deep Q-network (RA-DQN), which significantly enhances N3DNet's convergence performance and improves the network's convergence speed. Ultimately, by leveraging the trained network parameters, we fabricate N3DNet using 3D printing and establish a physical experimental system to facilitate its practical application.
+
+Extensive simulation and real experiments are conducted on both mode image and benchmark image processing datasets. Given that previous studies on mode processing in fiber communication systems have primarily relied on optical devices that necessitate only device design without the need for training [16, 37], accessible datasets in this domain are lacking. Taking the initiative, we introduce a dedicated mode image denoising dataset (MIDD) for six linearly polarized (LP) modes and three orbital angular momentum (OAM) modes that are widely used in scientific research and commercial fiber communication systems [30, 44]. This dataset consists of  $100\mathrm{K}$  noisy mode images for training and  $20\mathrm{K}$  noisy images for testing, all of which are captured from real-world fiber communication systems. In addition to MIDD, we conduct experiments on four synthetic noisy datasets and two real-world
+
+noisy datasets. The comprehensive experiments demonstrate that N3DNet significantly enhances denoising performance compared to previous optical computing methods while maintaining nearly identical processing speed. Specifically, it achieves an average performance improvement of 9.15 dB in PSNR, 0.248 in SSIM, and 0.202 in LPIPS compared to the best-performing optical computing methods. The processing time of N3DNet reaches the microsecond level, while its power consumption is in the nanojoule range. Moreover, in comparison with electronic chip-based noise reduction approaches, including both traditional and DNN-based methods, N3DNet not only achieves state-of-the-art (SOTA) performance but also boosts processing speed by nearly 3,800 times.
+
+Overall, the main contributions are outlined as follows:
+
+- We introduce N3DNet, an all-optical nonlinear diffractive deep neural network designed for image denoising at the speed of light.  
+- We propose an RA-DQN algorithm to optimize N3DNet, which is then fabricated using 3D printing to develop a physical experimental system for real-world applications.  
+- We introduce MIDD, a benchmark dataset for mode image denoising. It consists of 120K images captured in real scenarios, including single-mode, few-mode, and multimode fibers across various transmission distances.  
+- We conduct extensive simulated and real experiments across various datasets. The results demonstrate that N3DNet achieves SOTA performance with remarkable efficiency, operating approximately 3,800 times faster than methods relying on electronic chips.
+
+# 2. Related Work
+
+Image denoising is a critical aspect across various domains [9, 22, 50, 59], which aims to improve image qual
+
+ity by estimating clean images from noisy observations [15, 49, 61]. Over the years, researchers have proposed numerous denoising techniques based on electronic chips. Traditional methods include non-local means [8], total variation regularization [2], and BM3D [13]. More recently, DNN-based approaches, such as convolutional neural networks (CNNs) [31] and generative adversarial networks (GANs) [12], have shown superior performance in preserving fine details while effectively removing noise [32, 45, 54]. However, despite great potential, these methods frequently impose substantial computational burdens and latency issues, thereby limiting their scalability, especially in resource-constrained environments.
+
+Diffractive deep neural network (D $^2$ NN) [33] represents an all-optical diffractive neural network trained via deep learning [28], which comprises multiple transmitting and diffractive phase planes, each adorned with numerous neurons manipulating or guiding incident light through diffraction. In comparison with methods deployed on electronic devices [12, 19], D $^2$ NN offers numerous advantages such as ultra-high speed, low power consumption, wavelength multiplexing, and polarization multiplexing [34, 36]. The phases or amplitudes of neurons serve as parameters awaiting training within D $^2$ NN. Through iterative modulations of incident light across multiple diffractive surfaces, D $^2$ NN can achieve the capability of all-optical inference [33, 40, 52]. Recently, researchers have proposed an analog diffractive image (ADI) denoiser [23] that leverages the D $^2$ NN architecture for image denoising. However, this method falls short of achieving satisfactory results due to its negligence of nonlinear modeling capability and reliance on suboptimal optimization strategies.
+
+# 3. Methodology
+
+This section first elaborates on the propagation diagram of N3DNet (§ 3.1), as depicted in Fig. 2, followed by the introduction of the reinforcement learning algorithm (§ 3.2) aimed at optimizing N3DNet. Ultimately, the construction of the physical experimental system utilizing N3DNet for real applications (§ 3.3), as shown in Fig. 3, is delineated.
+
+# 3.1. Nonlinear Diffractive Denoising Deep Network
+
+The forward propagation of N3DNet, as shown in Fig. 2, consists of two components: the image encoding and predenoising module (I) and the all-optical diffractive propagation module (II). These components represent the encoding process of images and the transmission of optical signals in free space (prior to the input layer), as well as the propagation of optical signals across nonlinear diffractive layers, respectively.
+
+![](images/5e70b1b458d3ea5d19f30a32691ba75d1bde18270890b60418b6442165f496cc.jpg)  
+Figure 2. Forward propagation diagram of N3DNet.
+
+# 3.1.1. Image Encoding and Pre-Denoising Module
+
+The noisy input image is initially encoded onto an optical carrier through amplitude modulation [56, 57] in free space. This encoded signal can be represented as
+
+$$
+\boldsymbol {E} (x, y, z) = \boldsymbol {A} _ {s} (x, y) A _ {0} \exp \left[ - j \boldsymbol {k} \cdot \boldsymbol {r} (x, y, z) \right], \tag {1}
+$$
+
+where  $A_0$  and  $\pmb{A}_s(x,y)$  refer to the amplitude of the carrier light and the image signal, respectively. Moreover,  $\pmb{r} = x\pmb{e}_x + y\pmb{e}_y + z\pmb{e}_z$  denotes the position vector at point  $(x,y,z)$  and  $\pmb{k} = k_{x}\pmb{e}_{x} + k_{y}\pmb{e}_{y} + k_{z}\pmb{e}_{z}$  is the wave vector, which delineates the wave's propagation direction. It satisfies  $|\pmb{k}| = 2\pi /\lambda$ , where  $\lambda$  denotes the work wavelength. Additionally,  $j = \sqrt{-1}$  represents the imaginary unit.
+
+To achieve preliminary noise suppression and signal enhancement, we perform an optical Fourier transform on the encoded signal, followed by bandpass filtering. The filtered signal is represented as
+
+$$
+\boldsymbol {h} (x, y, z) = \mathcal {F} ^ {- 1} \left\{H (\tilde {u}, \tilde {v}) \cdot \mathcal {F} [ \boldsymbol {E} (x, y, z) ] \right\}, \tag {2}
+$$
+
+where  $H(\tilde{u},\tilde{v})$  denotes a bandpass filter with center frequency  $\tilde{u}$  and bandwidth  $\tilde{v}$ .  $\mathcal{F}(\cdot)$  and  $\mathcal{F}^{-1}(\cdot)$  represent the Fourier transform function and its inverse, respectively.
+
+Drawing from the Rayleigh-Sommerfeld diffraction equation [48], each neuron within the layers of N3DNet is regarded as a secondary source of a wave consisting of the following optical mode:
+
+$$
+w _ {i} ^ {l} (x, y, z) = \frac {z - z _ {i}}{d ^ {2}} \left(\frac {1}{2 \pi d} + \frac {1}{j \lambda}\right) \exp \left(\frac {j 2 \pi d}{\lambda}\right), \quad (3)
+$$
+
+where  $l$  denotes the  $l$ -th layer of the network,  $i$  represents the  $i$ -th neuron located at  $(x_{i},y_{i},z_{i})$  of layer  $l$ , and  $d$  is calculated as  $d = \sqrt{(x - x_i)^2 + (y - y_i)^2 + (z - z_i)^2}$ . Across our diffractive neural network, all neurons adhere to the optical propagation process. The input pattern  $h_i(x_i,y_i,z_i)$  of the  $i$ -th neuron in the input plane, is in general a complex-valued quantity and can carry information in its phase and amplitude channels. Accordingly, the resulting wave function  $g_i^0$  on the input layer of N3DNet is generated through the diffraction of the plane-wave interacting
+
+with the input:
+
+$$
+g _ {i} ^ {0} (x, y, z) = w _ {i} ^ {0} (x, y, z) h _ {i} \left(x _ {i}, y _ {i}, z _ {i}\right), \tag {4}
+$$
+
+which connects the input to the neurons of the first hidden layer, as shown in Fig. 2. Subsequently, the optical wave will propagate through the  $M$  hidden layers in N3DNet, as elaborated in the subsequent section.
+
+# 3.1.2. All-Optical Diffractive Propagation Module
+
+The amplitude and relative phase of the secondary wave are determined by the product of the input wave to the neuron and its transmission coefficient  $(p_i^l)$ , both of which are complex-valued functions. Consequently, the output of the  $i$ -th neuron in the  $l$ -th layer,  $g_i^l(x,y,z)$ , is calculated as
+
+$$
+g _ {i} ^ {l} = f _ {P E L} \left\{w _ {i} ^ {l} (x, y, z) p _ {i} ^ {l} \left(x _ {i}, y _ {i}, z _ {i}\right) \sum_ {k} g _ {k, i} ^ {l - 1} \right\}, \tag {5}
+$$
+
+where  $g_{k,i}^{l-1}(x_i, y_i, z_i)$  denotes the output from the  $k$ -th neuron in the  $(l-1)$ -th diffractive layer incident on the  $i$ -th neuron in the  $l$ -th layer. Accordingly, the term  $\sum_k g_{k,i}^{l-1}(x_i, y_i, z_i)$  represents the input wave to the  $i$ -th neuron in layer  $l$ . Besides,  $f_{PEL}$  refers to our proposed PEL activation function, which is
+
+$$
+f _ {P E L} (X) = \left\{ \begin{array}{l l} \beta X \exp (\alpha X), & \text {i f} X > 0, \\ 0, & \text {o t h e r w i s e .} \end{array} \right. \tag {6}
+$$
+
+To obtain this activation function, we initially utilize metasurface [18] composed of  $Si_{3}N_{4}$  and Er-doped  $TiO_{2}$  to achieve phase modulation in the incident light. Then, we collect data pairs consisting of input and output phases, and fit these data pairs to obtain Eq. (6), with  $\alpha = 0.5$  and  $\beta = 0.2$ . The secondary waves undergo diffraction between layers and interfere with each other to form a complex wave at the surface of the next layer, thereby supplying input to its neurons, as illustrated in Fig. 2.  $p_{i}^{l}(x_{i},y_{i},z_{i})$  in Eq. (5) refers to the transmission coefficient of the  $i$ -th neuron in layer  $l$ , expressed as a complex-valued function, and calculated as
+
+$$
+p _ {i} ^ {l} (x _ {i}, y _ {i}, z _ {i}) = a _ {i} ^ {l} \left(x _ {i}, y _ {i}, z _ {i}\right) \exp \left[ j \phi_ {i} ^ {l} \left(x _ {i}, y _ {i}, z _ {i}\right) \right], \quad (7)
+$$
+
+where  $a_{i}^{l}$  indicates the amplitude term of the  $i$ -th neuron in the  $l$ -th layer, and  $\phi_{i}^{l}$  is its phase term, with  $0 \leq a_{i}^{l} \leq 1$  and  $-\pi \leq \phi_{i}^{l} \leq \pi$ .
+
+From Eq. (5), the cells of the  $l$ -th phase plane perform complex modulation on the light, thereby modifying the original information of the optical wave. For a better understanding of these changes, Eq. (5) can be redefined with the relative amplitude of the secondary wave  $\hat{A}_i^l$  and the additional phase delay  $\Delta \Omega_i^l$  that the secondary wave encounters due to the input wave to the neuron and its transmission coefficient. Consequently, we have  $g_i^l(x,y,z) = f_{PEL}\{w_i^l(x,y,z) \hat{A}_i^l \exp(j\Delta \Omega_i^l)\}$ .
+
+In summary, each hidden layer involves computations of Eqs. (5) and (7), culminating in its output  $g^{l} \in \mathbb{R}^{H \times W}$ . Assuming N3DNet comprises  $M$  hidden layers (excluding the input and output planes), the input plane's output  $g_{i}^{0}$  is propagated through these  $M$  layers. The intensity of the resulting optical field  $I^{a}$  detected at the output plane can be expressed as:
+
+$$
+I _ {i} ^ {a} = \left| g _ {i} ^ {M + 1} \right| ^ {2}, \tag {8}
+$$
+
+where  $g_{i}^{M + 1} = \sum_{k}g_{k,i}^{M}\left(x_{i},y_{i},z_{i}\right)$  denotes the output of the  $i$ -th neuron in the output plane and  $|g_i^{M + 1}|$  represents its magnitude. Based on this forward propagation process, the results of the output plane  $I^a$  are compared with the intensity of the targets  $I^{t}$  and the resulting errors are backpropagated to iteratively update N3DNet.
+
+# 3.2. Training Algorithm of N3DNet
+
+To optimize N3DNet, we propose a novel reinforcement learning algorithm, named RA-DQN, which is adapted from DQN [41]. Its reward  $\mathcal{R}$  equals the negative loss  $\mathcal{L}$  of N3DNet, consisting of three components: Charbonnier loss [27]  $\mathcal{L}_{\mathcal{C}}$ , Fourier loss  $\mathcal{L}_{\mathcal{F}}$ , and FSIM loss [25]  $\mathcal{L}_{\mathcal{S}}$ . Among these,  $\mathcal{L}_{\mathcal{C}}$  assesses the disparity between the pixel values of the network outputs and targets. To restore high-frequency information in images,  $\mathcal{L}_{\mathcal{F}} = L_{1}(\mathcal{F}(\boldsymbol{I}^{a}), \mathcal{F}(\boldsymbol{I}^{t}))$  directs the model to learn frequency domain features and restore high-frequency information as effectively as possible, where  $L_{1}(\cdot, \cdot)$  represents the  $L_{1}$  loss. Additionally,  $\mathcal{L}_{\mathcal{S}}$  evaluates image quality by comparing the structure and features. Accordingly, the loss function utilized to optimize N3DNet is calculated as
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathcal {C}} \left(\boldsymbol {I} ^ {a}, \boldsymbol {I} ^ {t}\right) + \hat {\alpha} \mathcal {L} _ {\mathcal {F}} \left(\boldsymbol {I} ^ {a}, \boldsymbol {I} ^ {t}\right) + \hat {\beta} \mathcal {L} _ {\mathcal {S}} \left(\boldsymbol {I} ^ {a}, \boldsymbol {I} ^ {t}\right), \tag {9}
+$$
+
+where  $I^a$  and  $I^t$  represent the outputs and targets, respectively. Moreover,  $\hat{\alpha}$  and  $\hat{\beta}$  are two modulating hyperparameters used to adjust the relative strength of each loss term.
+
+During the optimization process, the state  $S$  refers to the phase values of neurons in all diffractive layers, denoted as  $\phi_i^l$ , where  $i$  ranges from 1 to  $H \times W$  and  $l$  ranges from 1 to  $M$ , with  $H \times W$  representing the number of cell grids in a phase plane. The action  $\mathcal{A}$  represents the phase changes across all cells, denoted as  $\Delta \phi_i^l$ . At each step  $t$ , the RA-DQN agent receives the current state  $S_t$  and outputs an action  $\mathcal{A}_t$ . Subsequently, the environment (i.e., N3DNet) generates a new state  $(S_{t+1})$  and reward  $\mathcal{R}_{t+1}$  based on  $\mathcal{A}_t$ . Consequently, the agent continually updates its parameters to enhance its decision-making abilities. The core of this process is the following value function iteration:
+
+$$
+\begin{array}{l} Q _ {\boldsymbol {\theta}} \left(\mathcal {S} _ {t}, \mathcal {A} _ {t}\right) \leftarrow Q _ {\boldsymbol {\theta}} \left(\mathcal {S} _ {t}, \mathcal {A} _ {t}\right) + \\ \gamma \left[ \mathcal {R} _ {t + 1} + \epsilon \max  _ {\mathcal {A}} \hat {Q} _ {\hat {\theta}} \left(\mathcal {S} _ {t + 1}, \mathcal {A}\right) - Q _ {\theta} \left(\mathcal {S} _ {t}, \mathcal {A} _ {t}\right) \right], \tag {10} \\ \end{array}
+$$
+
+![](images/a0042c1286036f0ed2c011b15a9d6a1e38444e5e2a6589ab79ebb0a5ee89b468.jpg)  
+Figure 3. Physical experimental system for applying N3DNet. The image is first encoded by the DMD, then undergoes a Fourier transform, bandpass filtering, and an inverse Fourier transform through a 4f system. Subsequently, it is denoised using the diffractive phase planes of N3DNet and finally captured by the CCD for imaging.
+
+![](images/6435e73234ffdd7242f14f839d4813fd585b148cca2a0fac90d483ed5e191044.jpg)
+
+where  $\theta$  and  $\hat{\theta}$  refer to the parameters of the deep Q-network  $Q$  and the target network  $\hat{Q}$ , respectively.  $\gamma$  and  $\epsilon$  represent the learning rate and discount factor, respectively, with settings following those of previous studies [20, 41, 47]. To enhance training stability, we apply a penalty to the disparity in Q-values between consecutive time steps when training the Q-network. Therefore, we minimize
+
+$$
+\begin{array}{l} \tilde {\mathcal {L}} (\boldsymbol {\theta}) = \left[ \mathcal {R} _ {t + 1} + \epsilon \max  _ {\mathcal {A}} \hat {Q} _ {\hat {\boldsymbol {\theta}}} \left(\mathcal {S} _ {t + 1}, \mathcal {A}\right) - Q _ {\boldsymbol {\theta}} \left(\mathcal {S} _ {t}, \mathcal {A} _ {t}\right) \right] ^ {2} \\ + \kappa \left[ Q _ {\boldsymbol {\theta}} \left(\mathcal {S} _ {t}, \mathcal {A} _ {t}\right) - Q _ {\boldsymbol {\theta}} \left(\mathcal {S} _ {t - 1}, \mathcal {A} _ {t - 1}\right) \right] ^ {2}, \tag {11} \\ \end{array}
+$$
+
+to optimize the deep Q-network, where  $\kappa$  denotes the regularization factor.
+
+# 3.3. Physical Experimental System
+
+The physical experimental system using N3DNet for image denoising is illustrated in Fig. 3. The energy source (optical carrier) is generated using a solid-state fiber laser operating at a wavelength of  $1,550~\mathrm{nm}$ . The coherent light wavefront is collimated using a relay lens, denoted as L1, followed by ensuring the single polarization property of the incident light using a polarizer, denoted as P1. Subsequently, the coherent light is reflected onto a digital micromirror device (DMD) at the correct incident angle utilizing a mirror. The DMD, which is mounted on a controller board, consists of  $1,280 \times 1,024$  micro-mirrors with a pitch of  $10.8\mu \mathrm{m}$ . Consequently, through the modulation of the DMD, images can be encoded onto the incident light.
+
+The optical field from the DMD is then directed into a 4f optical system [10], which is composed of two relay lenses (L2 and L3), a linear polarizer (P2), and a Fabry-Perot filter (FPF). Among these, L2 performs the Fourier transform; P2 ensures the single polarization property; FPF positioned at the Fourier plane achieves bandpass filtering; and L3 conducts the inverse Fourier transform. Utilizing 3D printing techniques, the hidden layers of N3DNet are fabricated
+
+![](images/d2174ab5c6bf0cec8e39a7e7586e9ed792cb70a5f72211daac92cb26e8048668.jpg)  
+Figure 4. Illustration of the nine modes in the MIDD dataset. Top: Noise mode images. Below: Clean mode images.
+
+with the trained parameters to modulate optical signals. The N3DNet consists of  $5 \times 1,000 \times 1,000$  modulation elements, each with a size of  $40~\mu \mathrm{m}$ . After processing by the 4f optical system, the optical signal is modulated by the hidden layers of N3DNet, which are fabricated by a standard 3D-printing material (VeroBlackPlus RGD875) that have a high zero-order diffraction efficiency of  $97\%$  [33]. Ultimately, the modulated light from the N3DNet is captured by a sensor (located in an infrared-enhanced charge-coupled device, CCD) for optical decoding onto the CCD imaging plane.
+
+# 4. Experimental Investigation
+
+# 4.1. Configuration
+
+Datasets. Currently, no existing dataset is available for mode image denoising in fiber communication systems. Therefore, we develop a benchmark MIDD dataset, which covers nine different modes, including six LP modes  $\mathrm{(LP_{01}}$ ,  $\mathrm{LP}_{11\mathrm{a}}$ ,  $\mathrm{LP}_{11\mathrm{b}}$ ,  $\mathrm{LP}_{21\mathrm{a}}$ ,  $\mathrm{LP}_{21\mathrm{b}}$ , and  $\mathrm{LP}_{02}$ ) and three OAM modes  $\mathrm{(OAM_1}$ ,  $\mathrm{OAM}_2$ , and  $\mathrm{OAM}_3$ ), as shown in Fig. 4.
+
+The dataset is generated through transmissions and imaging using various types of optical fibers. A standard optical fiber communication system [30] was employed for data collection, comprising a laser source with a communication wavelength of  $1,550\mathrm{nm}$ , a transmitter, an optical fiber, a lens, and an infrared-enhanced CCD. To construct the MIDD dataset, approximately 200 noisy images were
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">σ/ll</td><td colspan="5">PSNR (↑)</td><td colspan="5">SSIM (↑)</td><td colspan="5">LPIPS (↓)</td></tr><tr><td>BM3D</td><td>DnCNN</td><td>RIDNet</td><td>MT</td><td>N3DNet</td><td>BM3D</td><td>DnCNN</td><td>RIDNet</td><td>MT</td><td>N3DNet</td><td>BM3D</td><td>DnCNN</td><td>RIDNet</td><td>MT</td><td>N3DNet</td></tr><tr><td rowspan="2">MIDD</td><td>20</td><td>28.89</td><td>29.07</td><td>29.10</td><td>28.95</td><td>30.15</td><td>0.835</td><td>0.817</td><td>0.855</td><td>0.849</td><td>0.939</td><td>0.207</td><td>0.204</td><td>0.185</td><td>0.190</td><td>0.130</td></tr><tr><td>40</td><td>26.21</td><td>26.85</td><td>26.90</td><td>27.25</td><td>28.12</td><td>0.782</td><td>0.775</td><td>0.791</td><td>0.791</td><td>0.914</td><td>0.353</td><td>0.335</td><td>0.317</td><td>0.302</td><td>0.197</td></tr><tr><td rowspan="2">CSet9</td><td>25</td><td>29.95</td><td>31.65</td><td>31.71</td><td>31.70</td><td>31.68</td><td>0.941</td><td>0.955</td><td>0.955</td><td>0.957</td><td>0.967</td><td>0.162</td><td>0.155</td><td>0.170</td><td>0.165</td><td>0.101</td></tr><tr><td>50</td><td>27.46</td><td>28.93</td><td>29.26</td><td>29.29</td><td>30.01</td><td>0.902</td><td>0.922</td><td>0.927</td><td>0.923</td><td>0.930</td><td>0.289</td><td>0.268</td><td>0.234</td><td>0.238</td><td>0.175</td></tr><tr><td rowspan="2">CBSD68</td><td>25</td><td>28.69</td><td>30.48</td><td>30.67</td><td>30.73</td><td>30.70</td><td>0.900</td><td>0.931</td><td>0.932</td><td>0.933</td><td>0.941</td><td>0.157</td><td>0.149</td><td>0.146</td><td>0.150</td><td>0.095</td></tr><tr><td>50</td><td>25.79</td><td>27.35</td><td>27.65</td><td>27.68</td><td>28.12</td><td>0.836</td><td>0.870</td><td>0.878</td><td>0.882</td><td>0.880</td><td>0.328</td><td>0.300</td><td>0.245</td><td>0.242</td><td>0.190</td></tr><tr><td rowspan="2">Set12</td><td>25</td><td>27.59</td><td>29.92</td><td>30.01</td><td>29.96</td><td>30.05</td><td>0.777</td><td>0.842</td><td>0.850</td><td>0.845</td><td>0.855</td><td>0.220</td><td>0.159</td><td>0.120</td><td>0.162</td><td>0.159</td></tr><tr><td>50</td><td>24.62</td><td>26.52</td><td>26.48</td><td>26.68</td><td>26.80</td><td>0.712</td><td>0.731</td><td>0.702</td><td>0.765</td><td>0.780</td><td>0.359</td><td>0.262</td><td>0.242</td><td>0.315</td><td>0.195</td></tr><tr><td rowspan="2">BSD68</td><td>25</td><td>28.58</td><td>29.00</td><td>29.31</td><td>29.55</td><td>29.93</td><td>0.800</td><td>0.817</td><td>0.801</td><td>0.785</td><td>0.820</td><td>0.262</td><td>0.221</td><td>0.197</td><td>0.231</td><td>0.148</td></tr><tr><td>50</td><td>25.60</td><td>26.09</td><td>26.42</td><td>26.83</td><td>27.35</td><td>0.682</td><td>0.705</td><td>0.688</td><td>0.694</td><td>0.715</td><td>0.443</td><td>0.361</td><td>0.315</td><td>0.308</td><td>0.251</td></tr></table>
+
+![](images/cd97a7d342b364bfbe372418ea986bbcd0901c0a987d2cc17c6d49dac1e132d2.jpg)  
+$\sigma = 50$  
+15.54/0.611
+
+![](images/b8ba3523c381ef28058c464aa7287695bd53e03a18ce77c8f94899c7b3790925.jpg)  
+MPLC  
+16.25/0.603  
+Figure 5. Visualization (simulation experiments) showcasing the denoising performance of various methods on an image from CSet9.
+
+![](images/4d1473aa4e9c20138b148965617eaef42aab70171b4faa6b5e3ae6bd9dc34f80.jpg)  
+BM3D  
+27.44/0.290
+
+![](images/200e8da95175b810ca9114e10f9d804f302378f855a45327260e0de533200f03.jpg)  
+RIDNet  
+28.83/0.257
+
+![](images/47630ee4d45aa19cb4353556c6aa41db2560fed986ca02e841284ab81e0f059d.jpg)  
+MT  
+29.26/0.238
+
+![](images/68cd435b289f2d5a6398d5cedcbd23aa7e9128cc3ce0aac020ab5c92df4f7f5d.jpg)  
+N3DNet  
+30.00/0.181
+
+![](images/75323a036c2c6956c171e22bb60a075d6ce91387e10013213da32196e31ca257.jpg)  
+Ground truth  
+PSNR/LPIPS
+
+Table 1. Comparison of simulation results with advanced electronic chip-based denoising algorithms.  $\uparrow (\downarrow)$  denotes higher (lower) values are better. The best performance is highlighted in bold, while the second best is underlined.  
+
+<table><tr><td>Dataset</td><td>BM3D</td><td>DnCNN</td><td>RIDNet</td><td>MT</td><td>N3DNet</td></tr><tr><td>Nam</td><td>37.30</td><td>35.55</td><td>39.09</td><td>39.11</td><td>39.31</td></tr><tr><td>SIDD</td><td>30.88</td><td>26.21</td><td>38.71</td><td>38.90</td><td>38.97</td></tr></table>
+
+Table 2. The PSNR results for the two noisy real-world datasets.
+
+collected for each of ten different types and manufacturers of fibers: single-mode, few-mode, and multi-mode, across 50 transmission lengths  $(l)$  ranging from  $1\mathrm{km}$  to  $50\mathrm{km}$ . This process yields over 100K mode images in total. Clean images were acquired with transmission distances of less than  $1\mathrm{m}$ . Additionally, to assess the noise reduction performance, a total of 20K noisy mode images were collected for three additional optical fibers at transmission lengths of  $5\mathrm{km}$ ,  $12\mathrm{km}$ ,  $20\mathrm{km}$ ,  $24\mathrm{km}$ ,  $36\mathrm{km}$ ,  $40\mathrm{km}$ , and  $50\mathrm{km}$ . The data acquisition device was situated on a physics laboratory bench in the basement, designed to mitigate external interference from static electricity and vibrations.
+
+Besides the MIDD data, we assess the performance of various denoising methods on four widely recognized image datasets: CSet9, CBSD68, Set12, and BSD68. The synthetic training data with Gaussian noise for these test sets are generated following the methodology outlined by Chen et al. [11]. Additionally, we incorporate two noisy real-world datasets, namely Nam [43] and SIDD [1], with the training and testing data constructed in accordance with the methodology outlined by Anwar et al. [3].
+
+Evaluation Metrics. Building upon previous research [11, 45], we evaluate the performance of various methods using three image quality and perceptual metrics, including PSNR (dB) [26], SSIM [7], and LPIPS [55]. Furthermore, we compare the time and energy consumption of various denoising methods to assess their scalability.
+
+Settings. In the simulation experiments, the 5 hidden layers (diffractive phase planes) in N3DNet operate at an incident wavelength (i.e., center frequency in the bandpass filter) of  $1,550~\mathrm{nm}$ . These planes are spaced  $5\mathrm{mm}$  apart, each followed by a PEL activation layer. Moreover, every layer has dimensions of  $40~\mathrm{mm} \times 40~\mathrm{mm}$  and is divided into a grid of  $1,000 \times 1,000$  cells. The input and output layers have the same structure (including the number of units and plane spacing) as the hidden layer, except for omitting the PEL layer. Furthermore, the bandwidth of the bandpass filter is set to  $500\mathrm{GHz}$ . The model is trained from scratch using the RA-DQN algorithm with an initial learning rate of  $1 \times 10^{-4}$  and a batch size of 32 for 2,000 iterations. The values of the three hyperparameters in the training process,  $\hat{\alpha}, \hat{\beta}$ , and  $\kappa$ , are set to 0.1, 0.5, and  $5 \times 10^{-3}$ , respectively. All computations are performed on a Linux x64 server equipped with a 20-core 2.40 GHz CPU processor, 128 GB of RAM, and an NVIDIA RTX 3090 GPU. The experimental setups for all comparative methods are consistent with those described in the original papers. For real experiments, all electronic chip-based methods, e.g., MT, are quantized to INT8 and
+
+<table><tr><td rowspan="2">l</td><td colspan="5">PSNR (↑)</td><td colspan="5">SSIM (↑)</td><td colspan="5">LPIPS (↓)</td></tr><tr><td>W/o</td><td>MPLC</td><td>MT</td><td>ADI</td><td>N3DNet</td><td>W/o</td><td>MPLC</td><td>MT</td><td>ADI</td><td>N3DNet</td><td>W/o</td><td>MPLC</td><td>MT</td><td>ADI</td><td>N3DNet</td></tr><tr><td>12</td><td>14.13</td><td>15.81</td><td>28.35</td><td>22.75</td><td>29.87</td><td>0.591</td><td>0.587</td><td>0.844</td><td>0.751</td><td>0.934</td><td>0.410</td><td>0.407</td><td>0.191</td><td>0.285</td><td>0.132</td></tr><tr><td>24</td><td>14.02</td><td>15.15</td><td>27.71</td><td>20.39</td><td>28.93</td><td>0.481</td><td>0.489</td><td>0.830</td><td>0.708</td><td>0.929</td><td>0.485</td><td>0.465</td><td>0.195</td><td>0.352</td><td>0.198</td></tr><tr><td>36</td><td>12.78</td><td>13.89</td><td>26.21</td><td>17.83</td><td>27.45</td><td>0.458</td><td>0.480</td><td>0.793</td><td>0.637</td><td>0.899</td><td>0.521</td><td>0.492</td><td>0.306</td><td>0.426</td><td>0.205</td></tr><tr><td>50</td><td>11.09</td><td>11.25</td><td>25.03</td><td>15.17</td><td>26.47</td><td>0.412</td><td>0.431</td><td>0.754</td><td>0.553</td><td>0.877</td><td>0.663</td><td>0.635</td><td>0.337</td><td>0.508</td><td>0.230</td></tr></table>
+
+Table 3. Comparison of the results from real experiments with existing methods across various transmission lengths in the MIDD dataset. "W/o" denotes the results without denoising.
+
+![](images/f91f46905500f3f1bb237ba89790f3d07818a471ba2680b9267950dbe6a0e90b.jpg)  
+Figure 6. Visualization (real experiments) of N3DNet's denoising performance in the  $\mathrm{LP}_{21\mathrm{b}}$  mode under varying values of  $l$ .
+
+deployed on the Snapdragon 8 Gen 3 high-end SoC.
+
+# 4.2. Main Results
+
+Simulation Experiments. We compare N3DNet with both traditional and advanced electronic chip-based denoising methods, including BM3D [13], DnCNN [54], RIDNet [3], and MT [11]. DnCNN and RIDNet are based on CNNs, while MT is based on visual transformers. Table 1 presents the comparative results for the MIDD and four synthetic noisy datasets, underscoring that N3DNet achieves superior denoising performance across all three metrics. Specifically, it outperforms the best-performing baselines by an average of  $0.43\mathrm{dB}$  in PSNR, 0.032 in SSIM, and 0.066 in LPIPS. The effectiveness of N3DNet primarily stems from its reliance on pixel-level computations driven by the interference and diffraction of light. Because of interference and diffraction effects, it is possible to control both the intensity and phase of light at any point with a broader perspective. This method is significantly more complex than the multilayer structure in electronic chip-based neural networks, which only involve real-valued weights.
+
+Moreover, Fig. 5 visually compares the denoising performance of various methods, where MPLC is a traditional mode processor. The results demonstrate that N3DNet achieves SOTA denoising performance. Table 2 demonstrates the effectiveness of our approach on real-world noisy datasets. It is clear that N3DNet outperforms RIDNet and MT by a margin of  $0.24\mathrm{dB}$  and  $0.14\mathrm{dB}$ , respectively.
+
+Real Experiments. We utilize the constructed physical experimental system to perform real experiments on the MIDD dataset. Table 3 presents the comparison results among MPLC [6], MT [11], ADI [23], and N3DNet, where
+
+ADI directly utilizes the  $\mathrm{D}^2\mathrm{NN}$  architecture for image denoising. N3DNet consistently exhibits SOTA performance across a range of noise levels, underscoring its effectiveness in real-world denoising applications. Specifically, it demonstrates an average performance improvement of 9.15 dB in PSNR, 0.248 in SSIM, and 0.202 in LPIPS compared to the best-performing optical computing methods. Conversely, optical devices such as MPLC struggle with mode image denoising, resulting in poor performance. While ADI demonstrates improved performance compared to MPLC, its denoising capability is significantly inferior to that of N3DNet. This is primarily attributed to its suboptimal model structure and the oversight of the nonlinear modeling capabilities.
+
+It is worth noting that the results of N3DNet's physical experiments are slightly inferior to the numerical simulation results. This discrepancy may be attributed to errors introduced by factors such as 3D printing, the optical system, and encoding. Nevertheless, the errors associated with N3DNet are comparable to or slightly smaller than those observed in algorithms, e.g., MT, deployed on electrical chips. Additionally, we visualize the denoising performance for mode images using N3DNet in Fig. 6. These images are captured by the CCD in the form of infrared imaging maps. As the level of noise increases, the proportion of energy in non-signal regions rises. Nevertheless, the results indicate that even in the presence of strong noise, N3DNet can achieve significant denoising performance.
+
+# 4.3. Ablation Studies
+
+Comparison of Optimization Algorithms. The loss variations of various optimization algorithms are illustrated in Fig. 7(a). The initial phase values of N3DNet for all algorithms are established using the same seed. In comparison to traditional gradient descent algorithms such as Adam and SGD, DQN-based methods demonstrate superior effectiveness in learning the state-action value function for N3DNet, as well as in enhancing learning efficiency through the implementation of experience replay and a target network. Moreover, by introducing a penalty for disparity in the Q-value, RA-DQN smoothes the optimization path and reduces unnecessary fluctuations, leading to faster convergence and improved performance compared to DQN. Remarkably, af-
+
+![](images/397dfe36a7a3f003ba3c22a76cb8a7e9634f09ffcae5051825e334815df359cb.jpg)  
+Figure 7. (a): Loss variation across epochs using different optimization algorithms on the MIDD dataset ( $l = 50$ ). (b) and (c): Comparison of time and energy consumption across different methods. (d): 3D distribution of loss across various distances in layers and wavelengths.
+
+![](images/7aaf9f3dd3090f0400960dfd33166bcf101d5a3b6883229d12cfb5cd9d81691e.jpg)
+
+![](images/fd861aead240a48d4dd4d3fd4932c934aae69ebe530534735e58cdcaa7b268f5.jpg)
+
+![](images/0b8477643d0fe020ddae7b4c389b78edd67b13b301abfd4fb7d8de8c4bd141f0.jpg)
+
+<table><tr><td>Lc</td><td>Lf</td><td>Ls</td><td>PSNR (↑)</td><td>SSIM (↑)</td><td>LPIPS (↓)</td></tr><tr><td>X</td><td>X</td><td>X</td><td>14.890.00</td><td>0.4840.00</td><td>0.4790.00</td></tr><tr><td>✓</td><td>X</td><td>X</td><td>27.530.39</td><td>0.8500.04</td><td>0.1810.05</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>29.320.45</td><td>0.8710.06</td><td>0.1520.04</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>28.780.37</td><td>0.8940.05</td><td>0.1780.03</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>23.580.42</td><td>0.7310.03</td><td>0.2790.05</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>30.560.37</td><td>0.9450.03</td><td>0.1030.04</td></tr></table>
+
+Table 4. Ablation study on the configuration of the loss function. Both the average performance and standard deviation are provided. The first row shows the results without denoising.
+
+ter training for less than 750 epochs, the N3DNet trained with the RA-DQN algorithm converges, whereas most traditional algorithms require more than 2,000 epochs. Additionally, the minimum loss achieved with the RA-DQN algorithm (1.78) is lower than those obtained with other algorithms (e.g., SGD, 2.70), indicating the superior convergence performance of RA-DQN.
+
+Calculation Efficiency. Figs. 7(b) and (c) compare the latency and energy consumption of seven approaches deployed in real mode image denoising experiments. Here, PL [29] and MPLC [6] represent optical devices; ADI [23] is an analog diffractive image denoiser; and BM3D [13], RIDNet [3], and MT [11] are electronic chip-based methods. Unlike devices based on electrical neural networks, N3DNet operates without the need for electrical signal modulation, offering the benefits of faster processing and lower power consumption. Although both N3DNet and electricity-based methods achieve high PSNR values, significant disparities exist in terms of time and energy consumption. For  $1,000 \times 1,000$  pixel images, our device's computation time per image is  $4.4\mu s$ , which is three orders of magnitude faster than electricity-based algorithms (16.7 ms, deployed on QualcommSnapdragon 8 Gen 3 SoC processor). Additionally, N3DNet consumes approximately six orders of magnitude less energy than electrical methods. Impressively, compared with optical computing approaches, N3DNet significantly enhances performance with
+
+nearly identical time and energy consumption.
+
+Stability Analysis of Distance in Layers and Wavelength. Considering the inevitable errors in the distance between layers (5 mm) and the wavelength of incident light (1,550 nm) during the real experiments, we investigate the influence of disturbances in distance and wavelength on the loss in numerical experiments. As depicted in Fig. 7(d), when the distance between layers ranges from 2 mm to 8 mm and the wavelength varies from 1,540 nm to 1,560 nm, the loss consistently remains below 1.81, only approximately 1.69% higher than the optimal value of 1.78. This discrepancy falls entirely within the acceptable range of errors in the real-world experimental setup, which facilitates convenient processing and experimentation.
+
+Analysis of Loss Function. We examine the influence of loss function configuration on the denoising performance of N3DNet. The average performance across various datasets with  $l = 12$  km is reported in Table 4. Our adopted loss function demonstrates the highest efficacy. Moreover, all three loss terms are necessary and crucial for enhancing the denoising performance of N3DNet.
+
+# 5. Conclusion
+
+This study introduces N3DNet, an innovative all-optical nonlinear diffractive neural network, designed for image denoising at the speed of light. A newly proposed reinforcement learning algorithm is employed to optimize N3DNet, which is then fabricated using 3D printing with the trained parameters. Ultimately, a physical experimental system is constructed to apply N3DNet in real-world scenarios. Through extensive simulation and real experiments, we demonstrate that N3DNet not only outperforms existing methods in denoising performance but also significantly boosts processing speed, achieving a speedup of 3,800 times compared to electronic chip-based approaches. Given the ultrafast image processing speed, future research could explore extending this framework to address broader challenges in computer vision, such as video denoising, image super-resolution, and image restoration.
+
+# Acknowledgments
+
+This work is partially supported by the Shenzhen Science and Technology Program (Grant No. RCBS20231211090517022).
+
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+# All-directional Disparity Estimation for Real-world QPD Images
+
+Hongtao Yu $^{1}$  Shaohui Song $^{1}$  Lihu Sun $^{1}$  Wenkai Su $^{1}$  Xiaodong Yang $^{2}$  Chengming Liu $^{2}$
+
+<sup>1</sup> OMNIVISION, Wuhan, China <sup>2</sup> OMNIVISION, Santa Clara, CA
+
+# Abstract
+
+Quad Photodiode (QPD) sensors represent an evolution by providing four sub-views, whereas dual-pixel (DP) sensors are limited to two sub-views. In addition to enhancing autofocus performance, QPD sensors also enable disparity estimation in horizontal and vertical directions. However, the characteristics of QPD sensors, including uneven illumination across sub-views and the narrow baseline, render algorithm design difficult. Furthermore, effectively utilizing the two-directional disparity of QPD sensors remains a challenge. The scarcity of QPD disparity datasets also limits the development of learning-based methods. In this work, we address these challenges by first proposing a DPNet for DP disparity estimation. Specifically, we design an illumination-invariant module to reduce the impact of illumination, followed by a coarse-to-fine module to estimate sub-pixel disparity. Building upon the DPNet, we further propose a QuadNet, which integrates the two-directional disparity via an edge-aware fusion module. To facilitate the evaluation of our approaches, we propose the first QPD disparity dataset QPD2K, comprising 2,100 real-world QPD images and corresponding disparity maps. Experiments demonstrate that our approaches achieve state-of-the-art performance in DP and QPD disparity estimation.
+
+# 1. Introduction
+
+Quad photodiode (QPD) sensors [29] represent an advanced evolution of dual-pixel (DP) sensors [34, 47], where four pixels of the same color use one on-chip lens [29]. Due to the exceptional auto-focus (AF) performance, QPD sensors have gained widespread adoption in mobile phones. While DP-based image processing tasks, including deblurring [1, 45, 48], deraining [22], reflection removal [32], as well as depth estimation [8, 49], have demonstrated promising prospects, research on QPD sensors is relatively scarce. This work aims to bridge this gap by exploring disparity estimation using QPD sensors.
+
+Disparity estimation based on QPD sensors, as depicted in Fig. 1, presents several distinct characteristics compared to conventional stereo matching methods. Firstly, the pixel
+
+design of QPD sensors causes uneven illumination across views. Secondly, the narrow baseline in QPD sensors yields a tiny disparity, further increasing the matching difficulty. Thirdly, QPD sensors provide disparity information in two directions and effectively fusing the two-directional disparity is crucial to achieving better performance than DP sensors. Additionally, the disparity only exists in out-of-focus regions, which increases the difficulty of obtaining accurate ground truth.
+
+One potential strategy to obtain disparity from real QPD data is to utilize methods developed for DP sensors. Several supervised learning-based methods directly estimate depth [8, 30] or defocus maps [43]. However, without focus-plane depth information, we cannot obtain the corresponding disparity [19]. FaceDPNet [18] estimates facial disparity and normals, but their method is limited to facial data. Self-supervised methods [19, 33] rely on the symmetry of the Point Spread Function (PSF). However, the PSF for real QPD data calibrated using Mannan and Langer's method [25] exhibits asymmetry and is susceptible to noise and uneven illumination, as detailed in the supplementary material. Another strategy involves treating the images as pairs for stereo matching, but this often yields poor results due to the characteristics of QPD sensors [28]. As a result, existing methods for obtaining QPD disparity exhibit suboptimal performance, mainly due to the lack of QPD disparity datasets and appropriate algorithms.
+
+To fully exploit the two-directional information, we initially design a DPNet to estimate the disparity for DP data. Firstly, to mitigate the adverse effects of uneven illumination, we introduce an illumination-invariant module by utilizing differential convolution [37] to extract illumination-invariant features. Next, to obtain sub-pixel disparity, we design a coarse-to-fine module, which iteratively refines the initial disparity by interpolating within the disparity range. We further propose the QuadNet, which integrates two-directional information via an edge-aware fusion module for QPD data. A Census-based refinement further refines the fused disparity. To validate the effectiveness of our networks, we propose a QPD disparity dataset containing 2,100 real-world images and corresponding disparity maps. Directly acquiring disparity in natural scenes is challenging
+
+![](images/bed30474f7c284f0b9fb55d2d915771c4c475447d88e60f5f237c1a42e611a46.jpg)  
+(A) QPD camera formulation
+
+![](images/987bcf7e7c5aebbd811256c842cbd16d475b3ba640e1daefb92e68ec70ecf135.jpg)  
+(B) Sub-images generation from QPD
+
+![](images/a66432b8c3ff5ac5c0ca2fca578667cd53d751815d7114f0e18c0270409bd8c6.jpg)  
+(C) QPD bidisparity sample
+
+![](images/f97ad0cb5229f9ceef2d7664911ce6d6737884a6caa082ef48361ec2e766385f.jpg)  
+(D) QPD data property  
+Figure 1. (A) The disparity of QPD sensors only presents in defocused regions. Additionally, QPD sensors can provide all-directional disparity [17], including horizontal and vertical disparity. (B) The light rays passing through the on-chip lens fall on four photodiodes, enabling the generation of four sub-images via pixel binning. (C) Horizontal bidisparity sample. (D) The left and right sub-images exhibit uneven brightness (the mean difference is 4.8). The disparity between sub-image pairs is relatively small (the disparity is 3.12 pixel).
+
+ing [19]. Therefore, we first use the structured light to obtain depth information and then compute the disparity via calibration using the disparity-depth relationship [18, 19]. In summary, our contributions are as follows:
+
+- We introduce the first QPD disparity dataset, which contains 2,100 real-world QPD images and corresponding disparity maps, denoted as QPD2K.  
+- We propose the DPNet for DP disparity estimation and the QuadNet for QPD disparity estimation, with three novel modules fully considering the characteristics of QPD sensors. Our experiments demonstrate that our networks achieve state-of-the-art (SOTA) performance in DP and QPD disparity estimation.
+
+# 2. Related Work
+
+Disparity for DP. The increasing interest in DP sensors has led to the creation of several real and synthetic DP datasets. To obtain accurate depth information, researchers have employed multi-view geometry techniques to compute the 'ground truth' depth of images captured by DP sensors [7, 8, 49]. Notably, Kang et al. [18] created a large-scale DP facial dataset using a multi-camera structured light system, while Pan et al. [30] introduced a novel DP simulator that leverages a physics-based model of the PSF and depth to generate a realistic DP dataset. Li et al. [20] proposed a neural network-based approach to replace traditional handcrafted imaging models, enabling greater flexibility and improved accuracy in generating DP datasets. However, a significant limitation of these datasets is their inability to estimate the disparity directly of DP data due to the absence of focus-plane depth information [19]. Wu et al. [42] recently proposed a new QPD disparity dataset synthesized using the PSF model [2] with depth data [35], which does not reflect the characteristics of real QPD data.
+
+The disparity estimation of DP data has two primary ap
+
+proaches. The first approach formulates it as a stereo matching problem, which is challenging due to the narrow baseline issue, particularly when the left and right sub-images of DP data are blurry. To address this challenge, FaceDPNet [18] proposed an adaptive sampling module, while Monin et al. [28] developed a Continuous Cost Aggregation (CCA) method to obtain continuous depth information by fitting parabolas to the matching cost. Garg et al. [8] pioneered a deep depth estimation network based on a U-net structure, which was further optimized by Zhang et al. [49] by fusing DP information. More recently, CADS [10] improved the disparity and All-In-Focus estimation from DP sensors, while QPDNet [42] effectively predicted a disparity map from QPD data. The second method involves utilizing DP sensors' PSF symmetry to estimate disparity. Kim [19] proposed a kernel-split symmetry loss, building upon DPdisp [33], an optimization method that exploits the PSF symmetry of the left-right images.
+
+Stereo matching. We conduct a thorough examination of RAFT-stereo [23] and its subsequent improvements [6, 15, 21]. Building upon the success of RAFT [39], RAFT-stereo [23] was proposed for stereo matching with iterative refinement. CREStereo [21] further enhanced the algorithm's stability by incorporating a Transformer module and a cascaded recurrent network. Subsequently, CREStereo++ [15] developed an uncertainty-guided adaptive warping module, which improves the network's robustness. Additionally, Zhao et al. [50] proposed an error-aware refinement module that combines left-right warping, and later introduced a decoupling module to alleviate data coupling issues, enabling the transfer of detailed features across iterations [51]. Wang et al. [40] proposed a Selective Recurrent Unit, which can additively fuse hidden disparity information at multiple frequencies for edge and smooth regions. Furthermore, the multi-peak lookup strategy [6] improved the model's ability to deal with multipeak distribution.
+
+![](images/a31094fbf0196915dc0004c7f83cf29efee8874e038089cb71af5d5c2fdd2040.jpg)  
+(A) QPD disparity hardware
+
+![](images/49cf5dd00fd98c2bea87bb7852c64006499f35ea5e76f1cb783bc5d97de04564.jpg)  
+(B) Initial
+
+![](images/3fe7aeb4f07caaf77d80bdd79ce9c25b5f6529ad26d2f42236808005b4c3a366.jpg)  
+(C) Refinement
+
+![](images/4d03550ce942470800cd22860ba6d332390bb4f6dddd0118f5eaca6a4fab3b88.jpg)  
+(D) Post-processing  
+Figure 2. (A) Our hardware setup: stereo QPD sensors and a DLP projector. (B) Initial depth from speckle structured light (point cloud visualization). (C) Refined depth from stripe structured light. (D) Final depth after post-processing. (E) Disparity map.
+
+![](images/80d3c6aa8d9741c74d6f4508654960bba13df22e02b36916968b5c29b85e809f.jpg)  
+(E) Disparity map
+
+# 3. QPD2K Dataset
+
+The disparity can be applied to various image restoration tasks, such as deblurring [46] and deraining [22]. Nevertheless, existing datasets are primarily composed of depth data and do not provide corresponding focus-plane depth information, which renders it infeasible to obtain disparity through the disparity-depth relationship [8]. To overcome this limitation, we introduce QPD2K, the first high-resolution, real-world QPD disparity dataset, comprising 2,100 natural scenes and corresponding disparity maps.
+
+Hardware setup. We employ the OmniVision OV50A as our QPD data acquisition device, featuring a 50-megapixel image sensor with 1.0 micron pixel size. To acquire accurate depth, we employ the TI DLP4710 to construct a binocular structured light system. We use a chessboard to calibrate the disparity-depth relationship. Our QPD disparity acquisition system is illustrated in Fig. 2 (A).
+
+Disparity ground truth acquisition. The disparity-depth relationship in traditional stereo matching is governed by the equation  $d = f_{l}B / z$ , where  $d$  denotes the disparity,  $z$  represents the depth,  $B$  is the baseline, and  $f_{l}$  is the focal length. This relationship implies that disparity is inversely proportional to depth. In contrast, the QPD disparity-depth relationship [8] is as follows:
+
+$$
+D = \alpha \frac {A f _ {l}}{1 - f _ {l} / z _ {f}} \left(\frac {1}{z _ {f}} - \frac {1}{z}\right), \tag {1}
+$$
+
+where  $\alpha$  is a constant of proportionality,  $A$  is the size of the aperture,  $z_{f}$  is the focus distance,  $f_{l}$  is the focal length, and the QPD disparity  $D$  and the inverse depth  $1 / z$  are in an affine relation. However, directly obtaining a disparity from natural scenes is a challenging task. To circumvent this issue, we first acquire depth information and subsequently obtain the corresponding disparity through calibration [18].
+
+To establish a reliable disparity ground truth, we em
+
+ploy a structured light-based approach. Specifically, we project a speckle pattern onto the scene and employ RAFT-stereo [23] to compute the initial stereo depth (Fig. 2 (B)). Next, we project four phase-shifting sinusoidal patterns and seven Grey-coded patterns to acquire the absolute phase map [41]. We then utilize the absolute phase map to refine the initial stereo depth, yielding the refined depth (Fig. 2 (C)), which is further refined through a series of post-processing steps, including outlier removal, and median filtering [20], resulting in the post-processing depth (Fig. 2 (D)). To obtain the QPD disparity, we utilize Eq. (1) to fit the QPD disparity-depth curve. To mitigate the effects of uneven illumination, we employ the NCC [12] to compute the matching cost and refine this cost through interpolation to achieve sub-pixel horizontal disparity  $D_{h}$ . We compute the confidence level  $Conf_{h}$  by comparing the fitted curve with the original matching cost [13]. We repeat these steps to acquire the vertical disparity  $D_{v}$  and corresponding confidence  $Conf_{v}$ . Finally, we combine the two-directional disparity using confidence-weighted fusion:
+
+$$
+D _ {f} = \frac {D _ {h} \times C o n f _ {h} + D _ {v} \times C o n f _ {v}}{C o n f _ {h} + C o n f _ {v}}. \tag {2}
+$$
+
+Within the QPD disparity range, we obtain a set of pairs  $\{D_i,z_i\}$  and use the least squares method to fit the QPD disparity-depth relationship. This allows us to obtain the QPD disparity (Fig. 2 (E)). Additionally, the precision of our depth measurement is  $1mm$ .
+
+QPD2K summary. Our QPD2K dataset comprises 2100 QPD images and corresponding disparity maps with a resolution of  $3000 \times 2000$ . For convenience, we have split the QPD images into four sub-images. The dataset is partitioned into a training set of 2000 images and a testing set of 100 images. The disparity range is  $-4\text{pixel} \sim +4\text{pixel}$ . More details about the QPD2K dataset can be found in the supplementary material.
+
+![](images/7fa2b8610db8a3a6e4b4500eacb37f66a752bbe41caf4065cd042ecaa747927e.jpg)
+
+![](images/a2563005eea5a0b0c1d7fb43f14d99c233265049cee8e553f14b2b4a42835587.jpg)  
+Figure 3. The architecture of our DPNet network. To tackle the challenges of uneven illumination and the tiny baseline, we introduce two novel modules. Firstly, our illumination-invariant module mitigates the effects of uneven illumination. Secondly, our coarse-to-fine module refines the coarse disparity by a sub-pixel cost volume which is constructed through a sub-pixel shift around coarse disparity.
+
+![](images/efd8c0b3516b87f0e21c839a6d6fae8eb826dcf7efb52776103c9b7b82d5304f.jpg)
+
+# 4. Method
+
+In this section, we introduce DPNet (Fig. 3) for DP disparity estimation and then extend it to QuadNet (Fig. 4), leveraging the two-directional information provided by QPD data.
+
+# 4.1. DPNet
+
+The DPNet comprises two novel modules: an illumination-invariant module and a coarse-to-fine module. Given a DP input representation  $\mathbf{I}_{l,r} \in \mathbb{R}^{3 \times H \times W}$ , the illumination-invariant module extracts features  $\mathbf{f}$ ,  $\mathbf{g} \in \mathbb{R}^{C \times \frac{H}{4} \times \frac{W}{4}}$ , which are then used to obtain a coarse disparity map through the coarse disparity module. The coarse-to-fine module subsequently refines the coarse disparity map to generate a sub-pixel disparity  $\mathbf{D} \in \mathbb{R}^{1 \times H \times W}$ .
+
+Illumination-invariant module. As depicted in Fig. 1, the distinct sub-images from QPD data often exhibit obvious uneven illumination and noise effects, which increase the complexity of the feature matching. Vanilla convolution methods that rely on intensity-based feature extraction are sensitive to illumination. In contrast, edge information exhibits a higher invariance to changes in illumination intensity. To mitigate the impact of illumination variations, we leverage differential convolution (DC) [5, 37] to extract edge-based features, which yields robust features that are less sensitive to illumination changes.
+
+Our illumination-invariant module consists of two key components: the illumination-invariant feature extraction and the feature optimization. Specifically, we utilize a combination of four DCs and one Vanilla convolution to extract illumination-invariant features. We retain the central differential convolution (CDC) and angular differential convolution (ADC) and further incorporate two novel variants: horizontal sobel differential convolution (HSDC) and verti
+
+cal sobel differential convolution (VSDC). Considering the impact of noise in QPD data, we draw inspiration from the sobel operator kernel to design the HSDC and VSDC. For instance, given the input feature  $x$  and a  $3 \times 3$  convolution kernel  $w$ , the HSDC can be formulated as:
+
+$$
+\begin{array}{l} y = w _ {1} \left(x _ {1} - x _ {3}\right) + 2 w _ {4} \left(x _ {4} - x _ {6}\right) + w _ {7} \left(x _ {7} - x _ {9}\right), \\ = \sum_ {x _ {i} \in \mathcal {P}} w _ {i} ^ {\prime} \cdot x _ {i}, \tag {3} \\ \end{array}
+$$
+
+where  $x_{i}$  is a pixel of the input feature,  $w_{i}^{\prime}$  is an element in the  $3 \times 3$  convolution kernel,  $\mathcal{P}$  is the set of pixels sampled from the  $3 \times 3$  patch. Our feature optimization incorporates multiple residual layers and a feature self-attention layer [38] to augment the representational capacity of the feature network, improving the performance in challenging regions.
+
+Coarse disparity module. Given the DP features  $\mathbf{f},\mathbf{g}$  we construct a correlation cost volume as follows:
+
+$$
+\mathbf {C o r r} _ {i j k} = \sum_ {h} \mathbf {f} _ {h i j} \cdot \mathbf {g} _ {h i k}, \mathbf {C o r r} \in \mathbb {R} ^ {\frac {H}{4} \times \frac {W}{4} \times \frac {W}{4}}. \tag {4}
+$$
+
+We then construct a 4-level pyramid of correlation volumes by iteratively applying average pooling to the last dimension. The context encode [23] comprises a sequence of residual blocks and downsampling layers, producing multiscale context features. These features serve as inputs for the iterative hidden state of the GRU. We utilize GRU-based iterative updates to refine the disparity [23], yielding  $\mathbf{D}_{k + 1} = \mathbf{D}_k + \triangle \mathbf{D}_k$  at  $1 / 4$  resolution for the  $k$ -th iteration. Through this iterative process, we obtain the initial coarse disparity  $\mathbf{D}_{init}$ .
+
+Coarse-to-fine module. As shown in Fig. 1 (D), QPD sensors are characterized by a notably limited disparity
+
+range, which renders most stereo matching methods, designed for datasets such as KITTI [9, 27] or Middlebury [36], inapplicable to QPD/DP disparity estimation. To improve estimation accuracy, a common approach involves interpolating images or image features [16], which increases computational complexity. Drawing inspiration from the video super-resolution domain, where feature alignment is a crucial step towards performance improvement [3, 4], we adopt a coarse-to-fine approach. Specifically, we first produce a coarse disparity, followed by a refined search within the initial disparity scope to obtain a sub-pixel disparity.
+
+To reduce the search range of the disparity, we warp the feature layer of the right image to the left image, thereby reducing computational complexity and improving matching accuracy. We propose a sub-pixel group-wise correlation volume that splits features  $\mathbf{f}$ ,  $\mathbf{g}$  into  $N_{g}(N_{g} = 32)$  groups along the channel dimension and computes correlation maps group by group. The sub-pixel group-wise correlation is computed as follows:
+
+$$
+\mathbf {g} ^ {\prime} = \operatorname {W a r p} (\mathbf {g}, \mathbf {D} _ {\text {i n i t}}), \tag {5}
+$$
+
+$$
+\mathbf {C o r r} _ {s u b} = \frac {1}{N _ {c} / N _ {g}} \left\langle \mathbf {f} (x, y), \mathbf {g} ^ {\prime} (x - \mathbf {d} _ {s u b}, y) \right\rangle , \tag {6}
+$$
+
+where  $\langle \cdot, \cdot \rangle$  represents the inner product,  $N_{c}$  denotes the channel of  $\mathbf{f}$ ,  $\mathbf{d}_{sub}$  is the disparity index, and the scope of  $\mathbf{d}_{sub}$  is defined as  $[-D_r, D_r], D_r = 2$ , with a movement distance of 0.25 for each iteration. We achieve this by moving the warped features  $\mathbf{g}'$  through sub-pixel movements. Notably, different sub-pixel shift strategies for constructing the cost volume can yield varying results depending on the local scene configurations [14]. To address this, we implement a linear interpolation along the horizontal direction to acquire the sub-pixel shift, while avoiding the use of vertical data to maintain the linear relationship.
+
+However, relying solely on feature correlations can result in a lack of global information [44]. To solve this issue, we employ a lightweight 3D aggregation operation on the features  $\mathbf{Corr}_{sub}$  to introduce a sense of global coherence. Our cost aggregation consists of several 3D convolutional layers and residual blocks. Following the cost aggregation, we acquire the regularization cost volume  $\mathbf{Corr}_{reg}$ . Finally, we obtain the sub-pixel disparity  $\Delta \mathbf{D}_{sub}$  through soft argmin operation [11].
+
+$$
+\mathbf {p} (x, y, d _ {\text {s u b}}) = \operatorname {s o f t m a x} \left(\mathbf {C o r r} _ {\text {r e g}}\right), \tag {7}
+$$
+
+$$
+\Delta \mathbf {D} _ {s u b} = \sum_ {d _ {s u b} = - D} ^ {D} p (x, y, d _ {s u b}) \cdot d _ {s u b}, \tag {8}
+$$
+
+$p(x,y,d_{sub})$  measures the likelihood that the pixel  $\mathbf{I}_l(x,y)$  in the left image is matched to the pixel  $\mathbf{I}_r'(x - d_{sub},y)$  in the warped right image. We update the disparity:
+
+$$
+\mathbf {D} = \mathbf {D} _ {\text {i n i t}} + \Delta \mathbf {D} _ {\text {s u b}}. \tag {9}
+$$
+
+![](images/535d8e4495d2e0212b09fd7da925ebe6475a206cc9721b07b6fde85b6fe7583f.jpg)  
+Figure 4. Overview of our QuadNet network. We utilize edge features as the fusion weight to combine the two-directional disparity.
+
+# 4.2. QuadNet
+
+QPD data comprises both horizontal and vertical disparity, which can be represented as  $\mathbf{D}_h = \mathcal{N}(\mathbf{I}_l,\mathbf{I}_r)$ , and  $\mathbf{D}_v = \mathcal{N}(\mathbf{I}_u,\mathbf{I}_d)$ , where  $\mathcal{N}$  is the DPNet. However, a straightforward fusion of the disparity will introduce artifacts due to the inconsistencies between the reference images. For instance, in the case of horizontal lines, the horizontal disparity is often unreliable, whereas the vertical disparity can provide accurate information. To address this challenge, we utilize edge features as a reliability indicator for disparity estimation, enabling us to perform a weighted fusion based on the edge information to mitigate artifacts. Furthermore, we employ a census-based disparity refinement to further optimize the fusion artifacts.
+
+Edge-aware fusion module. We employ differential convolution to extract fusion weights, specifically focusing on horizontal and vertical edges as weights for disparity fusion. Taking the horizontal edge as an example, given the input  $\mathbf{I}_l\in \mathbb{R}^{3\times H\times W}$ , we utilize several residual layers to extract features  $\mathbf{f}_{init}\in \mathbb{R}^{C\times \frac{H}{4}\times \frac{W}{4}}$ . Subsequently, we use HSDC to extract horizontal edges, while leveraging the spatial attention module [37] to mitigate the interference of noise. To enhance multi-scale information, we utilize multiple layers of atrous convolution to enhance features. To obtain the final fusion weights, we first use a  $1\times 1$  convolution to reduce the feature dimension, followed by upsampling to the same resolution as the input and finally apply the sigmoid function to obtain the fusion weights  $\mathbf{W}_h\in \mathbb{R}^{1\times H\times W}$ . We repeat this process to acquire the vertical fusion weights  $\mathbf{W}_v\in \mathbb{R}^{1\times H\times W}$ . The final disparity is obtained by combining the two-directional disparity using Eq. (2).
+
+To further mitigate fusion artifacts, a common approach is disparity refinement through warp error [50, 51]. However, directly measuring the image brightness difference can lead to incorrect guidance due to uneven illumination and the influence of noise. To address this issue, we leverage the census transform, which provides a more reliable constancy assumption for realistic imagery by compensating for additive and multiplicative illumination changes, as well as changes to Gamma [26]. Specifically, we first apply the census transform  $CT$  to the images, and then utilize the soft Hamming distance  $HD$  to measure the warp error.
+
+![](images/a8f5e565849e3fc3d83fa71fada24b6d39850745277aa3bf11fe3109045d8933.jpg)
+
+![](images/9f16e29f4d7558ad8ec3bd428b0f1c4844316705c62e7a7bfc0a45c99dbcf59a.jpg)
+
+![](images/1d1276dba5f78a2c04dcac2e6f8dc53f2c1c0d0f84d0fbc694beec5d991d50fe.jpg)
+
+![](images/7e2546e64f93b65744b29356155b46f40afecb778874688d94c94415bd5c9dbf.jpg)  
+(A) Reference
+
+![](images/fdb640e2a445dce8d45f3b6243f12761e2cc16b70d1caefbd1111868ad6a9be1.jpg)
+
+![](images/4b5742891463275e40aada436ebab95d5e01b19598715817114022c69a551a1f.jpg)
+
+![](images/6a530c34fcdd3b33bb068a01a1732126978d768e2650ac85caffdd93c630e31d.jpg)
+
+![](images/6241a07d2b35950ba1515ee6d89b09fecaf79be5a21b4ea233497ec1c4af5582.jpg)  
+(B) SFBD [19]
+
+![](images/c378539a5cf970d96919c58d54081a8d6c75d68091e0328e555a642c26a2fc14.jpg)
+
+![](images/a93b09632f934511c18ed1d501eaedc79d28bcba9a0268f90798cf1170ddbde0.jpg)
+
+![](images/6403643da52f9b2dbc907134db46d6f040886095b3064eed21576e625212a206.jpg)
+
+![](images/8aab923a1b06d5c312d78617e9ff1405226a18be38d3541197229656a3701f5c.jpg)  
+(C) DLNR [51]
+
+![](images/8ed83ea4917dea5d5d713de0bbc4ca48a57245123c279280c531965b79ece38b.jpg)
+
+![](images/2f9a86af76a4c66dd05e4620fce20e5dd75ccb9fd7b7b79002fc5efbe8b71100.jpg)
+
+![](images/29854ec30d2d9c68d9f45ed10a9cd2dadf38ba7b796eb2c3ff4d79e1678bd83e.jpg)
+
+![](images/b4616a469de47da68611833546c57e7f0bc674bb6c0fb670c2de5dde612ccb09.jpg)  
+(D) S-IEGV [40]  
+Figure 5. Qualitative experimental results on QPD2K. Our DPNet demonstrates better performance in ill-posed and small disparity regions, while QuadNet shows the best overall performance. Zoom in for the best view.
+
+![](images/ced1061d10d1a43c2d6cd53888c3d4035ba0478d7e797cc4482066166c4bb74e.jpg)
+
+![](images/716654b1c157c2c942c454185b13e9650a4fba5df45d9d0ea0e8b2b88945194b.jpg)
+
+![](images/060687da0f11faa02e4d5c8563b9e6c0f2df4e4b9c8211a169cbbc4b7038524e.jpg)
+
+![](images/5d0c9b8c2becc4f7ccb13128f09a54ce23f90df57d4b4172b425149094af2e70.jpg)  
+(E) QPDNet [42]
+
+![](images/553558f3bd92a271bbaddb4bde2cd364a16bd85a3a25b2bc791b8a9e8bc94777.jpg)
+
+![](images/743dbd4c09b137dce17edb16c216c8ed4f4dd61b07f6062495f1e0690bd60868.jpg)
+
+![](images/f24d2aac5d44db52b15792beca50563f5d68cbaf82b68a9a8aedc3fde3dd2870.jpg)  
+(F) DPNet
+
+![](images/b35eb3925bb80858c9d2467d3f35dcb5660a8b3e8d9fa3d554de0bac5be79e53.jpg)
+
+![](images/4a66c63b3e3a7b74ad56889236d36782cb17b280e0ebf4ce068cbff99fa30671.jpg)
+
+![](images/3f66404a328277c127b03af847aa947ef803cc7cdaf84572f44ddf224a067902.jpg)
+
+![](images/480e7b9ad313781253421fb96ebd019e3cbf2a5bcf70e896f4304d22733b8c4c.jpg)  
+(G) QuadNet
+
+![](images/3b9fee30c2a04fc6306f11b1ba90452b7f3b54c0f2a573dee5c6a403d36de4c3.jpg)
+
+![](images/bd23a6c56f4d294d4fe9488950a7d86ee7142132151476e1de0dd619db6ae6f8.jpg)
+
+![](images/d20a6c1cd4a1bdc4b6b3efbdd9ee14145c7d0f91dcd1d57ae6e2e9dccef162f4.jpg)
+
+![](images/03d220b78560c98367186986c8acb909986eb738588fa21a2007e1bea425542f.jpg)  
+(H) GT
+
+$$
+\mathbf {I} _ {r} ^ {\prime} = \operatorname {W a r p} \left(\mathbf {I} _ {r}, \mathbf {D} _ {f}\right), \tag {10}
+$$
+
+$$
+\mathbf {E} _ {l} = H D \left(C T \left(\mathbf {I} _ {l}\right) - C T \left(\mathbf {I} _ {r} ^ {\prime}\right)\right), \tag {11}
+$$
+
+We combine the census warp error  $\mathbf{E}_l$  with the input  $\mathbf{I}_l$  and feed them into an hourglass network to obtain the refined disparity.
+
+$$
+\mathbf {D} _ {q p d} = \mathbf {D} _ {f} + H (C o n v ([ \mathbf {E} _ {l}, \mathbf {I} _ {l} ]), C o n v (\mathbf {D} _ {f})), \tag {12}
+$$
+
+where  $H$  represents the hourglass network, and  $\mathbf{D}_{qpd}$  is the final fused disparity.
+
+# 4.3. Loss Function
+
+We train the DPNet on the L1 distance between all predicted disparities  $\{\mathbf{D}_i\}_{i=1}^N$  and the ground truth disparity  $\mathbf{D}_{gt}$  with increasing weights. The total loss is defined as:
+
+$$
+\mathcal {L} _ {D P} = \sum_ {i = 1} ^ {N} \gamma^ {N - i} \left\| \mathbf {D} _ {i} - \mathbf {D} _ {g t} \right\| _ {1}, \tag {13}
+$$
+
+where  $\gamma = 0.9$ , and  $N$  is the number of iterations.
+
+We train the QuadNet on the L1 distance between the disparity  $\mathbf{D}_{qpd}$  and the ground truth disparity  $\mathbf{D}_{gt}$
+
+$$
+\mathcal {L} _ {q p d} = \left\| \mathbf {D} _ {q p d} - \mathbf {D} _ {g t} \right\| _ {1}. \tag {14}
+$$
+
+# 5. Experiments
+
+# 5.1. Implementation Details
+
+Our models are implemented in PyTorch, and all training and experimental procedures are conducted on two NVIDIA RTX 3090 GPUs. To effectively exploit the two-directional information inherent in QPD data, we first train
+
+the DPNet using the AdamW optimizer [24] with a one-cycle learning rate schedule, where the maximum learning rate is set to 0.0002. The GRU iteration is 22. We apply random cropping to the input to  $512 \times 384$  and set the batch size to 6. Subsequently, we train the QuadNet by freezing the weights of the DPNet and only updating the fusion module. We increase the batch size to 12 while keeping all other training strategies unchanged.
+
+# 5.2. Comparisons with State-of-the-art
+
+To evaluate the validity of our method, we conduct a comparative analysis with three categories of approaches: (1) methods that exploit the characteristics of DP sensors, including SFBD [19], CCA [28] and DPdisp [33], (2) methods that rely on stereo matching, including Mc-stereo [6], DLNR [51], S-RAFT [40], IEGV-Stereo [44], and (3) disparity estimation for QPD [42]. To ensure a fair comparison, we retrain the learning-based methods on QPD2K using the recommended parameters. Our evaluation metrics include bad 0.3, bad 0.5, bad 1, and end-point error (epe), as defined in [36]. In particular, we set the bad pixel percentages for thresholds  $0.3 \sim 1$ , which is suitable for small disparity compared to conventional stereo matching. The quantitative results on the QPD disparity dataset are presented in Tab. 1, and the qualitative results are shown in Fig. 5. The results indicate that supervised methods outperform methods that rely on the symmetry of the PSF [19, 33]. As mentioned above, PSFs are susceptible to noise and uneven illumination, leading to poor symmetry in real QPD data. Our DPNet exhibits superior performance compared to stereo matching-based methods, such as [6, 40, 44, 51]. This underscores the efficacy of our illumination-invariant module and coarse-to-fine module. Our QuadNet achieves optimal outcomes, highlighting the importance of the QPD
+
+<table><tr><td>Method</td><td>bad 0.3↓</td><td>bad 0.5↓</td><td>bad 1↓</td><td>epe↓</td></tr><tr><td>DPdisp [33]</td><td>0.969</td><td>0.943</td><td>0.779</td><td>1.670</td></tr><tr><td>SFBD [19]</td><td>0.927</td><td>0.870</td><td>0.367</td><td>1.150</td></tr><tr><td>CCA [28]</td><td>0.925</td><td>0.874</td><td>0.496</td><td>1.356</td></tr><tr><td>IEGV-Stereo [44]</td><td>0.926</td><td>0.877</td><td>0.739</td><td>1.719</td></tr><tr><td>QPDNet [42]</td><td>0.909</td><td>0.837</td><td>0.337</td><td>0.979</td></tr><tr><td>Mc-stereo [6]</td><td>0.478</td><td>0.334</td><td>0.181</td><td>0.675</td></tr><tr><td>S-RAFT [40]</td><td>0.438</td><td>0.285</td><td>0.038</td><td>0.345</td></tr><tr><td>S-IEGV [40]</td><td>0.437</td><td>0.293</td><td>0.089</td><td>0.386</td></tr><tr><td>DLNR [51]</td><td>0.329</td><td>0.189</td><td>0.034</td><td>0.272</td></tr><tr><td>DPNet (Ours)</td><td>0.273</td><td>0.160</td><td>0.033</td><td>0.238</td></tr><tr><td>QuadNet (Ours)</td><td>0.229</td><td>0.114</td><td>0.017</td><td>0.201</td></tr></table>
+
+disparity dataset and the effectiveness of our fusion module.
+
+![](images/16e30bf05af4885b079e2c6a36662055da998e66f6cc905bdfb676b45ae2d28e.jpg)
+
+![](images/c1035982a413d0f1dc9da5efb73e8185c3c9e879e7646499ce6a9dd7d9672fba.jpg)
+
+![](images/fb74f3ac642fdd4ef8d0b317cffa490e2fad1b81c427383bb30d41a7a4a3794a.jpg)
+
+![](images/5e5a21ec245a510d016ee29cd49f66d6ccbd1998c7a252100a28c89e5d334a60.jpg)  
+(D) w/ Illumination/Sub-pixel
+
+![](images/70c6087abca8c96dad9d9dc467812faf0869a8bf0d7457db0e5927e120494bc9.jpg)  
+(E) w/ All
+
+![](images/1c7fc365cd034d3596ac357bf71f55367ca27c97e43f01b3eb1b3327c9e9e3ad.jpg)  
+(F) GT  
+Figure 6. Ablation results on QPD2K dataset. Compared to the basic model, our modules effectively improve the results.
+
+# 5.3. Ablation Study
+
+Effectiveness of proposed modules. To validate the validity of our proposed modules, we present a quantitative comparison in Tab. 2, and the qualitative results are shown in Fig. 6. RAFT-stereo is our basic model, we introduce three novel modules: the illumination-invariant, the coarse-to-fine and the edge-aware fusion. The illumination-invariant module (IIM) reduces the model's sensitivity to illumination and noise conditions, meanwhile improving the background noise of the disparity. The coarse-to-fine module provides more accurate disparity boundary information, while the edge-aware fusion module effectively utilizes the two-directional disparity. Our experimental results demonstrate that each of the three innovative modules improves performance compared to the RAFT-stereo, and combining all three modules yields the best results.
+
+Illumination-invariant strategies. To mitigate the impact of illumination on QPD data, we employ a DC-based approach. To validate the rationality of our module design, we first replace the DCs with vanilla convolution and find that the performance is slightly improved compared to the baseline model. In contrast, our implementation achieves
+
+Table 1. Quantitative results on QPD2K dataset.  
+
+<table><tr><td colspan="4">Components</td><td colspan="4">QPD2K Dataset</td></tr><tr><td>Base</td><td>IIM</td><td>Sub-pixel</td><td>Fusion</td><td>bad 0.3↓</td><td>bad 0.5↓</td><td>bad 1↓</td><td>epe↓</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>0.445</td><td>0.299</td><td>0.055</td><td>0.353</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>0.318</td><td>0.188</td><td>0.034</td><td>0.264</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>0.301</td><td>0.178</td><td>0.035</td><td>0.259</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.273</td><td>0.160</td><td>0.033</td><td>0.238</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>0.229</td><td>0.114</td><td>0.017</td><td>0.201</td></tr></table>
+
+Table 2. Ablation study on modules.  
+
+<table><tr><td>Illumination conv</td><td>bad 0.3↓</td><td>bad 0.5↓</td><td>bad 1↓</td><td>epe↓</td></tr><tr><td>Vanilla conv</td><td>0.432</td><td>0.311</td><td>0.052</td><td>0.331</td></tr><tr><td>CDC+ADC</td><td>0.340</td><td>0.204</td><td>0.036</td><td>0.287</td></tr><tr><td>4 DCs</td><td>0.318</td><td>0.188</td><td>0.034</td><td>0.264</td></tr></table>
+
+Table 3. Illumination-invariant strategies.  
+
+<table><tr><td>Cost volume strategies</td><td>bad 0.3↓</td><td>bad 0.5↓</td><td>bad 1↓</td><td>efe↓</td></tr><tr><td>Group-wise [11]</td><td>0.415</td><td>0.287</td><td>0.046</td><td>0.312</td></tr><tr><td>Nearest</td><td>0.314</td><td>0.202</td><td>0.037</td><td>0.289</td></tr><tr><td>Phase</td><td>0.303</td><td>0.199</td><td>0.039</td><td>0.273</td></tr><tr><td>Bilinear</td><td>0.301</td><td>0.178</td><td>0.035</td><td>0.259</td></tr></table>
+
+Table 4. Cost volume strategies.  
+
+<table><tr><td>Fusion strategies</td><td>bad 0.3↓</td><td>bad 0.5↓</td><td>bad 1↓</td><td>epe↓</td></tr><tr><td>Indirect estimation [19]</td><td>0.961</td><td>0.923</td><td>0.748</td><td>1.453</td></tr><tr><td>Simple fusion</td><td>0.246</td><td>0.127</td><td>0.021</td><td>0.223</td></tr><tr><td>Conv fusion</td><td>0.247</td><td>0.125</td><td>0.018</td><td>0.211</td></tr><tr><td>Edge-aware fusion</td><td>0.229</td><td>0.114</td><td>0.017</td><td>0.201</td></tr></table>
+
+Table 5. Disparity fusion strategies.
+
+the best performance, as shown in Tab. 3. Our approach can effectively overcome the impact of illumination.
+
+Cost volume strategies. The construction of the cost volume is a critical component of the sub-pixel disparity estimation module. We conduct a thorough investigation into the cost volume construction approach, including Nearest, Phase, and Bilinear sampling methods. Table 4 demonstrates that the Bilinear sampling for sub-pixel shift achieves the best performance.
+
+Disparity fusion strategies. Effective utilization of the two-directional information in QPD data is crucial for enhancing model performance. We investigate various fusion strategies, including simple fusion (average weighting) and conv fusion (adding a 2D convolution layer as a fusion module). Table 5 demonstrates that edge-aware fusion achieves the best results. We also explore an indirect approach [19], which involves using the center image  $I_{C}$  as the reference image to estimate disparity:  $D_{l\rightarrow r} = D_{l\rightarrow c} + D_{c\rightarrow r}$ . However, our experimental results reveal that this approach yields subpar performance. We attribute this degradation to the limited disparity range in QPD data, which renders
+
+![](images/c29afdace0438ab5cbb65b6479dd4074fb6ec647168c49264cf9b42c993843c8.jpg)  
+(A) Reference
+
+![](images/8fec100f56d46f6ae94bd26612101892c08a008e483dc167f3cde647309f2235.jpg)  
+(B) DPdisp [33]
+
+![](images/24590d4c68e56215ee98feb3c46c4c31bebfdec52f1817e5232ef05aceabadd5.jpg)  
+(C) CCA [28]
+
+![](images/f5d1754813c5f3455134e1fe541c3a24970fe4ac6e519fea874e0adbd0149322.jpg)  
+(D) SFBD [19]  
+Figure 7. Qualitative experimental results on DP5K. Our DPNet performs better in blurred and depth-jump regions.
+
+![](images/8fb26009af1a9f796bdc45d5125410675e41c563e29a806a918a6292b269a080.jpg)  
+(E) FaceDPNet [18]
+
+![](images/f06a7fafea26600caf49d30f949dc69235cd0852fdd9a8fa47cc37263a4b5e99.jpg)  
+(F) DPNet
+
+![](images/dc93cc2213320f4e308bdf6157af7b935bdc36176b6c01b4781b6776a817c550.jpg)  
+(G) GT
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">DP5k [20]</td><td colspan="4">DP-disp [33]</td></tr><tr><td>AI(1)↓</td><td>AI(2)↓</td><td>|1 - ρs|↓</td><td>GM ↓</td><td>AI(1)↓</td><td>AI(2)↓</td><td>|1 - ρs|↓</td><td>GM ↓</td></tr><tr><td>DPdisp [33]</td><td>0.195</td><td>0.254</td><td>0.651</td><td>0.318</td><td>0.047</td><td>0.074</td><td>0.082</td><td>0.066</td></tr><tr><td>SFBD [19]</td><td>0.078</td><td>0.099</td><td>0.827</td><td>0.186</td><td>0.039</td><td>0.068</td><td>0.262</td><td>0.089</td></tr><tr><td>DDDNet [30]</td><td>0.081</td><td>0.119</td><td>0.962</td><td>0.210</td><td>0.061</td><td>0.099</td><td>0.103</td><td>0.085</td></tr><tr><td>FaceDPNet [18]</td><td>0.080</td><td>0.119</td><td>0.859</td><td>0.201</td><td>0.099</td><td>0.151</td><td>0.534</td><td>0.200</td></tr><tr><td>WDDNet [31]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.055</td><td>0.071</td><td>0.068</td><td>0.064</td></tr><tr><td>CCA [28]</td><td>0.195</td><td>0.258</td><td>0.686</td><td>0.326</td><td>0.041</td><td>0.068</td><td>0.061</td><td>0.055</td></tr><tr><td>DPNet (Ours)</td><td>0.034</td><td>0.063</td><td>0.645</td><td>0.111</td><td>0.025</td><td>0.047</td><td>0.055</td><td>0.040</td></tr></table>
+
+Table 6. Quantitative evaluation on DP5k and DP-disp benchmarks.
+
+estimating only half of the disparity insufficient.
+
+# 5.4. Zero-shot Generalization
+
+To further evaluate the robustness of our model, we conduct comparative experiments on DP5K [20] and DPdisp [33]. We compare DPNet with SOTA models, including DPdisp [33], SFBD [19], DDDNet [30], FaceDPNet [18], and WDDNet [31]. For a fair comparison, we use the authors' provided codes and weights and evaluate the results using both quantitative and qualitative metrics. Our evaluation metric is affine invariant [8, 30]:
+
+$$
+A I (p) = \underset {\beta_ {0}, \beta_ {1}} {\arg \min } \left(\frac {1}{N} \sum \left| D - \left(\beta_ {0} + \beta_ {1} \hat {D}\right) \right| ^ {p}\right) ^ {1 / p}. \tag {15}
+$$
+
+We also report Spearman's rank correlation coefficient  $\rho_{s}$  and geometric mean (GM).
+
+DP5K. The DP5K dataset [20] is used for the DP image simulator, but it also provides DP images and corresponding depth maps. Quantitative results are shown in Tab. 6, and qualitative results are shown in Fig. 7. Our DPNet performs best on the DP5K, and experiments show that our method can obtain stable results under different blur degrees.
+
+DP-disp. Our DPNet achieves the best performance on the DP-disp dataset [33], outperforming the next best performance method by about  $37.5\%$ . Quantitative results are presented in Tab. 6. Qualitative results are shown in Fig. 8.
+
+Our method demonstrates a significant advantage in clean background and fine details.
+
+![](images/e050ebd476dfb42bb7af2c2b601fef4c1ee5496299164af4a5bc845dc916464f.jpg)  
+(A) Reference
+
+![](images/ffe9e0f6a9cc8687aa593856db05c6bad4e40f55383aa3ce3ff735d4b97754a1.jpg)
+
+![](images/1bffb995e8244fb294227fe0b8ffb02ab88c7cbf1aad74135c851445f4441aa9.jpg)  
+(C) CCA [28]
+
+![](images/6a151592c7ae6874cd0795fe7424cc9e39ef45c079b375980a6dff41847bb843.jpg)  
+(D) SFBD [19]  
+Figure 8. Qualitative experimental results on DP-disp [33]. Our DPNet outperforms SOTA methods in detailed regions.
+
+![](images/6da8686d63a5072bb1403b73013dbf1aaad44317d17ef98513a9f7e65c3d49ae.jpg)  
+(B) DPdisp [33]  
+(E) DPNet
+
+![](images/a71214b289273676c3756a6e3b6bb35404fda22580c3c6af6545c9f917a2ecf7.jpg)  
+(F) GT
+
+# 6. Conclusion
+
+Our proposed QuadNet effectively addresses the challenges associated with disparity estimation for single QPD cameras, demonstrating robustness when applied to open datasets in conjunction with the DPNet. Furthermore, we contribute to the field by introducing the first QPD disparity dataset. To further enhance the practicality of our dataset, future research could focus on acquiring accurate ground truth disparity in open natural scenes and exploring the application of the disparity to image restoration tasks.
+
+# References
+
+[1] Abdullah Abuolaim and Michael S Brown. Defocus deblurring using dual-pixel data. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part X 16, pages 111-126. Springer, 2020. 1  
+[2] Abdullah Abuolaim, Mauricio Delbracio, Damien Kelly, Michael S Brown, and Peyman Milanfar. Learning to reduce defocus blur by realistically modeling dual-pixel data. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 2  
+[3] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. Basicvsr: The search for essential components in video super-resolution and beyond. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4947-4956, 2021. 5  
+[4] Kelvin CK Chan, Shangchen Zhou, Xiangyu Xu, and Chen Change Loy. Basicvsr++: Improving video superresolution with enhanced propagation and alignment. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5972-5981, 2022. 5  
+[5] Zixuan Chen, Zewei He, and Zhe-Ming Lu. Dea-net: Single image dehazing based on detail-enhanced convolution and content-guided attention. IEEE Transactions on Image Processing, 2024. 4  
+[6] Miaojie Feng, Junda Cheng, Hao Jia, Longliang Liu, Gangwei Xu, and Xin Yang. Mc-stereo: Multi-peak lookup and cascade search range for stereo matching. In 2024 International Conference on 3D Vision (3DV), pages 344–353. IEEE, 2024. 2, 6, 7  
+[7] Aryan Garg, Raghav Mallampali, Akshit Joshi, Shrisudhan Govindarajan, and Kaushik Mitra. Stereo-knowledge distillation from dpmv to dual pixels for light field video reconstruction. arXiv preprint arXiv:2405.11823, 2024. 2  
+[8] Rahul Garg, Neal Wadhwa, Sameer Ansari, and Jonathan T. Barron. Learning single camera depth estimation using dual-pixels. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 1, 2, 3, 8  
+[9] Andreas Geiger, Philip Lenz, and Raquel Urtasun. Are we ready for autonomous driving? the kitti vision benchmark suite. In 2012 IEEE conference on computer vision and pattern recognition, pages 3354-3361. IEEE, 2012. 5  
+[10] Bhargav Ghanekar, Salman Siddique Khan, Pranav Sharma, Shreyas Singh, Vivek Boominathan, Kaushik Mitra, and Ashok Veeraraghavan. Passive snapshot coded aperture dual-pixel rgb-d imaging. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 25348-25357, 2024. 2  
+[11] Xiaoyang Guo, Kai Yang, Wukui Yang, Xiaogang Wang, and Hongsheng Li. Group-wise correlation stereo network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3273-3282, 2019. 5, 7  
+[12] Heiko Hirschmuller and Daniel Scharstein. Evaluation of cost functions for stereo matching. In 2007 IEEE conference on computer vision and pattern recognition, pages 1-8. IEEE, 2007. 3
+
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\ No newline at end of file
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+# AlphaPre: Amplitude-Phase Disentanglement Model for Precipitation Nowcasting
+
+Kenghong Lin, Baoquan Zhang*, Demin Yu, Wenzhi Feng, Shidong Chen, Feifan Gao, Xutao Li, Yunming Ye* Harbin Institute of Technology, Shenzhen
+
+{linkenghong, deminy, 23b951053, chenshidong, 22S151126}@stu.hit.edu.cn,
+
+{baoquanzhang, lixutao, yeyunming}@hit.edu.cn
+
+# Abstract
+
+Precipitation nowcasting involves using current radar observation sequences to predict future radar sequences and determine future precipitation distribution, which is crucial for disaster warning, traffic planning, and agricultural production. Despite numerous advancements, challenges persist in accurately predicting both the location and intensity of precipitation, as these factors are often interdependent, with complex atmospheric dynamics and moisture distribution causing position and intensity changes to be intricately coupled. Inspired by the fact that in the frequency domain, phase variations are shown to correspond to changes in the position of precipitation, while amplitude variations are linked to intensity changes, we propose an amplitude-phase disentanglement model called AlphaPre, which separately learn the position and intensity changes of precipitation. AlphaPre comprises three key components: a phase network, an amplitude network, and an AlphaMixer. The phase network captures positional changes by learning phase variations, and the amplitude network models intensity changes by alternating between the frequency and spatial domains. The AlphaMixer then integrates these components to produce a refined precipitation forecast. Extensive experiments on four datasets demonstrate the effectiveness and superiority of our method over state-of-the-art approaches. Our code is publicly available at https://github.com/linkenghong/AlphaPre.
+
+# 1. Introduction
+
+Precipitation nowcasting, aiming to predict short-term rainfall within a time frame of a few minutes to a few hours, is a critical task in meteorology with significant implications for society. It holds diverse implications for human society, spanning critical areas including meteorological disaster preparedness, smart cities and agricultural strategizing.
+
+![](images/e0d78c02942a1e17b04890b8314d595b94f72ab1c8c7e66109634e47bd007441.jpg)  
+Figure 1. Illustration of the relationship between the amplitude-phase of radar images and precipitation processes. (a) By maintaining a constant amplitude and varying the phase, the effects of cloud deformation and displacement are observed. (b) The phase is held constant while the amplitude is varied, resulting in corresponding changes in precipitation intensity. These observations demonstrate that phase changes correspond to changes in the precipitation position, while amplitude variations are linked to changes in precipitation intensity.
+
+Given the importance of this task, many methods have been proposed, among which deep learning-based approaches have received growing attention and shown significant development in recent years [8].
+
+In spite of great progress with deep learning techniques, accurately predicting both the location and intensity of precipitation remains challenging [39]. This difficulty arises from the complex coupling between spatial and intensity
+
+changes in precipitation, which makes it hard to model these factors independently. The location of precipitation is largely driven by atmospheric dynamics, while the intensity depends on factors such as moisture availability and local atmospheric conditions. These two factors are not independent, as changes in the movement of the precipitation system often coincide with growth or dissipation, making the prediction task inherently complex [40]. To address this, separating spatial changes from intensity variations allows models to capture these underlying processes more effectively and independently. For precipitation systems, location and intensity changes exhibit different characteristics. Decoupling these factors allows the model to design specialized networks for each type of variation, enabling more effective modeling of location shifts and intensity changes individually.
+
+In this work, we first analyze the dynamic changes in radar images in the frequency domain. The results of this analysis shed us a light on how to disentangle positional and intensity changes. In Fig.1, we first use Fourier transform to decompose the radar image into amplitude and phase components. Then, by holding the amplitude/phase constant while varying the phase/amplitude, we examine the relationship between each component (phase or amplitude) and the precipitation process. In Fig.1(a), by holding the amplitude constant and linearly altering the phase, we can see the effect of precipitation region displacement. Additionally, by keeping the amplitude constant while replacing the phase with that from another frame, the precipitation region undergoes deformation. This demonstrates that phase variations in the frequency domain correspond to changes in the position of precipitation. In Fig.1(b), when the phase is held constant and the amplitude is increased, the precipitation intensity correspondingly increases; conversely, decreasing the amplitude results in reduced precipitation intensity. This demonstrates that amplitude variations in the frequency domain are associated with changes in precipitation intensity. These observations motivated us to leverage the relationship between phase and precipitation location, as well as amplitude and precipitation intensity, to design a network that separately learns the changes in amplitude and phase. In this manner, the two coupled factors can be effectively disentangled.
+
+Based on this notion, we propose a novel Amplitude-Phase Disentanglement model for Precipitation Nowcasting, called AlphaPre. AlphaPre divides the precipitation forecasting task into separate predictions for the phase and amplitude of radar images. Specifically, it consists of three main components: the phase network, the amplitude network, and the AlphaMixer. The phase network performs Fourier decomposition on historical radar images, using only the phase information to predict the phase of future radar images, thereby capturing precipitation loca
+
+tion changes. The amplitude network is designed to predict the amplitude of future radar images, focusing on capturing changes in precipitation intensity. Finally, the AlphaMixer integrates the predictions from both networks to produce a fine-grained precipitation forecast. By leveraging the distinct roles of amplitude and phase in the frequency domain, AlphaPre is able to address the critical challenge of highly coupled factors on intensity and location variations in nowcasting, providing more accurate predictions than existing deep learning methods.
+
+In summary, our main contributions are as follows:
+
+- We analyze the precipitation process from a frequency domain perspective and find that phase changes in radar images correspond to changes in precipitation location, while amplitude changes correspond to variations in precipitation intensity.  
+- We propose and design the architecture of AlphaPre, which includes a phase network that models positional changes by focusing on phase variations, and an amplitude network to better capture intensity variations. The integration of these networks through the AlphaMixer results in a refined and accurate precipitation forecast.  
+- We conduct extensive experiments on four publicly available radar echo datasets, and the results show that AlphaPre significantly improves performance, achieving state-of-the-art results in precipitation nowcasting.
+
+# 2. Related Work
+
+# 2.1. Spatiotemporal Prediction Method
+
+Spatiotemporal prediction methods can broadly be categorized into two main approaches: non-disentangled methods and disentangled methods. Non-disentangled methods typically consider multiple factors influencing spatiotemporal prediction jointly. A classic example of this approach is ConvLSTM [21], which combines CNNs and LSTM networks to simultaneously capture spatial correlations and temporal dependencies. The strong performance of such models has led to extensive research into CNN-RNN hybrid models [1, 10, 12, 22, 28-33]. Differing from the RNN-based architectures, SimVP [9] and TAU [23] discarded RNN structures and propose a fully CNN-based encoder-decoder framework, achieving simultaneous capture of spatial information within frames and dynamic information across frames. Earthformer [8] and MIMO [18] leverage transformers to construct encoder-decoder structures, demonstrating significant performance improvements in spatiotemporal prediction tasks. FourcastNet [20] integrates Fourier neural operators with a token mixer inspired by self-attention mechanisms to efficiently model global correlations in the data. Prediff [10] introduces a conditional latent diffusion model designed specifically for probabilistic forecasting and incorporates a knowledge control mechanism to ensure that predictions comply with domain
+
+specific physical constraints. In contrast, disentangled methods aim to separate the various factors that influence spatiotemporal dynamics, making it easier to learn underlying spatiotemporal correlations [2, 6, 7, 11, 38]. For instance, PhyDNet [12] introduces a physics-driven network that disentangles physical dynamics from complex and unknown information, enabling more accurate modeling of underlying processes. NowcastNet [40] models precipitation as a combination of advection of the motion field and intensity residuals based on the continuity equation. DiffCast [39] decomposes the precipitation process into global deterministic and local stochastic models, utilizing deterministic prediction models and diffusion models to capture these aspects separately.
+
+In this work, we disentangle the dynamic processes of precipitation from two perspectives: the positional changes and intensity variations of precipitation. This dual-focus on location and intensity allows our method to address the complexities of precipitation nowcasting in a novel way, distinguishing it from previous approaches.
+
+# 2.2. Amplitude-Phase Disentanglement
+
+Amplitude and phase play distinct roles in images, with amplitude representing the magnitude of frequency components and phase encoding spatial and structural information. This distinction has led to widespread applications of amplitude-phase disentanglement in areas such as image enhancement, adversarial robustness, and domain generalization [3, 27, 35, 37, 41]. In the context of face forgery detection, SPSL [17] explores the significance of the phase spectrum, demonstrating that incorporating phase information into CNN training can significantly boost detection accuracy. This work highlights the robustness of phase features in capturing subtle alterations in forged images. APR [4] conducts both qualitative and quantitative analyses of amplitude spectrum and phase spectrum for CNNs and proposes recombining amplitude and phase as a data augmentation technique to improve the robustness of CNN models against adversarial attacks. PADDLES [13] takes a different approach by focusing on training dynamics, introducing an early stopping technique that disentangles amplitude and phase features during training. In the realm of low-light image enhancement, UHDFour [16] utilizes amplitude-phase disentanglement within a Fourier-based cascaded network to enhance luminance while minimizing noise in low-light image enhancement. FACL [36] introduces Fourier Amplitude Loss and Fourier Correlation Loss as replacements for the commonly used MSE loss. The Fourier Amplitude Loss aims to enhance spatial clarity, while the Fourier Correlation Loss captures the overall structural information of the image. Distinct from the applications mentioned above, our model focuses on precipitation nowcasting, where we disentangle amplitude and phase to independently model the position and intensity changes of precipitation systems.
+
+# 3. Methodology
+
+# 3.1. Problem Definition
+
+Similar to previous works[8, 39], we formulate precipitation nowcasting as a spatio-temporal prediction problem. Given  $T_{i}$  historical observation sequence  $X = [X_{t}]_{t = -T_{i} + 1}^{0} \in \mathbb{R}^{T_{i} \times C \times H \times W}$ , where  $T_{i}$  is the length of the historical sequence,  $C$  denotes the number of channels at each space-time coordinate. In our radar echo setting,  $C = 1$ .  $H$  and  $W$  denote the spatial resolution of each frame. The precipitation nowcasting problem is to generate the most likely length- $T_{o}$  sequence  $Y = [Y_{t}]_{t = 1}^{T_{o}} \in \mathbb{R}^{T_{o} \times C \times H \times W}$  in the future.
+
+# 3.2. Preliminaries: Amplitude-Phase Spectrum
+
+Given a 2D image  $X \in \mathbb{R}^{H \times W}$ , the 2D Fourier Transform  $\mathcal{F}$  which converts  $X$  to its corresponding Fourier spectrum  $\hat{X} \in \mathbb{C}^{H \times W}$  can be defined as:
+
+$$
+\hat {X} (u, v) = \mathcal {F} (X) (u, v) = \sum_ {h = 0} ^ {H - 1} \sum_ {w = 0} ^ {W - 1} X (h, w) e ^ {- i 2 \pi \left(\frac {u h}{H} + \frac {v w}{W}\right)}, \tag {1}
+$$
+
+where  $h, w$  are the coordinates in the spatial domain and  $u, v$  are the coordinates in the frequency domain [19]. The Fourier spectrum can be represented by a amplitude spectrum  $\mathcal{A}(X)$  and a phase spectrum  $\mathcal{P}(X)$  as follows:
+
+$$
+\mathcal {A} (X) (u, v) = \sqrt {\Re^ {2} (\hat {X} (u , v)) + \Im^ {2} (\hat {X} (u , v))}, \quad (2)
+$$
+
+$$
+\mathcal {P} (X) (u, v) = \arctan \left(\frac {\Im (\hat {X} (u , v))}{\Re (\hat {X} (u , v))}\right), \tag {3}
+$$
+
+where  $\Re \left(\hat{X}(u,v)\right)$  and  $\Im \left(\hat{X}(u,v)\right)$  represent the real and imaginary parts of  $\hat{X}(u,v)$ , respectively.
+
+The Fourier spectrum can be reconstructed by combining the amplitude  $\mathcal{A}(X)(u,v)$  and phase  $\mathcal{P}(X)(u,v)$  as follows:
+
+$$
+\hat {X} (u, v) = \mathcal {A} (X) (u, v) \cdot e ^ {i \mathcal {P} (X) (u, v)}. \tag {4}
+$$
+
+The original image  $X(h,w)$  can then be restored using the inverse 2D Fourier Transform  $(\mathcal{F}^{-1})$
+
+$$
+X (h, w) = \mathcal {F} ^ {- 1} (\hat {X}) = \frac {1}{H W} \sum_ {u = 0} ^ {H - 1} \sum_ {v = 0} ^ {W - 1} \hat {X} (u, v) \cdot e ^ {i 2 \pi \left(\frac {u h}{H} + \frac {v w}{W}\right)}. \tag {5}
+$$
+
+The Fourier transform and its inverse can be calculated efficiently using the Fast Fourier Transform (FFT) [19] algorithm.
+
+![](images/cca057fa47469fa4b0708a5a0b0c8896604d045433c6eaf31df361ca91e13f7b.jpg)  
+Figure 2. The architecture of AlphaPre, which consists of the Phase Network, Amplitude Network, and AlphaMixer. The Phase Network processes the input phase through a Phase Module to predict future phase sequences  $\mathcal{P}_{pr}$ , optimized using the phase loss  $\mathcal{L}_P$ .  $\mathcal{P}_{pr}$  is also combined with the amplitude of the current radar image  $\mathcal{A}_0$  to generate the predicted sequence  $Y_{p}$ . The Amplitude Network, comprising multiple Spectral-Spatial blocks, captures dynamic changes in the amplitude spectrum and generates the predicted sequence  $Y_{a}$ , optimized with the amplitude loss  $\mathcal{L}_A$ . Finally, the AlphaMixer combines  $\mathcal{P}_{pr}$  and  $\mathcal{A}_{pr}$  to produce  $Y_{ap}$ . The sequences  $Y_{ap}$ ,  $Y_{p}$ , and  $Y_{a}$  are concatenated and passed through a network to produce the final prediction.
+
+# 3.3. The Proposed AlphaPre Framework
+
+As previously discussed, phase changes in radar images correspond to the position change of precipitation, and amplitude changes are linked to variations in precipitation intensity. Leveraging this insight, we designed AlphaPre, an amplitude-phase disentanglement model for precipitation nowcasting. The architecture of AlphaPre, illustrated in Figure 2, comprises three key components: the Phase Network, the Amplitude Network, and the AlphaMixer. The Phase Network applies a Fourier transform to the observed radar image sequence, decomposing it into its phase and amplitude components. The phase sequence is processed through the Phase Module, which learns the temporal evolution of phase changes, ultimately generating the predicted phase sequence for future radar images. This predicted phase sequence  $\mathcal{P}_{pr}$  is then combined with the amplitude of the last observed radar image  $\mathcal{A}_0$ , and an inverse Fourier transform is applied to reconstruct the future radar image sequence  $Y_{p}$  based on phase dynamics. A phase loss  $\mathcal{L}_P$  is designed to minimize the angular difference between the predicted and ground truth phases during training. The Amplitude Network employs an encoder to first extract spatial features from the radar observation sequence. Subsequently, the Amplitude Module, consisting of multiple Spectral-Spatial blocks, captures both temporal variations in spectral amplitude and spatial intensity changes, ensuring
+
+a comprehensive modeling of precipitation intensity evolution. An amplitude loss  $\mathcal{L}_A$  is introduced to guide the amplitude network, ensuring that the predicted amplitude aligns closely with the ground truth during the learning process. Finally, the AlphaMixer integrates the outputs from both the Phase and Amplitude Networks, effectively combining the learned phase and amplitude information to generate a more refined and accurate prediction of future precipitation. The subsequent sections will delve into the details of each network component.
+
+# 3.4. Phase Network
+
+The phase network is designed to model the positional changes of precipitation under the assumption that the current rainfall intensity remains constant. This means that the phase network only needs to predict the future phase sequence, which is then combined with the amplitude of the last observed frame and transformed back into the spatial domain using the inverse Fourier transform to generate the prediction. As shown in Figure 3, this network operates in three steps:
+
+Step 1 : Performing the Fourier transform on the radar observation sequence, the phase sequence  $\mathcal{P}_{-T_i + 1:0}$  (abbreviated as  $\mathcal{P}_{in}$ ) is obtained using Eq. 3, and the amplitude of the last observed frame  $\mathcal{A}_0$  is obtained using Eq. 2.
+
+![](images/d24adc3a47082e01cbaa24598e5df37a61bc38c1ff97387a21e2216ce5605ccc.jpg)  
+Figure 3. The architecture of the Phase Network.
+
+Step 2: Using a phase module to predict the future phase sequence  $\mathcal{P}_{1:T_o}$  (abbreviated as  $\mathcal{P}_{pr}$ ) from  $\mathcal{P}_{in}$ . We first merge the channel and temporal dimensions, transforming the input from  $[T_i,C,H,W]$  to  $[T_i\times C,H,W]$ . Given that  $C = 1$  in our task, this means that subsequent operations on the channel dimension essentially capture temporal features. Considering that phase variations at different frequencies may be influenced by their corresponding frequency coordinates, we concatenate these frequency coordinates with the channel dimension to enrich the feature representation. The frequency coordinates are as follows:
+
+$$
+U (u, v) = \frac {u}{H}, V (u, v) = \frac {v}{W}. \tag {6}
+$$
+
+Next, we stacks  $N_{p}$  ConvNormSiLU blocks (Conv1×1 +GroupNorm+SiLU) to capture temporal features:
+
+$$
+\mathcal {P} ^ {i} = \operatorname {S i L U} (\operatorname {G r o u p N o r m} (\operatorname {C o n v} _ {1 \times 1} (\mathcal {P} ^ {i - 1}))), \quad 1 \leq i \leq N _ {p}, \tag {7}
+$$
+
+where SiLU is a sigmoid-weighted linear unit activation. The input of first block is  $\mathcal{P}^0 = \operatorname{Cat}[\mathcal{P}_{in}; U; V] \in \mathbb{R}^{(T_iC + 2) \times H \times W}$ , the output of last block is  $\mathcal{P}^{N_p} \in \mathbb{R}^{T_oC \times H \times W}$ . To further enhance the feature representation, a residual connection is added, where the module's input is passed through a  $1 \times 1$  convolution and then combined with the module's output, allowing the network to capture and incorporate residual information. Finally, the output  $\mathcal{P}_{pr}$  is then reshaped back to  $[T_o, C, H, W]$ .
+
+Step 3 : By combining the predicted phase sequence  $\mathcal{P}_{pr}$  with the amplitude of the current radar image  $\mathcal{A}_0$  and applying the inverse Fourier transform, we obtain the predicted radar image sequence  $Y_{p}$ .
+
+Phase Loss Function. To ensure effective learning of phase dynamics, we design a phase loss function that calculates the angular distance between the predicted phase  $\mathcal{P}_{pr}$  and the ground truth phase  $\mathcal{P}_{gt}$ . Recognizing that high-frequency phases are often noisy, the loss function focuses
+
+![](images/f8c8d266874b5d73d602c7c3cb244caea9a6c0d1dbf83fc91dbccaf3fc742a3a.jpg)  
+Figure 4. The architecture of Amplitude Network.
+
+primarily on controlling the low-frequency phase components:
+
+$$
+\mathcal {L} _ {\mathrm {P}} = \frac {1}{4 k ^ {2}} \sum_ {- k \leq u, v \leq k} \left(1 - \cos \left(\mathcal {P} _ {g t} ^ {u, v} - \mathcal {P} _ {p r} ^ {u, v}\right)\right), \tag {8}
+$$
+
+where  $k$  is the truncated frequency.
+
+# 3.5. Amplitude Network
+
+The amplitude network adopts a different learning approach from the phase network. Unlike the phase network, it does not fix the phase and only learns amplitude changes. As the phase determines the details of the prediction, fixing the phase would significantly limit the network's learning capacity. Therefore, the amplitude network learns precipitation intensity changes in both the spatial and spectral domains. Then, a loss function is designed to constrain the amplitude of the predicted radar images. As shown in Figure 4, the amplitude network consists of an encoder, an amplitude module and a decoder.
+
+Encoder. The encoder is responsible for extracting the spatial features of the input sequence, and it is stacked by two ConvNormSiLU blocks (Conv3  $\times$  3+GroupNorm+SiLU):
+
+$$
+Z ^ {i} = \operatorname {S i L U} (\operatorname {G r o u p N o r m} \left(\operatorname {C o n v} _ {3 \times 3} \left(Z ^ {i - 1}\right)\right)), \quad i = 1, 2. \tag {9}
+$$
+
+Its input is  $Z^0 = X_{-T_i + 1:0} \in \mathbb{R}^{T_i \times C \times H \times W}$ , output is  $Z = Z^2 \in \mathbb{R}^{T_i \times D \times H \times W}$ ,  $D$  is the hidden dimension.
+
+Amplitude Module. The amplitude module is composed of  $N_{a}$  Spectral-Spatial blocks. Each Spectral-Spatial block first captures dynamic changes within the Fourier spectrum across the frequency domain and then captures spatial dynamics in the spatial domain. Firstly, the output of encoder  $Z$  undergoes a 2D Fourier transform along the spatial dimensions, yielding the Fourier spectrum  $\hat{Z}$ . To capture the
+
+temporal dynamics within the spectrum, two layers of complex MLPs are applied across the temporal dimension.
+
+$$
+\hat {Z} _ {o} = W _ {1} \left(\mathbb {C} \operatorname {R e L U} \left(W _ {0} \hat {Z} + b _ {0}\right)\right) + b _ {1}, \tag {10}
+$$
+
+where  $W_0 \in \mathbb{C}^{T_h \times T_i}$ ,  $b_0 \in \mathbb{C}^{T_h}$ ,  $W_1 \in \mathbb{C}^{T_o \times T_h}$ ,  $b_1 \in \mathbb{C}^{T_o}$  are the parameters of the two-layer complex MLP,  $T_h$  is the hidden temporal dimension and CReLU represents the Complex ReLU activation function [25]. The output spectrum  $\hat{Z}_o$  is then transformed back into the spatial domain using the 2D inverse Fourier transform:  $Z_o = \mathcal{F}^{-1}(\hat{Z}_o)$ . Since the aforementioned operations only capture dynamics along the temporal dimension and treat channels independently, the output  $Z_o$  is further processed by performing a convolution along the temporal-channel dimension. This step captures the dynamic interactions across channels and ensuring that both temporal and inter-channel dynamics are effectively modeled.
+
+Decoder. The decoder is responsible for reconstructing the predicted sequence from high-dimensional features. Similar to the encoder, the decoder consists of two ConvNormSiLU blocks, and generator the final predicted sequences  $Y_{a}$ .
+
+Amplitude Loss Function. As discussed earlier, it is necessary to constrain the amplitude of  $Y_{a}$  to ensure the network's capability in predicting precipitation intensity. First, we extract the amplitude  $\mathcal{A}_{pr}$  of  $Y_{a}$  using Eq.2, and then compute the loss between  $\mathcal{A}_{pr}$  and the amplitude of ground truth. However, due to the uneven distribution of amplitudes in the image, with a few low-frequency components having particularly high amplitudes, directly computing the loss could cause the model to focus only on these dominant low frequencies. To address this issue, we apply z-score normalization to the amplitude before calculating the loss. The mean and variance used for normalization are computed from the training set. The loss is defined as follows:
+
+$$
+\mathcal {L} _ {\mathrm {A}} = \frac {1}{4 k ^ {2}} \sum_ {- k \leq u, v \leq k} \left(\overline {{\mathcal {A}}} _ {g t} ^ {u, v} - \overline {{\mathcal {A}}} _ {p r} ^ {u, v}\right) ^ {2}, \tag {11}
+$$
+
+where  $\overline{\mathcal{A}}_{gt}$  and  $\overline{\mathcal{A}}_{pr}$  are the normalized amplitudes extracted from the ground truth and predicted values, respectively.
+
+# 3.6. AlphaMixer
+
+AlphaMixer integrates the outputs of the phase network and the amplitude network to achieve a more accurate prediction. It first combines the phase  $\mathcal{P}_{pr}$  learned by the phase network with the amplitude  $\mathcal{A}_{pr}$  learned by the amplitude network, and then applies the inverse Fourier transform to obtain the combined result  $Y_{ap}$ . This result is then concatenated with the individual outputs  $Y_{a}$  and  $Y_{p}$
+
+from the amplitude and phase networks, respectively, and is passed through a network consisting of two ConvNorm-SiLU blocks to generate the final prediction.
+
+The final loss function of the model consists of three components:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {M}} + \alpha \mathcal {L} _ {\mathrm {A}} + \beta \mathcal {L} _ {\mathrm {P}}, \tag {12}
+$$
+
+where  $\mathcal{L}_{\mathrm{M}}$  is the L2 loss between the final prediction and the ground truth, and  $\mathcal{L}_{\mathrm{A}}$  and  $\mathcal{L}_{\mathrm{P}}$  are the losses from Eq.11 and Eq.8, respectively.  $\alpha ,\beta$  are the corresponding loss weights.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We conducted experiments on four precipitation datasets. SEVIR [26] covers the United States with a spatial resolution of  $384\mathrm{km} \times 384\mathrm{km}$  and a temporal resolution of 5 minutes. MeteoNet [15] spans a region in France with a  $550\mathrm{km} \times 550\mathrm{km}$  resolution and 5-minute intervals. The Shanghai Radar dataset [5] records precipitation in Shanghai, at  $501\mathrm{km} \times 501\mathrm{km}$  with 6-minute intervals. CIKM [24] focuses on Guangdong, China, with a  $101\mathrm{km} \times 101\mathrm{km}$  resolution and 6-minute intervals. Following the setup in DiffCast [39], we reshaped all images to a resolution of  $128 \times 128$ . For all datasets except for CIKM, the input and output sequence lengths are set to 5 and 20. For the CIKM dataset, the input and output sequence lengths are set to 5 and 10. More details are provided in Appendix.
+
+Metrics. To assess the model performance, we employ four common metrics: Critical Success Index (CSI-M), Heidke Skill Score (HSS), Structural Similarity Index Measure (SSIM), and MSE to evaluate the quality of predictions, following [8, 39]. The CSI measures the accuracy of a model in correctly predicting precipitation events, taking into account both false alarms and missed detections. Following [8, 39], we measure multiple CSI scores with different thresholds (\{16, 74, 133, 160, 181, 219\} for SEVIR, \{12, 18, 24, 32\} for MeteoNet, \{20, 30, 35, 40\} for Shanghai and CIKM). Additionally, we report the mean CSI (CSI-M) to provide an overall accuracy assessment. The HSS evaluates the improvement of a model's predictions over random guessing, accounting for both correct and incorrect classifications.
+
+Baselines. We selected nine baselines for comparison with our proposed model: ConvGRU[22], MAU [1], SimVP [9], FourCastNet [20], EarthFormer[8], PhyDNet[12], EarthFarseer[34], NowcastNet[40], DiffCast[39]. The first five methods are non-disentangled approaches, while the last four are disentangled methods. Among these, DiffCast
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Type</td><td colspan="6">SEVIR</td><td colspan="6">MeteoNet</td></tr><tr><td>CSI-M↑</td><td>CSI-181↑</td><td>CSI-219↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td><td>CSI-M↑</td><td>CSI-24↑</td><td>CSI-32↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>ConvGRU</td><td>ND</td><td>0.2903</td><td>0.0879</td><td>0.0350</td><td>0.3619</td><td>0.6100</td><td>368.34</td><td>0.3401</td><td>0.2990</td><td>0.1431</td><td>0.4667</td><td>0.7833</td><td>12.85</td></tr><tr><td>MAU</td><td>ND</td><td>0.3076</td><td>0.1071</td><td>0.0516</td><td>0.3863</td><td>0.6505</td><td>355.48</td><td>0.3233</td><td>0.2839</td><td>0.0997</td><td>0.4452</td><td>0.7897</td><td>12.92</td></tr><tr><td>SimVP</td><td>ND</td><td>0.3108</td><td>0.1106</td><td>0.0517</td><td>0.3924</td><td>0.6508</td><td>383.56</td><td>0.3351</td><td>0.3002</td><td>0.1130</td><td>0.4573</td><td>0.7804</td><td>13.45</td></tr><tr><td>FourCastNet</td><td>ND</td><td>0.2686</td><td>0.0717</td><td>0.0339</td><td>0.3355</td><td>0.5976</td><td>410.27</td><td>0.3027</td><td>0.2533</td><td>0.1085</td><td>0.4216</td><td>0.6450</td><td>15.05</td></tr><tr><td>Earthformer</td><td>ND</td><td>0.2892</td><td>0.0844</td><td>0.0245</td><td>0.3665</td><td>0.6633</td><td>360.11</td><td>0.3205</td><td>0.2884</td><td>0.1237</td><td>0.4491</td><td>0.7772</td><td>14.43</td></tr><tr><td>PhyDNet</td><td>D</td><td>0.3017</td><td>0.1040</td><td>0.0278</td><td>0.3812</td><td>0.6532</td><td>357.63</td><td>0.3384</td><td>0.3194</td><td>0.1366</td><td>0.4673</td><td>0.7823</td><td>14.48</td></tr><tr><td>EarthFarseer</td><td>D</td><td>0.3004</td><td>0.0992</td><td>0.0413</td><td>0.3829</td><td>0.6327</td><td>388.91</td><td>0.3404</td><td>0.3170</td><td>0.1372</td><td>0.4726</td><td>0.7542</td><td>14.10</td></tr><tr><td>NowcastNet</td><td>D</td><td>0.2791</td><td>0.0770</td><td>0.0351</td><td>0.3512</td><td>0.6839</td><td>412.94</td><td>0.3427</td><td>0.3206</td><td>0.1598</td><td>0.4751</td><td>0.7879</td><td>15.64</td></tr><tr><td>DiffCast</td><td>D</td><td>0.3050</td><td>0.1300</td><td>0.0582</td><td>0.3996</td><td>0.6482</td><td>559.59</td><td>0.3512</td><td>0.3340</td><td>0.1808</td><td>0.4846</td><td>0.7887</td><td>17.93</td></tr><tr><td>AlphaPre</td><td>D</td><td>0.3259</td><td>0.1332</td><td>0.0545</td><td>0.4110</td><td>0.6884</td><td>345.18</td><td>0.3824</td><td>0.3633</td><td>0.2002</td><td>0.5164</td><td>0.7968</td><td>12.74</td></tr><tr><td rowspan="2"></td><td rowspan="2">Type</td><td colspan="6">Shanghai</td><td colspan="6">CIKM</td></tr><tr><td>CSI-M↑</td><td>CSI-35↑</td><td>CSI-40↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td><td>CSI-M↑</td><td>CSI-35↑</td><td>CSI-40↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>ConvGRU</td><td>ND</td><td>0.3612</td><td>0.3163</td><td>0.2062</td><td>0.4899</td><td>0.7796</td><td>33.56</td><td>0.3091</td><td>0.2009</td><td>0.1259</td><td>0.4006</td><td>0.6507</td><td>37.13</td></tr><tr><td>MAU</td><td>ND</td><td>0.3983</td><td>0.3621</td><td>0.2417</td><td>0.5346</td><td>0.7195</td><td>30.40</td><td>0.3039</td><td>0.2054</td><td>0.1241</td><td>0.3928</td><td>0.6325</td><td>40.74</td></tr><tr><td>SimVP</td><td>ND</td><td>0.3850</td><td>0.3549</td><td>0.2382</td><td>0.5194</td><td>0.7795</td><td>34.40</td><td>0.3052</td><td>0.2044</td><td>0.1321</td><td>0.3955</td><td>0.6538</td><td>38.06</td></tr><tr><td>FourCastNet</td><td>ND</td><td>0.3571</td><td>0.3108</td><td>0.2073</td><td>0.4868</td><td>0.5598</td><td>32.10</td><td>0.2980</td><td>0.1849</td><td>0.1015</td><td>0.3801</td><td>0.4359</td><td>36.14</td></tr><tr><td>Earthformer</td><td>ND</td><td>0.3503</td><td>0.3178</td><td>0.1872</td><td>0.4844</td><td>0.7298</td><td>35.57</td><td>0.3077</td><td>0.2039</td><td>0.1369</td><td>0.4001</td><td>0.6267</td><td>36.49</td></tr><tr><td>PhyDNet</td><td>D</td><td>0.3654</td><td>0.3236</td><td>0.2176</td><td>0.4957</td><td>0.7751</td><td>36.41</td><td>0.3038</td><td>0.2052</td><td>0.1287</td><td>0.3931</td><td>0.6541</td><td>39.56</td></tr><tr><td>EarthFarseer</td><td>D</td><td>0.3926</td><td>0.3608</td><td>0.2343</td><td>0.5330</td><td>0.5405</td><td>32.68</td><td>0.3000</td><td>0.2046</td><td>0.1259</td><td>0.3911</td><td>0.6373</td><td>39.87</td></tr><tr><td>NowcastNet</td><td>D</td><td>0.3953</td><td>0.3608</td><td>0.2450</td><td>0.5334</td><td>0.7902</td><td>33.56</td><td>0.2991</td><td>0.1940</td><td>0.1188</td><td>0.3865</td><td>0.6713</td><td>40.96</td></tr><tr><td>DiffCast</td><td>D</td><td>0.4089</td><td>0.3740</td><td>0.2606</td><td>0.5476</td><td>0.7879</td><td>36.35</td><td>0.3159</td><td>0.2009</td><td>0.1457</td><td>0.4085</td><td>0.6499</td><td>42.78</td></tr><tr><td>AlphaPre</td><td>D</td><td>0.4178</td><td>0.3854</td><td>0.2615</td><td>0.5534</td><td>0.7951</td><td>28.02</td><td>0.3194</td><td>0.2068</td><td>0.1416</td><td>0.4137</td><td>0.6568</td><td>35.18</td></tr></table>
+
+Table 1. Experiment results on four radar datasets. In the "Type" column, ND represents non-disentangled approaches, and D represents disentangled methods. The best results are highlighted in bold and the second-best results are underlined.
+
+is probabilistic models based on diffusion. The implementations of all baselines are based on the code provided by the authors.
+
+Implementation Details. We train our AlphaPre model for 100 epochs with a batch size of 4, a learning rate of  $1 \times 10^{-4}$ , and the Adam optimizer [14]. The loss weights  $\alpha$  and  $\beta$  are set to 0.1 and 0.01. The number of ConvNorm-SiLu blocks  $N_{p}$  in phase network is set to 3. The number of Spectral-Spatial blocks  $N_{a}$  in amplitude network is set to 3. The truncated frequency is set to 20. All experiments are carried out on a computer equipped with an Intel(R) Core(TM) i9-10920X CPU @ 3.50 GHz processor, GeForce RTX 3090*2 GPUs, and 64 GB of RAM.
+
+# 4.2. Experimental Results
+
+Table 1 presents the results of our AlphaPre model compared to other baselines across four radar datasets. It can be observed that our approach outperforms state-of-the-art methods, achieving  $2\%$  to  $8\%$  better CSI,  $1\%$  to  $6\%$  better HSS, and  $1\%$  to  $8\%$  better MSE, demonstrating the superiority of our model. We also report the CSI at higher thresholds, as it reflects the model's ability to predict heavy rainfall, which is a crucial factor in precipitation forecasting. As shown in Table 1, our model achieves significantly higher high-threshold CSI scores compared to other models, indicating its effectiveness in predicting intense precipitation events. Fig. 5 further illustrates the variation of
+
+![](images/2be35c03f0e0bf34f2c81bb28867060719dfd05de198e9bb9b47fdd2b4ffc7c5.jpg)  
+Figure 5. CSI and HSS metrics at different prediction time steps for various methods on the SEVIR dataset.
+
+![](images/4522148c5e1e698c66dfde76feb17f36d7bca5b3ca28caed84c4b52232a84665.jpg)
+
+CSI and HSS over different prediction time steps for various methods, showing that our model consistently achieves the best results across nearly all time steps. Fig. 6 presents a sample forecast, where other models generally tend to underestimate precipitation intensity in later prediction steps, whereas our model provides a higher, more accurate intensity prediction. Additionally, our precipitation boundaries are more precise, highlighting the effectiveness of our disentangled modeling of precipitation intensity and position.
+
+# 4.3. Ablation Studies
+
+Effect of Individual Components. Our model consists of three components: the phase network, the amplitude network, and the AlphaMixer. To validate the effectiveness of these designed components, several ablation models are conducted, including: (1) w/o Ampli, which removes the
+
+![](images/d85d43ad73873880fec6368e18fce4596f2fabd5409d5bf5dfc1655440e891b0.jpg)  
+Figure 6. A visualization example from the SEVIR dataset.
+
+![](images/d32a240e2f49d9597fbf2d7676c2888af62e9cb06f74175e85be155fbac0e70f.jpg)  
+Figure 7. Ablation study visualization on the SEVIR dataset.
+
+<table><tr><td>SEVIR</td><td>CSI-M↑</td><td>CSI-160↑</td><td>CSI-181↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>w/o Ampli</td><td>0.2634</td><td>0.1084</td><td>0.0799</td><td>0.3296</td><td>0.5529</td><td>483.05</td></tr><tr><td>w/o Phase</td><td>0.3064</td><td>0.1500</td><td>0.1117</td><td>0.3841</td><td>0.5444</td><td>368.85</td></tr><tr><td>w/o Mixer</td><td>0.3119</td><td>0.1652</td><td>0.1209</td><td>0.3928</td><td>0.6669</td><td>367.86</td></tr><tr><td>AlphaPre</td><td>0.3259</td><td>0.1753</td><td>0.1332</td><td>0.4110</td><td>0.6884</td><td>345.18</td></tr><tr><td>Shanghai</td><td>CSI-M↑</td><td>CSI-35↑</td><td>CSI-40↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>w/o Ampli</td><td>0.3326</td><td>0.2930</td><td>0.1815</td><td>0.4522</td><td>0.6764</td><td>35.98</td></tr><tr><td>w/o Phase</td><td>0.3892</td><td>0.3507</td><td>0.2338</td><td>0.5209</td><td>0.7309</td><td>31.53</td></tr><tr><td>w/o Mixer</td><td>0.4051</td><td>0.3713</td><td>0.2510</td><td>0.5382</td><td>0.7573</td><td>29.56</td></tr><tr><td>AlphaPre</td><td>0.4178</td><td>0.3854</td><td>0.2615</td><td>0.5534</td><td>0.7951</td><td>28.02</td></tr></table>
+
+amplitude network, and the AlphaMixer only take  $Y_{p}$  as input; (2) w/o Phase, which removes the phase network, and the AlphaMixer only take  $Y_{a}$  as input; (3) w/o AlphaMixer, where the results of the phase and amplitude networks are directly concatenated and passed through the subsequent network to obtain the final result. Table 2 shows the results of the ablation experiments, where removing any module leads to a significant drop in performance, indicating that each module plays a crucial role in enhancing the model's predictive capabilities. Fig. 7 provides further visualization of the ablation study results. When the amplitude network is removed, the model's ability to predict high-intensity precipitation notably decreases. However, the outline and details of the precipitation area remain clear and accurate, demonstrating the phase network's effectiveness in capturing spatial shifts. In contrast, removing the phase network results in somewhat blurred precipitation areas. Despite
+
+Table 2. The ablation study results for the components of AlphaPre.  
+
+<table><tr><td>SEVIR</td><td>CSI-M↑</td><td>CSI-160↑</td><td>CSI-181↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>w/o LA</td><td>0.3188</td><td>0.1632</td><td>0.1203</td><td>0.4098</td><td>0.6334</td><td>352.34</td></tr><tr><td>w/o LP</td><td>0.3199</td><td>0.1659</td><td>0.1264</td><td>0.4017</td><td>0.6274</td><td>350.15</td></tr><tr><td>AlphaPre</td><td>0.3259</td><td>0.1753</td><td>0.1332</td><td>0.4110</td><td>0.6884</td><td>345.18</td></tr><tr><td>Shanghai</td><td>CSI-M↑</td><td>CSI-35↑</td><td>CSI-40↑</td><td>HSS↑</td><td>SSIM↑</td><td>MSE↓</td></tr><tr><td>w/o LA</td><td>0.4035</td><td>0.3688</td><td>0.2555</td><td>0.5367</td><td>0.7469</td><td>31.11</td></tr><tr><td>w/o LP</td><td>0.4101</td><td>0.3775</td><td>0.2604</td><td>0.5461</td><td>0.6955</td><td>29.29</td></tr><tr><td>AlphaPre</td><td>0.4178</td><td>0.3854</td><td>0.2615</td><td>0.5534</td><td>0.7951</td><td>28.02</td></tr></table>
+
+Table 3. The ablation study results for the loss.
+
+this, the model still maintains good intensity predictions, highlighting the amplitude network's capability in capturing intensity changes. Removing AlphaMixer also leads to performance degradation, underscoring the importance of integrating phase and amplitude information.
+
+Effect of Loss. Our model incorporates two additional loss functions, and we conducted ablation experiments to analyze their impact on overall performance. The experimental results, shown in Table 3, indicate that removing the amplitude loss leads to a significant drop in CSI, especially at high thresholds. For example, on the SEVIR dataset, CSI-160 decreases by  $7\%$ , and CSI-181 drops by  $10\%$ . On the Shanghai dataset, CSI-35 decreases by  $4\%$ , and CSI-40 by  $2\%$ , highlighting the importance of amplitude loss in accurately predicting precipitation intensity. When the phase loss is removed, SSIM drops more noticeably, reflecting a loss in structural information of precipitation. On the SEVIR dataset, SSIM decreases by  $9\%$ , and on the Shanghai dataset, it drops by  $13\%$ . This highlights the importance of phase loss in accurately predicting the spatial location of precipitation.
+
+# 5. Conclusion
+
+In this work, we introduced a novel amplitude-phase disentanglement model for precipitation nowcasting, designed to address the complex dynamics of precipitation, including the location and intensity changes of precipitation particles. By leveraging the distinct roles of phase and amplitude in the frequency domain, our model effectively captures the position and intensity variations in precipitation, leading to more accurate predictions. Extensive experiments conducted on four datasets demonstrated that our approach outperforms state-of-the-art methods, highlighting its effectiveness and robustness in different scenarios.
+
+# Acknowledgments
+
+This work was supported in part by National Nature Science Foundation of China No. 62272130, No. 62376072, and Shenzhen Science and Technology Program No. KCXFZ20211020163403005, No. KCXFZ20240903093006009.
+
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+# An End-to-End Robust Point Cloud Semantic Segmentation Network with Single-Step Conditional Diffusion Models
+
+Wentao Qu $^{1}$ , Jing Wang $^{2}$ , YongShun Gong $^{3}$ , Xiaoshui Huang $^{4*}$ , Liang Xiao $^{1*}$  NJUST $^{1}$ , THU $^{2}$ , SDU $^{3}$ , SJTU $^{4}$
+
+{quwentao, jwang}@njust.edu.cn, huangxiaoshui@163.com, xiaoliang@mail.njust.edu.cn
+
+# Abstract
+
+Existing conditional Denoising Diffusion Probabilistic Models (DDPMs) with a Noise-Conditional Framework (NCF) remain challenging for 3D scene understanding tasks, as the complex geometric details in scenes increase the difficulty of fitting the gradients of the data distribution (the scores) from semantic labels. This also results in longer training and inference time for DDPMs compared to non-DDPMs. From a different perspective, we delve deeply into the model paradigm dominated by the Conditional Network. In this paper, we propose an end-to-end robust semantic Segmentation Network based on a Conditional-Noise Framework (CNF) of DDPMs, named CDSegNet. Specifically, CDSegNet models the Noise Network (NN) as a learnable noise-feature generator. This enables the Conditional Network (CN) to understand 3D scene semantics under multi-level feature perturbations, enhancing the generalization in unseen scenes. Meanwhile, benefiting from the noise system of DDPMs, CDSegNet exhibits strong robustness for data noise and sparsity in experiments. Moreover, thanks to CNF, CDSegNet can generate the semantic labels in a single-step inference like non-DDPMs, due to avoiding directly fitting the scores from semantic labels in the dominant network of CDSegNet. On public indoor and outdoor benchmarks, CDSegNet significantly outperforms existing methods, achieving state-of-the-art performance.
+
+# 1. Introduction
+
+Point cloud, as a fundamental 3D representation, provides the most crucial data structure support for 3D tasks. Benefiting from the rapid development of 3D devices and continuous innovation in data synthesis techniques, largescale scene point clouds have become accessible [1, 5, 10, 13]. Therefore, accurate semantic understanding of 3D scenes, applied to a wide range of 3D downstream tasks such as autonomous driving [47], robotic technology [36], and virtual reality [23], has gained increasing attention.
+
+![](images/882fde21ae9f2bf3ae0eeab560db3a1798704f03e9eea3f532fb587f44b2a8bb.jpg)  
+Figure 1. The training and inference difference between NCF and CNF. NCF dominated by NN, relies on the noise fitting quality, requiring extensive training and inference iterations. In contrast, CNF alleviates the noise fitting necessity by focusing on CN, cleverly avoiding this issue, alongside retaining the DDPM robustness.
+
+Encouraged by deep learning, a large number of learnable point cloud semantic segmentation methods have achieved significant results in recent years [8, 24, 50, 52, 53, 64]. Nevertheless, these methods often overlook the fact that raw point clouds from 3D devices are usually perturbed and sparse [5, 42], making them sensitive to data noise and sparsity [21, 43, 56]. This limits the optimal segmentation accuracy, especially recognizing in object boundaries and small objects [60, 61].
+
+Along another research line, DDPMs [16] with a strong noise-robust denoising architecture, originated from and flourished in image generation [11, 28, 41], have been explored in various 3D tasks [34, 39, 54, 66]. They typically consider the 3D task as a conditional generation problem, built upon the Noise-Conditional Framework (NCF, see Fig. 1(a)). In general, the Conditional Network (CN) extracts the conditional features for generating guidance. Meanwhile, the Noise Network (NN) predicts the scores [45] from task targets, dominating the results of tasks.
+
+Unfortunately, this framework poses challenges when applied to real-time 3D scene understanding tasks, such as autonomous driving. This is because, to better fit the scores from task targets, DDPMs typically require more training and inference steps compared to non-DDPMs [44, 45]. Al-
+
+though some methods can accelerate the DDPM sampling process [31, 44], they still require dozens of steps, alongside a sub-optimization process. Moreover, the complex distribution of 3D scenes makes it difficult for DDPMs to achieve satisfactory results in an end-to-end manner. (see Fig. 2)
+
+To address the above problems, in this paper, we rethink the existing end-to-end framework of conditional DDPMs, initially revealing some key insights into the DDPM advantages and limitations in point cloud semantic segmentation.
+
+Inspired by these core insights, we design a Conditional-Noise Framework (CNF, see Fig. 1(b)) of DDPMs, effectively preserving advantages and circumventing limitations. Unlike NCF, CNF treats NN and CN as the auxiliary network and the dominant network in 3D tasks, respectively. In this way, NN in CNF can still inherit the noise construction system of DDPMs, thus preserving the noise and sparsity robustness from DDPMs. Meanwhile, this also enables NN in CNF to relax the requirement of fitting the scores from task targets. Therefore, CNF allows the model to follow the DDPM pattern in training but not in inference, overcoming the demand for extensive iterations from DDPMs.
+
+Furthermore, we propose an end-to-end robust point cloud semantic segmentation network based on CNF, called CDSegNet. Specifically, CDSegNet treats NN as a lightweight noise-feature generator. The noise information from NN, effectively filtered via a Feature Fusion Module (FFM), reasonably perturbs the semantic features in CN. This motivates the generalization ability of CDSegNet in unknown scenes [32, 40, 51]. Meanwhile, under CNF, CDSegNet can follow the noise addition pattern of DDPMs during training, maintaining the robustness to noise from the modeled distribution [39] and the robustness to sparse scenes and insufficient data. Moreover, benefiting from the dominance of CN in CNF, CDSegNet can be regarded as a non-DDPM during inference. This enables CDSegNet to produce the semantic labels in a single-step inference.
+
+To the best of our knowledge, we are the first end-to-end attempt to introduce DDPMs into point cloud semantic segmentation [30, 65]. We lower the threshold and encourage more researchers to further explore applications of DDPMs to 3D tasks. Our key contributions can be summarized as:
+
+- We systematically analyze and identify the advantages and limitations of DDPMs with a Noise-Conditional Framework in point cloud semantic segmentation, offering new knowledge for DDPMs in 3D tasks.  
+- We design a Conditional-Noise Framework of DDPMs, preserving strengths while circumventing shortcomings.  
+- We propose an end-to-end robust point cloud segmentation network based on CNF, CDSegNet, exhibiting strong robustness and requiring only a single-step inference.  
+- Comprehensive experiments on large-scale indoor and outdoor benchmarks demonstrate that CDSegNet achieves significant performance and strong robustness.
+
+# 2. Related Works
+
+Learnable Point Cloud Semantic Segmentation. Benefiting from the powerful data-driven capability of deep learning, directly extracting features from point clouds to understand 3D scene semantics has become possible [8, 37, 38, 48]. Inspired by the aforementioned, a multitude of methods have emerged in recent years, achieving significant success in point cloud semantic segmentation. Early methods usually utilize RNNs to establish interactions between point cloud slices, attempting to improve feature extraction effectiveness through building ordered relationships within point clouds [19, 62]. However, the substantial computational cost greatly limits the input scale. To resolve this problem, some researchers focus on large-scale scene segmentation [12, 18, 26]. Although remarkable progress has been made, the methods are still constrained by a small receptive field, limiting the further improvement in segmentation results. Lately, some methods built upon Transformers have been proposed. These methods inherit the capability of modeling long-range dependencies, overcoming the limitations of the feature receptive field and thereby achieving state-of-the-art results [14, 24, 52, 53, 59, 64].
+
+Although existing methods focusing on segmentation accuracy have achieved impressive results, they overlook the fact that raw point clouds often exhibits perturbed and sparse. This leads to them sensitive to data noise and sparsity. In this paper, we introduce DDPMs with a Conditional-Noise Framework to address the above problem. This demonstrates the strong robustness to data noise and sparsity, while avoiding extensive training and inference steps.
+
+DDPMs for 3D Tasks. DDPMs, succeeded in image generation, have conducted some explorations in various 3D tasks. This typically transforms the 3D task as a conditional generation problem. [33] first introduces DDPMs into point cloud generation, providing inspiration for subsequent explorations. Then, some works attempt to extend DDPMs to point cloud completion [34, 66]. Subsequently, [39] undertakes preliminary investigations into DDPMs for point cloud upsampling. Furthermore, several works have integrated DDPMs into point cloud semantic segmentation using a pre-training (two-stage training) approach [30, 65].
+
+Although some explorations demonstrate the potential of DDPMs in 3D tasks, the two-stage training requirement in scene semantic understanding tasks demonstrate that DDPMs still face the challenge of fitting the scores in complex 3D scenes. Meanwhile, the dozens or even thousands of inference steps limit practical applications in 3D tasks with real-time requirements. In this paper, we propose an end-to-end robust point cloud semantic segmentation network based on our CNF of DDPMs. Thanks to CNF, our method circumvents directly fitting the scores from semantic labels in the dominant segmentation network, requiring only a single-step inference.
+
+# 3. Conditional DDPMs for PCSS
+
+In this section, we first introduce conditional DDPMs. Next, we identify the reason behind leveraging conditional DDPMs for point cloud semantic segmentation (PCSS) and discuss the limiting factors associating with this approach.
+
+# 3.1. Background
+
+Given a target data  $\pmb{x_0} \sim P_{data}$ , a guiding condition  $c \sim P_c$  and a latent variable  $z \sim P_{noise}$ , conditional DDPMs follow an auto-regressive process [39, 44]: a predefined diffusion process  $q$  that gradually destroys the data content until  $x_0$  degrades into  $z$ , and a trainable conditional generation process  $p_\theta$  that slowly generates the specific result until  $z$  is recovered to  $x_0$  under the guidance of the condition  $c$ . We can apply the framework to multiple 3D tasks [33, 34, 39]. In PCSS,  $x_0$  represents the target semantic label, while  $c$  means the segmented point cloud.
+
+We consider the noise as the fitting target, due to the better performance observed in experiments [16]. Then, the training objective under specific conditions is [39]:
+
+$$
+L (\theta) = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, I)} | | \epsilon - \epsilon_ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, C) | | ^ {2}, \tag {1}
+$$
+
+where  $C = \{c,t\}$  represents the conditions, while  $t\sim \mathcal{U}(T)$ $(T = 1000)$ . Therefore, unconditional generation  $(c = \emptyset)$  can be viewed as a special case of conditional DDPMs conditioned on the time label  $t$  for controlling the noise level. That is, our analysis is generalizable to any type of DDPMs.
+
+Meanwhile, under stochastic differential equations (SDEs), the target noise in conditional DDPMs can be converted into and from the score (the gradient of the data distribution) by a constant factor  $\alpha = -\frac{1}{\sqrt{1 - \overline{\alpha}_t}}$  [46]:
+
+$$
+\alpha \epsilon_ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, C) = s _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, C) \approx \nabla_ {\boldsymbol {x} _ {t}} \log P _ {t} (\boldsymbol {x} _ {t}). \tag {2}
+$$
+
+# 3.2. What Supports the Use of DDPMs in PCSS?
+
+Point clouds in real-world scenes are often noisy and sparse [5, 42]. Existing methods overlook this fact, making them sensitive to data noise and sparsity [21, 43, 56]. In this paper, we introduce DDPMs to address this issue.
+
+Noise robustness. Benefiting from the noise system, DDPMs inherently present the robustness to noise from the modeled distribution [39]. We further reveal the key sources of the robustness in the system: the noise samples and the noise fitting. According to Eq. 1, DDPMs can access multi-level noise samples  $x_{t}$  from the modeled distribution and use the standard noise  $\epsilon$  as the fitting target. This facilitates the model to understand the task information under modeled distribution perturbations, enhancing the adaptability to the relevant distribution noise. Sec. 5.3 further discusses and supports the conclusion.
+
+Sparsity robustness. DDPMs exhibit better performance on under-sampled data (sparse scenes and less
+
+data). In fact, this noise-adding manner can be formally regarded as a kind of data augmentation [6, 51, 57]:
+
+$$
+L (\theta) = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, I)} | | \epsilon - \epsilon_ {\boldsymbol {\theta}} \left(f _ {t} \left(\boldsymbol {x} _ {0}\right), \boldsymbol {C}\right) | | ^ {2}, \tag {3}
+$$
+
+where  $f_{t}(\pmb{x}_{0}) = \sqrt{1 - \overline{\alpha}_{t}}\pmb{\epsilon} + \sqrt{\overline{\alpha}_{t}}\pmb{x}_{0}$  [16]. The linear function  $f_{t}(\cdot)$  maps  $\pmb{x}_{0}$  to a more ambiguous latent distribution.
+
+This data augmentation can significantly alleviate the model overfitting (see Tab. 7 and Fig. 9), enhancing the generalization for outdoor sparse scenes (Sec. 5.1, Sec. 5.2 and Sec. 5.5) and less data (Sec. 5.4).
+
+# 3.3. What Limits the Use of DDPMs in PCSS?
+
+Unfortunately, DDPMs may hardly be applied to tasks with high real-time requirements, due to the extensive training and inference iterations they demand (see Fig. 2).
+
+As described in Eq. 1, the performance of DDPMs essentially lies in the noise fitting quality (the proof in the supplementary material). To better approximate the noise target, DDPMs require more training and inference iterations than non-DDPMs, due to the significant error of fitting distributions with a large difference in one step [31, 44, 45].
+
+We provide a proof, under a unified setting for DDPMs and non-DDPMs, DDPMs require more steps  $T$  to converge. For a semantic segmentation task, given a network  $f_{\theta}$  with sufficient fitting ability and a semantic sample pair  $(c, x_0)$ , the training objective of DDPMs and non-DDPMs can be consistently formulated as (assuming using MSE):
+
+$$
+L _ {\theta} = \frac {1}{T} \sum_ {t = 1} ^ {T} \left\| \boldsymbol {y} _ {t - 1} - f _ {\theta} (\boldsymbol {x} _ {t}, \boldsymbol {c}) \right\| ^ {2}, \tag {4}
+$$
+
+where the target  $y_{t-1}$  means the target noise conditioned on the time label  $t$  in DDPMs. Meanwhile, the input  $x_t = \mu_t + \sigma_t \epsilon$  [16], and we omit the time label  $t$  as part of the input.
+
+The inference process commonly follows:
+
+$$
+\boldsymbol {y} _ {\boldsymbol {t} - \boldsymbol {1}} ^ {\prime} = f _ {\theta} (\boldsymbol {x} _ {\boldsymbol {t}}, \boldsymbol {c}), \quad t \in [ 1, T ], \tag {5}
+$$
+
+where  $y_{t-1}^{\prime}$  means the predicted noise in DDPMs.
+
+According to Eq. 4 and Eq. 5, the sufficient convergence for DDPMs requires at least the step size  $T > 1$  to accommodate all  $y_{t-1}$  (training) and  $y_{t-1}'$  (inference), due to the significant error in one step. However, non-DDPMs only necessitate the step size  $T = 1$  (the input  $x_t = \emptyset$ ):
+
+$$
+L _ {\theta} = \left\| \boldsymbol {y} _ {\mathbf {0}} - f _ {\theta} (\emptyset , \boldsymbol {c}) \right\| ^ {2}, \quad \boldsymbol {y} _ {\mathbf {0}} ^ {\prime} = f _ {\theta} (\emptyset , \boldsymbol {c}), \tag {6}
+$$
+
+where the target  $y_0 = x_0$ , while  $y_0'$  means the predicted  $x_0$ .
+
+# 4. Methodology
+
+# 4.1. Conditional-Noise Framework
+
+To maintain the advantage sources (Sec. 3.2) and circumvent the limitation factors (Sec. 3.3), we design
+
+![](images/194ae9758f7fc54d47da85700768259d8c5c5b7b769d4e2fde7133b44b9a2d11.jpg)  
+Figure 2. We try several combinations for conditional DDPMs built on the baseline (Sec. 5.1) on ScanNet in (a). GD+CD (NCF) indicates that NN and CN are modeled as Gaussian [16] and categorical [2] diffusion (details in the supplementary material). To better fit noise, these combinations dominated by NN  $(3,4,5,6)$  require more iterations to converge than CNF, but exhibiting poorer performance, due to complex scene distribution. (b) shows the inference time cost of CNF and NCF under the same baseline. CNF achieves better performance with fewer iterations.
+
+a Conditional-Noise Framework (CNF) of DDPMs (see Fig. 1(b)). Unlike the Noise-Conditional Framework (NCF), CNF regards the Conditional Network  $(\mathrm{CN},f_{\psi})$  as the dominant task backbone and uses the Noise Network  $(\mathrm{NN},\epsilon_{\theta})$  as a auxiliary feature augmentation branch.
+
+Specifically, to perturb the features in CN, the condition  $c$  is added with noise instead of the target  $x_0$  in NN:
+
+$$
+L (\theta) = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, I)} | | \epsilon - \epsilon_ {\theta} (\boldsymbol {c} _ {t}, t) | | ^ {2}. \tag {7}
+$$
+
+Next, a Feature Fusion Module (FFM) is used to filter the noise information from NN, ensuring the feature perturbations in a reasonable manner.
+
+Furthermore, CN learns the task-related information under multi-level feature perturbations via FFM:
+
+$$
+L (\psi) = l _ {t a s k} \left(\boldsymbol {x} _ {\mathbf {0}}, f _ {\psi} \left(f _ {t} (\boldsymbol {c}), \boldsymbol {c}\right)\right), \tag {8}
+$$
+
+where  $f_{t}(c) = \mathcal{F}\mathcal{F}\mathcal{M}(c_{t}^{noise})$  means a nonlinear function.  $\mathcal{F}\mathcal{F}\mathcal{M}(\cdot)$  represents the Feature Fusion Module.  $c_{t}^{noise}$  means the noise feature from  $\epsilon_{\theta}$  with  $c_{t}$  as input.  $l_{task}(\cdot)$  indicates the task-related loss function.
+
+This simple and effective model paradigm:
+
+- Following Noise Construction System. Eq. 7 indicates that the noise system of DDPMs is still retained in NN, aligning with Eq. 1, maintaining the noise robustness.  
+- Aligning with Feature Augmentation. Eq. 8 shows that CN follows the feature augmentation pattern, aligning with Eq. 3, thereby enhancing the sparsity robustness for sparse scenes and less data.  
+- Relaxing Noise Fitting Requirement. Eq. 7 and Eq. 8 mean that the model performance relies on CN rather than NN, relaxing the noise fitting requirement, avoiding excessive training and inference iterations from DDPMs.
+
+Moreover, NN in CNF allows us to transcend the limitation of modeling Gaussian diffusion [16]. This means that CNF can use any distribution of DDPMs [3] (see Fig. 2).
+
+![](images/79463bfa3d5dd07e97b83ff5abec1c4c539559e5d051cd96ba32d122e0488f92.jpg)  
+Figure 3. The overall framework of CDSegNet. The auxiliary Noise Network (NN), seen as a noise-feature generator, modeling the diffusion process conditioned on the time label, perturbs the input features at different noise levels. Meanwhile, the Feature Fusion Module (FFM) controls the noise information flow direction, achieving the semantic feature augmentation by reasonably filtering the perturbations. Furthermore, the dominant Conditional Network (CN) predicts the segmentation results in a pure manner.
+
+# 4.2. Network Architecture
+
+In this section, we introduce the overall architecture of CDSegNet aligned with CNF. This consists of three primary components: the auxiliary Noise Network (NN), the Feature Fusion Module (FFM), and the dominant Conditional Network (CN), as clearly illustrated in Fig. 3 (the parameter and optimization details in the supplementary material).
+
+The Auxiliary Noise Network. NN constructs the noise system of DDPMs, perturbing the conditional point cloud. As mentioned in Sec. 4.1, NN should exhibit lighter, due to the insignificant noise fitting requirement. This follows the Transformer-U-Net architecture [52, 64], stacking two-stage standard Transformer blocks in the encoder and decoder. Meanwhile, similar to [52, 53], we utilize the effective grid pooling to achieve upsampling and downsampling. Moreover, the insignificant noise fitting also means that introducing the time label  $t$  in NN is sufficient to model the diffusion process without considering additional conditions.
+
+The Feature Fusion Module. FFM directs the information flow from NN to CN at the bottleneck stage. In fact, FFM can adaptively filter the noise information, making the feature augmentation from NN in a reasonable way, as excessive perturbations may harm the performance of CN.
+
+Specifically, FFM first performs the feature projection via MLPs,  $F_{cn}\in \mathbb{R}^{N_{cn}\times C_{cn}}\to (Q)\in \mathbb{R}^{N_{cn}\times C},F_{nn}\in \mathbb{R}^{N_{nn}\times C_{nn}}\to (K,V)\in \mathbb{R}^{N_{nn}\times C}$ . Subsequently, FFM filters the noise information via a Cross-Attention block [49]:
+
+$$
+\begin{array}{c} O = m l p (W V) + F _ {c n}, \\ F _ {c n} = f _ {c n} (O) + O \end{array} \tag {9}
+$$
+
+$$
+F = f f n (O) + O,
+$$
+
+where  $W\in \mathbb{R}^{N_{cn}\times N_{nn}} = \text{softmax}(\frac{QK^T}{\sqrt{C}})$ .
+
+We consider the unidirectional flow  $F_{nn} \xrightarrow{FFM} F_{cn}$ , due
+
+![](images/c4ab0bb99764c5331907f6ba965720f67e68230844eeab0e82dd69d89db0a680.jpg)  
+Figure 4. The visualization results on ScanNet. Our method achieves better semantic segmentation results in object boundaries, such as the boundary between the wall and the wall (red solid box) and the boundary between the wall and the window (blue solid box).
+
+![](images/b3f4b4a8784c2b6c2fff2deec834f26ec523a6ad26dc1eba8bae7507d53f5763.jpg)  
+Figure 5. The visualization results on ScanNet200. Our method achieves the clearer segmentation results in small object recognition, and segments the categories not labeled in the Ground Truth, such as the keyboard (black dashed box) and the whiteboard (orange solid box).
+
+to the better trade-off between the performance and computational cost and the sufficient diffusion modeling in NN.
+
+The Dominant Conditional Network. CN follows the architecture of NN, with four stages for both the encoder and decoder, focusing on the segmentation results. Meanwhile, besides the feature perturbations from NN, we use only the conditional point cloud as input, ensuring that CN concentrates purely on the scene semantic understanding.
+
+# 4.3. Training and Inference
+
+Training. Following [52, 53], we constrain the semantic segmentation results in CN:
+
+$$
+L (\psi) = C E \left(\boldsymbol {x} _ {0}, \boldsymbol {x} _ {0} ^ {\prime}\right) + \lambda \operatorname {L o v a z} \left(\boldsymbol {x} _ {0}, \boldsymbol {x} _ {0} ^ {\prime}\right), \tag {10}
+$$
+
+where  $CE(\cdot)$  represents the cross-entropy loss, while Lovasz  $(\cdot)$  follows [4].  $\lambda = 1$  means a weighting factor.
+
+Furthermore, we can optimize CNF from a multi-task perspective (the noise fitting in NN and the semantic label fitting in CN). This applies the Geometric Loss Strategy (GLS) [7], with a geometric mean weight, to alleviate the convergence speed difference between NN and CN, regulating the perturbations from NN in a reasonable manner:
+
+$$
+L _ {t o t a l} = \prod_ {i = 1} ^ {n} \sqrt [ n ]{L _ {i}} = \sqrt {L (\theta)} \cdot \sqrt {L (\psi)}, \tag {11}
+$$
+
+where  $n = 2$  means the number of tasks.
+
+Inference. Thanks to CNF, CDSegNet can be seen as a non-DDPM during inference, requesting only one step:
+
+$$
+\boldsymbol {x} _ {\mathbf {0}} ^ {\prime} = \mathcal {D} _ {c} \left(\mathcal {E} _ {c} (\boldsymbol {c}), \mathcal {F F M} \left(\mathcal {E} _ {n} \left(\boldsymbol {c} _ {\boldsymbol {T}}, T\right)\right)\right), \tag {12}
+$$
+
+where  $c_{T} \sim \mathcal{N}(0, I)$ , while  $x_{0}'$  means the predicted semantic label.
+
+# 5. Experiments
+
+# 5.1. Experiment Setup
+
+Dataset. Two indoor benchmarks (ScanNet [10], ScanNet200 [42]) and one outdoor benchmark (nuScenes [5]) are used for evaluations. For ScanNet and ScanNet200, we divide train/val/test with 1201/312/100 scenes like [52, 53]. Meanwhile, the official protocol is followed to split train/val/test into 700/150/150 scenes for nuScenes. The point clouds in ScanNet, ScanNet200 and nuScenes are voxelized into  $0.02\mathrm{m}$ ,  $0.02\mathrm{m}$  and  $0.05\mathrm{m}$ , respectively.
+
+Baseline. To demonstrate the effectiveness of our method, we set a baseline. This eliminates the diffusion modeling in NN of CDSegNet, converting NN into a lightweight CN that approximates the input using MSE.
+
+# 5.2. Comparison of Segmentation Results
+
+Indoor Dataset. We first conduct evaluations on indoor datasets. Tab. 1 shows that CDSegNet achieves significant performance on ScanNet and ScanNet200. Meanwhile, CDSegNet outperforms all other methods across all metrics on ScanNet. This is because, benefiting from the strong noise robustness, CDSegNet can achieve better results on object boundaries with more perturbations. Fig. 4 shows the visualization on ScanNet, further supporting the viewpoint. Moreover, CDSegNet also demonstrates significant results in recognizing small objects within more complex and perturbed scenes. As shown in Fig. 5, CDSegNet
+
+![](images/27bc1d899e9430212072cc4d5dad2191ad1775a40976427769801638b06f4761.jpg)  
+Figure 6. The visualization results on nuScenes. Our method produces remarkable results in small object recognition, such as the vegetation (red solid box and blue solid box).
+
+can more clearly identify small objects, such as the pillow (green solid box) and the whiteboard (orange solid box).
+
+Actually, as shown in Fig. 5, the Ground Truth sometimes includes incorrect annotations (e.g., some points of sofa are labeled as the pillow category) or may even omit annotations (e.g., the whiteboard and the keyboard). This may be one of the reasons why most models perform poorly on ScanNet200. Meanwhile, the significant results on mIoU indicate that our CDSegNet can achieve better performance in perturbed environments compared to other methods.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">ScanNet [10]</td><td colspan="3">ScanNet200 [42]</td></tr><tr><td>mIoU</td><td>mAcc</td><td>allAcc</td><td>mIoU</td><td>mAcc</td><td>allAcc</td></tr><tr><td>PTv1 [64]</td><td>70.8</td><td>76.4</td><td>87.5</td><td>29.8</td><td>40.5</td><td>78.4</td></tr><tr><td>MinkUNet [8]</td><td>72.3</td><td>79.4</td><td>89.1</td><td>28.3</td><td>39.8</td><td>77.9</td></tr><tr><td>ST [24]</td><td>74.3</td><td>82.5</td><td>90.7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OctFormer [50]</td><td>75.0</td><td>83.1</td><td>91.3</td><td>32.9</td><td>42.4</td><td>81.2</td></tr><tr><td>PTv2 [52]</td><td>75.5</td><td>82.9</td><td>91.2</td><td>31.4</td><td>42.0</td><td>80.7</td></tr><tr><td>PTv3 [53]</td><td>77.6</td><td>85.0</td><td>92.0</td><td>35.3</td><td>46.0</td><td>83.3</td></tr><tr><td>Baseline</td><td>77.5</td><td>85.1</td><td>91.9</td><td>35.4</td><td>45.5</td><td>83.6</td></tr><tr><td>Ours</td><td>77.9</td><td>85.2</td><td>92.2</td><td>36.3</td><td>45.9</td><td>83.9</td></tr></table>
+
+Table 1. The results on ScanNet and ScanNet200. Our method surpasses other methods in almost all metrics.
+
+Outdoor Dataset. We also conduct the validation on the outdoor benchmark. Compared to indoor scenes, the spatial distance between points in outdoor point clouds is larger. This causes more significant data sparsity. Tab. 2 shows that CDSegNet exhibits the excellent results, significantly outperforming existing methods on the mIoU. As mentioned in Sec. 4.1, CNF aligns with a feature augmentation strategy, improving generalization on sparse scenes. Fig. 6 further demonstrates the superiority of CDSegNet in small object recognition in large outdoor sparse scenes, such as the vegetation (red solid box and blue solid box).
+
+# 5.3. Validation for Noise Robustness
+
+We further validate the noise robustness of CDSegNet. This adds a Gaussian perturbation  $n_G \sim \mathcal{N}(n_G; 0, \tau I)$  to the normalized inputs of models [15, 39], i.e.,  $c' = c + n_G$ .
+
+Fig. 7 demonstrates the strong noise robustness of CD-SegNet on ScanNet and ScanNet200. Meanwhile, we can observed that Ours and Ours- $x_0$  are stronger than the baseline, validating the conclusion in Sec. 3.2. However, Ours- $x_0$  performs significantly weaker than Ours. Although
+
+Ours- $x_0$  retains the noise sample  $\boldsymbol{x}_t$  during training, the fitting target is  $\boldsymbol{x}_0$ , not  $\epsilon$ . This leads to the model lacking the further noise adaptability in scenes. We believe that the noise fitting in the noise system of DDPMs contributes mainly to the noise robustness (we hope to validate the conclusion in the future).
+
+![](images/c56a4e888bb037bf598bc98b0cf6ff0a6e7e00791dbe83fbdc64c1a4f96cac4c.jpg)  
+Figure 7. The noise robustness results on ScanNet and ScanNet200. Ours- $\pmb{x}_0$  means the fitting target is  $\pmb{x}_0$  in NN of CD-SegNet. Our method consistently outperforms all other methods.
+
+![](images/aa46a4e8b14ce4d0b670e2fc210ed023323908643cdaaa359c5f313fabd4c570.jpg)  
+Figure 8. The sparsity robustness results on under-sampled ScanNet. Our method demonstrates the best results in all cases.
+
+Furthermore, we investigate the robustness to noise from other distributions. Tab. 3 shows that although CDSegNet maintains strong performance across noise from other distributions, the performance is slightly reduced compared to Gaussian noise. Combined with Eq. 2, [39] provides an intuitive explanation from the perspective of the gradient of the data distribution, i.e., the predicted noise guiding  $\boldsymbol{x}_t \xrightarrow{\epsilon} \boldsymbol{x}_{t-1}, \epsilon \sim p_{noise}(\epsilon | \boldsymbol{x}_t, C)$ . In this paper, we provide a simpler explanation that is consistent with the source.
+
+According to Sec. 3.2, since DDPMs can see multi-level noise samples and fit the noise target from the modeled distribution during training, this makes that they can adapt to
+
+<table><tr><td>Methods</td><td>mIoU</td><td>barrier</td><td>bicycle</td><td>bus</td><td>car</td><td>vehicle</td><td>motor</td><td>pedestrian</td><td>cone</td><td>trailer</td><td>truck</td><td>drivable</td><td>others</td><td>sidewalk</td><td>terrain</td><td>manmade</td><td>vegetation</td></tr><tr><td>RangeNet53++ [35]</td><td>65.5</td><td>66.0</td><td>21.3</td><td>77.2</td><td>80.9</td><td>30.2</td><td>66.8</td><td>69.6</td><td>52.1</td><td>54.2</td><td>72.3</td><td>94.1</td><td>66.6</td><td>63.5</td><td>70.1</td><td>83.1</td><td>79.8</td></tr><tr><td>PolarNet [63]</td><td>71.0</td><td>74.7</td><td>28.2</td><td>85.3</td><td>90.9</td><td>35.1</td><td>77.5</td><td>71.3</td><td>58.8</td><td>57.4</td><td>76.1</td><td>96.5</td><td>71.1</td><td>74.7</td><td>74.0</td><td>87.3</td><td>85.7</td></tr><tr><td>Salsanext [9]</td><td>72.2</td><td>74.8</td><td>34.1</td><td>85.9</td><td>88.4</td><td>42.2</td><td>72.4</td><td>72.2</td><td>63.1</td><td>61.3</td><td>76.5</td><td>96.0</td><td>70.8</td><td>71.2</td><td>71.5</td><td>86.7</td><td>84.4</td></tr><tr><td>AMVNet [29]</td><td>76.1</td><td>79.8</td><td>32.4</td><td>82.2</td><td>86.4</td><td>62.5</td><td>81.9</td><td>75.3</td><td>72.3</td><td>83.5</td><td>65.1</td><td>97.4</td><td>67.0</td><td>78.8</td><td>74.6</td><td>90.8</td><td>87.9</td></tr><tr><td>Cylinder3D [67]</td><td>76.1</td><td>76.4</td><td>40.3</td><td>91.2</td><td>93.8</td><td>51.3</td><td>78.0</td><td>78.9</td><td>64.9</td><td>62.1</td><td>84.4</td><td>96.8</td><td>71.6</td><td>76.4</td><td>75.4</td><td>90.5</td><td>87.4</td></tr><tr><td>PVKD [17]</td><td>76.0</td><td>76.2</td><td>40.0</td><td>90.2</td><td>94.0</td><td>50.9</td><td>77.4</td><td>78.8</td><td>64.7</td><td>62.0</td><td>84.1</td><td>96.6</td><td>71.4</td><td>76.4</td><td>76.3</td><td>90.3</td><td>86.9</td></tr><tr><td>RPVNet [58]</td><td>77.6</td><td>78.2</td><td>43.4</td><td>92.7</td><td>93.2</td><td>49.0</td><td>85.7</td><td>80.5</td><td>66.0</td><td>66.9</td><td>84.0</td><td>96.9</td><td>73.5</td><td>75.9</td><td>76.0</td><td>90.6</td><td>88.9</td></tr><tr><td>SphereFormer [25]</td><td>79.5</td><td>78.7</td><td>46.7</td><td>95.2</td><td>93.7</td><td>54.0</td><td>88.9</td><td>81.1</td><td>68.0</td><td>74.2</td><td>86.2</td><td>97.2</td><td>74.3</td><td>76.3</td><td>75.8</td><td>91.4</td><td>89.7</td></tr><tr><td>PTv3 [53]</td><td>80.3</td><td>80.5</td><td>53.8</td><td>95.9</td><td>91.9</td><td>52.1</td><td>88.9</td><td>84.5</td><td>71.7</td><td>74.1</td><td>84.5</td><td>97.2</td><td>75.6</td><td>77.0</td><td>76.2</td><td>91.2</td><td>89.6</td></tr><tr><td>Baseline</td><td>80.4</td><td>80.1</td><td>53.2</td><td>95.9</td><td>92.0</td><td>56.5</td><td>89.2</td><td>84.1</td><td>71.2</td><td>73.1</td><td>84.4</td><td>96.9</td><td>76.5</td><td>77.2</td><td>75.8</td><td>91.3</td><td>89.4</td></tr><tr><td>Ours</td><td>81.2</td><td>80.1</td><td>53.5</td><td>97.0</td><td>92.3</td><td>62.3</td><td>89.7</td><td>84.2</td><td>71.7</td><td>72.2</td><td>85.9</td><td>97.2</td><td>76.5</td><td>77.8</td><td>76.9</td><td>91.4</td><td>89.7</td></tr></table>
+
+related distribution noise during inference. That is, DDPMs are definitely robust to noise from the modeled distribution compared to non-DDPMs. Moreover, the closer the noise distribution is to the modeled distribution, the better the noise robustness (the Laplace distribution); otherwise, this deteriorates (the Poisson distribution).
+
+Table 2. The results on nuScenes. Our method significantly outperforms other methods in the term of mIoU.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Smalle τ (mIoU)</td><td colspan="3">Big τ (mIoU)</td></tr><tr><td>τ=0.01</td><td>τ=0.05</td><td>τ=0.1</td><td>τ=0.5</td><td>τ=0.7</td><td>τ=1.0</td></tr><tr><td colspan="7">Gaussian Noise</td></tr><tr><td>PTv2 [52]</td><td>75.5</td><td>75.4</td><td>73.7</td><td>8.7</td><td>1.5</td><td>1.2</td></tr><tr><td>PTv3 [53]</td><td>77.6</td><td>77.4</td><td>76.9</td><td>45.8</td><td>26.0</td><td>12.9</td></tr><tr><td>Ours</td><td>77.9</td><td>77.7</td><td>77.2</td><td>57.0</td><td>46.7</td><td>35.9</td></tr><tr><td colspan="7">Uniform Noise</td></tr><tr><td>PTv2 [52]</td><td>75.5</td><td>75.5</td><td>75.2</td><td>51.2</td><td>45.7</td><td>20.6</td></tr><tr><td>PTv3 [53]</td><td>77.6</td><td>77.6</td><td>77.5</td><td>74.3</td><td>70.6</td><td>56.5</td></tr><tr><td>Ours</td><td>77.9</td><td>77.9</td><td>77.8</td><td>74.8</td><td>70.9</td><td>56.8</td></tr><tr><td colspan="7">Laplace Noise</td></tr><tr><td>PTv2 [52]</td><td>75.4</td><td>75.2</td><td>73.9</td><td>22.4</td><td>7.4</td><td>3.2</td></tr><tr><td>PTv3 [53]</td><td>77.6</td><td>77.4</td><td>76.2</td><td>30.1</td><td>14.5</td><td>8.3</td></tr><tr><td>Ours</td><td>77.8</td><td>77.6</td><td>76.7</td><td>43.0</td><td>26.7</td><td>14.3</td></tr><tr><td colspan="7">Possion Noise</td></tr><tr><td>PTv2 [52]</td><td>75.5</td><td>74.2</td><td>61.2</td><td>2.4</td><td>1.2</td><td>1.0</td></tr><tr><td>PTv3 [53]</td><td>77.6</td><td>77.1</td><td>73.6</td><td>5.7</td><td>2.8</td><td>1.5</td></tr><tr><td>Ours</td><td>77.8</td><td>76.8</td><td>73.3</td><td>6.5</td><td>3.0</td><td>1.9</td></tr></table>
+
+# 5.4. Validation for Sparsity Robustness
+
+We also conduct sparsity robustness experiments on the under-sampled ScanNet. This first randomly samples  $5\%$ ,  $10\%$ ,  $12.5\%$ ,  $25\%$ , and  $50\%$  from the training and validation set, respectively. Subsequently, the model is trained and fitted on the under-sampled training and validation set, while performing inference on the entire validation set.
+
+Fig. 8 illustrates the results. CDSegNet demonstrates the significant superiority on under-sampled data. As mentioned in Sec. 3.2, CNF aligns a learnable feature augmentation, mapping the features to more complex distributions, enhancing the overfitting resistance of models on less data.
+
+# 5.5. Generalization for CNF
+
+As mentioned in Sec. 4.1, CNF is a new network framework that introduces DDPMs into 3D tasks. Therefore, we further conduct the generalization experiments of CNF.
+
+Other backbones. We first conduct the experiments for introducing CNF into MinkUNet and PTv3. We only add FFM and NN of CDSegNet to MinkUNet (using MinkUNet
+
+achieving NN) and PTv3. In Tab. 4, by introducing CNF, MinkUNet and PTv3 exhibit the better results in multiple benchmarks, due to the feature augmentation through reasonable perturbations. Moreover, benefiting from the lightweight NN, the additional inference time and memory consumption introduced by CNF in MinkUnet and PTv3 are negligible. Furthermore, we observe that PTv3 is surprisingly slower than CDSegNet on nuScenes, as PTv3 utilizes time-consuming point-level element-wise addition for skip connections, while CDSegNet uses channel concatenation.
+
+Table 3. The results of multiple distribution noise robustness on ScanNet. Our method performs well on the Gaussian and Laplace noise (approximating the modeled distributions), but performs slightly poorly on the Poisson noise (far from the one).  
+
+<table><tr><td>Methods</td><td>Params</td><td>mIoU</td><td>τ=0.1</td><td>τ=0.5</td><td>τ=1.0</td><td>IT/MM</td></tr><tr><td colspan="7">ScanNet [10]</td></tr><tr><td>MinkUNet [8]</td><td>37.9M</td><td>72.3</td><td>70.0</td><td>3.6</td><td>0.1</td><td>63s/0.9G</td></tr><tr><td>PTv3 [53]</td><td>46.2M</td><td>77.6</td><td>77.5</td><td>45.8</td><td>12.9</td><td>53s/1.1G</td></tr><tr><td>Baseline</td><td>101.4M</td><td>77.5</td><td>76.9</td><td>46.1</td><td>13.0</td><td>55s/1.9G</td></tr><tr><td>MinkUNet+CNF</td><td>47.1M</td><td>73.5</td><td>73.4</td><td>35.4</td><td>12.2</td><td>63s/1.0G</td></tr><tr><td>PTv3+CNF</td><td>59.4M</td><td>77.7</td><td>77.4</td><td>60.1</td><td>33.2</td><td>53s/1.1G</td></tr><tr><td>CDSegNet</td><td>101.4M</td><td>77.9</td><td>77.6</td><td>57.0</td><td>35.9</td><td>56s/1.9G</td></tr><tr><td colspan="7">ScanNet200 [42]</td></tr><tr><td>MinkUNet [8]</td><td>37.9M</td><td>28.3</td><td>27.8</td><td>1.2</td><td>0.0</td><td>64s/0.9G</td></tr><tr><td>PTv3 [53]</td><td>46.2M</td><td>35.3</td><td>34.0</td><td>10.2</td><td>1.0</td><td>53s/1.1G</td></tr><tr><td>Baseline</td><td>101.4M</td><td>35.4</td><td>33.9</td><td>11.1</td><td>1.2</td><td>56s/1.9G</td></tr><tr><td>MinkUNet+CNF</td><td>47.1M</td><td>30.6</td><td>29.4</td><td>15.6</td><td>6.4</td><td>64s/0.9G</td></tr><tr><td>PTv3+CNF</td><td>59.4M</td><td>35.9</td><td>35.5</td><td>21.2</td><td>7.0</td><td>53s/1.1G</td></tr><tr><td>CDSegNet</td><td>101.4M</td><td>36.3</td><td>35.7</td><td>20.6</td><td>5.5</td><td>57s/1.9G</td></tr><tr><td colspan="7">nuScenes [5]</td></tr><tr><td>MinkUNet [8]</td><td>37.9M</td><td>73.4</td><td>45.4</td><td>1.0</td><td>1.0</td><td>733s/1.0G</td></tr><tr><td>PTv3 [53]</td><td>46.2M</td><td>80.3</td><td>63.9</td><td>1.1</td><td>1.1</td><td>163s/1.0G</td></tr><tr><td>Baseline</td><td>101.4M</td><td>80.4</td><td>64.5</td><td>1.1</td><td>1.1</td><td>128s/1.8G</td></tr><tr><td>MinkUNet+CNF</td><td>47.1M</td><td>75.7</td><td>55.3</td><td>1.3</td><td>1.3</td><td>735s/1.1G</td></tr><tr><td>PTv3+CNF</td><td>59.4M</td><td>81.0</td><td>64.8</td><td>1.3</td><td>1.3</td><td>126s/1.1G</td></tr><tr><td>CDSegNet</td><td>101.4M</td><td>81.2</td><td>66.2</td><td>3.8</td><td>3.8</td><td>129s/1.8G</td></tr></table>
+
+Table 4. The results of backbones on multiple benchmarks. 'IT' and 'MM' mean the inference time and the mean memory. We run on an NVIDIA 3090 GPU with batch size=1, without using test-time augmentation (TTA) and fragmented inference.  
+
+<table><tr><td>Methods</td><td>Params</td><td>Val</td><td>Test</td><td>Only using training data?</td><td>IT/MM</td></tr><tr><td>PTv3 [53]</td><td>46.2M</td><td>80.3</td><td>81.2</td><td>✓</td><td>163s/1.0G</td></tr><tr><td>PTv3+PPT [53]</td><td>97.3M</td><td>81.2</td><td>83.0</td><td>✗</td><td>-/-</td></tr><tr><td>PTv3+CNF</td><td>59.4M</td><td>81.0</td><td>82.8</td><td>✓</td><td>126s/1.1G</td></tr><tr><td>CDSegNet</td><td>101.4M</td><td>81.2</td><td>82.0</td><td>✓</td><td>129s/1.9G</td></tr></table>
+
+Table 5. The results on the nuScenes test set. Our method shows excellent generalization ability on the nuScenes test set.
+
+On Test set. We further evaluated on the nuScenes test set. PTv3+PPT adopts a multi-dataset joint training strategy (For a fair comparison, we avoid deliberately optimizing the results, as we cannot know how many datasets and tricks were actually used). In Fig. 5, PTv3+CNF, despite having nearly half the number of parameters and being trained only on the training set, performs slightly worse than PTv3+PPT.
+
+Other 3D tasks. We also introduce CNF into the other 3D tasks, classification. PointNet [37] and PointNet++ [38]
+
+are selected as backbones. We use an additional PointNet++ branch for modeling the diffusion process. Tab. 6 show that by introducing CNF, they exhibit significant improvements in classification, alleviating the sensitivity to noise.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="4">PointNet [37]</td><td colspan="4">PointNet++ [38]</td></tr><tr><td>CA</td><td>IA</td><td>τ=0.5</td><td>25%</td><td>CA</td><td>IA</td><td>τ=0.5</td><td>25%</td></tr><tr><td>Without CNF</td><td>86.9</td><td>90.5</td><td>2.4</td><td>19.8</td><td>90.4</td><td>92.3</td><td>2.5</td><td>20.0</td></tr><tr><td>With CNF</td><td>88.1</td><td>91.9</td><td>15.6</td><td>25.3</td><td>91.3</td><td>93.2</td><td>16.1</td><td>28.7</td></tr></table>
+
+Table 6. The classification results on ModelNet40 [55]. 'CA' means the class accuracy, while 'IA' stands for the instance accuracy. Introducing CNF improves the results in classification.
+
+# 5.6. Ablation Study
+
+The diffusion modeling. We first conduct the ablation study for the diffusion modeling in CDSegNet. Tab. 7 shows the results on ScanNet. Ours-CN surprisingly experiences a significant drop across all cases. We believe that the excessive parameters make the model overfit on ScanNet, resulting in the poor generalization. In fact, reducing the parameter number will transform Ours-CN into PTv3. This demonstrates that the reasonable perturbations can significantly enhance the overfitting resistance of CN. Fig. 9(a) further supports the conclusion.
+
+![](images/d4a769153a88f9d0cff3899168c8ca46b222fe55c76dec0b40dd27e37b4a5205.jpg)  
+Figure 9. (a) shows the training loss curves of Ours, PTv3 and Ours-CN on ScanNet. The loss curve of Ours-CN (with more parameters compare) is nearly identical to that of PTv3, but the poorer results during inference, indicating overfitting. However, Ours demonstrates the lower loss curve and better performance, as the reasonable perturbations from NN alleviates the model overfitting, enhancing the generalization. In (b), the linear schedule noise range ③ demonstrates the best trade-off.
+
+The noise schedule range. The noise schedule range is crucial for CDSegNet, controlling the perturbation degree. Generally, the noise schedule range is positively correlated with the robustness, while showing a negative correlation with the performance. This produces the trade-off between the segmentation performance and the noise robustness.
+
+In Fig. 9(b),  $③$  yields the best trade-off on ScanNet200. Meanwhile, the cosine noise schedule range [0, 1000] and the linear schedule noise range  $⑤$  correspond to the best results for ScanNet and nuScenes, respectively. This inspires us to choose a smaller schedule range for the more complex (ScanNet200) or sparser (nuScenes) scenes. Conversely, a larger range should be selected (ScanNet).
+
+The multi-task optimization. Benefiting from the dual branch architecture [20, 39], CDSegNet has two fitting objectives: the noise fitting and the semantic label fitting,
+
+coming from NN and CN, respectively. However, as mentioned in Sec. 3.3, the noise fitting typically converges more slowly, due to more fitting targets. This may cause the unreasonable noise information from NN to impair the ability of CN for understanding the scene semantics. Therefore, in addition to FFM, we also apply an effective loss balancing strategy to further alleviates the unreasonable noise perturbations (more optimizations in the supplementary material).
+
+We consider several loss balancing strategies: 1) Equal Weighting (EW). 2) Random Loss Weighting (RLW) [27]. 3) Uncertainty Weights (UW) [22]. 4) Geometric Loss Strategy (GLS) [7]. Tab. 8 shows that GLS produces the best results. Moreover, we observed that after balancing with GLS, the loss values from CN and NN become closer and exhibit smaller fluctuations. This can further inspire us to optimize the model with a multi-branch framework from a multi-task perspective. Meanwhile, to achieve better performance, the loss values among multiple tasks should be more compact and stable.
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Params</td><td colspan="3">Performance</td><td colspan="2">Robustness</td></tr><tr><td>mIoU</td><td>mAcc</td><td>allAcc</td><td>τ=0.5</td><td>25%</td></tr><tr><td>PTv3</td><td>46.2M</td><td>77.6</td><td>85.0</td><td>92.0</td><td>45.8</td><td>64.3</td></tr><tr><td>Ours-CN</td><td>88.1M</td><td>76.6</td><td>84.6</td><td>91.6</td><td>43.4</td><td>61.8</td></tr><tr><td>Baseline</td><td>101.4M</td><td>77.5</td><td>85.1</td><td>91.9</td><td>46.1</td><td>64.0</td></tr><tr><td>Ours</td><td>101.4M</td><td>77.9</td><td>85.2</td><td>92.2</td><td>57.0</td><td>66.5</td></tr></table>
+
+Table 7. Ablation study of the diffusion modeling in CDSegNet on ScanNet. The baseline means removing the diffusion modeling in NN. Meanwhile, Our-CN represents removing entire NN in CDSegNet, retaining only CN. This results demonstrate the importance of the diffusion modeling for CDSegNet.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">Performance</td><td colspan="2">Robustness</td></tr><tr><td>mIoU</td><td>mAcc</td><td>allAcc</td><td>τ=0.5</td><td>25%</td></tr><tr><td>EW</td><td>77.6</td><td>85.1</td><td>92.0</td><td>55.5</td><td>64.4</td></tr><tr><td>RLW [27]</td><td>77.4</td><td>85.0</td><td>91.9</td><td>54.1</td><td>63.9</td></tr><tr><td>UW [22]</td><td>77.6</td><td>85.0</td><td>92.1</td><td>55.6</td><td>65.1</td></tr><tr><td>GLS [7]</td><td>77.9</td><td>85.2</td><td>92.2</td><td>57.0</td><td>66.5</td></tr></table>
+
+Table 8. Ablation study of multi-task optimization on ScanNet. GLS shows the better performance and robustness for CDSegNet. 6. Conclusion
+
+In this paper, we systematically revealed some key insights of DDPMs in point cloud semantic segmentation. Meanwhile, to preserve the advantages while overcoming the limitations, a Conditional-Noise Framework of DDPMs is designed. Based on this, we further proposed an end-to-end robust point cloud segmentation network, CDSegNet. CDSegNet demonstrated the strong robustness to the data noise and sparsity, while requiring a single-step inference. Moreover, we provided a more understandable explanation for the noise robustness from DDPMs. Overall, we have lowered the barrier for applying DDPMs, with the hope of encouraging broader extensions of DDPMs in 3D tasks.
+
+Acknowledgments. This work was supported in part by the Frontier Technologies R&D Program of Jiangsu under grant BF2024070, in part by the National Natural Science Foundation of China under Grant 62471235, and in part by Hunan Natural Science Foundation Project (No. 2025JJ50338) and Shanghai Education Committee AI Project (No. JWAIYB-2).
+
+# References
+
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+# An Image-like Diffusion Method for Human-Object Interaction Detection
+
+Xiaofei Hui Haoxuan  $\mathbf{Q}\mathbf{u}^{\dagger}$  Hossein Rahmani Jun Liu Lancaster University
+
+{x.hui, h.qu5, h.rahmani, j.liu81}@lancaster.ac.uk
+
+# Abstract
+
+Human-object interaction (HOI) detection often faces high levels of ambiguity and indeterminacy, as the same interaction can appear vastly different across different human-object pairs. Additionally, the indeterminacy can be further exacerbated by issues such as occlusions and cluttered backgrounds. To handle such a challenging task, in this work, we begin with a key observation: the output of HOI detection for each human-object pair can be recast as an image. Thus, inspired by the strong image generation capabilities of image diffusion models, we propose a new framework, HOI-IDiff. In HOI-IDiff, we tackle HOI detection from a novel perspective, using an Image-like Diffusion process to generate HOI detection outputs as images. Furthermore, recognizing that our recast images differ in certain properties from natural images, we enhance our framework with a customized HOI diffusion process and a slice patchification model architecture, which are specifically tailored to generate our recast "HOI images". Extensive experiments demonstrate the efficacy of our framework.
+
+# 1. Introduction
+
+Human-object interaction (HOI) detection aims to predict all interactions between each human-object pair in an image, with each interaction represented as a <human-interaction-object> triplet. Its significance spans across diverse applications, such as robotics [41], visual question answering [6], and image captioning [59]. Recently, it has gained a great deal of research attention [34, 39, 52, 54, 55, 58, 62, 63]. Despite growing efforts, HOI detection still remains a challenging task. One reason is that the same interaction can look very differently across different human-object pairs, while different interactions can sometimes appear visually similar [2, 7]. Additionally, challenges also arise from other factors such as occlusions and cluttered backgrounds [28, 52, 67]. These challenges can lead to high noise and indeterminacy (ambiguity) in the HOI detection
+
+![](images/11b0c7520d83296975fe585f4775fed6ca30e75827b48c02f710cd0df907e87e.jpg)  
+Figure 1. Illustration of the HOI image (of shape  $H \times W \times 2$ ) formed over a human-object pair in (a) in which the human is watching and pushing the box. In this figure, we illustrate the case in which  $H = 5$  and  $W = 6$ . We use a black pixel to represent a pixel with value 0, and a white pixel to represent a pixel with value 1. As shown, the HOI image  $I^{hoi}$  in (d) is formed as the product of the vector  $v^{obj}$  in (b) and the matrix  $m^{int}$  in (c), in which  $v^{obj}$  (of shape  $H$ ) represents the object classification result, and  $m^{int}$  (of shape  $W \times 2$ ) represents the interaction prediction result.
+
+process, resulting in error-prone predictions [7].
+
+Recently, showing superb performance in generating high-quality images, image diffusion models [19, 43] have become powerful image generators across various fields [23, 27]. Specifically, these models typically transform noisy, indeterminate images into high-quality, determinate ones by gradually removing the noise. This process intuitively breaks down the potentially large gap between noisy images and high-quality ones into a series of smaller steps [49], making the transition smooth and quite manageable.
+
+Motivated by the efficacy of image diffusion models, in this work, for HOI detection—a task that also involves noise and indeterminacy—we explore tackling it through an image diffusion process. We start our exploration with a key observation: the outputs of HOI detection for each human-object pair can also form an image. Specifically, since HOI detection for each human-object pair can be viewed as two
+
+interrelated sub-tasks, i.e., object classification and interaction prediction [65], the output of HOI detection for each human-object pair can then be represented as an image in three steps: (1) Object classification. Firstly, let  $H$  denote the total number of object categories. As shown in Fig. 1 (b), the output of object classification can be represented as a probability distribution  $v^{obj}$  of size  $H$ . Especially, in the human-object pair illustrated in Fig. 1, the object category is "box". Thus, in  $v^{obj}$ , the entry corresponding to the "box" category has a value of 1. (2) Interaction prediction. Next, for the sub-task interaction prediction, it can be treated as a set of binary classification problems [13, 25], each determining the presence/absence of a certain interaction category within the current human-object pair. Consequently, let  $W$  denote the total number of interaction categories. As shown in Fig. 1 (c), the output of interaction prediction can then be represented as  $W$  probability distributions, each of size 2, collectively denoted as  $m^{int}$  of size  $W \times 2$ . Especially, in the human-object pair shown in Fig. 1, the interactions "push" and "watch" are present. Hence, in  $m^{int}$ , the two entries corresponding to the "presence" of "push" and "watch" both have values of 1. (3) Interrelation capturing. Finally, the interrelation between the above two subtasks can be captured via "multiplying" their corresponding outputs (i.e.,  $v^{obj}$  and  $m^{int}$ ). Specifically, to allow this multiplication, we introduce an additional dimension of size 1 to both  $v^{obj}$  and  $m^{int}$  (i.e., now  $v^{obj}$  is of size  $H \times 1$  and  $m^{int}$  is of size  $1 \times W \times 2$ ). Then, via multiplying  $v^{obj}$  and  $m^{int}$ , as shown in Fig. 1 (d), we can form the HOI detection output per human-object pair as an image  $I^{hoi}$  of shape  $H \times W \times 2$ , with height  $H$ , width  $W$ , and two channels. We call it an HOI image.
+
+Based on the above, inspired by [11], we observe that, we can recast HOI detection from a novel perspective as an HOI image generation problem, and obtain accurate HOI detection outputs via generating high-quality HOI images. To generate such high-quality HOI images, we can then use image diffusion models [19, 43] with their strong image generation abilities. To this end, in this work, we propose a novel framework HOI-IDiff performing HOI detection via an Image-like Diffusion process, as outlined below.
+
+Overall, following existing HOI detection methods [21, 61, 65], our framework first uses a pre-trained detector to prepare human and object bounding boxes, then handles the two interrelated sub-tasks of HOI detection: object classification and interaction prediction. Particularly, our framework tackles these two interrelated sub-tasks via optimizing the image diffusion model to generate a high-quality HOI image for each human-object pair. In specific, following existing diffusion model works [11, 19, 43], our framework's optimization of the image diffusion model operates in two phases: the forward process and the reverse process. In the forward process, the goal is to progressively add noise to the
+
+ground truth HOI images (an example is shown in Fig. 1), creating supervision signals for the reverse process to train the image diffusion model. Conversely, the reverse process aims to optimize the image diffusion model to reverse the forward process, generating high-quality HOI images from which accurate HOI detection results can be obtained.
+
+However, we emphasize that, directly using a typical image diffusion model [19, 43] to generate HOI images in our framework may not yield optimal results. This is because, typical image diffusion models are designed to generate natural images, whereas HOI images differ in certain properties from natural images. Specifically, as mentioned above, an HOI image is created as the product of its corresponding vector  $v^{obj}$  and matrix  $m^{int}$ , in which  $v^{obj}$  is a probability distribution, and  $m^{int}$  consists of  $W$  probability distributions. As a result, an HOI image essentially also represents  $W$  joint probability distributions. Considering this unique property of the HOI image, in our framework, rather than performing a typical diffusion process [19, 43], we instead introduce novel designs, specially customizing the diffusion process for generating high-quality HOI images.
+
+Moreover, unlike natural images in which neighboring pixels tend to be more directly correlated, in HOI images, more direct correlations are typically found among pixels within the same row or column. Hence, the architectures of existing image diffusion models [19, 43], which tend to focus on local neighborhood processing to effectively handle natural images, may be ill-suited for dealing with our HOI images. To handle this, we further adapt the diffusion model in our framework with a slice patchification architecture, specifically optimizing it for processing HOI images.
+
+The contributions of our work include: 1) From a novel perspective, we formulate HOI detection as an  $HOI$  image generation problem. We then handle this task via leveraging the strong image generation capabilities of image diffusion models to generate high-quality  $HOI$  images. 2) We incorporate several designs in our framework to further ensure the compatibility of the image diffusion model and the  $HOI$  images, from the perspectives of both the diffusion process and the model architecture. 3) Our framework achieves state-of-the-art performance on the evaluated benchmarks.
+
+# 2. Related Work
+
+HOI Detection. Due to the wide range of applications, HOI detection has received a lot of attention [3, 8, 9, 12, 13, 17, 21, 22, 29, 32, 33, 35, 40, 42, 45, 51, 53, 56, 60, 65, 66], and most of recent methods fall into two categories: one-stage methods and two-stage methods. Among them, one stage methods, such as UnionDet [29], PPDM [35], and GGNet [66], generally train an one-stage HOI detector to detect HOI triplets in a single forward pass. Besides one-stage methods, two-stage methods have also attracted much attention recently, due to their training efficiency [62, 63].
+
+In two-stage methods, most approaches first use an off-the-shelf detector to identify all humans and objects in the input image, followed by the recognition of interactions between every human-object pair. Qi et al. [45] introduced a method that represents HOI structures as graphs, incorporating graph neural networks to enhance HOI detection. Fang et al. [8] leveraged correlations among different human body parts to improve the identification of human-object interactions. More recently, Zhang et al. [63] explored how to better utilize visual contextual cues from the input image to enhance the performance of HOI detection.
+
+In this work, like existing two-stage methods, we also incorporate a pre-trained detector into our framework. Yet, unlike previous works, we introduce a novel perspective by reframing HOI detection as an HOI image generation task. This allows us to leverage the strong image generation abilities of image diffusion models to perform HOI detection.
+
+Diffusion Models [19, 43, 47] are originally introduced for image generation, where they show impressive capabilities. Since then, diffusion models have also been applied to various tasks, such as object counting [24], trajectory prediction [15], and human mesh recovery [10]. Broadly, most existing methods using diffusion models can be clustered into two main categories: those that use pre-trained diffusion models as implicit knowledge bases [5, 24, 26, 30, 31, 44, 54, 58, 64], and those that train the diffusion model to use its powerful step-by-step denoising ability [1, 10, 11, 14, 15, 18, 20, 57]. Our method falls into the latter category. Specifically, given that HOI images differ in certain properties from natural images, we customize the diffusion process of image diffusion models to better utilize their powerful denoising abilities for HOI detection.
+
+# 3. Revisiting Image Diffusion Models
+
+The image diffusion model [19, 43], which is a type of probabilistic generative model, operates in two phases: the forward process and the reverse process. In specific, in the forward process, an original sample like a high-quality image  $(d_0)$  is progressively diffused into a completely random noise (typically Gaussian noise)  $d_{K}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$  through a series of steps (i.e.,  $d_0\to d_1\to \ldots \to d_K$ ). In contrast, in the reverse process, the completely random noise  $d_{K}$  is guided to be step-by-step denoised towards the sample  $d_0$  (i.e.,  $d_{K}\rightarrow d_{K - 1}\rightarrow \dots \rightarrow d_{0}$ ). Notably, both the forward and reverse processes follow a Markov chain structure.
+
+Forward Process. The purpose of the forward process is to acquire necessary supervision signals, thereby enabling the training of the diffusion model in the reverse process. To achieve this, as the denoising in the reverse process is performed in a step-wise manner, we here first obtain both  $d_{K}$  and the intermediate step results  $\{d_k\}_{k = 1}^{K - 1}$  between  $d_0$  and  $d_{K}$ . In specific, leveraging  $d_0$ ,  $\{d_k\}_{k = 1}^K$  can be obtained
+
+one by one from  $d_{1}$  to  $d_{K}$  via the following equation as:
+
+$$
+d _ {k} = \sqrt {1 - \beta_ {k}} d _ {k - 1} + \sqrt {\beta_ {k}} \epsilon \tag {1}
+$$
+
+where  $\{\beta_{k}\in (0,1)\}_{k = 1}^{K}$  is a set of controllers that regulate the scale of the injected noise at each step, and  $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$  With the help of Eq. 1, following [19], we can further formulate  $d_{k}$  directly from  $d_0$  in a single step as:
+
+$$
+d _ {k} = \sqrt {\bar {\alpha} _ {k}} d _ {0} + \sqrt {1 - \bar {\alpha} _ {k}} \epsilon \tag {2}
+$$
+
+where  $\alpha_{k} = 1 - \beta_{k}$  and  $\overline{\alpha}_k = \prod_{s = 1}^k\alpha_s$ . According to Eq. 1 and Eq. 2, following [19], we can finally derive the supervision signal  $q(d_{k - 1}|d_k,d_0)$  that will be used for training during the reverse process as:
+
+$$
+q \left(d _ {k - 1} \mid d _ {k}, d _ {0}\right) = \mathcal {N} \left(d _ {k - 1}; \widetilde {\mu} _ {k} \left(d _ {k}, d _ {0}\right), \widetilde {\beta} _ {k} \mathbf {I}\right) \tag {3}
+$$
+
+where  $\widetilde{\mu}_k(d_k,d_0) = \frac{\sqrt{\overline{\alpha}_{k - 1}\beta_k}}{1 - \overline{\alpha}_k} d_0 + \frac{\sqrt{\alpha_k}(1 - \overline{\alpha}_{k - 1})}{1 - \overline{\alpha}_k} d_k$  and  $\widetilde{\beta}_k = \frac{1 - \overline{\alpha}_{k - 1}}{1 - \overline{\alpha}_k}\beta_k$ .
+
+Reverse Process. Given  $q(d_{k-1}|d_k, d_0)$ , in the reverse process, the diffusion model  $\theta$  is trained to predict the conditional probability  $p_\theta(d_{k-1}|d_k)$ , utilizing  $q(d_{k-1}|d_k, d_0)$  as the supervision signal. Leveraging  $\theta$ , we can formulate each reverse diffusion step as a function  $g$  with  $d_k$  and  $\theta$  as its inputs and with  $d_{k-1}$  as its output, i.e.,  $d_{k-1} = g(d_k, \theta)$ . Note that, once the diffusion model has been trained, the forward process is no longer required. Instead, during inference, we only perform the reverse process, in which the trained diffusion model is used to convert random Gaussian noise  $d_K \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$  into a sample  $d_0$  of the target distribution.
+
+# 4. Proposed Method
+
+In this work, from a novel perspective, we propose to reformulate HOI detection as an HOI image generation problem (as elaborated in Sec. 4.1), and tackle this task via utilizing the image diffusion model to generate high-quality HOI images. However, because HOI images differ from natural images, naively applying the typical image diffusion models [19, 43] to generate HOI images can be sub-optimal. Considering this, we here propose a novel HOI-IDiff framework, which is specially designed for the generation of HOI images. Specifically, in HOI-IDiff, we incorporate the diffusion model with a new HOI image diffusion process (as discussed in Sec. 4.2), as well as a new slice patchification model architecture (as introduced in Sec. 4.3).
+
+# 4.1. Problem Reformulation
+
+Below, we show how we reformulate HOI detection as an image generation problem, taking a pair of human and object as an example. Previous works [21, 65] have shown that, HOI detection for each human-object pair can be viewed as two interrelated sub-tasks: object classification and interaction prediction. Hence, in this work, we handle these two sub-tasks jointly. Specifically, as shown in Fig. 1, the HOI detection output for each human-object pair can
+
+be formulated as the product of a vector  $v^{obj}$  and a matrix  $m^{int}$ , which respectively denote the outputs of the object classification and interaction prediction sub-tasks.
+
+Here,  $v^{obj}$  of size  $H$  represents a discrete probability distribution, where  $H$  is the total number of object categories. In specific, in  $v^{obj}$ , the  $h$ -th element  $v^{obj}[h]$  represents the probability that the object in the current human-object pair belongs to the  $h$ -th object category. Meanwhile,  $m^{int}$  of size  $W \times 2$  represents a collection of  $W$  discrete probability distributions, each of size 2, where  $W$  is the total number of interaction categories. Specifically, in the  $w$ -th distribution of  $m^{int}$  (i.e.,  $m^{int}[w]$ ), the first element  $m^{int}[w,0]$  and the second element  $m^{int}[w,1]$  respectively represent the presence and absence probabilities of the  $w$ -th interaction in the current human-object pair.
+
+With  $v^{obj}$  and  $m^{int}$  defined as above, via multiplying them, we can represent the HOI detection output for each human-object pair as an HOI image  $I^{hoi}$  of size  $H \times W \times 2$ , with height  $H$ , width  $W$ , and two channels, as shown in Fig. 1. Notably, in  $I^{hoi}$ , the  $w$ -th vertical slice  $I^{hoi}[:w,:]$  of size  $H \times 2$  is derived as the product of two distributions (i.e.,  $v^{obj}$  of size  $H$  and  $m^{int}[w]$  of size 2). This leads the HOI image to hold a unique property: each of its vertical slice essentially represents a joint probability distribution that sums to 1. Note that, this property also holds conversely. Specifically, for a matrix of size  $H \times W \times 2$ , as long as each of its vertical slice forms a probability distribution summing to one, it represents an HOI image, and we can uniquely decompose it into its corresponding vector  $v^{obj}$  and matrix  $m^{int}$  (with the analysis provided in supplementary).
+
+Observing that the outputs of HOI detection can be reformulated as two-channel HOI images via above, we thus are motivated to reframe HOI detection as an image generation problem, harnessing the powerful image generation capabilities of image diffusion models.
+
+# 4.2. HOI Image Diffusion Process
+
+From the above, we observe that, generating high-quality HOI images enables us to achieve accurate HOI detection outputs. This allows us to recast HOI detection as an HOI image generation problem, and tackle HOI detection by focusing on generating high-quality HOI images. In this section, we then introduce how we generate high-quality HOI images in our framework, via an image diffusion process. In specific, though typical (natural) image diffusion models [19, 43] could be naively applied here to generate HOI images, as HOI images differ in certain properties from natural images, this naive application can lead to sub-optimal performance. Hence, in this work, we aim to propose a novel HOI image diffusion process tailored specifically for HOI image generation. Yet, designing such a diffusion process can be challenging. This is because, as mentioned below, to make the designed diffusion process suitable for the HOI
+
+detection task and for the HOI images, the process is expected to hold the following three attributes:
+
+Attribute 1: Firstly, recall that like existing HOI detection works [21, 62, 63, 65], our framework begins by passing the input image through a pre-trained detector. In this step, besides the human and object bounding boxes, the detector also provides a prior categorical distribution for each detected object, in the form of a probability vector of length  $H$ . These distributions encode valuable prior information about object categories. Thus, in our framework, rather than starting denoising from completely random noise, for each identified human-object pair, we would like to first initialize a noisy HOI image using the prior categorical distribution of the object in the pair. Next, we aim to instead use this noisy (yet not completely random) HOI image as the starting point for the denoising process in the reverse diffusion process. This allows us to effectively leverage prior information, guiding the diffusion model to generate more accurate HOI images. Notably, to achieve the above and satisfy this attribute, during the forward diffusion process, we need to diffuse towards the initialized noisy HOI image instead of towards completely random noise, for acquiring appropriate supervision signals for the training of the diffusion model.
+
+Attribute 2: Meanwhile, as explained in Sec. 4.1, compared to natural images, the HOI image possesses a unique property. That is, each of its vertical slice (of size  $H \times 2$ ) derived as the product of two distributions (i.e., the distribution  $v^{obj}$  and a distribution in  $m^{int}$ ), essentially represents a joint probability distribution that sums to 1. Considering this, to guide the diffusion model to generate accurate HOI images in the reverse diffusion process from noisy initializations, in the forward process, we aim to ensure all intermediate results at different diffusion steps to retain their vertical slices as probability distributions that sum to 1. As mentioned in Sec. 4.1, this ensures that the intermediate result at each diffusion step essentially forms an HOI image.
+
+Attribute 3: With the above two attributes in place, the proposed diffusion process shall be made compatible for the HOI image generation problem. Meanwhile, we observe that, in existing diffusion works [19], the formulation of the supervision signal  $q(d_{k-1}|d_k, d_0)$  in the forward diffusion process is a crucial step [11]. Specifically, with  $q(d_{k-1}|d_k, d_0)$  formulated, during each reverse step, once the probability distribution  $p_\theta(d_{k-1}|d_k)$  is predicted from the diffusion model, the difference between  $q(d_{k-1}|d_k, d_0)$  and  $p_\theta(d_{k-1}|d_k)$  can be then used to optimize the diffusion model effectively [11, 19]. Hence, in our diffusion process, we aim to still allow for the formulation of  $q(d_{k-1}|d_k, d_0)$ .
+
+Above, we introduce the three attributes that an image diffusion process is urged to satisfy for it to generate high-quality HOI images. Notably, based on these attributes, a typical natural image diffusion model is clearly not suitable
+
+![](images/931dd1a2f72f7b869b487d728d2b211c9a1b4d0510876fc24d6971dbff9666fe.jpg)  
+Figure 2. Illustration of our HOI image diffusion process. As indicated by the red arrows from right to left, the forward HOI image diffusion process gradually diffuses the ground-truth HOI image  $I_0^{hoi}$  towards  $I_K^{hoi}$  (i.e.,  $I_0^{hoi} \to \ldots \to I_{K-1}^{hoi} \to I_K^{hoi}$ ). Conversely, as shown by the green arrows from left to right, in the reverse HOI image diffusion process, conditioned on the appearance feature  $f_a$ , the diffusion model  $\theta$  is guided to progressively reconstruct a desired high-quality HOI image  $\hat{I}_0^{hoi}$  from  $I_K^{hoi}$  (i.e.,  $I_K^{hoi} \to \hat{I}_{K-1}^{hoi} \to \ldots \to \hat{I}_0^{hoi}$ ).
+
+for generating HOI images, as it satisfies neither Attribute 1 nor Attribute 2. In light of this, to generate high-quality HOI images, in this work, we propose a novel HOI image diffusion process that comprehensively satisfies all the above three attributes. Below, we first describe how our proposed process initializes the noisy HOI image mentioned in Attribute 1. We then discuss the corresponding forward and reverse processes in our proposed approach. We also illustrate the HOI image diffusion process in Fig. 2.
+
+Noisy HOI image initialization. To initialize the noisy HOI image for a certain human-object pair such that it can be used as the start point of the reverse diffusion process, as described in Sec. 4.1, we simply need to initialize its corresponding vector  $v^{obj}$  and matrix  $m^{int}$ . Among which, for  $v^{obj}$ , as mentioned above, a prior distribution has been provided by an off-the-shelf detector in the form of a probability vector, so we directly set  $v^{obj}$  to be this vector. Yet for  $m^{int}$ , since no prior is provided by the detector, we here simply set all values in  $m^{int}$  to 0.5, initializing each interaction category with an equal probability of being present or absent in the current human-object pair. Via the above, we can derive both  $m^{int}$  and  $v^{obj}$ . Their product can then be used to initialize the noisy HOI image accordingly.
+
+Forward process. After introducing the initialization of the noisy HOI image, we now explain the forward process of our HOI image diffusion method. For simplicity, we illustrate this process by focusing on a single vertical slice of the HOI image. Let  $d_0$  represent the  $w$ -th vertical slice of the ground-truth HOI image  $I_0^{h\circ i}$ , and let  $K$  denote the total number of diffusion steps. The forward process begins by diffusing  $d_0$  to derive  $\{d_k\}_{k=1}^K$  (i.e.,  $d_0 \to d_1 \to \ldots \to d_K$ ). We then use  $\{d_k\}_{k=0}^K$  to obtain the posterior distributions  $\{q(d_{k-1}|d_k, d_0)\}_{k=1}^K$ , which serve as supervision signals for training the diffusion model in the reverse process.
+
+In particular, during deriving  $d_{k}$ , to ensure that our HOI image diffusion process satisfies the above-mentioned attributes, let  $d_{init}$  denote the  $w$ -th vertical slice of the noisy HOI image initialized in the current human-object pair. Our
+
+initial aim is to guide  $d_{k}$  to gradually converge towards  $d_{init}$  as  $k$  becomes large. To achieve this, we get inspired by that given suitable input parameters, a Multinomial distribution  $P^{Mu}$  can converge to any discrete probability distributions (e.g.,  $d_{init}$ ) [46]. Motivated by this, we perform our forward HOI image diffusion process as follows.
+
+Specifically, at each diffusion step, to acquire  $d_{k}$  from  $d_{k-1}$ , similar to the typical natural image forward diffusion process in Eq. 1, we inject a small noise to  $d_{k-1}$  as:
+
+$$
+d _ {k} = \left(1 - \beta_ {k}\right) d _ {k - 1} + \beta_ {k} \epsilon^ {M u} \tag {4}
+$$
+
+However, in Eq. 4, we make two changes compared to Eq. 1. (1) Firstly, instead of from  $\mathcal{N}(\mathbf{0},\mathbf{I})$ , we sample  $\epsilon^{Mu}$  from the Multinomial distribution  $P_T^{Mu}(T,d_{init})$ , where  $T$  is a hyperparameter representing the Multinomial distribution's number of trials, and  $d_{init}$  provides the sampling probability for the distribution in each trial. Moreover, the subscript  $T$  means that, after finishing the  $T$  sampling trials, we further divide the sampling result by  $T$  to ensure that elements in  $\epsilon^{Mu}$  sum to 1. By sampling  $\epsilon^{Mu} \sim P_T^{Mu}(T,d_{init})$ , we would later show that this can enable  $d_k$  to finally converge to  $d_{init}$  as  $k$  becomes large. (2) Secondly, instead of  $\sqrt{1 - \beta_k}$  and  $\sqrt{\beta_k}$  in Eq. 1,  $1 - \beta_k$  and  $\beta_k$  is used to respectively regulate  $d_{k-1}$  and  $\epsilon^{Mu}$  in Eq. 4. By doing so, as  $(1 - \beta_k) + \beta_k = 1$ , for  $d_{k-1}$  and  $\epsilon^{Mu}$  as two probability distributions each sums to 1, we can ensure  $d_k$  at each diffusion step  $k$  to also maintain a probability distribution sums to 1, satisfying Attribute 2.
+
+Next, we show that, via mapping  $d_{k-1}$  to  $d_k$  via Eq. 4, our HOI image diffusion process can also satisfy Attribute 1. Specifically, with the help of Eq. 4,  $d_k$  can be derived from  $d_0$  approximately as the following (with the derivation provided in supplementary):
+
+$$
+d _ {k} = \bar {\alpha} _ {k} d _ {0} + (1 - \bar {\alpha} _ {k}) \bar {\epsilon} ^ {M u} \tag {5}
+$$
+
+where  $\alpha_{k} = 1 - \beta_{k},\overline{\alpha}_{k} = \prod_{s = 1}^{k}\alpha_{s},$ $\bar{\epsilon}^{Mu}\sim P_{S_kT}^{Mu}(S_kT,d_{init}),$  and  $S_{k} =$
+
+$\frac{(1 - \overline{\alpha}_k)^2}{(\prod_{j = 2}^k\alpha_k)^2\beta_1^2 + (\prod_{j = 3}^k\alpha_k)^2\beta_2^2 + \ldots + \beta_k^2}$ . Next, from Eq. 5,
+
+we can observe that, when  $K$  becomes large and  $\overline{\alpha}_K$  correspondingly decreases to nearly zero, the distribution of  $d_K$  reaches the Multinomial distribution  $P_{S_kT}^{Mu}(S_kT,d_{init})$  (i.e.,  $d_K\sim P_{S_kT}^{Mu}(S_kT,d_{init})$ ). In this case, leveraging the property of the Multinomial distribution [11, 46], we have  $\mathbb{E}[d_K] = d_{init}$ . In other words, from Eq. 5, we can conclude that our forward diffusion process does gradually diffuse towards the initialized noisy HOI image. This ensures that our diffusion process also satisfies Attribute 1.
+
+At this point, our HOI image diffusion process has satisfied Attribute 1 and Attribute 2. Next, at the final stage of our forward process, we would like to satisfy Attribute 3, and obtain the supervision signal  $q(d_{k-1}|d_k, d_0)$ . Specifically, based on the properties of the Markov chain structure [11],  $q(d_{k-1}|d_k, d_0)$  in our framework can be derived as:
+
+$$
+\begin{array}{l} q (d _ {k - 1} | d _ {k}, d _ {0}) = \Big (\gamma_ {k} \big (P _ {\frac {T (d _ {k} - (1 - \beta_ {k}) d _ {k - 1})}{\beta_ {k}}} (d _ {k - 1}; T, d _ {i n i t}, d _ {k}) \big) \\ \left. \times \left(P _ {\frac {S _ {k - 1} T \left(d _ {k - 1} - \bar {\alpha} _ {k - 1} d _ {0}\right)}{1 - \bar {\alpha} _ {k - 1}} \left(d _ {k - 1}; S _ {k - 1} T, d _ {i n i t}, d _ {0}\right)\right)\right) \tag {6} \\ \end{array}
+$$
+
+where  $\gamma_{k} = \left(\sum_{d_{k - 1}}\left(\left(P_{\frac{T(d_{k} - (1 - \beta_{k})d_{k - 1})}{\beta_{k}}}^{Mu}\right)(d_{k - 1};T,d_{init},d_{k})\right)\right.$
+
+$$
+\left. \right.\left. \times \left(P _ {\frac {S _ {k - 1} T (d _ {k - 1} - \overline {{\alpha}} _ {k - 1} d _ {0})}{1 - \overline {{\alpha}} _ {k - 1}}} \left(d _ {k - 1}; S _ {k - 1} T, d _ {i n i t}, d _ {0}\right)\right)\right) ^ {- 1}.
+$$
+
+We also include more details w.r.t. the derivation of Eq. 6 in Supplementary. Furthermore, the formulation of  $\gamma_{k}$  also reveals that it does not vary with any observed  $d_{k - 1}$ . Thus, during implementation, for computational efficiency, we regard  $\gamma_{k}$  to be a fixed hyperparameter and set  $\gamma_{k} = 1$ .
+
+Reverse process. In the reverse process, our objective is to guide the diffusion model  $\theta$  to learn to reconstruct the desired high-quality HOI images from their initial noisy version. For simplicity, same as in the forward process above, we here demonstrate the reverse diffusion process also by focusing on a single vertical slice of the HOI image. The reverse process can then be formulated as a step-wise denoising procedure from  $d_{K}$  to  $\hat{d}_0$  (i.e.,  $d_{K} \rightarrow \hat{d}_{K-1} \rightarrow \dots \rightarrow \hat{d}_{0}$ ). Here, we use  $\hat{d}_k$  to represent the version of  $d_{k}$  that is estimated by the diffusion model  $\theta$ , for distinguishing it with  $d_{k}$  in the above forward process.
+
+However, generating the desired  $\hat{d}_0$  purely through the reverse process from  $d_K$  can be challenging. This is due to the absence of essential appearance details—like those of the human and object in the current human-object pair—in  $d_K$ . Notably, these details can be crucial for precise HOI predictions. To address this, during our reverse process, we also incorporate these appearance details from the input image to guide the diffusion model  $\theta$ , enabling it to produce  $\hat{d}_0$  with more accuracy. In particular, for each human-object pair, we reuse the feature extracted from the pre-trained detector w.r.t. the pair in the input image as the appearance feature  $f_a$ . This feature  $f_a$  is then fed into the diffusion
+
+model  $\theta$  to guide its reverse process. In addition to  $f_{a}$ , following existing diffusion works [19, 48], at each reverse diffusion step, we also build a unique step embedding  $f_{s}^{k}$  to incorporate the step number  $(k)$  information into the diffusion model  $\theta$ . This aids  $\theta$  in learning to perform denoising at each reverse step. Via the above, we can finally form each reverse diffusion step as a function  $g$ , with  $\hat{d}_k, \theta, f_a$ , and  $f_{s}^{k}$  as its inputs and with  $\hat{d}_{k-1}$  as its output:
+
+$$
+\hat {d} _ {k - 1} = g \left(\hat {d} _ {k}, \theta , f _ {a}, f _ {s} ^ {k}\right) \tag {7}
+$$
+
+Above, for simplicity, we introduce our HOI image diffusion process by focusing on a single vertical slice of the HOI image. Notably, the same diffusion process is actually applied simultaneously across all vertical slices of the HOI image. This means, the above diffusion process is performed on the entire HOI image as a whole.
+
+# 4.3. Model Architecture
+
+In this section, we describe the architecture of our diffusion model. Notably, though our model could directly adopt the architecture of typical natural image diffusion models [19, 43] without making any modification, doing so may not yield optimal results. This is because, in natural images, more direct correlations often exist among neighboring pixels, leading typical image diffusion models to incorporate local neighborhood processing (e.g., local convolution [19] or local patchification [43]) in their architectures. Differently, HOI images exhibit more direct correlations primarily within horizontal or vertical slices (rows or columns) of pixels. Specifically, in an HOI image, each horizontal slice of pixels represents the interaction prediction output under a given object category, while each vertical slice of pixels demonstrates the object classification output under a certain interaction category. For instance, in the HOI image illustrated in Fig. 1, the first horizontal slice represents the interaction prediction output when the object category is "box". The above implies that, in an HOI image, instead of neighboring pixels, pixels within the same (horizontal or vertical) slice generally tend to exhibit more direct correlations.
+
+Considering this property of the HOI image, in our framework, for our diffusion model to adequately process HOI images, we design it with a slice patchification architecture. Overall, our architecture builds on DiT [43], a transformer-based diffusion model architecture that has been popularly used in processing and generating natural images. However, unlike DiT which transforms the input image into local patches, our architecture employs a slice patchification operation. In this operation, rather than local patches, an HOI image of shape  $H \times W \times 2$  is instead converted into  $H$  horizontal slice patches (each of shape  $W \times 2$ ) and  $W$  vertical slice patches (each of shape  $H \times 2$ ). By doing so, this slice patchification operation encourages the diffusion model to prioritize correlations within each slice, enhancing its ability to process HOI images. After slice
+
+patchification, we obtain a total of  $H + W$  patches. Next, to further capture the potential (indirect) correlations across different slices in the HOI image, similar to [43], we further convert these  $H + W$  patches into  $H + W$  equal-dimensional tokens, and pass the resulting tokens into a Multi-Head Self-Attention layer. Specifically, we perform the above patch-to-token conversion using two MLP layers.
+
+Based on such as a slice patchification architecture, our diffusion model can then process HOI images effectively.
+
+# 4.4. Overall Training and Testing
+
+Training. In our framework, during training, we first build the diffusion model with the architecture introduced in Sec. 4.3. Next, we optimize the model via the HOI image diffusion process explained in Sec. 4.2, and guide the model to generate high-quality HOI images (as illustrated in Fig. 2). Specifically, during the optimization of the diffusion model, in the forward process, for each human-object pair, to ensure  $I_K^{hoi}$  better represents the initialized noisy HOI image, we diffuse  $M$  samples of  $I_K^{hoi}$  from the ground-truth HOI image  $I_0^{hoi}$ . We then apply the reverse process to all  $M$  samples, rather than relying on only a single sample of  $I_K^{hoi}$ . Additionally, we incorporate the MSE loss, calculated between the supervision signals and the diffusion model's predictions at each diffusion step.
+
+Testing. During testing, given an input image, similar to existing methods [21, 62, 65], we first use a pre-trained detector to detect human and object bounding boxes and form human-object pairs. Then, following Sec. 4.2, we initialize a set of noisy HOI images, one for each human-object pair, and feed them parallelly into the diffusion model. Finally, we post-process the HOI images predicted by the diffusion model to acquire the HOI detection results as follows.
+
+To determine object categories, we first observe that, each object in the input image could belong to multiple human-object pairs. In light of this, we categorize an object by examining all human-object pairs that include it. Specifically, let  $\hat{I}_{avg}^{hoi}$  (with shape  $H\times W\times 2$ ) represent the average of all predicted HOI images that have their corresponding human-object pairs to include a certain object. To classify this object, we first sum  $\hat{I}_{avg}^{hoi}$  along its last two axes, reducing it to a vector of length  $H$ . We then apply the argmax operation to this vector. Next, to determine the interaction categories present within each human-object pair, let  $\hat{I}_0^{hoi}$  (of shape  $H\times W\times 2$ ) represent the predicted HOI image corresponding to a specific human-object pair, and let  $h$  denote the index of the above-determined object category in this pair. Then, we can see if the presence probability of this interaction category is larger than the absence probability (i.e., via checking if  $\hat{I}_0^{hoi}[h,w,0] > \hat{I}_0^{hoi}[h,w,1]$ ) to find out if the  $w$ -th interaction category is present in the current pair. During testing, we can obtain the HOI detection results from the HOI images predicted by the diffusion model.
+
+<table><tr><td rowspan="3">Method</td><td colspan="6">HICO-DET</td><td colspan="2">V-COCO</td></tr><tr><td colspan="3">Default setting</td><td colspan="3">Known objects setting</td><td></td><td></td></tr><tr><td>Full</td><td>Rare</td><td>Non-rare</td><td>Full</td><td>Rare</td><td>Non-rare</td><td>APs1role</td><td>APs2role</td></tr><tr><td>Gkioxari et al. [13]</td><td>9.94</td><td>7.16</td><td>10.77</td><td>-</td><td>-</td><td>-</td><td>40.0</td><td>48.0</td></tr><tr><td>Kim et al. [29]</td><td>17.58</td><td>11.72</td><td>19.33</td><td>19.76</td><td>14.68</td><td>21.27</td><td>47.5</td><td>56.2</td></tr><tr><td>Tamura et al. [50]</td><td>29.90</td><td>23.92</td><td>31.69</td><td>32.38</td><td>26.06</td><td>34.27</td><td>58.8</td><td>61.0</td></tr><tr><td>Zhang et al. [62]</td><td>32.62</td><td>28.62</td><td>33.81</td><td>36.08</td><td>31.60</td><td>37.47</td><td>61.3</td><td>67.1</td></tr><tr><td>Liao et al. [36]</td><td>34.95</td><td>31.50</td><td>36.08</td><td>38.22</td><td>34.94</td><td>39.37</td><td>63.6</td><td>65.9</td></tr><tr><td>Ma et al. [40]</td><td>37.18</td><td>30.71</td><td>39.11</td><td>38.93</td><td>31.93</td><td>41.02</td><td>-</td><td>-</td></tr><tr><td>Zhang et al. [63]</td><td>44.32</td><td>44.61</td><td>44.24</td><td>47.81</td><td>48.38</td><td>47.64</td><td>64.1</td><td>70.2</td></tr><tr><td>Yuan et al. [61]</td><td>45.09</td><td>43.23</td><td>45.64</td><td>-</td><td>-</td><td>-</td><td>72.1</td><td>74.1</td></tr><tr><td>Chen et al. [7]</td><td>35.78</td><td>29.80</td><td>37.56</td><td>37.59</td><td>31.36</td><td>39.36</td><td>-</td><td>-</td></tr><tr><td>Wang et al. [52]</td><td>39.34</td><td>39.90</td><td>39.17</td><td>42.24</td><td>42.86</td><td>42.05</td><td>65.8</td><td>69.9</td></tr><tr><td>Yang et al. [58]</td><td>44.53</td><td>44.48</td><td>44.55</td><td>-</td><td>-</td><td>-</td><td>66.2</td><td>67.6</td></tr><tr><td>Luo et al. [39]</td><td>45.04</td><td>45.61</td><td>44.88</td><td>48.16</td><td>48.37</td><td>48.09</td><td>71.1</td><td>75.6</td></tr><tr><td>Wu et al. [55]</td><td>46.01</td><td>46.74</td><td>45.80</td><td>49.50</td><td>50.59</td><td>49.18</td><td>63.0</td><td>68.7</td></tr><tr><td>Ours</td><td>47.71</td><td>48.36</td><td>47.52</td><td>50.56</td><td>51.95</td><td>50.14</td><td>73.4</td><td>76.1</td></tr></table>
+
+Table 1. Performance comparison on the HICO-DET and V-COCO datasets.
+
+# 5. Experiments
+
+To evaluate the efficacy of our framework, we conduct experiments on the HICO-DET and V-COCO datasets.
+
+HICO-DET [4] is a large-scale HOI detection dataset. It contains 47,776 images, 80 object categories, and 117 interaction categories. Moreover, it consists of three subsets: (1) the full subset, including all 600 HOI triplets, (2) the rare subset, containing 138 HOI triplets with fewer than 10 training samples, and (3) the non-rare subset, comprising the remaining 462 HOI triplets. Following [61-63], we evaluate our method under both the Default and Known object settings. We report the mAP metric across all subsets.
+
+V-COCO [16], as a sub-set of MS-COCO [37], is another popularly used HOI detection dataset. It contains 10,346 images, 80 object categories, and 24 interaction categories. Following [61-63], we report the mAP metric and evaluate our method under the  $AP_{role}^{S1}$  and  $AP_{role}^{S2}$  settings.
+
+Implementation details. We conduct our experiments on an RTX 6000 Ada GPU. We follow [61] to use DDETR [68] and detect objects in our framework. During training, we optimize the diffusion model using the AdamW optimizer [38] with an initial learning rate of 1e-4. We set the batch size to be 8. Moreover, we set the hyperparameters  $K$  to 50,  $T$  to 2000, and  $M$  to 10. More details are in supplementary.
+
+# 5.1. Experimental Results
+
+In Tab. 1, we compare our approach with existing HOI detections methods. Compared to existing methods, our framework consistently achieves the best performance across all the evaluation settings, showing its effectiveness.
+
+# 5.2. Ablation Studies
+
+Following previous works [52, 62], we conduct extensive ablation experiments on the Default setting of HICO-DET. Impact of the key components of our HOI-IDiff framework. In our HOI-IDiff framework, we first propose an HOI image diffusion process to enhance the compatibility
+
+<table><tr><td>Method</td><td>Full</td><td>Rare</td><td>Non-rare</td></tr><tr><td>I: Typical natural image diffusion process</td><td>42.50</td><td>42.71</td><td>42.44</td></tr><tr><td>II: HOI-IDs with initializing noisy HOI image</td><td>44.16</td><td>44.60</td><td>44.03</td></tr><tr><td>III: HOI-IDs with noisy HOI image as condition</td><td>45.69</td><td>46.34</td><td>45.50</td></tr><tr><td>IV: HOI-IDs maintaining to be distributions</td><td>45.91</td><td>46.01</td><td>45.88</td></tr><tr><td>V: HOI-IDs with architecture in [19]</td><td>43.95</td><td>44.45</td><td>43.80</td></tr><tr><td>VI: HOI-IDs with architecture in [43]</td><td>44.16</td><td>44.56</td><td>44.04</td></tr><tr><td>VII: HOI-IDs w/o horizontal slice patches</td><td>45.11</td><td>45.41</td><td>45.02</td></tr><tr><td>VIII: HOI-IDs w/o vertical slice patches</td><td>45.81</td><td>45.93</td><td>45.77</td></tr><tr><td>HOI-IDs</td><td>47.71</td><td>48.36</td><td>47.52</td></tr></table>
+
+of the image diffusion model and the HOI images. To evaluate the efficacy of this process, we test the following four variants. In variant I (typical natural image diffusion process), we directly use the typical natural image diffusion process [19] to train our diffusion model. In variant II (HOIDiff w/o initializing noisy HOI image), we use our HOI image diffusion process. Yet, we start denoising from completely random noise instead of from the noisy HOI image. Moreover, in variant III (HOI-IDiff with noisy HOI image as condition), we still start denoising from completely random noise, but we use the noisy HOI image as the condition for the reverse process. Lastly, in variant IV (HOI-IDiff diffusion process w/o maintaining to be distributions), instead of  $1 - \beta_{k}$  and  $\beta_{k}$  in Eq. 4, we use back  $\sqrt{1 - \beta_k}$  and  $\sqrt{\beta_k}$  in Eq. 1 as regulators, and thus no longer keep the intermediate steps during the forward process to be a set of discrete probability distributions. As shown in Tab. 2, compared to our framework, the performance of variant I drops significantly. This shows the importance of ensuring the compatibility between the image diffusion model and the HOI images. Moreover, our framework also outperforms variants II-IV. This further shows the efficacy of the different designs we made in our HOI image diffusion process.
+
+Next, we further build the diffusion model in our framework with a slice patchification architecture. To validate this design, we test other four variants. In variant V (HOIDiff with architecture in [19]), we use the typical diffusion model architecture in [19] to build our model, while in variant VI (HOI-IDiff with architecture in [43]), we adopt the architecture in [43]. Moreover, in variant VII (HOIDiff w/o horizontal slice patches), we still employ the model architecture with the slice patchification operation but we patchify the HOI image only into  $W$  vertical slice patches. Lastly, in variant VIII (HOI-IDiff w/o vertical slice patches), we patchify the HOI image only into  $H$  horizontal slice patches. As shown in Tab. 2, our framework leveraging the slice patchification model architecture consistently outperforms these four variants from variant V to variant VIII. This further shows the advantage of the slice patchification architecture in HOI image generation.
+
+Impact of the HOI image formulation process. In our framework, we formulate the HOI image  $I^{hoi}$  as the product of  $v^{obj}$  of size  $H$  and  $m^{int}$  of size  $W \times 2$  ( $H \times W \times 2$ )
+
+Table 2. Evaluation on the key components of HOI-IDiff.  
+
+<table><tr><td>Method</td><td>Full</td><td>Rare</td><td>Non-rare</td></tr><tr><td>I: W × 2 HOI image</td><td>46.43</td><td>47.22</td><td>46.19</td></tr><tr><td>II: H &amp; W × 2 HOI images</td><td>46.83</td><td>47.47</td><td>46.64</td></tr><tr><td>III: H × W × 2 HOI image</td><td>47.71</td><td>48.36</td><td>47.52</td></tr><tr><td>IV: Box coordinates &amp; H × W × 2 HOI image</td><td>47.79</td><td>48.36</td><td>47.62</td></tr></table>
+
+Table 3. Evaluation on the HOI image formulation process. Note that, even when we only generate  $W \times 2$  HOI images, we still achieve SOTA performance.
+
+HOI image). To validate the efficacy of this formulation, we test three variants. In variant I ( $W \times 2$  HOI image), for each human-object pair, we first obtain its object category directly from the off-the-shelf object detector. Next, we generate only  $m^{int}$ , as the HOI image, through the diffusion process. In variant II ( $H \& W \times 2$  HOI images), we formulate  $v^{obj}$  and  $m^{int}$  as two separate HOI images, and generate each of them through a separate diffusion process. Lastly, in variant IV (Box coordinates &  $H \times W \times 2$  HOI image), during diffusion, besides generating high-quality HOI images of size  $H \times W \times 2$ , we also refine the bounding box coordinates for each human-object pair. As shown in Tab. 3, our framework and these three variants all achieve better performances than the existing state-of-the-art method [55]. Moreover, our framework ( $H \times W \times 2$  HOI image) outperforms variants I and II. Meanwhile, our framework achieves compatible performance compared to variant IV which additionally refines bounding box coordinates. Thus, considering the framework's complexity as well, in our diffusion process, we generate  $H \times W \times 2$  HOI images, but do not additionally refine the bounding box coordinates.
+
+![](images/54e6e94838a3de4cfe1b31e448e93000980b26b274ac1d1c382a4acd844fe19c.jpg)  
+Figure 3. Visualization of the HOI image diffusion process.
+
+Visualization of the diffusion process. In Fig. 3, we visualize the HOI images produced throughout the reverse diffusion process on V-COCO. As shown, our HOI-IDiff framework effectively eliminates noise and indeterminacy from the initially noisy HOI image in a step-wise manner, ultimately generating a high-quality HOI image. For better visibility, the figure is normalized with log function.
+
+# 6. Conclusion
+
+In this paper, from a novel perspective, we recast HOI detection as an  $HOI$  image generation problem. Correspondingly, we propose an innovative image-diffusion-based HOI detection framework, which tackles the HOI detection task via generating high quality  $HOI$  images through a carefully-designed  $HOI$  image diffusion process. Our framework consistently achieves state-of-the-art performance on two commonly-used evaluation benchmarks.
+
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+# Analyzing the Synthetic-to-Real Domain Gap in 3D Hand Pose Estimation
+
+Zhuoran Zhao $^{1*}$  Linlin Yang $^{2\dagger}$  Pengzhan Sun $^{3}$  Pan Hui $^{1}$  Angela Yao $^{3}$
+
+<sup>1</sup>The Hong Kong University of Science and Technology (Guangzhou), China
+
+$^{2}$ Communication University of China, China  $^{3}$ National University of Singapore, Singapore
+
+zzhao074@connect.hkust-gz.edu.cn, lyang@cuc.edu.cn, panhui@ust.hk,
+
+{pengzhan,ayao}@comp.nus.edu.sg
+
+# Abstract
+
+Recent synthetic 3D human datasets for the face, body, and hands have pushed the limits on photorealism. Face recognition and body pose estimation have achieved state-of-the-art performance using synthetic training data alone, but for the hand, there is still a large synthetic-to-real gap. This paper presents the first systematic study of the synthetic-to-real gap of 3D hand pose estimation. We analyze the gap and identify key components such as the forearm, image frequency statistics, hand pose, and object occlusions. To facilitate our analysis, we propose a data synthesis pipeline to synthesize high-quality data. We demonstrate that synthetic hand data can achieve the same level of accuracy as real data when integrating our identified components, paving the path to use synthetic data alone for hand pose estimation. Code and data are available at: https://github.com/delaprada/HandSynthesis.git.
+
+# 1. Introduction
+
+3D hand pose estimation from monocular RGB images plays an important role in computer vision, human-computer interaction, and AR/VR applications [5, 16, 18]. It is challenging since the hand has severe occlusion problems and depth ambiguity. Most recent methods [11, 25, 31] rely heavily on 3D ground-truth labels for training, but obtaining these labels is expensive and time-consuming. Therefore, there is strong interest in using synthetic data, as it does not require any annotation effort. In face recognition [2, 43] and 3D human pose estimation [3], state-of-the-art is achievable with only synthetic training sets. However, there is still a large synthetic-to-real gap for 3D hand pose estimation [14, 17, 22, 48], despite recent efforts to diversify backgrounds, pose distributions, camera viewpoints, and hand textures for synthetic data. Pre-training on syn
+
+![](images/d85e16bb0beaa952187fddf6cbf02baff98903aa93302479e96cb992ff647d95.jpg)  
+Figure 1. We present a systematic study of the synthetic-to-real gap for 3D hand pose estimation by decomposing the synthetic data to establish associations between hand image components and predictions.
+
+thetic and fine-tuning with real data, or mixed synthetic and real training, is still much better than training with only synthetic data [10, 14, 17, 22, 33]. These observations beg the question: What contributes to the synthetic-to-real gap in 3D hand pose estimation?
+
+Many synthetic hand datasets exist but are difficult to analyze since they differ from real hand datasets across multiple aspects (e.g., pose distribution, background, texture, etc.), which cannot be separated. Therefore, we propose a data synthesis pipeline to facilitate our study. The pipeline efficiently synthesizes high-quality data with diverse backgrounds, lighting, and hand textures. With full control over the rendering pipeline, we can decompose synthetic data to analyze associations between different hand image components and predictions to enhance synthetic-to-real gap analysis (see Fig. 1). Moreover, since our pipeline can synthesize controllable pair-wise data, it can benefit future research for further analysis and enhance model performance for downstream applications.
+
+We analyze the synthetic-to-real gap from four aspects:
+
+Table 1. Representative synthetic hand datasets. HDR denotes high dynamic range scenes. HDR Res. denotes HDR background resolution, with higher values being more realistic and less blurry. For lighting, "manual" denotes manually defined settings while "dynamic" denotes diverse lighting conditions consistently applied across the foreground hand and background scene. "NS" means normal and specular maps for hand texturing. "GR" means the hand data generation and image rendering pipeline.  
+
+<table><tr><td>Dataset</td><td>Data Size</td><td>Background</td><td>HDR Type</td><td>HDR Res.</td><td>Lighting</td><td>Texture</td><td>NS</td><td>Template</td><td>Hand Type</td><td>GR</td></tr><tr><td>RHD [52]</td><td>44K</td><td>static</td><td>-</td><td>-</td><td>manual</td><td>limited</td><td>✘</td><td>Mixamo</td><td>single hand</td><td>✘</td></tr><tr><td>ObMan [17]</td><td>154K</td><td>static</td><td>-</td><td>-</td><td>manual</td><td>limited</td><td>✘</td><td>MANO</td><td>hand object</td><td>✓</td></tr><tr><td>DARTset [14]</td><td>800K</td><td>static</td><td>-</td><td>-</td><td>manual</td><td>diverse</td><td>✘</td><td>DART</td><td>single hand</td><td>✓</td></tr><tr><td>Ego3D [24]</td><td>55K</td><td>static</td><td>-</td><td>-</td><td>manual</td><td>limited</td><td>✘</td><td>Mixamo</td><td>two hands</td><td>✘</td></tr><tr><td>Re:InterHand [33]</td><td>1.5M</td><td>HDR</td><td>Indoor</td><td>7K</td><td>dynamic</td><td>diverse</td><td>✘</td><td>MANO</td><td>two hands</td><td>✘</td></tr><tr><td>RenderIH [22]</td><td>1M</td><td>HDR</td><td>Indoor &amp; Outdoor</td><td>1K</td><td>dynamic</td><td>diverse</td><td>✘</td><td>A-MANO</td><td>two hands</td><td>✓</td></tr><tr><td>Ours</td><td>460K</td><td>HDR</td><td>Indoor &amp; Outdoor</td><td>4K</td><td>dynamic</td><td>diverse</td><td>✓</td><td>NIMBLE</td><td>single hand</td><td>✓</td></tr></table>
+
+appearance, hand pose, object occlusion, and hand skeleton topology, which are essential for hand pose estimation. From the appearance perspective, we first find that the presence of the forearm is important for pose estimation models to locate the wrist, affecting overall pose accuracy. Secondly, amplitude spectrum augmentation [9] is crucial for enhancing the model's robustness when the domain shifts from synthetic to real. Thirdly, increasing the background and hand texture diversity is important in reducing the synthetic-to-real gap, but their influence saturates beyond a certain amount. From the pose perspective, we observe that the pose difference between synthetic and real data affects the synthetic-to-real performance. However, performance gains tend to plateau after a certain threshold as more real hand poses are used for data synthesis. Notably, we find that using only a subset of real hand poses for synthesizing hand data enables the model trained on such data to achieve comparable performance to using all real hand poses. This outcome demonstrates that the data synthesized by our pipeline effectively facilitates learning hand representations.
+
+Unlike the human face and body, the hand has greater self-occlusion and interacting object occlusions. Yet, only a few synthetic hand datasets feature hand-object interactions. Incorporating object occlusions into synthetic training data improves model generalization on real-world test samples. Additionally, we observe that pose estimation models can associate hand poses with specific objects. Modeling specific object occlusions as a prior can improve performance when encountering similar objects. Finally, synthetic and real datasets often use different hand skeleton topologies [13, 34]. This discrepancy can cause inaccurate evaluation and label adaptation is necessary.
+
+By incorporating different hand image components, models trained with only our synthesized data can achieve state-of-the-art performance compared with real data. Moreover, models trained on a mixture of real and synthetic data outperform those trained only on real data for in- and cross-domain generalization. We summarize our contributions as follows:
+
+1. We present the first systematic study of the synthetic-to-real gap of 3D hand pose estimation. Having full control over the rendering pipeline, we establish associations between hand-image components and predictions by decomposing synthetic data.  
+2. We propose a high-quality synthetic data synthesis pipeline that supports our analysis and enables future applications to boost model performance.  
+3. We demonstrate that synthetic data can achieve the same level of accuracy as real data while paving the path to use synthetic data alone for hand pose estimation.
+
+# 2. Related Work
+
+Synthetic Hand Datasets. Building real-world 3D hand datasets is a challenging and time-consuming task. Recording often requires multi-camera systems or depth sensors [15, 32, 49, 53]. After data collection, manual or semiautomated labeling is required for ground truth. Synthetic data is a more time- and cost-effective alternative even if the images are not always photo-realistic; RHD [52], SynthHands [35] and ObMan [17] are three early examples of single hands, ego-centric hands, and hand grasping objects. More recently, Dartset [14] introduced a wrist-enhanced hand model and hands with different accessories. Ego3D [24], Re:InterHand [33] and RenderIH [22] feature two hands interacting, from both ego-centric [24] and third-person views [22, 33]. The datasets differ in their skeleton topology, consideration of background, lighting, and hand texture for rendering (see Tab. 1). The stand-alone efficacy of these synthetic datasets is unestablished, as most are used only for pre-training and then supplemented with either real or mixed data fine-tuning [10, 14, 17, 22, 33]. As we will show, these datasets still exhibit a significant synthetic-to-real gap; our work is the first systematic study to examine this gap for 3D hand pose estimation.
+
+Synthetic-to-Real 3D Hand Pose Estimation. Several works have explored using synthetic data to enhance the generalization performance on real-world data for hand pose estimation. In the depth domain, [30, 42] estimated
+
+![](images/c634975b506b0020cbfb8c261d9be5b2c229cda408cce2f1340151ca4d2a7da3.jpg)  
+Figure 2. (a) Real images (blue) have richer hand texture information and complex environments than synthetic images (red). Arms and interacting objects are often present in real images. (b) Real datasets have higher variation in amplitude values than synthetic ones across all frequency bands.
+
+hand pose from synthetic depth. For event data, Eventhands [39] used synthetic event streams for training to capture hand poses. Our work focuses on the RGB domain; one of the original works [52] proposes a synthetic RGB dataset (RHD), which reports better generalization results than a limited stereo real hand dataset. Other works learn from both labeled synthetic and unlabeled real-world data, using strategies such as pseudo-labeling and consistency training [48], reconstruction-based approach [28], multimodality supervisions [6, 27], input and output representations alignment to build a unified framework for various domain adaptive pose estimation [19].
+
+# 3. Synthetic-to-Real Hand Analysis
+
+This work verifies the hand image components (Sec. 3.1) that contribute to the synthetic-to-real gap in hand pose estimation. To that end, we develop a hand image synthesis pipeline (Sec. 3.2) for high-quality synthetic images that control the diversity of hand textures, backgrounds, and poses. We apply a compositional strategy (Sec. 3.3) to show the impact of arms and interacting objects. Moreover, we show the connection between occlusion levels and the hand object prior (Sec. 3.4).
+
+# 3.1. Hand Image Component
+
+A typical hand image consists of the hand, the arm, interacting object(s), and the background. Comparing real hand images [8, 15, 40, 53] with synthetic ones [14, 17, 22, 46, 52], we observe several differences across these components (see Fig. 2(a)). We summarize the differences below.
+
+Appearance. (1) The hands in real images come from multiple subjects and exhibit diverse hand textures; in synthetic images, the textures are limited and unrealistic. (2) Real images often feature complex and diverse environments, whereas synthetic images generally have simple and limited backgrounds. (3) Real images feature hands together with the arms, while synthetic images often only have a floating hand without the arm. (4) PASTA [9] showed that synthetic images have less variance than real images in their high-frequency components for semantic segmentation. We similarly analyze the variance of the amplitude in the frequency spectrum for real versus synthetic hand datasets (see Fig. 2(b)). We find that synthetic hand datasets have less variance than real datasets across the entire frequency spectrum.
+
+Objects. (1) Real images often feature hand-object interactions, leading to various occlusions. (2) Some objects may appear in both real train and test sets, while others are never seen in the synthetic datasets. Therefore, the synthetic datasets may lack the prior information on object occlusion that is present in the real datasets.
+
+Skeleton Topology. The skeletons may differ for real and synthetic hand data. The skeleton topology is a systematic difference between human-annotated and synthetic labels created by parametric or commercial models.
+
+# 3.2. Hand Image Synthesis
+
+We propose a rendering process (see Fig. 3) starting with a parametric hand model that models bones, muscles, skins, and textures. We then sample hand poses from real-world hand datasets. To push the boundary of realism, each hand is 'dressed up' with high-resolution textures and dynamic backgrounds under varying lighting conditions.
+
+Hand Model. We choose the NIMBLE [23] hand model, which takes pose  $\theta$ , shape  $\beta$  and texture  $\alpha$  parameters as inputs and generates a realistic 3D hand:
+
+$$
+\mathcal {N} (\theta , \beta , \alpha) = \{\mathcal {G} (\theta , \beta), \mathcal {A} (\alpha) \}. \tag {1}
+$$
+
+Above,  $\mathcal{G}(\theta ,\beta)$  denotes the hand geometry, including skin, muscle, and bone meshes. The term  $\mathcal{A}(\alpha)$  models the hand texture, including diffuse, specular, and normal maps. Most existing synthetic hand datasets [14, 17, 22] use the
+
+![](images/46f9668b73a60a0677ef4dbd5021c292dd88a2bc2cfb0368a95aa29e21751fc9.jpg)  
+Figure 3. Image synthesis process.
+
+![](images/382c24131a2f37c3c87a530298dd69439dc2ce614607efe7feadc9114e6b0469.jpg)  
+Figure 4. Same hand in different textures.
+
+MANO hand model [38]. NIMBLE has a finer 3D mesh, with 5,990 vertices and 9,984 triangular faces, compared to the 778 vertices and 1,538 faces of MANO. NIMBLE and MANO have different topologies, including differences in both the number of joints (25 vs. 21) and their positions (See Supp. Sec. F).
+
+Hand Pose. We keep our pose distribution consistent with the target real datasets (i.e., FreiHAND [53] and DexYCB [8]) to eliminate its influence during our analysis. We derive the hand pose by fitting the NIMBLE hand mesh to the MANO hand mesh. During the fitting process, we optimize the pose, shape, rotation, and translation parameters in two stages to avoid poor fitting results (See Supp. Sec. B). Since our data synthesis pipeline is controllable and generalizable, we further augment our pose distribution with the fitting algorithm in three ways: (1) sampling poses from ObMan [17] to incorporate more hand-object interaction, (2) randomly synthesizing poses from NIMBLE space, and (3) sampling from VAE prior built with depth-based hand datasets [1].
+
+Hand Texture. We synthesize rich hand textures using the NIMBLE model; it is formulated by  $\mathcal{A}(\alpha) = \bar{A} + \Phi \alpha$ , where  $\alpha$  is the appearance parameter,  $\bar{A}$  is the average appearance and  $\Phi$  are the model principal components. Existing synthetic hand datasets have unrealistic hand textures or limited texture diversity (e.g., RenderIH only offers 30 textures). NIMBLE hand textures are the linear interpolation of 38 photo-realistic hand texture assets from different ages, genders, and races to enhance texture diversity. Some examples are shown in Fig. 4.
+
+Background and Lighting. We use 669 HDRI scenes from [50] as the background; these images feature realistic indoor and outdoor scenes and have been used by [3, 22, 33, 41] to provide highly photo-realistic rendered scenes. Some examples are shown in Fig. 5.
+
+Rendering. We render with Blender Python based on the ray-tracing rendering engine Cycles [4]. First, we import the skin mesh and apply texture to the mesh with diffuse, specular, and normal maps. The camera is set based on
+
+![](images/8c5b7f5c66f27b3b9a31057a1d5d8946efaf3c0abd5179ed93f2fa40d7c5c360.jpg)  
+Figure 5. Same hand and hand texture in different backgrounds and lighting. The same hand looks different under different backgrounds and lighting.
+
+![](images/9342da6acdea199ff1496cb9e8d936461b6f3218632d2099bf65dff081440b13.jpg)  
+Figure 6. Synthetic hand images with realistic hand textures, backgrounds, lighting, arms, and interacting objects.
+
+the target real datasets' camera intrinsics when analyzing. Backgrounds and textures are selected randomly. This setup creates an automated rendering pipeline contained within Python with minimal effort. It takes around 1 second to render an image with a single RTX A5000 GPU, with further parallelization speedups. More details can be found in Supplementary Sec. C.
+
+# 3.3. Decomposition and Composition
+
+Since our work focuses on analyzing the importance of different components, we segment the arm and object from real images and compose them into synthetic images, as shown in Fig. 1. The composition is more practical and serves as a better control case than rendering these components.
+
+To segment the arm and object from real images, we use the pre-trained object detector Grounding DINO [29] to extract bounding boxes for these components. The bounding box crops are then fed into the segmentation network SAM [21] to estimate the corresponding segmentation masks. For each real image  $I_{real}^{i}$ , where  $i \in [1, N]$ ,  $N$  is the number of poses in the target real dataset, we extract the bounding boxes  $bbox^{i}$  of the arm or interacting object with input text prompts  $x$  by object detector  $D(\cdot): bbox^{i} = D(x)$ . Then the bounding boxes  $bbox^{i}$  are passed to SAM  $S(\cdot)$  to obtain the corresponding masks  $M^{i}: M^{i} = S(bbox^{i})$ . The final synthetic image  $\tilde{I}_{syn}^{j}$  with arm and interacting object can be defined as follows:
+
+$$
+\begin{array}{l} \tilde {I} _ {\text {s y n}} ^ {j} = \left(1 - M _ {\text {o b j}} ^ {i} - M _ {\text {a r m}} ^ {i}\right) \odot I _ {\text {s y n}} ^ {j} \\ + M _ {\mathrm {o b j}} ^ {i} \odot I _ {\text {r e a l}} ^ {i} + M _ {\text {a r m}} ^ {i} \odot I _ {\text {r e a l}} ^ {i}, \tag {2} \\ \end{array}
+$$
+
+where  $I_{syn}^{j}$  denotes the rendered synthetic image,  $M_{obj}^{i}$  and
+
+![](images/d6441406ec6b156b0ccde93bb58ba4c6382bdeeca3a0b78f93fb983883ef6166.jpg)  
+Figure 7. We build a VAE object occlusion prior and use this prior to refine the predicted hand poses.
+
+$M_{arm}^{i}$  denote the extracted object mask and arm mask,  $\odot$  denotes element-wise multiplication and  $j = k*N + i$ , where  $k\in \mathbb{Z}_{\geq 0}$ . In this way, we get the final synthetic images. Examples are shown in Fig. 6.
+
+# 3.4. Object Occlusion Levels and Priors
+
+To analyze the influence of object occlusion in synthetic-to- real adaptation, we divide the validation set into different levels of occlusion using [45], which provides finger-level occlusion labels (five fingers and palm) for each hand, ranging from 0 (least) to 6 (highest). Moreover, to show the connection between occlusion levels and hand object priors, we employ a VAE prior to reconstruct occluded joints based on visible joints. Similar to [47, 54], we use the VAE [20] to construct the object occlusion prior, which consists of an encoder  $q(z|x_{3D})$  and a decoder  $p(x_{3D}|z)$  (see Fig. 7). During the training stage, input 3D pose  $x_{3D}$  is first randomly masked to increase reconstruction diversity. Then the encoder maps the masked 3D pose  $x_{3D}$  to latent space  $z$ , and the decoder reconstructs a 3D pose  $\hat{x}_{3D}$ . A Kullback-Leibler divergence loss and a 3D joint loss are used to train the object occlusion prior:
+
+$$
+L _ {V A E} = \lambda L _ {K L} + \| \hat {x} _ {3 D} - x _ {3 D} \| _ {2} ^ {2}. \tag {3}
+$$
+
+During the refinement stage, we use the pre-trained VAE prior to refine the predicted joints. More details are provided in Secs. D and E of the Supplementary.
+
+# 4. Experiments
+
+# 4.1. Datasets and Metrics
+
+We use FreiHAND and Dex-YCB as the target real datasets and synthesize their corresponding synthetic datasets, SynFrei and SynDex, for analysis.
+
+- FreiHAND [53] has 130k training and 4k testing images of a single hand. Each training sample features a real RGB image captured on a green screen background and three extra images with synthetic backgrounds.  
+- Dex-YCB [8] is a large-scale 3D hand-object dataset with over 582k images, featuring objects from the YCB dataset [44]. We use the default "S0" train/test split and a reduced version of the training set, with 35k images for analysis.
+
+- HO3D-v2 [15] features 3D hand-object interactions, with 66k training and 11k testing images. The ten interacting objects used in the dataset are from the YCB dataset. We use HO3D-v2 to perform cross-dataset validation to evaluate the model's performance on samples with unseen interacting objects.  
+- MOW [7] is a 3D dataset of humans manipulating objects in-the-wild, including 512 annotated samples. It is used as the test set to evaluate the generalization ability.
+
+Evaluation Metrics. We evaluate hand pose and shape accuracy using standard metrics PA-MPJPE and PA-MPVPE in cm, which compare the mean per joint position error and mean per vertex position error of prediction and ground truth after Procrustes Alignment.
+
+# 4.2. Baselines and Training Details
+
+We reproduce five 3D hand pose estimation methods: S²HAND [12], CMR [11], METRO [25], MeshGraphormer [26] and simpleHand [51] on the real target datasets as baselines using their official training code. Additionally, we reproduce these methods on our synthesized datasets with amplitude spectrum augmentation [9] (See Supplementary Sec. A) for comparisons to demonstrate the effectiveness of our data synthesis pipeline. All baselines are trained with one NVIDIA RTX A5000 GPU. We mainly use S²HAND to analyze the synthetic-to-real gap.
+
+# 4.3. Comparisons with Baselines
+
+We train five methods on the real dataset FreiHAND as baselines and on our synthesized SynFrei to show the effectiveness of our synthetic data synthesis pipeline. As shown in Tab. 2, models trained with only our synthetic dataset can achieve state-of-the-art results, which achieve  $97\%$ ,  $91\%$ ,  $88\%$ ,  $91\%$  and  $84\%$  of the performance of models trained with the real dataset for  $\mathrm{S}^2$  HAND, CMR, METRO, Mesh-Graphormer, and simpleHand respectively. These results indicate a synthetic-to-real gap of around  $0.1~\mathrm{cm}$ . We notice decreased performance when training with only synthetic data, especially with stronger model backbones. We speculate that the stronger models over-fit more easily to the synthetic data, affecting the synthetic-to-real generalization performance.
+
+We also train  $S^2$  HAND on the reduced version of Dex-YCB and our synthesized SynDex, achieving comparable performance on the Dex-YCB test set of 0.86 cm vs. 0.87 cm in PA-MPJPE.
+
+# 4.4. Comparison with Other Synthetic Datasets
+
+We compare with DARTset [14], which has a more diverse pose distribution, hand wrists, and accessories but lacks dynamic backgrounds, interacting objects, and amplitude spectrum augmentation. DARTset samples their hand poses from FreiHAND and augments them by linear
+
+![](images/651f2ae259afbe020506b47786379ebe2d7efd4257ead6c1c8dfdbbaf5344f3d.jpg)  
+Figure 8. (a) Synthetic dataset size influence. (b) Background and hand texture diversity influence. (c) The percentage of real hand poses used for synthesizing data. The green lines indicate the saturation points.
+
+![](images/7dd4577093ffec439cdfcd20e739f9cc06b581268a64ebf604c0a26d40099a5b.jpg)
+
+![](images/9fafd750599329fa07ed5d66a8a27ad4b5b9ceef33dc77f7723d40733a0332a1.jpg)
+
+Table 2. Comparisons of methods trained on FreiHAND and only our SynFrei on the FreiHAND test set (PA-MPJPE↓ / PA-MPVPE↓).  
+
+<table><tr><td>Method</td><td>Real FreiHAND</td><td>Our SynFrei</td><td>Syn→Real</td></tr><tr><td>S2HAND [12]</td><td>0.99 / 1.02</td><td>1.02 / 1.05</td><td>97%</td></tr><tr><td>CMR [11]</td><td>0.77 / 0.78</td><td>0.85 / 0.88</td><td>91%</td></tr><tr><td>METRO [25]</td><td>0.69 / 0.71</td><td>0.78 / 0.79</td><td>88%</td></tr><tr><td>MeshGraphormer [26]</td><td>0.69 / 0.70</td><td>0.76 / 0.78</td><td>91%</td></tr><tr><td>simpleHand [51]</td><td>0.65 / 0.66</td><td>0.77 / 0.79</td><td>84%</td></tr></table>
+
+Table 3. Comparisons of methods trained on DARTset and our SynFrei on the FreiHAND test set (PA-MPJPE $\downarrow$  / PA-MPVPE $\downarrow$ ). The results of DARTset are from its paper.  
+
+<table><tr><td>Method</td><td>DARTset</td><td>SynFrei</td></tr><tr><td>CMR</td><td>2.56 / 2.57</td><td>0.85 / 0.88</td></tr><tr><td>METRO</td><td>1.77 / 1.75</td><td>0.78 / 0.79</td></tr></table>
+
+interpolating the synthesized pose from A-MANO space and FreiHAND sample pose. As shown in Tab. 3, CMR and METRO trained with our SynFrei outperform DARTset despite our dataset size being half DARTset (325,600 vs. 758,378). Moreover, CMR trained with our SynDex outperforms DARTset on the FreiHand test set (1.92 / 1.98), even with different pose distributions.
+
+Comparisons between single- and two-hand datasets are challenging due to the domain gap. We still evaluate the cross-dataset generalization on the HO3D-v2 test set for models trained with SynFrei and RenderIH [22]. We only take the right-hand results of the RenderIH model. Models trained with SynFrei achieve better cross-dataset evaluation than RenderIH of  $1.41\mathrm{cm}$  vs.  $1.76\mathrm{cm}$  in PA-MPJPE. This result can be attributed to the limited expressiveness of interacting hands, which fails to let the model learn handobject interactions, and the blurry background effects in RenderIH images due to the low background resolution.
+
+# 4.5. Appearance Analysis
+
+Dataset Size and Diversity Influence. We analyze the influence of the synthetic dataset size on synthetic-to-real per
+
+Table 4. Arm, amplitude spectrum augmentation, and interacting object influence on FreiHAND and Dex-YCB test sets (PAMPJPE↓). "Amp Aug" is short for amplitude spectrum augmentation.  $\times$  refers to assigning RGB values to the arm and object mask positions.  
+
+<table><tr><td></td><td colspan="3">Components</td><td colspan="2">Train set</td></tr><tr><td></td><td>Arm</td><td>Amp Aug</td><td>Object</td><td>SynFrei</td><td>SynDex</td></tr><tr><td>(i)</td><td></td><td>✓</td><td>✓</td><td>1.07</td><td>0.90</td></tr><tr><td>(ii)</td><td>✓</td><td></td><td>✓</td><td>1.11</td><td>0.89</td></tr><tr><td>(iii)</td><td>✓</td><td>✓</td><td></td><td>1.07</td><td>0.95</td></tr><tr><td>(iv)</td><td>✗</td><td>✓</td><td>✗</td><td>1.04</td><td>0.92</td></tr><tr><td>(v)</td><td>✓</td><td>✓</td><td>✓</td><td>1.02</td><td>0.87</td></tr></table>
+
+formance. As illustrated in Fig. 8(a) and, as expected, there are diminishing returns with adding more data. When SynFrei's synthetic dataset size reaches  $8 \times 32,560$ , performance gains plateau, and the trend of error decrease becomes flat.
+
+We further render synthetic datasets at this full size of  $8 \times 32,560$  samples, but with varying levels of diversity:  $50\%$ ,  $25\%$ , and  $5\%$ , where each value indicates the percentage of the full background and hand texture assets. As shown in Fig. 8(b), more diverse backgrounds and hand textures can reduce the synthetic-to-real gap. This result suggests that enriching the background and texture assets is useful when synthesizing data. However, the performance plateaus at  $50\%$ , indicating that around 300 indoor and outdoor HDRI scenes are sufficient for synthesizing hand data. Several techniques can be implemented in our synthesis pipeline to further improve performance, such as changing camera viewpoints, flipping or rotating backgrounds, and adjusting skin tone contrast, brightness, or subsurface color.
+
+Arm Influence. We analyze the importance of the arm by removing it from synthetic images. Tab. 4 shows increases in PA-MPJPE for models trained with SynFrei and SynDex without the arm component comparing Rows (i) and (v). Fig. 9(a) shows that the model trained on SynFrei without the arm tends to misinterpret parts of the arm as the wrist, especially if the arm occupies a large portion of the image. Such errors do not occur for SynFrei with arms. Since the
+
+![](images/f27942e9a31e834b41ec44f41c6a5c233b175c88c849ad2fb499d74c7b324c23.jpg)  
+Ground Truth
+
+![](images/e71b65790819d9fcf2946ca66972c454c59a654b3f956fd347e58bfdc07c4661.jpg)  
+Real
+
+![](images/644decd63a254f91c181c8065f25d55e71d181e5254084f520e8aff510b4ffa8.jpg)  
+Syn  
+(a)
+
+![](images/80802bb5c63ed53c0940b6656370996ef43269a72cb67b6b4ce25989a2bdce7a.jpg)  
+Syn (random)  
+Figure 9. (a) Comparisons of model trained with FreiHAND (Real), our SynFrei (Syn), our SynFrei with random arm (random), and our SynFrei (w/o arm) on FreiHAND test set. (b) Comparisons of model trained with FreiHAND, SynFrei, SynFrei with random interacting object and SynFrei (w/o object) on the FreiHAND test set.
+
+![](images/7804807d94ea28ce66278e18d1ac8c361a2142a614fdc42a366f5c4888cb69a8.jpg)  
+Syn (w/o arm)
+
+![](images/8796444af564c499be34efd2449e3016c5d0857d286e6f6b4a3eb1ded95c90d1.jpg)  
+Ground Truth
+
+![](images/d2398c6081d83a19a9a5d8656c6e60b23ebfec8109abed62ffb46e4d0ba487df.jpg)  
+Real
+
+![](images/28b086f2a833936284a9a18d766f8bc5df74b547acd8e446e1f8cf4fb760f190.jpg)  
+Syn  
+(b)
+
+![](images/13cdb33e60d578e8ec2878902fe1e05e4033907fc41bf0e2bb761be4b8d807c5.jpg)  
+Syn (random)
+
+![](images/4fe14b2783b4ffec2b0fa1e4bd886d6361e72db4df68fa033c39da951691bb0d.jpg)  
+Syn (w/o obj)
+
+arm and hand share similar colors, models can easily be confused and incorrectly locate the root joint on the arm rather than the wrist if synthetic images lack arm information. This result suggests that the arm is an important cue for locating the wrist, thus affecting the overall hand pose.
+
+Amplitude Spectrum Augmentation Influence. We find that amplitude spectrum augmentation is a crucial component. Removing it results in increases in PA-MPJPE for both SynFrei  $(0.09\mathrm{cm})$  and SynDex  $(0.02\mathrm{cm})$  (see Tab. 4 Rows (ii) and (v)). This suggests that the ability of amplitude spectrum augmentation to distort amplitude information while preserving phase information (e.g., hand structure) can enhance model robustness when the domain shifts from synthetic to real.
+
+Random Arm and Object Occlusion Influence. We further randomize the arm and object incorporated into the hand image by assigning RGB values to the corresponding arm and object mask positions described in Sec. 3.3. For the arm, we assign it to the mean RGB value of the hand to better imitate hand-arm compatibility. For the object occlusion, we assign a random RGB value to the object position. Tab. 4 Rows (iv) and (v) show that with random arm and object occlusion, although the synthetic-to-real gaps slightly increase compared with segmenting from real images, the synthetic-to-real performance can still achieve  $95\%$  and  $93\%$  on FreiHAND and Dex-YCB test sets. This result reveals that the model can learn how to locate the wrist position and interacting objects accurately without highly realistic arm or object occlusion information (see Fig. 9).
+
+# 4.6. Pose Analysis
+
+We analyze the influence of hand pose on the synthetic-to-real performance by controlling the number of real hand poses used for data synthesis. Note that we still diversify each hand with different backgrounds and textures for rendering. As shown in Fig. 8(c), the synthetic-to-real performance improves when synthetic hand poses approach the
+
+real ones. This result suggests that the pose difference between the synthetic and real datasets introduces a synthetic-to-real gap. We also observe that the model trained with synthetic data can achieve around  $80\%$  of the final performance using only  $5\%$  of total real poses. With  $20\%$  of real poses, the performance increases to around  $90\%$ , and with  $40\%$  of real poses, it reaches  $97\%$ . In other words, synthetic hand images effectively enable the model to learn visual representations, while core hand poses are sufficient to achieve good generalization performance.
+
+# 4.7. Object Occlusion Analysis
+
+Tab. 4 Rows (iii) and (v) show increases in PA-MPJPE after removing the interacting objects from SynFrei  $(0.05\mathrm{cm})$  and SynDex  $(0.08\mathrm{cm})$ , especially for the Dex-YCB test set, which features more hand-object interactions. When the object largely occludes the hand, the predicted hand pose does not interact with the object right after removing interacting objects from synthetic images (see Fig. 9(b)).
+
+Occlusion Levels. We use the HO3D-v2 dataset for cross-dataset validation, which features hand-object interactions. Since HO3D-v2 test set labels are not publicly available, we separate the original train set into train and validation sets.
+
+We compare models' performance on validation sets under three training settings: S²HAND trained with HO3D-v2 train set  $(S_1)$ , FreiHAND  $(S_2)$ , and SynFrei  $(S_3)$ . As shown in Fig. 10(a), a performance gap exists between  $S_1$  and  $S_2$ ,  $S_3$ . As the occlusion level rises,  $S_2$  and  $S_3$  degrade due to their lack of object occlusion information in the validation sets, while  $S_1$  improves, which incorporates this prior.
+
+We further investigate the distribution of unique object amount across each occlusion level and discover a relationship between the performance of  $S_{1}$  and the unique object amount. As shown in Fig. 10(b),  $S_{1}$  performs the best on occlusion level 6, which has the least amount of unique objects. With object occlusion prior information in validation sets,  $S_{1}$  can associate hand poses with specific objects. Also, higher occlusion levels are often associated
+
+![](images/8cd2e5fbf40a7a56b06b195afe3834b380490d287d23d9f09917e6e8cc24f3d2.jpg)  
+Figure 10. (a) Comparisons of  $S_{1}$ ,  $S_{2}$  and  $S_{3}$  on validation sets with different occlusion levels.  $S_{2}$  and  $S_{3}$  after object occlusion prior refinement are denoted as  $S_{2}$ -refine and  $S_{3}$ -refine. (b) Relationship between the performance of  $S_{1}$  and the number of unique objects at each occlusion level.
+
+![](images/d708b95371a93c130ebdfc4159a28205b8f374eb14dd68f3e8c1a89d74bff103.jpg)
+
+with larger objects, which impose greater constraints on hand poses and result in smaller variations in poses. Therefore,  $S_{1}$  demonstrates improved performance on higher occlusion levels. However, without object occlusion information, the performances of  $S_{2}$  and  $S_{3}$  decline as the occlusion levels increase. These findings show that object occlusion prior contributes to the synthetic-to-real gap.
+
+Object Occlusion Prior. We use Dex-YCB to train a VAE object occlusion prior (See Sec. 3.4), which includes the objects in HO3D-v2. As shown in Fig. 10(a), the synthetic-to-real performance of  $S_{3}$  improves after applying the VAE object occlusion prior to refine the predicted joints ( $S_{3}$ -refine). Incorporating the object occlusion prior bridges the gap between synthetic and real hand datasets with high levels of occlusion. While previous works use prior information to refine poses in real-to-real scenarios [36, 37, 54], our findings also show its utility in synthetic-to-real adaptation.
+
+Through our object occlusion analysis, we provide a potential training scheme to better adapt synthetic data to real applications. Models can initially be trained on large-scale synthetic data to learn hand representations. Existing hand-object interaction datasets can then be used to provide useful prior information to refine the predictions and further reduce the synthetic-to-real gap.
+
+# 4.8. Hand Skeleton Topology Analysis
+
+Different hand skeleton topologies can have different joint definitions [13]. This can introduce a synthetic-to-real gap since the synthetic data's skeleton topology may differ from real datasets. To analyze the influence of hand skeleton topology difference, we train  $\mathrm{S}^2\mathrm{HAND}$  without label adaption and obtain NIMBLE joints as the ground-truth joints by fitting NIMBLE mesh to MANO mesh for training. Note that the NIMBLE skeleton differs from the MANO skeleton (see Supp. F), and we remove the extra anatomical joints of NIMBLE when evaluating. As shown in Tab. 5, training with NIMBLE joints and without label adaption, the synthetic-to-real error increases from  $1.02~\mathrm{cm}$  to  $1.28~\mathrm{cm}$ . This result demonstrates that differences in hand skeleton
+
+Table 5. Hand skeleton topology differences.  
+
+<table><tr><td>Label Adaptation</td><td>PA-MPJPE↓</td></tr><tr><td>-</td><td>1.28</td></tr><tr><td>✓</td><td>1.02</td></tr></table>
+
+Table 6. Cross-dataset generalization results in PA-MPJPE  $\downarrow$  .  ${}^{ \dagger  }$  : results come from the official evaluation server.  
+
+<table><tr><td>Test Set Train Set</td><td>FreiHAND</td><td>Dex-YCB</td><td>HO3D-v2†</td><td>RHD</td><td>MOW</td></tr><tr><td>FreiHAND</td><td>0.99</td><td>1.14</td><td>1.39</td><td>1.40</td><td>1.47</td></tr><tr><td>+ SynFrei</td><td>0.95</td><td>1.11</td><td>1.28</td><td>1.32</td><td>1.38</td></tr><tr><td>Dex-YCB</td><td>1.63</td><td>0.86</td><td>1.25</td><td>1.72</td><td>1.24</td></tr><tr><td>+ SynDex</td><td>1.49</td><td>0.82</td><td>1.15</td><td>1.65</td><td>1.18</td></tr></table>
+
+topology between synthetic and real datasets can introduce bias to the prediction.
+
+# 4.9. Cross-Dataset Evaluation
+
+We demonstrate the ability of our synthetic data to bridge the gap across different hand datasets through cross-dataset generalization using  $\mathbf{S}^2\mathbf{H}\mathbf{A}\mathbf{N}$ . As shown in Tab. 6, the model trained with a mixture of real and synthetic data achieves better results than only real data for in- and cross-domain generalization. For example, the model trained with Dex-YCB and SynDex performs better than with only DexYCB on the FreiHAND test set. The difference may be because Dex-YCB mostly consists of indoor images, while the FreiHAND test set contains many outdoor images. Incorporating synthetic images with both indoor and outdoor environments bridges this gap. These results prove our synthetic data is a good complement to real data, both in- and cross-domain. More results can be found in Supplementary Sec. H.
+
+# 5. Conclusion
+
+This paper proposes the first systematic study of the synthetic-to-real gap of 3D hand pose estimation. We analyze the synthetic-to-real gap with respect to appearance, hand pose, object occlusion, and hand skeleton topology. We impressively demonstrate that synthetic hand data can achieve the same level of accuracy as real hand data while paving the path to use synthetic data alone. Models trained on a mixture of real and our synthetic data outperform those trained only on real data for in-domain and cross-domain generalization. Our proposed data synthesis pipeline can create high-quality synthetic hand images to alleviate our reliance on real data and benefit future research and applications.
+
+# Acknowledgements
+
+This research / project is supported by the Ministry of Education, Singapore, under the Academic Research Fund Tier 1 (FY2022). Additionally, this work is supported by the National Natural Science Foundation of China (No. 62406298), the Guangzhou Municipal Nansha District Science and Technology Bureau (No.2022ZD012), the HSBC project L0562, and the Fundamental Research Funds for the Central Universities, Communication University of China (CUC24XT07).
+
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\ No newline at end of file
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+# Anatomical Consistency and Adaptive Prior-informed Transformation for Multi-contrast MR Image Synthesis via Diffusion Model
+
+Yejee Shin $^{1*}$  Yeeun Lee $^{1*}$  Hanbyol Jang $^{1}$
+
+Geonhui Son $^{1}$  Hyeongyu Kim $^{1}$  Dosik Hwang $^{1,2\dagger}$
+
+1 Yonsei University 2 Korea Institute of Science and Technology
+
+{yejeeshin, dldpdms0109, hanstar4, higun2, lion4309, dosik.hwang}@yonsei.ac.kr
+
+# Abstract
+
+Multi-contrast magnetic resonance (MR) images offer critical diagnostic information but are limited by long scan times and high cost. While diffusion models (DMs) excel in medical image synthesis, they often struggle to maintain anatomical consistency and utilize the diverse characteristics of multi-contrast MR images effectively. We propose APT, a unified diffusion model designed to generate accurate and anatomically consistent multi-contrast MR images. APT introduces a mutual information fusion module and an anatomical consistency loss to preserve critical anatomical structures across multiple contrast inputs. To enhance synthesis, APT incorporates a two-stage inference process: in the first stage, a prior codebook provides coarse anatomical structures by selecting appropriate guidance based on precomputed similarity mappings and Bezier curve transformations. The second stage applies iterative unrolling with weighted averaging to refine the initial output, enhancing fine anatomical details and ensuring structural consistency. This approach enables the preservation of both global structures and local details, resulting in realistic and diagnostically valuable synthesized images. Extensive experiments on public multi-contrast MR brain images demonstrate that our approach significantly outperforms state-of-the-art methods. The source codes are available at https://github.com/yejees/APT.
+
+# 1. Introduction
+
+Multi-contrast magnetic resonance (MR) images serve as a crucial non-invasive modality for the detection and treatment of brain disorders. Multiple modalities offer complementary information that enhances patient characterization and guides clinical decisions. By integrating data from multiple imaging modalities, clinicians can obtain a
+
+more comprehensive view of tumors and lesions, thereby improving diagnostic accuracy and optimizing treatment planning. However, acquiring multi-contrast MR images is time-consuming and costly, posing discomfort for patients and increasing the risk of motion artifacts that reduce image quality [9, 24, 36, 40].
+
+Diffusion Models (DMs) [8, 32] have gained increasing attention in recent research due to their robust mode diversity and high-quality image generation capabilities [6, 37], with growing applications in medical image synthesis [16, 26, 28]. DMs iteratively denoise samples to capture complex structural details, making them valuable for tasks requiring fine-grained anatomical accuracy. However, the stochastic nature of the denoising process can disrupt the preservation of consistent anatomical structures [25], potentially compromising the clinical relevance of synthesized images. Moreover, translation across multiple modalities presents challenges in maintaining anatomical consistency while effectively integrating the diverse characteristics of multi-contrast MR images [14].
+
+In this study, we introduce APT, a unified diffusion model that incorporates Anatomical Consistency and an Adaptive Prior-informed Transformation to ensure anatomically consistent synthesis of multi-contrast MR images. To maintain anatomical consistency throughout the synthesis process, APT implements a comprehensive framework. First, we utilize a pretrained biomedical vision-language model [41] to extract anatomical features from multi-contrast images, which are then integrated through a mutual information fusion module. To enhance structural alignment, we propose an anatomical consistency loss that compares fused features from randomly selected multicontrast images of the same patient with the overall feature set. These anatomically-aware features guide the diffusion model via cross-attention, ensuring the preservation of critical anatomical structures during synthesis.
+
+The prior codebook is a memory mechanism designed to provide optimally initialized images for missing contrast images during inference. It achieves this by leveraging the
+
+similarity between each contrast image and augmented versions of multi-contrast images generated using Bézier curve transformation functions [27]. It comprises three key components for each contrast image: index mappings, transformation functions, and intensity scaling weights, enabling the generation of more accurate and high-fidelity images.
+
+For inference, we propose a two-stage process to generate missing contrast MR images. The first stage initializes the generation from an anatomically-informed prior provided by the pre-computed codebook, rather than starting from a complete noise state. This prior serves as a structured starting point, which is enhanced in the subsequent reverse diffusion process [8]. The second stage refines detailed anatomical structures affected by the stochastic diffusion process through iterative unrolling near the final step, applying weighted averaging to ensure anatomical precision in the generated images. This approach ensures both global anatomical consistency and accurate local structural details. We validate our approach with experiments on two public multi-contrast brain MRI datasets, demonstrating that our method outperforms existing methods in multi-contrast MR image synthesis.
+
+In summary, our contributions are as follows:
+
+- We propose APT, an anatomically-aware diffusion model that utilizes multi-contrast MR images to generate accurate and anatomically consistent MR image synthesis.  
+- We introduce a mutual information fusion module and an anatomical consistency loss to enhance anatomical alignment in synthesized MR images.  
+- We designed a prior codebook to provide anatomically-informed initialization for target image synthesis.  
+- Two-stage inference strategy employed prior-informed transformation and iterative unrolling to refine anatomical details, ensuring consistent and accurate MR image generation.
+
+# 2. Related Work
+
+# 2.1. CLIP
+
+Contrastive Language-Image Pre-training (CLIP) [29] is a powerful pre-training framework that has been trained on a large-scale dataset, demonstrating exceptional generalization capabilities and interpretability. This text supervision allows CLIP vision encoder to excel in various tasks [17, 22, 23, 30, 35]. Recently, CLIP has gained prominence in the medical imaging field, leading to the development of biomedical vision-language foundation models (VLMs) built on contrastive learning [7, 34, 41]. PubMedCLIP [7] is a vision-language encoder pretrained on medical image-caption pairs sourced from PubMed articles. BiomedCLIP [41] adapts the CLIP model for the biomedical domain and optimizes the tokenizer and context size to effectively handle lengthy biomedical literature.
+
+These domain-specific adjustments enable BiomedCLIP to achieve enhanced performance across various tasks compared to existing biomedical VLMs.
+
+# 2.2. Multi-Contrast MR Image Synthesis
+
+Multi-contrast MR images utilize multiple contrast technique to image the identical anatomical structures, providing essential complementary insights for the diagnosis and assessment of tumors and lesions [12, 20]. However, acquiring multi-modality MR imaging requires substantial time and expense [11, 15, 38], limiting its practicality in clinical settings. Trans-modal MR image synthesis addresses these limitations by mapping available MRI modalities to the target domain of missing modalities, effectively generating missing contrasts and enhancing MRI's clinical utility [3, 10, 42]. Generative adversarial networks (GANs) are widely utilized in medical image translation by learning mappings between distinct image distributions [5, 13, 18, 19, 39, 44]. MM-GAN [31] consists of a CNN-based generator and discriminator, designed to handle diverse source-target modality mappings within a single network. Despite these advances, GANs face inherent instability during training due to the nature of adversarial loss, leading to problems like mode collapse and vanishing gradients [6, 13].
+
+# 2.3. Diffusion for MR Image Synthesis
+
+Diffusion models have recently emerged as a leading approach in generative modeling, known for their robust mode coverage and high-quality image generation [6, 8, 37]. Diffusion models are probabilistic frameworks based on a bidirectional Markov chain, where Denoising Diffusion Probabilistic Models (DDPM) [8] optimizes conditional probability by aligning noise in the forward and reverse processes using a specialized loss function. LDM [30] integrates cross-attention modules within a U-Net architecture, facilitating the generation of images under various conditions with greater efficiency. Diffusion models have shown great potential in the field of medical imaging synthesis [16, 26, 28], offering new possibilities for enhancing diagnostic accuracy in clinical settings by generating target domain images using source domain data. SynDiff [28] is the first adversarial diffusion model that leverages a cycle-consistent architecture for unsupervised training of a conditional diffusion model. M2DN [26] employs a multi-input multi-output framework, enabling efficient modality synthesis across various missing scenarios.
+
+# 3. Methodology
+
+We introduce APT, a unified model for multi-contrast MR image synthesis, integrating anatomical consistency and adaptive prior-informed transformation. Fig. 1 illustrates
+
+![](images/9841878a7a2491759fc40999637c0f8c84f1be24c083112048835768093e09e8.jpg)  
+Figure 1. Overview of the proposed training framework for multi-contrast MR image synthesis using a conditional diffusion model.  $z_{s}^{all}$  denotes the vector representing all multi-contrast images of subject  $s$ , while  $z_{s}^{sub}$  denotes the vector representing a sub-sampled image of subject  $u$ .
+
+![](images/208928c658327c134eaac3fb974b5f6188c7bd14bc1f603a927a35992212bf15.jpg)  
+Figure 2. Prior Codebook for Prior-informed Transformation. The left section illustrates augmented versions of target contrast image  $x^{c}$  generated using Bézier curves.  $x^{c'}$  denotes transformed images of each contrast  $x^{c}$ .
+
+the main training framework, which consists of (a) anatomical information alignment using a mutual information fusion module and (b) a conditional diffusion model. MR image synthesis is guided by a prior codebook (Fig. 2) and employs a two-stage inference strategy (Fig. 3) to refine generated images from coarse to fine details.
+
+# 3.1. Anatomical Information Alignment
+
+Mutual Information Fusion Let  $x = \{x^{1},x^{2},\dots ,x^{C}\}$  represent a set of multi-contrast MR images for the same subject, where each  $x^c$  corresponds to a different modality. As demonstrated in [21], text-image joint training can enrich visual features with semantically aligned information, enhancing the model's ability to capture more comprehensive representations. To capture these features from each contrast image, the vision encoder processes each  $x^{c}$  within the pretrained VLM, generating feature maps for each contrast. The mutual information fusion (MIF) module, shown in Fig. 1 (a), utilizes self-attention to learn how each contrast image influences others, capturing dependencies across contrasts. A feed-forward network (FFN) refines the feature maps for enhanced representations. The refined feature maps are aggregated to obtain a compact representation that captures the mutual information across contrasts,
+
+resulting in the final feature representation  $z_{s}^{all}$ , where  $s$  denotes the subject-level fusion of all contrasts.
+
+Anatomical Consistency Loss To align the anatomical information between different contrasts effectively, we utilize a contrastive learning framework [29]. Two types of feature vectors are generated:  $z_{s}^{all}$ , derived from processing all  $C$  contrasts  $\{x^{1}, x^{2}, \ldots, x^{C}\}$  through the MIF module, and  $z_{s}^{sub}$ , obtained from a randomly selected subset of  $C - 1$  contrasts. The vectors  $z_{s}^{all}$  and  $z_{s}^{sub}$  represent a positive pair, with other combinations serving as negatives.
+
+The contrastive loss is then defined as:
+
+$$
+\mathcal {L} _ {\text {A n a t o m y}} = - \log \frac {\exp \left(z _ {s} ^ {a l l ^ {\top}} z _ {s} ^ {s u b} / \tau\right)}{\exp \left(z _ {s} ^ {a l l ^ {\top}} z _ {s} ^ {s u b} / \tau\right) + \sum_ {i \neq s} \exp \left(z _ {s} ^ {a l l ^ {\top}} z _ {i} ^ {s} / \tau\right)} \tag {1}
+$$
+
+where  $\tau$  is a learnable temperature parameter, and  $z_{i}$  represents a negative sample feature vector from a different subject. This loss function promotes similarity between  $z_{s}^{all}$  and  $z_{s}^{sub}$ , while discouraging similarity with negative samples  $z_{i}$ . This alignment facilitates a unified multi-contrast representation, ensuring anatomical consistency across modalities.
+
+# 3.2. Conditional Diffusion Model
+
+After pretraining the MIF module to capture shared anatomical features across contrasts, we leverage these pretrained features as conditioning inputs for a conditional diffusion model (CDM) [30] to synthesize multi-contrast MR images, as shown in Fig. 1 (b). The feature vector  $z_{s}^{all}$ , generated from the pretrained MIF module, is integrated into the U-Net architecture through cross-attention layers. Within these layers, the incorporation of  $z_{s}^{all}$  ensures that anatomical consistency is preserved at each diffusion step, guiding the model to synthesize images that are structurally coherent across contrasts. The objective function is defined as:
+
+$$
+\mathcal {L} _ {\text {d i f f u s i o n}} = \mathbb {E} _ {x _ {0}, \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} \left(x _ {t}, t, z _ {s} ^ {\text {a l l}}\right) \| _ {2} ^ {2} \right] \tag {2}
+$$
+
+![](images/72f7317bdc7b3e57898f0fc8169744f8bb89692272481107f1b7a1e83e304188.jpg)  
+Stage 1. Prior-informed Transformation (PiT)  
+Figure 3. Overview of the proposed inference framework. The process includes (1) structurally consistent initialization using prior-informed guidance to generate coarse anatomical structure, and (2) iterative refinement with weighted averaging to enhance fine details in the synthesized images.
+
+where  $x_0$  is the original multi-contrast images that integrate information from all available contrasts,  $x_t$  the noisy image at step  $t$ ,  $\epsilon$  the added noise, and  $\epsilon_{\theta}(x_t, t, z_s^{all})$  the predicted noise. At each step  $t$ , the model receives a noisy image  $x_t$  and progressively denoises it with  $z_s^{all}$ , maintaining anatomical consistency.
+
+# 3.3. Prior Codebook
+
+To facilitate effective multi-contrast MR image synthesis, we construct a prior codebook that captures the relationships between different MR contrasts. The codebook stores three essential components: (1) index mappings for high-similarity image pairs, (2) transformation functions, and (3) intensity scaling weights, as shown in Fig. 2.
+
+To generate diverse variations of multi-contrast images, we employ Bézier curves [27] defined with two endpoints  $(P_0$  and  $P_{3})$  and two control points  $(P_{1}$  and  $P_{2})$ :
+
+$$
+B (r) = \sum_ {i = 0} ^ {n} \binom {n} {i} P _ {i} (1 - r) ^ {n - i} r ^ {i}, \quad n = 3, r \in [ 0, 1 ] \tag {3}
+$$
+
+where  $r$  is a parameter along the curve, with domain and range set within  $[-1, 1]$ . The transformed contrast images are denoted as  $\Phi(B(r), x^c)$ . Through different Bézier curve parameters, diverse variations are generated for each contrast, resulting in transformed images for each of the C contrasts with 4 different parameter settings.
+
+Using the VLM vision encoder, we compute attention maps between all image pairs in the training dataset to identify similar pairs, excluding self-similar and self-transformed images. These mappings are stored in the codebook for efficient retrieval during inference. For each high-similarity pair identified, we compute contrast-specific scaling factors  $\sigma_{\mathrm{tar},\mathrm{tm}}$  by extracting mean values from the images, enabling adjustment of overall intensity levels to match the target contrast characteristics.
+
+# 3.4. Two-Stage Inference Process
+
+The inference process in our framework is designed to synthesize missing MR images through a two-stage approach, as illustrated in Fig. 3.
+
+Stage1: Prior-informed Transformation In the first stage, we leverage the prior codebook to generate suitable guidance images for each missing contrast. Given the available contrast images, we first identify corresponding index mappings from the codebook for the missing modality. These mappings are then used to select appropriate transformation functions, which are applied to the source images. The transformed images are further adjusted using pre-computed intensity scaling factors  $\sigma_{\mathrm{tar,trn}}$  to ensure global intensity consistency. This prior-informed transformation process generates anatomically consistent guidance images that serve as structural references for the missing contrast synthesis.
+
+The reverse diffusion process starts at intermediate step  $M$ , with  $T > T / 2 > M > 0$ , where  $T$  denotes the total number of steps in the forward diffusion process. This enables the model to begin from a more informed point, preserving structural consistency by leveraging prior knowledge. At each step  $t$ , the model iteratively refines the predicted image  $x_0$  using the following process:
+
+$$
+\hat {x} _ {0} ^ {(t)} \leftarrow \hat {x} _ {0} ^ {(t)} - \alpha \cdot \nabla_ {x _ {t}} \| A (\hat {x} _ {0} ^ {(t)}) - y \| _ {2} ^ {2} \tag {4}
+$$
+
+where  $\hat{x}_0^{(t)}$  represents the predicted image at time step  $t$ ,  $\alpha$  is a step-size parameter for gradient descent,  $A(.)$  denotes an operator that extracts only the known contrast regions from  $\hat{x}_0^{(t)}$ , and  $y$  represents the known multi-contrast images. This gradient-driven refinement iteratively improves  $x_0$ , ensuring that the generated image stays consistent with the available contrasts and prior guidance.
+
+Table 1. Quantitative results of the comparison study on BraTS2021 and ADNI datasets. The best PSNR and SSIM values are in bold.  
+
+<table><tr><td rowspan="3"></td><td colspan="8">BraTS</td><td colspan="6">ADNI</td></tr><tr><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td colspan="2">T2-w</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td colspan="2">PD</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>MM-GAN [31]</td><td>23.35</td><td>0.882</td><td>25.13</td><td>0.925</td><td>20.40</td><td>0.869</td><td>24.93</td><td>0.920</td><td>20.40</td><td>0.784</td><td>23.61</td><td>0.820</td><td>24.5</td><td>0.826</td></tr><tr><td>HiNET [43]</td><td>24.36</td><td>0.898</td><td>23.50</td><td>0.923</td><td>23.64</td><td>0.886</td><td>26.10</td><td>0.930</td><td>20.14</td><td>0.793</td><td>23.97</td><td>0.838</td><td>24.44</td><td>0.833</td></tr><tr><td>ResViT [4]</td><td>23.72</td><td>0.871</td><td>24.13</td><td>0.914</td><td>23.71</td><td>0.877</td><td>26.30</td><td>0.928</td><td>19.62</td><td>0.768</td><td>23.95</td><td>0.833</td><td>24.65</td><td>0.827</td></tr><tr><td>ADM [6]</td><td>21.58</td><td>0.833</td><td>22.79</td><td>0.887</td><td>23.83</td><td>0.868</td><td>22.84</td><td>0.855</td><td>16.53</td><td>0.659</td><td>21.37</td><td>0.767</td><td>22.31</td><td>0.795</td></tr><tr><td>SynDiff [28]</td><td>21.98</td><td>0.846</td><td>23.74</td><td>0.924</td><td>24.49</td><td>0.856</td><td>25.17</td><td>0.916</td><td>20.40</td><td>0.794</td><td>22.83</td><td>0.813</td><td>24.75</td><td>0.821</td></tr><tr><td>M2DN [26]</td><td>23.83</td><td>0.870</td><td>24.01</td><td>0.905</td><td>22.65</td><td>0.899</td><td>24.66</td><td>0.901</td><td>19.59</td><td>0.773</td><td>22.99</td><td>0.777</td><td>23.99</td><td>0.801</td></tr><tr><td>Ours</td><td>25.52</td><td>0.920</td><td>25.88</td><td>0.942</td><td>24.54</td><td>0.903</td><td>27.44</td><td>0.951</td><td>20.82</td><td>0.804</td><td>24.56</td><td>0.854</td><td>24.48</td><td>0.849</td></tr></table>
+
+Stage2: Iterative Unrolling In the second stage, we enhance the details of the coarsely generated image from Stage 1 by iteratively unrolling the conditional diffusion process with a weighted averaging technique, aiming to generate a refined image. After completing  $S$  steps of the reverse diffusion process in Stage 1, Stage 2 performs  $N$  unrolling iterations, starting from a step close to zero, to progressively refine the initial output. This iterative process improves both anatomical details and overall image quality by fine-tuning the structure at each iteration.
+
+At each iteration  $n$  within the current diffusion step  $t$ , the predicted image  $\hat{x}_0^{(t,n+1)}$  is updated through weighted averaging. The update is a combination of the previous prediction  $\hat{x}_0^{(t,n)}$  and the current prediction  $\hat{x}_0^{(t,n+1)}$ , expressed as:
+
+$$
+\hat {x} _ {0} ^ {(t, n + 1)} \leftarrow \hat {x} _ {0} ^ {(t, n)} \cdot \left(1 - w _ {n}\right) + \hat {x} _ {0} ^ {(t, n + 1)} \cdot w _ {n} \tag {5}
+$$
+
+where  $w_{n}$  is the weighting factor at iteration  $n$ , controlling the balance between the previous and current predictions. This update mechanism aligns with the reverse diffusion process, allowing for iterative refinement of both the global and finer details of the generated image.
+
+# 4. Experiments and Analysis
+
+# 4.1. Setup
+
+Datasets We evaluate the model on BraTS 2021 [2] and Alzheimer's Disease Neuroimaging Initiative (ADNI) [1] datasets. The BraTS 2021 dataset comprises a total of 2,040 cases of multi-parametric brain tumor MRI scans, including T1-weighted (T1-w), post-contrast T1-weighted (T1Gd (Gadolinium)), T2-weighted (T2-w), and T2 FluidAttenuated Inversion Recovery (FLAIR) volumes. These scans, collected from multiple institutions, reflect variations in imaging protocols and equipments. All images were resized to  $256\times 256$  pixels and processed as 2D slices.  $80\%$  of the data was allocated for training, and the test set includes 200 slices from 50 randomly selected subjects. The ADNI dataset includes 737 MRI scans from both cognitively unimpaired and Alzheimer's Disease (AD) patients. The dataset includes T1-w, T2-w, and Proton Density (PD)
+
+sequences, which were resized to  $256 \times 256$  pixels. For training,  $80\%$  of the data was used, while the test set consists of 150 slices from 30 randomly selected subjects.
+
+Implementation Details The proposed method was implemented with the MIF module trained while maintaining a frozen BiomedCLIP [41] vision encoder. The parameter  $C$  was configured to 4 for the BraTS 2021 dataset and 3 for the ADNI dataset, with a subset of  $C - 1$  randomly selected during each training iteration. The training utilized a batch size of 512 and was conducted for 500 epochs. For MR image synthesis, a UNet-based conditional diffusion model (CDM) [30] was employed. The training was performed for 250k iterations on the BraTS 2021 dataset and 350k iterations on the ADNI dataset, with an Adam optimizer set at a learning rate of  $1 \times 10^{-4}$  and a batch size of 16. The diffusion model employed a cosine noise schedule over 1000 timesteps  $T$ . For Bézier curve transformation, we employed four parameter settings for  $(P_0, P_1, P_2, P_3)$ : two increasing transformations  $(-1, -1, 1, 1)$ ,  $(-1, -0.5, 0.5, 1)$  and two decreasing transformations  $(1, 1, -1, -1)$ ,  $(1, 0.5, -0.5, -1)$ . The parameters  $M$ ,  $S$ ,  $\alpha$ ,  $w_n$  were set to 400, 20, 20, and 0.5 for the BraTS 2021 dataset, and 200, 20, 50, and 0.5 for the ADNI dataset, respectively. In the second stage, the parameter  $N$  was set to 50. All experiments were conducted on an Ubuntu 20.04 operating system, utilizing two NVIDIA RTX A6000 Tensor Core GPUs.
+
+# 4.2. Comparison with State-of-the-art Methods
+
+Quantitative Results We compared our method with six recent state-of-the-art (SOTA) methods for multi-contrast MR image synthesis, including three advanced generative adversarial networks [4, 31, 43] and three diffusion-based approaches [6, 26, 28]. In Table 1, quantitative comparisons for the BraTS 2021 and ADNI datasets are presented using two widely recognized evaluation metrics: Peak Signal-to-Noise Ratio (PSNR) [33] and Structural Similarity Index (SSIM). The results illustrate the performance in synthesizing the missing target contrast image using  $C - 1$  provided source contrast images. We evaluate all possible combina
+
+![](images/e6ae396ee03507723dc7748a4d3ccce4ea70363b8c1e965f2471eebcf1e26b07.jpg)  
+Figure 4. Qualitative results of comparison study on BraTS 2021 dataset. Yellow arrows indicate regions where the methods differ.
+
+![](images/055638492a551e0b84ad539d9a864a20d2e512fe98975933827392d676ccd46c.jpg)  
+Figure 5. Qualitative results of comparison study on ADNI dataset. Yellow arrows indicate regions where the methods differ.
+
+Table 2. Quantitative results of the ablation study on BraTS2021 and ADNI datasets. CDM denotes conditional diffusion models. U denotes unified synthesis model; A denotes synthesis with adaptive prior information; I denotes synthesis unrolled iteratively in stage 2. For start step  $M$ , 400 and 200 correspond to BraTS and ADNI datasets, respectively. The best PSNR and SSIM values are in bold.  
+
+<table><tr><td rowspan="2" colspan="3"></td><td colspan="7">BraTS</td><td colspan="5">ADNI</td></tr><tr><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td>T2-w</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td>PD</td></tr><tr><td>Method</td><td>Start step M</td><td>Sampling steps S</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>CDM (U)</td><td>1000</td><td>50</td><td>25.40</td><td>0.919</td><td>25.18</td><td>0.935</td><td>22.02</td><td>0.889</td><td>26.56</td><td>0.946</td><td>20.11</td><td>0.784</td><td>23.77</td><td>0.830</td></tr><tr><td>CDM (U)</td><td>1000</td><td>20</td><td>25.02</td><td>0.912</td><td>24.80</td><td>0.934</td><td>21.93</td><td>0.891</td><td>26.32</td><td>0.94</td><td>19.59</td><td>0.765</td><td>23.38</td><td>0.819</td></tr><tr><td>CDM (U)</td><td>400 / 200</td><td>20</td><td>24.42</td><td>0.917</td><td>24.12</td><td>0.934</td><td>21.06</td><td>0.885</td><td>24.08</td><td>0.936</td><td>19.42</td><td>0.767</td><td>23.07</td><td>0.819</td></tr><tr><td>CDM (U+A)</td><td>400 / 200</td><td>20</td><td>25.09</td><td>0.915</td><td>25.58</td><td>0.938</td><td>24.81</td><td>0.902</td><td>27.30</td><td>0.947</td><td>20.45</td><td>0.796</td><td>23.71</td><td>0.831</td></tr><tr><td>Ours (U+A+I)</td><td>400 / 200</td><td>20</td><td>25.52</td><td>0.920</td><td>25.88</td><td>0.942</td><td>24.54</td><td>0.903</td><td>27.44</td><td>0.951</td><td>20.82</td><td>0.804</td><td>24.56</td><td>0.854</td></tr></table>
+
+tions, showing that our method generally achieves higher quantitative results compared to other models. The im
+
+provement in evaluation metrics highlights our method's capability to effectively capture intricate details and structural
+
+Table 3. Quantitative results of the ablation study of adaptive selected prior information on BraTS2021 and ADNI datasets. The best PSNR and SSIM values are in bold.  
+
+<table><tr><td rowspan="2"></td><td colspan="7">BraTS</td><td colspan="6">ADNI</td><td></td></tr><tr><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td>T2-w</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td colspan="2">PD</td><td></td></tr><tr><td>Prior Information</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>Zero</td><td>24.20</td><td>0.916</td><td>24.09</td><td>0.934</td><td>20.74</td><td>0.883</td><td>24.34</td><td>0.937</td><td>19.49</td><td>0.770</td><td>23.01</td><td>0.819</td><td>24.12</td><td>0.835</td></tr><tr><td>Gaussian Noise</td><td>24.42</td><td>0.917</td><td>24.12</td><td>0.934</td><td>21.06</td><td>0.885</td><td>24.08</td><td>0.936</td><td>19.42</td><td>0.767</td><td>23.07</td><td>0.819</td><td>24.09</td><td>0.835</td></tr><tr><td>Random Prior Selection</td><td>24.84</td><td>0.915</td><td>25.09</td><td>0.935</td><td>20.89</td><td>0.884</td><td>23.50</td><td>0.929</td><td>19.69</td><td>0.774</td><td>23.58</td><td>0.828</td><td>24.50</td><td>0.837</td></tr><tr><td>Adaptive Prior Selection</td><td>25.09</td><td>0.915</td><td>25.58</td><td>0.938</td><td>24.81</td><td>0.902</td><td>27.30</td><td>0.947</td><td>20.45</td><td>0.796</td><td>23.71</td><td>0.831</td><td>24.46</td><td>0.839</td></tr></table>
+
+Table 4. Quantitative results of the ablation study of stage 2 on BraTS 2021 and ADNI datasets. For start step  $M$ , 40 and 20 correspond to BraTS and ADNI datasets, respectively.  
+
+<table><tr><td rowspan="2" colspan="3"></td><td colspan="7">BraTS</td><td colspan="6">ADNI</td><td></td></tr><tr><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td>T2-w</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td colspan="2">PD</td><td></td></tr><tr><td>Stage</td><td>Start step M</td><td>Total iterations N</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>2</td><td>40/20</td><td>10</td><td>25.31</td><td>0.917</td><td>25.93</td><td>0.942</td><td>24.83</td><td>0.906</td><td>27.44</td><td>0.949</td><td>20.63</td><td>0.800</td><td>24.26</td><td>0.849</td><td>23.96</td><td>0.847</td></tr><tr><td>2</td><td>40/20</td><td>25</td><td>25.35</td><td>0.919</td><td>25.99</td><td>0.943</td><td>24.71</td><td>0.905</td><td>27.52</td><td>0.952</td><td>20.74</td><td>0.803</td><td>24.48</td><td>0.851</td><td>24.27</td><td>0.849</td></tr><tr><td>2</td><td>40/20</td><td>50</td><td>25.52</td><td>0.920</td><td>25.88</td><td>0.942</td><td>24.54</td><td>0.903</td><td>27.44</td><td>0.951</td><td>20.82</td><td>0.804</td><td>24.56</td><td>0.854</td><td>24.48</td><td>0.849</td></tr><tr><td>2</td><td>40/20</td><td>100</td><td>25.61</td><td>0.920</td><td>25.85</td><td>0.942</td><td>23.75</td><td>0.900</td><td>27.60</td><td>0.952</td><td>20.73</td><td>0.804</td><td>24.59</td><td>0.855</td><td>24.38</td><td>0.849</td></tr><tr><td>2</td><td>40/20</td><td>200</td><td>25.53</td><td>0.920</td><td>25.77</td><td>0.940</td><td>23.60</td><td>0.898</td><td>27.53</td><td>0.952</td><td>20.63</td><td>0.803</td><td>24.62</td><td>0.857</td><td>24.25</td><td>0.849</td></tr></table>
+
+information in MR images.
+
+Qualitative Results Figure 4 and Figure 5 show qualitative comparisons of the existing methods, with Figure 4 for the BraTS 2021 dataset and Figure 5 for the ADNI dataset. As shown in Figure 4, our model preserves anatomical details more effectively, particularly in generating tumor areas. In Figure 5, our method also generates finer details, capturing the cortical distortions characteristic of AD and improving the depiction of detailed structures.
+
+# 4.3. Ablation Study
+
+Effect of Start Step  $M$  and Sampling Steps  $S$  in CDM Table 2 illustrates the results of ablation for the start step  $M$  and the number of sampling steps  $S$  in the conditional diffusion model (CDM). Larger values of  $M$  and  $S$  are associated with higher PSNR and SSIM values, indicating improvements in image fidelity and anatomical detail; however, this comes with increased computational cost. In contrast, reducing the sampling steps  $S$  leads to faster inference times, though it causes a reduction in PSNR and SSIM, reflecting a potential decrease in image quality.
+
+Ablation of Model Components Table 2 presents the ablation study on the unified synthesis model (U), adaptive prior information (A), and iterative unrolling (I) to evaluate their contributions to synthesis performance. Adding adaptive prior information  $(\mathrm{U} + \mathrm{A})$  improves PSNR and SSIM across both datasets, suggesting that it enhances anatomical accuracy and realism. Further improvement is observed with iterative unrolling in Stage 2  $(\mathrm{U} + \mathrm{A} + \mathrm{I})$ , which helps capture finer anatomical details and reduce artifacts. These results highlight the complementary benefits of adaptive prior information and iterative unrolling in producing high-quality synthesized images.
+
+![](images/252a5ee3d31aec8dd1ccc365912b061c5b4e20bf8e76aacc8e43433e5252162b.jpg)  
+Z1all
+
+![](images/8712d91bac0ba3ba4ca4bc0f643f5d8aca7192bf5022f8dba9b213df752af912.jpg)  
+Z2 all
+
+![](images/d5fde9d257c51c8e8bbe4c12ee138db3019deec7a374558b736bc2db439fa2c0.jpg)  
+Z3all
+
+![](images/bb2b5c2467a2da0e9a442ee9e7f2644bfdc422934cb54c214caaf2d6b44b7431.jpg)  
+Z4 all
+
+![](images/f519d13a8b035f2d8c56dc5df7af0883d00bc4b39a39ebdd878ccad7a8fae483.jpg)  
+Figure 6. Anatomical alignment analysis using diverse  $z^{\mathrm{all}}$ . The left column shows the four paired contrast images (FLAIR, T1-w, T1Gd, T2-w) used to generate  $z^{\mathrm{all}}$ , followed by synthesized FLAIR from this anatomical feature representation.
+
+![](images/63c22854bfad393b2c7243d90c71b04b92071b320b5ee913d8cdc3d5676b1dd6.jpg)
+
+![](images/59dd737330ad8ba43d7e19860f6261028861538fafff3643c21d90ac9dd382b8.jpg)
+
+![](images/e827fe30d2dcf20f2492ec640d2b591835a3daa5e17c4b199db6127ff11e6914.jpg)
+
+Impact of Adaptive Prior Information Table 3 shows the impact of adaptive prior information on synthesis performance. Different prior selection strategies, including zero prior, Gaussian noise, random prior selection, and adaptive prior selection, are evaluated. The adaptive prior selection generally produces higher PSNR and SSIM values, demonstrating its effectiveness in guiding the synthesis process to generate anatomically realistic images. Notably, for the BraTS dataset, the T1Gd contrast images show a substantial improvement in PSNR, with an increase of approximately 4 dB when using adaptive prior selection rather than random prior selection. This result indicates that incorporating adaptive prior information enhances the model's ability to capture relevant anatomical features across contrasts.
+
+Effect of Iterative Unrolling in Stage 2 Table 4 presents the results of the ablation study on iterative unrolling in Stage 2. Stage 1 is consistently applied across all experi
+
+Table 5. Quantitative results evaluating the effect of different starting steps  $M$  on synthesis performance. The experiments are conducted without Stage 2.  
+
+<table><tr><td rowspan="2"></td><td colspan="8">BraTS</td><td colspan="6">ADNI</td></tr><tr><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td colspan="2">T2-w</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td colspan="2">PD</td></tr><tr><td>Start step M</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>1000</td><td>25.02</td><td>0.912</td><td>24.80</td><td>0.934</td><td>21.93</td><td>0.891</td><td>26.32</td><td>0.94</td><td>19.59</td><td>0.765</td><td>23.38</td><td>0.819</td><td>24.30</td><td>0.836</td></tr><tr><td>500</td><td>25.47</td><td>0.918</td><td>25.32</td><td>0.937</td><td>24.46</td><td>0.901</td><td>27.16</td><td>0.947</td><td>19.84</td><td>0.777</td><td>23.35</td><td>0.823</td><td>24.15</td><td>0.837</td></tr><tr><td>400</td><td>25.09</td><td>0.915</td><td>25.58</td><td>0.938</td><td>24.81</td><td>0.902</td><td>27.30</td><td>0.947</td><td>19.91</td><td>0.780</td><td>23.46</td><td>0.825</td><td>24.35</td><td>0.838</td></tr><tr><td>200</td><td>22.90</td><td>0.879</td><td>25.23</td><td>0.939</td><td>25.12</td><td>0.903</td><td>27.06</td><td>0.947</td><td>20.45</td><td>0.796</td><td>23.71</td><td>0.831</td><td>24.46</td><td>0.839</td></tr><tr><td>100</td><td>19.75</td><td>0.829</td><td>24.55</td><td>0.935</td><td>24.61</td><td>0.899</td><td>25.02</td><td>0.933</td><td>20.40</td><td>0.797</td><td>23.93</td><td>0.839</td><td>24.23</td><td>0.838</td></tr><tr><td>40</td><td>17.97</td><td>0.782</td><td>23.26</td><td>0.921</td><td>21.34</td><td>0.878</td><td>22.83</td><td>0.905</td><td>18.70</td><td>0.769</td><td>22.67</td><td>0.825</td><td>22.07</td><td>0.808</td></tr><tr><td>20</td><td>17.44</td><td>0.761</td><td>22.02</td><td>0.91</td><td>18.70</td><td>0.858</td><td>21.99</td><td>0.889</td><td>17.45</td><td>0.748</td><td>21.25</td><td>0.799</td><td>20.76</td><td>0.750</td></tr></table>
+
+Table 6. Quantitative results for scenarios of random missing modalities on BraTS 2021 dataset.  
+
+<table><tr><td colspan="4">Scenarios</td><td colspan="2">FLAIR</td><td colspan="2">T1-w</td><td colspan="2">T1Gd</td><td colspan="2">T2-w</td></tr><tr><td>FLAIR</td><td>T1-w</td><td>T1Gd</td><td>T2-w</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>-</td><td>-</td><td>23.54</td><td>0.914</td><td>21.20</td><td>0.869</td><td>21.67</td><td>0.904</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>23.54</td><td>0.893</td><td>-</td><td>-</td><td>22.22</td><td>0.883</td><td>25.62</td><td>0.931</td></tr><tr><td></td><td></td><td>✓</td><td></td><td>22.25</td><td>0.869</td><td>24.27</td><td>0.912</td><td>-</td><td>-</td><td>23.24</td><td>0.898</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>23.40</td><td>0.893</td><td>23.93</td><td>0.925</td><td>23.17</td><td>0.889</td><td>-</td><td>-</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>24.26</td><td>0.899</td><td>27.06</td><td>0.948</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>-</td><td>-</td><td>24.74</td><td>0.930</td><td>-</td><td>-</td><td>23.03</td><td>0.924</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>-</td><td>-</td><td>24.50</td><td>0.938</td><td>21.14</td><td>0.886</td><td>-</td><td>-</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>24.08</td><td>0.898</td><td>-</td><td>-</td><td>-</td><td>-</td><td>26.52</td><td>0.939</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>26.40</td><td>0.923</td><td>-</td><td>-</td><td>23.30</td><td>0.896</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>25.26</td><td>0.914</td><td>25.11</td><td>0.935</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></table>
+
+Table 7. Quantitative results for scenarios of random missing modalities on ADNI dataset.  
+
+<table><tr><td colspan="3">Scenarios</td><td colspan="2">T1-w</td><td colspan="2">T2-w</td><td colspan="2">PD</td></tr><tr><td>T1-w</td><td>T2-W</td><td>PD</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>✓</td><td></td><td></td><td>-</td><td>-</td><td>22.56</td><td>0.802</td><td>22.43</td><td>0.799</td></tr><tr><td></td><td>✓</td><td></td><td>20.37</td><td>0.798</td><td>-</td><td>-</td><td>23.98</td><td>0.851</td></tr><tr><td></td><td></td><td>✓</td><td>17.04</td><td>0.663</td><td>22.05</td><td>0.764</td><td>-</td><td>-</td></tr></table>
+
+iments, while Stage 2 explores the impact of varying the number of unrolling iterations  $(N)$ . The results demonstrate that increasing the unrolling iterations in Stage 2 generally improves PSNR and SSIM, indicating that iterative refinement in Stage 2 enhances image quality. A slight performance decrease is observed when  $N = 200$ , indicating that an excessive number of iterations may lead to overfitting or diminishing returns in terms of image quality. This demonstrates that there is an optimal range for the number of iterations to achieve high-quality synthesized images while avoiding potential performance degradation.
+
+Anatomical Alignment Analysis To analyze the effectiveness of anatomical feature alignment, we generate FLAIR image using only  $z^{all}$  conditioning from noise, without any additional guidance or refinement steps as shown in Fig. 6. Each row presents synthesized FLAIR image generated using the corresponding  $z^{all}$ . The distinct results across different  $z^{all}$  features, along with the preserved anatomical characteristics from the input contrast combinations, demonstrate that our mutual information fusion module effectively captures and aligns the anatomical features.
+
+Analysis of Starting Step  $M$  Table 5 demonstrates the impact of different starting steps  $\mathbf{M}$  on synthesis performance. The results show that initializing from intermediate steps yields better performance compared to starting from random noise. The improvement is attributed to the adaptive prior information at intermediate steps. These steps already contain established structural and contextual details, allowing the model to leverage this information effectively. Consequently, images synthesized from optimal starting steps exhibit higher PSNR and SSIM values, resulting in clearer and more consistent image details.
+
+Performance with Random Missing Modalities Table 6 and Table 7 present the quantitative results for scenarios with randomly missing modalities across BraTS and ADNI datasets. For the BraTS dataset, as shown in Table 6, the model maintains consistent performance with PSNR above 23 dB and SSIM above 0.89 in most scenarios, even when multiple input modalities are missing. Similarly, for the ADNI dataset, as shown in Table 7, although performance metrics show some variation depending on which modalities are missing, the model maintains reasonable results. However, when only PD is available as input, the performance metrics show relatively lower values, which can be attributed to the inherently low contrast between gray and white matter in PD-weighted images.
+
+# 5. Conclusion
+
+This paper presents APT, a unified framework for multi-contrast MRI synthesis using conditional diffusion models. Our approach effectively captures anatomical structures using a mutual information fusion module for anatomical consistency. For inference, we propose a two-stage synthesis process that leverages adaptive prior-informed transformation and iterative unrolling with weighted averaging, demonstrating consistent and robust performance across various missing modality scenarios. The results highlight the potential of our method to enhance medical imaging by producing reliable and detailed MR images, contributing to more informed diagnostic and treatment decisions.
+
+Acknowledgements. This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University (RS-2020-II201361), the KIST Institutional Program (2E33801, 2E33800), and Yonsei Signature Research Cluster Program of 2024 (2024-22-0161).
+
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+# Anchor-Aware Similarity Cohesion in Target Frames Enables Predicting Temporal Moment Boundaries in 2D
+
+Jiawei Tan $^{1}$ , Hongxing Wang $^{1,2*}$ , Junwu Weng $^{3}$ , Jiaxin Li $^{1}$ , Zhilong Ou $^{1}$ , Kang Dang $^{4}$
+
+$^{1}$ School of Big Data and Software Engineering, Chongqing University, China
+
+$^{2}$ Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, China
+
+3ByteDance Intelligent Creation
+
+$^{4}$ School of AI and Advanced Computing, XJTLU Entrepreneur College (Taicang), Xi'an Jiaotong-Liverpool University, Suzhou, China
+
+{jwtan, ihxwang}@cqu.edu.cn, we0001wu@e.ntu.edu.sg, jiaxin_li@cqu.edu.cn,
+
+zlou@stu.edu.cn, Kang.Dang@xjtlu.edu.cn
+
+# Abstract
+
+Video moment retrieval aims to locate specific moments from a video according to the query text. This task presents two main challenges: i) aligning the query and video frames at the feature level, and ii) projecting the query-aligned frame features to the start and end boundaries of the matching interval. Previous work commonly involves all frames in feature alignment, easy to cause aligning irrelevant frames with the query. Furthermore, they forcibly map visual features to interval boundaries but ignoring the information gap between them, yielding suboptimal performance. In this study, to reduce distraction from irrelevant frames, we designate an anchor frame as that with the maximum query-frame relevance measured by the established Vision-Language Model. Via similarity comparison between the anchor frame and the others, we produce a semantically compact segment around the anchor frame, which serves as a guide to align features of query and related frames. We observe that such a feature alignment will make similarity cohesive between target frames, which enables us to predict the interval boundaries by a single point detection in the 2D semantic similarity space of frames, thus well bridging the information gap between frame semantics and temporal boundaries. Experimental results across various datasets demonstrate that our approach significantly improves the alignment between queries and video frames while effectively predicting temporal moment boundaries. Especially, on QVHighlights Test and ActivityNet Captions datasets, our proposed approach achieves  $3.8\%$  and  $7.4\%$  respectively higher than current state-of-the-art R1@.7 performance. The code is available at https://github.com/ExMorgan-Alter/AFAFSGD.
+
+# 1. Introduction
+
+Video moment retrieval (VMR) aims to locate the start and end timestamps of the most semantically relevant segments in a video based on natural language queries. It holds a broad spectrum of applications, including video highlight detection [24] and video summarization [12].
+
+Due to the modality gap between video and text, VMR requires aligning the two modalities in the shared feature space. To this end, most existing methods [17, 25, 26] rely on the vision-language model (VLM) to embed query text features into frame features. However, they tend to inject text information into all video frames, easy to suffer from irrelevant frames being aligned with the text. Alleviating irrelevant frames selection is challenging because we do not know which frames are truly relevant to the query text. In this study, we observe that the video frame that is most relevant to the query can commonly stand out from the others by the VLM based query-frame similarity ranking, as illustrated in Fig. 1, which was overlooked by previous VLM related methods [17, 18, 27, 35, 36]. To catch more query-related frames, we anchor the top-ranked relevant frame to select a semantically compact segment where each frame has strong visual-textual similarity with the anchor frame. The semantically compact segment provides a rich semantic guidance, which enables us to have a focused attention for improved query-frame alignment in the feature space. Along this line, we propose the anchor-aware feature alignment  $(\mathrm{A}^2\mathrm{FA})$  scheme (Figs. 3 and 4) to adapt video frame representations to being better aligned with that of the query.
+
+As a video moment is determined by its time interval from its start to end boundaries, query-frame alignment in the feature space does not reach the goal of VMR until the two temporal boundaries can be obtained. Previous methods either rely on frame features to estimate the probability
+
+![](images/3fc255b1325d850d4642eab1e8bc5e635e94e6fdf6d72bee5df50621d885a635.jpg)  
+Query: A group of young people check into their AirBnB and love it.
+
+of candidate intervals being the target interval [9, 33, 40] or directly regress the frame features to interval boundaries [18, 20, 35, 39]. However, they forcibly transform frame features into temporal boundaries, disregarding the inherent information heterogeneity between frame semantics and temporal boundaries, which results in suboptimal retrieval performance. To bridge this gap, we explore the properties of aligned frame features as a stepping stone from feature space to temporal boundary space. Compared with the unaligned frame features, the query-related aligned frame features are highly similar to each other, as exemplified in Fig. 2. The position coordinate of the upper right corner of the block with high similarity values exactly implies the start time and end time of the matching interval. This observation inspires us to design the Frame-Frame Similarity Guided Detection  $(\mathrm{F}^2\mathrm{SGD})$  (Fig. 3), in which we reformulate the interval boundary prediction as a single point detection problem in the 2D similarity space. In this way, the information heterogeneity between features and temporal boundaries is naturally compensated based on the similarity between frames. Notably, our method avoids performing interval boundary detection in the 1D query-frame similarity space, which requires separate start and end boundary detection and additional post-processing. Instead, by operating in a 2D similarity space, where the start and end timestamps are coupled, our approach eliminates the need for post-processing.
+
+In a nutshell, our contributions include:
+
+- We propose A²FA, which links the anchor frame identified by the established VLM with its semantically related frames to enable targeted alignment of query text and related video frames in feature space.  
+- In the field of VMR, we are the first to perform temporal
+
+![](images/c2ab47d6c917cd832933a128c6a28d46968ea807c1f59fac2f1d1560f2279fff.jpg)  
+Figure 1. Query-frame similarity obtained by the popular VLM, CLIP [29]. Not all frames within the ground-truth matching interval exhibit high similarities with the query, but the most relevant one almost always appear in the ground-truth. Besides, matching frames are semantically related to each other, which motivates us to propagate from the most query-related frames, which we denote as anchor, to the rest frames for better modality alignment between query and video frames.  
+(a) Similarity Between Unaligned Frame Feature
+
+![](images/4146395f7d217aae408f90553f40617ddb1e5f9a75dc9722da8057631d5452cd.jpg)  
+Query: Women gives a speech with a mic.  
+(b) Similarity Between Aligned Frame Feature  
+Figure 2. Illustration of how VMR is converted into a single point detection in 2D similarity space. The query-related aligned frame features exhibit high similarity to each other compared to unaligned frame features. For the targeted matching interval  $[t_2, t_4]$  to the query, the start time  $t_2$  and end time  $t_4$  exactly correspond to the 2D coordinate  $(t_2, t_4)$  of the upper right corner of the high-value block in the frame-frame similarity matrix. This observation enables us to narrow the information gap between frame features and temporal boundaries.
+
+boundary detection in a 2D similarity space, rather than in frame feature space, to bridge the information gap between frame features and temporal boundaries.
+
+- We perform comprehensive evaluations on three video moment retrieval datasets: QVHighlights [18], CharadesSTA [8], and ActivityNet Captions [16]. Our proposed method surpasses previous approaches by large margins.
+
+# 2. Related Work
+
+Video moment retrieval aims to identify a semantically consistent video clip for a given query sentence and output the start and end boundaries of that clip. To achieve this, it must not only align text and video modalities but also map the aligned visual representations to the temporal coordinates of the clip. Below, we discuss relevant methods from these two aspects.
+
+Video-Text Modality Alignment seeks to enhance the similarity between the features of query text and related frames. To this end, previous methods [3, 4, 38] embed query text features into relevant frame features. Encouraged by the recent success in adopting vision-language models (VLMs) for video understanding [10, 14], many methods [20, 22, 32, 34] are built on frame-wise features from VLMs. Most of methods [23, 25, 27, 30, 37] employ the cross-attention mechanism [31] to inject the query text features into relevant frame features. However, they make all frames embedded with query text information, resulting in aligning irrelevant frames with the query text. To mitigate the involvement of irrelevant frames, we exploit a fact that has been neglected by previous VLM meth
+
+![](images/dc590f500425b5f489a09f9382782ea351acdc9cf112fc3afd4b22a5b86b953c.jpg)  
+Figure 3. The proposed method for video moment retrieval. It enhances the alignment between the query text and video frames in the feature space by Anchor-Aware Feature Alignment (A²FA, see Fig. 4 for more details), bringing about high similarity between query-related frames. This, in turn, facilitates transforming frame features into precise temporal boundaries by Frame-Frame Similarity Guided Detection (F²SGD).  $\widehat{\mathbb{M}}$  denotes matrix multiplication.
+
+ods [9, 13, 23, 25, 26, 35]: the video frames most relevant to the query can stand out from other video frames through VLM-based query-frame similarity ranking. In this way, we take a semantically compact segment based on the semantic relations between the top-ranked relevant frames and the remaining frames as a semantic guide to align text with video frames at the feature level.
+
+Moment Localization involves projecting the aligned frame features to the start and end timestamps of the matching interval. Enumeration-based [9, 40] and anchor-based methods [21, 22] assess whether a candidate interval matches the query, while regression-based methods [36, 39] directly project features onto the corresponding temporal pairs. However, these methods forcibly map the alignment features to interval coordinates, ignoring the information heterogeneity between visual semantics and coordinate, resulting in suboptimal retrieval performance. In contrast, We bridge the gap from frame features to temporal boundaries by the similarity between frame features. We identify the position coordinates of the upper-right corner of the high-similarity block in the 2D frame similarity space to determine the start and end boundaries of the target interval.
+
+# 3. Method
+
+# 3.1. Problem Formulation
+
+Given an untrimmed video  $\mathcal{V}$  with  $N$  sampled frames and a query sentence  $\mathcal{Q}$ , video segment retrieval aims to learn a detector  $\mathcal{D}$  to identify the start  $s$  and end boundaries  $e$  of the segment consisting of frames relevant to the query. Since the query-related frames do not stand out from the entire video without the help of the query, a mechanism  $\mathcal{F}$  is need to inject query information into the query-related frames, with more discriminative aligned frame features  $\mathbf{V}^{\mathrm{a}}$ . This enable  $\mathcal{D}$  to act on  $\mathbf{V}^{\mathrm{a}}$  for better boundary detection. In this study, as illustrated in Fig. 3, we propose Anchor-Aware
+
+Feature Alignment (A²FA) for  $\mathcal{F}$  and Frame-Frame Similarity Guided Detection (F²SGD) for  $\mathcal{D}$ .
+
+# 3.2. Anchor-Aware Feature Alignment
+
+To represent video  $\mathcal{V}$  and query  $\mathcal{Q}$  of different modalities, we follow the widely practice of using frozen pre-trained CLIP [29] encoding for both. By CLIP encoding, we obtain  $N$  frame  $d$ -dimension features  $\pmb{V} = [\pmb{v}_1,\pmb{v}_2,\dots,\pmb{v}_N]\in$ $\mathbb{R}^{N\times d}$  for the video and a sentence-level query feature  $\pmb{q}\in \mathbb{R}^d$  for the query sentence.
+
+Given the heterogeneity between visual and textual modalities, it is essential to align the query sentence with the matching video frames at the feature level. The key to alignment is to maximize the similarity between the matching frame and the query sentence. To this end, we propose the anchor-aware feature alignment (A²FA), which takes an anchor-aware segment from the video to guide modality alignment in video moment retrieval.
+
+Generating Anchor-Aware Mask. We design an anchor-aware mask to focus on potential matching frames. Since the matched frames should be semantically similar to each other in both visual and textual levels, we embed the query feature  $\mathbf{q}$  into the frame features  $\mathbf{V}$ , based on the following query-frame similarity weighting, yielding query-embedded visual features  $V^{\mathrm{e}} = [\pmb{v}_1^{\mathrm{e}},\pmb{v}_2^{\mathrm{e}},\dots,\pmb{v}_N^{\mathrm{e}}]\in \mathbb{R}^{N\times d}$ :
+
+$$
+\boldsymbol {v} _ {i} ^ {\mathrm {e}} = \cos (\boldsymbol {q}, \boldsymbol {v} _ {i}) \boldsymbol {q} + (1 - \cos (\boldsymbol {q}, \boldsymbol {v} _ {i})) \boldsymbol {v} _ {i}, \tag {1}
+$$
+
+where  $\cos (\pmb {q},\pmb {v}_i)$  denotes the cosine similarity between its input features.
+
+We then rely on  $V^{\mathrm{e}}$  to generate the anchor-aware mask. At first, we identify the anchor frame most similar to the query, which is indexed by:
+
+$$
+\mathcal {A} = \underset {i \in [ 1, N ]} {\arg \max } (\cos \left(\boldsymbol {v} _ {i} ^ {\mathrm {e}}, \boldsymbol {q}\right)). \tag {2}
+$$
+
+![](images/0f0e4c2f442e56afb3a86d7df764103344a2c99dca2df8348f61fed4888d9a3b.jpg)  
+Figure 4. Details of re-weighting and aligning stages in the proposed  $\mathrm{A}^2\mathrm{FA}$ . We re-weight frame features by comparing the query-aggregated visual feature. After re-weighting, frame features become more aligned with the query feature based on frame-text scores.
+
+Intuitively, frames that are semantically related to the anchor frame are likely to match the query. To this end, we apply dynamic time warping (DTW) to detect a semantic transition point in each of the intervals  $[1, \mathcal{A}]$  and  $[\mathcal{A}, N]$ , by which the semantic connection on both sides of the semantic transition point can be maximized [28]. We denote  $b^{\mathrm{L}}$  and  $b^{\mathrm{R}}$  the two semantic transition points, which can be obtained by
+
+$$
+b ^ {\mathrm {L}} = \underset {b = 1, \dots , \mathcal {A}} {\arg \max } \left(\sum_ {i = 2} ^ {b} \cos \left(\boldsymbol {v} _ {1} ^ {\mathrm {e}}, \boldsymbol {v} _ {i} ^ {\mathrm {e}}\right) + \sum_ {j = b + 1} ^ {\mathcal {A}} \cos \left(\boldsymbol {v} _ {\mathcal {A}} ^ {\mathrm {e}}, \boldsymbol {v} _ {j} ^ {\mathrm {e}}\right)\right), \tag {3}
+$$
+
+$$
+b ^ {\mathrm {R}} = \underset {b = \mathcal {A}, \dots , N} {\arg \max } \left(\sum_ {i = \mathcal {A}} ^ {b} \cos \left(\boldsymbol {v} _ {\mathcal {A}} ^ {\mathrm {e}}, \boldsymbol {v} _ {i} ^ {\mathrm {e}}\right) + \sum_ {j = b + 1} ^ {N} \cos \left(\boldsymbol {v} _ {N} ^ {\mathrm {e}}, \boldsymbol {v} _ {j} ^ {\mathrm {e}}\right)\right). \tag {4}
+$$
+
+As a result, we have a semantically related interval to the anchor frame  $\pmb{v}_{\mathcal{A}}^{\mathrm{e}}$
+
+$$
+[ b ^ {\mathrm {L}}, b ^ {\mathrm {R}} ] = [ b ^ {\mathrm {L}}, \mathcal {A} ] \cup [ \mathcal {A}, b ^ {\mathrm {R}} ], \tag {5}
+$$
+
+which provides a coarse estimate on candidate matching to the query and cannot be used directly as a prediction result.
+
+Based on  $[b^{\mathrm{L}}, b^{\mathrm{R}}]$ , we define the anchor-aware mask  $\pmb{m} = [m_1, m_2, \dots, m_N] \in \mathbb{R}^N$  in the following, which will mask frames semantically unrelated to the anchor frame but keeping those semantically related frames unmasked during query-frame feature alignment.
+
+$$
+m _ {i} = \left\{ \begin{array}{c c} 0, & i \in [ b ^ {\mathrm {L}}, b ^ {\mathrm {R}} ], \\ - \infty , & i \notin [ b ^ {\mathrm {L}}, b ^ {\mathrm {R}} ]. \end{array} \right. \tag {6}
+$$
+
+Re-weighting Frame Features. It is evident that some frames in  $[b^{\mathrm{L}}, b^{\mathrm{R}}]$  may be irrelevant to the query. To address this issue, as shown in Fig. 4, we re-weight the frame-level features by comparing the query-aggregated visual features with each frame. To be specific, we employ the
+
+cross-attention mechanism to map the sentence feature  $\mathbf{q}$  as the attention query to guide the aggregation of frame features  $\mathbf{V}$ , which are mapped as the attention key and value. This process fuses the frame features related to the query to form query-aggregated visual feature  $\mathbf{g} \in \mathbb{R}^d$ :
+
+$$
+\boldsymbol {A} ^ {\mathrm {g}} = \operatorname {s o f t m a x} \left(\boldsymbol {Q} ^ {\mathrm {g}} \boldsymbol {q} \left(\boldsymbol {K} ^ {\mathrm {g}} \boldsymbol {V}\right) ^ {\mathrm {T}} + \boldsymbol {m}\right), \tag {7}
+$$
+
+$$
+\boldsymbol {g} = \boldsymbol {A} ^ {\mathrm {g}} \left(\boldsymbol {V} ^ {\mathrm {g}} \boldsymbol {V}\right) ^ {\mathrm {T}}, \tag {8}
+$$
+
+where  $Q^{\mathrm{g}}, K^{\mathrm{g}}$ , and  $V^{\mathrm{g}}$  are learnable matrices.
+
+We further compare  $\pmb{g}$  with each visual representation to assign high scores to frames that are relevant to the query, resulting in query relevance scores  $\boldsymbol{r} = [r_1,r_2,\dots,r_N]\in$ $\mathbb{R}^N$  ..
+
+$$
+r _ {i} = \tanh  \left(w \left(\boldsymbol {W} _ {1} ^ {\mathrm {r}} \boldsymbol {v} _ {i} \left(\boldsymbol {W} _ {2} ^ {\mathrm {r}} \boldsymbol {g}\right) ^ {\mathrm {T}}\right) + \beta\right), \tag {9}
+$$
+
+where  $\pmb{W}_1^{\mathrm{r}}$  and  $\pmb{W}_2^{\mathrm{r}}$  are learnable matrices,  $w$  and  $\beta$  are learnable scales, and tanh is the hyperbolic tangent activation function. The re-weighted frame features  $\pmb{V}^{\mathrm{r}} = [\pmb{v}_1^{\mathrm{r}},\pmb{v}_2^{\mathrm{r}},\dots,\pmb{v}_N^{\mathrm{r}}]\in \mathbb{R}^{N\times d}$  are then computed as:
+
+$$
+\boldsymbol {v} _ {i} ^ {\mathrm {r}} = r _ {i} \boldsymbol {v} _ {i}. \tag {10}
+$$
+
+Aligning Query and Frame Representations. Once having  $V^{\mathrm{r}}$ , we proceed to align it with the query feature  $q$ . As shown in Fig. 4, we assess relations between the reweighted frame features and the query text as:
+
+$$
+\boldsymbol {\alpha} = \operatorname {s i g m o i d} \left(\boldsymbol {W} _ {1} ^ {\mathrm {a}} \boldsymbol {V} ^ {\mathrm {r}} \left(\boldsymbol {W} _ {2} ^ {\mathrm {a}} \boldsymbol {q}\right) ^ {\mathrm {T}} + \boldsymbol {m}\right), \tag {11}
+$$
+
+where  $\alpha = [\alpha_{1},\alpha_{2},\dots,\alpha_{N}]\in \mathbb{R}^{N}$  indicates frame-text matching scores,  $W_{1}^{\mathrm{a}}$  and  $W_{2}^{\mathrm{a}}$  are learnable matrices.
+
+After that, we embed query information into frame-level features to obtain aligned frame features  $V^{\mathrm{a}} = \left[\pmb{v}_1^{\mathrm{a}},\pmb{v}_2^{\mathrm{a}},\dots,\pmb{v}_N^{\mathrm{a}}\right]\in \mathbb{R}^{N\times d}$  based on  $\alpha$  as follows:
+
+$$
+\boldsymbol {v} _ {i} ^ {\mathrm {a}} = \alpha_ {i} \boldsymbol {q} + (1 - \alpha_ {i}) \boldsymbol {v} _ {i} ^ {\mathrm {r}}. \tag {12}
+$$
+
+The closer  $\alpha_{i}$  is to 1, the closer the aligned visual features of the  $i$ -th frame are to the query feature  $\pmb{q}$ , so that the similarity between the aligned visual features of the  $i$ -th frame and the query features is maximized.
+
+# 3.3. Frame-Frame Similarity Guided Detection
+
+Although the relevant frames are enriched with query text information and become more discriminative in the video frame feature sequence, there is an information gap between these frame features and the start and end coordinates of the interval required by VMR. In order to smoothly convert from frame features to temporal boundaries, we propose a novel detector, frame-frame similarity guided detection  $(\mathrm{F}^2\mathrm{SGD})$ , by leveraging the properties of aligned frame features. Concretely, aligned frame features naturally boost the similarity between frames within the matching interval while weakening the similarity between matching and non-matching frames. As has been shown in Fig. 2, the frames within the matching interval are represented as high-value blocks in the inter-frame similarity matrix. Coincidentally, the top-right corner of the high-value square blocks corresponds to the start and end timestamps of the matching interval.
+
+Formally, as shown in Fig. 3, given the aligned frame similarity matrix  $S^{\mathrm{a}}$ , with the entry  $S_{ij}$  being the cosine similarity between  $v_{i}^{\mathrm{a}}$  and  $v_{j}^{\mathrm{a}}$ , we aim to detect the top-right vertex of high-value square blocks. To accomplish this, we apply a CNN-based network on  $S^{\mathrm{a}}$ , followed by a multilayer perceptron (MLP) to estimate the probability of each position in  $S^{\mathrm{a}}$  being the top-right vertex of a high-value square, having a vertex score matrix  $P \in \mathbb{R}^{N \times N}$ :
+
+$$
+\boldsymbol {P} = \operatorname {M L P} \left(\operatorname {C N N s} \left(\boldsymbol {S} ^ {\mathrm {a}}\right)\right), \tag {13}
+$$
+
+where  $\mathrm{CNNs}(\cdot)$  consists of two layer convolutional layers with kernel size of  $C$ , and  $\mathrm{MLP}(\cdot)$  is a MLP classifier.
+
+# 3.4. Training and Inference
+
+For the training, we use the mean squared error (MSE) loss to penalize the squared element-wise differences between the predicted vertex score matrix and the ground truth, as defined below:
+
+$$
+L = \left\| \boldsymbol {P} - \boldsymbol {G} \right\| _ {2} ^ {2}, \tag {14}
+$$
+
+where  $G$  is the ground truth matrix,  $G(t^{\mathrm{s}},t^{\mathrm{e}})$  is set to 1 for the ground truth start and end timestamps  $(t^{\mathrm{s}},t^{\mathrm{e}})$ , with all other elements being 0.
+
+During inference, we select the indices of the top- $k$  values in  $\pmb{P}$  as the predicted interval boundaries  $\{(\widehat{s}_i,\widehat{e}_i)\}_{i = 1}^k$ :
+
+$$
+\left\{\left(\widehat {s} _ {1}, \widehat {e} _ {1}\right), \dots , \left(\widehat {s} _ {k}, \widehat {e} _ {k}\right) \right\} = \underset {1 \leq i \leq j \leq N} {\arg \operatorname {t o p} k} P _ {i, j}, \tag {15}
+$$
+
+where  $k$  is the number of candidate intervals. When retrieving multiple video segments,  $k > 1$ ; otherwise,  $k = 1$ .
+
+# 4. Experiments
+
+# 4.1. Settings
+
+Datasets: We evaluate our method on three large-scale Video Moment Retrieval (VMR) benchmark datasets:
+
+QVHighlights [18] contains 10,148 videos, each approximately 150 seconds long. Every video is annotated with at least one query, with an average query length of 11.3 words. The target moment for each query has an average duration of 24.6 seconds. The dataset has 7,218 queries for training, 1,150 queries for validation (val for short), and 1,542 queries for test. The test set is kept on Codalab to ensure fair comparison. Following [18, 25, 27], we use the training split for training, both the val and test splits for testing, and the val split for ablation. ActivityNet Captions [16] comprises 20,000 videos, each averaging 2 minutes in duration, with 72,000 query-segment pairs. Each query contains an average of 13.5 words. The dataset is divided into training (37,421 pairs), val-1 (17,505 pairs), and val-2 (17,031 pairs) subsets. Following prior works [1, 35], we use the training set for training, val-1 for validation, and val-2 for testing.
+
+Charades-STA [8] consists of 9,848 indoor videos, each averaging 30.6 seconds in length. It includes 16,128 query-moment pairs, split into a training set with 12,408 pairs and a test set with 3,720 pairs.
+
+Metrics: The most commonly used metrics for VMR are R1@ $\tau$  and mAP@ $\tau$ . R1@ $\tau$  measures the percentage of top-1 retrieved moments that have an Intersection over Union (IoU) greater than  $\tau$ . We report R1@ $\tau$  results with  $\tau$  values of 0.5 and 0.7. mAP@ $\tau$  calculates the average precision (AP) at a specific  $\tau$  value thresholding IoU, and mAP@Avg returns the mean average precision (mAP) across multiple  $\tau$  values. We let  $\tau = 0.75$  for mAP@ $\tau$ , and  $\tau$  range from 0.5 to 0.95 in increments of 0.05 for mAP@Avg.
+
+Implementation details: The frequency of our sampling frames is consistent with previous methods [17, 18, 26]. For the QVHighlights and ActivityNet Captions datasets, we extract one frame every two seconds. For Charades-STA, due to the shorter duration of videos, we extract one frame per second. Frame features are encoded using the CLIP visual extractor (ViT-B/32), while sentence features are obtained using CLIP text extractor. The convolution size  $C$  in Eq. (13) is 21 for the QVHighlights dataset and 27 for the Charades-STA and ActivityNet Captions datasets. Following the previous methods [18, 25, 26], the number of candidate intervals  $k$  in the QVHighlights dataset is 10, and in other datasets it is 1. Model weights are initialized by Xavier [7]. We use Adam optimizer [15] with a batch size of 128. During the total 10 training epochs, we apply a linear warm-up strategy to gradually increase the learning rate to 0.0001 in the initial stage, and then decay the learning rate according to a cosine schedule in the remaining stages. We train our model on an NVIDIA RTX 3060 GPU.
+
+# 4.2. Comparison with State-of-the-Art Methods
+
+Results on QVHighlights [18]. As can be seen from Table 1, on QVHighlights, our method significantly outper
+
+<table><tr><td rowspan="3">Method</td><td rowspan="3">Backbone</td><td colspan="4">Val</td><td colspan="4">Test</td></tr><tr><td colspan="2">R1</td><td colspan="2">mAP</td><td colspan="2">R1</td><td colspan="2">mAP</td></tr><tr><td>@.5</td><td>@.7</td><td>@.75</td><td>avg</td><td>@.5</td><td>@.7</td><td>@.75</td><td>Avg</td></tr><tr><td>Moment DETR [18] (NIPS&#x27;21)</td><td>CLIP</td><td>53.5</td><td>34.1</td><td>30.8</td><td>32.4</td><td>55.8</td><td>33.8</td><td>31.2</td><td>32.7</td></tr><tr><td>QD-DETR [27] (CVPR&#x27;23)</td><td>CLIP</td><td>59.7</td><td>42.3</td><td>37.5</td><td>37.5</td><td>60.8</td><td>41.8</td><td>37.1</td><td>38.3</td></tr><tr><td>EaTR [11] (ICCV&#x27;23)</td><td>CLIP</td><td>54.9</td><td>36.0</td><td>33.5</td><td>34.1</td><td>54.6</td><td>34.0</td><td>32.6</td><td>33.2</td></tr><tr><td>TR-DETR [30] (AAAI&#x27;24)</td><td>CLIP</td><td>63.6</td><td>43.9</td><td>39.7</td><td>39.6</td><td>60.2</td><td>41.4</td><td>37.0</td><td>37.2</td></tr><tr><td>UVCOM [34] (CVPR&#x27;24)</td><td>CLIP</td><td>64.8</td><td>48.0</td><td>42.7</td><td>42.3</td><td>62.7</td><td>46.9</td><td>42.6</td><td>42.1</td></tr><tr><td>CG-DETR [26] (CoRR&#x27;23)</td><td>CLIP</td><td>66.6</td><td>49.9</td><td>44.2</td><td>43.9</td><td>64.5</td><td>46.0</td><td>41.6</td><td>41.8</td></tr><tr><td>QD-VMR [6] (CoRR&#x27;24)</td><td>CLIP</td><td>67.7</td><td>52.3</td><td>48.1</td><td>46.2</td><td>66.7</td><td>48.6</td><td>42.8</td><td>43.1</td></tr><tr><td>BAM-DETR [17] (ECCV&#x27;24)</td><td>CLIP+SF</td><td>65.1</td><td>51.6</td><td>48.6</td><td>47.6</td><td>62.7</td><td>48.6</td><td>46.3</td><td>45.4</td></tr><tr><td>\( R^2 \)-Tuning [25] (ECCV&#x27;24)</td><td>CLIP</td><td>67.7</td><td>51.9</td><td>-</td><td>47.9</td><td>68.7</td><td>52.1</td><td>-</td><td>47.6</td></tr><tr><td>Mr. BLIP [1] (CoRR&#x27;24)</td><td>BLIP-2</td><td>76.1</td><td>63.4</td><td>55.8</td><td>-</td><td>74.8</td><td>60.5</td><td>53.4</td><td>-</td></tr><tr><td>Ours</td><td>CLIP</td><td>79.4</td><td>64.8</td><td>64.1</td><td>63.0</td><td>80.8</td><td>64.3</td><td>64.3</td><td>63.4</td></tr></table>
+
+forms all other state-of-the-art (SOTA) methods across all metrics. Notably, among those utilizing CLIP backbone encoder, ours performs better than the SOTA method [25] by  $12.1\%$  on R1@.5,  $12.2\%$  on R1@.7, and  $15.8\%$  on mAP@Avg on the test split. The excellent performance results from improved alignment between query text features and video frame features, as well as bridging the information gap between frame features and temporal boundary. Notably, our method surpasses CG-DETR [26], which also aims to avoid query-irrelevant frames from participating in modality alignment, underscoring the superiority of our feature alignment  $\mathrm{A}^2\mathrm{FA}$ . Even when compared with Mr. BLIP [1] that leverages a more advanced backbone encoder, our method shows a  $6.0\%$  improvement in R1@0.5, a  $3.8\%$  increase in R1@0.7, and a  $10.9\%$  gain in mAP@0.75 on the test split. This further highlights the superiority of our proposed method.
+
+Results on ActivityNet Captions. Table 2 shows that our method suppresses all reported SOTA results on the ActivityNet Captions dataset, demonstrating its effectiveness. Compared with Mr. BLIP [1] using a better backbone, our model still achieves substantial improvements across all metrics. The findings on this dataset are consistent with the conclusions drawn from the QVHighlights results.
+
+Results on Charades-STA. In Table 3, we can see that our method beats other SOTAs on Charades-STA. However, the performance improvement is less significant compared to QVHighlights and ActivityNet Captions. This may be due to the shorter video lengths in Charades-STA videos, making it more challenging to differentiate and accurately localize the target intervals. Despite this, our model still achieves competitive results, highlighting its versatility across different VMR data environments.
+
+Table 1. Comparison between our results and the previous reported on QVHighlights val and test splits. CLIP or BLIP-2 denotes CLIP [29] or BLIP-2 [19] is applied as visual and text encoders. SF denotes motion feature extractor SlowFast [5]. The best are indicated in Bold. “-” denotes that result does not get published.  
+
+<table><tr><td>Method</td><td>Backbone</td><td>R1@.5</td><td>R1@.7</td></tr><tr><td>Moment DETR [18] (NIPS&#x27;21)</td><td>CLIP</td><td>36.1</td><td>20.4</td></tr><tr><td>QD-DETR [27] (CVPR&#x27;23)</td><td>CLIP</td><td>36.9</td><td>21.4</td></tr><tr><td>UVCOM [34] (CVPR&#x27;24)</td><td>CLIP</td><td>37.0</td><td>21.5</td></tr><tr><td>CG-DETR [26] (CoRR&#x27;23)</td><td>CLIP</td><td>38.8</td><td>22.6</td></tr><tr><td>UnLoc-L [35] (ICCV&#x27;23)</td><td>CLIP</td><td>48.3</td><td>30.2</td></tr><tr><td>Mr. BLIP [1] (CoRR&#x27;24)</td><td>BLIP-2</td><td>53.9</td><td>35.6</td></tr><tr><td>Ours</td><td>CLIP</td><td>71.1</td><td>43.0</td></tr></table>
+
+Table 2. Comparison between our results and the previous reported on ActivityNet Captions. CLIP or BLIP-2 denotes CLIP [29] or BLIP-2 [19] is applied as visual and text encoders.  
+
+<table><tr><td>Method</td><td>Backbone</td><td>R1@.5</td><td>R1@.7</td></tr><tr><td>Moment DETR [18] (NIPS&#x27;21)</td><td>SF+CLIP</td><td>52.1</td><td>30.6</td></tr><tr><td>QD-DETR [27] (CVPR&#x27;23)</td><td>SF+CLIP</td><td>57.3</td><td>32.6</td></tr><tr><td>UVCOM [34] (CVPR&#x27;24)</td><td>SF+CLIP</td><td>59.3</td><td>36.6</td></tr><tr><td>CG-DETR [26] (CoRR&#x27;23)</td><td>SF+CLIP</td><td>58.4</td><td>36.3</td></tr><tr><td>BAM-DETR [17] (ECCV&#x27;24)</td><td>SF+CLIP</td><td>59.9</td><td>39.4</td></tr><tr><td>R2-Tuning [25] (ECCV&#x27;24)</td><td>CLIP</td><td>59.8</td><td>37.0</td></tr><tr><td>UnLoc-L [35] (ICCV&#x27;23)</td><td>CLIP</td><td>60.8</td><td>38.4</td></tr><tr><td>UniMD+Sync. [39] (ECCV&#x27;24)</td><td>I3D+CLIP</td><td>63.9</td><td>44.5</td></tr><tr><td>Mr. BLIP [1] (CoRR&#x27;24)</td><td>BLIP-2</td><td>69.3</td><td>49.2</td></tr><tr><td>Ours</td><td>CLIP</td><td>83.8</td><td>50.1</td></tr></table>
+
+Table 3. Comparison between our results and the previous reported on the Charades-STA test split. CLIP or BLIP-2 denotes CLIP [29] or BLIP-2 [19] is applied as visual and text encoders. SF and I3D denotes motion feature extractor SlowFast [5] and I3D network [2].
+
+# 4.3. Ablation Studies
+
+We conduct ablation studies on the QVHighlights val dataset to evaluate the effectiveness of our proposed method for video moment retrieval. Experiments use the more challenging R1@.7 and mAP@Avg metrics. We also include
+
+![](images/990bb70bae4b5f6628ca4554c1bdba2a07fa095c89895c2b3ee5aeef8e453d04.jpg)  
+(a) Before Alignment
+
+![](images/633a8fde414f9750b2d3cdc88887003459bd205a04174f93361f3b3afda99194.jpg)  
+(b) After Alignment by CG-DETR
+
+![](images/044891f07f36b6b3a4948ba88a438ea7153c9c1a01b36c9c8c6e4b888c86a0ad.jpg)  
+(c) After Alignment by Ours
+
+more results, such as model parameter comparisons and visualizations, in the supplementary.
+
+Effectiveness of our proposed  $\mathrm{A}^2\mathrm{FA}$  in making similarity cohesive. Fig. 5 illustrates the similarity distribution between the query and the matching or non-matching intervals before and after alignment. To better compare the results after alignment, we show the similarity distribution of CG-DETR [26], a SOTA method dedicated to removing irrelevant frame alignment. It is clear that the two distributions still overlap after CG-DETR alignment, while our method makes the two distributions clearly separated. It demonstrates that our  $\mathrm{A}^2\mathrm{FA}$  effectively distinguishes matching intervals from non-matching ones in the frame feature space.
+
+Advantages of using 2D similarity space to detect temporal boundaries. Fig. 6 compares our proposed  $\mathrm{F}^2\mathrm{SGD}$  method based on 2D similarity space with some representative detectors that forcibly map frame features to temporal boundaries. In specific, TAN [40] estimates the probability that an enumerated interval matches the query, while DETR-like methods [18] use transformers to predict the center and length of the matching interval. BR [20] employs convolutional networks to regress the start and end boundaries. Our proposed  $\mathrm{F}^2\mathrm{SGD}$  outperforms these competitors, demonstrating the advantages of temporal boundary detection in the 2D similarity space.
+
+Impacts of anchor-aware masks  $(\mathbf{A}^2\mathbf{M})$  generated by different VLMs. Table 4 compares the performance of different VLMs, including CLIP [29] and BLIP-2 [19], used as encoders and in  $\mathrm{A}^2\mathrm{M}$  generation defined in Eq. (6). Obviously, the more advanced VLMs like BLIP-2 are used to generate  $\mathrm{A}^2\mathrm{M}$ , the better our method performs, indicating that the method of generating  $\mathrm{A}^2\mathrm{M}$  is compatible with different VLMs. Furthermore, the choice of VLM for  $\mathrm{A}^2\mathrm{M}$  generation has a greater impact on method performance than the choice of VLM as the encoder.
+
+Necessity of refining the interval from Eq. (5). Table 5 presents the predication ability of  $[b^{\mathrm{L}}, b^{\mathrm{R}}]$  coarsely estimated by Eq. (5) in comparison with our finally refined result by Eq. (15). While  $[b^{\mathrm{L}}, b^{\mathrm{R}}]$  alone cannot accurately
+
+![](images/89d75018d80cd6c67897a59c32dfb9668abfc98fdf64a09661f22fe2e8a2a634.jpg)  
+Figure 5. Cosine similarity distribution between query and matching intervals or non-matching intervals on the QVHighlights val split, including (a) before alignment, (b) alignment by CG-DETR [26], and (c) alignment by our  $\mathrm{A}^2\mathrm{FA}$ .  
+Figure 6. Comparison of our  $\mathrm{F}^2\mathrm{SGD}$  with other detectors that forcibly convert frame features to coordinates, including TAN [40], DETR [18], boundary regression (BR) [20].
+
+<table><tr><td>Backbone</td><td>A2M</td><td>R1@.7</td><td>mAP@Avg</td></tr><tr><td rowspan="2">CLIP</td><td>CLIP</td><td>64.8</td><td>63.0</td></tr><tr><td>BLIP-2</td><td>66.0</td><td>65.1</td></tr><tr><td rowspan="2">BLIP-2</td><td>CLIP</td><td>64.8</td><td>63.1</td></tr><tr><td>BLIP-2</td><td>66.1</td><td>65.6</td></tr></table>
+
+Table 4. Performance of anchor-aware masks (A²M) generated by different VLMs.  
+
+<table><tr><td>Method</td><td>R1@.7</td><td>mAP@Avg</td></tr><tr><td>Intermediate results by Eq. (5)</td><td>23.8</td><td>31.4</td></tr><tr><td>Final results by Eq. (15)</td><td>64.8</td><td>63.0</td></tr></table>
+
+Table 5. Comparison of the intermediate result of Eq. (5) and the final result of Eq. (15).
+
+match the target interval, its integration as masks into our method significantly improves the performance, highlighting the necessity of our method in subsequent refinement.
+
+Component ablation. Table 6 presents the results of evaluating the contribution of each component in our method to overall performance. The first row shows the baseline results using only frame-query similarity for moment retrieval. After introducing the proposed  $\mathrm{F}^2\mathrm{SGD}$  module,
+
+![](images/533dc3b96832a1f2a9181595b11ff849c379b3702c180fb41fc55e41d3ba3a2c.jpg)  
+Figure 7. Visualized comparisons of the proposed method with the SOTA methods TaskWeave [36] and UVCOM [34]. GT denotes ground-truth matching intervals for reference.
+
+<table><tr><td colspan="2">A2FA</td><td rowspan="2">F2SGD</td><td rowspan="2">R1@.7</td><td rowspan="2">mAP@Avg</td></tr><tr><td>Reweight</td><td>Align</td></tr><tr><td>-</td><td>-</td><td>-</td><td>5.2</td><td>7.7</td></tr><tr><td>-</td><td>-</td><td>✓</td><td>39.6</td><td>43.3</td></tr><tr><td>-</td><td>✓</td><td>✓</td><td>57.6</td><td>56.4</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>64.8</td><td>63.0</td></tr></table>
+
+Table 6. Ablation study on our proposed method in different inclusions of  $\mathrm{A}^2\mathrm{FA}$  in Sec. 3.2 and  $\mathrm{F}^2\mathrm{SGD}$  in Sec. 3.3.  $\checkmark$  signifies "included", while - "excluded".  
+
+<table><tr><td>Method</td><td>Alignment</td><td>R1@.7</td><td>mAP@Avg</td></tr><tr><td rowspan="2">MRNet-S [9]</td><td>Original</td><td>46.6</td><td>41.6</td></tr><tr><td>A2FA</td><td>47.7</td><td>46.8</td></tr><tr><td rowspan="2">Moment-DETR [18]</td><td>Original</td><td>34.1</td><td>32.4</td></tr><tr><td>A2FA</td><td>49.1</td><td>48.1</td></tr><tr><td rowspan="2">UniVTG [20]</td><td>Original</td><td>40.9</td><td>35.5</td></tr><tr><td>A2FA</td><td>55.8</td><td>55.4</td></tr></table>
+
+R1@0.7 and mAP@Avg increase to  $34.4\%$  and  $35.7\%$ , respectively, highlighting the importance of detecting temporal boundaries in the 2D similarity space. The improvement in metrics by adding the 'Align' module further underscores the benefit of considering the relationships between query-relevant and irrelevant frames. The 'Reweight' module is added to achieve optimal performance.
+
+Pluggability of  $\mathbf{A}^2\mathbf{FA}$ . Table 7 reports the performance of competitors and our proposed  $\mathrm{A}^2\mathrm{FA}$  mentioned in Sec. 3.2 followed with different detectors, including TAN [40], DETR [18], and Regression [20]. Across all combinations,  $\mathrm{A}^2\mathrm{FA}$  outperforms competing methods, demonstrating its superiority and plug-and-play compatibility.
+
+Pluggability of  $\mathbf{F}^2\mathbf{SGD}$ . Table 8 shows the performance of our proposed  $\mathrm{F}^2\mathrm{SGD}$  when combined with different alignment methods. Results indicate that  $\mathrm{F}^2\mathrm{SGD}$  consistently improves over the original alternatives, emphasizing its generality to any aligning methods and advantage across different alignment techniques.
+
+Convolution kernel size in  $\mathbf{F}^2\mathbf{SGD}$ . Table 9 reports the effect of varying the convolution kernel size  $C$  in  $\mathbf{F}^2\mathbf{SGD}$ . All
+
+Table 7. Performance of different methods with their alignment modules replaced by our  $\mathrm{A}^{2}\mathrm{{FA}}$  .  
+
+<table><tr><td>Method</td><td>Detection</td><td>R1@.7</td><td>mAP@Avg</td></tr><tr><td rowspan="2">UVCOM [34]</td><td>Original</td><td>47.5</td><td>43.2</td></tr><tr><td>F2SGD</td><td>51.1</td><td>49.1</td></tr><tr><td rowspan="2">CG-DETR [26]</td><td>Original</td><td>52.1</td><td>44.9</td></tr><tr><td>F2SGD</td><td>55.8</td><td>49.6</td></tr><tr><td rowspan="2">TaskWeave [36]</td><td>Original</td><td>50.1</td><td>45.4</td></tr><tr><td>F2SGD</td><td>52.4</td><td>47.8</td></tr></table>
+
+Table 8. Comparison of different methods with their original temporal boundary detection modules replaced by our  $\mathrm{F}^{2}$  SGD.  
+
+<table><tr><td>C</td><td>17</td><td>21</td><td>25</td><td>29</td></tr><tr><td>R1@.7</td><td>63.9</td><td>64.8</td><td>64.1</td><td>63.6</td></tr><tr><td>mAP@Avg</td><td>62.4</td><td>63.0</td><td>62.3</td><td>62.4</td></tr></table>
+
+Table 9. Impact of convolution kernel size  $C$  in  ${\mathrm{F}}^{2}\mathrm{{SGD}}$  .
+
+performance metrics peak when the kernel size is set to 21, which allows  $\mathrm{F}^2\mathrm{SGD}$  to effectively perceive matching intervals of varying lengths in the QVHighlights dataset.
+
+Visualization of retrieval results. In Fig. 7, we present a sample result of VMR on the QVHighlights val dataset. We provide ground-truth annotations for reference and also include the previous state-of-the-art methods, TaskWeave [36] and UVCOM [34], for comparison. Both TaskWeave and UVCOM simply use VLM as a feature extractor and directly regress frame features into target interval boundaries, which leads to inaccurate interval boundary positioning. In contrast, the intervals predicted by our method have a high overlap with the target interval, thanks to our targeted modality alignment and the bridging of the information gap between frame features and temporal boundaries.
+
+# 5. Conclusion
+
+We propose a novel framework for VMR. The proposed  $\mathrm{A^2FA}$  aligns feature modalities by anchor-aware masks, enhancing the cohesion of query-related frame similarities. It enables our  $\mathrm{F^2SGD}$  to effectively detect temporal boundaries in the 2D similarity space, bridging the gap between frame features and temporal boundaries. Experimental results in public datasets show the effectiveness and superiority of our proposed approach over previous SOTAs.
+
+# Acknowledgments
+
+This work is supported in part by the National Natural Science Foundation of China under Grant 61976029 and the Key Project of Chongqing Technology Innovation and Application Development under Grant cstc2021jscx-gksbX0033.
+
+# References
+
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+# AniDoc: Animation Creation Made Easier
+
+![](images/69acd8a01bf106a625d92a6b5a632bdbd44d76467f03cc07e3b6b6b255eae233.jpg)
+
+![](images/6d0b00bae1b050ae39adf9331172f357019c64bd14b37acd75e38c56c8f695ca.jpg)  
+Figure 1. AniDoc colorizes a sequence of sketches based on a character design reference with high fidelity, even when the sketches significantly differ in pose and scale. Additionally, the model supports sparse sketch inputs, enabling effective interpolation and high-quality colorization simultaneously, as shown in the last row.
+
+# Abstract
+
+The production of 2D animation follows an industry-standard workflow, encompassing four essential stages: character design, keyframe animation, in-between, and coloring. Our research focuses on reducing the labor costs in the above process by harnessing the potential of increasingly powerful generative AI. Using video diffusion models as the foundation, AniDoc<sup>1</sup> emerges as a video line art colorization tool, which automatically converts sketch sequences into colored animations following the reference character specification. Our model exploits correspondence matching as an explicit guidance, yielding strong robustness to the variations (e.g., posture) between the reference
+
+character and each line art frame. In addition, our model could even automate the in-betweening process, such that users can easily create a temporally consistent animation by simply providing a character image as well as the start and end sketches. Our code is available at: https://yihao-meng.github.io/AniDoc_demo.
+
+# 1. Introduction
+
+The animation industry, particularly in the realm of 2D anime production, relies heavily on the meticulous process of coloring line art to bring characters and scenes to life. Colorization of line art [11, 12, 17, 33, 42, 51, 65] in videos is a critical task that not only adds aesthetic value but also enhances the storytelling experience by conveying emotions and actions vividly. Automating this process holds signifi
+
+![](images/74423362b26c6f25b3fff847c8408e64740e35e576aa1aa872a5eba212bb8105.jpg)  
+Figure 2. Illustration of the workflow of 2D animation production.
+
+cant potential to streamline production workflows, reduce labor costs, and accelerate content creation, meeting the growing demand for high-quality animated content.
+
+In the current anime production pipeline, artists typically begin with character design sheets that define the visual attributes of characters. These designs are then translated into keyframe sketches — crucial frames that outline the primary poses and movements in a scene. Next, artists create in-between sketches, which are the frames drawn between the keyframes to define the detailed movement and transition [40, 63]. Traditionally, these frames are manually colored, a time-consuming task that involves careful attention to ensure consistency with the original character designs. Fig. 2 illustrates each step of this pipeline. Our work aligns seamlessly with this pipeline, aiming to automate the colorization process while maintaining fidelity to the original character designs and ensuring temporal consistency across frames.
+
+However, automating line art colorization [25, 57] presents several challenges. One primary difficulty lies in the mismatch between the character design and the line art sketches, where the angles, proportions, and poses in the design may not align with those in the keyframe sketches. Additionally, achieving temporal consistency is crucial; colorizing each frame individually can lead to flickering or inconsistencies, detracting from the viewer's experience [5, 31, 62]. Previous approaches [18, 44, 54] have attempted to address these challenges but with limitations. They often assume the availability of colorized versions of keyframes and rely on dense line art guidance. This assumption significantly increases the workload on artists, as it requires manual coloring of multiple keyframes and detailed line art inputs, making the process tedious and labor-intensive. Moreover, some methods suffer from color information leakage due to their training pipelines. Specifically, they use non-binarized sketches extracted from color images using neural networks for training, unintentionally incorporating color information from the original images into the sketches. This information leakage undermines the practicality of these methods, as real-world sketches do not contain such implicit color information—a concern we analyze further in our methodology.
+
+To overcome these challenges, we propose a novel all-in-one model that streamlines the colorization process within a single framework. Our model leverages the priors from pretrained diffusion-based video generation models [1, 36],
+
+harnessing their ability to capture temporal dynamics and visual coherence. The key designs of our approach are as follows: Correspondence-guided Colorization: We address the misalignment between the reference character design and the input line art sketches by incorporating an explicit correspondence mechanism. The injection module is designed to integrate color and style information from the reference into the line art, effectively improving color accuracy and consistency. Binarization and Background Augmentation: To reflect real usage scenarios, we binarize the condition sketches, forcing the model to truly learn to extract color information from the reference character design, rather than relying on recovering color information leaked from the non-binarized sketches. This constraint poses additional challenges for the model to accurately colorize the line art. To mitigate the instability during training due to this reduced information, we incorporate background augmentation strategy which greatly improve the colorization result. Sparse Sketch Training: Our model employs a two-stage training strategy that first learns the colorization ability and then removes the intermediate sketches to learn the interpolation ability. By learning the interpolation between keyframes, our model maintains temporal consistency without extensive human intervention.
+
+Our method demonstrates superior performance both quantitatively and qualitatively compared to existing approaches. It effectively colorizes line art sketches in videos, maintaining high fidelity to the reference character designs and ensuring temporal consistency across frames. Moreover, we demonstrate that a single reference character image can be used to colorize sketches from different segments featuring the same character, even when these sketches differ significantly in scale, pose, and action from the reference design. Our work represents a significant step toward automated, efficient, and artistically consistent animation production, with potential applications extending beyond anime to various forms of digital art and media.
+
+# 2. Related Work
+
+# 2.1. Line Art Image Colorization
+
+Line art colorization [2, 10, 22, 27, 28, 37, 56-58, 61] differs from natural image colorization, as it lacks an illuminance channel and only contains structural information, offering more flexibility. Traditional methods [35, 41] rely on users manually adding color to specific regions. The advent of deep learning has advanced this field, with techniques like color hint points [55], color scribbles [8], text tags [23], and natural language prompts [64]. Reference-based colorization, where users provide a reference image to guide the coloring, has also gained popularity. Methods like [38] use segmented graphs, while Chen et al. [6] employ active learning, and [3] apply attention networks. AnimeDiffu
+
+sion [4] introduces the first diffusion-based reference-based framework for anime face colorization. However, these methods colorize sketch images separately, struggling with temporal coherence when colorize a sequence of sketches.
+
+# 2.2. Reference-based Line Art Video Colorization
+
+Several approaches extend reference-based colorization to videos. Given an input of reference image, these methods colorize the corresponding sketch sequence based on the reference image's color information. LCMFTN [60] trains a model using animation frame pairs but lacked temporal coherence. TCVC [44] uses previously colored frames to maintain short-term consistency, but errors accumulate over time. TRE-Net [46] mitigates this by using both the first frame and previously generated frames. ACOF [54] propagates colors based on optical flow but requires refinement. The most recent work LVCD [18] proposes the first video diffusion model to colorize sketch video, but suffer from the issue of non-binarized sketch information leakage, limiting its real-world applicability. Most importantly, all of these methods require the color version of the first frame of each video clip, while in the actual anime production workflow, colorists typically only receive the character design image and need to use that image to colorize different clips featuring the character.
+
+# 2.3. Video Interpolation
+
+With the rapid development of controllable video generation models [30, 50], video interpolation has achieved increasingly better results. Unlike reference-based colorization, video interpolation [9, 16, 19, 20, 24, 39, 47] aims to generate in-between frames from both the first and last frames. SparseCtrl [13] and SEINE [7] extend video interpolation using pretrained text-to-video diffusion models and additional image conditions. Shi et al. [39] adapt video interpolation for cartoon animation with temporal constraint networks. AnimeInterp [40] interpolates middle frames by warping with predicted flows. ToonCrafter [49] introduces a diffusion-based video interpolation model. Zhu et al. [63] proposes a thin-plate spline-based interpolation module for animation sketch inbetweening. We aim at an all-in-one model that simultaneously performs automatic interpolation and colorization for anime. However, more precise interpolation methods [47], can be integrated to achieve enhanced control over sketch manipulation.
+
+# 3. Method
+
+We formally define the problem of line art video colorization with reference images. Given a reference image  $I_{\mathrm{ref}}$  that encapsulates the desired color and style of the character and a sequence of binarized line art sketches  $\{S_t\}_{t=1}^T$ , where  $S_t$  is the sketch at time frame  $t$ , our objective is to generate a sequence of colorized frames  $\{I_t\}_{t=1}^T$  such that:
+
+1. Each frame  $I_{t}$  is a colorized version of the sketch  $S_{t}$ .  
+2. The colorization is consistent with the character design.  
+3. The sequence  $\{I_t\}$  is temporally coherent, ensuring smooth transitions without flickering artifacts.
+
+Formally, we aim to learn a function  $f$  that maps the sketches and the reference image to the colorized frames:
+
+$$
+\left\{I _ {t} \right\} _ {t = 1} ^ {T} = f \left(\left\{S _ {t} \right\} _ {t = 1} ^ {T}, I _ {\text {r e f}}\right). \tag {1}
+$$
+
+# 3.1. Motivation and Pipeline Design
+
+We summarize the shortcomings of state-of-the-art approaches when handling real-world animation production scenarios and design modules to overcome them.
+
+Mismatch Between Character Design and Input Sketches. Existing methods rely on the assumption that the reference image is strongly pixel-aligned with the first frame of the sketch sequence. When the reference provided is not the first-frame image, but instead a character design from a different angle, the model struggles to correctly match the colors and details, as shown in Fig. 5. This limitation necessitates manual coloring for each clip's keyframes in the animation, which is labor-intensive and counteracts the benefits of automation. To address this, we aligns and transfers color information from reference character design to input sketches with correspondence-guided control module, as described in Sec. 3.2.
+
+Degradation with Binarized Sketches. Previous methods often rely on sketches extracted from color images using learned neural networks. These non-binarized sketches contain unintended color information leaks from the original color images, although invisible to the human eye. When training with these non-binarized sketches, the model tends to learn how to recover these hidden color information rather than correctly learning to find the corresponding parts in the reference to color the sketch, resulting in models that perform poorly when applied to binarized sketches. As depicted in Fig. 4, when previous methods are applied to binarized sketches, the outputs suffer from severe degradation. The colorization is inaccurate, and the visual quality is significantly reduced compared to when non-binarized sketches are used. To address this issue, we mirror the real production conditions by adopting the binary sketch in training and apply background augmentation to enhance the robustness as in Sec. 3.3.
+
+Reliance on Dense Sketches as Conditions. Previous methods often require dense sketches to maintain temporal consistency. Manually drawing inbetweening sketches in an animation is costly. We aim to use only  $S_{1}, S_{T}$  to further improve the scalability of automatic creation and propose the sparse sketch training scheme in Sec. 3.4.
+
+Pipeline Design. Following Stable Video Diffusion (SVD) [1], our main architecture consists of a denoising 3D U-Net designed for video generation. The reference
+
+![](images/f142229b456be76c3aed1b10c0f2967317eb0797bef2ee47f3ba652dbca384a5.jpg)  
+Figure 3. Overview of AniDoc pipeline. We adopt a two-stage training strategy. In the dense-sketch training stage, we explicitly extract matching keypoints pairs between the reference image and each frame of the training video, constructing point maps to represent the correspondences. In the sparse-sketch training stage, we remove the intermediate frame sketches and use the matching points from the start and end frames to interpolate point trajectories, which guide the generation of the intermediate frames.
+
+![](images/86f3e1edefe568ec2c9c1596b440470ad7a8ea1eed823487a73d054e9fd8828b.jpg)
+
+![](images/ba5a55244ee4c4dcf3c610feede2098ef318f8b6bed6303208a09ef372d7f642.jpg)
+
+![](images/f2a21e16176e46aa8b04634fc5bca2e6d7948cebd365e0e376b3f5e32255bebe.jpg)  
+Reference
+
+![](images/b2f8e7e43edbab38f48cc983d68bb793be3813afe819d92563f86cc771bbe915.jpg)
+
+![](images/31cdd2c6de7e897b67b88440666c5c0b9182a2463488eeeea14c2c484a8e4861.jpg)  
+Non-binarized sketch
+
+![](images/aa33f2e7f292fffb22d6f6feda3c4a716bf6395a20f7c7ac05da91ce0734ce57.jpg)
+
+![](images/d96d1dcf6583023e263ecf1d34cb74c1028ea4371509111ae85bb9c285f66d65.jpg)  
+Binarized sketch  
+Figure 4. Illustration of color leakage issue in non-binarized sketch. For previous video colorization method [18], when given non-binarized sketch, even if the reference is an empty image, it can still generate colorized results with similar color pattern to the ground truth. After binarizing the sketch, the colorization results degrade significantly.
+
+image latent is duplicated across the number of frames and concatenated along the channel dimension with the noisy latent so that the reference image information can be integrated into the colorization process through multiple self-attention layers in the 3D U-Net encoder. To inject the correspondence between the reference character design and the sketch, we explicitly extract corresponded keypoints and construct point maps. The correspondence information and sketch information are then encoded by a 3D U-Net dual branch similar to [59], and injected into the main branch as control signals. To construct training pairs of reference character designs and corresponding sketch sequences, we select long videos from the Sakuga-42M dataset [32], where the characters naturally undergo rich transformations, including changes in position, posture, angle, scale, etc., which align with the needs of our model.
+
+The training objective for our model is as follows:
+
+$$
+\mathcal {L} = \mathbb {E} _ {z _ {t}, z ^ {0}, t, \epsilon} \left[ \left\| \epsilon - \epsilon_ {\theta} ^ {c} (z _ {t}; t, z ^ {0}, c _ {s k e t c h}, c _ {c o r r}) \right\| ^ {2} \right], (2)
+$$
+
+where  $z^0$  denotes VAE-encoded latent feature of the reference image,  $c_{sketch}$  means the sketch control signal,  $c_{corr}$  means the correspondence control signal, and  $\epsilon_{\theta}^{c}$  is the combination of the denoising U-Net and the control branch.
+
+# 3.2. Correspondence-guided Colorization
+
+During training, we use an off-the-shelf keypoint matching method LightGlue [26] with SIFT descriptor [29] to extract matching keypoints between the reference image and the first frame of the training video. The matched keypoints are denoted as  $\{(x_{\mathrm{ref}}^i,y_{\mathrm{ref}}^i),(x_1^i,y_1^i)\}_{i = 1}^n$ , where  $n$  refers to the number of matching pairs. Based on these matched keypoints, we construct a point map pair  $P_{1} = (P_{\mathrm{ref}},P_{1,\mathrm{sketch}})$ , representing the matching correspondence of the reference image and the first frame. Each point map is in the size of  $H\times W$  (same as the image resolution), where the coordinates corresponding to the matched keypoints are marked with the same integer label:
+
+$$
+P _ {\mathrm {r e f}} \left(x _ {\mathrm {r e f}} ^ {i}, y _ {\mathrm {r e f}} ^ {i}\right) = P _ {1, \mathrm {s k e t c h}} \left(x _ {1} ^ {i}, y _ {1} ^ {i}\right) = i. \tag {3}
+$$
+
+For unmatched pixels, the value is set to 0.
+
+We then employ Co-Tracker [21] to track the movement of keypoints  $\{(x_1^i,y_1^i)\}_{i = 1}^n$  in each frame and construct correspondence point maps in the same way. As a result, we obtain a point map  $P_{\mathrm{seq}} = \{P_t\}_{t = 1}^T\in \mathbb{R}^{2\times T\times H\times W}$  which explicitly encodes the correspondence between the reference image and each sketch in the training video.
+
+We concatenate the point map  $P_{\mathrm{seq}}$  with the reference image  $I_{\mathrm{ref}}$  together as explicit correspondence guidance
+
+information and integrate it into the control branch. Specifically, for a given keypoint  $(x_{t}^{i},y_{t}^{i})$  in sketch frame  $S_{t}$ , the model can use the point map  $P_{t}$  to obtain the corresponding location  $(x_{\mathrm{ref}}^i,y_{\mathrm{ref}}^i)$  in the reference image  $I_{\mathrm{ref}}$  and extract corresponding color information at that location. Thus, our video generation process can be represented as:
+
+$$
+\{I _ {t} \} _ {t = 1} ^ {T} = D (I _ {\mathrm {r e f}}, E (\{S _ {t} \} _ {t = 1} ^ {T}, \{P _ {t} \} _ {t = 1} ^ {T}, I _ {\mathrm {r e f}})), \quad (4)
+$$
+
+where  $D$  refers to the denoising process of the 3D diffusion U-net,  $E$  refers to the control branch encoder.
+
+Semantic Keypoint Matching During Inference. During training, we apply LightGlue [26] with SIFT descriptor [29] for keypoint selection and matching between the reference image and the training video frames due to its fast speed. However, during inference, we do not have the ground truth color image to extract corresponding keypoints. Methods like the SIFT descriptor, which are focusing on low-level image feature, fail to correctly match keypoints between the color reference image and the sketch due to the large domain gap. One recent work DIFT [43] have found that features extracted by diffusion models can achieve semantic-level matching. Thus, during inference, we first extract keypoints in the reference character design using X-Pose [52], and find the matching keypoints in the given sketch using semantic feature DIFT.
+
+# 3.3. Binarization and Background Augmentation
+
+In real animation production, sketches provided to colorists are typically binarized line drawings without grayscale shading or hidden color information. To simulate this real-world condition, we apply a binarization process to the extracted sketches during training by setting pixel values greater than 200 to 255 and others to 0. This converts the sketch  $S_{\mathrm{raw}}$  into a binary image  $S_{\mathrm{bin}}$ , with black lines (0) and white background (255).
+
+Using binarized sketches as conditioning inputs poses significant challenges for the model. One primary issue is the ambiguity between the background and large white regions in the foreground. Both are represented by the same pixel value (255), making it difficult for the model to distinguish. This ambiguity can lead to confusion during colorization, resulting in erroneous outputs where the model may incorrectly color background regions or fail to accurately color foreground elements. Such failure cases are evident in our ablation studies (refer to Sec. 4.4).
+
+To address this problem, we enhance the training process through background augmentation. Specifically, we randomly remove the background of the reference image with a  $50\%$  probability during training process, using an off-the-shelf background removal model [34]. This forces the model to learn to distinguish between the foreground and background regions. In the foreground region, the model learns to extract color information from the correct areas of
+
+the reference character design. In the background region, the model is required to rely more heavily on its internal generative prior, enabling it to produce a background that is coherent with the foreground character.
+
+# 3.4. Sparse Sketch Training
+
+To further reduce the necessity of drawing intermediate sketches for animations with simple motions, we introduce a sparse sketch training strategy in a two stage way. In the first stage, the training is conducted with all frame sketches available. We hope that the model learns how to correctly extract information from the point map in this stage, which will guide the training in the next stage.
+
+After completing the first stage training, we remove the sketch condition for intermediate frames and use keypoints information to guide the interpolation. Inspired by [48], we additionally transform the keypoint coordinates into a Gaussian heatmap  $G_{t}$  which is more suitable for trajectory control, and concatenate  $G_{t}$  with the original point map  $P_{t}$  together. Specifically, the model is conditioned on the start and end sketches,  $S_{1}$  and  $S_{T}$ , as well as the pointmap  $P_{t} \oplus G_{t}$  at each frame:
+
+$$
+\left\{I _ {t} \right\} _ {t = 1} ^ {T} = D \big (I _ {\mathrm {r e f}}, E \big (S _ {1}, S _ {T}, \left\{P _ {t} \oplus G _ {t} \right\} _ {t = 1} ^ {T}, I _ {\mathrm {r e f}} \big) \big). \quad (5)
+$$
+
+Noted that during training the point trajectories are obtained through point tracking in the training video using CoTracker [21], while during inference we extract matching keypoints pairs between the start and end sketches and linearly interpolate the intermediate point trajectories.
+
+In this sparse-sketch training stage, we randomly select up to 5 keypoints, corresponding to 5 trajectories. The selection probability is determined by the magnitude of the motion, with trajectories having larger motion being more likely to be selected. Guided by the keypoint trajectories, our model can produce smooth intermediate colorized frames with only sparse sketch inputs.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Our method is built upon SVD and is trained on the Sakuga-42M [32] dataset, which comprises a large number of anime clips with diverse styles. To create reference images and sketch videos with large differences, we exclude clips with fewer than 50 frames, ultimately retaining around 150k video clips. We set the interval between the reference image and the first frame of the target video to 32 frames, with the target video length being 14 frames. During the first training stage, where the generation is conditioned on per-frame sketches, we simultaneously fine-tune all parameters of both the U-Net and ControlNet, including both the spatial and temporal attention layers. This is done for 100k steps using the AdamW optimizer with a learning rate
+
+![](images/97e862eedfcda82ea1be2fb6a74abd8710a29677f6e10cf70ce37e565aa10149.jpg)  
+Figure 5. Visual comparison of reference-based colorization with four methods LVCD [18], LVCD+IP-Adapter [53], ID-animator [14], ToonCrafter [49].
+
+of  $1 \times 10^{-5}$ , at a resolution of  $256 \times 256$  due to GPU memory constraints. Subsequently, we freeze other layers and fine-tune the spatial layers for an additional 10k steps
+
+at a resolution of  $512 \times 320$ . We randomly select up to 50 keypoints to enhance the model's robustness to varying numbers of keypoints. During the sparse sketch training
+
+![](images/12e45774fc12d252add6f1c837e9bb97d90c50d2c0b5c1eea13e4c9ed17ec153.jpg)  
+Figure 6. Ablations on each component. "w/o matching" indicates without the corresponding matching module, "w/o binarize" indicates without binarization and background augmentation.
+
+stage, we remove the middle frames' sketches and further fine-tuned all parameters for 100k steps. The training is conducted on 16 NVIDIA A100 GPUs with a total batch size of 16, and the entire training process takes 5 days.
+
+# 4.2. Comparison
+
+To comprehensively evaluate the coloring ability of our model, we randomly select 200 clips from 10 different eras and styles of anime to construct the test set. We select corresponding character design images (without background) as reference images.
+
+We compare our proposed method with two state-of-the-art reference-based line art video colorization frameworks: LVCD [18] and ToonCrafter [49], both of which are based on video diffusion models. Since LVCD's original setting requires the colorized version of the first sketch as a reference, we also compare it with the IP-Adapter [53] + LVCD version. In this case, we first use a diffusion-based image colorization method IP-Adapter to colorize the first frame's sketch, and then use this colored image as the reference for LVCD. For ToonCrafter, which requires color versions of both the start and end frames, we first use IP-Adapter to colorize the sketches of both frames. Additionally, we select a recent video personalization method, ID-animator [14], which excels at identity preservation in general domains and can achieve a similar function to colorization when combined with ControlNet [59].
+
+Qualitative Comparison. As shown in Fig. 5, our method produces significantly clearer textures and better preserves the character's identity. It performs especially well in scenarios with substantial differences between the reference character design and input sketches, where LVCD and ID-Animator fail to accurately colorize the sketches. Even when providing the colorized first frame using IP-Adapter for these baselines, our method still outperforms them in both visual quality and identity preservation.
+
+Quantitative Comparison. We evaluate the quality of the colorized animations in two aspects: 1). Frame and Video Quality: we adopt Frechet Inception Distance [15] (FID)
+
+Table 1. Quantitative comparison with existing baselines on reconstruction and generative metrics.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>FID↓</td><td>FVD↓</td></tr><tr><td>ID-Animator</td><td>15.61</td><td>0.3129</td><td>0.5151</td><td>158.16</td><td>677.61</td></tr><tr><td>LVCD</td><td>15.77</td><td>0.6446</td><td>0.2580</td><td>121.98</td><td>584.33</td></tr><tr><td>LVCD + IP</td><td>16.52</td><td>0.6404</td><td>0.2639</td><td>118.28</td><td>496.45</td></tr><tr><td>ToonCrafter + IP</td><td>14.97</td><td>0.3983</td><td>0.4532</td><td>110.48</td><td>492.10</td></tr><tr><td>AniDoc (Ours)</td><td>19.23</td><td>0.7720</td><td>0.1704</td><td>54.33</td><td>230.18</td></tr></table>
+
+Table 2. Ablations on correspondence matching module and binarization + background augmentation.  
+
+<table><tr><td>Settings</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>FID↓</td><td>FVD↓</td></tr><tr><td>w/o binary</td><td>15.41</td><td>0.6639</td><td>0.2471</td><td>94.89</td><td>503.23</td></tr><tr><td>w/o matching</td><td>17.80</td><td>0.7068</td><td>0.2252</td><td>75.91</td><td>273.86</td></tr><tr><td>AniDoc (Ours)</td><td>19.23</td><td>0.7720</td><td>0.1704</td><td>54.33</td><td>230.18</td></tr></table>
+
+to measure image quality and assess video quality using Frechet Video Distance [45] (FVD). 2). Colorization Accuracy: we measure the similarity of the colorized frames and the original animation frames using reconstruction metrics including PSNR, SSIM, and LPIPS. For all the metrics, we resize the frames to  $256 \times 256$  and remove the background for every frame because the reference character design does not include background information.
+
+As shown in Tab. 1, our method achieves the best scores across all metrics, indicating high-quality colorization results. For a more comprehensive assessment, we recommend reviewing the supplementary comparison videos.
+
+# 4.3. Flexible Usage
+
+We assess the flexibility of our model in three distinct settings, as depicted in Fig. 7.
+
+Same Reference with Varying Sketches. By using the same reference, our model is able to generate consistent colorizations across different video clips, even when the sketches differ significantly in terms of pose or scale.
+
+Same Sketch with Different References. When applying different reference images to the same sketch sequence, our method preserves the identity of the character while adapting the finer details, such as lighting and background, according to the distinct styles of the references.
+
+Sparse Input Sketches. Thanks to our two-stage training strategy, AniDoc supports animation with sparse sketches. By using only the start and end sketches, the model effectively produces smooth and coherent animations.
+
+# 4.4. Ablation Study
+
+We perform ablation studies Tab. 2 on two key components. Effect of Correspondence Matching. Without the correspondence matching module, the model struggles to
+
+![](images/5a892cbe6856db48f7007fcaac304512b85b764f19d1317ab16b93ff4164cffd.jpg)  
+Same Reference
+
+![](images/a97673b23e74d6776b4640a80cd4725629c6c42d031aa6cce803f9e29e929f6f.jpg)  
+(a) Animation with different sketches
+
+![](images/604489458ed85baf8333555c852e0a025a362c0b9fd223bbac191e90e3d92a01.jpg)  
+Different references  
+(b) Animation with the same sketch
+
+![](images/d03dabc9a9fce5302be0c3da9ad3aa83ddce4ef23fa6050935bb5607da404744.jpg)  
+(c) Animation with sparse sketches  
+Figure 7. Illustration of the flexible usage of our model. Figure (a) shows the ability of using same reference to colorize different sketches. Figure (b) demonstrates the robustness to different references. Figure (c) shows the sparse-sketch generation results.
+
+localize and transfer detailed color information accurately. As shown in the Fig. 6, the character's black sideburns have not been colored correctly, and the pink color of the hair has mistakenly been applied to the clothing. Incorporating correspondence matching ensures precise alignment between the reference and the input sketches, significantly improving color accuracy.
+
+Effect of Background Augmentation. Without background augmentation during training, the model struggles to distinguish between the foreground (character) and the background. Consequently, it may generate frames where certain regions are incorrectly colorized as pure white or contain artifacts, due to the limited information provided by the binarized sketches. Incorporating background augmentation helps the model to better understand scene context, leading to more accurate and visually pleasing results.
+
+# 5. Conclusion
+
+In this paper, we introduced a novel all-in-one model for automatic lineart video colorization that integrates seamlessly with existing anime production pipelines. Our approach tackles key challenges such as misalignment between character designs, limited information in binarized sketches and situations with only sparse sketches. Comprehensive experiments demonstrate that our method outperforms state-of-the-art baselines in both quality and temporal consistency. For future work, we aim to incorporate interactive point control to handle subtle color variations and develop stronger, more efficient video models to support longer and higher-quality animation creation, further enhancing the efficiency and creativity of animation production.
+
+Acknowledgements: This work was supported by Ant Group Research Intern Program.
+
+# References
+
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\ No newline at end of file
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+# AniGS: Animatable Gaussian Avatar from a Single Image with Inconsistent Gaussian Reconstruction
+
+Lingteng Qiu $^{1*}$  Shenhao Zhu $^{1,3*}$  Qi Zuo $^{1*}$  Xiaodong Gu $^{1*}$   
+Yuan Dong $^{1}$  Junfei Zhang $^{1}$  Chao Xu $^{1}$  Zhe Li $^{1,4}$  Weihao Yuan $^{1}$  Liefeng Bo $^{1}$   
+Guanying Chen $^{2\dagger}$  Zilong Dong $^{1\dagger}$
+
+$^{1}$ Tongyi Lab, Alibaba Group  $^{2}$  Shenzhen Campus of Sun Yat-sen University
+
+$^{3}$ Nanjing University  $^{4}$ Huazhong University of Science and Technology
+
+![](images/a6bcb100f49eb9b91619c086c30573d10998c0b9d25de0afd855dde83b1a92b4.jpg)
+
+![](images/6a669c6ffa93906fe4b0f8d8edaab68ae70101874ef5c53a920db59a7e447fca.jpg)
+
+![](images/6470c0e47fdabb71eacaa1daeac8e6604490e6c5d0b767471042dbea87c46182.jpg)  
+Figure 1. 3D Avatar Reconstruction and Animation Results of AniGS. Given a single human image as input, AniGS is capable of reconstructing a high-fidelity 3D avatar in a canonical pose, which can be used for both photorealistic rendering and real-time animation.
+
+![](images/600285cf4a734107fccab3a0d30c0ddd00b8d4de6b96e658a9900eb2df155f23.jpg)
+
+# Abstract
+
+Generating animatable human avatars from a single image is essential for various digital human modeling applications. Existing 3D reconstruction methods often struggle to capture fine details in animatable models, while generative approaches for controllable animation, though avoiding ex
+
+plicit 3D modeling, suffer from viewpoint inconsistencies in extreme poses and computational inefficiencies. In this paper, we address these challenges by leveraging the power of generative models to produce detailed multi-view canonical pose images, which help resolve ambiguities in animatable human reconstruction. We then propose a robust method for 3D reconstruction of inconsistent images, enabling real-time rendering during inference. Specifically, we adapt a transformer-based video generation model to generate
+
+multi-view canonical pose images and normal maps, pretraining on a large-scale video dataset to improve generalization. To handle view inconsistencies, we recast the reconstruction problem as a 4D task and introduce an efficient 3D modeling approach using 4D Gaussian Splating. Experiments demonstrate that our method achieves photorealistic, real-time animation of 3D human avatars from in-the-wild images, showcasing its effectiveness and generalization capability. Our code will be available on https://github.com/aigc3d/AniGS.
+
+# 1. Introduction
+
+Generating animatable human avatars has become increasingly important for a wide range of applications, such as virtual reality, gaming, and human-robot interaction. However, creating an animatable human avatar with diverse shapes, appearances, and clothing from a single image remains a challenging problem.
+
+Despite significant progress in human reconstruction from a single image [50, 59, 63, 79, 86], the reconstructed models are often difficult to animate. This is because the reconstructed human pose is aligned with the input pose, which is usually non-canonical, requiring complex rigging to enable animation. For animatable avatar reconstruction, methods based on predicting parametric human models (e.g., SMPL [46]) with geometry offset refinement often struggle to capture fine details [3]. Additionally, methods relying on implicit surface reconstruction face challenges in generalization, primarily due to the lack of large-scale, rigged 3D human datasets for training [20, 29, 78].
+
+Recently, controllable human image animation has made significant progress with diffusion models [27, 90], which generate animated images directly. These methods achieve realistic results and are easy to animate by input control poses, but suffer from inconsistencies across views due to the lack of a global representation. In addition, these methods also face efficiency issues due to the high computational effort per animation frame.
+
+Motivated by the success of diffusion models in generating multi-view images of objects [45, 68], several methods have explored fine-tuning these models to generate multiview human images from a single input, followed by 3D reconstruction using multi-view techniques [21, 44]. Specifically, CharacterGen [53] demonstrates the ability to generate cartoon-style avatars from a single image by first producing multi-view canonical pose images. To reconstruct the 3D model from these potentially inconsistent multiview images, a transformer-based 3D reconstruction model is trained. However, training both the multi-view diffusion model and the reconstruction model requires a synthetic 3D rigged human dataset to render multi-view canonical images, limiting the generalization ability of these models.
+
+To address these challenges, we adapt a transformer-based video generation model [26] to predict multi-view images and normal maps, by incorporating guidance support from the reference image and human poses. Our generation model can be trained on large-scale, in-the-wild video data, thereby enhancing its generalization.
+
+Despite the high-quality multi-view images generated by our method, inconsistencies still arise, which can affect the 3D reconstruction. By considering these inconsistencies as the dynamic variations within a temporal sequence, we can reformulate the problem of 3D reconstruction from inconsistent images as a 4D reconstruction task. Observing the effectiveness of 4D Gaussian splatting (4DGS) in dynamic scene modeling [47, 75, 83], we introduce an efficient 4DGS to fit the multi-view images. After optimization, the high-fidelity 3D avatar model can be obtained as the model in the canonical space of the 4DGS (see Fig. 1).
+
+In summary, the key contributions of this paper are as follows:
+
+- We introduce a method for multi-view canonical pose image generation using a video generation model, trained on unconstrained human pose video data, without the need for synthetic 3D rigged human datasets.  
+- We introduce a new perspective to the problem of 3D animatable avatar reconstruction from inconsistent images, formulating it as a 4D reconstruction task and introducing an efficient 4D Gaussian Splatting model.  
+- Experiments demonstrate that our method generates high-fidelity animatable avatars from a single image, enabling photorealistic and real-time animation during inference.
+
+# 2. Related Work
+
+Single-Image Human Reconstruction and Generation Early methods for single-image human reconstruction primarily formulated this problem as geometry offset prediction for mesh-based statistical models for naked [15, 32, 35, 36, 40, 64, 69, 71] or clothed [2, 4, 5, 8, 30, 39, 55, 76, 89] human body, with some approaches extending this to texture prediction [5, 8]. While a consistent naked topology simplifies animation, it is less effective for modeling diverse clothing styles. To deal with the cloth-style variation in the wild, numerous notable approaches [6, 10, 16, 62, 63, 79–81, 87, 88] utilize implicit functions as representations for 3D human models, enabling them to capture complex topologies without suffering from resolution constraints.
+
+Recently, the rise of generative models has blurred the boundaries between reconstruction and generation processes. Some methods [21, 44, 48] utilize the input image as a conditional element, leveraging generative techniques such as GANs [17, 25, 48, 82], Image Diffusion Models [12], and Video Diffusion Models [41, 44, 67] to synthesize 3D human models. The concurrent work Magic-
+
+Man [21] has explored the idea of generating multi-view human images and normal maps given the input image. Unlike these methods, which generate static models, our approach generates multi-view canonical pose images, followed by 3D modeling to reconstruct animatable human models.
+
+Animatable Human Generation Reconstructing animatable avatars remains a challenging problem. Early methods often adopt a parametric-model-based solution [3]. To better model the clothed human body, methods like ARCH [20, 29] adopts an implicit function representation to represent the geometry of the human body. Other works focus on animatable avatar reconstruction from monocular videos [31, 58, 74] or multi-view videos [13, 42, 54]. With the advent of text-to-3D techniques [56], several methods have explored generating 3D avatars from text prompts [11, 28, 37, 72].
+
+Recently, CharacterGen [53] achieves cartoon-style avatar generation from a single image by generating multi-view images with a diffusion model, followed by transformer-based shape reconstruction. In contrast, our work focuses on in-the-wild animatable human avatars, using a video generation model pretrained on large-scale in-the-wild videos to improve generalization. Additionally, we propose a robust 3D reconstruction method based on 4DGS, avoiding the need for training a transformer reconstruction model.
+
+Controllable Human Image Animation Original 2D diffusion models [61] primarily focus on generating single-view images and do not support human animation. Animate Anyone [27] introduces a reference net into the diffusion models to preserve the identity of the input image and incorporates a lightweight, pose-guided network for guidance. Champ [90], MIMO [49], and Human4DiT [67] employ 3D-level shape guidance [46, 51] rather than sparse 2D keypoints, enabling more accurate, controllable image generation under human attributes conditions.
+
+Although they can produce vivid human-centric animation videos, body distortion, and identity mutation often occur when the animated human turns back at wide angles. Additionally, these methods require several minutes to generate a video sequence given the human poses [67, 90], limiting their practicality in interactive applications. In contrast, by leveraging an explicit high-fidelity 3D Gaussian model, our methods achieve real-time photorealistic rendering at inference time.
+
+# 3. Preliminary
+
+Human Parametric Model The SMPL [46] and SMPL-X [51] parametric models are widely used for human body representation. These models utilize skinning techniques and blend shapes derived from a dataset of thousands of 3D body scans. Specifically, SMPL-X employs shape parame
+
+ters  $\beta \in \mathbb{R}^{20}$  and pose parameters  $\theta \in \mathbb{R}^{55\times 3}$  to represent body mesh deformations.
+
+Diffusion Transformer Model for Video Generation
+Diffusion Probabilistic Models [24, 70] use a forward Markov chain to gradually transform a sample  $x_0$  drawn from the data distribution  $p(x)$  into a noisy equivalent  $q(x)$ :
+
+$$
+q \left(x _ {t}\right) = \sqrt {\alpha_ {t}} \cdot x _ {0} + \sqrt {1 - \alpha_ {t}} \cdot \epsilon , t \in (0, T), \tag {1}
+$$
+
+where  $\epsilon \sim \mathcal{N}(0,I)$  denotes Gaussian noise,  $T$  is the final time step,  $t$  is the current time step, and  $\alpha_{t}$  is the noisy schedule parameter.
+
+The CogVideo model [26, 84] is an open-source Text-to-Video (T2V) diffusion model that employs a Transformer architecture [52], referred to as  $\mu_{\theta}$ , to model the reverse diffusion process. The transformer model processes the current noisy sample  $x_{t}$ , the associated time step  $t$ , and optional conditioning inputs  $c$  to estimate the noise  $\epsilon$ . The loss function for training the denoising model is:
+
+$$
+\mathcal {L} _ {\theta} = \mathbb {E} _ {x _ {0}, c, t} \| x _ {0} - \mu_ {\theta} (x _ {t}, c, t) \| ^ {2}. \tag {2}
+$$
+
+3D Gaussian Splatting 3D Gaussian Splatting [33] represents 3D data using a collection of 3D Gaussians. Each Gaussian is defined by a center  $\mathbf{x} \in \mathbb{R}^3$ , a scaling factor  $\mathbf{s} \in \mathbb{R}^3$ , and a rotation quaternion  $\mathbf{q} \in \mathbb{R}^4$ . Additionally, it includes an opacity value  $\alpha \in \mathbb{R}$  and a color feature  $\mathbf{c} \in \mathbb{R}^C$  for rendering purposes, with spherical harmonics capturing view-dependent effects. Rendering these Gaussians involves projecting them onto the image plane as 2D Gaussians and applying alpha compositing for each pixel in a front-to-back order. Recent methods [47, 75, 83] extend 3D Gaussian Splatting to capture dynamic 4D scenes by incorporating a temporal embedding.
+
+# 4. Method
+
+# 4.1. Overview
+
+Given an input human image  $I \in \mathbb{R}^{H \times W \times 3}$ , our goal is to create an animatable 3D avatar represented by a 3DGS model. This avatar can be animated by applying new human pose conditions during inference. To facilitate animation, it is crucial to reconstruct the 3D avatar in a canonical pose, simplifying the rigging process. The 3D avatar in this canonical pose can be rigged using the aligned SMPL-X model or other off-the-shelf rigging methods [1]. As shown in Fig. 2, our framework consists of two main stages.
+
+In the first stage, we employ a reference image-guided video generation model to produce high-quality multi-view canonical human images and their corresponding normals from the input image. In the second stage, we reconstruct the 3D model using these generated images. However, despite the high quality of the generated images, multiview inconsistencies still arise due to the nature of the
+
+(a) Multi-view Canonical Image Generation  
+![](images/e20159388cec28af0a70d990894c6581a2eaa66ec8353e2715e5b943bcd1cdde.jpg)  
+(a) Multi-view Canonical Image and Normal Generation
+
+(b) 3D Reconstruction from Inconsistent Images  
+Figure 2. Overview of the proposed AniGS. In the first stage, a reference image-guided video generation model is employed to produce high-quality multi-view canonical human images along with their corresponding normals, based on the input image. In the second stage, a robust 3D model reconstruction method is applied, using 4D Gaussian Splatting (4DGS) optimization to handle subtle appearance variations across the generated views.  
+![](images/33ba94c7ecfefb21fbb11c732f6dccd56e9ae9ee46cf1f46916cca6c6da69e74.jpg)  
+(b) 3D Reconstruction from Multi-view Inconsistent Images
+
+diffusion-based video generation model. Consequently, directly applying traditional multi-view reconstruction methods to these images often results in the loss of detail and the introduction of artifacts.
+
+To tackle the issue of view inconsistencies, we formulate this problem as a 4D reconstruction task and introduce an efficient 4D Gaussian Splitting model to account for the appearance variations at different timesteps (i.e., viewpoints). After optimization, a high-fidelity 3D model can be obtained as the model in the canonical space of the 4DGS.
+
+# 4.2. Multi-view Canonical Image Generation
+
+Given a reference human image in an arbitrary pose, our goal in the first stage is to generate multi-view RGB images of the same subject in a canonical pose. Motivated by recent successes in controllable image generation through video models [27, 84], we adapt a diffusion transformer-based video generation model to reposition the human subject to a canonical pose and generate multi-view images.
+
+Specifically, the video generation model takes as input the reference image and SMPL-X pose conditions to produce multi-view images. Here, the rotation of the camera in relation to the subject is treated as equivalent to subject rotation.
+
+Reference-guided Canonical Video Generation We extend the CogVideo model [26] to achieve reference image-guided and SMPL-X pose-guided video generation. This model includes a transformer-based denoiser and a Variational Autoencoder (VAE) that maps input videos or images into a high-dimensional latent space.
+
+The reference image  $I$  is first encoded into VAE features  $\mathbb{F}_i\in \mathbb{R}^{B\times 1\times C\times HW}$ , while the latent representations for video noise are denoted by  $\mathbb{F}_v\in \mathbb{R}^{B\times f\times C\times HW}$ , where  $B$  represents the batch size,  $f$  the number of output frames,
+
+$C$  the number of latent feature channels, and  $HW$  the total number of input feature tokens.
+
+To ensure that generated multi-view images retain the identity of the reference image, we fuse the reference image features and latent features during the denoising process. We achieve this by concatenating the reference image features and latent features along the frame channel, yielding  $\mathbb{F}_c\in \mathbb{R}^{B\times (f + 1)\times C\times HW}$  at each DiT block, which allows for feature interaction through self-attention.
+
+To guide the video generation with input human poses, we integrate a lightweight pose guidance network inspired by CHAMP [90]. This network extracts guidance features from the canonical SMPL-X normal,  $N_{\mathrm{splx}}$ , which are added to the corresponding noisy latents to direct the denoising process.
+
+Joint Multi-view RGB and Normal Generation To enhance multi-view reconstruction with normal supervision [14, 45], we further extend the video generation framework to simultaneously produce multi-view RGB images and normal maps, conditioned on a reference image and its corresponding normal map, as predicted by an existing method [14].
+
+We employ the CogVideo-2B architecture [84] as our base model, which comprises 30 DiT blocks. We modify the first three DiT blocks into two branches, one for RGB and the other for normal inputs. Similarly, we modify the last three DiT blocks into two branches that simultaneously output multi-view RGB images and normal maps.
+
+To effectively integrate image and normal features, we first share the weights of the middle 24 DiT blocks for both RGB and normal feature processing. Secondly, we insert a multi-modal attention module between every three shared DiT blocks and the head of the middle DiT blocks. For this multi-modal attention block, we concatenate the RGB
+
+and normal features at the token level, resulting in  $\mathbb{F}_m\in$ $\mathbb{R}^{B\times f\times C\times 2HW}$
+
+Training Strategy To enhance the generalization capabilities of our model in the face of limited large-scale synthetic datasets, we first pre-train the video generation model on a large-scale, in-the-wild dataset consisting of 100,000 single-human animation videos. As ground-truth normal maps are unavailable for in-the-wild data, we use Sapiens [34] and Multi-HMR [7] to generate pseudo labels for both normal maps and SMPL-X human poses. During training, we randomly sample frames from these videos to predict short video segments.
+
+Following pre-training, we generate synthetic 3D data assets to obtain self-rotated RGB images along with corresponding ground-truth normal maps. To maintain the model's generalizability, we use a training strategy that allocates  $10\%$  probability to in-the-wild data and  $90\%$  to synthetic data.
+
+# 4.3. 3D Reconstruction from Inconsistent Images
+
+Once multi-view images are generated by the diffusion model, we can reconstruct a 3D Gaussian human model in canonical space. However, due to subtle appearance variations across views in the generated images, directly applying 3D Gaussian Splitting (3DGS) optimization degrades the quality of the reconstructed avatar (see Fig. 3).
+
+Problem Formulation To address the challenges of 3D reconstruction from inconsistent views, it is necessary to handle the shape and appearance variations in each view. Viewing these inconsistencies as analogous to dynamic variations within a temporal sequence, we can reformulate the problem of 3D reconstruction from inconsistent images as a 4D reconstruction task. Inspired by the recent success of 4D Gaussian Splatting in dynamic scene modeling [47, 75, 83], we adopt a 4DGS approach to achieve efficient optimization and rendering.
+
+The 4DGS framework is composed of a canonical space and a per-frame deformation module. The canonical space represents a static 3D model (e.g., defined as the first frame), while the per-frame deformation module estimates shape and color variations of each 3D Gaussian, conditioned on the frame index, to fit the video sequence.
+
+Our goal is to optimize both the canonical space and the deformation module based on the generated inconsistent images. Once optimized, this process yields a multi-view consistent Gaussian avatar model representing the shape in canonical space.
+
+4D Gaussian Splating Model Following existing dynamic Gaussian splating methods [75], the deformation of 3D Gaussians is modeled by a deformation field network. We employ an efficient spatial-temporal encoder architecture consisting of a multi-resolution HexPlane and a compact MLP [9, 18, 66]. This structure encodes both the
+
+![](images/db94541efc536965a704e4a769637ec423efb0ebceaa1accaae2fcca40c9bbdc.jpg)  
+(a) Multi-view Inconsistence
+
+![](images/c74f4fbf522f4d558241ebf950816859358530bc7ffa42062056f2cb1c27a6db.jpg)  
+(b) Multi-view Reconstruction  
+Figure 3. Inconsistencies caused by subtle variations in the generated multi-view images, which will degrade the 3D reconstruction quality. The red boxes highlights the inconsistent areas.
+
+temporal and spatial features information of 3D Gaussians across six 2D voxel planes, incorporating temporal effects.
+
+Once the 3D Gaussians features are encoded, separate MLPs are employed to compute the deformation for position  $\Delta \mathbf{x}$ , rotation  $\Delta \mathbf{r}$ , and scaling  $\Delta \mathbf{s}$ . Then, the deformed 3D Gaussian  $(\mathbf{x}', \mathbf{r}', \mathbf{s}')$  can be expressed as:
+
+$$
+\left(\mathbf {x} ^ {\prime}, \mathbf {r} ^ {\prime}, \mathbf {s} ^ {\prime}\right) = \left(\mathbf {x} + \Delta \mathbf {x}, \mathbf {r} + \Delta \mathbf {r}, \mathbf {s} + \Delta \mathbf {s}\right). \tag {3}
+$$
+
+Shape Regularization In multi-view generation, both RGB images and normal maps are produced, allowing us to regularize the 4DGS optimization process using surface normal regularization. Specifically, we apply an  $L_{1}$  loss on the rendered normals,  $\mathcal{L}_{\mathrm{normal}}$ , to guide the optimization.
+
+To mitigate the occurrence of spikes artifacts during avatar animation, which is often due to excessively large or elongated 3D Gaussian ellipsoids, we incorporate an anisotropy regularizer,  $\mathcal{L}_{\mathrm{ar}}$ , to constrain the shape of the 3D Gaussians, following [77].
+
+4DGS Optimization In line with existing reconstruction methods [33, 57, 65], we employ L1 loss for both color  $\mathcal{L}_{\mathrm{color}}$  and mask supervision  $\mathcal{L}_{\mathrm{mask}}$ . We also include a grid-based total variation loss,  $\mathcal{L}_{tv}$ , as proposed in [75], to promote smooth deformation across views. For the human mask labels, we obtain pseudo ground-truth masks using SAM2 [60]. The total reconstruction loss is formulated as:
+
+$$
+\mathcal {L} _ {r} = \mathcal {L} _ {\text {c o l o r}} + \lambda_ {m} \mathcal {L} _ {\text {m a s k}} + \lambda_ {n} \mathcal {L} _ {\text {n o r m a l}} + \lambda_ {t v} \mathcal {L} _ {t v} + \lambda_ {a r} \cdot \mathcal {L} _ {a r}, \tag {4}
+$$
+
+where the weights for different loss terms are set as  $\lambda_{m} = 0.1$ ,  $\lambda_{n} = 0.05$ ,  $\lambda_{ar} = 0.001$ , and  $\lambda_{tv} = 1$ .
+
+Point Cloud Initialization of 4DGS Point cloud initialization is critical for 3DGS optimization. We begin by generating a coarse mesh from the multi-view images and sample points on its surface to initialize the 3DGS points.
+
+Specifically, we deform the predicted SMPL-X mesh to fit the generated multi-view RGB masks and normal maps. We use the Nvidiffrast rasterizer [38] to render both the foreground and normal map of the deformed mesh. To reduce artifacts caused by inconsistencies in the multi-view images, we apply a Laplacian loss and an edge loss to regularize the mesh deformation. Further details are provided in the supplementary materials.
+
+# 4.4. Animation
+
+The reconstructed avatar is represented in a canonical space, aligned spatially with the canonical pose of the human body parametric model, SMPL-X. This alignment enables us to use SMPL-X driving parameters to animate the reconstructed avatar, making it fully animatable in 3D. To better handle cloth with large deformation, we apply a diffusion-based skinning method [43, 58], which transfers SMPL-X skinning weights throughout the entire human canonical space. During animation, skinning weights are obtained by querying the weights in space via bilinear interpolation. Additional details are provided in the supplementary materials.
+
+# 5. Experiments
+
+In this section, we thoroughly evaluate the effectiveness of our proposed methods by conducting a comprehensive comparison with state-of-the-art approaches.
+
+Training Datasets For training the multi-view generation model, we first conduct a pretraining phase using a large dataset of dynamic human videos. Specifically, we collect approximately 200,000 dynamic human videos from various online sources. From this, we manually select single-person videos to create our in-the-wild training dataset, which consists of around 100,000 video samples. During the fine-tuning phase, we leverage a combination of public synthetic 3D datasets to render multi-view images. These datasets include 2K2K [19], Thuman2.0, Thuman2.1 [85], and CustomHumans [22], along with commercial datasets such as Thwindom and RenderPeople. Note that no rigged human models are used for training. In total, we utilize 6,124 synthetic human scans.
+
+Inference Our model can generate an animatable 3D avatar in a canonical pose within a few minutes using a single RTX-3090 GPU. Specifically, it takes approximately 5 minutes to generate 30 frames of multi-view RGB and normal images. The 4DGS optimization process takes around 5 minutes. Once the multi-view reconstruction is complete, we set the time parameter  $t = 0$  to obtain the final Gaussian point clouds. After optimization, the avatar can be animated and rendered in real time.
+
+Table 1. Quantitative results on multi-view canonical image generation.  $^+$  denotes using our generated canonical pose image as input, and \* indicates that we fine-tune this approach on the multiview synthetic dataset. Normal Loss is the cosine similarity loss between the predicted and ground-truth normal.  
+
+<table><tr><td>Methods</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Normal Loss ↓</td></tr><tr><td>MagicMan+ [90]</td><td>23.775</td><td>0.911</td><td>0.1077</td><td>0.134</td></tr><tr><td>CHAMP* [90]</td><td>20.025</td><td>0.894</td><td>0.1458</td><td>-</td></tr><tr><td>Ours</td><td>23.125</td><td>0.907</td><td>0.1023</td><td>0.101</td></tr></table>
+
+Table 2. Quantitative comparison of 3D modeling on Human4DiT Synthetic Datasets.  
+
+<table><tr><td>Methods</td><td>LPIPS ↓</td><td>CLIP score ↑</td><td>FID ↓</td><td>User ↑</td></tr><tr><td>SiTH [86]</td><td>0.1607</td><td>86.854</td><td>86.895</td><td>2.134</td></tr><tr><td>LGM [73]</td><td>0.1567</td><td>86.686</td><td>82.121</td><td>2.617</td></tr><tr><td>MagicMan [21]</td><td>0.1479</td><td>82.693</td><td>144.642</td><td>2.095</td></tr><tr><td>CharacterGen [53]</td><td>0.1638</td><td>87.154</td><td>88.751</td><td>2.481</td></tr><tr><td>En3D [48]</td><td>0.1576</td><td>82.975</td><td>131.32</td><td>2.549</td></tr><tr><td>Ours</td><td>0.1085</td><td>90.370</td><td>77.879</td><td>4.199</td></tr></table>
+
+# 5.1. Comparison with Existing Methods
+
+Evaluation Dataset We choose 50 rigged human avatars from Human4DiT [67] to evaluate our performance on multi-view canonical-pose image generation and 3D reconstruction metrics. For animation metrics, we use Blender software to obtain ground-truth video sequences and export the motion sequence to drive the created human models. We then compute photometric metrics in the foreground area to evaluate our performance on animation.
+
+Baselines Our pipeline includes canonical multi-view generation, multi-view reconstruction, and human animation. For the multi-view generation task, we choose the state-of-the-art MagicMan [21] and CHAMP [90] as baselines. Notably, since CHAMP does not specifically train on self-rotated synthetic human datasets, we fine-tune this approach on our rendering datasets for a fair comparison.
+
+For multi-view canonical human reconstruction tasks, we compare with the animatable human generation methods [48], CharacterGen [53]. Additionally, we also conducted comparison experiments with static clothed human reconstruction methods, including SiTH [23], MagicMan [21], and LGM [73] using our generated canonical pose image input. For human animation, we conduct comparison experiments with En3D and CharacterGen on the synthetic dataset.
+
+Evaluation on Multi-view Canonical Generation As reported in Table 1, our method outperforms CHAMP in multi-view image generation, clearly demonstrating its effectiveness. It is important to note that MagicMan [21] is specifically designed for multi-view generation of static humans and cannot generate canonical pose images. There-
+
+![](images/080ed26f49a7b72c9c9c5d3c3ea47e3297250a66936e118379f3f6fc78c7897c.jpg)  
+Figure 4. Visual comparison on canonical pose 3D avatar reconstruction from the single-view image. Since SiTH, MagicMan, and LGM cannot reconstruct canonical pose shapes from the input, we take our generated front-view canonical pose image as input to these methods.
+
+![](images/345c218e8d5075e0eef57d30ff4add7dc24c06da6f9895df420c30a5e8e70685.jpg)  
+(a) Effects of the normal regularization  $\mathcal{L}_{\mathrm{normal}}$
+
+![](images/450d262619f421091852f76190011c98274c9715d8cc8ac14a5fea192c1927c6.jpg)  
+(b) Effects of the anisotropic regularization  $\mathcal{L}_{ar}$  
+Figure 5. Ablation study for the shape regularization.
+
+fore, we use our generated canonical pose images as input for MagicMan. While MagicMan achieves better PSNR
+
+![](images/17b2c5eea0e146417b70b5b81719ef3e5deab04b468ff62c89f417fb3017c196.jpg)  
+Figure 6. Ablation study for shape initialization strategy.
+
+metrics, it is not suitable for animatable avatar generation. Additionally, our method achieves lower normal errors in the generated normal maps, further emphasizing its superior performance.
+
+Evaluation on Canonical Shape Reconstruction To assess the quality of canonical shape reconstruction, we render each reconstructed model from 24 different views and compute LPIPS and FID scores. The average CLIP score is computed by comparing the input RGB image with all rendered views.
+
+Table 3. Quantitative results on human animation.  
+
+<table><tr><td>Methods</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td></tr><tr><td>CharacterGen [53]</td><td>17.570</td><td>0.644</td><td>0.205</td></tr><tr><td>En3D [21]</td><td>19.244</td><td>0.751</td><td>0.174</td></tr><tr><td>Ours</td><td>21.475</td><td>0.857</td><td>0.137</td></tr></table>
+
+![](images/86495c728f822f48fe1b93f0c7009eba51d83f5e33e3e40b19dc4d54f735c721.jpg)  
+Figure 7. Comparison of reconstruction with 3DGS and 4DGS.
+
+Since this evaluation is closely related to generation tasks, we also conduct a user study to assess the similarity between the generated model and the ground truth. We randomly sample 20 cases and carry out an anonymous ranking survey with 40 participants across all baselines. The final metric represents the average ranking score, with a maximum score of 5 for each model. As shown in Table 2, our method consistently outperforms the baselines on all the metrics, justifying its design.
+
+As demonstrated in Figure 4, our method produces significantly better canonical pose shape reconstructions than previous methods, with higher fidelity to the input image and enhanced sharpness in both texture and body shape details (e.g., clothing, faces, and hands). Note that since the texture refinement code for MagicMan [21] has not been released, the 3D reconstruction results for MagicMan do not include texture refinement.
+
+Evaluation on Human Animation We compare the animation sequences of different methods with the rendered ground-truth sequences. As is demonstrated in Table 3, our method outperforms the baseline methods in terms of rendering quality in the animation sequences. Compared to the second-best method En3D, our method achieves improvements of 2.231, 0.106, and 0.037 in PSNR, SSIM, and LIPIs, respectively. Qualitative results are included in the supplementary materials.
+
+# 5.2. Ablation Study
+
+Shape Regularization We conduct an ablation study to evaluate the design of the shape regularization. Specifically, Fig. 5 (a) demonstrates that normal regularization effectively reduces random noise and enhances surface details, while Fig. 5 (b) shows that anisotropic regularization helps eliminate spikes in novel pose animations.
+
+Initialization of 4DGS Figure 6 compares the results of
+
+Table 4. Quantitative comparison between 3DGS and 4DGS.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Reconstruction Results</td><td colspan="4">Animation Results</td></tr><tr><td>FID ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LIPIS ↓</td><td>FID ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LIPIS ↓</td></tr><tr><td>3DGS</td><td>114.645</td><td>21.910</td><td>0.877</td><td>0.120</td><td>248.498</td><td>20.313</td><td>0.771</td><td>0.156</td></tr><tr><td>4DGS</td><td>77.879</td><td>22.954</td><td>0.893</td><td>0.109</td><td>165.174</td><td>21.475</td><td>0.857</td><td>0.137</td></tr></table>
+
+4DGS optimization using random points, SMPL mesh, and the proposed coarse mesh as initialization.
+
+Without any shape prior, the Gaussian model initialized with random points struggles to optimize, resulting in blurry outputs. Initializing with the SMPL mesh provides a better shape prior for body representation but faces difficulties in accurately modeling points that are farther from the body. In contrast, the coarse mesh initialization provides a good starting point for the optimization.
+
+3DGS Reconstruction vs. 4DGS Reconstruction Table 4 presents the quantitative results of an ablation study comparing 4DGS and 3DGS Reconstruction on the Human4DiT synthetic datasets. Compared to 3DGS reconstruction, the 4DGS metrics show improvements of 36.766, 0.044, 0.016, and 0.011 in FID, PSNR, SSIM, and LIPIs for the reconstruction task. In the animation task, improvements of 83.324, 1.162, 0.146, and 0.19 were observed in the same metrics. Figure 7 illustrates a qualitative comparison of 3DGS and 4DGS reconstruction. The 3DGS reconstruction faces challenges with inconsistent inputs, resulting in issues such as blurriness and floating artifacts. This ablation study clearly demonstrates that 4DGS effectively addresses the inconsistencies present in multi-view images and significantly improves the quality of the reconstruction results.
+
+# 6. Conclusion
+
+In this work, we present a robust approach to generate animatable human avatars from a single image. We introduce a reference image-guided video generation model to produce high-quality multi-view canonical human images and their corresponding normal maps. To handle view inconsistencies, we propose a 4D Gaussian Splatting (4DGS)-based method for reconstructing high-fidelity 3D avatars. Comprehensive evaluation demonstrates that our method enables photorealistic, real-time animation of 3D human avatars from in-the-wild images.
+
+Limitations While our method supports real-time inference, it still requires several minutes to optimize an animatable avatar. Moreover, our model currently struggles with half-body human image inputs. In future work, we aim to explore feed-forward 3D reconstruction techniques.
+
+Acknowledgement This work was supported in part by NSFC (Grant Nos. 62202409, 62472453), Guangdong Natural Science Foundation (Grant No. 2025A1515010782), and Shenzhen Science and Technology Program (Grant No. RCBS20221008093241052).
+
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\ No newline at end of file
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+# AniGrad: Anisotropic Gradient-Adaptive Sampling for 3D Reconstruction From Monocular Video
+
+Noah Stier
+
+Alex Rich
+
+Pradeep Sen
+
+Tobias Höllerer
+
+{noahstier, anrich, psen, holl}@ucsb.edu  
+University of California, Santa Barbara
+
+![](images/0e0e6261d7c675dd6079aebccd7834d0946964d321d228493f970f93e1b6f38e.jpg)  
+Figure 1. Reconstruction with adaptive & anisotropic resolution. Our 3D reconstruction system allocates computational resources effectively, using a variable sample pattern that adapts to the local surface complexity and orientation. A) The floor, which is flat and consistently oriented, is accurately reconstructed with a coarse resolution (4 cm). B) The cabinet is coarsely sampled in the vertical dimension because it exhibits no variation along that axis. Horizontally, however, it is sampled finely enough to accurately localize the surface. C) Object boundaries and other high-curvature structures are densely sampled to avoid aliasing, and to maintain high fidelity. The scene shown here is from ScanNet++ [39].
+
+# Abstract
+
+Recent image-based 3D reconstruction methods have achieved excellent quality for indoor scenes using 3D convolutional neural networks. However, they rely on a high-resolution grid in order to achieve detailed output surfaces, which is quite costly in terms of compute time, and it results in large mesh sizes that are more expensive to store, transmit, and render. In this paper we propose a new solution to this problem, using adaptive sampling. By re-formulating the final layers of the network, we are able to analytically bound the local surface complexity, and set the local sample rate accordingly. Our method, AniGrad<sup>1</sup>, achieves an order of magnitude reduction in both surface extraction latency and mesh size, while preserving mesh accuracy and detail.
+
+# 1. Introduction
+
+3D reconstruction from images is a key capability for many important applications such as augmented reality, robotics, and 3D digital asset creation. In order to achieve high-quality reconstructions at interactive speeds, many recent methods [2, 5, 12, 18, 22, 32-35] focus on using feedforward end-to-end neural networks. These models can generalize to new scenes at test time, and they do not require time-consuming direct optimization or volume rendering.
+
+The common approach among these methods is to build a 3D feature volume by back-projecting deep image features using their camera parameters, and then use a 3D convolutional neural network (CNN) to estimate a 3D truncated signed distance function (TSDF) over the scene. This framework has achieved excellent results, but it is limited in terms of resolution due to the cubic cost of its voxel-based
+
+representation. To address this, FineRecon [34] proposed to keep voxel size fixed at  $4\mathrm{cm}$ , and to sub-sample on a  $4\times 4\times 4$  grid of query points within each near-surface voxel, to achieve a higher resolution. This introduces a two-level resolution hierarchy: a coarse  $4\mathrm{cm}$  voxel grid, and a fine  $1\mathrm{cm}$  sub-sample grid. While that strategy does enable more detail, it requires long inference times ( $>30~\mathrm{s}$ ), which is prohibitive for online applications.
+
+In this paper we propose a solution to this bottleneck, based on the observation that not all near-surface voxels need to be sub-sampled at such a high resolution. Rather, the ideal sub-sample rate is proportional to the degree of local surface variation: flat regions like walls and floors require a lower sampling density than thin or curved structures like the legs of a chair. Furthermore, the ideal subsample rate is often asymmetrical across dimensions: the TSDF near the floor varies highly along the gravitational axis, but it is nearly constant along any axis parallel to the floor surface. Therefore, we posit that the ideal sub-sample rate is both adaptive and anisotropic. Note: throughout this paper, we use a fixed  $4\mathrm{cm}$  voxel size; all references to adaptive/local resolution and sample rates are referring to the sub-sample rate, illustrated in Fig 2.
+
+Finding the ideal local resolution is challenging, because it presents a chicken-and-egg problem: we need the local surface structure in order to determine the correct resolution, but we do not know the surface structure until we have reconstructed it.
+
+We propose a solution to this problem. We re-formulate the final layers of the network to give us advance knowledge of the predicted geometry, before sampling any TSDF predictions. Specifically, we re-interpret each voxel's feature vector as a weight vector for a linear combination of local 3D basis functions. The advantage is that just by examining the predicted basis weights, we can gain insight into the local TSDF structure, before we begin the sub-sampling process. This insight enables us to compute the appropriate sub-sample rates. The strategy that we develop is guaranteed not to alias the predicted TSDF, beyond a user-selected minimum variation threshold. The key contributions of this paper are as follows.
+
+1. We propose to express the predicted TSDF as a linear combination of learned basis functions, and we reformulate the network to output this representation.  
+2. Using this representation, we introduce an algorithm for adaptive, anisotropic sampling that enables 3D reconstruction with an order of magnitude fewer query points, while guaranteeing a user-specified, acceptable degree of aliasing.  
+3. We demonstrate this strategy using the ScanNet dataset [8], showing that it results in an order of magnitude reduction in both surface extraction latency and mesh size, while maintaining state-of-the-art accuracy.
+
+![](images/a7c3c2db98f6a0372ba3e583d595667d72a615e3ccc3ae0ba88cb739694b9865.jpg)  
+Figure 2. We capture fine details without reducing the voxel size (black). Instead, we sample our query points (blue) at a sub-voxel resolution. Unlike FineRecon [34] (left), our sub-sampling rate (right) adapts to the local predicted surface (yellow), enabling significant time savings. The red Xs indicate voxels that are pruned by occupancy filtering before sub-sampling, because they are too far from a surface.
+
+![](images/25aa66ce93851dd96396ee14ec931aeb9bd16b113a39f98876354af931ba968a.jpg)
+
+# 2. Related Work
+
+3D CNN-based TSDF reconstruction. Image-based 3D reconstruction is a classic problem, traditionally solved by multi-view stereo (MVS) [13, 30, 31], with recent MVS methods based on deep learning [3, 17, 26-28]. Here, we focus on the recent methods that are most related to ours, that use a 3D CNN to reconstruct a scene as a TSDF volume. This method was first used in the RGB-D domain [9, 10], and Atlas [22] proposed to handle the RGB-only case by densely back-projecting image features over the scene. Since then, numerous improvements have been introduced including sparse convolutions [35], multi-view fusion mechanisms [2, 12, 32], visibility and geometric constraints [14, 24, 40], self-supervision [15, 19], SLAM pose updates [33], depth guidance [16, 18, 34], and refinement via differentiable rendering [41, 43]. Our work builds on this research, focusing on adaptive resolution for efficiency. Adaptive resolution in 3D reconstruction. Adaptive resolution is highly desirable in most 3D reconstruction scenarios, and many solutions have been proposed. Occupancy filtering is a common approach that discards free space to focus on surfaces [12, 18, 32, 35]. Related approaches use semantic segmentation or object detection to assign higher resolution to certain object types [4, 38, 42]. Iterative mesh subdivision is common in multi-view stereo [11, 20, 23]. Several methods set the local resolution based on viewing distance [36, 37], and others use active depth sensors to estimate local surface complexity [42]. In contrast, our adaptive resolution is fully automatic, RGB-only, agnostic to object type, and does not require any form of preliminary explicit 3D model. Ours is also the first, to our knowledge, to study adaptive resolution in the context of image-based TSDF reconstruction with 3D CNNs, following Atlas [22].
+
+Sub-voxel resolution. With a voxel-based method, it is not tractable to reduce the voxel size indefinitely in pursuit of greater detail. Reconstructing sub-voxel detail has thus
+
+been a topic of recent interest. In this vein, FineRecon [34] is the most similar method to ours. It uses trilinear interpolation to sub-sample its  $4\mathrm{cm}$  feature grid on a  $1\mathrm{cm}$  grid of query points, achieving high resolution at the cost of high inference time. At the core of this paper, our re-formulation with local basis functions allows us to replace that operation with a new algorithm for adaptive sub-voxel resolution. Fig. 2 illustrates the resulting large reduction in query points.
+
+# 3. Intuition and proposed approach
+
+We first observe that the ideal local resolution is closely tied to the gradient of the predicted TSDF. For instance, if the maximum absolute gradient within some local volume is known to be  $[0, 0, 0]$ , then the predicted TSDF is locally constant, and a single query point is sufficient (a sample rate of 1 in all dimensions). If instead the gradient is higher in a particular dimension, additional query points are necessary to avoid aliasing.
+
+The key question is, how can we know the maximum absolute gradient within a local volume? We could sample many query points and compute the per-point gradient, but this would still require many samples to find the maximum. Instead, our solution is to express the TSDF prediction as a weighted sum of local 3D basis functions (Section 4.2, Eq. 1), where our network predicts the basis weight vector per voxel. This re-formulation allows us to use a shortcut: we analyze the basis functions in a one-time, offline step to determine their individual maximum values and gradients. Then, at test time, we can use this information to quickly bound the maximum gradient of the weighted sum, as shown in Section 5.1.
+
+Finally, we set the local sample rate proportionally to the gradient bound. This defines a non-uniform grid over the scene, and we extract a mesh using a non-uniform variant [29] of marching cubes [21] (see Section 5.2).
+
+# 4. Model architecture
+
+Our system takes as input a set of RGB images, along with the camera intrinsics and extrinsics, and reconstructs the scene by predicting the TSDF at a set of query points  $p \in \mathbb{R}^3$ .
+
+# 4.1. Building the scene feature volume
+
+We use a 2D-3D convolutional backbone to generate a 3D feature volume in scene space. Our implementation is based on FineRecon [34], and we summarize the main steps here.
+
+1. A 2D CNN extracts a 2D feature map from each image.  
+2. The 2D features are densely back-projected into scene space to populate an initial 3D feature volume.  
+3. A 3D U-Net processes the 3D features to produce the final scene feature volume  $\mathcal{F}$  and a predicted occupancy volume  $\hat{O}$ .
+
+# 4.2. TSDF prediction with fixed basis functions
+
+Our key architectural novelty is to re-interpret the voxel feature  $\mathcal{F}(v)$  as a basis weight vector for a set of local basis functions  $\beta_{i}$  centered at voxel  $v$ . Each nearby voxel  $v$  makes an independent TSDF prediction  $\hat{d}_v$  for query point  $p = [x,y,z]$  as follows:
+
+$$
+\hat {d} _ {v} (p) = \sum_ {i} \mathcal {F} (v) ^ {(i)} \beta_ {i} (p - c _ {v}). \tag {1}
+$$
+
+$\mathcal{F}(v)^{(i)}$  is the  $i^{\mathrm{th}}$  element of the voxel feature vector  $\mathcal{F}(v)$  and  $c_{v}$  is the center of voxel  $v$ . To represent the basis functions in a compact and easily-learnable way, we express each basis function  $\beta_{i}$  as the  $i^{\mathrm{th}}$  output channel of a coordinate MLP  $\theta$ ,
+
+$$
+\beta_ {i} (p) = \theta (p) ^ {(i)}. \tag {2}
+$$
+
+To reduce voxel boundary artifacts, we aggregate the predictions from nearby voxels using a volume-weighted average to predict the final TSDF,
+
+$$
+\hat {d} (p) = \sum_ {v \in N (p)} \hat {d} _ {v} (p) \operatorname {v o l} \left(p - c _ {v}\right), \tag {3}
+$$
+
+where the neighborhood  $N(p)$  is the set of voxels whose centers are found by rounding each of eight  $p = [x,y,z]$  either up or down to the nearest whole voxel size. The weights  $\mathrm{vol}(p - c_v)$  can be interpreted as tri-linear interpolation weights,
+
+$$
+\operatorname {v o l} ([ x, y, z ]) = | V - x | \cdot | V - y | \cdot | V - z |, \tag {4}
+$$
+
+where  $V$  is the voxel size.
+
+With this representation, the 3D CNN's output volume  $\mathcal{F}$  defines a continuous TSDF field in  $\mathbb{R}^3$ , since  $\mathcal{F}$  consists of weights for continuous basis functions. To extract an explicit mesh surface, we must first discretize this field by sampling it, evaluating  $\hat{d}$  at a set of query points.
+
+# 4.3. Occupancy filtering
+
+When making our TSDF predictions, we simply ignore any voxels with occupancy probability  $\hat{O} < 0.5$ , effectively masking them out for the sake of surface extraction.
+
+# 5. Surface Extraction
+
+When we set our local sample rates, we do not set them for each voxel. We instead set them for each central cube (CC), as illustrated in red in Fig. 3a. This is because of the smoothing defined in Eq. 3, which means that the TSDF at a given point depends on the feature vectors of all eight neighboring voxels, and the TSDF is thus continuously differentiable within a CC. We adopt the CC as the basic spatial unit for adaptive sub-sampling; in other words, we take the CC to be the "local volume" referenced in Section 3.
+
+![](images/89c4d096dfa6ebe864134d9599e94b06a7ed25b61fdbf1ee3f22b224c3f1efbd.jpg)  
+Figure 3. a) Our predicted TSDF is continuously differentiable within the central cube (CC, red). b) For each CC  $s$  we compute the maximum gradient bound  $\phi(s)$ , shown here in a 1D example as the slope of the blue line. By setting the spatial sampling rate to  $\Delta x = \frac{\Delta d}{\phi_x(s)}$ , we are guaranteed to capture every predicted TSDF change of at least  $\Delta d$ .
+
+# 5.1. Adaptive sample rates
+
+We set our local resolution proportionally to the maximum TSDF gradient within a CC. However, we do not know this maximum gradient a priori. We could estimate it with a Monte Carlo approach, but it would undermine our goal of reducing the required sample count. Instead, we analytically bound the gradient within the CC. For brevity, we present the process for one dimension only, developing an upper bound on  $\left| \frac{\partial}{\partial x} \hat{d}(p) \right|$  that allows us to define the appropriate sample rate in the  $x$  dimension. We name this bound  $\phi_x(s)$ , for a CC that we call  $s$ . By definition,
+
+$$
+\phi_ {x} (s) \geq \max  _ {p \in s} | \frac {\partial}{\partial x} \hat {d} (p) |. \tag {5}
+$$
+
+By differentiating, we find that  $\phi_x(s)$  can be bounded in terms of each nearby voxel's maximum gradient and the maximum TSDF differences across voxels (full derivation in Supp.),
+
+$$
+\begin{array}{l} \phi_ {x} (s) \leq \max  _ {v = 0.. 7} \left\{\max  _ {p} | \frac {\partial}{\partial x} \hat {d} _ {v} (p) | \right\} + \\ \max  _ {v = [ 0, 1, 4, 5 ]} \left\{\max  _ {p} | \hat {d} _ {v + 2} (p) - \hat {d} _ {v} (p) | \right\}. \tag {6} \\ \end{array}
+$$
+
+Note, however, the terms  $\max_p\left|\frac{\partial}{\partial x}\hat{d}_v\right|$  and  $\max_p\left|\hat{d}_v - \hat{d}_w\right|$ . We do not know these per-voxel maxima a priori. Therefore, we further develop upper bounds on those terms. Here we only show this process for the first term,  $\max_p\left|\frac{\partial}{\partial x}\hat{d}_v\right|$ , leaving the second for the Supp. We can expand the absolute value into a max and a min,
+
+$$
+\max  _ {p} \left| \frac {\partial}{\partial x} \hat {d} _ {v} (p) \right| = \max  \left\{\left| \max  _ {p} \frac {\partial}{\partial x} \hat {d} _ {v} (p) \right|, \left| \min  _ {p} \frac {\partial}{\partial x} \hat {d} _ {v} (p) \right| \right\}. \tag {7}
+$$
+
+Considering just the max term for illustration, and leaving the details for the Supp., we find,
+
+$$
+\max  _ {p} \frac {\partial}{\partial x} \hat {d} _ {v} (p) \leq \sum_ {i} \mathcal {F} (v) ^ {(i)}. \left\{ \begin{array}{l l} \max  _ {p} \frac {\partial}{\partial x} \beta_ {i} (p) & \mathcal {F} (v) ^ {(i)} \geq 0 \\ \min  _ {p} \frac {\partial}{\partial x} \beta_ {i} (p) & \mathcal {F} (v) ^ {(i)} <   0 \end{array} . \right. \tag {8}
+$$
+
+The terms  $\max_p\frac{\partial}{\partial x}\beta_i(p)$  and  $\min_p\frac{\partial}{\partial x}\beta_i(p)$  can be computed in a one-time offline step, after training: we densely sample each basis over the domain of one voxel, and compute the gradient by finite differences. Eq. 8 is an important result: it says that we can bound the TSDF gradient within a voxel as a function of the voxel feature, and the maximum gradients of the individual bases, which are available for free at test time. Plugging this back into Eq. 7 and then Eq. 6, we can quickly compute  $\phi_x$  for each CC.
+
+We then compute the desired distance between sample points as
+
+$$
+\Delta x = \frac {\Delta d}{\phi_ {x} (s)}. \tag {9}
+$$
+
+By spacing our samples at most  $\Delta x$  apart, we are guaranteed to capture every predicted TSDF change of at least  $\Delta d$ . This is because  $\phi$  is a gradient bound, so the predicted TSDF variation cannot exceed it. Thus, the parameter  $\Delta d$  represents a maximum acceptable degree of aliasing. In practice, our final per-CC sample rates are clamped and rounded up to the nearest integer,
+
+$$
+R _ {x} = \min  \left(\left\lceil \frac {1}{\Delta x} \right\rceil , R _ {\max }\right), \tag {10}
+$$
+
+where  $R_{\mathrm{max}}$  is a cap that can be set to avoid diminishing returns at high resolutions.
+
+# 5.2. Non-uniform marching cubes
+
+We use dual marching cubes (DMC) [29] to extract the zero-isosurface. DMC was introduced as a way to run marching cubes [21] on octrees. Its main steps are 1) generate the dual grid by connecting sample points as shown by the dotted lines in Fig. 4, and 2) run marching cubes on the dual grid. Degenerate dual cells (appearing as dotted triangles in Fig. 4) are handled by duplicating the cell vertices to make them topological cubes.
+
+To adapt DMC to our problem setting, we make two modifications. First, we skip two of DMC's preliminary stages (feature isolation and octree construction) that are designed to generate and optimize the sample point locations. This is because in our framework the sample point locations are already determined by our adaptive sampling strategy. Second, whereas DMC recurses through its multilevel octree using a fixed number of operations per octree cell, we instead build the dual grid iteratively, computing the centers and the connectivity of the dual cells as a function of the adaptive sample rates.
+
+![](images/6d2a3ad40d52595b4194abb58c64b35a74c278079da3b992fdb52e1bca0a4a23.jpg)  
+Figure 4. Each central cube (CC) has a sample rate in each dimension, chosen arbitrarily for this 2D illustration. Dual marching cubes (DMC) [29] generates the dual grid by connecting the sample points as shown by the dotted lines, and then it runs marching cubes [21] on the resulting graph, handling degenerate cells by duplicating their vertices to make them topological cubes. The green line shows the zero-isosurface of the underlying continuous TSDF, and the yellow line shows the surface extracted by adaptive sampling and DMC.
+
+# 6. Training
+
+To train our system we assume the existence of a ground truth surface mesh for each scene, and we train in a fully-supervised manner.
+
+# 6.1. Ground truth generation
+
+We sample two sets of training points from the ground truth mesh. First,  $P_{\mathrm{surf}}$  is a set of points obtained by uniform random sampling over the mesh surface, and for each point  $p \in P_{\mathrm{surf}}$  we also sample the local mesh surface normal  $\vec{S}(p)$ . Second,  $P_{\mathrm{unif}}$  is a set of points sampled on a 4 cm regular grid throughout the entire volume of the scene. We compute the ground truth TSDF  $d(p), p \in P_{\mathrm{unif}}$  by rendering the ground truth mesh to a set of depth maps, and running TSDF fusion [6]. We also define the ground truth occupancy  $O$  as
+
+$$
+O (p) = | d (p) | <   t, p \in P _ {\text {u n i f}}, \tag {11}
+$$
+
+where  $t$  is the truncation distance parameter of the TSDF fusion. Similar to Atlas [22] we then mark any entirely unobserved columns of points as unoccupied, to avoid producing artifacts outside the scene walls. However, we use a cumulative product test to make sure we only apply this label outside of the scene walls, and not in the center of the scene, which is frequently unobserved. This prevents the pillar artifacts that can be seen in previous work [22]. Finally, we filter by occupancy to further define a new subset of points that are near surfaces,  $P_{\mathrm{occ}} = \{p : p \in P_{\mathrm{unif}}, O(p) = 1\}$ .
+
+# 6.2. Loss function
+
+Unlike previous works that rely solely on direct TSDF supervision, we find that supervising the TSDF gradient leads to better results. Inspired by Neural Poisson [7], we begin with a squared-error gradient loss,
+
+$$
+\mathcal {L} _ {\operatorname {g r a d}} (p) = \| \nabla \hat {d} (p) - \vec {S} (p) \| _ {2} ^ {2}, p \in P _ {\text {s u r f}}, \tag {12}
+$$
+
+where  $\nabla \hat{d}$  is the analytical gradient of our TSDF prediction and  $\vec{S}$  is the ground truth mesh surface normal. We find that to get the best quality, an additional constraint is necessary to enforce 0 TSDF magnitude at the surface,
+
+$$
+\mathcal {L} _ {\text {s u r f}} (p) = | \hat {d} (p) |, p \in P _ {\text {s u r f}}. \tag {13}
+$$
+
+We then apply a weaker form of direct TSDF supervision based on the smooth  $L_{1}$  loss [25],
+
+$$
+\operatorname {s m o o t h} _ {L _ {1}} (x) = \left\{ \begin{array}{l l} 0. 5 x ^ {2} & | x | <   1 \\ | x | - 0. 5 & | x | \geq 1, \end{array} \right. \tag {14}
+$$
+
+and we only apply this loss within occupied regions. Our TSDF loss is thus
+
+$$
+\mathcal {L} _ {\text {d i s t}} (p) = \operatorname {s m o o t h} _ {L _ {1}} (\hat {d} (p) - d (p)), p \in P _ {\mathrm {o c c}} \tag {15}
+$$
+
+The occupancy predictions are trained on points uniformly sampled throughout the scene,
+
+$$
+\mathcal {L} _ {\mathrm {o c c}} (p) = \mathrm {B C E} (\hat {O} (p), O (p)), p \in P _ {\text {u n i f}}. \tag {16}
+$$
+
+We finally add the basis gradient loss,
+
+$$
+\mathcal {L} _ {\text {b a s i s}} (p) = \left| \mathcal {F} (v) ^ {(i)} \nabla \beta_ {i} (p) \right|, p \in P _ {\text {u n i f}} \cup P _ {\text {s u r f}}, v \in N (p). \tag {17}
+$$
+
+Without this loss, we notice that the network may reconstruct low-gradient regions, such as empty space, by summing two bases with high gradient in opposite directions. This causes us to estimate a high gradient bound and thus over-sample. This loss encourages the network to learn a minimal-gradient representation, which allows us to reduce our sample rates. Our combined training loss is then,
+
+$$
+\mathcal {L} = \lambda_ {g} \mathcal {L} _ {\text {g r a d}} + \lambda_ {s} \mathcal {L} _ {\text {s u r f}} + \lambda_ {d} \mathcal {L} _ {\text {d i s t}} + \lambda_ {o} \mathcal {L} _ {\text {o c c}} + \lambda_ {b} \mathcal {L} _ {\text {b a s i s}}. \tag {18}
+$$
+
+# 7. Implementation details
+
+Like FineRecon [34], we find that there are diminishing returns at resolutions finer than  $1\mathrm{cm}$ . We therefore set the parameter  $\Delta d = 1\mathrm{cm}$ , aiming to resolve structures at least  $1\mathrm{cm}$  thick. Similarly, we set  $R_{\max} = 4$ , thus clamping our finest resolution to  $1\mathrm{cm}$ . We set  $\lambda_s = \lambda_d = \lambda_o = \lambda_b = 1$  and  $\lambda_g = 3$ . Training takes about 30 hours with two NVIDIA 4090 GPUs, and testing for all methods is done on one NVIDIA 4090.
+
+![](images/841ae183bcae35e6dd8029f36071b62e2eddb45c00173889d6e2900ba411ef8e.jpg)  
+Atlas
+
+![](images/276feeeb16359f87b73178f1db383af988e85e63d42ab084c5bb142495e4166b.jpg)  
+NeuralRecon
+
+![](images/a41bff2ec4f171ac607ca3e44fcbdd04101dde1ad16f805745cd32aa0a4ecf63.jpg)  
+VoRTX
+
+![](images/7bd4d39ee6c5adb76bb650acfe9b4567b318ea8134858bea9ce26b9042a8c49e.jpg)  
+FineRecon
+
+![](images/54e687e0211fa2e5727dad5d0e59f9e1a51a7662bf76ef2b9d6ca4b003af01b4.jpg)  
+Ours
+
+![](images/6a0a71f4bb3c51718795ac40dcbaeff142756016b8907e6eab19ad7c55263ba2.jpg)  
+Ground truth
+
+![](images/8c2b3aa920eee8488a626f65e7026a30d72561dd246f8233886ba912bf3bbb00.jpg)
+
+![](images/be001b860218b1dca6c75ae3a8e7b2bd9d43b53e7580c9f30805572340506dd5.jpg)
+
+![](images/2f5656baaccecea4fd37e0da397d44309ac4354c9d5eeb5e5fcedebbeb1d787e.jpg)
+
+![](images/f25b312bd13afd149d88805954e6bb7c0a2ae8f168df843e0fc31cfeea2845be.jpg)
+
+![](images/bd62d92c4f3e7ffd6766cd36677e951d79c32da8cd4b27b3e69235737214c5c8.jpg)
+
+![](images/96e10f520d3e0947534e5fa7e3a673cc782455df4cdbc9d2eb04cd1004b4f176.jpg)
+
+![](images/b40fb8edfb926c5aa64d90375d1961a7a01ef3fda6a46965e661fcf1f26e208f.jpg)
+
+![](images/6fb0d05851ec8c3ad4de6ff20ebda9cb8e8674b05d1b21249d1c1827c43c5e23.jpg)
+
+![](images/6a1f9cb587111c72ca98af5604c541bd1eb7d70f63ebfbbb1d00c5bda3c3f11d.jpg)
+
+![](images/ed92dde4bed448ac22f3bb1f8e08dc20f31777866c35c9dbbdbf6d7798b82dcc.jpg)
+
+![](images/c0d75c33ce359592be3e8e26ffe4b907fec84967a716e6d8dbe5bbee1fe18366.jpg)
+
+![](images/0692d38ebdcebd893623afc5de92ff9c8d3ac6f0749a9fae81d96880da692234.jpg)
+
+![](images/60fa3de6afcd435406505cd415f5b38c3fedb9badcc54983f7ec0f5fed661f81.jpg)
+
+![](images/65d3f95c1fb07bfdf58668c3e28c86915c643058330a17052e3e825e49683e10.jpg)
+
+![](images/be7c457b1a73a4fdbe62bc393e42fee4ced12e5729cd06619cca7614ccbe4a1c.jpg)
+
+![](images/c1db5f05280f85775cee43fa1e3fde184e515af42137f6bc983a5a0abbf7c0e5.jpg)
+
+![](images/5b9b38683edcb3994569a0ae094f34e17ed65ba55cd9bb7dbc92717bf9eba22e.jpg)
+
+![](images/50f739b0f3462942e6ae973f24e7a2face5a84e0ce01fd05266f9c581b89c20d.jpg)
+
+![](images/59a7b8f53aad1ccd6f8979126b162bab948fcc81f931d9a2359835454c2a81af.jpg)
+
+![](images/dfb2e520123fe2c4ca8f2bfa27e79e42f5fcdf8db9ed9cb2fb5e6d967ddca55b.jpg)
+
+![](images/7522c7f275e8de9fb2338f45c75ebfc98ef6257d0ad2b411cd33c1e2d305feb5.jpg)
+
+![](images/73ac648d9c03bda4b2853a11eaf8816a35abcd8b5273dc0b6cfec35af28d2584.jpg)
+
+![](images/798e04485f909fe62f7f806a4988ea16f1571e7c171fbe7da750d9228ea59136.jpg)
+
+![](images/989258a363522812668fbdcadaea1f56b3f9afcf76c096041e2b5777ab40d580.jpg)
+
+![](images/de127b824cd7faa18e7c1c9c51b11a1d8d7c13804125e5f7c315fd780ba72ad0.jpg)
+
+![](images/521fd4c6e7a67d113a34a3f4b69a14c764e2cf30184d64adb21b4f30988a265f.jpg)
+
+![](images/9bce69d223c4b17d2e4e6863c7ffb8e694f0b991becee80c4485613efa75965b.jpg)
+
+![](images/377e705dc19f9e4cbd93f3b4a5455d7a84b046b31e9ea07f51db680b08277d8f.jpg)
+
+![](images/ff8b2ef06ce8dec01ff1564fda9e8df6fc8f21cefcd17e070b407dd3719ce318.jpg)
+
+![](images/b6708a73917f600a1fafeb6a35048ace70894c382148e8b74b200d37839f2aa0.jpg)
+
+![](images/0193f96486f2484b4cd0fe3e386028fa030599e44c5a1ff63a041a7d540e5640.jpg)  
+Figure 5. Qualitative comparison on the ScanNet dataset [8]. In terms of accuracy, our results are on par with the state of the art (FineRecon [34]). However, as shown in Table 1, our method is an order of magnitude faster to extract surfaces. Our surfaces also tend to be quite smooth, without the bumpy textures produced by the other methods (Atlas [22], NeuralRecon [35], VoRTX [32], and FineRecon [34]).
+
+![](images/b7ad3c7e7e1aeabc5def4e3268384c61108d7974e1b3e28f2709ed832af321c6.jpg)
+
+![](images/f6c4750dfca8d0fdfcf73dd2c3608cd5352f74b30470ad6e3d25235d1f901b8f.jpg)
+
+![](images/116c269f07c0fe797c673707652f2d5633f5e5d949237591ebca1117950fdac8.jpg)
+
+![](images/6ab23d42d4b11628850d575bb886dfcf33ba397f7abd4d8e37363cd47a89fa3b.jpg)
+
+![](images/4c2f6fc54c5bcdf3239fe0eb385236c2ce4a8bdd7bf122870326787a59119cca.jpg)
+
+<table><tr><td>Method</td><td>Resolution</td><td>F-Score ↑</td><td>Chamf. (cm) ↓</td><td>Mesh size (MB) ↓</td><td>Per-frame (ms) ↓</td><td>SEL (s) ↓</td></tr><tr><td>Atlas</td><td>4cm (uniform)</td><td>65.4</td><td>6.13</td><td>2.58</td><td>29.4</td><td>0.93</td></tr><tr><td>NeuralRecon</td><td>4cm (uniform)</td><td>60.4</td><td>7.75</td><td>3.59</td><td>8.4</td><td>0.20</td></tr><tr><td>VoRTX</td><td>4cm (uniform)</td><td>69.5</td><td>5.59</td><td>2.13</td><td>7.3</td><td>2.04</td></tr><tr><td>FineRecon</td><td>1cm (uniform)</td><td>74.1</td><td>4.39</td><td>54.85</td><td>37.8</td><td>24.81</td></tr><tr><td>Ours</td><td>1cm (adaptive)</td><td>74.0</td><td>5.29</td><td>5.47</td><td>10.2</td><td>1.11</td></tr></table>
+
+![](images/69f2cd896bd0cc2f6a20dee1ed5b01feb49f80dd5bcf9b9df2d93344fa5ad007.jpg)  
+Figure 6. Visual ablation study. Panels a-e correspond to Table 2 row a-e. All of these loss components are critical to achieving good surface quality with a low SEL.
+
+Table 1. Quantitative results on ScanNet. Our model reduces output mesh size and surface extraction latency (SEL) each by an order of magnitude relative to the state of the art (FineRecon [34]), with virtually no loss in F-score.  
+
+<table><tr><td></td><td>\( \mathcal{L}_{basis} \)</td><td>\( \mathcal{L}_{grad} \)</td><td>\( \mathcal{L}_{surf} \)</td><td>F-score ↑</td><td>Chamf. \( \downarrow \) (cm)</td><td>SEL \( \downarrow \) (s)</td></tr><tr><td>a)</td><td>✓</td><td>✓</td><td>✓</td><td>74.0</td><td>5.29</td><td>1.11</td></tr><tr><td>b)</td><td></td><td>✓</td><td>✓</td><td>74.0</td><td>5.16</td><td>2.8</td></tr><tr><td>c)</td><td>✓</td><td></td><td>✓</td><td>73.1</td><td>6.33</td><td>2.4</td></tr><tr><td>d)</td><td>✓</td><td>✓</td><td></td><td>70.1</td><td>5.68</td><td>0.94</td></tr><tr><td>e)</td><td>✓</td><td></td><td></td><td>71.4</td><td>5.62</td><td>1.0</td></tr></table>
+
+Table 2. Ablation study on ScanNet. We ablate  $L_{basis}$ ,  $L_{grad}$ , and  $L_{surf}$ , because they are new additions relative to prior works in this area. We observe that  $L_{basis}$  and  $L_{grad}$  are important for surface extraction latency (SEL).  $L_{grad}$  and  $L_{surf}$  are both important for mesh quality, as shown here and in Figure 6.
+
+# 8. Experiments
+
+# 8.1. Reconstructing ScanNet
+
+We evaluate our method on the ScanNet dataset [8] of 1,613 indoor scans. We use the official train/val/test split, and we report all results on the test set (100 scenes).
+
+Baselines. We compare our method to several others based on 3D CNNs. Atlas [22] is the first such system to our knowledge. NeuralRecon [35] and VoRTX [32] use sparse convolutions to manage computational cost, while FineRecon [34] uses depth guidance from SimpleRecon [28] to achieve very high quality, with longer compute times.
+
+Metrics. We report F-Score and Chamfer distance using the method from TransformerFusion [2]. F-score measures coarse mesh accuracy at a 5 cm threshold, whereas Cham-
+
+fer distance factors in shorter-range error (see Supp. for full definitions). We measure the per-frame time to extract features from each image and fuse them into the feature volume, and we measure the surface extraction latency (SEL). SEL is the time to obtain a surface mesh from the feature volume, and it includes the 3D CNN, any post-processing, and polygonization with marching cubes.
+
+Qualitative results. Fig. 5 shows that our meshes are similar to FineRecon [34] overall, but they tend to be smoother, eliminating FineRecon's bumpy texture. Thus we have reduced the inference time while improving the visual quality.
+
+Quantitative results. Table 1 confirms that our coarse accuracy, as measured by F-score, is on par with the state of the art. Our Chamfer distance is second-best; we attribute this to our choice not to use depth guidance, resulting in faster per-frame time than FineRecon, at the cost of missing some details. Table 3 shows a breakdown of SEL and its components. Ours incurs an average cost of  $170\mathrm{ms}$  to compute the adaptive sample rates, but this saves over 21s overall relative to FineRecon.
+
+Ablation study. In Table 2 and Fig. 6 we study the effects of various components of the supervision. In b, we show that disabling  $\mathcal{L}_{basis}$  leads to oversampling and a factor of three increase to SEL. In c, we see that when  $\mathcal{L}_{grad}$  is disabled,  $\mathcal{L}_{surf}$  squashes all near-surface TSDF predictions to zero, causing major surface artifacts. In d and e, we observe that disabling  $\mathcal{L}_{surf}$ , or  $\mathcal{L}_{surf}$  and  $\mathcal{L}_{grad}$  together, significantly degrades the surface quality.
+
+<table><tr><td></td><td>Transformer</td><td>3D CNN</td><td>Sample rate computation</td><td>Sub-sampling</td><td>Marching cubes / DMC</td><td>Total SEL</td><td># samples</td></tr><tr><td>Atlas</td><td>-</td><td>0.74</td><td>-</td><td>-</td><td>0.19</td><td>0.93</td><td>22.1M</td></tr><tr><td>NeuralRecon</td><td>-</td><td>0.11</td><td>-</td><td>-</td><td>0.09</td><td>0.20</td><td>2.4M</td></tr><tr><td>VoRTX</td><td>1.77</td><td>0.20</td><td>-</td><td>-</td><td>0.07</td><td>2.04</td><td>0.5M</td></tr><tr><td>FineRecon</td><td>-</td><td>0.14</td><td>-</td><td>21.68</td><td>2.58</td><td>24.81</td><td>25.9M</td></tr><tr><td>Ours (unif.)</td><td>-</td><td>0.12</td><td>-</td><td>3.27</td><td>2.02</td><td>4.90</td><td>25.9M</td></tr><tr><td>Ours</td><td>-</td><td>0.12</td><td>0.17</td><td>0.35</td><td>0.48</td><td>1.11</td><td>3.3M</td></tr></table>
+
+Table 3. Breakdown of the time costs for surface extraction latency (SEL), in seconds. Ours (unif.) has the same architecture and weights as Ours, but uses a dense 1 cm sampling strategy like FineRecon. Comparing Ours (unif.) to FineRecon shows that our sub-sampling is  $6.6 \times$  faster due to our architectural changes (additional discussion in Supp.). Comparing Ours (unif.) to Ours shows a further  $9.4 \times$  reduction in sub-sampling time due to our adaptive sampling, leading to a  $22.3 \times$  overall SEL reduction relative to FineRecon. Note, Atlas uses a large fixed size scene volume leading to high sample count. NeuralRecon and VoRTX reduce this using sparsity (occupancy filtering). FineRecon and Ours (unif.) also leverage sparsity, but have high sample count due to dense sub-sampling.
+
+# 8.2. Reconstructing ScanNet++
+
+We have trained and tested our method on the newer ScanNet++ dataset [39], and we find that it generalizes well with no parameter changes needed. Fig. 1 shows an example. Previous works have not been thoroughly evaluated on this new dataset so it is difficult to provide fair baselines, but we include our metrics and qualitative results in the Supp.
+
+# 9. Discussion
+
+Mesh quality. We produce high-quality meshes, without resorting to expensive depth guidance. We are able to do this because our supervision is entirely based on the ground truth mesh, instead of using noisy depth maps, thus giving our model access to a higher-quality training signal.
+
+Analytical gradient bounds. A core element of our work is the derivation of a fast and effective local gradient bound. It is also possible to derive such a bound for previous models [2, 34]; however, we found the resulting bounds were not tight enough to be useful, causing extreme over-sampling. Our basis functions are thus critical to our approach.
+
+# 9.1. Limitations and future work
+
+Our resolution is adaptive within each voxel, thus our resolution is never coarser than the voxel size. This presents an opportunity for further gains, particularly for large flat surfaces: in the future, perhaps we can reach across voxels to achieve a sample rate even coarser than the voxel size.
+
+As shown in Fig. 1B and 1C, our method can result in thin, sliver-shaped triangles, which are not optimal in terms of mesh size and complexity. Our method still greatly reduces mesh size overall, but addressing these slivers may yield further improvement, possibly by regularizing the sample rates or by adding a re-meshing step.
+
+Regarding representational capacity, we use a fixed number of basis functions (64). While the space of possible output geometries is quite large, there may be opportunities for improvement by allowing the network to steer the bases
+
+via rotation or other transforms. Furthermore, our sample rates are always defined along the coordinate axes. As a result, we expect the greatest efficiency when the scene surfaces are predominantly axis-aligned. A pre-alignment step might help maximize these gains, and future work may explore more flexible sampling patterns.
+
+While the ideal sample distance defined in Eq. 9 provides a guarantee against aliasing, we note that this refers to aliasing of the model's predicted continuous TSDF field. It is of course possible to alias the true scene TSDF. In addition, with Eq. 10 we cap the maximum sample rate; thus, the guarantee is technically not valid in those capped regions, but we see very little evidence of aliasing in practice.
+
+# 10. Conclusion
+
+We have presented AniGrad, a 3D reconstruction system for monocular video that automatically adapts its resolution to the local 3D surface structure. To make this possible, we have introduced a new representation of the predicted TSDF as a linear combination of learned, local 3D basis functions. This representation enables us to efficiently compute bounds on the local TSDF gradient, and we set the local resolution proportionally to this bound. As a result, we can extract a mesh from our feature volume with a latency reduction of over  $20\times$ , without sacrificing accuracy. This method makes 3D reconstruction more accessible for compute-limited devices, which otherwise may not meet the necessary speed and throughput requirements. This is essential for applications such as mobile augmented reality and robotics that need to repeatedly extract surface meshes with low latency. Our method makes a step in this direction.
+
+# Acknowledgements
+
+Support for this work was provided in part by ONR grant N00014-23-1-2118 as well as NSF grant IIS-2211784. We would also like to thank Ziyue Feng for many insightful discussions during the early stages of this project.
+
+# References
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+# Animer: Animal Pose and Shape Estimation Using Family Aware Transformer
+
+Jin Lyu $^{1,\ast}$ , Tianyi Zhu $^{2,\ast}$ , Yi Gu $^{3}$ , Li Lin $^{1,4}$ , Pujin Cheng $^{1,4}$ , Yebin Liu $^{5}$ , Xiaoying Tang $^{1,\dagger}$ , Liang An $^{5,\dagger}$ $^{1}$ Southern University of Science and Technology  
+ $^{2}$ China Mobile Research Institute  
+ $^{3}$ The Hong Kong University of Science and Technology  
+ $^{4}$ The University of Hong Kong  $^{5}$ Tsinghua University
+
+# Abstract
+
+Quantitative analysis of animal behavior and biomechanics requires accurate animal pose and shape estimation across species, and is important for animal welfare and biological research. However, the small network capacity of previous methods and limited multi-species dataset leave this problem underexplored. To this end, this paper presents AniMer to estimate animal pose and shape using family aware Transformer, enhancing the reconstruction accuracy of diverse quadrupedal families. A key insight of AniMer is its integration of a high-capacity Transformer-based backbone and an animal family supervised contrastive learning scheme, unifying the discriminative understanding of various quadrupedal shapes within a single framework. For effective training, we aggregate most available open-sourced quadrupedal datasets, either with 3D or 2D labels. To improve the diversity of 3D labeled data, we introduce CtrlAni3D, a novel large-scale synthetic dataset created through a new diffusion-based conditional image generation pipeline. CtrlAni3D consists of about 10k images with pixel-aligned SMAL labels. In total, we obtain 41.3k annotated images for training and validation. Consequently, the combination of a family aware Transformer network and an expansive dataset enables AniMer to outperform existing methods not only on 3D datasets like Animal3D and CtrlAni3D, but also on out-of-distribution Animal Kingdom dataset. Ablation studies further demonstrate the effectiveness of our network design and CtrlAni3D in enhancing the performance of AniMer for in-the-wild applications. Project page: https://luoxue-star.github.io/AniMer_project_page/.
+
+# 1. Introduction
+
+Animal pose and shape estimation from images is essential for capturing animal behavior, biomechanics, and interac
+
+tions with their environment, thereby yielding vital insights for animal welfare, agriculture, ecology and life sciences. The integration of geometric and appearance information from diverse species into a unified deep neural network represents a significant step to comprehensively interpret the intricate and dynamic animal world. A notable endeavor in this domain involves the estimation of pose and shape parameters from an articulated animal template known as the SMAL model [52], primarily targeting general quadrupeds. While extensive researches have been conducted regarding single species or families, such as horses [18, 54, 55] and dogs [4, 5, 17, 35-37], investigations into other quadrupedal species, including cats, cows or hippos, remain relatively underexplored.
+
+The reconstruction of multiple species within a single network is hampered by the limited capacity of backbones and the scarcity of multi-species datasets annotated with SMAL labels. Recent advancements in human mesh recovery via the SMPL model [23] have proved that using a high-capacity backbone in conjunction with large-scale datasets significantly enhances the accuracy of human pose and shape estimation in diverse settings [6, 10, 30]. However, this simple and effective paradigm remains untested within the context of animal studies. Xu et al. [45] introduce the first large-scale dataset Animal3D featuring SMAL mesh annotations; nevertheless, their study predominantly utilizes CNN-based networks such as HMR [13] and WLDO [5].
+
+In this paper, we present AniMer, a systematic approach pursuing accurate animal pose and shape estimation using Transformer which surpasses existing methodologies on all benchmarks. This success relies on two key scaling factors: scaled backbone and scaled dataset. In previous animal researches, the well-known scaled Transformer backbone proposed by ViT [46] has only been used for 2D animal pose estimation. We go beyond it by connecting ViT with a Transformer-based decoder to yield SMAL parameters, following HMR2.0 [10]. Different from HMR2.0, our Transformer is family aware by applying a new animal family supervised contrastive learning scheme, which enhances the
+
+![](images/10043b276b3c27dd69c34068baa67ccdcab0d4f596184859b2becf3c196b8df2.jpg)  
+Figure 1. CtrlAni3D dataset statistics and visual samples. Ten samples are shown for ten species in the same order of pie plot. For each image pair, the left side displays the generated animal image whose background comes from either COCO [22] or AI-synthesis, while the right side presents the rendering of the SMAL mesh label. Note that the synthesis process naturally considers generating truncated images.
+
+discrimination of animal shapes through class token. Moreover, due to the limited available data space and prior knowledge of animals compared to that of human, we change the residual parameter decoding used by HMR [13] and HMR2.0 [10] to direct parameter decoding, and adopt a two-stage training scheme to train on 3D dataset first instead of training on full dataset directly.
+
+Acquiring a large number of animal images with full 3D annotations is difficult, and synthetic datasets can mitigate the scarcity of real data. The plausibility of traditional CG-generated animal images is hindered by the coarse texture quality and sophisticated lighting and shadow control. These limitations motivate our usage of ControlNet [51] to create high quality AI hallucinated images conditioned on SMAL structures. This principle effectively bridges the domain gap between parametric labels and images, and help us to create a novel large scale dataset named CtrlAni3D with minimal human labor involved. Specifically, we prompt ControlNet with textual descriptions of animal behaviors and rendered SMAL mask and depth images, resulting in highly realistic visual outputs, as illustrated in Fig. 1. To ensure dataset quality, we use SAM2.0 [33] together with manual verification to filter implausible generated images. Finally, CtrlAni3D comprises 9711 images annotated with pixel-aligned SMAL mesh, and its scalable nature allows for further expansion. Finally, we obtain scaled dataset for AniMer training by aggregating most available open-sourced quadrupedal datasets and our CtrlAni3D, resulting
+
+in a comprehensive set of 41.3k images annotated with either 3D mesh or 2D keypoints.
+
+To rigorously evaluate the efficacy of the AntiMer model and the CtrlAni3D dataset, we conduct extensive empirical studies. Our findings indicate that AntiMer, when trained on the same full multi-species datasets, significantly outperforms CNN-based methods such as HMR and WLDO [5], which serve as baselines in the Animal3D research. Besides, compared with HMR2.0, our animal family supervised contrastive learning scheme improves the pose and shape estimation precision on all benchmarks. Through comprehensive ablation studies, we verify that CtrlAni3D enhances the generalization abilities of AntiMer on the out-of-distribution (OOD) Animal Kingdom dataset [29], which is unseen during training.
+
+# 2. Related Works
+
+Animal Pose and Shape Estimation. Compared to keypoint-based animal pose estimation methods [8, 26, 31, 50], surface-based methods could provide both shape and pose information simultaneously. In this paper, we focus on template-based methods instead of template-free methods [11, 20, 47, 49]. Reconstructing shape templates has been studied in various types of animal families such as birds [44], mice [2], non-human primates [28] and quadrupeds [53]. For quadrupeds, Zuffi et al. [52] proposes the well-known SMAL, which is built upon 41 scans of ani-
+
+mal toys. Due to the limited geometry accuracy of SMAL for representing specific species, most previous methods stride over predicting SMAL parameters only and further enhance the geometry of horses and dogs. For example, Li et al. [18] designs the horse-specific hSMAL model and applies it to the problem of video lameness detection. VAREN [55] further improves hSMAL with high quality horse scans. Similarly, the use of SMAL for dog mesh recovery is addressed by adding bone lengths control [5], by adding per-vertex deformation [17], by introducing breed loss [35], by ground contact constraints [36], or by temporal avatar optimization [37]. Though high quality reconstruction has been achieved on horses and dogs, end-to-end SMAL estimation has not been fully addressed on other challenging species. Animal3D [45] provides the first large scale 3D benchmark for general quadruped SMAL estimation, yet neglects in-depth research on the network design and training.
+
+Transformer Based Human Mesh Recovery. The Transformer architecture [42] has revolutionized the field of Natural Language Processing (NLP) by enabling unprecedented accuracy and efficiency in a wide range of tasks. Inspired by its success in NLP, one of the core part of Transformer, i.e. self-attention, has been widely used for human mesh recovery [16, 38, 39, 43]. Dosovitskiy [9] proposes Vision Transformer(ViT), which divides an image into patches as the input to Transformer. ViT has achieved state-of-the-art performance on several computer vision tasks including human mesh recovery using SMPL [10, 16, 38, 39, 43]. Among all these works, HMR2.0 [10] is a milestone which demonstrates the effectiveness of simply using ViT backbone and large scale datasets to achieve accurate mesh recovery and inthe-wild generalization ability. Inspired by this, HaMeR [30] employs ViT backbone to achieve highly accurate hand mesh recovery, which is further extended to interacting hands [21]. Similarly, SMPLer-X [6] scales up expressive human pose and shape estimation using ViT backbone and the combination of 32 datasets. Although impressive results have been achieved in human mesh recovery, the effect of ViT backbone for animal pose and shape estimation remains unexplored.
+
+Synthetic Animal Training. Compared to human pose estimation which benefits from large-scale datasets, acquiring annotated images of animals is significantly more difficult. Therefore, synthetic dataset would alleviate this problem by rendering the input and output simultaneously. Most previous methods only attempt to render RGB images [7, 27, 32, 36, 40, 45] or depth images [14] using traditional computer graphics pipelines, ignoring the image hallucination ability of generative AI models such as stable diffusion [34] or ControlNet [51]. Although traditional CG rendering achieves success in assisting network training, large scale high quality CG assets are expensive to obtain, and the plausibility of rendered images is hindered the so
+
+phisticated lighting and shadow control. In contrast, Ma et al. [25] uses 3D visual prompts and large language model (LLM) text prompts to generate diverse images from a static CAD model, pioneering a new direction. We extend their idea to animal image synthesis from dynamic SMAL animations to construct the CtrlAni3D dataset. The most similar concurrent work to us is SPAC-Net [12] which performs style-transfer from synthetic domain to real domain using ControlNet [51]. However, they rely on textured CAD assets instead of untextured SMAL, making it difficult to assist SMAL pose and shape estimation.
+
+# 3. Reconstructing Animals Using AntiMer
+
+# 3.1. Preliminaries
+
+The SMAL Model. The SMAL model, denoted as  $\mathcal{M}(\beta, \theta, \gamma)$ , is a 3D parametric shape model designed for quadrupeds. The shape parameter  $\beta \in \mathbb{R}^{41}$  is derived from 41 3D scans of various animal figurines, including cats, dogs, horses, cows, and hippos [52]. The pose parameter  $\theta \in \mathbb{R}^{35 \times 3}$  represents the rotation of each joint relative to its parent joint, expressed in terms of axis-angle. Controlled by  $\beta$  and  $\theta$ , the SMAL model outputs a mesh with vertices  $V \in \mathbb{R}^{3889 \times 3}$  and faces  $F \in \mathbb{N}^{7774 \times 3}$  through linear blend skinning (LBS) process. The animal body joints are regressed from vertices by  $J \in \mathbb{R}^{35 \times 3} = W \cdot V$ , where  $W \in \mathbb{R}^{35 \times 3889}$  represents a linear mapping matrix.
+
+Camera Projection. Following Goel et al. [10],  $\pi(\cdot)$  represents the projection process of a weak-perspective camera model, determined by a translation vector  $T \in \mathbb{R}^3$ , a fixed focal length  $f = 1000$  and thereby a fixed intrinsic matrix  $K$ . The global orientation  $R$  is the rotation of SMAL root joint, therefore we ignore it here. Consequently, a 3D point  $X$  is projected as 2D point  $x$  by  $x = \pi(X) = \Pi(K(X + T))$ , where  $\Pi$  converts homogeneous coordinates  $(u, v, d)^T$  to pixel coordinates  $(u / d, v / d)^T$ .
+
+# 3.2. The Architecture of AniMer
+
+The full architecture of AntiMer is shown in Fig. 2. Given an image  $I \in \mathbb{R}^{H \times W \times 3}$  and a class token  $\mathbf{x}_{\text{class}} \in \mathbb{R}^{1 \times 1280}$ , we first utilize a ViT encoder to extract image feature tokens  $\mathbf{F} \in \mathbb{R}^{192 \times 1280}$ , while the class token interacts with the image to capture information about the animal family. We then feed the feature tokens  $\mathbf{F}$  into a SMAL transformer decoder to obtain a feature vector  $\mathbf{f} \in \mathbb{R}^{1 \times 1024}$ . Finally, independent multi-layer perceptrons (MLPs) are used to predict the shape parameters  $\hat{\beta}$ , pose parameters  $\hat{\theta}$ , and camera parameters  $\hat{\pi}$ , where  $\hat{\cdot}$  means estimated parameters. At the same time, the class token is fed into the predictor head for animal family supervised contrastive learning, which will be detailed in Sec. 3.3. Note that the weights of ViT encoder are pretrained using Xu et al. [46], which significantly enhances mesh recovery performance.
+
+![](images/82b17ea1e7fb0f2becc30bb2f2fcd86d2178f7f32039e475286eaf378347b9c4.jpg)  
+Figure 2. AntiMert network architecture. AntiMert consists of (1) a ViT encoder that extracts image features; (2) a transformer decoder that processes the image features from the encoder; (3) a predictor head (MLPs) that generates animal family feature for supervised contrastive learning; and (4) a regression head (MLPs) that estimates the shape  $\hat{\beta}$ , pose  $\hat{\theta}$ , and camera parameters  $\hat{\pi}$ .
+
+Despite the class token, AntiMer features two key differences compared with previous HMR2.0 [10] and HaMeR [30]. First, both HMR2.0 and HaMeR regress the residual SMPL/MANO parameters with respect to the nonzero mean parameters computed from large scale motion databases. In contrast, we choose to directly decode the final SMAL parameters due to limited SMAL pose prior. Second, both HMR2.0 and HaMeR train on the whole datasets in single stage. Instead, we train AntiMer in two stages. At the first stage, we train AntiMer using only 3D data to ensure the network could predict feasible shapes and poses. At the second stage, all 3D and 2D data are introduced for training. The insight is that the size of 3D datasets for animal is much smaller than that of human at present, resulting in an imbalanced 3D and 2D data scale. Unless otherwise specified, we train two stages for 500 and 700 epochs respectively.
+
+# 3.3. Animal Family Supervised Contrastive Learning
+
+Different from human whose SMPL shape parameters come from the same multivariate normal distribution, animals demonstrate at least two levels of shape differences: interfamily level and intra-family level. For example, dogs share similar shapes between each other, yet share distinct shapes with cows. To capture such two levels of shape distributions in AniMer, we propose an animal family loss based on supervised contrastive learning [15].
+
+Specifically, we employ a learnable class token [9] to represent the animal family. First, this token  $\mathbf{x}_{\text{class}}$  together with a minibatch of images  $I \in \mathbb{R}^{B \times 3 \times H \times W}$  are fed into the ViT encoder. Typically,  $B = 16$ . Then, an MLP head is utilized to generate the animal family feature  $z$  from the class token. Finally, we directly apply supervised contrastive
+
+learning to  $z$  through loss  $\mathcal{L}_{\mathrm{con}}$  defined as follows:
+
+$$
+\mathcal {L} _ {\mathrm {c o n}} = \sum_ {i \in I} \frac {- 1}{| P (i) |} \sum_ {p \in P (i)} \frac {\exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {z} _ {p} / \tau\right)}{\sum_ {o \in O (i)} \exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {z} _ {o} / \tau\right)}. \tag {1}
+$$
+
+Within a minibatch,  $P(i)$  represents the samples that share the same family label of  $i$ ,  $O(i)$  represents the samples other than  $i$ . The notation  $|P(i)|$  denotes the size of this set.  $\tau \in \mathbb{R}^{+}$  is a scalar temperature parameter.
+
+# 3.4. Loss Functions
+
+To align animal images with reconstruction results, we train our model using a comprehensive loss function that incorporates various 2D and 3D annotations. We define the main loss function  $\mathcal{L}_{\mathrm{total}}$  as a weighted sum of several loss components, each focusing on different aspects of the model's performance. The main loss function is given by
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {3 \mathrm {D}} \mathcal {L} _ {3 \mathrm {D}} + \lambda_ {2 \mathrm {D}} \mathcal {L} _ {2 \mathrm {D}} + \lambda_ {\text {p r i o r}} \mathcal {L} _ {\text {p r i o r}} + \lambda_ {\text {a d v}} \mathcal {L} _ {\text {a d v}} \tag {2} \\ + \lambda_ {\text {c o n}} \mathcal {L} _ {\text {c o n}}. \\ \end{array}
+$$
+
+Here,  $\lambda_{\mathrm{3D}} = 0.05, \lambda_{\mathrm{2D}} = 0.01, \lambda_{\mathrm{prior}} = 0.001, \lambda_{\mathrm{adv}} = 0.0005, \lambda_{\mathrm{con}} = 0.0005$  are the loss weights. For 3D training data, all losses are used. For samples without 3D annotations, the 3D loss  $\mathcal{L}_{\mathrm{3D}}$  is disabled.
+
+3D Loss. For images annotated with SMAL model parameters  $\beta$  and  $\theta$ , we supervise these parameters directly to enable fast convergence. We also supervise the estimated 3D keypoints  $\hat{K}_{3D}$  with ground truth  $K_{3D}$  to achieve better 3D joint localization. The full 3D loss function is
+
+$$
+\mathcal {L} _ {\mathrm {3 D}} = \lambda_ {\beta} \| \hat {\beta} - \beta \| _ {2} ^ {2} + \lambda_ {\theta} \| \hat {\theta} - \theta \| _ {2} ^ {2} + \| \hat {K} _ {3 D} - K _ {3 D} \| _ {1}, \tag {3}
+$$
+
+where  $\lambda_{\beta} = 0.01$  and  $\lambda_{\theta} = 0.2$  are loss weights.  $||\cdot ||_2^2$  denotes squared L2 norm, while  $||\cdot ||_1$  represents L1 norm.
+
+2D Loss. Most training data only contain 2D-level annotations such as 2D keypoints or masks. For these data, we
+
+![](images/bcd590638aa64aeac5d35e3b76d81439020964b6abacb7cf41ded93d7c199be6.jpg)  
+Figure 3. CtrlAni3D dataset generation pipeline. The whole pipeline contains three parts: (a) Text prompt generation. (b) Conditional image generation. (c) Image generation and post-processing.
+
+supervise 2D keypoints during training using
+
+$$
+\mathcal {L} _ {2 D} = \left| \left| \pi \left(\hat {K} _ {3 D}\right) - K _ {2 D} \right| \right| _ {1}. \tag {4}
+$$
+
+Note that, masks are only used for evaluation.
+
+Prior Loss. For images with only 2D annotations, to ensure that the predicted shape and pose parameters are reasonable, we enforce them to be close to a prior distribution by calculating the Mahalanobis distance. The prior loss is
+
+$$
+\mathcal {L} _ {\text {p r i o r}} = \lambda_ {\beta} (\hat {\beta} - \mu_ {\beta}) ^ {T} \Sigma_ {\beta} ^ {- 1} (\hat {\beta} - \mu_ {\beta}) + (\hat {\theta} - \mu_ {\theta}) ^ {T} \Sigma_ {\theta} ^ {- 1} (\hat {\theta} - \mu_ {\theta}), \tag {5}
+$$
+
+where  $\lambda_{\beta} = 0.5$ ,  $\mu_{\beta}$ ,  $\Sigma_{\beta}$ ,  $\mu_{\theta}$ , and  $\Sigma_{\theta}$  are the mean and covariance of the prior distributions given by SMAL [52].
+
+Adversarial Loss. Finally, we adopt a discriminator to further ensure that the model outputs natural poses and shapes, therefore we employ an adversarial loss similar to HMR [13]. This loss is designed to make the predicted parameters indistinguishable from real distribution:
+
+$$
+\mathcal {L} _ {\mathrm {a d v}} = \sum_ {k} \left(D _ {k} (\theta , \beta) - 1\right) ^ {2}, \tag {6}
+$$
+
+where  $D_{k}$  represents a discriminator.
+
+# 4. CtrlAni3D Dataset
+
+SMAL Structure Condition. The dataset generation pipeline is illustrated in Fig. 3. Given a posed SMAL mesh and viewpoint, we render it into mask map and depth map as the condition images to guide the structure of images generated by a pre-trained ControlNet [51]. To guarantee the diversity of the poses and shapes, we randomly sample  $\beta$  from the Gaussian distributed shape space provided by SMAL [52], and sample a more diverse range of  $\theta$  from a
+
+combined pose space presented by dog [5, 36] and horse motion [19]. This is reasonable because the quadrupeds expressed by SMAL share similar anatomical structures. About the viewpoint for rendering, each dimension of the global rotation vector is uniformly sampled from  $(-\pi, \pi)$  while the position is uniformly sampled between  $[-0.5, -0.5, 4]$  and  $[0.5, 0.5, 8]$ , therefore possible truncated images may be generated to enhance the robustness of training.
+
+Text Condition. To further control the style of generated images  $x$ , we seek to use text prompt. We first manually classify the sampled 3D meshes into 10 species: cat, tiger, lion, cheetah, dog, wolf, horse, zebra, cow and hippo, and use species name as one keyword. When hard to distinguish (e.g., some hard cases of zebra/horse), we use both animal names as prompts and select the one with the highest cycle consistency. The second keyword is the pose description, e.g. "stands" in Fig. 3, which is assigned by human annotator according to the 3D mesh. Based on these keywords, ChatGPT [1] is employed to complete a prompt sentence  $c_t$  depicting possible animal behaviors. Finally, both  $c_v$  and  $c_t$  act as the prompts of ControlNet for realistic and rich image generation.
+
+Semi-Automated Filtering. Note that, not all generated images are perfectly aligned with conditions. To address this, we design a semi-automated filtering strategy to lower the burden of annotators. First, SAM2 [33] is utilized to extract the foreground mask of the generated images, enabling cycle-consistency checking by comparing to conditioned mask. Further, we manually filter out images that do not match the mesh poses to ensure good data quality. Each synthetic image has a resolution of  $512 \times 512$  and includes well-aligned annotations for  $\beta$ ,  $\theta$ ,  $\gamma$  and 3D keypoints. By comparing rendered depth image the projected keypoint depths, we also
+
+obtain visible 2D keypoints as annotation. Supplementary Material demonstrates both success cases and failure cases that are manually filtered.
+
+Backgrounds. To ensure the background diversity, we randomly sample COCO [22] images to serve as backgrounds for 2/7 of the CtrlAni3D images. The selection of the proportion of the COCO background can be referenced in the Supplementary Materials.
+
+# 5. Experiments
+
+# 5.1. Setup
+
+Datasets. We curate and aggregate multiple datasets containing 2D and 3D annotations for animals. The full dataset include the training split of Animal Pose [7], APT-36K [48], AwA-Pose [3], Stanford Extra [5], Zebra synthetic [54], Animal3D [45], and our own CtrlAni3D. Only Animal3D, CtrlAni3D and Zebra synthetic have 3D annotations. The full dataset contains  $41.3\mathrm{k}$  images, and validation ratio is  $3/20$ . For evaluation, we mainly use the test part of Animal3D and CtrlAni3D, and Animal Kingdom dataset [29]. Note that, Animal Kingdom serves as out-of-distribution (OOD) benchmark because it contains very challenging in-the-wild images which are never seen during training. Only 8 quadruped species from Animal Kingdom are selected for testing. For more details about the datasets, please refer to the Supplementary Material.
+
+Training Details. Our model is implemented by Pytorch. We use AdamW [24] optimizer with a linear learning rate decay schedule. The initial learning rate is  $1.25 \times 10^{-6}$ . The entire training takes a week on a NVIDIA RTX 4090 GPU. Metrics. Several 3D and 2D metrics are employed to fully assess the model performance, listed below. PA-MPJPE is Procrustes-Aligned Mean Per Joint Position Error for regressed 3D keypoints. PA-MPVPE is Procrustes-Aligned Mean Per Vertex Position Error for SMAL vertices. PCK is Percentage of Correct Keypoints given a threshold. In this paper, PCK is only used for evaluating 2D keypoints. PCK@HTH uses half the head-to-tail distance as the threshold. By setting threshold to 0.1 and 0.15, we get commonly used PCK@0.1 and PCK@0.15 metrics. AUC is Area Under the Curve value when the PCK threshold gradually increase from 0 to 1. Note that, MPJPE without Procrustes-Alignment is not used because large animal size variations would cause imbalanced MPJPE among species.
+
+# 5.2. Multi-Species Experiments
+
+Following the practice of Animal3D dataset [45], we utilize HMR [13] and WLDO [5] as baselines. Furthermore, to highlight the significance of our ViT backbone and backbone pretraining, we compare the final AniMer with two variants: AniMer-a which replaces ViT backbone with ResNet152, and AniMer-b which discards ViT pretraining. To be fair,
+
+all above methods are trained on our full dataset with the same losses and the same two-stage training strategies. Also, we compare to HMR2.0 [10] to highlight our special design choices. Ablation study on different encoder and decoder designs can be found in the Supplementary Material.
+
+Quantitative results are shown in Tab. 1. We observed that our AntiMer method achieved state-of-the-art results and that both 3D metrics and 2D metrics consistently outperformed previous work on multiple datasets. Specifically on Animal Kingdom dataset, AntiMer demonstrates strong robustness and improves over the previous work for all the metrics. Qualitative results in Fig. 4 show that AntiMer aligns with images much better for thin structures such as legs and tails. More qualitative results are shown in Supplementary Material.
+
+# 5.3. Ablation Study on CtrlAni3D
+
+To further demonstrate the effectiveness of our proposed CtrlAni3D dataset in enhancing network capabilities, we conduct a series of ablation experiments. We compare models trained on different combinations of Animal3D dataset (A3D), CtrlAni3D dataset (C3D), and other datasets (others). The hyperparameter training settings remain unchanged.
+
+Specifically, Tab. 2 indicates that our model, when trained with CtrlAni3D, exhibits superior performance even on previously unseen in-the-wild data. Qualitative comparisons in Fig. 5 further demonstrates that training with CtrlAni3D helps AniMer to yield more accurate animal terminal body parts such as tails, limbs and faces.
+
+To further emphasize the superiority of our diffusion based pipeline over traditional CG synthetic dataset, we follow the experiments performed by Animal3D [45], see Tab. 3. Specifically, "HMR" means directly training HMR on Animal3D. "HMR-Synthetic" pretrains HMR with a CG-based synthetic dataset generated by textured SMAL [53] for 100 epochs before training on Animal3D. Similarly, "HMR-CtrlAni3D" pretrains HMR on CtrlAni3D for 100 epochs. It is clearly shown that CtrlAni3D provides better pretraining than traditional CG based synthetic data. Additional ablation studies on CtrlAni3D, as well as a comparison between CtrlAni3D and Animal3D, can be found in the Supplementary Material.
+
+# 5.4. Ablation Study on Animal Family Supervised Contrastive Learning
+
+Finally, we conduct experiments to demonstrate the effects of animal family supervised contrastive learning. Tab. 4 presents the quantitative results on Animal3D, CtrlAni3D, and Animal Kingdom. As we can see, AniMer trained with  $\mathcal{L}_{\mathrm{con}}$  outperforms the model that does not utilize  $\mathcal{L}_{\mathrm{con}}$ . The improved PA-MPVPE and PA-MPJPE metrics indicate that  $\mathcal{L}_{\mathrm{con}}$  enhances the model's capabilities in shape and pose estimation, respectively.
+
+![](images/9322351b0e8cb90b958aa469498614d5afcfdfe55cb6713766b53ccb72b4f5eb.jpg)  
+Figure 4. Qualitative comparisons on Animal3D, CtrlAni3D and Animal Kingdom datasets. We compare our results with HMR [13], WLDO [5], AniMer-a (ResNet152 backbone), AniMer-b (no pretraining) and HMR2.0 [10].
+
+In addition, to provide a more intuitive understanding of the effect of  $\mathcal{L}_{\mathrm{con}}$ , Fig. 6 presents the t-SNE [41] visualization of the class token on Animal3D test set. It is evident that  $\mathcal{L}_{\mathrm{con}}$  brings the features of animals from the same family closer together, thereby enhancing the model's ability to distinguish between the shapes of animals from different families. Fig. 7
+
+further demonstrates that  $\mathcal{L}_{\mathrm{con}}$  enables the model to better distinguish between different animal families. As shown in Fig. 7, when trained without  $\mathcal{L}_{\mathrm{con}}$ , the model incorrectly predicts a zebra, bear, and antelope as a dog, zebra, and cow, respectively. More discussion about family contrastive loss can be found in the Supplementary Material.
+
+Table 1. Quantitative comparisons on Animal3D, CtrlAni3D and AnimalKingdom datasets. Bold numbers indicate the best values. P@H, P@0.1, P@0.15, PAJ, and PAV represent PCK@HTH, PCK@0.1, PCK@0.15, PA-MPJPE, and PA-MPVPE, respectively.  
+
+<table><tr><td>Dataset</td><td colspan="4">Animal3D</td><td colspan="4">CtrlAni3D</td><td colspan="4">Animal Kingdom</td></tr><tr><td>Metric</td><td>AUC↑</td><td>P@H↑</td><td>PAJ↓</td><td>PAV↓</td><td>AUC↑</td><td>P@H↑</td><td>PAJ↓</td><td>PAV↓</td><td>AUC↑</td><td>P@H↑</td><td>P@0.1↑</td><td>P@0.15↑</td></tr><tr><td>HMR</td><td>76.3</td><td>60.8</td><td>123.5</td><td>133.9</td><td>80.8</td><td>67.0</td><td>123.5</td><td>133.9</td><td>70.2</td><td>64.0</td><td>12.8</td><td>25.6</td></tr><tr><td>WLDO</td><td>78.2</td><td>68.7</td><td>112.3</td><td>125.2</td><td>88.7</td><td>86.7</td><td>71.5</td><td>83.4</td><td>70.1</td><td>64.3</td><td>14.6</td><td>27.6</td></tr><tr><td>AniMer-a</td><td>75.2</td><td>57.2</td><td>115.5</td><td>128.7</td><td>80.3</td><td>66.0</td><td>117.0</td><td>129.4</td><td>68.9</td><td>62.5</td><td>10.2</td><td>21.3</td></tr><tr><td>AniMer-b</td><td>60.6</td><td>38.9</td><td>147.9</td><td>157.6</td><td>78.5</td><td>65.9</td><td>102.3</td><td>112.6</td><td>45.4</td><td>31.8</td><td>4.0</td><td>9.2</td></tr><tr><td>HMR2.0</td><td>86.7</td><td>84.6</td><td>94.1</td><td>98.5</td><td>91.8</td><td>93.0</td><td>60.9</td><td>66.4</td><td>77.3</td><td>73.9</td><td>22.7</td><td>40.2</td></tr><tr><td>AniMer</td><td>88.9</td><td>89.5</td><td>80.4</td><td>85.7</td><td>93.8</td><td>95.4</td><td>44.1</td><td>47.6</td><td>82.9</td><td>83.7</td><td>34.9</td><td>54.7</td></tr></table>
+
+Table 2. Effect of CtrlAni3D on 2D datasets. We report AUC, PCK@0.1 and PCK@0.15 as 2D metrics. Bold numbers indicate the best performance.  
+
+<table><tr><td rowspan="2">Testset</td><td colspan="3">Training Data</td><td colspan="3">2D Metric</td></tr><tr><td>A3D</td><td>C3D</td><td>others</td><td>AUC↑</td><td>PCK@0.1↑</td><td>PCK@0.15↑</td></tr><tr><td rowspan="4">Animal Kingdom</td><td>✓</td><td>✓</td><td>✓</td><td>82.7</td><td>33.8</td><td>53.2</td></tr><tr><td>✓</td><td>✓</td><td></td><td>81.9</td><td>32.1</td><td>51.8</td></tr><tr><td>✓</td><td></td><td>✓</td><td>82.1</td><td>33.7</td><td>53.2</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>82.9</td><td>34.9</td><td>54.7</td></tr><tr><td rowspan="4">Animal Pose</td><td>✓</td><td>✓</td><td>✓</td><td>85.5</td><td>41.5</td><td>63.7</td></tr><tr><td>✓</td><td>✓</td><td></td><td>82.9</td><td>33.4</td><td>55.4</td></tr><tr><td>✓</td><td></td><td>✓</td><td>85.3</td><td>40.4</td><td>63.0</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>85.8</td><td>42.9</td><td>65.1</td></tr></table>
+
+![](images/a8e169c664716ceab69068d336b53de07d6c45011795c6c1ede5331ce054eda5.jpg)
+
+![](images/eac951ac0b36e86880b20d10d37d00dfad2448a93706f193ee6a6091dec3aeea.jpg)  
+Input Image
+
+![](images/9e312d935dd3df3dfcf68eb5be56f00c4995f6240b26b62e18ada763eba6a2c6.jpg)
+
+![](images/510802fde6908b16e8854dd106af1e76838fda5768fb9c39a058ad9178fecae5.jpg)  
+w/o CtrlAna3D
+
+![](images/0c55e1ea646f90b7495f7df292d2f26c9ec33adb386fcddf85cb9db86e789833.jpg)
+
+![](images/a41b1e4e926dc7b4d049ed48701a30222a6eea974f12296e1ad871707be1e4b9.jpg)  
+w/ CtrlAni3D
+
+Table 3. CtrlAni3D v.s. CG synthetic data. The values of "HMR-Synthetic" are borrowed from paper Xu et al. [45].  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Animal3D</td></tr><tr><td>PCK@HTH↑</td><td>PA-MPJPE↓</td></tr><tr><td>HMR</td><td>60.5</td><td>127.8</td></tr><tr><td>HMR-Synthetic</td><td>63.1</td><td>124.8</td></tr><tr><td>HMR-CtrlAni3D</td><td>64.0</td><td>121.9</td></tr></table>
+
+Table 4. Effect of animal family supervised contrastive learning. \*\* indicates training on Animal3D and CtrlAni3D only. PAJ: PA-MPJPE.PAV:PA-MPVPE.P@0.1:PCK@0.1.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Animal3D</td><td colspan="2">CtrlAni3D</td><td colspan="2">Animal Kingdom</td></tr><tr><td>PAJ↓</td><td>PAV↓</td><td>PAJ↓</td><td>PAV↓</td><td>AUC↑</td><td>P@0.1↑</td></tr><tr><td>w/o Lcon*</td><td>82.5</td><td>88.0</td><td>54.6</td><td>59.2</td><td>81.4</td><td>30.4</td></tr><tr><td>w/ Lcon*</td><td>80.8</td><td>86.0</td><td>46.1</td><td>50.2</td><td>81.9</td><td>32.1</td></tr><tr><td>w/o Lcon</td><td>81.3</td><td>86.7</td><td>44.7</td><td>48.4</td><td>82.7</td><td>34.4</td></tr><tr><td>w/ Lcon</td><td>80.4</td><td>85.7</td><td>44.1</td><td>47.6</td><td>82.9</td><td>34.9</td></tr></table>
+
+# 6. Conclusion
+
+Summary. This paper presents AniMer, a simple yet effective method for accurate animal pose and shape estimation. The key to the success of AniMer is a large capacity Trans-
+
+![](images/3227191c7aa357e74c1914666b8d1321dfbc161d0902dd203ae6c6f31cb0df3d.jpg)  
+Figure 6. The t-SNE [41] visualization of the class token on the Animal3D test set. With the inclusion of  $\mathcal{L}_{\mathrm{con}}$ , features of animals from the same family are more closely clustered.
+
+![](images/1dbea5f14c63ee24d485994b7bfed9427f90d1348459e4d80b9ebce5edcdbe98.jpg)  
+Figure 5. Effect of CtrlAni3D on Animal Kingdom dataset. Input and result images are zoom-in cropped for visualization. Training with CtrlAni3D enhances the model's ability to align tails, limbs and faces. Orange arrows indicate misalignments, while blue arrows indicate better alignments.  
+Figure 7. Effect of animal family supervised contrastive learning. Without animal family supervised contrastive learning, the estimation is prone to incorrect shapes for animal families.
+
+former backbone together with an aggregated large scale dataset. Within the aggregated dataset, we propose a novel synthetic general quadruped dataset CtrlAni3D, which is rendered by prompting a controllable text-to-image generation model ControlNet. Benefiting from our family aware design philosophy, AniMer outperforms previous methods not only on 3D quadrupedal datasets, but also on 2D in-the-wild datasets. We believe the principles behind AniMer would inspire the mesh recovery tasks of the whole animal kingdom, and enable several down-stream applications such as avatar creation and behavioral analysis.
+
+Limitations and Future Work. The solution space of AntiMer is limited to the pose and shape space of SMAL model. For species (e.g. birds or goats) whose shapes are far from the linear shape space of SMAL, building specific animal models, enhancing vertex deformations and introducing bone length scale are necessary to yield pixel-aligned results. Besides, motion blur and severe occlusions would harm the reconstruction results. In the future, AntiMer would be strengthened with better animal parametric models and spatio-temporal methods.
+
+# References
+
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+Acknowledgements. This study was supported by the National Key Research and Development Program of China (2023YFC2415400); the National Natural Science Foundation of China (T2422012, 62071210, 62125107); the Guangdong Basic and Applied Basic Research (2024B1515020088); the Shenzhen Science and Technology Program (RCYX20210609103056042); the Guangdong Basic and Applied Basic Research (2021A1515220131); the High Level of Special Funds (G030230001, G03034K003); the Shuimu Tsinghua Scholar Program (2024SM324).  
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\ No newline at end of file
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+# AniMo: Species-Aware Model for Text-Driven Animal Motion Generation
+
+Xuan Wang $^{1*}$  Kai Ruan $^{2*}$  Xing Zhang $^{3}$  Gaoang Wang $^{1\boxtimes}$
+
+<sup>1</sup> Zhejiang University <sup>2</sup> Renmin University of China <sup>3</sup> New Hope Liuhe Co., Ltd.
+
+xuanw@zju.edu.cn, kairuan@ruc.edu.cn, zhangxing@newhope.cn, gaoangwang@intl.zju.edu.cn
+
+* Equal contribution ≈ Corresponding author
+
+https://github.com/WandererXX/AniMo
+
+# Abstract
+
+Text-driven motion generation has made significant strides in recent years. However, most existing works focus on human motion, largely overlooking the rich and diverse behaviors of animals. Understanding and synthesizing animal motion have important applications in wildlife conservation, animal ecology, and biomechanics. Animal motion modeling presents unique challenges due to species diversity, varied morphological structures, and different behavioral patterns in response to similar textual descriptions. To address these challenges, we propose AniMo for text-driven animal motion generation. AniMo consists of two stages: motion tokenization and text-to-motion generation. In the motion tokenization stage, we encode motions using a joint-aware spatiotemporal encoder with species-aware feature modulation, enabling the model to adapt to diverse skeletal structures across species. In the text-to-motion generation stage, we employ masked modeling to jointly learn the mapping from textual descriptions to motion tokens. Additionally, we introduce AniMo4D, a large-scale dataset containing 78,149 motion sequences and 185,435 textual descriptions across 114 animal species. Experimental results show that AniMo achieves superior performance on both the AniMo4D and AnimalML3D datasets, effectively capturing diverse morphological structures and behavioral patterns across animal species.
+
+# 1. Introduction
+
+Text-to-motion generation, which transforms textual descriptions into semantically consistent and realistic 3D motions, has attracted significant attention recently. This technology has diverse applications in domains such as robotics, virtual/augmented reality (VR/AR), video games, and content creation [65]. While existing methods succeed in generating realistic motion [12, 27, 34, 47, 56, 61], they pre
+
+![](images/9ca89f7aa1f614559e6411e50f00385829aa346629538406cfc63c98b1dfab85.jpg)  
+The female red kangaroo fights, taunts and then reacts swiftly.
+
+![](images/8bf5ed2c152ea948271146243cc60e744a501a89da6521364be9be473ed5821a.jpg)  
+The male Indian elephant stands still before dying.  
+Figure 1. Examples of animal motions. Animals exhibit more diverse morphological structures and behavior patterns, making it challenging to generate motions from text-only prompts. (Yellow represents animal attributes, Green represents animal species, and Blue represents motions.)
+
+dominantly focus on human behavior, largely ignoring the rich and diverse motion patterns exhibited by animals. Expanding motion generation beyond human holds significant potential for animal management, wildlife conservation, ecological research, and biomechanics [9, 30, 39, 41].
+
+In this work, we focus on animal motion, an area that remains relatively under-explored compared to human motion. As shown in Figure 1, modeling animal motion presents unique challenges due to the vast diversity in
+
+species morphology and behavioral patterns. Unlike the relatively uniform human skeletal structure, animals display diverse body forms, from quadrupeds to birds, each with distinct motion patterns. Furthermore, while human behaviors tend to follow consistent patterns, animal behaviors exhibit significant variability influenced by species, morphology, and environmental factors. For example, "walking" differs fundamentally between crocodiles and giraffes due to their distinct limb structures and dynamics.
+
+To address these challenges, we introduce AniMo, a model specifically designed for text-driven animal motion generation. AniMo follows a two-stage framework: motion tokenization and text-to-motion generation. During motion tokenization, we discretize motion data using an encoder-decoder architecture equipped with a quantization mechanism. Unlike existing methods [12, 15, 54], which encode motion sequences using a Temporal Convolutional Network (TCN) [21], we adopt a joint-aware spatiotemporal encoder to better capture spatial and temporal dynamics. Furthermore, to accommodate species-specific morphology, we introduce species-aware feature modulation, which adaptively adjusts skeletal structures based on the animal species and attributes. In the text-to-motion generation stage, we condition the model on textual descriptions, along with animal species and attributes, to establish a mapping from textual descriptions to motion tokens.
+
+Additionally, we introduce AniMo4D, a large-scale dataset with 78,149 motions and 185,435 textual descriptions across 114 species. We conduct experiments on AniMo4D and use the AnimalML3D dataset [52] as an out-of-distribution (OOD) test set. AniMo achieves strong performance across multiple metrics, demonstrating its ability to generate diverse, realistic animal motions from text.
+
+In summary, our key contributions are as follows:
+
+- We propose AniMo, a novel model using a joint-aware spatiotemporal encoder to capture both spatial and temporal features of animal motion, along with species-aware feature modulation for adaptive scaling across species.  
+- We introduce AniMo4D, a comprehensive dataset comprising 78,149 motion sequences and 185,435 annotated textual descriptions spanning 114 animal species.  
+- We conduct extensive experiments on the AniMo4D and AnimalML3D datasets, demonstrating the superiority of AniMo. Our quantitative evaluations show that AniMo effectively generates species-specific morphological structures and motion sequences that align with the behavioral patterns of each species.
+
+# 2. Related Work
+
+# 2.1. Text-driven Human Motion Generation
+
+Numerous studies attempt to generate motion from text, primarily due to its user-friendliness. Existing text-to-motion
+
+generation approaches can be broadly categorized into three types: diffusion-based, autoregressive, and masked modeling methods. Diffusion methods describe motion generation as a text-conditioned denoising process [2, 4, 16, 18, 19, 25, 40, 47, 49, 55, 56, 60, 62-64]. The latter two approaches first encode motions into discrete tokens, which are then reconstructed. Autoregressive methods [3, 15, 27, 50, 54, 61] use a GPT-like [37] approach. For instance, T2M-GPT [54] encodes motions using Vector Quantized Variational Autoencoders (VQ-VAE) [48] and conditions on text to guide token generation. AttT2M [61] models individual body parts, incorporating spatial information. Masked modeling methods [12, 32-34, 58] follow a BERT-like [7] approach. MMM [34] encodes motions with VQ-VAE, constructs a large-scale codebook with a factorized code method [28], and employs a Masked Transformer to predict masked tokens. MoMask [12] utilizes Residual Vector Quantization (RVQ) [22, 53] for quantization, with a Masked Transformer for predicting base layer tokens and a Residual Transformer for predicting residual layer tokens. However, existing masked modeling methods do not explicitly incorporate spatial information in motion encoding. To address this limitation, we propose a joint-aware spatiotemporal encoder that captures skeletal spatial dependencies, ensuring the generated motion tokens effectively represent spatiotemporal dynamics.
+
+# 2.2. Text-driven Animal Motion Generation
+
+Progress in animal text-to-motion generation has lagged behind that of human motion generation due to limited data. OmniMotionGPT [52] addresses this issue through transfer learning, jointly training on human and animal motion data. However, it still relies on human motion during inference, limiting purely text-driven generation. Motion Avatar [59] uses SinMDM [36] for data augmentation to create the Zoo-300K dataset. It extends MoMask [12] to model animal motion and integrates a large language model as planner with 3D generation for avatar meshes. However, these methods often overlook essential animal-specific characteristics, particularly the morphological diversity across different species. To address this limitation, we introduce species-aware feature modulation, which accommodates the diverse morphological structures of different animal species.
+
+# 2.3. Animal Motion Dataset
+
+Several studies have constructed animal motion datasets. The RGBD-Dog dataset [17] captured skeletal data from seven dogs using motion capture devices. Similarly, Shooter et al. [42] introduced the 3DDogs-Wild dataset using indoor motion capture systems. The Deforming Things4D dataset [23] was synthesized using Blender scripts [5] with Mixamo characters [14] to produce diverse mo
+
+![](images/f8b3b954e61920bdfc5af3c9dec3ee985d1691fdb9986a12b1a9a4c5488ed77a.jpg)
+
+![](images/c460d551ba915731a0f4d55e15724deaa8923c70012a806aa7c095de2a69a9ff.jpg)  
+Figure 2. The architecture of AniMo. Our network operates in two main stages: (a) Motion Tokenization, which discretizes continuous motion representations. It adopts an encoder-decoder structure with Residual Vector Quantization. The encoder leverages a Joint-Aware Spatiotemporal Encoder to capture spatiotemporal motion features, followed by Species-Aware Feature Modulation for adaptive feature scaling. A Discriminator is employed during training to ensure realistic motion reconstruction. (b) Text-to-Motion Generation, which maps text inputs to motion tokens. A Base Transformer with masked modeling predicts the base layer tokens, while a Residual Transformer predicts the tokens for the remaining layers. (c) Inference: Given a text prompt, motion sequences that conform to animal morphology and behavior are generated sequentially using the Base Transformer, Residual Transformer, Codebook, and Decoder.
+
+tion data. However, these datasets lack textual descriptions, limiting their applicability in text-to-motion tasks. Recent efforts have incorporated text annotations into animal motion datasets. Yang et al. [52] extracted skeletal data from DeformingThings4D, and Zhang et al. [59] expanded animal motions in the Zoo-300K dataset using SinMDM [36]. However, these datasets contain a limited number of original animal motion sequences and exhibit restricted species representation. To address these gaps, we introduce the AniMo4D dataset with 78,149 motion sequences and 185,435 textual descriptions across 114 species.
+
+# 3. Method
+
+Our goal is to generate animal motions based on textual descriptions while ensuring consistency with animal morphol
+
+ogy and behavioral patterns. As shown in Figure 2, we propose AniMo, which comprises two training stages: motion tokenization (Section 3.1) and text-to-motion generation (Section 3.2). In the motion tokenization stage, we utilize a species-aware encoder-decoder architecture with a quantization mechanism to discretize continuous motion representations into motion tokens. In the text-to-motion generation stage, we employ a masked motion modeling mechanism to establish a mapping from text to motion tokens. During inference, textual descriptions are first mapped to discrete motion tokens, and then transformed into continuous motion sequences through the pre-trained decoder.
+
+# 3.1. Stage 1: Motion Tokenization
+
+Given a motion sequence  $\mathbf{X} = [\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_T]$ , where  $\mathbf{x}_t \in \mathbb{R}^d$ ,  $T$  represents the number of frames and  $d$  denotes
+
+the motion dimension, our goal is to train an autoencoder and a learnable codebook to discretize motion embeddings while ensuring accurate reconstruction of the motion sequence  $\hat{\mathbf{X}}$ . Specifically, we employ Residual Vector Quantization (RVQ) [12, 53] to learn fine-grained multi-layer discrete codebooks. To enrich feature learning and capture complex motion patterns from diverse species, we introduce a joint-aware spatiotemporal encoder enhanced with species-aware feature modulation for motion encoding. Additionally, following the concept of GANs [10, 20, 57], we incorporate a discriminator to differentiate between  $\mathbf{X}$  and  $\hat{\mathbf{X}}$ , thereby enhancing the reconstruction quality.
+
+Joint-Aware Spatiotemporal Encoder. In widely used motion representations [11],  $\mathbf{x}_t$  is represented as a feature vector in a one-dimensional format. Most existing methods process  $\mathbf{x}_t$  directly through the encoder [15, 54] without explicitly modeling its spatial feature. To address this limitation, we propose a joint-aware spatiotemporal encoder designed to explicitly capture both spatial and temporal dependencies in motion data. For spatial motion encoding, we reorganize the motion data with  $n_j$  joints into a joint-aware representation:  $\left[\mathbf{x}_t^r;\mathbf{x}_t^j;\mathbf{x}_t^f\right]$ , where  $\mathbf{x}_t^r$ ,  $\mathbf{x}_t^j$ , and  $\mathbf{x}_t^f$  denote the root joint, non-root joints, and foot-ground contact features, respectively. These components are then projected into the feature space via linear transformations:
+
+$$
+\mathbf {h} _ {t} = \left[ \mathbf {h} _ {t} ^ {r}; \mathbf {h} _ {t} ^ {j}; \mathbf {h} _ {t} ^ {f} \right] = \left[ \mathbf {W} _ {r} \mathbf {x} _ {t} ^ {r}; \mathbf {W} _ {j} \mathbf {x} _ {t} ^ {j}; \mathbf {W} _ {f} \mathbf {x} _ {t} ^ {f} \right], \tag {1}
+$$
+
+where  $\mathbf{W}_r, \mathbf{W}_j, \mathbf{W}_f$  are learnable weight parameters.
+
+Next, the joint-aware features  $\mathbf{h}_t$  are processed by a Spatial Transformer (S-Trans). To incorporate the morphological structure of animal motion, we impose constraints on the S-Trans's attention mask. Specifically, we represent the skeleton as a tree rooted at the pelvis joint. For any joint pair  $(A,B)$ , the attention mask  $\mathcal{M}_{A,B}$  is defined as:
+
+$$
+\mathcal {M} _ {A, B} = \left\{ \begin{array}{l l} 0, & \text {i f A , B a r e o n t h e s a m e l i m b} \\ - \infty , & \text {o t h e r w i s e} \end{array} \right. \tag {2}
+$$
+
+The S-Trans processes the motion embeddings  $\mathbf{h}_{1:T}$  using self-attention with the attention mask  $\mathcal{M}$  as follows:
+
+$$
+\mathbf {Q} = \mathbf {h} _ {1: T} \mathbf {W} _ {Q}, \quad \mathbf {K} = \mathbf {h} _ {1: T} \mathbf {W} _ {K}, \quad \mathbf {V} = \mathbf {h} _ {1: T} \mathbf {W} _ {V}, \tag {3}
+$$
+
+$$
+\mathbf {h} _ {1: T} ^ {s} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {T}}{\sqrt {d _ {k}}} + \mathcal {M}\right) \mathbf {V}, \tag {4}
+$$
+
+where  $\mathbf{W}_Q$ ,  $\mathbf{W}_K$ , and  $\mathbf{W}_V$  are the learnable parameters of the S-Trans. The resulting motion embeddings  $\mathbf{h}_{1:T}^s$  are enhanced with spatial structural information.
+
+Finally, the spatially enhanced features  $\mathbf{h}_{1:T}^{s}$  processed by a Temporal Convolutional Network (TCN) [21] to capture temporal dynamics, producing the final spatiotemporal
+
+features  $\mathbf{h}_{1:n}^{st}$ , where  $n = \lceil T / r\rceil$  and  $r$  is the downsampling rate. Without loss of generality, we denote  $\mathbf{h}^{st}$  without the subscript  $t$  for simplicity.
+
+Species-Aware Feature Modulation. Different species possess diverse morphological structures. As shown in Figure 3(c), the relative spine lengths across species can vary by orders of magnitude. While the feature representation  $\mathbf{h}^{st}$  primarily encodes motion information, it also implicitly captures certain morphological characteristics. To better account for species-specific morphological variations, we propose Species-Aware Feature Modulation (SAFM). Specifically, we employ a feature-wise linear modulation strategy [31] to adaptively scale  $\mathbf{h}^{st}$ :
+
+$$
+\mathbf {h} ^ {m} = \boldsymbol {\gamma} \odot \mathbf {h} ^ {s t} + \boldsymbol {\beta}, \tag {5}
+$$
+
+where  $\odot$  denotes element-wise multiplication, and  $\gamma$  and  $\beta$  are scaling parameters generated by combining the CLIP [38] text encoder with a Multi-Layer Perceptron (MLP). These parameters are learned by encoding animal species  $s$  along with specific animal attributes  $a$  (male, female, or juvenile):
+
+$$
+\gamma , \beta = \operatorname {M L P} \left(\operatorname {C L I P} _ {\text {t e x t}} ([ a, s ]).\right) \tag {6}
+$$
+
+As a result, the latent motion feature  $\mathbf{h}^m$  is dynamically modulated to accommodate different species.
+
+Residual Vector Quantization. To encode motion features, we employ a quantization mechanism  $Q(\cdot)$ , where a continuous vector is replaced by its nearest code entry (referred to as motion tokens) from a codebook  $\mathcal{C}$ . To obtain more fine-grained motion tokens, we perform iterative quantization to the latent sequence  $\mathbf{h}^m$  using  $V + 1$  quantization layers [12, 22, 53], where each layer successively refines the residual from the previous step.
+
+Formally, let  $v = 0,1,\dots ,V$  denote the index of the quantization layer. We initialize the residual representation as  $\mathbf{r}^0 = \mathbf{h}^m$ . The quantization process is then formulated as:
+
+$$
+\mathbf {h} ^ {v} = Q \left(\mathbf {r} ^ {v}\right), \quad \mathbf {r} ^ {v + 1} = \mathbf {r} ^ {v} - \mathbf {h} ^ {v}. \tag {7}
+$$
+
+The final quantized motion representation is obtained by summing the quantized sequences across all layers:
+
+$$
+\mathbf {h} ^ {q} = \sum_ {v = 0} ^ {V} \mathbf {h} ^ {v}. \tag {8}
+$$
+
+During training, the codebook  $\mathcal{C}$  is updated using an Exponential Moving Average (EMA) and a codebook reset strategy [51, 54], facilitating stable and high-quality representation learning.
+
+The quantized representation  $\mathbf{h}^q$  is then passed through a decoder to reconstruct the motion sequence, resulting in
+
+![](images/32cd0b797227ca67ed416c264217ae0618ee9692610c688b8303454bfb4acc34.jpg)  
+(a) Word cloud of the species.  
+(b) Word cloud of the motion labels.  
+Figure 3. Visualization results on the AniMo4D dataset.
+
+![](images/77a9853801eac7f114469584dd653660387454c96cdd5e3fbbb43063c11c80f3.jpg)  
+(c) Distribution of animal spine length.
+
+the output  $\hat{\mathbf{X}}$ . The overall training objective combines a reconstruction loss and a latent embedding loss at each quantization layer:
+
+$$
+\mathcal {L} _ {\mathrm {r v q}} = \left\| \mathbf {X} - \hat {\mathbf {X}} \right\| _ {1} + \alpha \sum_ {v = 1} ^ {V} \left\| \mathbf {r} ^ {v} - \operatorname {s g} \left[ \mathbf {h} ^ {v} \right] \right\| _ {2} ^ {2}, \tag {9}
+$$
+
+where  $\mathrm{sg}[\cdot ]$  denotes the stop-gradient operation, and  $\alpha$  is a weighting factor for the embedding constraint.
+
+To ensure the realism of the reconstructed motion, we introduce a discriminator  $D(\cdot)$  that differentiates between the generated motion  $\hat{\mathbf{X}}$  and the real motion  $\mathbf{X}$ . The adversarial loss is formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {a d v}} = \mathbb {E} _ {\mathbf {X} \sim p _ {\mathrm {d a t a}}} [ \log D (\mathbf {X}) ] + \mathbb {E} _ {\hat {\mathbf {X}} \sim p _ {\mathrm {g e n}}} \left[ \log \left(1 - D (\hat {\mathbf {X}})\right) \right]. \tag {10}
+$$
+
+The overall training objective combines the RVQ loss and the adversarial loss, and is expressed as:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\mathrm {r v q}} + \lambda \mathcal {L} _ {\mathrm {a d v}}, \tag {11}
+$$
+
+where  $\lambda$  is a hyperparameter that controls the balance between the RVQ loss and the adversarial loss.
+
+After training, each motion sequence  $\mathbf{X}$  can be represented as  $V + 1$  discrete motion token sequences  $M = [m_{1:n}^{v}]_{v=0}^{V}$ , where motion token  $m_{i}^{j} \in \{1,2,\dots,|\mathcal{C}|\}$  is the index of codebook embedding.
+
+# 3.2. Stage 2: Text-to-Motion Generation
+
+In this stage, our goal is to learn the mapping from textual descriptions to pre-trained motion tokens. Since the first layer of our multi-layer codebook contains the most essential information, we use a Base Transformer (B-Trans) to predict the base layer motion tokens  $m_{1:n}^{0} \in \mathcal{R}^{n}$ . To condition the model, we input the animal attributes  $a$ , species  $s$ , and textual description  $d$  into the CLIP text encoder, resulting in a condition vector  $\mathbf{c} = \mathrm{CLIP}_{\mathrm{text}}([a,s,d])$ .
+
+Table 1. Statistics of the text-motion datasets.  
+
+<table><tr><td>Dataset</td><td>#Motions</td><td>#Texts</td><td>Duration (h)</td><td>#Species</td></tr><tr><td>HumanML3D [11]</td><td>14,616</td><td>44,970</td><td>28.59</td><td>1</td></tr><tr><td>KIT-ML [35]</td><td>3,911</td><td>6,248</td><td>10.33</td><td>1</td></tr><tr><td>AnimalML3D [52]</td><td>1,240</td><td>3,720</td><td>0.82</td><td>36</td></tr><tr><td>Zoo-300K [59]</td><td>1,153</td><td>300,000*</td><td>-</td><td>65</td></tr><tr><td>AniMo4D (Ours)</td><td>78,149</td><td>185,435</td><td>84.29</td><td>114</td></tr></table>
+
+Note: * utilized SinMDM [36] to augment motion data to 300K, and generated 300K corresponding texts.
+
+The base layer tokens are predicted using a masked motion modeling approach. Specifically, a portion of the tokens in the original motion sequence  $m^0$  is replaced with [MASK] tokens according to a masking probability  $p_{\mathrm{mask}}$ . This modified sequence  $\tilde{m}_i^0$  is subsequently fed into the B-Trans, which predicts the actual tokens at the [MASK] positions. The model is trained by minimizing the negative log-likelihood of the target token predictions:
+
+$$
+\mathcal {L} _ {\text {b a s e}} = \sum_ {\tilde {m} _ {i} ^ {0} = [ \text {M A S K} ]} - \log p _ {\theta} \left(m _ {i} ^ {0} | \tilde {m} ^ {0}, \mathbf {c}\right), \tag {12}
+$$
+
+To predict the motion tokens for the remaining  $V$  layers, we employ a Residual Transformer (R-Trans). In addition to the text condition  $\mathbf{c}$ , we also condition the model on the residual layer  $\mathrm{ID} j \in (1, V)$ . The R-Trans predicts the tokens for the  $j$ -th quantization layer, with the following training objective:
+
+$$
+\mathcal {L} _ {\text {r e s}} = \sum_ {j = 1} ^ {V} \sum_ {i = 1} ^ {n} - \log p _ {\phi} \left(m _ {i} ^ {j} \mid m _ {i} ^ {1: j - 1}, \mathbf {c}, j\right), \tag {13}
+$$
+
+where  $m_i^j$  denotes the token from the  $j$ -th quantization layer for sequence index  $i$ , and  $m_i^{1:j-1}$  represents the embedded tokens from the preceding layers.
+
+Inference. During inference, given a text condition  $\mathbf{c}$ , we first initialize all base-layer tokens as [MASK], i.e.,  $m^0 = [\mathrm{MASK}]$ . The B-Trans predicts the base layer tokens as  $\hat{m}^0 = \mathrm{B - Trans}(m^0,c)$ . For each subsequent quantization layer  $j\in \{1,2,\dots ,V\}$ , the R-Trans predicts the tokens  $\hat{m}^j$  for the  $j$ -th layer based on the previously predicted tokens from layers 1 to  $j - 1$  and the condition  $\mathbf{c}$ , i.e.,  $\hat{m}^j = \mathrm{R - Trans}(\hat{m}^{1:j - 1},\mathbf{c},j)$ . After predicting all layers, the full quantized motion token sequence is obtained as  $\hat{m}^{1:V} = [\hat{m}^0,\hat{m}^1,\dots ,\hat{m}^V]$ . The final motion embedding  $\hat{\mathbf{h}}^q$  is retrieved from the pre-trained codebook, and the motion sequence  $\hat{\mathbf{X}}$  is reconstructed using the pre-trained decoder:  $\hat{\mathbf{X}} = \mathrm{Decoder}(\hat{\mathbf{h}}^q)$ .
+
+# 4. Experiments
+
+Datasets. To validate the effectiveness of our model, we conducted experiments using the AniMo4D and AnimalML3D [52] datasets. Building on prior success with synthetic data techniques demonstrated in previous research [17, 29, 43], we curated AniMo4D from Planet Zoo [6], a simulation game known for its high-quality animal models and motions. Specifically, we utilize cobra-tools<sup>1</sup> to extract the animal models and animations. We then conduct exploratory data analysis and define a unified skeletal structure with  $n_j = 30$  joints, selecting the most frequently occurring and cross-species-compatible joints, balancing joint coverage with species inclusiveness (with some incompatible species, such as penguins, discarded). Furthermore, we annotate each motion with textual descriptions generated by Llama [8], Qwen [1], and Deepseek [24], followed by manual cleaning to ensure high quality. AniMo4D contains 78,149 motion sequences and 185,435 textual descriptions across 114 species. Figure 3(a) and Figure 3(b) illustrate the distribution of animal species and motion labels. The motion sequences range from 20 to 300 frames. Table 1 provides a comparison with existing text-to-motion datasets, highlighting AniMo4D's compatibility. We split the dataset into training, validation, and testing sets with ratios of 0.80, 0.05, and 0.15, respectively.
+
+For the AnimalML3D dataset, used as an out-of-distribution (OOD) test set, we selected 1,150 motion samples with sequence lengths ranging from 20 to 300 frames. To ensure consistency, we unified the number of joints to 30 across all datasets and preprocessed the joint data in the T2M format [11], where the data has dimensionality  $(T,d)$ , with  $T$  representing the sequence length and  $d = 359$  denoting the motion dimension.
+
+Evaluation metrics. Following T2M [11], we trained text-motion matching components on the AniMo4D and
+
+AnimalML3D datasets to encode motions and text for evaluation. We evaluate performance using the following metrics: (1) Frechet Inception Distance (FID): This metric calculates the distance between feature distributions of generated and ground truth motions, assessing quality and realism. (2) R-Precision and Multimodal Distance (MM-Dist): R-Precision measures semantic alignment between text and generated motions, reporting Top-1, Top-2, and Top-3 accuracy. MM-Dist quantifies the distance between motion and text embeddings. (3) Diversity: This metric computes the mean pairwise Euclidean distance among generated motions for different descriptions, reflecting variability. (4) Multimodality: This evaluates the diversity of motions generated from a single text prompt. (5) Mean Per Joint Position Error (MPJPE): MPJPE measures the average Euclidean distance between predicted and ground truth joint positions, directly assessing skeletal motion accuracy.
+
+Baselines. To the best of our knowledge, no publicly available models are specifically designed for pure text-driven animal motion generation. While OmniMotionGPT [52] can generate animal motions, it requires additional human motions as references. Motion Avatar [59] focuses on generating mesh-based animal avatars rather than motion sequences. Therefore, we selected several state-of-the-art text-driven human motion generation models to serve as our baselines, including: T2M [11], MDM [47], T2M-GPT [54], AttT2M [61], MMM [34] and MoMask [12]. To adapt these models for animal motion, we modified their skeletal definitions to align with those used in AniMo4D. Each baseline model was retrained using its default parameters, and we evaluated their performance on both the AniMo4D and AnimalML3D datasets.
+
+Implementation Details. In line with the configuration in Guo et al. [12], we configure RVQ with 6 quantization layers in the first stage, each with a codebook size of  $512 \times 512$  and a downsampling rate of  $r = 4$ . We use the AdamW optimizer [26] with  $[\beta_{1}, \beta_{2}] = [0.9, 0.99]$ . The weighting factor  $\alpha$  is set to 0.02, and the adversarial loss weight coefficient  $\lambda$  is set to 0.002. In the second stage, both the B-Trans and R-Trans consist of 6 transformer layers, each with 6 attention heads and a latent dimension of 384. The learning rate is set to  $2 \times 10^{-4}$ , with linear warm-up periods of 80k and 16k iterations for the first and second stages, respectively. We use batch sizes of 128 and 64 for these stages. For text encoding, we employ the CLIP ViT-B/32 model [38]. All experiments are conducted on NVIDIA GeForce RTX 4090 GPUs.
+
+# 4.1. Quantitative Results
+
+Following [11, 47], each experiment was conducted 10 times, and the metrics are reported as mean values with
+
+Table 2. Comparison of text-driven motion generation on the AniMo4D test set. The right arrow  $(\rightarrow)$  indicates that values closer to the ground truth motion are better. The best results for each metric are shown in bold.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">R-Precision ↑</td><td rowspan="2">FID ↓</td><td rowspan="2">MM-Dist ↓</td><td rowspan="2">Diversity →</td><td rowspan="2">MModality ↑</td></tr><tr><td>Top-1 ↑</td><td>Top-2 ↑</td><td>Top-3 ↑</td></tr><tr><td>Real</td><td>0.854±.002</td><td>0.947±.001</td><td>0.974±.001</td><td>0.002±.000</td><td>0.897±.001</td><td>4.751±.078</td><td>-</td></tr><tr><td>T2M [11]</td><td>0.604±.002</td><td>0.722±.002</td><td>0.807±.001</td><td>0.107±.000</td><td>1.391±.002</td><td>4.362±.053</td><td>0.314±.015</td></tr><tr><td>MDM [47]</td><td>0.303±.002</td><td>0.444±.001</td><td>0.534±.002</td><td>1.017±.005</td><td>2.525±.002</td><td>3.953±.051</td><td>0.264±.016</td></tr><tr><td>T2M-GPT [54]</td><td>0.581±.002</td><td>0.732±.002</td><td>0.807±.002</td><td>0.218±.003</td><td>1.505±.003</td><td>4.281±.050</td><td>0.519±.018</td></tr><tr><td>AttT2M [61]</td><td>0.573±.002</td><td>0.734±.002</td><td>0.816±.001</td><td>0.265±.002</td><td>1.497±.002</td><td>4.360±.042</td><td>0.362±.012</td></tr><tr><td>MMM [34]</td><td>0.628±.002</td><td>0.770±.002</td><td>0.838±.002</td><td>0.268±.001</td><td>1.411±.002</td><td>4.318±.053</td><td>0.178±.008</td></tr><tr><td>MoMask [12]</td><td>0.708±.002</td><td>0.870±.002</td><td>0.932±.001</td><td>0.143±.000</td><td>1.223±.001</td><td>4.441±.053</td><td>0.415±.013</td></tr><tr><td>AniMo (Ours)</td><td>0.774±.002</td><td>0.908±.002</td><td>0.953±.001</td><td>0.029±.000</td><td>1.063±.002</td><td>4.664±.052</td><td>0.368±.015</td></tr></table>
+
+Table 3. Comparison of text-driven motion generation in out-of-distribution (OOD) experiments on the AnimalML3D dataset. The right arrow  $(\rightarrow)$  indicates that values closer to the ground truth motion are better. The best results for each metric are shown in bold.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">R-Precision ↑</td><td rowspan="2">FID ↓</td><td rowspan="2">MM-Dist ↓</td><td rowspan="2">Diversity →</td><td rowspan="2">MModality ↑</td></tr><tr><td>Top-1 ↑</td><td>Top-2 ↑</td><td>Top-3 ↑</td></tr><tr><td>Real</td><td>0.696±.002</td><td>0.881±.004</td><td>0.939±.005</td><td>0.011±.001</td><td>0.972±.015</td><td>4.738±.037</td><td>-</td></tr><tr><td>T2M [11]</td><td>0.102±.017</td><td>0.226±.017</td><td>0.304±.016</td><td>2.906±.153</td><td>3.972±.012</td><td>3.396±.056</td><td>0.803±.043</td></tr><tr><td>MDM [47]</td><td>0.074±.042</td><td>0.135±.041</td><td>0.187±.050</td><td>3.134±.149</td><td>4.276±.015</td><td>3.286±.052</td><td>0.737±.044</td></tr><tr><td>T2M-GPT [54]</td><td>0.135±.005</td><td>0.233±.005</td><td>0.311±.006</td><td>2.843±.085</td><td>3.920±.014</td><td>3.990±.048</td><td>0.947±.038</td></tr><tr><td>AttT2M [61]</td><td>0.122±.003</td><td>0.219±.003</td><td>0.290±.005</td><td>2.893±.045</td><td>4.043±.021</td><td>3.463±.033</td><td>0.887±.072</td></tr><tr><td>MMM [34]</td><td>0.115±.003</td><td>0.191±.004</td><td>0.251±.004</td><td>2.943±.094</td><td>4.019±.008</td><td>3.324±.034</td><td>0.843±.069</td></tr><tr><td>MoMask [12]</td><td>0.133±.003</td><td>0.234±.004</td><td>0.321±.004</td><td>2.887±.032</td><td>3.970±.016</td><td>3.320±.047</td><td>1.062±.058</td></tr><tr><td>AniMo (Ours)</td><td>0.144±.004</td><td>0.254±.004</td><td>0.336±.005</td><td>2.710±.086</td><td>3.867±.017</td><td>3.377±.054</td><td>0.947±.042</td></tr></table>
+
+95% confidence intervals. As shown in Table 2, AniMo outperforms other methods across key evaluation metrics on the AniMo4D dataset. It achieves superior R-Precision, reflecting stronger alignment between text prompts and motions. Notably, AniMo achieves a significantly lower FID score, indicating more realistic and higher-quality motions. Moreover, Its lower MM-Dist further demonstrates strong semantic consistency between text and motion. Although MModality is slightly lower than that of some other methods, AniMo's high R-Precision and low MM-Dist emphasize text adherence over extreme diversity while still maintaining strong diversity.
+
+Furthermore, we performed out-of-distribution (OOD) evaluations on the AnimalML3D dataset. As shown in Table 3, due to the distributional shift between datasets, the performance of all models degraded. Nonetheless, AniMo continues to achieve superior performance across multiple metrics despite these challenging conditions.
+
+# 4.2. Qualitative Results
+
+Figure 4(a) idemonstrates the model's ability to generate motions for different species given similar textual descriptions, highlighting its capacity to capture the unique morphological characteristics of each species. For example, the okapi and the proboscis monkey exhibit substantial differences in skeletal structure and size, with the okapi being
+
+larger. The model also learns species-specific behaviors: the proboscis monkey appears more agile in swimming, using its upper limbs more, while the snow leopard uses all four limbs in a coordinated way. Additionally, Figure D2 (in Supp.) presents the qualitative results of AniMo compared to baseline models. These qualitative results further substantiate the model's ability to generate diverse and realistic animal motions.
+
+# 4.3. Ablation Study
+
+To assess the effectiveness of our model components, we performed an ablation study, evaluating both the first-stage reconstruction and the full generation pipeline, as shown in Table 4. The results indicate that the removal of any component leads to a decline in performance across all key metrics. Among the components, the Spatial Transformer (S-Trans) proves to be the most critical, as its removal results in the largest increase in FID, underscoring its importance in capturing spatiotemporal features for high-quality motion synthesis. Moreover, removing the discriminator  $D(\cdot)$  yields the highest MPJPE, emphasizing its crucial role in ensuring realistic skeletal motion. Eliminating the Species-Aware Feature Modulation (SAFM) also degrades performance. These findings confirm the contributions of each component to the overall architecture and further demonstrate the robustness of our design.
+
+![](images/5299d5c10f870a25bd23e702b7eb4dd3353f5d8fe0960ccf97ec8a2afc328862.jpg)  
+(a) Different animals exhibit distinct morphological structures and behavioral patterns for similar text prompts.  
+Figure 4. Motions generated by AniMo. The results demonstrate that AniMo has learned different animal species and behavior patterns, and can transfer motions to novel animals as well as perform cross-species transformations.
+
+# 4.4. Application
+
+Motion Transfer. AniMo demonstrates a strong understanding of intrinsic animal behaviors, facilitating effective motion transfer across species. This capability is evidenced in Figure 4(b), where the model successfully transfers a drinking motion from a wisent to a grey seal, even though such examples are absent in the AniMo4D training set. The generated motion naturally aligns with the grey seal's morphological structure, enabling a wide range of applications, including animation, wildlife simulation, behavioral studies, and creative design, such as character development and digital art creation [44, 45]. Furthermore, as both the text input and animal attributes are encoded using CLIP, the model leverages CLIP's semantic representations to map species into the latent space, enabling seamless motion transfer to unseen species.
+
+Cross-species Motion Inpainting. AniMo achieves cross-species motion inpainting through a mask-based inference approach, leveraging its species-aware architecture and comprehensive understanding of animal behavior patterns. The process consists of tokenizing the original motion sequence, replacing target segments with [MASK] tokens, and feeding the modified sequence along with textual descriptions into the B-Trans and R-Trans. Figure 4(c) illustrates this capability, showing smooth transitions between concatenated motions from different
+
+Table 4. Ablation study on the AniMo4D dataset.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Reconstruction</td><td colspan="2">Generation</td></tr><tr><td>FID↓</td><td>MPJPE↓</td><td>FID↓</td><td>MM-Dist↓</td></tr><tr><td>AniMo</td><td>0.035</td><td>0.206</td><td>0.037</td><td>1.063</td></tr><tr><td>w/o SAFM</td><td>0.044</td><td>0.249</td><td>0.056</td><td>1.301</td></tr><tr><td>w/o S-Trans</td><td>0.063</td><td>0.214</td><td>0.071</td><td>1.241</td></tr><tr><td>w/o D(·)</td><td>0.055</td><td>0.325</td><td>0.091</td><td>1.197</td></tr></table>
+
+species, with the inpainted process highlighted in blue. This enables seamless motion editing and completion, particularly valuable for animation production where continuous motion sequences need to be generated from fragmented recordings or different species [13, 46].
+
+# 5. Conclusion
+
+In this paper, we introduced AniMo to tackle the challenges of text-driven animal motion generation. By leveraging a joint-aware spatiotemporal encoder and species-aware feature modulation, AniMo effectively captures the unique morphological and behavioral traits of various species. Comprehensive evaluations on the AniMo4D and AnimalML3D datasets demonstrate that our approach consistently outperforms existing methods across multiple quantitative metrics, generating motions that conform to animal morphological structures and behavioral patterns.
+
+# Acknowledgments
+
+# References
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+# Animate and Sound an Image
+
+Xihua Wang<sup>1</sup> Ruihua Song<sup>1</sup>
+
+Boyuan Li Yihan Wu
+
+Yuyue Wang
+
+Chongxuan Li
+
+Hongteng Xu
+
+Xin Cheng
+
+Yunfeng Wang
+
+$^{2}$ ZHI-TECH GROUP
+
+<sup>1</sup>Gaoling School of Artificial Intelligence, Renmin University of China
+
+xihuaw@ruc.edu.cn, songruihua.bloon@outlook.com
+
+# Abstract
+
+This paper addresses a promising yet underexplored task, Image-to-Sounding-Video (I2SV) generation, which animates a static image and generates synchronized sound simultaneously. Despite advances in video and audio generation models, challenges remain to develop a unified model for generating naturally sounding videos. In this work, we propose a novel approach that leverages two separate pretrained diffusion models and makes vision and audio influence each other during generation based on the Diffusion Transformer (DiT) architecture. First, the individual video and audio pretrained generation models are decomposed into input, output, and expert sub-modules. We propose using a unified joint DiT block to integrate the expert sub-modules to effectively model the interaction between the two modalities, resulting in high-quality I2SV generation. Then, we introduce a joint classifier-free guidance technique to boost the performance during joint generation. Finally, we conduct extensive experiments on three popular benchmark datasets, and in both objective and subjective evaluation our method surpass all the baseline methods in almost all metrics. Case studies show our generated sounding videos are high quality and synchronized between video and audio.
+
+# 1. Introduction
+
+The real world is constantly in motion and sound. Mimicking this dynamic nature is essential for content generation and foundational for building world models. For a long time, the generative community has predominantly focused on single-modality synthesis, exploring architectures [16, 36], generative frameworks [29, 34], and scaling properties [3, 10, 36] to enhance video or audio quality. Though capable of producing high-fidelity video [3, 23, 51] or audio [10, 32] separately, current single-modality generators struggle to create naturally paired sounding videos. Bridging two modalities to jointly generate sounding videos remains understudied, persisting as an open challenge.
+
+![](images/cb5b5a3be6ac745f4c9401def2e333d89cbd8180e749046aee37da599c251eda.jpg)  
+Input image
+
+![](images/60f590b8c3ea996167611cc84ce1215e3d1e58117a8009df65652ce1d456644e.jpg)
+
+![](images/62456b502733705c3cd86969674758535946def3529b40c588b37fe39b08dc1c.jpg)  
+Figure 1. Cases for Image-to-Sounding-Video (I2SV) generation. Comparison with the other four schemes shows that our method significantly outperforms the other schemes regarding synchronization between the generated video and audio when animating and sounding an image in high quality. Zoom in to see details.
+
+![](images/6f2dd0811ce49386525a6149c481d0588f825101daea30a8005bb41803007e92.jpg)  
+I2VA(ours) (synchronized barking)
+
+![](images/510eea0df0cd91a133210abea26dc7b9d2984ebbdd895972693810e842396ca8.jpg)
+
+![](images/a1e2b7738d0b85c199fcae610f1bf0cb91fb39815d4af3c57b1bcc4c7f8472fb.jpg)
+
+Several works initially address sounding video generation, either unconditionally or via text conditioning. Unconditional approaches [39, 43, 47] are limited to specific domains, such as dance [26] or landscapes [25] scenes, hindering an efficient exploration of open-domain capabilities. The unconditional generation also falls short when compared to conditional generation in terms of quality [27]. Text-conditioned approaches [18, 33, 44] offer more flexibility but face bottlenecks in processing the text modality. The performance heavily relies on constructing high-quality video-audio captions and modeling alignment with caption. This diverts the model's focus away from modeling the interaction between video and audio modalities, leading to a lack of sufficient fine-grained cross-modal interactions. Some works explore guidance techniques [13, 49] to enhance performance of aforementioned approaches at inference time, but do not directly address their problems. Both paths achieve generating sounding videos in suboptimal quality, neither shows to be a scalable way to explore sounding video generation with stable generation quality and focusing on audiovisual interaction mechanisms.
+
+We propose formulating sounding video generation as an image-to-sounding-video (I2SV) task, where a static image serves as both the conditional input and the initial frame for generating a synchronized audiovisual sequence. Unlike unconditional or text-conditioned approaches, I2SV emphasizes bridging visual and auditory modalities while enabling open-domain sounding video generation. Based on existing works, there are three potential solutions to this task. (1) Independent parallel generation employs separate image  $\rightarrow$  audio [40] and image  $\rightarrow$  video [3] models, but risks temporal or semantic inconsistencies (e.g., a closed-mouth dog paired with barking sounds in Figure 1). (2) Sequential generation via cross-modal [32, 48, 55, 56] pipelines (image  $\rightarrow$  audio  $\rightarrow$  video or image  $\rightarrow$  video  $\rightarrow$  audio) reduces inconsistencies but suffers from error propagation—erroneous video outputs could corrupt subsequent audio generation. (3) Coarse-grained I2SV frameworks like CoDi [44] utilize contrastive learning for modality interaction, yet their semantic alignment remains insufficient for high-dimensional, temporally precise audiovisual synchronization. Developing a unified model that enables fine-grained cross-modal interaction while preserving temporal and semantic consistency remains a challenge.
+
+To address this challenge, we propose a simple yet effective approach based on the diffusion transformer (DiT) [36] architecture for modeling the interaction between video and audio, using a single model to achieve image-to-sounding video generation. The capabilities of the DiT model have been recently validated across various generative domains, able to generate high-quality single modality data [4, 6, 10] and even fit unconditional video-audio joint [47] or text-image joint [2] distributions. We further investigate the potential of DiT in modeling sounding video. Rather than directly estimating a joint video-audio distribution using a DiT model trained from scratch, we leverage the powerful existing single modality generative models as submodules. Specifically, given two expert diffusion models, a pretrained video generation model, and an audio generation model, regardless of whether they are based on UNet [3, 31] or DiT architectures, we decompose them into submodules in different types and then use a Joint Block to combine these submodules, forming a single DiT block. We find that such approach can leverage the expertise of pre-trained single-modality models while enabling the fine-grained interaction between the two modalities, thereby achieving high-quality image-to-sounding video generation.
+
+We further improve the inference mechanism for I2SV joint generation. The classifier-free guidance (CFG) [15] for conditional generation is extensively employed in current research, demonstrating strong capabilities in following conditions and producing high-fidelity generation results. Typically, the CFG technique is applied for single-modality generation. We observe that in the joint genera
+
+tion model, the standard vanilla CFG may not be optimal as it only steers alignment with conditions without steering joint interactions. We introduce a joint classifier-free guidance (JointCFG) technique that employs the comparison between marginal distribution and joint distribution to refine the guidance effect. Further, we found that gathering inference results from submodules into JointCFG further improves guidance (JointCFG*).
+
+Our contributions are: (1) We propose an innovative JointDiT architecture that leverages pretrained video and audio diffusion models and uses a Joint Block to model their interaction. (2) We introduce an improved CFG technique in joint generation scenarios that significantly enhances the performance of JointDiT, which is also applicable to other joint frameworks. (3) We benchmark I2SV task. Through detailed experiments, our method achieves state-of-the-art performance, as demonstrated on our demo page<sup>1</sup>.
+
+# 2. Related Work
+
+Video and audio are inherently co-occurring modalities, and modeling their paired relationships is crucial towards estimating the real world. However, research on generation for both modalities has taken a long journey before converging. Video Generation. In visual generation domain, the focus is on progressively modeling more complex visual distributions. This has evolved from generating low-resolution images [34] to producing high-resolution images [38] and further extending image models towards video generation [6, 12, 41]. As for video, the community concentrates on generating higher-fidelity, higher-resolution and longer-duration videos [3, 23, 51, 54, 58]. Along with this, there is a research line focuses on controllability, such as incorporating image conditions to significantly control the visual content [23, 28, 51], as opposed to relying on text only.
+
+Audio Generation. The audio domain shares a similar trend. Development follows a path of generating higher-quality audio at fixed lengths [10, 30, 50], covering more types (e.g., sound, speech, music) [46], and extending audio length [9]. With the exploration of more complex tasks, along with scaling models and data, both video and audio modalities can now estimate highly complex unimodal distributions, yielding impressive unimodal generation results. Video-Audio Cross-Generation. While unimodal generation excels, simply combining the outputs of both modalities does not yield a coherent result. To achieve fully consistent (e.g., semantic and synchronization) audiovisual outcomes, recent work has focused on conditioning between modalities to model their relationships. This includes generating videos from sound [25, 52, 55], speech [14] or music [7], or conversely, generating sound for a silent video [8, 32, 48, 56]. Such approaches establish connec
+
+tions between the two modalities in a cross conditional manner, aiming for harmonized cross-generation results.
+
+Video-Audio Joint Generation. Direct joint distribution modeling provides inherent modality consistency advantages over sequential generation that risks error propagation (e.g., video generation artifacts affecting subsequent audio synthesis). Current joint generation paradigms fall into two categories: (1) Leveraging two pre-trained video and audio models, where additional classifiers [13, 49] or cross-attentions [18, 33] guide joint generation. This way lacks fine-grained bidirectional interaction between modalities. (2) Training a new model from scratch to directly model the joint distribution [39, 43, 47]. While this approach allows finer-grained interactions, skipping unimodal learning is often inefficient, leading to poor generation quality and being limited to preliminary unconditional generation.
+
+Efficiently modeling the joint distribution and capturing fine-grained interactions between video and audio remains an open challenge. Our work addresses this issue through exploring the I2SV task, focusing on the interaction between visual and audio modalities, especially the efficient interaction way of two pre-trained generative models.
+
+# 3. Method
+
+# 3.1. Preliminary: Unimodal Diffusion Models
+
+Basics. Diffusion Models (DMs) are probabilistic generative models that learn to iteratively transform random noise into clean data. Typical DMs estimate single modalities (e.g., video or audio), using various frameworks like DDPMs [34] or EDMs [20]. The forward diffusion process gradually corrupts clean data into Gaussian noise following a predefined schedule. During training, a DM  $D_{\theta}$  learns to reverse this corruption in several timesteps. We exemplify this with a video DM  $D_{\theta_v}$  under the EDM-framework and an audio DM  $D_{\theta_a}$  under the DDPM-framework. EDM directly adds Gaussian noise  $\pmb{n}_{\sigma}$  with  $\sigma^2$  -variance to clean video latents  $\pmb{v}_0$  at continuous timestep  $t(\sigma) = 0.25\log \sigma$  where  $\log \sigma$  is sampled from  $\mathcal{N}(P_{\mathrm{mean}},P_{\mathrm{std}}^2)$  ( $P_{\mathrm{mean}}, P_{\mathrm{std}}$  are predefined hyperparameters [3]). DDPM combines Gaussian noise  $\epsilon$  and clean audio latents  $\pmb{a}_0$  linearly at discrete timestep  $t$  following a predefined schedule  $\bar{\alpha}_t$ . Both frameworks train denoising networks to predict clean latents from noisy inputs conditioned on  $c_v$  or  $c_a$  at each continuous or discrete timestep. The training objective minimizes an L2 loss between predicted and ground-truth latents:
+
+$$
+\mathcal {L} \left(\theta_ {v}\right) = \mathbb {E} \left[ \| \boldsymbol {v} _ {0} - D _ {\theta_ {v}} \left(\boldsymbol {v} _ {0} + \boldsymbol {n} _ {\sigma}; c _ {v}, t (\sigma)\right) \| ^ {2} \right], \tag {1}
+$$
+
+$$
+\mathcal {L} \left(\theta_ {a}\right) = \mathbb {E} \left[ \left\| \boldsymbol {a} _ {0} - D _ {\theta_ {a}} \left(\sqrt {\bar {\alpha} _ {t}} \boldsymbol {a} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}; c _ {a}, t\right) \right\| ^ {2} \right]. \tag {2}
+$$
+
+Guidance Methods. Widely used Classifier-free guidance (CFG) [15] is a technique for DM inference that enhances generation quality and conditional alignment. It adjusts the denoising direction through linear extrapolation between conditional and unconditional predictions at each timestep.
+
+Take a video DM as illustration:
+
+$$
+\begin{array}{r l} D _ {\theta_ {v}} ^ {\mathrm {C F G}} \left(\boldsymbol {v} _ {t}; c _ {v}, t\right) & = D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t}; c _ {v}, t\right) \\ & + \omega \left(D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t}; c _ {v}, t\right) - D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t}; \varnothing , t\right)\right), \end{array} \tag {3}
+$$
+
+where  $\omega$  governs guidance strength and  $\varnothing$  indicates null conditions for unconditional generation. In practice, both conditional and unconditional DMs can be implemented through a shared network  $D_{\theta_v}$  by randomly replacing  $c_{v}$  with null embeddings during training (e.g.,  $10\%$  of time).
+
+Recent Autoguidance (AG) [21] introduces guidance with a bad version of conditional DM rather than with an unconditional version in CFG. It substitutes the unconditional DM term in Equation 3 with an early training-stage checkpoint (less-optimized bad version) of the conditional DM. This way demonstrates performance comparable to CFG while eliminating the need for explicit unconditional training.
+
+# 3.2. JointDiT Architecture
+
+Let  $i$  denote conditional image data,  $\pmb{v}_0\in \mathbb{R}^{T_v\times S_v\times C_v}$  and  $\pmb{a}_{0}\in \mathbb{R}^{T_{a}\times S_{a}\times C_{a}}$  represent paired clean latents of video and audio data respectively, where  $T,S,$  and  $C$  denote temporal, spatial (or frequential for audio), and channel dimensions. Given input image  $i$  and noised inputs  $\pmb{v}_t$  and  $\pmb{a}_{t}$  at each timestep (see Section 3.1), the goal of JointDiT is to model cross-modal interactions and predict the clean paired latents  $(\hat{\pmb{v}}_0,\hat{\pmb{a}}_0)$ , i.e., I2SV, as illustrated in Figure 2(b).
+
+Architecture Overview. As shown in Figure 2(b), JointDiT consists of three main components: an Input Block, multiple Joint Blocks, and an Output Block. To effectively model the two modalities within one model while addressing their heterogeneity, JointDiT incorporates both shared interaction layers and modality-specific layers.
+
+The Input Block contains two independent input layers, the V-Input and A-Input layers, which preprocess video and audio data respectively. The Joint Block comprises three types of layers: (1) modality-specific layers (V-Expert and A-Expert) that focus on intra-modal interactions, such as self-attention and conditional image processing (e.g., concatenation or cross-attention, see Supplementary A); (2) a global full attention layer that models fine-grained cross-modal interactions across temporal, spatial, and sequential dimensions using global attention without inductive biases; and (3) modality-specific feedforward layers (V-Feedforward and A-Feedforward), following the standard DiT design [36]. Each layer is followed by modality-specific adaptive layer normalization (AdaLN) [36]. Finally, the Output Block includes two independent layers, V-Out and A-Out, which decode the processed representations into the clean latents  $\hat{\pmb{v}}_0$  and  $\hat{\pmb{a}}_0$ , respectively.
+
+Input, Expert, and Output Layers. To efficiently model modality-specific pattern, JointDiT directly leverages pretrained unimodal DMs  $D_{\theta_v}$  and  $D_{\theta_a}$  (from any architecture
+
+![](images/e094f85e604d30cdd1f5764b31fa6babeca47fc1ca0dcfd9a82f438e7fc63a70.jpg)  
+Figure 2. JointDiT. (a) Pretrained Unimodal Denoisers. JointDiT integrates pretrained video and audio denoisers by first decoupling them into specific submodules and then treats them as three types of layers for joint modeling: input layer, expert layer and output layer. (b) JointDiT Structure. The architecture consists of three types of blocks: Input Block contains two independent modality-specific input layers derived from the pretrained denoisers. Joint Block features a full attention layer to facilitate cross-modal interactions between video and audio. Output Block includes two modality-specific output layers to generate the final denoising results for each modality. (c) Implementation of Full Attention Layer in the Joint Block. The Perceiver Joint Attention mechanism is designed to handle the heterogeneous nature of video and audio data, effectively managing the significant channel dimension disparity between the two modalities while interaction.
+
+![](images/48e0e0673846e10a1e211117f1ee74f21b7c79f5d9d5b56ff316c3275704876d.jpg)
+
+or training framework), as the modality-specific Input, Expert, and Output layers. Based on previous works [53] that prove intermediate representations of DMs contain high-level semantics, we hypothesize that earlier layers of DMs focus on representation and understanding, while later layers are dedicated to decoding and generation. Based on this intuition, earlier (understanding) layers from  $D_{\theta_v}$  and  $D_{\theta_a}$  are used as Input and Expert layers, where cross-modal interactions (needs understanding) are introduced among these layers, while later (generation) layers are employed as Output layers for modality-specific decoding.
+
+Figure 2(a) illustrates this with a six-layer UNet-based DM (each UNet block is treated as a layer in this paper). The first layer serves as the Input layer, the second and third layers act as Expert layers within the first and second Joint Blocks, and the fourth to sixth layers collectively form the Output layer (detailed layer setting in Supplementary A). JointDiT thus provides a framework for decoupling single-modality DMs and effectively integrating them into a unified joint modeling architecture.
+
+Full Attention Layer. At full attention layer in Joint Block, JointDiT firstly flattens video  $\mathbf{v}_t$  and audio  $\mathbf{a}_t$  data into  $\overline{\mathbf{v}}_t \in \mathbb{R}^{(T_v \times S_v) \times C_v}$  and  $\overline{\mathbf{a}}_t \in \mathbb{R}^{(T_a \times S_a) \times C_a}$  and concatenates them into a sequence of  $[\overline{\mathbf{v}}_t, \overline{\mathbf{a}}_t]$ . For their interaction, due to the inherent heterogeneity and different redundancy of video and audio data (e.g.,  $\mathbf{v}_t$  has  $\sim 200$  times higher spatial dimension but  $\sim 4$  times lower temporal dimension
+
+compared to  $a_{t}$ , and  $\sim 2$  times channels in our setting), a naive full attention mechanism—where both modalities are projected to the same channel dimension and vanilla self-attention is applied to the concatenated sequence—fails to effectively model cross-modal interactions, as evidenced by our experiments (Section 4.5).
+
+To address this limitation, we introduce a balanced interaction mechanism, termed Perceiver Joint Attention, which is designed to accommodate modality-specific characteristics as shown in Figure 2(c). Inspired by prior work [19], we modify the shared Q (query) K (key) V (value) projections to be modality-specific. Separate QK projections for video and audio project  $\boldsymbol{v}_t$  and  $\boldsymbol{a}_t$  into the same QK dimension for Query-Key calculation, while separate V projections map them into a Value dimension distinct from QK. Finally, separate out-projections return them to their original channels after attention operation.
+
+# 3.3. Training of JointDiT
+
+JointDiT integrates the optimization objectives of two pretrained DMs: DDPM formulation in  $D_{\theta_a}$  (AudioLDM [31]) and preconditioning EDM formulation in  $D_{\theta_v}$  (SVD [3]), as detailed in Section 3.1. Our unified training strategy preserves both objectives while enabling joint optimization.
+
+A key distinction between DDPM and EDM lies in their timestep parameterization: DDPM uses discrete timesteps  $t\sim \mathcal{U}\{1,\dots,1000\}$ , while EDM uses continuous timesteps
+
+$t(\sigma) = 0.25\log \sigma$  with  $\log \sigma \sim \mathcal{N}(P_{\mathrm{mean}},P_{\mathrm{std}}^2)$ . To schedule noise across modalities, we introduce a unified timestep  $t_\mathrm{uni}\sim \mathcal{U}(0,1)$  that controls both processes through:
+
+$$
+t = \left[ 1 0 0 0 t _ {\text {u n i}} \right], \quad \text {f o r D D P M}, \tag {4}
+$$
+
+$$
+\log \sigma = P _ {\text {m e a n}} + P _ {\text {s t d}} \cdot \Phi^ {- 1} \left(t _ {\text {u n i}}\right), \quad \text {f o r E D M}, \tag {5}
+$$
+
+where  $\Phi^{-1}$  is the inverse cumulative distribution function of the standard normal distribution. This parameterization enables JointDiT to inherit the original training objectives of both base DMs (under any diffusion frameworks) with minimal adaptation, maintaining their pretrained knowledge. The joint optimization objective combines both losses through linear interpolation:
+
+$$
+\left(\hat {\boldsymbol {v}} _ {0}, \hat {\boldsymbol {a}} _ {0}\right) = D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {v} _ {t _ {\mathrm {u n i}}}, \boldsymbol {a} _ {t _ {\mathrm {u n i}}}; i, t _ {\mathrm {u n i}}\right), \tag {6}
+$$
+
+$$
+\mathcal {L} \left(\theta_ {\text {j o i n t}}\right) = \mathbb {E} \left[ \lambda_ {1} \| \boldsymbol {v} _ {0} - \hat {\boldsymbol {v}} _ {0} \| ^ {2} + \lambda_ {2} \| \boldsymbol {a} _ {0} - \hat {\boldsymbol {a}} _ {0} \| ^ {2} \right], \tag {7}
+$$
+
+where  $\pmb{v}_{t_{\mathrm{uni}}}$  and  $\pmb{a}_{t_{\mathrm{uni}}}$  are noisy data introduced in Equation 1 and 2 with  $t_{\mathrm{uni}}, \lambda_1$  and  $\lambda_2$  control modality weighting. This formulation preserves the mathematical foundations of both diffusion frameworks while enabling efficient joint training through a shared timestep coordinate system.
+
+# 3.4. Inference of JointDiT
+
+For unimodal generation (e.g., videos), vanilla classifier-free guidance (CFG) operates as the following formulation:
+
+$$
+\underbrace {D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t} ; i , t\right)} _ {\text {T a r g e t d i s t r i b u t i o n}} + \omega \Big (\underbrace {D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t} ; i , t\right) - D _ {\theta_ {v}} \left(\boldsymbol {v} _ {t} ; \varnothing , t\right)} _ {\text {G u i d a n c e c o r r e c t i o n}} \Big), \tag {8}
+$$
+
+where the first term estimates the conditional distribution, while the second term enhances sample quality by steering predictions toward conditional outputs and away from unconditional counterparts, serving as a correcting term.
+
+Extending this to joint generation, we substitute  $D_{\theta_v}$  and  $\pmb{v}_t$  with  $D_{\theta_{\mathrm{joint}}}$  and  $(\pmb{v}_t,\pmb{a}_t)$ . Vanilla CFG correction becomes:
+
+$$
+D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {v} _ {t}, \boldsymbol {a} _ {t}; i, t _ {\text {u n i}}\right) - D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {v} _ {t}, \boldsymbol {a} _ {t}; \varnothing , t _ {\text {u n i}}\right). \tag {9}
+$$
+
+JointCFG and JointCFG*. While effective for condition alignment, the vanilla correction term above neglects modality-interaction enhancement. To address this, we redesign the negative term by simultaneously removing conditional inputs and modality interactions (through block-diagonal attention masking on full attention layer):
+
+$$
+\left. D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {v} _ {t}, \boldsymbol {a} _ {t}; i, t _ {\mathrm {u n i}}\right) - \left[ D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {v} _ {t}; \varnothing , t _ {\mathrm {u n i}}\right), D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {a} _ {t}; \varnothing , t _ {\mathrm {u n i}}\right) \right], \right. \tag {10}
+$$
+
+where the full-attn-masked model generates modality-isolated predictions. This redesigned correction term extends CFG to joint generation, introducing a joint guidance, namely joint-classifier-free guidance (JointCFG). This mechanism simultaneously enforces condition adherence and cross-modal consistency, visualized in Figure 3.
+
+Inspired by Autoguidance [21] (Section 3.1) that bad version DMs serve as effective guides, we further develop
+
+![](images/73b670ba8206b1a38a114551a3217678e2aad8d0d4807f84920a7f8b52822069.jpg)  
+Figure 3. Comparison between refined Joint Classifier-Free Guidance (Joint-CFG*) and conventional CFG in the context of joint generation. We utilize bad versions of two unimodal generation results to boost the CFG performance in the joint generation.
+
+modality-specific bad model  $D_{\theta_{\mathrm{joint}}}^*$  upon JointCFG by removing full attention layers in Joint Blocks. This partial model produces suboptimal single-modality predictions due to the lack of parameters for modality interaction. The enhanced correction term becomes:
+
+$$
+\left. D _ {\theta_ {\text {j o i n t}}} \left(\boldsymbol {z} _ {v}, \boldsymbol {z} _ {a}; i, t _ {\mathrm {u n i}}\right) - \left[ D _ {\theta_ {\text {j o i n t}}} ^ {*} \left(\boldsymbol {z} _ {v}; \varnothing , t _ {\mathrm {u n i}}\right), D _ {\theta_ {\text {j o i n t}}} ^ {*} \left(\boldsymbol {z} _ {a}; \varnothing , t _ {\mathrm {u n i}}\right) \right]. \right. \tag {11}
+$$
+
+JointCFG with this correction term is named JointCFG*. It further improves joint generation quality.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Implementation Details. For video and audio representations  $\boldsymbol{v}_0$  and  $\boldsymbol{a}_0$ , we utilize latents sampled from the Variational Autoencoder (VAE) from SVD [3] and AudioLDM2 [31], respectively. For processing conditional images: (1) V-Expert layer: Following SVD, the image is encoded using its VAE, duplicated to latent frame length, and concatenated with noisy video latents along the channel dimension. Additionally, CLIP [37] embeddings are extracted for cross-attention. (2) A-Expert layer: We modify AudioLDM2 by encoding the image using CLIP and add the image embeddings to the timestep embeddings. In the full-attention layer, without any conditional image input, this layer focuses on the interaction between the time sequences of the two modalities. We apply 3D and 2D rotary position embeddings (RoPE) [42] to  $\boldsymbol{v}_t$  and  $\boldsymbol{a}_t$ , respectively, for QK computation in this layer. For integrating pretrained unimodal DMs, we preserve the original Input, Expert, and Output layer designs [3, 31] for simplified implementation. Dataset. We establish the I2SV task using three benchmark datasets: AVSync15 [55], Landscape [25], and GreatestHits [35]. (1) AVSync15: Derived from VGGSound [5], this dataset features synchronized audio and video across 15 categories, with video durations ranging from 2 to 10 seconds. It includes 1350 training videos and 150 test videos.
+
+<table><tr><td rowspan="2">GenProcess</td><td rowspan="2">Method</td><td colspan="2">Video Quality</td><td colspan="2">Audio Quality</td><td colspan="2">VA Consistency</td><td colspan="2">Condition Alignment</td></tr><tr><td>FVD↓</td><td>KVD↓</td><td>FAD↓</td><td>KL↓</td><td>IB-VA↑</td><td>AV-Align↓</td><td>IB-IV↑</td><td>IB-IA↑</td></tr><tr><td rowspan="2">I→V || I→A</td><td>SVD[3] + IM2Wav[40]</td><td>444</td><td>37.7</td><td>34.9</td><td>3.08</td><td>12.8</td><td>1.866</td><td>87.0</td><td>13.6</td></tr><tr><td>SVD[3] + AudioLDM[31]-v</td><td>444</td><td>37.7</td><td>30.3</td><td>2.58</td><td>24.9</td><td>1.352</td><td>87.0</td><td>24.7</td></tr><tr><td rowspan="4">I→V + V→A</td><td>SVD[3] + Diff-Foley[32]</td><td>444</td><td>37.7</td><td>32.2</td><td>3.31</td><td>19.8</td><td>1.693</td><td>87.0</td><td>18.8</td></tr><tr><td>SVD[3] + FoleyCrafter[56]</td><td>444</td><td>37.7</td><td>31.6</td><td>2.19</td><td>29.8</td><td>1.792</td><td>87.0</td><td>28.7</td></tr><tr><td>SVD[3] + TiVA[48]</td><td>444</td><td>37.7</td><td>35.5</td><td>3.70</td><td>17.4</td><td>1.834</td><td>87.0</td><td>17.1</td></tr><tr><td>SVD[3] + SeeingHearing[49]</td><td>444</td><td>37.7</td><td>35.2</td><td>3.40</td><td>29.6</td><td>1.569</td><td>87.0</td><td>27.4</td></tr><tr><td rowspan="2">I→A + A†→V</td><td>IM2Wav[40] + AVSyncD[55]</td><td>645</td><td>64.4</td><td>34.9</td><td>3.08</td><td>12.9</td><td>1.352</td><td>83.2</td><td>12.7</td></tr><tr><td>AudioLDM[31]-v + AVSyncD[55]</td><td>610</td><td>64.4</td><td>30.3</td><td>2.58</td><td>25.5</td><td>1.285</td><td>83.7</td><td>24.4</td></tr><tr><td rowspan="3">I→T→V+ I→T→A</td><td>Qwen.[1] + CogV.-2B[51] + SDA[10]</td><td>1172</td><td>157</td><td>32.3</td><td>3.29</td><td>24.8</td><td>1.970</td><td>68.6</td><td>22.1</td></tr><tr><td>Qwen.[1] + CogV.-5B[51] + SDA[10]</td><td>1148</td><td>138</td><td>32.3</td><td>3.29</td><td>24.9</td><td>1.928</td><td>70.5</td><td>22.1</td></tr><tr><td>Qwen.[1] + Hunyuan.[23] + SDA[10]</td><td>1094</td><td>140</td><td>32.3</td><td>3.29</td><td>26.0</td><td>2.155</td><td>70.2</td><td>22.1</td></tr><tr><td rowspan="2">I→VA</td><td>CoDiI[44]</td><td>1873</td><td>369.3</td><td>44.8</td><td>5.61</td><td>5.3</td><td>1.772</td><td>51.9</td><td>4.8</td></tr><tr><td>JointDiT (ours)</td><td>326</td><td>15.2</td><td>23.9</td><td>1.36</td><td>37.5</td><td>1.296</td><td>87.7</td><td>36.3</td></tr></table>
+
+Table 1. Automatic evaluation on the AVSync15 dataset, assessing video-audio quality, semantic and temporal consistency, and conditional alignment (with input image). Best and second-best results are highlighted. A† indicates models requiring text input assistance despite audio. Abbreviations: SVD and SDA denote Stable Video Diffusion [3] and Stable Audio Open 1.0 [10], while Qwen., CogV., Hunyuan. denote Qwen-VL-7B [1], HunyuanVideo [23], CogVideoX [51] (1.0). For fairness, only T2V mode (not TI2V) is used for HunyuanVideo and CogVideoX respectively. JointDiT achieves state-of-the-art results across all metrics, with competitive synchronization scores.
+
+(2) Landscape: Comprising 928 videos across nine natural landscape categories. (3) Greatest Hits: Contains 977 videos of humans striking objects with drumsticks. Both AVSync15 and Landscape provide category labels in text, but no text information is used in any setting. Training and testing are conducted using the video's first frame as the conditional image and the full video as the ground truth. The task emphasizes the model's ability to understand static visual information and generate dynamic and synchronized visual and audio outputs, without relying on textual cues.
+
+Baseline. We evaluate five I2SV methods: (1)  $\mathrm{I} \to \mathrm{V} \parallel \mathrm{I} \to \mathrm{A}$ : Video and audio are independently generated using Stable Video Diffusion (SVD) [3] for I2V and IM2Wav [40] or AudioLDM-v for I2A. AudioLDM-v is adapted from AudioLDM2 [31] by replacing text features with image features and fine-tuning on VGGSound. (2)  $\mathrm{I} \to \mathrm{V} + \mathrm{V} \to \mathrm{A}$ : Video is generated via SVD, followed by audio generation using V2A models (e.g., Diff-Foley [32], FoleyCrafter [56], TiVA [48], Seeing-and-Hearing [49]). Videos are repeated to match V2A requirements and then truncated to target length. (3)  $\mathrm{I} \to \mathrm{A} + \mathrm{A} \to \mathrm{V}$ : Audio is generated via IM2Wav or AudioLDM-v, then used with AVSyncD [55] for video generation, requiring audio, image, and text prompts as inputs. Dataset category labels serve as text prompts. (4)  $\mathrm{I} \to \mathrm{T} \to \mathrm{V} + \mathrm{I} \to \mathrm{T} \to \mathrm{A}$ : Captions are generated using vision large language models (e.g., Qwen-VL [1]), then used for T2V generation via HunyuanVideo [23] or CogVideoX [51], and T2A generation via Stable Audio Open [10]. This pipeline is evaluated on diverse AVSync15 scenarios. (5)  $\mathrm{I} \to \mathrm{VA}$ , i.e., I2SV: CoDi [44], a general any-to-any generation model, is tested for direct I2SV generation.
+
+Evaluation Metrics. We assess the generated sounding videos across four perspectives: (1) Video Quality: We employ FVD [45] and KVD [45]metrics, commonly used in the video generation domain. (2) Audio Quality: Melception [17] computes FAD [22],
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">GreatestHits</td><td colspan="3">LandScape</td></tr><tr><td>FVD↓</td><td>FAD↓</td><td>AV↓</td><td>FVD↓</td><td>FAD↓</td><td>AV↓</td></tr><tr><td colspan="7">I → V || I → A</td></tr><tr><td>SVD[3] + A.LDM[31]-v</td><td>441</td><td>26.65</td><td>1.392</td><td>402</td><td>2.28</td><td>1.414</td></tr><tr><td>SVD[3] + IM2Wav[40]</td><td>441</td><td>29.14</td><td>1.886</td><td>402</td><td>1.61</td><td>2.005</td></tr><tr><td colspan="7">I → V + V → A</td></tr><tr><td>SVD[3] + Diff-Foley[32]</td><td>441</td><td>27.99</td><td>1.706</td><td>402</td><td>2.81</td><td>1.830</td></tr><tr><td>SVD[3] + FoleyCrafter[56]</td><td>441</td><td>29.26</td><td>1.936</td><td>402</td><td>1.60</td><td>1.996</td></tr><tr><td>SVD[3] + TiVA[48]</td><td>441</td><td>29.51</td><td>1.925</td><td>402</td><td>4.18</td><td>1.919</td></tr><tr><td>SVD[3] + SeeingHearing[49]</td><td>441</td><td>24.86</td><td>1.666</td><td>402</td><td>3.59</td><td>1.634</td></tr><tr><td colspan="7">I → A + A† → V</td></tr><tr><td>A.LDM[31]-v + AVSyncD[55]</td><td>287</td><td>26.65</td><td>1.219</td><td>697</td><td>2.28</td><td>1.196</td></tr><tr><td>IM2Wav[40] + AVSyncD[55]</td><td>320</td><td>29.14</td><td>1.777</td><td>707</td><td>1.61</td><td>1.256</td></tr><tr><td colspan="7">I → VA</td></tr><tr><td>CoDi[44]</td><td>1314</td><td>24.97</td><td>1.143</td><td>1233</td><td>5.20</td><td>1.250</td></tr><tr><td>JointDiT</td><td>173</td><td>1.08</td><td>1.462</td><td>262</td><td>1.60</td><td>1.178</td></tr></table>
+
+Table 2. Performance on GreatestHits and Landscape. AV denotes AV-Align metric here. Best and second-best are highlighted.
+
+while PasST [24] calculates the KL score [48]. (3) Video-Audio Quality: Semantic alignment is measured using ImageBind [11] (IB-VA), and temporal synchronization is evaluated with a refined AV-Align score [52] (details in Supplementary B). (4) Condition Alignment: ImageBind assesses the alignment of generated video or audio with the input image (IB-IV, IB-IA). Additionally, we employ Motion Score (MS) [3] in the ablation study to indicate the dynamics of the generated video.
+
+# 4.2. Comparison with Baselines
+
+Table 1 presents a performance comparison between our model and the baseline models on the AVSync15 dataset. In objective evaluations, our model surpasses all baselines in terms of video quality, audio quality, and semantic alignment between video and audio, indicated by FVD, KVD, FAD, KL, and IB-VA metrics.
+
+![](images/fdec641904ddc26f20907b652d5f7848d58c3e2615e916f5d282e83564a6a656.jpg)  
+Figure 4. Qualitative Results. We present three instances from AVSync15, each generated by a different model. Instances produced by JointDiT exhibit high visual quality and dynamics, preserving details (e.g., finger movements in Case 2), and ensuring high correlation between audio and video in terms of semantics and temporal synchronization (e.g., rooster raising its head when crowing in Case 1 and cap gun firing when shooting in Case 3). More cases can be viewed at our dempage https://anonymoushub4ai.github.io/JointDiT.
+
+This demonstrates that the generation of video and audio can mutually enhance each other, which also validates the effectiveness of the JointDiT framework. Only AV-Align metric indicates that JointDiT slightly underperforms the AudioLDM-v+AVSyncD model in the image-to-audio-to-video pipeline, achieving second place with a score of 1.296, slightly worse than 1.285. Notably, although HunyuanVideo and CogVideoX demonstrate stronger T2V capabilities, the process of converting images to text in the I2SV task results in significant information loss. This, in turn, makes it challenging for the second-stage T2V results to align with the original image information, as indicated by low FVD, KVD, and IB-IV scores. Table 2 shows different models' performance on the GreatestHits and Landscape dataset. JointDiT achieves the best results on every metric of LandScape dataset, and leads in FVD and FAD metrics of GreatestHits dataset. Comprehensive experiment results on multiple datasets validate that JointDiT is capable of generating high-quality, semantics-aligned and synchronized video and audio.
+
+# 4.3. User studies
+
+We also conducted subjective evaluations on AVSync15 in Table 3. We evaluated from five dimensions: Video Quality (VQ), Audio Quality (AQ), Semantic Matching between Video and Audio (Sem), Synchronization between Video and Audio (Sync), and Overall Sounding Video Effect (Overall). The evaluation scores ranged from 0 to 5, with 0.5 as the scoring unit and higher
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">User Study ↑</td></tr><tr><td>VQ</td><td>AQ</td><td>Con</td><td>Sync</td><td>Overall</td></tr><tr><td>SVD[3] + AudioLDM[31]-v</td><td>1.28</td><td>1.33</td><td>1.31</td><td>1.25</td><td>1.26</td></tr><tr><td>SVD[3] + SeeingHearing[49]</td><td>1.30</td><td>1.25</td><td>1.24</td><td>1.21</td><td>1.23</td></tr><tr><td>AudioLDM[31]-v + AVSyncD[55]</td><td>1.19</td><td>1.33</td><td>1.36</td><td>1.30</td><td>1.28</td></tr><tr><td>CoDi[44]</td><td>0.91</td><td>0.95</td><td>0.87</td><td>0.87</td><td>0.92</td></tr><tr><td>JointDiT</td><td>1.48</td><td>1.55</td><td>1.60</td><td>1.51</td><td>1.52</td></tr></table>
+
+Table 3. User study results on AVSync15 dataset. We compare with baseline models from different I2SV generation approaches across: VQ (Video Quality), AQ (Audio Quality), Con (Semantic Consistency), Sync (Synchronization), and Overall (Composite Performance). Human ratings are averaged per metric, with best and second-best highlighted. JointDiT achieves superior performance across all evaluation dimensions.
+
+scores indicate better results. We sample 100 results from each model with same condition and have them rated by 10 annotators, with the final score being the average of their ratings. The results of the subjective evaluations demonstrate that JointDiT outperforms other methods in all five dimensions. Interestingly, the automatic metrics are not entirely consistent with human evaluation results. For example, for video-audio synchronization, our method achieved the best human evaluation result, with AudioLDM-v+AVSyncD coming second, but the objective metrics ranked them in reverse order. This further suggests that despite our improvements on objective metrics (Supplementary B), they
+
+![](images/3e2e0d1096891b0e932540ff7ee2e79cff64757ee2d190f77dab42260024cf8e.jpg)  
+Figure 5. Case study on GreatestHits and Landscape datasets. JointDiT is capable of generating temporally and semantically consistent sounding videos across diverse I2SV scenarios.
+
+still cannot perfectly align with human evaluations. We leave potential improvements to the automatic evaluation for future work.
+
+# 4.4. Case study on Joint-DiT
+
+Figure 4 illustrates a case comparison between JointDiT and the baseline models. The two types of methods, image-to-video + image-to-audio and image-to-video-to-audio, first generate videos from images. However, the video dynamics produced by SVD, a unimodal video generation model, often lack entity dynamic other than lens and perspective movings. For instance, for an input image of a chicken (case1) and a gun (case3), the SVD-generated results merely move the lens slightly and do not include entity actions such as the chicken raising its head or the gun shaking when fired. The pipeline method of I2A2V often leads to the accumulation of errors and confuses the model in the later stages of the pipeline. For example, in the third line of case 3, the I2A model generated a radio voice but the condition image was of a gun, causing the subsequent IA2V model to produce some unstable images, as shown in the dashed box. The early I2VA method, CoDi, due to its coarse-grained interaction, leads to poor overall generation quality. In contrast, the cases generated by our JointDiT have good visual quality and dynamics, and also maintain details (finger movements in case 2), and can generate sound that matches the video semantics and is synchronized (case 1 crowing when the chicken raises its head, case 3 gun firing when smoke appears). In addition to the general generation performance of AVSync15, Figure 5 further presents the generation results of JointDiT on the GreatestHits and Landscape datasets. The results demonstrate that JointDiT is capable of effectively handling data from specific domains, such as natural scenery near ocean waves and human actions while striking objects. Moreover, it can produce coherent and natural paired video and audio contents that meets with physical laws within the contexts provided by the first frame of a scene.
+
+<table><tr><td>JointDiT</td><td>FVD↓</td><td>FAD↓</td><td>IB-VA↑</td><td>AV-Align↓</td><td>MS→</td></tr><tr><td>w/ JointCFG*</td><td>653.7</td><td>27.6</td><td>37.4</td><td>1.288</td><td>10.73</td></tr><tr><td>w/ JointCFG</td><td>661.6</td><td>28.1</td><td>36.9</td><td>1.273</td><td>10.15</td></tr><tr><td>w/ vanilla CFG</td><td>662.8</td><td>28.2</td><td>36.1</td><td>1.266</td><td>10.19</td></tr><tr><td>w/o Joint Block</td><td>819.5</td><td>30.1</td><td>36.2</td><td>1.363</td><td>5.32</td></tr><tr><td>w/o Perceiver Attn</td><td>921.2</td><td>29.3</td><td>34.4</td><td>1.240</td><td>5.54</td></tr></table>
+
+Table 4. Ablation studies on guidance methods and architecture, evaluated on a randomly sampled subset of AVSync15 test for efficiency. MS represents motion scores. The w/o Joint Block setting refers to removing the Joint Block from JointDiT, resulting in the fine-tuned setting of two pretrained DMs. The w/o perceiver attn setting replaces perceiver joint attention with standard self-attention. These two architecture-ablation settings are inferred with vanilla CFG as w/o Joint Block not applicable with JointCFG.
+
+# 4.5. Ablation Studies
+
+Guidance Techniques. Table 4 compares three CFG techniques: Enhanced JointCFG (w/ joint-CFG*), vanilla CFG and JointCFG. The table reveals that the enhanced JointCFG* significantly improves image quality, sound quality, and IB-VA, albeit at a slight cost to AV-Align metrics. However, it also consistently enhances the motion score, introducing more dynamic changes to the video. JiontDiT Architecture. In the bottom part of Table 4, we conducted an ablation study on the JointDiT architecture, comparing three settings: our final version (w/ joint-CFG*), a version without the Joint Block trained on AVSync15 (essentially fine-tuning independent video and audio denoisers on AVSync15), and a version substituting perceiver full attention with vanilla full attention. Tests are performed on the same randomly selected 75 images. The results demonstrate that our final version achieves the highest image quality, audio quality, and IB-VA audio-video semantic matching. Interestingly, our architecture introduces more dynamic changes, as indicated by the motion score, addressing the challenge of lacking of dynamic variation in the image-to-video task [57]. This suggests that a well-designed interaction facilitates more visual dynamics in the joint generation of video and audio.
+
+# 5. Conclusion and Future Work
+
+To solve the task of Image-to-Sounding Video (I2SV) generation, we propose a novel approach using the DiT architecture to model the interaction between video and audio modalities. We combine the expert pretrained diffusion generation submodules using a unified Joint Block. We further introduce introduce a joint classifier-free guidance technique to refine the guidance effect.
+
+In future work, we plan to extend JointDiT to joint or cross-generation tasks involving the text modality. We also intend to further investigate the relationships among the three modalities and explore the scalability of JointDiT using larger-scale datasets across additional modalities, aiming to develop a more foundational text-video-audio model towards the world model.
+
+# Acknowledgement
+
+This work is supported by the National Natural Science Foundation of China (No. 62276268), Public Computing Cloud, Renmin University of China and ZHI-TECH GROUP.
+
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\ No newline at end of file
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+# AnimateAnything: Consistent and Controllable Animation for Video Generation
+
+Guojun Lei $^{1*}$ , Chi Wang $^{1*}$ , Rong Zhang $^{4}$ , Yikai Wang $^{2}$ , Hong Li $^{3,5*}$ , Weiwei Xu $^{1\dagger}$ $^{1}$  Zhejiang University  $^{2}$  Tsinghua University  
+ $^{3}$  Beihang University  $^{4}$  Zhejiang Gongshang University  $^{5}$  ShengShu  
+guojunlei@zju.edu.cn, wangchi1995@zju.edu.cn, link0502@buaa.edu.cn  
+zhangrong@zjgsu.edu.cn, yikaiw@outlook.com, xww@cad.zju.edu.cn
+
+![](images/187720f0f331099667828ab1ecd6a771017a0c263ab701c683e880e1ec8ad994.jpg)  
+Figure 1. Animate anything. Consistent and controllable animation for different kinds of control signals. Given a reference image and corresponding user prompts, our approach can animate arbitrary characters, generating clear stable videos while maintaining consistency with the appearance details of the reference object.
+
+# Abstract
+
+We present a unified controllable video generation approach AnimateAnything that facilitates precise and consistent video manipulation across various conditions, including camera trajectories, text prompts, and user motion annotations. Specifically, we carefully design a multiscale control feature fusion network to construct a common motion representation for different conditions. It explicitly converts all control information into frame-by-frame optical flows. Then we incorporate the optical flows as motion priors to guide the final video generation. In addition, to reduce the flickering issues caused by large-scale motion, we propose a frequency-based stabilization module. It can
+
+enhance temporal coherence by ensuring the video's frequency domain consistency. Experiments demonstrate that our method outperforms the state-of-the-art approaches. For more details and videos, please refer to the anonymous webpage: https://yu-shaonian.github.io/Animate_Anything/.
+
+# 1. Introduction
+
+The emergence of Sora [5] has led to a breakthrough in large-scale video generation. Recently, controllable video generation [17, 22, 45, 51], i.e. controlling camera trajectories and object movements, has gained significant attention. It has expanded applications of video generation, making them directly applicable to film production and virtual reality. However, due to the high complexity of large-scale
+
+camera and object movements, achieving precise control over video generation in such cases remains challenging.
+
+MotionCtrl [45] and CameraCtrl [17] support camera trajectory manipulation for dynamic video generation, but they rely solely on text input. Since text descriptions provide only the overall characteristics of a video and cannot convey specific details precisely, it is insufficient to manipulate the video generation process only using text prompts. In contrast, image guidance, such as user-annotated trajectories or reference videos, can present more detailed visual cues. Motion-I2V [38] allows for image-based guidance but only enables slight object movements through user drag annotations, such as adjusting eye direction or indicating leg motion. It is not capable of manipulating the camera trajectory of a video. MOFA-Video [31] achieves control over detailed, pixel-level movements but is also limited to small-scale camera movement. To ensure global consistency in dynamic videos, MOFA-Video requires users to specify the movement direction for each local region of the input image that may move, making the process overly complex for user interaction.
+
+This paper focuses on image-to-video (I2V) generation that simultaneously processes dynamic control signals, such as arrow-based motion annotations, camera movements, and reference videos. However, the integration of these signals is challenging due to their different modalities, making the direct combination with a single video generation model difficult. Current approaches [15] typically attempt to train each control signal individually (for instance, through Lora [24]), and then collaboratively apply these signals to enhance video generation results. Nevertheless, these methods often necessitate careful parameter tuning or denoising strategies, making it difficult to maintain video stability, which can lead to flickering effects or incoherent pixel motion caused by different control signals. Some methods [31, 38] aim to facilitate the controllable generation of local motion in videos by introducing optical flow fields; however, they are ineffective in addressing camera motion signals, as camera movement introduces global motion information that is independent of the subject's motion. Based on the insights presented above, we speculate that if the local motion of the subject and the global motion of the camera can be unified into a representation of frame-by-frame pixel movements, namely optical flow, it would support the guidance of the video generation model's behavior, thereby possessing the potential to achieve synchronous control of various signals.
+
+The key challenge is to handle incoherent pixel motion caused by different control signals. For instance, as Fig. 2 shows, the optical flow generated from different control signals varies greatly. Camera motion involves global movement, affecting both foreground and background pixels (the first row of Fig. 2), while a single motion annotation mainly
+
+![](images/c9fb7865189d75550e798ed45d0ab8bfdcfaee3ccaeee965efb24e9cafc71e3b.jpg)  
+Figure 2. The generated optical flow by our method with different condition signals. Given a specific image, from top to bottom are optical flows generated with camera trajectory, arrow-based motion annotation, and both conditions, respectively.
+
+influences localized foreground pixel motion (the second row of Fig. 2). Simultaneously introducing these two conditions directly may result in control signal conflicts, making the model confused about the following movements (the third row of Fig. 2). It is difficult to directly integrate these conditions through existing methods, since it demands considering both the individual impact of each condition and their complex interactions, such as projection transformations and occlusion completion. Therefore, we strategically design various condition-injection modules based on the representation and correlations of different control signals to enable unified optical flow generation.
+
+Therefore, we propose an innovative two-stage video generation method to achieve multi-condition joint control. In the first stage, we convert various motion control signals into a unified optical flow, which is then used to guide the final video generation in the second stage. To further enhance video stability, we convert features from the time domain to the frequency domain and introduce a spectral attention mechanism to improve the overall quality of the generated videos.
+
+The main contributions are summarized as follows:
+
+- We introduce a two-stage pipeline to achieve stable and flexible video generation with different kinds of control signals. In the first stage, all control signals convertible to flows will be unified into a frame-by-frame optical flow, which is then fed into the second stage to synchronize with text controls for high-quality video generation.  
+- We utilize an adaptive feature refinement in the frequency domain. This operation effectively suppresses instability and flickering in the generated video by modifying the temporal frequency features within the video.  
+- We perform extensive experiments to demonstrate the superiority of our method over state-of-the-art methods both quantitatively and qualitatively.
+
+# 2. Related Work
+
+Controllable Video Generation. Text-to-video (T2V) generation has received significant attention in recent years, especially after the emergence of Sora [24]. Typically, in this area, the text-based control information is injected
+
+via cross-attention mechanisms [17, 45]. While Magic-Time [54] introduces a novel GPT [1]-based "Magic TextEncoder" to enhance text comprehension ability. However, text-driven approaches often fail to convey video details precisely. As a result, methods driven by text and image simultaneously have become popular, significantly addressing these limitations. To achieve more effective video generation, pioneers [10, 13, 25, 43, 59] have explored generating videos under the guidance of some easily obtainable signals such as edges, depth, optical flow, or bounding boxes. Taking reference video as motion guidance, MotionClone [29] enables motion cloning by treating temporal-attention weights as motion representation. Recently, with the immense potential of the film industry and virtual reality applications, precise control over camera and object motion trajectories has gained increasing interest.
+
+Camera Trajectory Driven Video Generation. To facilitate camera trajectory control,AnimateDiff [15] trains additional motion LoRA [21] modules for each specific camera path. However, this method lacks precise control of camera trajectory and cannot generate videos for unseen camera trajectories. A straightforward solution to these issues is to treat camera parameters as additional conditions for video generation. MotionCtrl [45] employs 12 pose matrix parameters as frame-level conditions to explicitly introduce camera trajectory. Nevertheless, this method still shows limitations in capturing the necessary geometric information for precise camera control. CameraCtrl [17] enhances camera information integration by using plucker embeddings to represent camera trajectories. To integrate the camera embedding more effectively, VD3D [2] and CamCo [49] introduce a ControlNet [57]-like conditioning mechanism and an epipolar attention module, respectively.
+
+Object Motion Trajectory Driven Video Generation. CameraCtrl [17] and MotionCtrl [45] support basic motion control through text description, which are often imprecise. Compared to T2V's object motion control based on motion descriptions, the Image-to-video (I2V) method generates videos from object motion trajectories. It allows for a more precise and user-friendly description of object positions, movement directions, and motion amplitude within the scene. Yin et al. [53], Hao et al. [16] and Shi et al. [38] introduce explicit optical flow as an intermediate representation to guide video generation. Similarly, MOFA-Video takes sparse motion hints as input and generates dense optical flows to warp multi-scale features to guide the process.
+
+Motion-I2V [38] is the most relevant method to ours, as both use a two-stage framework and select optical flow as an intermediate motion representation. In the first stage of optical flow generation, Motion-I2V derives optical flow from text and reference motion field images. In contrast, we treat optical flow as a unified visual motion representation that incorporates reference images, drag actions, and view-
+
+point changes. This allows for a more comprehensive and balanced handling of diverse visual conditions. In the second stage, while Motion-I2V directly integrates optical flow with text and images, we employ the Expert AdaLN [51] to promote feature space alignment adaptively, enabling a deep fusion of multimodal features. This enhancement improves the capability and generalization of this stage, allowing it to perform effectively even when the image and optical flow are not fully aligned.
+
+# 3. Methods
+
+In this section, we present AnimateAnything, a unified controllable video generation approach for precise and consistent video customization across various conditions. As the pipeline illustrated in Fig. 3, we convert all visual control signals into a unified optical flow representation and then utilize it to guide the final video generation. In the following subsections, we will provide a detailed explanation of preliminary knowledge, each module of the pipeline, and the corresponding training strategies. Firstly, we provide a brief overview of Video Diffusion Models in Sec. 3.1. Afterward, we present the architecture of converting all control signals into unified flows in Sec. 3.2. Then, we introduce how the flows guide the final video generation in Sec. 3.3. Finally, we give detailed descriptions of the frequency stabilization module 3.4 and training strategy 3.5.
+
+# 3.1. Video Diffusion Models
+
+The video diffusion model builds on the concept of image diffusion probabilistic models, extending into the temporal dimension. It captures the dynamic relationships between frames in a video sequence, allowing for the generation of continuous and high-quality video content. By learning to reverse the added noise, it ensures temporal consistency and coherence in the generated videos. Let  $x_0 \in R^{f \times h \times w \times c}$  represent a video latent variable, where  $f$  is the total number of frames, each of size  $h \times w$  with  $c$  channels. The forward diffusion process is modeled as a chain that incrementally adds Gaussian noise to the original video, defined as follows:
+
+$$
+x _ {t} = \sqrt {\bar {\alpha} _ {t}} x _ {t - 1} + \sqrt {(1 - \bar {\alpha} _ {t})} \epsilon , \epsilon \sim N (0, 1), \tag {1}
+$$
+
+where  $t \in \{1, \dots, T\}$  denotes the timestep,  $\bar{\alpha}_t$  regulates the intensity of noise added at each  $t$ , and  $\epsilon$  is drawn from standard Gaussian noise. In the reverse process, a denoising model is learned to estimate  $p(x_{t-1}|x_t)$ , typically parameterized by a neural network  $\theta$ . The optimization objective is to minimize the following loss function: A denoising model, parametrized by neural network  $\theta$ , estimates  $p(x_{t-1}|x_t)$  in the reverse process, minimizing the given loss function:
+
+$$
+\mathcal {L} (\theta) = \mathbb {E} _ {x _ {0}, \epsilon , \mathcal {C}, t} \left[ \| \epsilon - \dot {\epsilon} _ {\theta} (x _ {t}, \mathcal {C}, t) \| _ {2} ^ {2} \right], \tag {2}
+$$
+
+![](images/5728518a0f3d28a75d0c403cd55d31c2b367cfe6dc4d4b20f9d1f6b34a7ba299.jpg)  
+Figure 3. **AnimateAnything Pipeline**. The pipeline consists of two stages: 1) Unified Flow Generation, which creates a unified optical flow representation by leveraging visual control signals through two synchronized latent diffusion models, namely the Flow Generation Model (FGM) and the Camera Reference Model (CRM). The FGM accepts sparse or coarse optical flow derived from visual signals other than camera trajectory. The CRM inputs the encoded reference image and camera trajectory embedding to generate multi-level reference features. These features are fed into a reference attention layer to progressively guide the FGM's denoising process in each time step, producing a unified dense optical flow. 2) Video Generation, which compresses the generated unified flow with a 3D VAE encoder and integrates it with video latents from the image encoder using a single ViT block. The final output is then combined with text embeddings to generate the final video using the DiT blocks.
+
+where  $\mathcal{C}$  denotes the guidance conditions, like text. To train a video generation diffusion model using images, the image encoding is typically concatenated with the  $x_{t}$ , enabling the model to efficiently use its semantic features.
+
+# 3.2. Stage 1: Unified Flow Generation
+
+In this stage, we carefully design different injection modules based on the characteristics of each control signal and their relationship to achieve unified optical flow generation. In detail, we categorize the injection modules into explicit and implicit injection based on the attributes of visual control signals. The explicit injection module is proposed to control signals that can be directly converted into sparse optical flow for one or some frames, such as arrow-based motion annotation on specific pixels. The implicit injection is to incorporate control signals that are difficult to directly convert to pixel-level optical flow like camera trajectory. Finally, since information in the reference image, such as semantic categories, is directly related to various control signals, the image is involved in both implicit and explicit injection methods. In the following, we will explain the detailed operations for explicit and implicit injection, and further discuss the unified control signal at this stage.
+
+Explicit Injection. As shown in Fig. 3, we explicitly convert different explicit control signals into initial sparse optical flow, and then apply a classical latent diffusion model [34], namely the Flow Generation Model (FGM), to transform it into dense optical flows. For these signals like arrow-based motion annotation, we use the following pipeline for conversion. Given a reference im
+
+age, the user can label various motion trajectories on the image to represent the desired movements of objects and the environment. Take one trajectory for example, the trajectory can be regarded as a 2D point set,  $\mathcal{M} \in \mathbb{R}^{P \times 2} = [(x_0, y_0), (x_1, y_1), \ldots, (x_{P-1}, y_{P-1})]$ , where  $P$  is the point number. The sparse control points can be extracted from  $\mathcal{M}$  with bicubic interpolation and then used to generate a point-wise sparse motion flow  $F^s$  in the following equation, the same as MOFA-Video [31], allowing us to guide the object motions and environmental changes effectively.
+
+$$
+F _ {l - 1} ^ {s} \left(x _ {i}, y _ {i}\right) = \hat {\mathcal {T}} _ {l} \left(x _ {i}, y _ {i}\right) - \hat {\mathcal {T}} _ {0} \left(x _ {i}, y _ {i}\right) \tag {3}
+$$
+
+where  $l \in \{1, 2, \dots, L - 1\}$ ,  $i$  denotes each pixel in the image. We also use CMP [56] to enhance sparse optical flows. Theoretically, any visual control signals convertible to sparse optical flow through extraction [50] or generation [9, 52], such as audio [9, 14], videos, and object landmarks [55], etc., can be input to FGM.
+
+Implicit Injection. For implicit control signals like camera trajectory condition, we adopt the progressive condition injection design ofAnimateAnyone [22] and implicitly embed it into the FGM denoising process through the Camera Reference Model (CRM) progressively. The CRM employs a pre-trained image generation network based on the U-Net [35] architecture  $(\mathrm{SD1.5}^{1})$  and is initialized with original weights. It integrates camera trajectories with the reference image to get multi-scale reference features at specific
+
+time steps through camera motion attention, which uses image latents as query, camera features as both the key and value in the original cross-attention part. Then these features are utilized to guide the generation of dense optical flow via the reference attention layer in the FGM the same as AnimateAnyone. In order to better describe the camera pose, we use Plücker embeddings [39] as the representation of camera trajectory. Given the extrinsic and intrinsic camera parameters  $\mathbf{R},\mathbf{t},\mathbf{K}_f$  for the  $f$ -th frame, we derive a Plücker embedding  $\ddot{\pmb{p}}_{f,h,w}v\in \mathbb{R}^6$  for each pixel located at  $(h,w)$ . This embedding represents the vector from the camera center to the pixel's position as:
+
+$$
+\ddot {\boldsymbol {p}} _ {f, h, w} = \left(\boldsymbol {t} _ {f} \times \hat {\boldsymbol {d}} _ {f, h, w}, \hat {\boldsymbol {d}} _ {f, h, w}\right) \tag {4}
+$$
+
+$$
+\hat {\boldsymbol {d}} _ {f, h, w} = \frac {\boldsymbol {d}}{\| \boldsymbol {d} _ {f , h , w} \|}, \quad \boldsymbol {d} _ {f, h, w} = \boldsymbol {R} _ {f} \boldsymbol {K} _ {f} [ w, h, 1 ] ^ {\top} + \boldsymbol {t} _ {f} \tag {5}
+$$
+
+Computing Plücker embedding for each pixel results in a representation  $\ddot{P} \in \mathbb{R}^{6 \times F \times H \times W}$  for a specified trajectory. To inject the trajectory representation into the reference motion network, we designed a trajectory encoder structurally similar to the camera encoder in CameraCtrl [17]. However, we improved the architecture: after each 2D ResNet block, we replaced the temporal attention with self-attention and output multi-scale trajectory features.
+
+Through the combined use of explicit and implicit injection, we can effectively mitigate the incoherent pixel motion caused by different control signals. In addition, we used Unimatch [50] to extract a high-quality optical flow from training videos as ground truth during training. Similar to Motion-I2V [38], we trained a Flow Variational Autoencoder (VAE) to compress the optical flow of the pixel space into a latent flow space reducing computational resources.
+
+# 3.3. Stage 2: Video Generation
+
+In the second stage, we aim to use the unified dense optical flow representation from the previous stage to guide the video generation model in creating a final video that aligns with the semantics of the reference image and annotations, as shown in Fig. 3. For the video generation model, we inherit from CogVideoX framework [19, 51]. However, we introduce optical flow as a conditional guidance. Specifically, we use a flow encoder to encode the flows as the flow latent  $z_{f}$ . The flow encoder adopts four symmetrically arranged stages, respectively performing  $2 \times$  downsampling and upsampling by the interleaving of ResNet block stacked stages achieving a  $4 \times$  compression in the temporal dimension and an  $8 \times 8$  compression in the spatial dimension similar to the 3D VAE encoder [51]. Then we use a single basic Vision Transformer (ViT) block[12] to query video latents  $z_{v}$  from the flow latents  $z_{f}$  before calculating self-attention in the ViT block.
+
+$$
+z _ {v} ^ {\prime} = \text {A t t e n t i o n (Q , K , V)} = \text {S o f t m a x} \left(\mathrm {Q K} ^ {\mathrm {T}}\right) \mathrm {V}, \tag {6}
+$$
+
+![](images/2c3c7a0a37486ccaac2b408754a651a1c07c34775f2d0409a0b57edfd321cf94.jpg)  
+Figure 4. Video stabilization Module
+
+![](images/0453e1cb4b256a85c645d07d49c7504d77bb17140b8fd14ddec9aefdc6b850eb.jpg)
+
+where  $Q = W^{Q}z_{v}, K = W^{K}z_{f}, V = W^{V}z_{f}$ . Notably, the flow feature maps only serve as key and value features. At the same time, the text prompts go through the text encoder using the google-research T5 model [33]. The result of the transformer block is then concatenated with text embedding before going through the full-attention transformer block. As shown in Fig. 3, we only train the optical flow encoder, input transformer block, and our video smoothing module (detailed in Sec. 3.4), keeping the parameters of other parts fixed to reduce the training difficulty.
+
+# 3.4. Frequency Stabilization
+
+In the previous two subsections, we effectively incorporated a large amount of motion control into our network through a two-stage design, supporting the generation of significant motion variations. In such cases, the corresponding optical flow may change drastically, making it prone to flickering and instability in the final video. To solve this problem, we review the video generation task from the perspective of information encoding. Treating the generated video as a sequence of images, flickering typically occurs due to misalignment of features between frames. This stems from the training of video generation models, where noise added to different frames at the same time step is independent. Despite temporal interactions among features, it remains challenging to prevent noise from negatively affecting the continuity and stability of video features. This instability will greatly affect the video generation quality. Compared to temporal features, frequency-domain features can more directly reveal some essential video-level information from a different perspective with individual frequency components, which is important for suppressing flickering issues. Thus, we adaptively modify the frequency-domain features extracted with the Fast Fourier Transform (FFT) [11] to maintain temporal stability. Specifically, as shown in Fig. 4, we modify the attention mechanism in the Diffusion Transformer (DiT) [32] architecture by first applying an FFT to each weight matrix to obtain its spectral features. We then multiply these features by a parameterized weight matrix  $W$ , followed by an inverse FFT (InvFFT) to restore the original temporal-domain feature. This is then used to compute
+
+Table 1. Video quality comparison.  
+
+<table><tr><td rowspan="2"></td><td colspan="5">WebVid10M</td><td colspan="5">OpenVid</td></tr><tr><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>FID↓</td><td>FVD↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>FID↓</td><td>FVD↓</td></tr><tr><td>Motion-I2V</td><td>0.375</td><td>16.14</td><td>0.487</td><td>94.77</td><td>720</td><td>0.329</td><td>15.28</td><td>0.488</td><td>72.14</td><td>704</td></tr><tr><td>MOFA-Video</td><td>0.351</td><td>18.43</td><td>0.603</td><td>57.12</td><td>524</td><td>0.300</td><td>19.64</td><td>0.655</td><td>52.66</td><td>654</td></tr><tr><td>DynamiCrafter</td><td>0.268</td><td>18.56</td><td>0.532</td><td>63.73</td><td>685</td><td>0.393</td><td>13.83</td><td>0.402</td><td>59.61</td><td>751</td></tr><tr><td>CogVideoX+image</td><td>0.147</td><td>24.22</td><td>0.762</td><td>59.20</td><td>486</td><td>0.164</td><td>22.61</td><td>0.762</td><td>43.29</td><td>547</td></tr><tr><td>Pyramid-Flow</td><td>0.152</td><td>24.99</td><td>0.792</td><td>55.78</td><td>470</td><td>0.122</td><td>23.37</td><td>0.789</td><td>39.48</td><td>453</td></tr><tr><td>Open-Sora</td><td>0.179</td><td>23.21</td><td>0.725</td><td>58.33</td><td>552</td><td>0.117</td><td>22.78</td><td>0.760</td><td>44.48</td><td>512</td></tr><tr><td>Ours</td><td>0.135</td><td>25.22</td><td>0.810</td><td>48.11</td><td>380</td><td>0.113</td><td>25.04</td><td>0.836</td><td>33.12</td><td>322</td></tr></table>
+
+dot-product attention, ensuring the consistency of scene features along the temporal direction during video generation.
+
+# 3.5. Training Strategy
+
+We conducted experiments on a server equipped with  $8 \times$  NVIDIA Tesla A800 80G GPUs. In the first stage, for optical flow generation, we primarily use the Real10K [62] and DL3DV10K [28] datasets for training, which contain approximately 600,000 data samples. In the second stage, for video generation, we utilize the WebVid10M [4] and OpenVid [30] datasets, comprising roughly 12 million data samples. Both datasets are large and diverse, covering various aspects of daily life from multiple sources, ensuring strong generalization.
+
+Currently, achieving large-scale camera trajectory control for video generation remains a significant challenge. One of the major difficulties is the limited availability of video data with camera trajectory poses. The datasets available are Real10K [62] and DL3DV10K [28], but both are primarily indoor or static scene datasets. The video model trained on these datasets is unsuitable for dynamic scenes, while the generation is prone to failure. Another difficulty is that the dynamic video datasets available rarely contain pose information due to the difficulty of camera pose estimation in dynamic scenes using structure-from-motion (SfM) methods like COLMAP [37]. So, we organize and augment the data, and we further decompose the training of the first stage to achieve multi-condition controllable network training with limited data. Through careful search, we found that many videos on OpenVid [30] are shot from fixed camera positions, which can serve as a good starting point to boost dynamic training. We select a batch of videos with roughly fixed camera positions by evaluating the motion magnitude of the global optical flow, totaling around 10,000 videos. Our model is to first train the initial model on the Real10K dataset, then set the camera viewpoint of this batch of videos to be fixed at the origin, and subsequently train our model using the selected dynamic videos.
+
+Given that the optical flow data required for the second stage is directly sourced from the video, both stages can be trained independently, with connection only needed during the inference process. Additionally, we apply noise to the
+
+Table 2. Video consistency quality comparison. SubC: Subject Consistency; MoS: Motion Smoothness; AesQ: Aesthetic Quality.  
+
+<table><tr><td rowspan="2"></td><td colspan="3">WebVid10M</td><td colspan="3">OpenVid</td></tr><tr><td>SubC ↑</td><td>MoS ↑</td><td>Aesq ↑</td><td>SubC ↑</td><td>MoS ↑</td><td>Aesq ↑</td></tr><tr><td>DynamiCrafter</td><td>0.832</td><td>0.958</td><td>0.443</td><td>0.910</td><td>0.964</td><td>0.536</td></tr><tr><td>CogVideoX+image</td><td>0.855</td><td>0.984</td><td>0.443</td><td>0.929</td><td>0.987</td><td>0.567</td></tr><tr><td>Pyramid-Flow</td><td>0.906</td><td>0.991</td><td>0.438</td><td>0.941</td><td>0.991</td><td>0.537</td></tr><tr><td>Open-Sora</td><td>0.897</td><td>0.989</td><td>0.438</td><td>0.954</td><td>0.990</td><td>0.524</td></tr><tr><td>Ours</td><td>0.928</td><td>0.991</td><td>0.474</td><td>0.971</td><td>0.993</td><td>0.600</td></tr></table>
+
+optical flow in the training of the second stage to enhance the learning capability of the video generation model.
+
+# 4. Experiments
+
+We evaluate our method through quantitative metrics that confirm both the generation quality and its alignment with control signals, alongside visualizing the generated results for further qualitative comparison.
+
+# 4.1. Image-to-Video Generation Ability.
+
+As shown in Tab. 1, four classical image-level quality metrics, including Fréchet Inception Distance (FID) [18], SSIM [44], PSNR [20] and LPIPS [58], are used to evaluate the quality of the generated video frames with Motion-I2V [38], MOFA-Video [31], DynamiCrafter [48], CogVideoX[51], PyramidFlow [26], and OpenSora [61], and video-level metric Fréchet Video Distance (FVD) [40] is applied to assess video-level quality, similar to previous video generation methods [6-8, 27, 46]. Following CogVideo [51] and PyramidFlow [26], we employed several metrics from VBench [23] to evaluate the Subject Consistency (SubC), Motion Smoothness (MoS) and Aesthetic Quality (AesQ) of Our Video as shown in Tab. 2 and Fig. 9 on OpenVid [30] and WebVid10M [3] datasets. With optical flow guidance, our methods can achieve better performance especially when the generated video contains human motions and animal motions.
+
+# 4.2. Control Signals Driven I2V Generation.
+
+Camera Trajectory. The distance between predicted and ground-truth camera trajectories is used to measure the camera alignment. Here, we use ParticleSfM[60], VggSfM[41] and DUSt3R[42] to evaluate our camera tra
+
+![](images/0dcc85ddd4fdbb79716bb8f52cd51fd822cd238c7f2a6b6913bdbe2af36e8f59.jpg)  
+Figure 5. Camera trajectory comparison with other trajectory-based methods
+
+Table 3. Quantitative comparisons (Pose got by DUSt3R, Vg-gSfM, and ParticleSfM). We compare against prior works on basic trajectory and random trajectory respectively. T-Err, R-Err represent translation error and rotation error.  
+
+<table><tr><td rowspan="3"></td><td colspan="5">Basic Trajectory</td><td colspan="5">Difficult Trajectory</td></tr><tr><td colspan="2">DUSt3R</td><td colspan="2">VggSfM</td><td>ParticleSfM</td><td colspan="2">DUSt3R</td><td colspan="2">VggSfM</td><td>ParticleSfM</td></tr><tr><td>T-Err↓</td><td>R-Err↓</td><td>T-Err↓</td><td>R-Err↓</td><td>T-Err↓</td><td>T-Err↓</td><td>R-Err↓</td><td>T-Err↓</td><td>R-Err↓</td><td>T-Err↓</td></tr><tr><td>CameraCtrl</td><td>0.090</td><td>0.300</td><td>1.405</td><td>0.177</td><td>2.277</td><td>0.825</td><td>0.082</td><td>0.306</td><td>1.559</td><td>0.144</td></tr><tr><td>MotionCtrl</td><td>0.057</td><td>0.233</td><td>1.324</td><td>0.258</td><td>1.811</td><td>0.868</td><td>0.060</td><td>0.267</td><td>0.875</td><td>0.137</td></tr><tr><td>Ours</td><td>0.041</td><td>0.159</td><td>1.036</td><td>0.125</td><td>1.648</td><td>0.685</td><td>0.053</td><td>0.203</td><td>0.447</td><td>0.119</td></tr></table>
+
+jection with CameraCtrl[17] and MotionCtrl[45] on basic trajectory (sample every 8 frames) and difficult trajectory (sample every max frame we can sample) in Real10K [63] shown in Tab. 3 and Fig. 5. Specifically, we estimate the camera trajectories for both the generated and real videos using the same methods to eliminate the potential scale differences caused by different Structure-from-Motion (SfM) techniques. And, we evaluate the quality of these trajectories by evaluating the scale and differences in the rotation and translation parameters of the camera matrix using rotation error and translation error, as outlined in He et al. [17], Wang et al. [45].
+
+User Arrow Annotation. As shown in Fig. 1, we can turn any kind of user drags into corresponding optical flows, which are then treated as the unified guidance for the final video generation. For this part, we compare with cur
+
+![](images/66707512923e41ef3740cd50b6154cb0ab0edb5b550abbbf92edaa66a1e0fb18.jpg)  
+Figure 6. Motion Transfer comparison with state-of-the-art methods.
+
+rent state-of-the-art user drag animation methods MOFA-Video [31], DragAnything [47], Motion-I2V [38] shown in Fig. 7. Our method can achieve more stable and consistent video generation on specific user drags. More results can be seen on the anonymous project webpage.
+
+Reference Video. We demonstrate the capability of our Stage 2 in generating animations driven by reference videos, where a dense optical flow can be extracted. First, we test the case that the optical flow and given images are
+
+![](images/ea1ba9ec1766c4ed09623bf8498ab4ef1fa4302da83643cd3ce1ee95cf8bf47d.jpg)  
+Figure 7. Users drag animation comparison with other animation methods.
+
+![](images/0b55179b5959144bdb435f020a435dc69b54c0ef8f056a9f5a483773f0ea832d.jpg)  
+Figure 8. Human face animation with optical flow extracted from reference video
+
+well aligned. Specifically, we generated the reference image by replacing or stylizing the subject in the first frame of the video as the reference image [36]. As shown in Fig. 6, it can be seen that Motion-I2V lacks sensitivity to a wide range of motions. Although MotionClone and MOFA-Video can achieve significant video motions, they result in style inconsistency and artifacts. Our generated results maintain significant motion alignment without a skeleton or facial keypoint extraction, while achieving optimal subject consistency. To better evaluate the generalization, we further experiment on the facial replacement task with the setting that the image and the unified optical flow are not perfectly aligned. The dense optical flow here inputted to Stage 2 is directly extracted from another facial motion video. As shown in Fig. 8, our Stage 2 can tolerate some misalignments while still performing effectively, producing consistent expressions and lip motions. This provides our method with greater flexibility and robustness.
+
+# 4.3. Ablation Study And Analysis
+
+**Setup.** To verify the effectiveness of the components in our video generation pipeline, we designed several sets of ablation experiments on Real10K [63]. (1) The multi-frame camera encoding is added to the latent variables and used as input to the DiT blocks. (2) We replicate the first half of the blocks of FGM as a reference network and then add the output of each block of the reference network to the output
+
+![](images/6d8208e089065365271be0c0d4ba10dcb8c482ddd0092c5d199b5b0be7c02c91.jpg)  
+Figure 9. Image to video generation comparison with current state-of-the-art methods.
+
+Table 4. Ablation study.  
+
+<table><tr><td rowspan="2"></td><td colspan="5">Visual Quality</td><td colspan="2">Trajectory Alignment</td></tr><tr><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>FID↓</td><td>FVD↓</td><td>TransErr↓</td><td>RotErr↓</td></tr><tr><td>Camera embedding</td><td>0.401</td><td>14.22</td><td>0.531</td><td>52.46</td><td>346</td><td>0.551</td><td>0.048</td></tr><tr><td>ControlNet-Like</td><td>0.400</td><td>14.21</td><td>0.528</td><td>50.96</td><td>356</td><td>0.737</td><td>0.050</td></tr><tr><td>w/o FS</td><td>0.241</td><td>17.88</td><td>0.615</td><td>46.85</td><td>311</td><td>0.671</td><td>0.059</td></tr><tr><td>w/o noise</td><td>0.228</td><td>19.32</td><td>0.654</td><td>49.38</td><td>474</td><td>0.425</td><td>0.048</td></tr><tr><td>Full Model</td><td>0.142</td><td>23.22</td><td>0.796</td><td>41.67</td><td>168</td><td>0.354</td><td>0.047</td></tr></table>
+
+of the corresponding original block, like ControlNet. (3) and (4) both use the globally estimated optical flow from the video data as input, with the distinction that (3) removes Frequency Stabilization (FS), while (4) does not apply noise before feeding the global optical flow into the Flow Encoder.
+
+Analysis. As shown in Tab. 4, From the first two rows, we can see the superiority of using a unified optical flow representation, which surpasses other camera control signal guidance methods in terms of visual quality and camera rule prediction. The third row reflects that not using Frequency Stability during the training process leads to a significant drop in performance. However, it is still better than the other two camera signal guidance methods. The fourth row illustrates that the noise application conducted before feeding the Optical Flow into the Flow encoder effectively enhances the robustness of the generation.
+
+# 5. Conclusion
+
+In this paper, we present a unified controllable video generation approach enabling precise and consistent video manipulation across various conditions. We unified Flow as a joint control signal by converting diverse visual control signals (e.g., object motion, camera motion) into a joint optical flow representation. Then the unified flows are used to guide the final video generation. This strategy reduces the complexity of handling multiple, isolated control signals and promotes consistency in the generated video. In addition, we propose a frequency-based stabilization module to preserve the key features in the frequency domain and reduce the flickering issues caused by large-scale motion. Experiments demonstrate that this two-stage pipeline can control the video generation precisely and have impressive generalization capabilities.
+
+# Acknowledgments
+
+We thank all the anonymous reviewers for their constructive comments. Weiwei Xu is partially supported by NSFC (No. 62421003). Rong Zhang is partially supported by NSFC (No. 62302449) and Zhejiang Provincial Natural Science Foundation of China (No. LQ23F020009). This paper is supported by the Information Technology Center and State Key Lab of CAD&CG, Zhejiang University.
+
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+# Annotation Ambiguity Aware Semi-Supervised Medical Image Segmentation
+
+Suruchi Kumari Pravendra Singh*
+
+Indian Institute of Technology Roorkee
+
+{suruchi_k@cs.iitr.ac.in, pravendra.singh@cs.iitr.ac.in}
+
+# Abstract
+
+Despite the remarkable progress of deep learning-based methods in medical image segmentation, their use in clinical practice remains limited for two main reasons. First, obtaining a large medical dataset with precise annotations to train segmentation models is challenging. Secondly, most current segmentation techniques generate a single deterministic segmentation mask for each image. However, in real-world scenarios, there is often significant uncertainty regarding what defines the "correct" segmentation, and various expert annotators might provide different segmentations for the same image. To tackle both of these problems, we propose Annotation Ambiguity Aware Semi-Supervised Medical Image Segmentation (AmbiSSL). AmbiSSL combines a small amount of multi-annotator labeled data and a large set of unlabeled data to generate diverse and plausible segmentation maps. Our method consists of three key components: (1) The Diverse Pseudo-Label Generation (DPG) module utilizes multiple decoders, created by performing randomized pruning on the original backbone decoder. These pruned decoders enable the generation of a diverse pseudo-label set; (2) a Semi-Supervised Latent Distribution Learning (SSLDL) module constructs a common latent space by utilizing both ground truth annotations and pseudo-label set; and (3) a Cross-Decoder Supervision (CDS) module, which enables pruned decoders to guide each other's learning. We evaluated the proposed method on two publicly available datasets. Extensive experiments demonstrate that AmbiSSL can generate diverse segmentation maps using only a small amount of labeled data and abundant unlabeled data, offering a more practical solution for medical image segmentation by reducing reliance on large labeled datasets.
+
+# 1. Introduction
+
+Automatic medical image segmentation is a crucial step in developing effective clinical applications. Despite the re
+
+![](images/e26ee16278f7ffb6ebe66c70deac5c0cb2f93f9bf10d9beca126d85d2d916688.jpg)  
+Figure 1. In semi-supervised segmentation (top), few labeled samples and abundant unlabeled data are utilized, producing a single label map per image. Existing ambiguity-aware methods (middle) use multiple annotations per image, generating multiple segmentations. AmbiSSL, by contrast, leverages both unlabeled data and a limited amount of labeled data with multiple annotations, enabling the generation of multiple segmentations per image.
+
+markable progress of deep learning-based methods in medical image segmentation [9, 11, 33], their use in clinical practice [4] remains limited for two main reasons. First, acquiring a large, accurately annotated medical dataset for segmentation is challenging, as it requires pixel-level annotations, which are both time-consuming and costly to produce. Second, existing methods typically provide only a single segmentation map, while medical images often contain regions of inherent ambiguity, and a single "correct"
+
+segmentation map may not exist. This ambiguity can stem from blurred or low-contrast images [34], complex anatomical structures [10, 23], varying interpretations by human raters, or specific downstream objectives [4]. Overlooking this ambiguity can negatively impact downstream analysis, diagnosis, and treatment.
+
+Recent studies address the above issues separately, noting that while acquiring labeled data is challenging, obtaining unlabeled data is more practical [7]. Consequently, semi-supervised learning (SSL) has emerged as an effective paradigm that can achieve performance comparable to supervised learning at a lower cost [6, 7]. In SSL, a small set of labeled data is utilized alongside a substantial amount of unlabeled data. Several SSL techniques have been developed specifically for medical image segmentation [14]; however, these methods typically yield only a single segmentation mask for a given input image.
+
+Independently, stochastic or ambiguous segmentation techniques generate multiple plausible segmentations during inference, capturing task-related uncertainty [19, 25, 35]. Despite this progress, training a model for ambiguous segmentation still requires annotations from multiple experts, which is costly and time-consuming. However, obtaining a small annotated dataset is feasible, and acquiring unlabeled data is relatively easy. Consequently, our work focuses on leveraging a small annotated dataset together with abundant unlabeled data to achieve diverse segmentation results.
+
+Given the importance of both challenges in medical image segmentation, it is essential to develop a framework that can leverage both labeled and unlabeled data while simultaneously generating multiple plausible segmentation maps. To this end, we propose AmbiSSL, a novel annotation ambiguity aware semi-supervised approach for medical image segmentation (Figure 1). Our method comprises three key modules to effectively utilize the labeled and unlabeled data: (1) A Diverse Pseudo-label Generation (DPG) module that leverages multiple decoders, created through randomized pruning of the original backbone decoder. This pruning selectively removes weights from the final layers, resulting in varied representations across decoders. These diverse features from each decoder are then concatenated with sampled latent codes from the prior distribution to generate a diverse pseudo-label set. To further enhance quality, outputs from the multiple decoders are aggregated into an ensemble, refining the pseudo-label set for subsequent training, (2) The Semi-Supervised Latent Distribution Learning (SSLDL) module constructs a common latent space by incorporating both ground truth annotations and pseudo-label sets, and (3) The Cross-Decoder Supervision (CDS) module enables a pseudo-label set generated by one pruned decoder to guide the training of another, promoting cross-supervision that encourages the decoders to learn comple
+
+mentary features and correct each other's mistakes.
+
+Our Contributions: Our work presents the first solution to address annotation ambiguity in semi-supervised medical image segmentation. To tackle this, we introduce a DPG module, which utilizes multiple decoders created by performing random pruning on the original backbone decoder. These pruned decoders enable the generation of a diverse pseudo-label set. Secondly, we develop SSLDL module, which leverages both ground truth annotations and pseudolabel sets to construct a common latent space, where different latent codes lead to diversified segmentation results. Furthermore, to enable a comprehensive evaluation of our method, we establish several baselines that represent common approaches in the field, providing a fair comparison to assess the performance of our approach. Extensive experiments on two datasets with different label settings demonstrate that our framework provides diverse segmentation results, effectively utilizing the unlabeled data and reducing reliance on large labeled datasets.
+
+# 2. Related work
+
+# 2.1. Semi-supervised Medical Image Segmentation.
+
+In the context of SSMIS, a variety of approaches have emerged to leverage both labeled and unlabeled data [20]. One common strategy is pseudo-labeling, where the model generates labels for unlabeled images, which are then used in subsequent training cycles [14]. Pseudo-labeling can be further divided into self-training and co-training methods. Self-training involves a single model generating pseudolabels for unlabeled data, which are iteratively used to refine the model's predictions [5, 7]. In contrast, co-training involves training two or more models simultaneously on the same data but with different views or feature sets [6]. Each model provides pseudo-labels for the other, reducing the risk of reinforcing the same errors. The mutual correction framework (MCF) [32] introduces two distinct subnetworks that leverage their differences to identify and correct the model's cognitive biases.
+
+Another popular method involves consistency regularization, which encourages the model to produce stable predictions for unlabeled data under various perturbations, such as adding noise or applying transformations. Sajjadi et al. [26] propose a model that maintains consistency by evaluating outputs from augmented samples. Tarvainen et al. [30] present a teacher-student framework that utilizes exponential moving average weights to improve consistency. Furthermore, hybrid methods that combine different semi-supervised techniques, such as combining pseudolabeling with consistency regularization, have demonstrated improved performance in various medical imaging challenges [2].
+
+All these methods perform well for medical image seg
+
+mentation. However, they are unable to handle multiple label maps from different expert annotators and typically produce only a single segmentation mask for a given input image.
+
+# 2.2. Ambiguous Medical Image Segmentation
+
+Stochastic segmentation methods aim to generate multiple plausible segmentations at inference time, which helps represent uncertainty in challenging tasks. Estimating uncertainty allows users to assess their confidence in a segmentation, helping them make informed decisions and guiding subsequent processes. Various methods exist to capture this uncertainty. A popular approach is to estimate pixel-level probability [16, 17] by applying dropout to spatial features, though this often leads to inconsistent outputs [19]. An alternative, simpler approach involves training an ensemble of deep models for more stable predictions, though these may lack diversity and miss rare variations due to independent training [21]. To address these limitations, the probabilistic U-Net [19] incorporates pixel correlations using a multivariate Gaussian distribution with low-rank covariance. Other methods integrate hierarchical representations for UNet-based models through variational auto-encoders [18]. Recently, diffusion models have also been explored for ensembling and producing stochastic segmentations [25, 36]. However, these methods are relatively slow during training and inference due to the inherent nature of diffusion.
+
+Despite the progress, all these methods require annotations for each image from multiple radiologists, which is costly and time-consuming. In contrast, our work focuses on using a small annotated dataset along with abundant unlabeled data to achieve diverse segmentation results.
+
+# 3. Method
+
+In Annotation Ambiguity Aware Semi-Supervised Medical Image Segmentation (AmbiSSL), we work with labeled data  $D_{l} = \{(x_{i}^{l},Y_{set}^{i})\}_{i = 1}^{R}$  and unlabeled data  $D_{u} = \{x_{i}^{u}\}_{i = 1}^{S}$ , where  $R$  represents the number of labeled images and  $S$  represents the number of unlabeled images. Here, each  $Y_{set}^{i} = \{y_{1},y_{2},\ldots ,y_{a}\}$  is a collection of annotations for image  $x_{i}^{l}$ , with  $a$  representing the number of annotations per image. These annotations reflect variations in expert criteria and preferences. Our goal is to learn a shared latent space from  $D_{l}$  and  $D_{u}$ . This latent space can then be sampled to generate diverse segmentation outcomes, capturing the variations in expert annotations.
+
+# 3.1. Semi-Supervised Latent Distribution Learning
+
+We utilize two separate encoders  $E_{\theta}^{\mathrm{prior}}$  and  $E_{\theta}^{\mathrm{post}}$  to generate the prior and posterior distributions, respectively [19]. Additionally, an encoder-decoder architecture  $F_{\theta}^{b}$  is used for feature extraction, and a segmentation head  $F_{\theta}^{\mathrm{seg}}$  maps
+
+![](images/88c719aadf3fc090a12eafca88ad48d254360e70bdba52051cca6245e2e6d0a1.jpg)  
+Figure 2. Depiction of the Diverse Pseudo-Label Generation module, which utilizes a backbone network with an encoder-decoder architecture and incorporates two additional decoders transformed through random pruning. For each decoder, latent codes are sampled from the prior distribution and combined with the backbone features to generate the pseudo-label set.
+
+the latent space to segmentation results. The prior distribution for labeled data  $x^{l}$  is modeled as a multivariate normal distribution with a diagonal covariance matrix, denoted as:  $D^{\mathrm{prior}}(x^{l}) = \mathcal{N}(\mu_{\mathrm{prior}}^{l},\sigma_{\mathrm{prior}}^{l})$ . The posterior distribution for the labeled data is defined as the joint distribution over the labeled data  $x^{l}$  and its corresponding annotator set  $Y_{set}$ , represented as:  $D^{\mathrm{post.}}(x^{l},Y_{set}) = \mathcal{N}(\mu_{\mathrm{post.}}^{l},\sigma_{\mathrm{post.}}^{l})$ .
+
+The corresponding mean values and variances for  $x^l$  in the prior and posterior distributions are determined as follows:
+
+$$
+\mu_ {\text {p r i o r}} ^ {l}, \sigma_ {\text {p r i o r}} ^ {l} = E _ {\theta} ^ {\text {p r i o r}} \left(x ^ {l}\right), \quad \mu_ {\text {p o s t}} ^ {l}, \sigma_ {\text {p o s t}} ^ {l} = E _ {\theta} ^ {\text {p o s t}} \left(x ^ {l}, Y _ {\text {s e t}}\right), \tag {1}
+$$
+
+Next, we consider the unlabeled data, denoted as  $x^{u}$  for weak augmentation and  $x^{\hat{u}}$  for strong augmentation. Unlike the labeled data, we model the prior distribution for the unlabeled data as a Laplace distribution, represented as  $E_{\theta}^{\mathrm{prior}}(x^{u}) = \mathcal{G}(\mu_{\mathrm{prior}}^{u}, b_{\mathrm{prior}}^{u})$ , where  $\mathcal{G}$  represents the Laplace distribution and  $b$  is the scale parameter of the Laplace distribution. For unlabeled data, we utilize two pseudo-label sets  $\hat{P}^{u;\phi,\theta}$  and  $\hat{P}^{u;\xi,\theta}$  to calculate the posterior, and the process for generating both sets are described in Section 3.2. However, since pseudo-labels are not as reliable as ground truths provided by human annotators, employing a normal distribution in this context would impose excessive confidence on the pseudo-labels, potentially leading to overfitting and skewed results. This is because the normal distribution is sensitive to outliers and assigns exponentially decreasing probabilities to values far from the mean. In contrast, the Laplace distribution assigns higher probabilities to these values, thereby not placing excessive confidence in the pseudo-label set. The posterior
+
+![](images/14ad3fc0e6c456ef2b8208c52504d31680e4c11839eeee47d5feb797915c39ee.jpg)  
+Figure 3. Illustration of two key modules of AmbiSSL: (Top) Semi-Supervised Latent Distribution Learning (SSLDL) module, which constructs a shared latent space from labeled and unlabeled data, where different latent codes lead to diversified segmentation results. (Bottom) Cross-Decoder Supervision (CDS) module, where pseudo-labels generated by one randomly pruned decoder guide the training of another pruned decoder.
+
+for the unlabeled data is modeled as  $D^{\mathrm{post}}(x^{u},\hat{P}^{u:\phi ,\theta}) = \mathcal{G}(\mu_{\mathrm{post}}^{u:\phi},b_{\mathrm{post}}^{u:\phi})$  and  $D^{\mathrm{post}}(x^{\tilde{u}},\hat{P}^{u:\xi ,\theta}) = \mathcal{G}(\mu_{\mathrm{post}}^{\hat{u}:\xi},b_{\mathrm{post}}^{\hat{u}:\xi})$ . The corresponding mean and scale values for  $x^{u}$  in the prior and posterior distributions are determined as follows:
+
+$$
+\mu_ {\text {p r i o r}} ^ {u}, b _ {\text {p r i o r}} ^ {u} = E _ {\theta} ^ {\text {p r i o r}} \left(x ^ {u}\right), \quad \mu_ {\text {p o s t}} ^ {u}, b _ {\text {p o s t}} ^ {u} = E _ {\theta} ^ {\text {p o s t}} \left(x ^ {u}, \hat {P} ^ {u; \phi , \theta}\right). \tag {2}
+$$
+
+$$
+\mu_ {\text {p r i o r}} ^ {\hat {u}}, b _ {\text {p r i o r}} ^ {\hat {u}} = E _ {\theta} ^ {\text {p r i o r}} \left(x ^ {\hat {u}}\right), \quad \mu_ {\text {p o s t}} ^ {\hat {u}}, b _ {\text {p o s t}} ^ {\hat {u}} = E _ {\theta} ^ {\text {p o s t}} \left(x ^ {\hat {u}}, \hat {P} ^ {u; \xi , \theta}\right). \tag {3}
+$$
+
+After calculating the prior and posterior, A common Kullback-Leibler divergence (KL) loss is used to align the two distributions:
+
+$$
+\mathcal {L} _ {k l} ^ {l} = K L \left(D ^ {\text {p r i o r}} \left(x ^ {l}\right), D ^ {\text {p o s t .}} \left(x ^ {l}, Y _ {\text {s e t}}\right)\right). \tag {4}
+$$
+
+$$
+\mathcal {L} _ {k l} ^ {u; \phi} = K L \left(D ^ {\text {p r i o r}} \left(x ^ {u}\right), D ^ {\text {p o s t .}} \left(x ^ {u}, \hat {P} ^ {u; \phi , \theta}\right)\right). \tag {5}
+$$
+
+$$
+\mathcal {L} _ {k l} ^ {\hat {u}; \xi} = K L \left(D ^ {\text {p r i o r}} \left(x ^ {\hat {u}}\right), D ^ {\text {p o s t .}} \left(x ^ {\hat {u}}, \hat {P} ^ {u; \xi , \theta}\right)\right). \tag {6}
+$$
+
+# 3.2. Diverse Pseudo label Generation
+
+For labeled data, we have the multi-annotator set  $Y_{set}$ , which guides the diversified segmentation process. Since  $Y_{set}$  is unavailable for unlabeled data, we generate pseudolabel sets to facilitate learning from the unlabeled samples. We utilize the backbone  $F_{\theta}^{b}$ , which can be further divided into an encoder  $E_{\theta}^{b}$  and a decoder  $D_{\theta}^{b}$ . Additionally, two
+
+more decoders are used: the random pruned decoders  $D_{\phi}^{b}$  and  $D_{\xi}^{b}$ . The architectures of  $D_{\xi}^{b}$  and  $D_{\phi}^{b}$  are similar to  $D_{\theta}^{b}$ ; however, to generate diverse pseudo-label sets, we use a pruning transformation module to convert the model  $f_{\theta}$  with parameters  $\theta = \{W_1,\dots ,W_n\}$  into  $f_{\tilde{\theta}}$
+
+This pruning transformation is applied to the weight matrices in the final layers of the decoder, beginning from a threshold layer  $L$ . For each layer  $k \geq L$ , the weight matrix  $W_{k}$  is modified by a layer-specific pruning mask  $M_{k} \in \{0,1\}$ , which determines whether each weight in  $W_{k}$  is retained or pruned. The transformed weight matrix  $\tilde{W}_{k}$  is defined as:
+
+$$
+\tilde {W} _ {k} = M _ {k} \odot W _ {k} + (1 - M _ {k}) \odot \lambda \left(W _ {k}\right), \tag {7}
+$$
+
+where  $\lambda (W_k)$  is given by:
+
+$$
+\lambda \left(W _ {k}\right) = \left\{ \begin{array}{l l} \operatorname {T o p} a \left(W _ {k}\right) & \text {w i t h p r o b a b i l i t y} q _ {k} \\ W _ {k} & \text {w i t h p r o b a b i l i t y} 1 - q _ {k} \end{array} \right. \tag {8}
+$$
+
+Here, "Top  $a(W_k)$ " retains the top  $a\%$  of weights by magnitude, and sets the remaining weights to 0. This pruning is applied exclusively to the final layers of the decoder, introducing targeted variability in these layers. The pruning probability  $q_k$  for each decoder layer controls the level of
+
+variability in the pruned features, generating diverse views to enhance training on unlabeled data.
+
+We generate pseudo-labels from all three decoders with gradients turned off, as shown in Figure 2. The procedure for generating pseudo-labels is consistent across the three decoders: we first sample latent codes  $z^{prior:u}$  from the prior distribution of the unlabeled data,  $D^{prior:u}$ , matching the number of multiple expert annotations available for the labeled data. This latent code is then concatenated with encoder-decoder features specific to each decoder and fed into the specific segmentation to generate the final pseudolabels. For clarity, we use decoder-specific notation to represent the entire encoder-decoder features. Although the decoders differ, the encoder remains the same across all three. Mathematically, the pseudo-label generation process is detailed below.
+
+$$
+\hat {P} ^ {u; \theta} = F _ {\theta} ^ {s e g} \left(\hat {z} ^ {\text {p r i o r : u}}, D _ {\theta} ^ {d} \left(x ^ {u}\right)\right) \tag {9}
+$$
+
+$$
+\hat {P} ^ {u; \phi} = F _ {\phi} ^ {s e g} \left(\hat {z} ^ {\text {p r i o r : u}}, D _ {\phi} ^ {d} \left(x ^ {u}\right)\right) \tag {10}
+$$
+
+$$
+\hat {P} ^ {u; \xi} = F _ {\xi} ^ {s e g} \left(\hat {z} ^ {\text {p r i o r : u}}, D _ {\xi} ^ {d} \left(x ^ {u}\right)\right) \tag {11}
+$$
+
+To improve the quality of the pseudo-labels, we create an ensemble of two sets from the three generated, as described below:
+
+$$
+\hat {P} ^ {u; \phi , \theta} = \hat {P} ^ {u; \phi} + \hat {P} ^ {u; \theta} \tag {12}
+$$
+
+$$
+\hat {P} ^ {u; \xi , \theta} = \hat {P} ^ {u; \xi} + \hat {P} ^ {u; \theta} \tag {13}
+$$
+
+This ensemble strategy combines the strengths of different models, yielding higher-quality pseudo-labels for further model training.
+
+# 3.3. Training
+
+To learn from labeled data, we train all three decoders on labeled samples by first randomly sampling a latent code from the posterior distribution, denoted as  $z_{\mathrm{random}}^{\mathrm{post:1}} \in \mathbb{R}^{D \times 1 \times 1}$ . This latent code is then scaled to match the image dimensions. We concatenate this scaled latent code with backbone features, passing them through the segmentation head to produce the segmentation result:
+
+$$
+P _ {\eta} ^ {\text {p o s t}: l} = F _ {\eta} ^ {\text {s e g}} \left(z _ {\text {r a n d o m}} ^ {\text {p o s t}: l}, D _ {\eta} ^ {d} \left(x ^ {l}\right)\right), \quad \eta \in \{\theta , \phi , \xi \}.
+$$
+
+Here, we use the symbol  $\eta$  for brevity to represent the three decoders  $\theta$ ,  $\phi$ , and  $\xi$ . Since there is no inherent correspondence between  $z_{\mathrm{random}}^{\mathrm{post:1}}$  and the label set  $Y_{\mathrm{set}}$ , we randomly select an annotation  $Y_{\mathrm{random}}$  from the available annotations in  $Y_{\mathrm{set}}$ , following [12, 15]. We then apply the conventional Dice loss (DSC) [27] as shown below:
+
+$$
+\mathcal {L} _ {\mathrm {s e g}} ^ {l: \eta} = \mathrm {D S C} (P _ {\eta} ^ {\mathrm {p o s t}: l}, Y _ {\mathrm {r a n d o m}}), \quad \eta \in \{\theta , \phi , \xi \}.
+$$
+
+In line with [27], we apply a re-parameterization trick to sample  $z_{\mathrm{random}}^{\mathrm{post:1}}$  from the posterior distribution  $D^{\mathrm{post:1}}$ , enabling gradient backpropagation for model training.
+
+Furthermore, to enhance prediction diversity, following the approach in [35], we utilize a bound prediction task for segmentation training. This involves calculating the intersection and union of the annotation set,  $Y_{\mathrm{bound}} = \{Y_{\mathrm{inter}}, Y_{\mathrm{union}}\}$ , as supervision labels. Sampling multiple latent codes from the prior distribution,  $D^{\mathrm{prior}}$ , yields multiple segmentation results with their intersection and union denoted by  $P_{\mathrm{bound}}^{\mathrm{prior}} = \{P_{\mathrm{inter}}^{\mathrm{prior}}, P_{\mathrm{union}}^{\mathrm{prior}}\}$ . The complementary segmentation loss is then calculated as:
+
+$$
+\mathcal {L} _ {\text {b o u n d}} = \operatorname {D S C} \left(P _ {\text {i n t e r .}} ^ {\text {p r i o r}}, A _ {\text {i n t e r .}}\right) + \operatorname {D S C} \left(P _ {\text {u n i o n}} ^ {\text {p r i o r}}, A _ {\text {u n i o n}}\right).
+$$
+
+Final supervised segmentation loss can be depicted as follows:
+
+$$
+\mathcal {L} _ {s u p} = \alpha_ {l} * \mathcal {L} _ {k l} ^ {l; \eta} + \mathcal {L} _ {\mathrm {s e g}} ^ {l; \eta} + \beta * \mathcal {L} _ {\text {b o u n d}} ^ {l; \eta} \quad \eta \in \left\{\theta , \phi , \xi \right\} \tag {14}
+$$
+
+Cross-Decoder Supervision. For unlabeled data, we sample latent codes for weakly and strongly augmented unlabeled data,  $z_{\mathrm{random}}^{\mathrm{post}:u,\phi}$  and  $z_{\mathrm{random}}^{\mathrm{post}:\hat{u},\xi}$ , from  $D^{\mathrm{post}:u,\phi}$  and  $D^{\mathrm{post}:\hat{u},\xi}$ , respectively. The scaled latent code  $z_{\mathrm{random}}^{\mathrm{post}:u,\phi}$  is concatenated with features from  $\mathcal{D}_\phi^d$ , and similarly,  $z_{\mathrm{random}}^{\mathrm{post}:\hat{u},\xi}$  is concatenated with features from  $\mathcal{D}_\xi^d$ . These concatenated features are then passed through their respective segmentation heads to obtain the final segmentation results, as shown below:
+
+$$
+P _ {\phi} ^ {\text {p o s t :} u} = F _ {\phi} ^ {\text {s e g}} \left(z _ {\text {r a n d o m}} ^ {\text {p o s t :} u: \phi}, D _ {\phi} ^ {d} \left(x ^ {u}\right)\right), \tag {15}
+$$
+
+$$
+P _ {\xi} ^ {\text {p o s t :} \hat {u}} = F _ {\xi} ^ {\text {s e g}} \left(z _ {\text {r a n d o m}} ^ {\text {p o s t :} u: \xi}, D _ {\xi} ^ {d} \left(x ^ {\hat {u}}\right)\right). \tag {16}
+$$
+
+Cross-decoder supervision involves using the output of one decoder to guide the learning of another decoder, encouraging both decoders to learn complementary features, as shown in Figure 3. To implement this, we randomly select predictions from the two decoders during training [12, 15]. Specifically, we randomly choose  $\hat{P}_{\mathrm{random}}^{u:\phi}$  from the set  $\hat{P}_{\mathrm{set}}^{u:\phi}$  and  $\hat{P}_{\mathrm{random}}^{u:\xi}$  from the set  $\hat{P}_{\mathrm{set}}^{u:\xi}$ . These randomly selected predictions are then used in the computation of the segmentation losses between the output of one decoder and the randomly chosen prediction from the other decoder. This process ensures that each decoder is supervised by the other's output in a cross-wise manner. The resulting losses are computed as follows:
+
+$$
+\mathcal {L} _ {\text {s e g}} ^ {u: \phi} = \mathcal {L} _ {\text {D i c e}} \left(P _ {\phi} ^ {\text {p o s t}: u}, \hat {P} _ {\text {r a n d o m}} ^ {u: \xi}\right), \tag {17}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {s e g}} ^ {\hat {u}: \xi} = \mathcal {L} _ {\mathrm {D i c e}} \left(P _ {\xi} ^ {\text {p o s t :} \hat {u}}, \hat {P} _ {\text {r a n d o m}} ^ {u: \phi}\right). \tag {18}
+$$
+
+To facilitate gradient backpropagation during training, we employ a reparameterization trick [27] to sample  $z_{\mathrm{random}}^{\mathrm{post}: \mathrm{u}, \phi}$  and  $z_{\mathrm{random}}^{\mathrm{post}: \hat{u}, \xi}$  from the posterior distributions  $D^{\mathrm{post}: \mathrm{u}, \phi}$  and  $D^{\mathrm{post}: \hat{u}, \xi}$ , respectively.
+
+The final unsupervised loss can be depicted as follows:
+
+$$
+\mathcal {L} _ {\text {u n s u p}} ^ {\phi} = \alpha_ {u} * \mathcal {L} _ {\mathrm {k l}} ^ {u: \phi} + \mathcal {L} _ {\text {s e g}} ^ {u: \phi} \tag {19}
+$$
+
+$$
+\mathcal {L} _ {\text {u n s u p}} ^ {\xi} = \alpha_ {u} * \mathcal {L} _ {\mathrm {k l}} ^ {\hat {u}: \xi} + \mathcal {L} _ {\text {s e g}} ^ {\hat {u}: \xi} \tag {20}
+$$
+
+Overall, the model is trained with both supervised and unsupervised loss as:
+
+$$
+\mathcal {L} _ {\text {f i n a l}} = \mathcal {L} _ {\text {s u p}} + \mu * \left(\mathcal {L} _ {\text {u n s u p}} ^ {\phi} + \mathcal {L} _ {\text {u n s u p}} ^ {\xi}\right) \tag {21}
+$$
+
+where  $\mu$  follows the epoch-dependent Gaussian ramp-up strategy [24], gradually increasing the contribution of the unsupervised loss over time. During inference, we use the prior network  $E_{\theta}^{\mathrm{prior}}$ , along with the encoder  $E_{\theta}^{b}$  and decoder  $D_{\phi}^{b}$ , to generate diverse segmentation results.
+
+# 4. Experiments and Results
+
+# 4.1. Dataset
+
+We evaluate our method on the two segmentation datasets: the public lung nodule segmentation dataset (LIDC-IDRI) [1] and ISIC 2018 dataset [8].
+
+LIDC-IDRI dataset. The LIDC-IDRI dataset comprises 1,609 2D thoracic CT scans from 214 subjects, with each scan accompanied by four binary masks that mark lung nodules. Notably, 12 radiologists were involved in the annotation process [1]. This dataset is commonly used for lung nodule diagnosis. Consistent with standard practice [19], the scans are cropped and centered to a size of  $128 \times 128$ . Following [31], we use a four-fold cross-validation setup at the patient level for our experiments.
+
+The ISIC dataset. The ISIC dataset [8] includes dermoscopic images designed for the segmentation and identification of skin lesions, specifically targeting melanoma and nevi. It comprises 120 color (RGB) images, each annotated by three experts. In line with [31], the images are cropped to a size of  $256 \times 256$ . We use a four-fold cross-validation setup at the patient level for our experiments.
+
+# 4.2. Implementation Details
+
+We use the Adam optimizer with an initial learning rate of 1e-4 for model training. All experiments are performed in a consistent environment on a single NVIDIA A5000 GPU with 24 GB memory, and the model contains a total of 31.60 million parameters. To prevent overfitting, an L2 regularization term is also applied, following the approach in [19, 27]. For more details on implementation, please refer to the supplementary material.
+
+# 4.3. Benchmarks
+
+Our method is the first to perform ambiguous semi-supervised medical image segmentation. Existing ambiguous segmentation methods cannot handle unlabeled data, while current SSL methods are limited to producing only a single segmentation mask. To ensure a fair comparison, we establish baselines that are representative of common semi-supervised image segmentation methods. To enable the baseline methods to handle annotations from multiple experts and learn a common latent space, we utilize the prior and posterior networks [19], training them with a loss function to bring them closer together. The features from the backbone networks and the common latent code from the prior network are concatenated to generate the pseudo-label set. The baseline methods presented below differ in how they utilize the unlabeled data.
+
+Baseline I: In this baseline, we utilize a self-training approach, where a single model generates pseudo-labels for unlabeled data, which are iteratively used to refine the model's predictions [22]. To avoid noisy pseudo-labels, only those with high confidence (above a set threshold) are used to train the model in a self-training manner on the unlabeled data.
+
+Baseline II: In this baseline, we utilize a cross-pseudo supervision approach [6], where two distinct networks are trained simultaneously. Each network learns from the other's predictions while also leveraging its own views of the data. The model is trained on these pseudo-labels in a cross-correction manner, enabling both networks to iteratively refine each other's predictions.
+
+Baseline III: In this baseline, a consistency regularization method is used to leverage unlabeled data by enforcing consistency between model predictions on weakly and strongly augmented versions of the same input [28]. The consistency loss encourages the model to generate similar predictions for both augmentations.
+
+# 4.4. Evaluation Metrics
+
+We employ four evaluation metrics to assess our method's performance. To estimate diversity, we utilize two standard metrics: the Generalized Energy Distance (GED) [3, 19] and the soft Dice score  $(Dicesoft)$  [13, 31]. The GED quantifies prediction diversity, while  $Dicesoft$  evaluates the consistency of generated results. Specifically, GED is formulated as:
+
+$$
+G E D = 2 \mathbb {E} [ d (P, A) ] - \mathbb {E} [ d (P, P ^ {\prime}) ] - \mathbb {E} [ d (A, A ^ {\prime}) ] \tag {22}
+$$
+
+where  $P$  and  $P'$  are independent samples from the prediction set  $P_{set}$ , and  $A$  and  $A'$  from the annotation set  $A_{set}$ . Here,  $d$  denotes the distance function  $d(a,b) = 1 - IoU(a,b)$ , as in [19]. A lower GED value suggests greater variation across segmentation outputs.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Ratio</td><td colspan="2">Diversity Performance</td><td colspan="2">Personalized Performance (%)</td></tr><tr><td>Labeled</td><td>Unlabeled</td><td>GED ↓</td><td>Dicesoft ↑</td><td>Dice max ↑</td><td>Dice match ↑</td></tr><tr><td>Upper Bound</td><td>100%</td><td>0</td><td>0.1461</td><td>90.24</td><td>90.75</td><td>90.51</td></tr><tr><td>Prob. U-Net [19]</td><td></td><td></td><td>0.2792</td><td>60.22</td><td>81.26</td><td>80.22</td></tr><tr><td>CM-Global [29]</td><td></td><td></td><td>0.3342</td><td>85.38</td><td>85.88</td><td>85.41</td></tr><tr><td>CM-Pixel [37]</td><td>60 (5%)</td><td>0</td><td>0.3367</td><td>85.40</td><td>85.79</td><td>85.34</td></tr><tr><td>Pionono [27]</td><td></td><td></td><td>0.2479</td><td>76.26</td><td>84.80</td><td>84.43</td></tr><tr><td>D-Persona [35]</td><td></td><td></td><td>0.2532</td><td>72.73</td><td>86.24</td><td>84.79</td></tr><tr><td>Baseline I</td><td></td><td></td><td>0.2268</td><td>86.76</td><td>87.10</td><td>86.83</td></tr><tr><td>Baseline II</td><td>60 (5%)</td><td>1146 (95%)</td><td>0.2169</td><td>87.02</td><td>87.51</td><td>87.23</td></tr><tr><td>Baseline III</td><td></td><td></td><td>0.2153</td><td>87.29</td><td>87.92</td><td>87.56</td></tr><tr><td>Ours</td><td></td><td></td><td>0.1872</td><td>88.34</td><td>88.98</td><td>88.75</td></tr><tr><td>Prob. U-Net [19]</td><td></td><td></td><td>0.2679</td><td>83.09</td><td>86.83</td><td>85.87</td></tr><tr><td>CM-Global [29]</td><td></td><td></td><td>0.2833</td><td>87.68</td><td>88.28</td><td>88.02</td></tr><tr><td>CM-Pixel [37]</td><td>120 (10%)</td><td>0</td><td>0.2808</td><td>87.87</td><td>88.18</td><td>87.94</td></tr><tr><td>Pionono [27]</td><td></td><td></td><td>0.2364</td><td>86.52</td><td>87.19</td><td>86.92</td></tr><tr><td>D-Persona [35]</td><td></td><td></td><td>0.2021</td><td>87.14</td><td>88.12</td><td>87.86</td></tr><tr><td>Baseline I</td><td></td><td></td><td>0.1881</td><td>88.13</td><td>88.49</td><td>88.25</td></tr><tr><td>Baseline II</td><td>120 (10%)</td><td>1086 (90%)</td><td>0.1834</td><td>88.36</td><td>88.60</td><td>88.40</td></tr><tr><td>Baseline III</td><td></td><td></td><td>0.1779</td><td>88.75</td><td>89.23</td><td>89.08</td></tr><tr><td>Ours</td><td></td><td></td><td>0.1620</td><td>89.86</td><td>90.03</td><td>89.84</td></tr></table>
+
+Table 1. Performance of our proposed AmbiSSL framework on the LIDC-IDRI dataset under four different settings: with  $5\%$  and  $10\%$  labeled data, compared against existing methods; with  $5\%$  labeled data, utilizing the remaining unlabeled data; and with  $10\%$  labeled data, utilizing the remaining unlabeled data, both compared with baseline methods.
+
+The  $Dicesoft$  metric calculates the average Dice similarity score over multiple threshold levels to compare soft predictions  $P_{soft}$  and soft annotations  $A_{soft}$ , averaged across  $T$  binary evaluations as:
+
+$$
+D i c e _ {s o f t} = \frac {1}{T} \sum_ {i = 1} ^ {T} D i c e ([ P _ {s o f t} > \tau_ {i} ], [ A _ {s o f t} > \tau_ {i} ]) \tag {23}
+$$
+
+where  $\tau$  is a threshold selected from  $\{0.1, 0.3, 0.5, 0.7, 0.9\}$  and  $T = 5$ .
+
+To further assess the personalized segmentation performance, we employ two set-to-set metrics:  $Dice_{max}$  and  $Dice_{match}$ . Specifically,  $Dice_{max}$  quantifies the highest overlap between the prediction set and the annotation set, representing the maximum alignment achieved. In contrast,  $Dice_{match}$  imposes a one-to-one matching criterion, requiring that each annotation has a unique corresponding prediction with closely aligned segmentation results. In this context,  $Dice_{max}$  serves as an upper limit for  $Dice_{match}$ , with the difference between them reflecting the level of unique alignment between each expert annotation and the predictions. Smaller differences between  $Dice_{max}$  and  $Dice_{match}$  indicate that each expert annotation has a distinct, well-aligned prediction.
+
+# 4.5. Performance on LIDC-IDRI
+
+Table 1 presents the evaluation of our model on the LIDC-IDRI dataset, where the average performance from a fourfold cross-validation is reported. We show the results for existing state-of-the-art ambiguous methods, which use only  $5\%$  and  $10\%$  labeled data and no unlabeled data, since these
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Ratio</td><td colspan="2">Diversity Performance</td><td colspan="2">Personalized Performance (%)</td></tr><tr><td>Labeled</td><td>Unlabeled</td><td>GED↓</td><td>Dicesoft↑</td><td>Dicemax↑</td><td>Dicematch↑</td></tr><tr><td>Upper Bound</td><td>100%</td><td>0</td><td>0.2160</td><td>87.86</td><td>88.54</td><td>88.34</td></tr><tr><td>Prob. U-Net [19]</td><td></td><td></td><td>0.3851</td><td>57.61</td><td>82.73</td><td>81.73</td></tr><tr><td>CM-Global [29]</td><td></td><td></td><td>0.3751</td><td>78.00</td><td>83.00</td><td>82.45</td></tr><tr><td>CM-Pixel [37]</td><td>9 (10%)</td><td>0</td><td>0.3727</td><td>79.32</td><td>83.92</td><td>82.24</td></tr><tr><td>Pionono [27]</td><td></td><td></td><td>0.3461</td><td>52.15</td><td>73.61</td><td>72.87</td></tr><tr><td>D-Persona [35]</td><td></td><td></td><td>0.3504</td><td>66.20</td><td>83.92</td><td>83.22</td></tr><tr><td>Baseline I</td><td></td><td></td><td>0.3459</td><td>79.97</td><td>80.56</td><td>80.37</td></tr><tr><td>Baseline II</td><td>9 (10%)</td><td>81 (90%)</td><td>0.3421</td><td>81.54</td><td>82.02</td><td>81.67</td></tr><tr><td>Baseline III</td><td></td><td></td><td>0.3377</td><td>79.54</td><td>79.58</td><td>79.54</td></tr><tr><td>Ours</td><td></td><td></td><td>0.3358</td><td>83.40</td><td>83.35</td><td>83.29</td></tr><tr><td>Prob. U-Net [19]</td><td></td><td></td><td>0.3160</td><td>80.74</td><td>83.29</td><td>82.83</td></tr><tr><td>CM-Global [29]</td><td>18 (10%)</td><td>0</td><td>0.3594</td><td>83.35</td><td>85.33</td><td>84.45</td></tr><tr><td>CM-Pixel [37]</td><td></td><td></td><td>0.3280</td><td>83.60</td><td>85.01</td><td>84.76</td></tr><tr><td>Pionono [27]</td><td></td><td></td><td>0.2541</td><td>66.43</td><td>80.36</td><td>78.32</td></tr><tr><td>D-Persona [35]</td><td></td><td></td><td>0.3139</td><td>83.85</td><td>84.11</td><td>83.22</td></tr><tr><td>Baseline I</td><td></td><td></td><td>0.2927</td><td>82.22</td><td>82.37</td><td>82.27</td></tr><tr><td>Baseline II</td><td>18 (20%)</td><td>72 (80%)</td><td>0.2732</td><td>83.32</td><td>83.76</td><td>83.21</td></tr><tr><td>Baseline III</td><td></td><td></td><td>0.2862</td><td>82.62</td><td>83.78</td><td>83.63</td></tr><tr><td>Ours</td><td></td><td></td><td>0.2444</td><td>85.87</td><td>86.21</td><td>85.92</td></tr></table>
+
+Table 2. Performance of our proposed AmbiSSL framework on the ISIC dataset under four different settings: with  $10\%$  and  $20\%$  labeled data, compared against existing methods; with  $10\%$  labeled data, utilizing the remaining unlabeled data; and with  $20\%$  labeled data, utilizing the remaining unlabeled data, both compared with baseline methods.
+
+methods are not capable of handling unlabeled data. Subsequently, we report the results for three baseline methods and our approach using  $5\%$  and  $10\%$  labeled data, with the remaining data being unlabeled. The results show that utilizing unlabeled data is beneficial and leads to improvements compared to using only a small amount of labeled data. When compared to the upper bound, our method achieves competitive results even with significantly fewer labeled samples. For example, with  $10\%$  labeled data, our method reduces the GED score to 0.1620, achieving a soft Dice score of  $89.86\%$ , surpassing the performance of all other baselines in terms of prediction diversity and accuracy. These results highlight the effectiveness of our framework in leveraging both a small labeled dataset and abundant unlabeled data, while still generating diverse and meaningful segmentation results.
+
+Further, we also show the visualization results of the AmbiSSL framework, as shown in Figure 4. We can see that AmbiSSL provides a set of predictions that are diverse and match those of the human annotators. Additional visualization results are provided in the supplementary material.
+
+# 4.6. Performance on ISIC Dataset
+
+Table 2 presents the evaluation of our model on the ISIC dataset. The same experiments were performed as with the LIDC dataset; however, the percentage of labeled data used is  $10\%$  and  $20\%$ , as the ISIC dataset is comparatively smaller, and results with  $5\%$  labeled data were unstable. Our approach consistently outperforms the baselines in terms of both prediction diversity and accuracy, even with fewer labeled samples. For instance, with  $20\%$  labeled data, our method achieves a soft Dice score of  $85.87\%$ , and sig-
+
+<table><tr><td rowspan="3">αu</td><td colspan="3">LIDC-IDRI</td><td colspan="3">ISIC</td></tr><tr><td colspan="2">Scans Used</td><td>Metrics</td><td colspan="2">Scans Used</td><td>Metrics</td></tr><tr><td>Labeled</td><td>Unlabeled</td><td>GED↓ Dicesoft↑</td><td>Labeled</td><td>Unlabeled</td><td>GED↓ Dicesoft↑</td></tr><tr><td>0.3</td><td></td><td></td><td>0.1987 88.33</td><td></td><td></td><td>0.3412 83.52</td></tr><tr><td>0.5</td><td>60(5%)</td><td>1146(95%)</td><td>0.1872 88.34</td><td>9(10%)</td><td>81(90%)</td><td>0.3358 83.40</td></tr><tr><td>1.0</td><td></td><td></td><td>0.2134 86.75</td><td></td><td></td><td>0.3533 79.65</td></tr><tr><td>0.3</td><td></td><td></td><td>0.1765 88.95</td><td></td><td></td><td>0.2645 85.32</td></tr><tr><td>0.5</td><td>120(10%)</td><td>1086(90%)</td><td>0.1620 89.86</td><td>18(20%)</td><td>72(80%)</td><td>0.2444 85.87</td></tr><tr><td>1.0</td><td></td><td></td><td>0.1876 85.88</td><td></td><td></td><td>0.3014 81.19</td></tr></table>
+
+![](images/df50845c5c7a8cf2ae69cac777bb0f81acec9f215b95474a1a286e4de789896c.jpg)  
+Figure 4. Comparison of segmentation results of our proposed AmbiSSL framework on the LIDC-IDRI dataset with human annotators.
+
+Table 3. Ablation study of the weights  ${\alpha }_{u}$  in the unsupervised loss function.  
+
+<table><tr><td>L</td><td>a%</td><td>GED↓</td><td>Dicesoft↑(%)</td><td>L</td><td>a%</td><td>GED↓</td><td>Dicesoft↑(%)</td></tr><tr><td>0</td><td></td><td>0.1742</td><td>88.51</td><td rowspan="5">2</td><td>20</td><td>0.1751</td><td>88.21</td></tr><tr><td>1</td><td rowspan="2">50</td><td>0.1613</td><td>88.78</td><td>30</td><td>0.1749</td><td>88.61</td></tr><tr><td>2</td><td>0.1620</td><td>89.86</td><td>40</td><td>0.1678</td><td>89.44</td></tr><tr><td>3</td><td></td><td>0.1689</td><td>89.32</td><td>50</td><td>0.1620</td><td>89.86</td></tr><tr><td>4</td><td></td><td>0.1732</td><td>89.55</td><td>60</td><td>0.1667</td><td>89.65</td></tr></table>
+
+Table 4. Ablation studies of different  $L$  and  $a\%$  values in the pruning-transformed decoder of our framework, evaluated on the LIDC-IDRI dataset with  ${10}\%$  labeled and the remaining unlabeled data. The number of samples is set to 10 for all comparisons.
+
+nificantly reducing the GED score to 0.2444.
+
+# 5. Ablation Experiments
+
+# 5.1. Weights in Loss Function
+
+In this section, we study the impact of the hyperparameter  $\alpha_{u}$ . We vary  $\alpha_{u}$  across  $\{0.3, 0.5, 1.0\}$  to observe changes in performance. As shown in Table 3, we achieve the best results across all datasets by setting  $\alpha_{u} = 0.5$ . However, a noticeable drop occurs when  $\alpha_{u}$  is set to 1.0. For the supervised hyperparameter  $\alpha_{l}$ , we set its value to 1.0, and for  $\beta$ , we use a value of 0.5.
+
+# 5.2. Design Choices for Random Pruned Decoders
+
+Our method incorporates two randomly pruned decoders to generate a diverse pseudo-label set with different views. In this section, we examine the impact of two key factors in the pruning process: the threshold layer  $L$  (which determines where pruning begins) and the pruning percentage  $a\%$  (which defines the proportion of weights pruned in each
+
+layer). Table 4 summarizes the results of the pruning experiments, where we first vary  $L$  and keep  $a\%$  constant. When  $L = 0$ , pruning is applied across all layers of the decoder, resulting in higher sparsity. As  $L$  increases, pruning is applied only to the final layers of the decoder. For example, with  $L = 2$ , pruning starts at the third layer, resulting in a GED score of 0.1620 and a DiceSoft score of 89.86, indicating an improvement in prediction diversity.
+
+Next, we fix  $L$  and vary the pruning percentage  $a\%$ . As the pruning percentage increases, the GED score decreases, showing that higher pruning percentages lead to more diverse predictions. Specifically, the GED score decreases with increasing  $a\%$ , reaching the lowest value of 0.1620 and the highest DiceSoft score of 89.86 at  $a = 50\%$ , indicating that the model is able to generate more diverse yet meaningful segmentation results.
+
+# 6. Conclusion and Future Work
+
+In this paper, we introduce AmbiSSL, the first framework designed to address annotation ambiguity in semi-supervised learning for medical image segmentation. Our framework leverages both labeled and unlabeled data to generate multiple plausible segmentation maps simultaneously. To achieve this, we propose the DPG module, which produces diverse pseudo-label sets using randomly pruned decoders. Additionally, we employ semi-supervised latent distribution learning, utilizing both ground truth annotations and pseudo-label sets to construct a common latent space where different latent codes result in varied segmentation outcomes. Finally, Cross-Decoder Supervision enables the pruned decoders to enhance their performance through mutual guidance. Extensive experiments on two publicly available datasets demonstrate that AmbiSSL generates diverse segmentation maps, effectively utilizing unlabeled data and reducing dependence on large labeled datasets.
+
+Despite the significant progress demonstrated by our method, its performance remains below that of fully annotated methods. To bridge this gap, future work should explore additional strategies to further enhance the effectiveness of annotation ambiguity aware semi-supervised learning.
+
+# References
+
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+Roth, and Daguang Xu. Unetr: Transformers for 3d medical image segmentation. In WACV, pages 574-584, 2022. 1  
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+[16] Alex Kendall and Yarin Gal. What uncertainties do we need in bayesian deep learning for computer vision? Advances in neural information processing systems, 30, 2017. 3  
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+Computer-Assisted Intervention, pages 109-118. Springer, 2022. 6  
+[25] Aimon Rahman, Jeya Maria Jose Valanarasu, Ilker Hacihaliloglu, and Vishal M Patel. Ambiguous medical image segmentation using diffusion models. In CVPR, pages 11536-11546, 2023. 2, 3  
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+# AnomalyNCD: Towards Novel Anomaly Class Discovery in Industrial Scenarios
+
+Ziming Huang $^{1,*}$  Xurui Li $^{1,*}$  Haotian Liu $^{1,*}$  Feng Xue $^{4}$  Yuzhe Wang $^{1}$  Yu Zhou $^{1,2,3,\dagger}$
+
+$^{1}$ School of Electronic Information and Communications, Huazhong University of Science and Technology  
+<sup>2</sup> Hubei Key Laboratory of Smart Internet Technology, Huazhong University of Science and Technology  
+<sup>3</sup>Artificial Intelligence Research Institute, Wuhan JingCe Electronic Group Co., LTD  
+$^{4}$ Department of Information Engineering and Computer Science, University of Trento
+
+# Abstract
+
+Recently, multi-class anomaly classification has garnered increasing attention. Previous methods directly cluster anomalies but often struggle due to the lack of anomaly-prior knowledge. Acquiring this knowledge faces two issues: the non-prominent and weak-semantics anomalies. In this paper, we propose AnomalyNCD, a multi-class anomaly classification network compatible with different anomaly detection methods. To address the non-prominence of anomalies, we design main element binarization (MEBin) to obtain anomaly-centered images, ensuring anomalies are learned while avoiding the impact of incorrect detections. Next, to learn anomalies with weak semantics, we design mask-guided representation learning, which focuses on isolated anomalies guided by masks and reduces confusion from erroneous inputs through corrected pseudo labels. Finally, to enable flexible classification at both region and image levels, we develop a region merging strategy that determines the overall image category based on the classified anomaly regions. Our method outperforms the state-of-the-art works on the MVTec AD and MTD datasets. Compared with the current methods, AnomalyNCD combined with zero-shot anomaly detection method achieves a  $10.8\%$ $F_{1}$  gain,  $8.8\%$  NMI gain, and  $9.5\%$  ARI gain on MVTec AD, and  $12.8\%$ $F_{1}$  gain,  $5.7\%$  NMI gain, and  $10.8\%$  ARI gain on MTD. Code is available at https://github.com/HUST-SLOW/AnomalyNCD.
+
+# 1. Introduction
+
+In recent years, industrial anomaly detection [22, 24, 31, 53] has garnered remarkable performance. It locates visual anomalies on industrial products but without recognizing fine-grained anomaly categories. For downstream anomaly treatments, it is necessary to recognize the anomaly classes, such as fracture, ablation, etc., and even discover novel
+
+anomaly categories that are constantly emerging.
+
+Several anomaly clustering approaches [1, 28, 40] have been proposed to address the multi-class anomaly classification task, as illustrated in Fig. 1 (a). These approaches typically employ a two-step process: anomaly localization followed by feature extraction from the anomalous regions for clustering. However, the effectiveness of these methods is limited when dealing with homogeneous anomaly patterns that exhibit differences in shape, appearance, and location, primarily due to the lack of prior knowledge of anomaly types. Therefore, our study aims to classify unseen anomalies by leveraging prior knowledge of seen anomalies, thereby overcoming the limitations of current methods.
+
+Through detailed investigation, we find two primary obstacles in leveraging prior knowledge of known anomalies, which prevent existing classification network to industrial anomalies. ① Non-prominence Anomalies: Classification in natural scenes assumes that subjects are centered in the images so that networks easily extract their semantics, while this assumption is not true in industrial scenarios. ② Low-semantics Anomalies: In contrast to natural objects, industrial anomalies are typically less semantic, making the network hard to focus on anomalies but prone to background.
+
+In this paper, we overcome both obstructions and propose a multi-class anomaly classification network that aligns with the concept of novel class discovery (NCD), as illustrated in 1 (c). This network learns to classify isolated anomalies by focusing the model's attention on real anomaly regions. Firstly, to address the non-prominence issue, we propose a main element binarization (MEBin) method. MEBin isolates the primary anomaly regions by extracting them from anomaly detection (AD) results. This binarization process alleviates the negative impact of errors within AD results on the subsequent multi-class anomaly learning, enabling compatibility with various AD algorithms. Secondly, to tackle low-semantics anomalies, we propose mask-guided representation learning. It leverages the anomaly masks generated by MEBin to direct the network's attention specifically to individual anomalous re
+
+(a) Anomaly Clustering  
+![](images/6f28074d3b820de407554e49c3df332f67292ad3e01383a202de6c441a17175b.jpg)  
+$\leftarrow$  Base classes training  
+$\leftarrow$  Novel classes training/inference  
+Pixel-wise multiplication
+
+(b) NCD in natural scenario  
+![](images/9856cc55df2428764454626fffc1db4ff2f32513fac774dbd98f0ac2bbc1bfa8.jpg)  
+$\longleftrightarrow$  Inference  
+Frozen  
+Trainable  
+SL Supervised Learning Prediction of novel classes
+
+(c) AnomalyNCD  
+Figure 1. Comparison between solutions organizing anomalies into groups. (a) Anomaly clustering methods extract the features of the anomaly region and employ unsupervised clustering algorithms to cluster the anomalies. (b) Vanilla NCD methods typically employ a trainable feature extractor and classifier. These components process object-centered images from both known and unknown classes. (c) Our method aims to learn features of isolated anomaly regions using anomaly-centered sub-images and masks from MEBin.  
+![](images/e4bb3e9c1ceff0a9df17853a1ecc9d40e2064e7ba2b2b92733d5b9501dfc0b04.jpg)  
+SSL Self-Supervised Learning Prediction of base classes
+
+gions, ensuring our network learns more discriminative features specific to anomalies and classifies each individual anomaly. Additionally, we use corrected pseudo labels in this learning method to prevent false-positive anomalies from training. Finally, to achieve more flexible classification in both region and image levels, we propose a region merging strategy, which determines the image category according to the classification of each region in the image. Experimental results on the MVTec AD [5] and MTD datasets [23] demonstrate the effectiveness of AnomalyNCD.
+
+In summary, the major contributions of our work are:
+
+- We propose the first method based on self-supervised manner in multi-class anomaly classification, named AnomalyNCD. It can be seamlessly combined with different anomaly detection methods and classify unseen anomalies detected into homogeneous groups.  
+- We study the challenges of learning from anomalous regions in industrial scenarios, motivating us to propose MEBin and mask-guided representation learning for our network to focus on real anomalous regions and learn discriminative features of isolated anomalies.  
+- AnomalyNCD surpasses existing anomaly clustering methods and NCD methods on the MVtec AD and MTD datasets, providing a decent foundation for downstream anomaly treatments in industrial scenarios.
+
+# 2. Related Work
+
+# 2.1. Image Clustering in Industrial Scenarios
+
+Directly clustering the images cannot perform well in multiclass anomaly classification. To address this issue, two studies build the clustering pipeline specific for fine-grained anomaly classes. Sohn et al. [40] proposed a simple but effective method to aggregate the patch features by anomaly map weighting. Lee et al. [28] only aggregates the patch
+
+features with the higher anomaly score to determine the classes. However, both methods rely on frozen models that cannot learn features specific to anomalies. Therefore, we adopt self-supervised learning to discover novel classes from unlabeled anomalies.
+
+# 2.2. Novel Class Discovery
+
+Novel Class Discovery setting was first formalized in [18]. The early methods follow a two-stage pipeline [18, 20, 21]. The first stage is to learn representation from the base set to obtain prior knowledge for classification, which serves as the basis for the second one to train the model on the novel set. Recent methods are one-stage [19, 46, 56]. By handling the base set and novel set simultaneously, one-stage methods extract better representations with less bias towards the base classes. NCD has been applied in several fields, such as medical image classification [14, 58], semantic segmentation [55] and point cloud segmentation [37, 49]. In this paper, we introduce the NCD architecture into multi-class industrial anomaly classification for the first time.
+
+# 2.3. Binarization Approach
+
+Binarization is a crucial preprocessing step for various vision tasks, e.g., edge detection [6, 59], segmentation [10, 16, 57], document image processing [7, 34, 41], medical image processing [39, 42], object detection [50-52], etc. Otsu [35] determines the optimal threshold to separate the foreground and background by maximizing the between-class variance of the pixel intensities. DiffuMask [48] utilizes cross-attention maps and adaptive thresholding to generate binary maps. However, these methods usually obtain fragmented false-positive regions when segmenting the anomalies, which harms the region-level anomaly class prediction. To alleviate this, we propose the main element
+
+![](images/122d41e092b6ec5984e498ab0657fc202c0a15690b68c660d8bba69fab810ba6.jpg)  
+Figure 2. Illustration of the Training Process for AnomalyNCD. First, we apply main element binarization (MEBin) to segment anomaly masks from detection results and generate anomaly-centered sub-images. Second, we introduce mask-guided representation learning to learn discriminative features of anomalies, classifying sub-images into various categories.
+
+binarization strategy to extract only the primary anomaly region, thereby reducing the impact of false positives on representation learning.
+
+# 3. Method
+
+The proposed AnomalyNCD aims to automatically discover and recognize the visual categories of industrial anomalies. Fig. 2 illustrates its overall framework. To extract main anomaly regions from detection results, we outline the main element binarization method (Sec. 3.2). Guided by these anomaly regions, we then apply mask-guided representation learning (Sec. 3.3) to extract and classify discriminative features of anomalies within these regions. Finally, a region merging strategy (Sec. 3.4) ensures robust image-level classification based on all anomaly regions.
+
+# 3.1. Problem Definition
+
+Given a set of unlabelled images  $\mathcal{D}^{\mathbf{u}} = \{I_i^{\mathbf{u}}|i\in [1,N^{\mathbf{u}}]\}$ , the goal of AnomalyNCD is to assign them into  $\mathcal{C}^{\mathbf{u}}$  classes (named "Novel" previously), where  $\mathcal{C}^{\mathbf{u}}$  is known as a priori, referring to vanilla NCD [15, 17, 45]. To provide a better foundation for learning novel classes, we follow previous NCD tasks to assume a set of labeled anomaly images  $\mathcal{D}^{\mathrm{l}} = \{(I_{i}^{\mathrm{l}},y_{i}^{\mathrm{l}},\mathbf{M}_{i}^{\mathrm{l}})|i\in [1,N^{\mathrm{l}}]\}$  with  $\mathcal{C}^{\mathrm{l}}$  classes available (named "Base" previously), where  $y_{i}^{1}\in \mathbb{R}^{1\times (\mathcal{C}^{1} + \mathcal{C}^{\mathrm{u}})}$  is the one-hot class label, and  $\mathbf{M}_i^1$  is the ground truth anomaly mask of image  $I_{i}^{1}\in \mathcal{D}^{1}$ .  $\mathcal{D}^{\mathrm{l}}$  supplies the auxiliary knowledge of the industrial anomalies for grouping the images in  $\mathcal{D}^{\mathrm{u}}$ . To further generalize our study, we also perform experiments with different  $\mathcal{D}^{\mathrm{l}}$  and without  $\mathcal{D}^{\mathrm{l}}$  in the Appendix F.
+
+# 3.2. Main Element Binarization
+
+To provide a clear anomaly indication of unlabeled images, we use an anomaly detection method on  $I_{i}^{\mathbf{u}}$  to generate the anomaly probability map, denoted as  $A_{i} \in$
+
+![](images/4e78c66e59bd0b252d828c337b9069a5e472be922c43337d4a4a086f74943108.jpg)  
+Figure 3. Pipeline of the Main Element Binarization. In 3D visualization, we show the changes of segmented regions under different thresholds. The 3D map (a) corresponds to the 2D binary segmentation mask  $(a)$ .
+
+$[0,1]^{H\times W}$ . However,  $A_{i}$  inevitably contains false positives (over-detections) and false negatives (missed detections). These errors can negatively affect multi-class anomaly classification. To address this, we propose a Main Element Binarization (MEBin) approach. It extracts the principal anomaly structures (Main Element) from  $A_{i}$  by focusing on stable regions across small threshold variations. Overall, the MEBin consists of three steps: 1 Predefine a range  $[\mathbf{s}_{\mathrm{min}},\mathbf{s}_{\mathrm{max}}]$  for threshold exploration; 2 Binarize  $A_{i}$  across all thresholds within this range; 3 Identify the main elements in  $A_{i}$  based on the changes of segmented regions under different binarization results.
+
+The first step: To capture all potential anomalies across the set  $\{A_i | i \in [1, N^{\mathbf{u}}]\}$ , the upper limit  $\mathbf{s}_{\max}$  is set to 1. Conversely, the lower limit,  $\mathbf{s}_{\min}$ , is determined by the minimum anomaly score found across the set  $\{A_i | i \in [1, N^{\mathbf{u}}]\}$ , represented as  $\mathbf{s}_{\min} = \min(s_1, s_2, \dots, s_{N^{\mathbf{u}}})$ , where  $s_i = \max(A_i)$ . Such a lower limit helps minimize the likelihood of normal image pixels being segmented.
+
+The second step: To analyze the segmented regions
+
+change with thresholds, we uniformly sample  $\mathcal{T}$  thresholds  $\{\epsilon_j|j\in [1,\mathcal{T}]\}$  in  $[\mathbf{s}_{\mathrm{min}},\mathbf{s}_{\mathrm{max}}]$ . For each threshold  $\epsilon_{j}$ , the anomaly map  $A_{i}$  is binarized into a mask  $M_i^j$  ..  $M_{i}^{j} = \mathbb{1}[A_{i} > \epsilon_{j}]$ , where  $\mathbb{1}[.\cdot ]$  is the indicator function. To reduce the meaningless and fragmented segmentation, we further apply an erosion operation to each mask  $M_{i}^{j}$ .
+
+The third step: We identify main anomaly regions through two operations. First, let  $\delta_i^j$  denote the number of individual regions segmented in  $M_{i}^{j}$ , each region is an independent connected component. We observe that the amount of the main regions in the anomaly map  $A_{i}$  can be characterized by the non-zero value that appears most frequently in  $\{\delta_i^j | j \in [1, T]\}$ , denoted as  $\bar{\delta}_i$ . Second, to segment the main regions, we take the longest continuous threshold range where only  $\bar{\delta}_i$  regions are segmented. The main anomaly regions remain stable within this threshold range, as shown in Fig. 3.
+
+- If this range is shorter than  $\tau$ , there is no anomaly region to be segmented.  
+- Conversely, if this range exceeds  $\tau$ , it confirms stable anomaly segmentation within this threshold range. In this case, we select the minimum threshold from the identified range to segment anomalies as completely as possible.
+
+Finally, we use the selected threshold to segment  $A_{i}$  into the binary mask, denoted as  $\mathbf{M}_i^{\mathbf{u}}$ . In this way, the unlabeled images set  $\mathcal{D}^{\mathbf{u}}$  are extended with the binary masks:  $\{(I_i^{\mathbf{u}},\mathbf{M}_i^{\mathbf{u}})|i\in [1,N^{\mathbf{u}}]\}$ .
+
+Anomaly-Centered Sub-Image Cropping. To focus the model on anomalous regions, we crop each region in  $\mathbf{M}_i^{\mathbf{u}}$  individually into anomaly-centered sub-images. Specifically, for each region in  $\mathbf{M}_i^{\mathbf{u}}$ , we use the minimum bounding square to crop the sub-image from  $I_i^{\mathbf{u}}$  and its mask from  $\mathbf{M}_i^{\mathbf{u}}$ . Then the sub-images of  $I_i^{\mathbf{u}}$  can be denoted as  $\{x_{i,1}^{\mathbf{u}}, x_{i,2}^{\mathbf{u}}, \ldots\}$ , and the corresponding masks cropped from  $\mathbf{M}_i^{\mathbf{u}}$  are denoted as  $\{m_{i,1}^{\mathbf{u}}, m_{i,2}^{\mathbf{u}}, \ldots\}$ . To align labeled and unlabeled inputs, we use the same cropping operation to extract sub-images and masks for the labeled data set  $\mathcal{D}^1$ , denoted as  $\{(x_{i,1}^1, m_{i,1}^1), (x_{i,2}^1, m_{i,2}^1), \ldots | i \in [1, N^1]\}$ . These are then merged with the unlabeled data in the same structures, represented as  $\{(x_{i,k}, m_{i,k}, y_{i,k}) | i \in [1, N^1 + N^{\mathbf{u}}], k \in [1, \bar{\delta}_i]\}$ , where  $\bar{\delta}_i$  indicates the number of sub-images per image, and  $y_{i,k}$  is the one-hot class label for each labeled sub-image, matching the label of the  $i^{\mathrm{th}}$  image if it belongs to  $\mathcal{D}^1$ . Implementation details of the cropping process are supplied in the Appendix C.
+
+# 3.3. Mask-Guided Representation Learning
+
+# 3.3.1. Mask-Guided Vision Transformer (MGViT)
+
+MGViT is built on vision transformer (ViT). Thus we review its structure.
+
+Vision transformer [13] processes an input image by dividing it into  $\mathbf{N}$  fixed-size patches. Each patch is treated as a "token" and is flattened into an embedding vector of length
+
+![](images/4bd161ec4d6c9804e5433f0b3f76a15cc3fd7c1ed74b722814cb7019929c18be.jpg)  
+Figure 4. Visualization of the self-attention of the [CLS] token on the last layer's heads. DINO attention refers to the [CLS] token extracted from a DINO pre-trained ViT that mainly focuses on a foreground object. AnomalyNCD uses a mask to direct the [CLS] token's attention to the anomalous regions.
+
+$D$ . ViT has  $L$  sequential transformer layers, each containing self-attention layers and feed-forward neural networks. In addition, a special class token [CLS], is propagated from the first layer to the final layer where it serves as the basis for classification. In the self-attention of the  $l^{\mathrm{th}}$  layer, the input patches undergo linear projections to form the queries, keys, and values  $\mathbf{Q}_{l - 1},\mathbf{K}_{l - 1},\mathbf{V}_{l - 1}\in \mathbb{R}^{(\mathsf{N} + 1)\times D}$ . Here, ViT captures the relationships between the image patches by self-attention mechanism Attn as follows:
+
+$$
+A t t n = \operatorname {s o f t m a x} \left(\operatorname {c o n c a t} \left(\mathbf {Q} _ {l - 1} ^ {\mathrm {c l s}} \mathbf {K} _ {l - 1} ^ {\top}, \mathbf {Q} _ {l - 1} ^ {\text {p a t c h}} \mathbf {K} _ {l - 1} ^ {\top}\right)\right) \mathbf {V} _ {l - 1} \tag {1}
+$$
+
+where we divide  $\mathbf{Q}_{l-1}$  into  $\mathbf{Q}_{l-1}^{\mathrm{cls}} \in \mathbb{R}^{1 \times D}$  and  $\mathbf{Q}_{l-1}^{\mathrm{patch}} \in \mathbb{R}^{\mathrm{N} \times D}$  to represent class token and patch tokens separately.
+
+Insufficient Focus on Anomalies. The ViT excels in semantic representation but fails to detect weak semantic anomalies. Fig. 4 demonstrates this using the self-attention map of the [CLS] token in the last layer of a DINO-pretrained ViT [9]. In the  $1^{\text{st}}$  row's example, the model highlights the salient object (metal grid) in an image, rather than the local anomaly. This observation means that the network over-focuses on learning background.
+
+Mask-Guided Attention. To address the issue above, we propose mask-guided attention to direct ViT's focus on the anomalous region. Specifically, the input sub-image  $x_{i,k}$  is fed into the ViT, and we assume the token number is N. At the same time, its mask  $m_{i,k}$  is resized to  $\sqrt{\mathbb{N}} \times \sqrt{\mathbb{N}}$  by average pooling and then flattened into a vector  $\mathcal{M} \in \mathbb{R}^{N \times 1}$ . Subsequently, we insert the constant 1 at the beginning of  $\mathcal{M}$  to align its size with the tokens. Next, we use the mask vector in the self-attention mechanism for re-directing focus, which has three possible design choices.
+
+1. Adding the mask  $\mathcal{M}$  on both class and patch tokens.  
+2. Adding the mask  $\mathcal{M}$  on the patch tokens.  
+3. Adding the mask  $\mathcal{M}$  on the class token.
+
+The  $1^{\mathrm{st}}$  and  $2^{\mathrm{nd}}$  designs suppress the rich contextual features in patch tokens that are crucial for classification, and our network only focuses on classifying anomalies rather than segmenting. Thus, the  $3^{\mathrm{rd}}$  one is recommended as the most suitable design, and the experiment also verifies its effectiveness. Such a design can be formulated as follows:
+
+$$
+A t t n = \operatorname {s o f t m a x} (\operatorname {c o n c a t} \left(\mathbf {Q} _ {l - 1} ^ {\mathrm {c l s}} \mathbf {K} _ {l - 1} ^ {\top} + \overline {{\mathcal {M}}} , \mathbf {Q} _ {l - 1} ^ {\text {p a t c h}} \mathbf {K} _ {l - 1} ^ {\top}\right)) \mathbf {V} _ {l - 1} \tag {2}
+$$
+
+where  $\overline{\mathcal{M}}$  denotes the converted mask vector that is compatible with the attention mechanism [12]:
+
+$$
+\overline {{\mathcal {M}}} (i) = \left\{ \begin{array}{l l} 0, & \text {i f} \mathcal {M} (i) > 0. 5 \\ - \infty , & \text {o t h e r w i s e} \end{array} \right. \tag {3}
+$$
+
+Note that, in the ViT, the self-attention in the last  $L_{m}$ -layer is replaced with the mask-guided attention to form MGViT. Fig. 4 reveals that the [CLS] token focuses on anomalous regions by using our mask-guided attention. Even though the predicted masks do not align with the ground truth accurately, the network still focuses on the anomaly roughly.
+
+# 3.3.2. Model Training
+
+Given a sub-image pair  $(x_{i,k},m_{i,k})$ , we first apply random augmentation to generate two views  $(\tilde{x}_{i,k},\tilde{m}_{i,k})$  and  $(\hat{x}_{i,k},\hat{m}_{i,k})$ . Following DINO [9], we feed these two views into the teacher and student networks respectively, which have shared MGViT and classification heads with different softmax temperatures. For labeled sub-images, the ground truth labels are converted into one-hot vectors to serve as supervision targets for the student network. For unlabeled sub-images  $\tilde{x}_{i,k},\hat{x}_{i,k}$ , we generate pseudo labels  $\hat{q}_{i,k},\tilde{q}_{i,k} \in \mathbb{R}^{1 \times (\mathcal{C}^1 + \mathcal{C}^{\mathrm{u}})}$  by the "teacher" one, which employs a sharp temperature  $\tau_t$  to produce confident predictions. The entries of labeled classes  $(\mathcal{C}^1)$  in the pseudo labels are set to 0. The "student" one, using a smooth temperature  $\tau_s$ , is trained to align its probability predictions  $\hat{p}_{i,k},\tilde{p}_{i,k} \in \mathbb{R}^{1 \times (\mathcal{C}^1 + \mathcal{C}^{\mathrm{u}})}$  with either ground truth labels (for labeled data) or pseudo labels (for unlabeled data). This dual supervision ensures effective learning from both labeled and unlabeled data.
+
+Our training objective follows existing category discovery methods [45, 47] and includes classification objective and representation learning objective. The classification objective contains ground truth label supervision  $\mathcal{L}_{\mathrm{cls}}^1$  on labeled sub-images, and pseudo label supervision  $\mathcal{L}_{\mathrm{cls}}^{\mathbf{u}}$  on unlabeled sub-images. The representation learning objective contains self-supervised contrastive learning  $\mathcal{L}_{\mathrm{rep}}$  [11] on both labeled sub-images and unlabeled sub-images, and supervised contrastive learning  $\mathcal{L}_{\mathrm{rep}}^1$  [26] on only labeled sub-images. Finally, we adopt a mean-entropy maximization regularizer  $\mathcal{L}_{\mathrm{reg}}^{\mathbf{u}}$  [8] for unlabeled sub-images. More details about the training procedure are provided in Appendix A.
+
+The overall loss of training objective is written as:
+
+$$
+\mathcal {L} = \lambda \left(\mathcal {L} _ {\text {r e p}} ^ {\mathbf {l}} + \mathcal {L} _ {\text {c l s}} ^ {\mathbf {l}}\right) + (1 - \lambda) \left(\mathcal {L} _ {\text {r e p}} + \mathcal {L} _ {\text {c l s}} ^ {\mathbf {u}} + \mu \mathcal {L} _ {\text {r e g}} ^ {\mathbf {u}}\right) \tag {4}
+$$
+
+![](images/80d852c687798a0c243941c4fffe7bc55bca26f7c68f8a0103527926f9527ec2.jpg)  
+Figure 5. Region merging strategy for image-level classification. Using average prediction, the output of normal cropped images (Sub-image-2) leads to final misclassification, while area-weighted prediction can reduce the negative effect of normal cropped images on the final result.
+
+where  $\lambda$  is a hyperparameter that balances the supervised loss and the self-supervised loss.  $\mu$  is the coefficient of the regularization.
+
+Pseudo Labels Correction. The error in pseudo labels leads to the false learning objective for the classification model. To mitigate these errors, especially the false detection of anomalous regions, we propose to use anomaly scores (described in Sec 3.2) to correct pseudo labels. Let  $s_{i,k}$  denote the anomaly score for  $x_{i,k}$ , we weightedly judge whether the view  $\hat{x}_{i,k}$  should be labeled as normal or assigned the generated pseudo labels.
+
+$$
+\hat {q} _ {i, k} \leftarrow w _ {i, k} \mathbf {e} + (1 - w _ {i, k}) \hat {q} _ {i, k}; \quad w _ {i, k} = \max  (0. 5 - s _ {i, k}, 0) \tag {5}
+$$
+
+where  $w_{i,k}$  is the weight for normal.  $\mathbf{e} \in \mathbb{R}^{1 \times (\mathcal{C}^{\mathrm{l}} + \mathcal{C}^{\mathrm{u}})}$  denotes a unit vector whose  $(\mathcal{C}^{\mathrm{l}} + 1)$ -th value is 1 and all other values are 0, in which we use the first class in the  $\mathcal{C}^{\mathrm{u}}$  classes as normal. If  $s_{i,k}$  is smaller, the more likely the sub-image  $\hat{x}_{i,k}$  is normal, and  $\hat{q}_{i,k}$  is closer to  $\mathbf{e}$ . Thus, such correction forces the network to separate normal sub-images from the train set. In the same way, the pseudo label  $\tilde{q}_{i,k}$  is updated.
+
+# 3.4. Region Merging for Image Classification
+
+For flexible classification in both sub-image and image levels, we aim to determine the image's anomaly class according to its sub-image classification. Intuitively, a naive method is to average the predictions of all sub-images within an image. However, false classification of the overdetected region may mislead the image class. As shown in Fig. 5, Sub-image-1 and Sub-image-2 are classified to Class-2 and Class-3, respectively, where the wrong prediction of Sub-image-2 misleads the image class in Fig. 5 (b).
+
+To address this issue, we propose a region merging approach to robustly classify images. We found that misclassification is mostly over-detected regions that are much
+
+<table><tr><td>Datasets</td><td>Metric</td><td>IIC[25]</td><td>GATCluster[33]</td><td>SCAN[44]</td><td>UNO[15]</td><td>GCD[45]</td><td>SimGCD[47]</td><td>AMEND[3]</td><td>AC[40] (Unsup.)</td><td>MuSc [30] +AnomalyNCD</td></tr><tr><td rowspan="3">MVTec AD [5]</td><td>NMI</td><td>0.093</td><td>0.136</td><td>0.210</td><td>0.146</td><td>0.417</td><td>0.452</td><td>0.431</td><td>0.525</td><td>0.613</td></tr><tr><td>ARI</td><td>0.020</td><td>0.053</td><td>0.103</td><td>0.052</td><td>0.302</td><td>0.346</td><td>0.333</td><td>0.431</td><td>0.526</td></tr><tr><td>F1</td><td>0.285</td><td>0.264</td><td>0.335</td><td>0.342</td><td>0.553</td><td>0.569</td><td>0.542</td><td>0.604</td><td>0.712</td></tr><tr><td rowspan="3">MTD [23]</td><td>NMI</td><td>0.064</td><td>0.028</td><td>0.041</td><td>0.034</td><td>0.211</td><td>0.105</td><td>0.138</td><td>0.179</td><td>0.268</td></tr><tr><td>ARI</td><td>0.020</td><td>0.009</td><td>0.029</td><td>0.011</td><td>0.115</td><td>0.048</td><td>0.067</td><td>0.120</td><td>0.228</td></tr><tr><td>F1</td><td>0.252</td><td>0.243</td><td>0.282</td><td>0.221</td><td>0.381</td><td>0.293</td><td>0.324</td><td>0.346</td><td>0.509</td></tr></table>
+
+Table 1. Quantitative results on the MVTec AD and MTD dataset. All the methods only use unlabeled images as input. The best-performing result is in bold, the second best result is underlined.  
+
+<table><tr><td>Datasets</td><td>Metric</td><td>AC[40] (Semi-sup.)</td><td>UniFormaly[28] (0.953 / 0.837)</td><td>PatchCore[38] (0.938 / 0.729) +AnomalyNCD</td><td>RD++[43] (0.950 / 0.741) +AnomalyNCD</td><td>EfficientAD[4] (0.917 / 0.731) +AnomalyNCD</td><td>PNI[2] (0.942 / 0.516) +AnomalyNCD</td><td>CPR[29] (0.964 / -) +AnomalyNCD</td></tr><tr><td rowspan="3">MVTec AD [5]</td><td>NMI</td><td>0.608</td><td>0.547</td><td>0.670</td><td>0.631</td><td>0.516</td><td>0.675</td><td>0.736</td></tr><tr><td>ARI</td><td>0.489</td><td>0.433</td><td>0.601</td><td>0.542</td><td>0.394</td><td>0.609</td><td>0.674</td></tr><tr><td>F1</td><td>0.652</td><td>0.645</td><td>0.769</td><td>0.721</td><td>0.641</td><td>0.769</td><td>0.805</td></tr><tr><td rowspan="3">MTD [23]</td><td>NMI</td><td>0.390</td><td>0.421</td><td>0.380</td><td>0.368</td><td>0.220</td><td>0.181</td><td>-</td></tr><tr><td>ARI</td><td>0.314</td><td>0.322</td><td>0.390</td><td>0.361</td><td>0.188</td><td>0.219</td><td>-</td></tr><tr><td>F1</td><td>0.490</td><td>0.609</td><td>0.617</td><td>0.600</td><td>0.467</td><td>0.465</td><td>-</td></tr></table>
+
+Table 2. Quantitative results on the MVTec AD and MTD dataset. All the methods use unlabeled images and labeled normal images as input. We evaluate the AUPRO metric across various anomaly detection approaches on two datasets, e.g., (0.953 / 0.837), the first one on the MVTec AD dataset and the second on the MTD dataset. For the metrics of multi-class anomaly classification, the best-performing result is in bold, the second best result is underlined. The unofficial results are marked in gray.
+
+smaller than real anomalies. Therefore, we define an area-related weight  $\alpha_{i,k}^{\mathbf{u}}$  for each sub-image  $x_{i,k}^{\mathbf{u}}$ , which is used in determining the image category:
+
+$$
+\alpha_ {i, k} ^ {\mathbf {u}} = \frac {\exp \left(\sqrt {\mathbf {a} _ {i , k} ^ {\mathbf {u}}} / \tau_ {\alpha}\right)}{\sum_ {k = 1} ^ {\bar {\delta} _ {i}} \exp \left(\sqrt {\mathbf {a} _ {i , k} ^ {\mathbf {u}}} / \tau_ {\alpha}\right)} \tag {6}
+$$
+
+where  $\mathbf{a}_{i,k}^{\mathbf{u}}$  is the area of anomaly in  $x_{i,k}^{\mathbf{u}}$ , and  $\tau_{\alpha}$  is the temperature value. Then, for an image  $I_{i}^{\mathbf{u}}$  composed by sub-images  $\{x_{i,k}^{\mathbf{u}}|k\in [1,\bar{\delta}_i]\}$ , the prediction logit is  $p_i^{\mathbf{u}} = \sum_{k = 1}^{\bar{\delta}_i}\alpha_{i,k}^{\mathbf{u}}p_{i,k}^{\mathbf{u}}$ , where  $p_{i,k}^{\mathbf{u}}$  is the probability prediction of  $x_{i,k}^{\mathbf{u}}$  generated by the student network. As shown in Fig. 5 (a), the prediction  $p_i^{\mathbf{u}}$  depends more on  $p_{i,1}^{\mathbf{u}}$ , which has a larger weight  $\alpha_{i,1}^{\mathbf{u}}$  and a correct prediction.
+
+# 4. Experiments
+
+# 4.1. Experimental setting
+
+# 4.1.1. Datasets
+
+We conduct experiments on industrial datasets MVTec AD [5] and Magnetic Tile Defect (MTD) [23]. MVTec AD has industrial product images of 10 object categories and 5 texture categories. Each product category has at least two anomaly classes. Following [40] and [28], we remove the combined anomaly classes for a fair comparison. Notice that our method can also handle the combined anomaly class, as described in the Appendix G. MTD dataset has 952 normal images and 392 abnormal images, the abnor
+
+mal images are divided into five anomaly classes. We follow [40] that uses  $80\%$  of normal images as the reference images and the rest as the test images. For both datasets, we use the single-blade sub-dataset in Aero-engine Blade Anomaly Detection Dataset (AeBAD-S) [54] with the normal class removed, as our default labeled image set  $\mathcal{D}^1$ .
+
+# 4.1.2. Implementation details
+
+We use ViT-B/8 [13] pre-trained with DINO [9] as our feature extractor. The self-attention in the last 9 layers are replaced with our mask-guided attention. During training, all the layers of ViT are fixed except the last layer. For anomaly detection methods preceding AnomalyNCD, we choose zero-shot method MuSc [30], one-class methods PatchCore [38], EfficientAD [4], RD++ [43], PNI [2] and CPR [29]. More details are in the Appendix B.
+
+# 4.1.3. Competing methods
+
+We compare our method with two state-of-the-art industrial anomaly clustering methods, UniFormaly [28] and Anomaly Clustering [40] that has two settings: an unsupervised one (Unsup.) and a semi-supervised one (Semisup.). The former setting only inputs unlabeled images for clustering, while the latter one uses labeled normal images, same as the input of one-class anomaly detection. We also employ three deep clustering methods, IIC [25], GAT-Cluster [33], and SCAN [44], which cluster unlabeled images directly. In addition, four NCD methods in the nature scene are considered for comparison, UNO [15], GCD
+
+<table><tr><td></td><td>Avg FPR ↓</td><td>Avg FNR ↓</td><td>NMI ↑</td><td>ARI ↑</td><td>F1 ↑</td></tr><tr><td>ε = 0.1</td><td>0.572</td><td>0.617</td><td>0.554</td><td>0.482</td><td>0.650</td></tr><tr><td>ε = 0.3</td><td>0.678</td><td>0.742</td><td>0.499</td><td>0.404</td><td>0.587</td></tr><tr><td>ε = 0.5</td><td>0.484</td><td>0.165</td><td>0.567</td><td>0.458</td><td>0.640</td></tr><tr><td>ε = 0.7</td><td>0.269</td><td>0.247</td><td>0.495</td><td>0.395</td><td>0.623</td></tr><tr><td>ε = 0.9</td><td>0.544</td><td>0.593</td><td>0.077</td><td>0.013</td><td>0.337</td></tr><tr><td>Otsu [35]</td><td>0.676</td><td>0.525</td><td>0.382</td><td>0.268</td><td>0.499</td></tr><tr><td>Ours</td><td>0.153</td><td>0.035</td><td>0.613</td><td>0.526</td><td>0.712</td></tr></table>
+
+Table 3. Ablation study of different binarization approaches on the MVTec AD dataset. The best-performing result is in bold.
+
+[45], SimGCD [47] and AMEND [3]. As in our method, the AeBAD-S dataset is used as labeled abnormal images.
+
+# 4.1.4. Evaluation metrics
+
+We report three widely used metrics for the evaluation of clustering: the  $F_{1}$  score, the normalized mutual information (NMI) [32], and the adjusted rand index (ARI) [36]. We use the Hungarian algorithm [27] to match the predicted clusters to the ground truth labels. For methods using anomaly maps, we measure the segmentation per-region overlap (AUPRO) with  $30\%$  FPR [5] to explore the impact of anomaly detection performance on the multi-class classification. All metrics are calculated by the official code.
+
+# 4.2. Quantitative results
+
+We report the results of the multi-class anomaly classification on the MVTec AD and MTD datasets in Table 1 and 2. Notably, AnomalyNCD is compatible with all the anomaly detection methods to enable subsequent multiclass anomaly classification.
+
+All methods in Table 1 only use unlabeled images as input. Compared to Anomaly Clustering [40], AnomalyNCD combined with zero-shot anomaly detection method MuSc [30], achieves  $8.8\%$  gains on NMI,  $9.5\%$  gains on ARI, and  $10.8\% F_1$  gains, proving that AnomalyNCD extracts more discriminative features than Anomaly Clustering through contrastive learning in anomalous regions. AnomalyNCD also outperforms state-of-the-art NCD methods, achieving  $16.1\%$  gains on NMI,  $18.0\%$  gains on ARI, and  $14.3\% F_1$  gains. The performance advantage of AnomalyNCD is due to focusing on anomalies inside images.
+
+In Table 2, all methods utilize both unlabeled images and labeled normal images from the same product. We integrate AnomalyNCD with various one-class AD methods. Utilizing CPR, which has the highest AUPRO, achieves the best performance on the MVtec AD dataset: NMI increases by  $10.7\%$ , ARI by  $14.9\%$ , and  $F_{1}$  score by  $9.6\%$ , surpassing other methods. On the MTD dataset, although the segmentation AUPRO of all AD methods is lower than that of Uniformly, PatchCore+AnomalyNCD still achieves improvements of  $6.8\%$  in ARI and  $0.8\%$  in  $F_{1}$  score.
+
+![](images/aa4d6942d51791802392cc3c307ca6af93fe6aa25e81d662f9d68ca013df31fc.jpg)  
+(a) CPR
+
+![](images/a41628508eb245d484c589097bb35c8febe629cf7e1fb0fb2a5376fb152dd226.jpg)  
+(b) PNI  
+Figure 6. The results of various anomaly detection (AD) methods under multiple fixed thresholds. The horizontal dashed line represents the results of MEBin. Notably, the optimal fixed thresholds differ across AD methods, while our MEBin consistently outperforms the fixed threshold results.
+
+![](images/b34d222bfc42d5e89da9a21b47dc3ec1b0148ca170b9e88d11d74224895eb690.jpg)  
+Figure 7. T-SNE visualization of sub-images on the MVTec AD dataset. We choose metal nut, hazelnut and wood as examples. The different colors of dots represent their anomaly classes.
+
+# 4.3. Ablation Study
+
+# 4.3.1. Effectiveness of main element binarization
+
+Table 3 compares MEBin's performance with the Otsu method [35] and fixed thresholds. Since the missed detection is more critical than over-detection in industrial scenarios, we define an anomaly as detected if the intersection over union (IoU) between the actual and predicted bounding boxes exceeds 0.1. Then we calculate the FPR and FNR for these binarization methods. MEBin demonstrates lower FPR and FNR than fixed thresholds and Otsu, leading to better multi-class classification results. Compared to the fixed thresholds, MEBin adaptively determines an optimal threshold for each image adaptation and achieves a  $7.2\%$ $F_{1}$  improvement. The Otsu tends to over-detect, particularly in normal images, making it less effective for this task.
+
+In Fig. 6, we further apply MEBin on different one-class AD methods, which exhibit varying optimal fixed thresholds. For example, the optimal threshold of CPR [29] is near 0.5, whereas for PNI [2] it is approximately 0.3. MEBin's adaptive threshold selection for each image outperforms all fixed thresholds for the whole image set.
+
+<table><tr><td>Mask Mechanism</td><td>NMI</td><td>ARI</td><td>F1</td></tr><tr><td>(a) w/o MGA</td><td>0.598</td><td>0.494</td><td>0.698</td></tr><tr><td>(b) all tokens</td><td>0.507</td><td>0.382</td><td>0.600</td></tr><tr><td>(c) patch tokens</td><td>0.563</td><td>0.467</td><td>0.686</td></tr><tr><td>(d) class token (Ours)</td><td>0.613</td><td>0.526</td><td>0.712</td></tr></table>
+
+Table 4. Compared with different mask attention mechanisms on the MVtec AD dataset, the best-performing result is in bold.  
+
+<table><tr><td rowspan="2">Lm</td><td colspan="3">MVTec AD</td><td colspan="3">MTD</td></tr><tr><td>NMI</td><td>ARI</td><td>F1</td><td>NMI</td><td>ARI</td><td>F1</td></tr><tr><td>1</td><td>0.606</td><td>0.508</td><td>0.690</td><td>0.191</td><td>0.157</td><td>0.420</td></tr><tr><td>3</td><td>0.608</td><td>0.511</td><td>0.694</td><td>0.209</td><td>0.173</td><td>0.436</td></tr><tr><td>6</td><td>0.613</td><td>0.519</td><td>0.713</td><td>0.253</td><td>0.214</td><td>0.492</td></tr><tr><td>9</td><td>0.613</td><td>0.526</td><td>0.712</td><td>0.268</td><td>0.228</td><td>0.509</td></tr><tr><td>12</td><td>0.609</td><td>0.521</td><td>0.712</td><td>0.249</td><td>0.213</td><td>0.492</td></tr></table>
+
+# 4.3.2. Discussion of the mask-guided attention
+
+The mask-guided attention (MGA) directs ViT to focus on tokens within the mask (anomalous region). We show the t-SNE visualization in Fig. 7. With MGA in the  $2^{nd}$  row, image features have larger inter-class distances (e.g. metal nut) and smaller intra-class distances (e.g. hazelnut and wood) than those without MGA in the  $1^{st}$  row. In terms of metrics on MVtec AD, our MGA has a  $1.5\%$  NMI gain,  $3.2\%$  ARI gain, and  $1.4\%$ $F_{1}$  gain shown in Table 4.
+
+We conduct experiments to introduce the binary mask into different tokens in Table 4. (b) introduces the binary mask on [CLS] token and patch tokens. (c) introduces it on patch tokens. Our MGA (d) only performs on [CLS] token, which is directly input into the classifier. We make patch tokens have a global receptive field to introduce more surrounding information indirectly into [CLS] token. Compared to other mask strategies, our MGA achieves  $5.0\%$  NMI,  $5.9\%$  ARI, and  $2.6\%$ $F_{1}$  improvements.
+
+# 4.3.3. The influence of the mask-guided layer  $L_{m}$
+
+In our method, we introduce mask-guided attention in the last  $L_{m}$  layers of ViT. As reported in Table 5, we conduct the experiments with different  $L_{m}$ . The results demonstrate that using mask-guided attention in the last 9 layers yields better performance on both datasets. When  $L_{m}$  is small, the [CLS] token cannot adequately focus on the anomaly within the binary mask. In contrast, when  $L_{m} = 12$ , the [CLS] token completely lost contextual information around the anomaly, resulting in a drop in metrics.
+
+# 4.3.4. Discussion of merging strategies
+
+In Table 6, we report results using different merging strategies. (i) averaging the predictions of the sub-images, (ii) utilizing the anomaly scores of the sub-images as weights to merge, and (iii) using our region merging strategy. Strategy (iii) achieves better metrics than (i) and (ii) on both
+
+Table 5. Ablation study on the position of mask-guided layers on MVTec AD and MTD datasets. Best results in bold.  
+
+<table><tr><td rowspan="2">Merge</td><td colspan="3">MVTec AD</td><td colspan="3">MTD</td></tr><tr><td>NMI</td><td>ARI</td><td>F1</td><td>NMI</td><td>ARI</td><td>F1</td></tr><tr><td>(i) Avg</td><td>0.610</td><td>0.521</td><td>0.709</td><td>0.257</td><td>0.223</td><td>0.501</td></tr><tr><td>(ii) Score Avg</td><td>0.600</td><td>0.513</td><td>0.703</td><td>0.228</td><td>0.208</td><td>0.485</td></tr><tr><td>(iii) Area Avg</td><td>0.613</td><td>0.526</td><td>0.712</td><td>0.268</td><td>0.228</td><td>0.509</td></tr></table>
+
+Table 6. Compared with different merging strategies on the MVTec AD and MTD datasets.  
+
+<table><tr><td></td><td>Precision</td><td>Recall</td><td>NMI</td><td>ARI</td><td>F1</td></tr><tr><td>w/o PLC</td><td>0.797</td><td>0.727</td><td>0.597</td><td>0.517</td><td>0.714</td></tr><tr><td>w PLC</td><td>0.821</td><td>0.876</td><td>0.613</td><td>0.526</td><td>0.712</td></tr></table>
+
+Table 7. The ablation experiment of pseudo label correction (PLC) on the MVTec AD dataset. We evaluate the precision and recall of the normal class.
+
+datasets. In anomaly detection, noise inevitably leads to over-detections, which have small areas but large anomaly scores. Directly averaging results over all sub-images is inaccurate, especially when many false positive sub-images are involved. Similarly, using anomaly scores as weights is also inappropriate. In contrast, our merging method, which assigns weights to multiple sub-image predictions based on area, achieves more robust merged predictions.
+
+# 4.3.5. Effect of Pseudo Label Correcting
+
+Our Pseudo Label Correcting (PLC) aims to reduce the impact of over-detections from the anomaly detection process. Although over-detected sub-images are normal, they have large appearance differences, which makes it difficult to correctly group them into the same normal class. Table 7 presents the precision and recall of the normal class. After applying PLC, recall improves by  $14.9\%$ , which means that some misclassified normal sub-images are corrected by our PLC. Additionally, a  $1.6\%$  improvement in NMI is observed in the multi-class classification results.
+
+# 5. Conclusion
+
+In this paper, we propose a novel multi-class anomaly classification method AnomalyNCD, which is compatible with existing anomaly detection methods. Firstly, we propose the main element binarization approach to isolate most overdetections and missed detections brought by anomaly detection methods. Secondly, we crop each anomalous region and leverage mask-guided representation learning to focus the network on the local anomaly and learn discriminative representations. Finally, our region merging strategy achieves flexible classification at sub-image and image levels during inference. While the performance of AnomalyNCD is generally influenced by the quality of the anomaly detection method, our AnomalyNCD outperforms all the current industrial anomaly clustering methods and NCD methods in the nature scene.
+
+# 6. Acknowledgments
+
+# References
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+# Anomize: Better Open Vocabulary Video Anomaly Detection
+
+Fei Li $^{1,2\#}$  Wenxuan Liu $^{3,4\#}$  Jingjing Chen $^{2}$  Ruixu Zhang $^{1}$  Yuran Wang $^{1}$  Xian Zhong $^{4}$  Zheng Wang $^{1*}$
+
+$^{1}$ National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University
+
+$^{2}$ Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University
+
+$^{3}$ State Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University
+
+<sup>4</sup>Hubei Key Laboratory of Transportation Internet of Things, Wuhan University of Technology lifeiwhu@whu.edu.cn, liuwx66@pku.edu.cn
+
+# Abstract
+
+Open Vocabulary Video Anomaly Detection (OVVAD) seeks to detect and classify both base and novel anomalies. However, existing methods face two specific challenges related to novel anomalies. The first challenge is detection ambiguity, where the model struggles to assign accurate anomaly scores to unfamiliar anomalies. The second challenge is categorization confusion, where novel anomalies are often misclassified as visually similar base instances. To address these challenges, we explore supplementary information from multiple sources to mitigate detection ambiguity by leveraging multiple levels of visual data alongside matching textual information. Furthermore, we propose incorporating label relations to guide the encoding of new labels, thereby improving alignment between novel videos and their corresponding labels, which helps reduce categorization confusion. The resulting Anomize framework effectively tackles these issues, achieving superior performance on UCF-CRIME and XD-VIOLENCE datasets, demonstrating its effectiveness in OVVAD.
+
+# 1. Introduction
+
+Video Anomaly Detection (VAD) identifies anomaly in videos and is widely used in public safety systems. Traditional VAD methods can be categorized based on the type of training data used. Semi-supervised VAD [3, 22, 49] is trained exclusively on normal samples, detecting anomalies as deviations from learned normal patterns. In contrast, weakly supervised VAD [13, 33, 50] is trained on both normal and anomalous samples but lacks precise temporal labels, treating VAD as a binary classification problem. Both methods focus on detecting specific anomaly within a closed set and exhibit limitations in open-world scenarios.
+
+![](images/52b5defeaa7ecee1cac29b44887010721f35d171c29888b5b141d914d01932e7.jpg)  
+Figure 1. Challenges Related to Novel Anomalies. (a) Detection ambiguity: The model struggles to assign accurate anomaly scores to unfamiliar frames containing novel anomalies. (b) Categorization confusion: Novel anomalies are misclassified as visually similar base instances from the training set.
+
+![](images/791640fb09c83caab38906e007fb9f61cc76c85e9eb196dee7758ecae3a26b55.jpg)
+
+Recent research has explored open-set VAD [1, 9], where anomalies seen in training are considered base cases, while others are treated as novel cases. It trains on normal and base anomalies to detect all anomalies, overcoming the limitations of closed-set detection. However, it struggles with understanding anomaly categories, leading to unclear outputs [42]. Consequently, a leading study [42] has further investigated open vocabulary (OV) VAD, which aims to detect and categorize all anomalies using the same training data as open-set VAD, offering more informative results.
+
+Novel anomalies in OVVAD introduce two challenges that remain unexplored by existing methods: (1) Detection ambiguity, where the model often lacks sufficient information to accurately assign anomaly scores to unfamiliar data, as shown in Fig. 1(a). Current methods rely on training or fine-tuning the model, which is inherently limited and cannot adapt to the variability of samples in an open setting. (2) Categorization confusion, where novel cases visually similar to base cases are misclassified, as shown in Fig. 1(b). OV tasks generally rely on multimodal alignment for categorization. Since the model tends to extract visual features for novel videos similar to base videos, these features are more likely to align with base label encodings, leading to miscategorization. Traditional OV methods use pre-trained encoders to encode text, where the input contains labels with
+
+![](images/3b39cd50603180e5b08c1f08e375a8e490d81739a5cb8c1be399b09b9ca88c25.jpg)  
+Figure 2. Feature Visualization of Our Design. (a) Text augmentation shifts ambiguous frames to the anomalous feature space. In the static stream, text represents anomaly-related nouns (e.g., "abandoned fire starter"), while in the dynamic stream, it denotes label descriptions. (b) Group-guided text encoding improves the alignment of novel anomalies with novel labels, especially for those resembling base samples.
+
+unified templates [16, 29, 44, 45] or embeddings [2, 4, 53]. These methods rely solely on pre-trained encoders without spatial guidance in label encoding, limiting multimodal alignment for novel cases.
+
+To address detection ambiguity, we introduce a Text-Augmented Dual Stream mechanism with dynamic and static streams, each focusing on different visual features augmented by corresponding textual information. The dynamic stream captures sequential information through temporal visual encoding, augmented by label descriptions related to dynamic characteristics. The static stream captures scene information through original contrastive language-image pre-training (CLIP)-encoded visual features, augmented by a concept library related to static characteristics. The complementarity between dynamic and static data is crucial: certain anomalies rely on temporal information, such as tailing, while others depend on contextual cues, such as running on a highway. Synergistic training of the streams ensures mutual supplementation and constraints, delivering comprehensive temporal and contextual information, minimizing overfitting to specific anomaly categories, and improving overall performance. Additionally, the augmentation follows common-sense reasoning. To detect anomalies in real-world scenarios, we first define the anomaly and establish correlations between visual data and anomaly texts, providing a reference for detection within the overall context. Similarly, we augment visual features with relevant anomaly text, providing additional information for detection. As shown in Fig. 2(a), novel visual features that cause ambiguous detections are shifted into the anomalous feature space with support from text, helping the model better assess unfamiliar anomalies.
+
+To address categorization confusion, we introduce a Group-Guided Text Encoding mechanism, encoding labels using group-based descriptions, with labels sharing similar visual characteristics grouped together. As shown in Fig. 2(b), this mechanism establishes connections be
+
+tween base and novel data through grouping, positioning the encodings of novel labels close to those of base labels, where videos associated with both base and novel labels are visually similar, thereby enhancing multimodal alignment for novel data. For novel labels not grouped with base labels, the descriptions provide contextual support to pretrained encoders for text encoding, thus enhancing alignment. Compared to previous methods mainly relying on pre-trained models, our approach strengthens the guidance of the feature space for novel labels, achieving more effective alignment for categorization.
+
+With the Anomize framework, we achieve notable results across both XD-VIOLENCE [41] and UCF-CRIME [33] datasets. For anomaly detection, we obtain a  $2.78\%$  overall improvement on XD-VIOLENCE and  $8.21\%$  on novel cases, with UCF-CRIME results comparable to a more complex state-of-the-art model. For categorization, we achieve a  $25.61\%$  overall increase in Top-1 accuracy on XD-VIOLENCE and  $5.71\%$  on UCF-CRIME, with improvements of  $56.53\%$  and  $4.49\%$  on novel cases, respectively.
+
+In summary, our contributions are threefold:
+
+- To address detection ambiguity, we discover the importance of providing sufficient informational support. We combine dynamic and static streams to effectively constrain and complement each other. Operating at different levels of visual features, each stream is augmented with corresponding textual information, offering comprehensive support for detection.  
+- To tackle categorization confusion, we emphasize the importance of establishing connections between labels to guide their encodings. We propose a text encoding mechanism that groups labels based on visual characteristics and generates corresponding descriptions for encodings.  
+- Our Anomize framework targets the challenges of novel anomalies that remain unexplored, offering new insights for OVVAD and demonstrating superior performance on two widely-used datasets, particularly for novel cases.
+
+# 2. Related Work
+
+# 2.1. Video Anomaly Detection
+
+Semi-Supervised VAD. Existing semi-supervised video anomaly detection (VAD) methods are typically categorized into three groups: one-class classification (OCC), reconstruction-based models, and prediction-based models, all of which are trained exclusively on normal data. OCC models [31, 32, 35, 40, 49] classify anomalies by identifying data points that fall outside a learned hypersphere of normal data. However, defining normality can be ambiguous, which often reduces their effectiveness [23, 46]. Reconstruction-based methods [3, 25, 30, 48, 52] use deep auto-encoders (DAEs) to learn normal patterns, detecting anomalies through high reconstruction errors. However,
+
+DAEs may still reconstruct anomalous frames with low error, weakening detection performance. Prediction models [5, 8, 18, 22, 24, 26], often utilizing GANs, forecast future frames and identify anomalies by comparing predicted frames with actual frames.
+
+Weakly-Supervised VAD. Weakly-supervised video anomaly detection (WSVAD) identifies anomalies using only video-level labels without precise temporal or spatial information. WSVAD methods typically frame the task as a multiple instance learning (MIL) problem [19, 33, 34, 39, 50], where videos are divided into segments, and predictions are aggregated into video-level anomaly scores. Sultani et al. [33] first define the WSVAD paradigm using a deep multiple-instance ranking framework. Recent methods focus on optimizing models. Tian et al. [34] introduce RTFM, which combines dilated convolutions and self-attention to detect subtle anomalies, while Zaheer et al. [50] add a clustering-based normalcy suppression mechanism. Other approaches [13, 27] leverage pre-trained models to gain task-agnostic knowledge. Wu et al. [43] propose VadCLIP, which uses CLIP [29] for dual-branch outputs of anomaly scores and labels.
+
+Open-Set VAD. Open-set VAD models are trained on normal behaviors and base anomalies to detect all anomalies, addressing the challenges of open-world environments. Acsintoae et al. [1] first introduce open-set VAD, along with a benchmark dataset and evaluation framework. Zhu et al. [54] combine evidential deep learning and normalizing flows within a multiple instance learning framework. Hirschorn et al. [9] propose a lightweight normalizing flows framework that utilizes human pose graph structures.
+
+Our method provides both detection and categorization results in an open setting, focusing on addressing the challenges related to novel anomalies.
+
+# 2.2. Open Vocabulary Learning
+
+Recent advancements in pre-trained vision-language models [11, 29] have spurred significant interest in open vocabulary tasks, including object detection [6, 15, 51], semantic segmentation [7, 20, 47], and action recognition [12, 14, 21, 36]. These studies leverage the pre-trained knowledge of multimodal models, demonstrating strong generalization. Wu et al. [42] first introduce open vocabulary video anomaly detection (OVVAD) using the pre-trained model CLIP. However, most methods emphasize the visual encoder while neglecting the text encoder, limiting zero-shot capabilities. Our method explores the text encoder and incorporates a guided encoding mechanism to enhance multimodal alignment in OVVAD.
+
+# 3. Proposed Anomize Method
+
+# 3.1. Overview
+
+Following Wu et al. [42], we define the training sample set as  $D = \{(v_i, y_i)\}_{i=1}^{N+A}$ , which consists of  $N$  normal samples  $D_n$  and  $A$  abnormal samples  $D_a$ . Here,  $v_i$  represents video samples, and  $y_i \in \mathbb{C}_{\mathrm{base}}$  denotes the corresponding anomaly labels. Each  $v_i \in D_a$  contains at least one anomalous frame, while  $v_i \in D_n$  consists entirely of normal frames. The complete label set  $\mathbb{C}$  includes both base and novel anomaly labels. The objective of OVVAD is to train a model on  $D$  to predict frame-level anomaly scores and video-level anomaly labels from  $\mathbb{C}$ .
+
+Fig. 3 illustrates the overview of framework. We leverage the encoder of the pre-trained CLIP model for its strong generalization capabilities. Video frames are processed by the CLIP image encoder  $\Phi_{\mathrm{visual}}$  to extract original visual features  $x_{f} \in \mathbb{R}^{n \times d}$ , where  $n$  is the number of frames and  $d$  is the feature dimension. These features are temporally modeled by a lightweight temporal encoder. The original features, augmented by a concept library ConceptLib, pass through the static stream, while temporal features, augmented by label descriptions, pass through the dynamic stream. The prediction from each stream is obtained and aggregated to generate the final frame-level anomaly score  $s \in \mathbb{R}^{n \times 1}$ . For categorization, a multimodal alignment method is used. A fused visual feature is first generated, and the CLIP text encoder  $\Phi_{\mathrm{text}}$  extracts textual features via the group-guided text encoding mechanism. Frame-level predictions are then obtained through alignment and aggregated for the final video-level result  $p_{\mathrm{video}}$ .
+
+# 3.2. Lightweight Temporal Encoder
+
+We utilize the frozen  $\Phi_{\mathrm{visual}}$  for visual features to leverage its zero-shot capabilities. However, since CLIP is pretrained on image-text pairs, it lacks temporal modeling for video. Recent methods [14, 37, 38] commonly introduce a temporal encoder. However, this often leads to performance degradation on novel cases, as the additional parameters in the encoder may become specialized for the training set, leading to overfitting. Therefore, we adopt a lightweight long short-term memory (LSTM) [10] for temporal modeling, resulting in the temporal visual feature  $x_{\mathrm{tem}} \in \mathbb{R}^{n \times d}$ :
+
+$$
+x _ {\text {t e m}} = \operatorname {L S T M} \left(x _ {f}\right). \tag {1}
+$$
+
+Other parameter-efficient models may also be suitable, as discussed in the supplementary material.
+
+# 3.3. Group-Guided Text Encoding
+
+Previous methods mainly rely on the generalization capabilities of pre-trained models without task-specific guidance, often leading to categorization confusion. We introduce a group-guided text encoding mechanism to address this.
+
+![](images/c66cbf29e592a91e68ad07baad3756d8681de372f2068aa00593d42e731bc826.jpg)
+
+![](images/4d079611d4d1d5d8225ebcded20eb1e12c2a9e1b1e1a7aa52173c1a228595092.jpg)
+
+![](images/b68c6495d0ac29df390af3dd45b56fbe66f236e185c88c11b31896a0c7047afc.jpg)  
+Figure 3. Overview of Our Anomize Framework. (a) Process for obtaining label features via the Group-Guided Text Encoding mechanism. (b) Creation of the concept library ConceptLib for anomaly detection. (c) The framework processes anomaly labels and video frames to generate frame-level anomaly scores and detected labels. Scoring is performed using a Text-Augmented Dual Stream mechanism, where each stream receives corresponding text and visual features, and the fused scores are produced as output. For labeling, the model aligns label features from the Group-Guided Text Encoding mechanism with the fused original and temporal visual encodings. Both the text and image encoders, pre-trained on CLIP, remain frozen without further optimization.
+
+We leverage large language models (LLM), specifically GPT-4 [28], for textual encoding. We first use the prompt prompt<sub>group</sub> to group labels, ensuring that corresponding videos in each group exhibit high visual similarity. Then, we apply the prompt prompt<sub>desc</sub> to generate text descriptions for each label based on the grouping. These descriptions capture shared elements while emphasizing unique characteristics within each group, ensuring the encodings remain similar yet distinguishable:
+
+$$
+\operatorname {r e s u l t} _ {\text {g r o u p}} = \operatorname {G P T} \left(\operatorname {p r o m p t} _ {\text {g r o u p}}, \mathbb {C}\right), \tag {2}
+$$
+
+$$
+\operatorname {r e s u l t} _ {\text {d e s c}} = \operatorname {G P T} \left(\operatorname {p r o m p t} _ {\text {d e s c}}, \operatorname {r e s u l t} _ {\text {g r o u p}}\right), \tag {3}
+$$
+
+where  $\text{result}_{\text{group}}$  and  $\text{result}_{\text{desc}}$  represent the label groups and their descriptions. The descriptions are then passed into the frozen CLIP text encoder  $\Phi_{\text{text}}$  to obtain encodings  $t_{\text{desc}} \in \mathbb{R}^{c \times d}$ , where  $c$  is the number of anomaly labels:
+
+$$
+t _ {\text {d e s c}} = \Phi_ {\text {t e x t}} \left(\text {r e s u l t} _ {\text {d e s c}}\right). \tag {4}
+$$
+
+These encodings are used for multimodal alignment. For the visual features, we combine the temporal and original encodings, preserving the knowledge captured by the pretrained model:
+
+$$
+x _ {\text {f u s e d}} = x _ {\text {t e m}} + \alpha x _ {f}, \tag {5}
+$$
+
+where  $\alpha$  is a scalar weight. The prediction probabilities for video frames are expressed as:
+
+$$
+p _ {\text {f r a m e}} = \frac {x _ {\text {f u s e d}} t _ {\text {d e s c}} ^ {\top}}{\| x _ {\text {f u s e d}} \| \| t _ {\text {d e s c}} \|}, \tag {6}
+$$
+
+where  $p_{\mathrm{frame}} \in \mathbb{R}^{n \times c}$  represents the probability distribution over  $c$  anomaly labels for each frame. To obtain the video-level prediction, we select the top  $M$  probabilities for each label and average these top values, where  $M$  is the total number of frames divided by 16:
+
+$$
+p _ {\text {a v g}} = \sigma \left[ \frac {1}{M} \sum_ {k = 1} ^ {M} \operatorname {T o p} M \left(p _ {\text {f r a m e}} [ j ]\right) \right] _ {j = 1} ^ {c}, \tag {7}
+$$
+
+where  $p_{\mathrm{avg}} \in \mathbb{R}^c$  is the average probabilities for each label after applying the softmax function  $\sigma(\cdot)$ . Finally, the video-level prediction  $p_{\mathrm{video}}$  is determined as the label with the highest average probability:
+
+$$
+p _ {\text {v i d e o}} = \arg \max  _ {j} p _ {\text {a v g}} ^ {(j)}. \tag {8}
+$$
+
+# 3.4. Augmenter
+
+In our method, both streams utilize text to enhance visual encodings via a unified augmenter. The augmenter takes visual encodings  $e_{\mathrm{visual}}$  and textual encodings  $e_{\mathrm{text}}$  as input. These are processed by a multi-head attention layer  $\mathrm{MHA}(\cdot)$ , where  $e_{\mathrm{visual}}$  acts as the query and  $e_{\mathrm{text}}$  acts as the key and value. This operation extracts the most relevant textual features for supplementation, denoted as  $e_{\mathrm{refine}}$ :
+
+$$
+e _ {\text {r e f i n e}} = \mathrm {M H A} \left(e _ {\text {v i s u a l}}, e _ {\text {t e x t}}, e _ {\text {t e x t}}\right). \tag {9}
+$$
+
+A fully connected layer  $\mathrm{FC}(\cdot)$  linearly projects the visual encoding, which is concatenated with the refined textual features and passed through a multi-layer perceptron
+
+$\mathrm{MLP}(\cdot)$  for dimensionality reduction. This results in the augmented output  $e_{\mathrm{aug}}$ :
+
+$$
+e _ {\mathrm {a u g}} = \operatorname {M L P} \left(\left[ e _ {\text {r e f i n e}}; \operatorname {F C} \left(e _ {\text {v i s u a l}}\right) \right]\right), \tag {10}
+$$
+
+# 3.5. Text-Augmented Dual Stream
+
+In open settings, models may struggle to assess unfamiliar anomalies due to limited information. We propose a Text-Augmented Dual Stream mechanism with complementary dynamic and static streams, each augmented by relevant text to provide sufficient support for detection.
+
+Since video anomaly detection (VAD) relies on temporal cues, we employ a dynamic stream to predict anomaly scores  $s_{\mathrm{dyn}} \in \mathbb{R}^{n \times 1}$  based on refined visual features  $f_{\mathrm{aug}} \in \mathbb{R}^{n \times d}$ , derived from temporal visual features and augmented by label descriptions via the augmenter in Sec. 3.4:
+
+$$
+f _ {\text {a u g}} = \text {A u g m e n t e r} \left(x _ {\text {t e m}}, t _ {\text {d e s c}}\right), \tag {11}
+$$
+
+$$
+s _ {\mathrm {d y n}} = \text {S i g m o i d} \left(\mathrm {F C} \left(f _ {\mathrm {a u g}} + \mathrm {M L P} \left(f _ {\mathrm {a u g}}\right)\right)\right), \tag {12}
+$$
+
+where Sigmoid  $(\cdot)$  converts predictions to [0, 1].
+
+Since the dynamic stream is limited in scene context, we employ a static stream with original visual features augmented by anomaly-relevant concept data.
+
+Specifically, we create a concept library ConceptLib containing key features related to anomalies. These features are generated by  $\Phi_{\mathrm{text}}$  from various nouns describing significant characteristics of the anomalies:
+
+$$
+\operatorname {C o n c e p t L i b} = \Phi_ {\text {t e x t}} (\operatorname {G P T} (\operatorname {p r o m p t} _ {\text {c o n c}}, \mathbb {C})), \tag {13}
+$$
+
+where  $\mathrm{prompt}_{\mathrm{conc}}$  is a prompt for relevant nouns. We then compute the cosine similarity between the visual feature of frame  $i$ ,  $x_{f}^{(i)}$ , and concept features  $h \in \mathrm{ConceptLib}$ :
+
+$$
+\left. \operatorname {s i m} \left(x _ {f} ^ {(i)}, h\right) = \frac {x _ {f} ^ {(i)} h ^ {\top}}{\left\| x _ {f} ^ {(i)} \right\| \| h \|\right). \tag {14}
+$$
+
+The top  $K$  relevant concept features  $h_f^{(i)}\in \mathbb{R}^{K\times d}$  and their scores  $s_f^{(i)}\in \mathbb{R}^K$  are selected:
+
+$$
+h _ {f} ^ {(i)}, s _ {f} ^ {(i)} = \operatorname {T o p} K \left(\operatorname {s i m} \left(x _ {f} ^ {(i)}, h\right)\right). \tag {15}
+$$
+
+The selected features are then weighted by their scores and concatenated to form refined textual features for the video:
+
+$$
+h _ {f} ^ {\text {n e w}} = \left[ \sigma \left(s _ {f} ^ {(i)}\right) \odot h _ {f} ^ {(i)} \right] _ {i = 1} ^ {n}. \tag {16}
+$$
+
+Next, the refined features  $h_f^{\mathrm{new}} \in \mathbb{R}^{n \times k \times d}$  and the original visual features  $x_f$  are passed through the augmenter to generate the augmented encoding  $x_{\mathrm{aug}} \in \mathbb{R}^{n \times d}$ :
+
+$$
+x _ {\mathrm {a u g}} = \operatorname {A u g m e n t e r} \left(x _ {f}, h _ {f} ^ {\text {n e w}}\right). \tag {17}
+$$
+
+Similar to the dynamic stream,  $x_{\mathrm{aug}}$  is fed into a detector for anomaly score prediction  $s_{\mathrm{sta}}$  in the static stream:
+
+$$
+s _ {\mathrm {s t a}} = \text {S i g m o i d} \left(\mathrm {F C} \left(x _ {\mathrm {a u g}} + \mathrm {M L P} \left(x _ {\mathrm {a u g}}\right)\right)\right). \tag {18}
+$$
+
+Finally, the outputs of the two streams are aggregated for the overall anomaly score prediction  $s$ :
+
+$$
+s = \beta s _ {\mathrm {d y n}} + (1 - \beta) s _ {\mathrm {s t a}}, \tag {19}
+$$
+
+where  $\beta$  is a tunable parameter balancing the contributions of the dynamic and static streams.
+
+# 3.6. Objective Functions
+
+First Training Stage. In the first stage, we focus on video anomaly categorization to train the LSTM while freezing other modules to prevent optimization conflicts. We use cross-entropy loss  $\mathcal{L}_{\mathrm{ce}}$  for categorization. To prevent overfitting to normal data due to class imbalance, we add a separation loss  $\mathcal{L}_{\mathrm{sep}}$  to enhance the distinction between normal and anomalous predictions. The loss for the first stage is:
+
+$$
+\mathcal {L} _ {\mathrm {c a t}} = \mathcal {L} _ {\mathrm {c e}} + \mathcal {L} _ {\mathrm {s e p}}, \tag {20}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {c e}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} g _ {i} \log \left(p _ {\text {a v g}, i}\right), \tag {21}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {s e p}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} | \max  \left(p _ {\text {a v g}, i} [ 1: ]\right) - p _ {\text {a v g}, i} [ 0 ] | + 1, \tag {22}
+$$
+
+where  $p_{\mathrm{avg},i}$  denotes the predicted probabilities for the  $i$ -th video, and the normal label is at the first index.  $g_{i}$  is the one-hot ground truth, and  $N$  denotes the batch size.
+
+Second Training Stage. In the second stage, we focus on anomaly detection to train the static and dynamic streams while freezing other modules. Following Wu et al. [43], we apply the MIL loss. Specifically, we first average the top  $M$  frame anomaly scores to obtain the video-level prediction  $\hat{q}_i$ , then compute the loss  $\mathcal{L}_{\mathrm{X - MIL}}$  for each stream using binary cross-entropy to quantify the difference between predictions and binary labels  $q_i$ , where  $q_{i} = 1$  denotes an anomaly and  $X\in \{D,S\}$  denotes the type of stream. Additionally, we apply a weight  $w_{i}$  in this phase to tackle data imbalance by increasing the penalty for incorrect scores related to anomalous videos. The loss is defined as follows:
+
+$$
+\mathcal {L} _ {\text {d e t}} = \mathcal {L} _ {\mathrm {D} - \mathrm {M I L}} + \mathcal {L} _ {\mathrm {S} - \mathrm {M I L}}, \tag {23}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {X - M I L}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} w _ {i} \left(q _ {i} \log \left(\hat {q} _ {i}\right) + \left(1 - q _ {i}\right) \log \left(1 - \hat {q} _ {i}\right)\right). \tag {24}
+$$
+
+<table><tr><td>Method</td><td>AP</td><td>\( AP_b \)</td><td>\( AP_n \)</td><td>AUC</td><td>\( AUC_b \)</td><td>\( AUC_n \)</td></tr><tr><td>Zhu et al.* [54]</td><td>64.40</td><td>-</td><td>-</td><td>78.82</td><td>-</td><td>-</td></tr><tr><td>Sultani et al. [33]</td><td>52.26</td><td>51.25</td><td>54.64</td><td>78.25</td><td>86.31</td><td>80.12</td></tr><tr><td>Wu et al. [41]</td><td>55.43</td><td>52.94</td><td>64.10</td><td>82.24</td><td>90.62</td><td>84.13</td></tr><tr><td>RTFM [34]</td><td>58.99</td><td>55.72</td><td>65.97</td><td>84.47</td><td>92.54</td><td>85.87</td></tr><tr><td>Wu et al. [42]</td><td>66.53</td><td>57.10</td><td>76.03</td><td>86.40</td><td>93.80</td><td>88.20</td></tr><tr><td>Ours</td><td>69.31</td><td>57.37</td><td>84.24</td><td>84.49</td><td>93.00</td><td>87.05</td></tr></table>
+
+Table 1. Detection Metrics (\%) Comparisons for XD-VIOLENCE (left) and UCF-CRIME (right). The best results are highlighted in bold, our method is shaded in gray, the symbol * indicates different category divisions, and underlined values represent the second-best results.
+
+# 4. Experimental Results
+
+# 4.1. Datasets and Implementation Details
+
+Datasets. We evaluate the performance of Anomize on two widely-used benchmark datasets. XD-VIOLENCE [41] is the largest dataset focused on violent events in videos, containing 3,954 training videos and 800 testing videos. The videos are collected from movies and YouTube, capturing six types of anomalous events across diverse scenarios. UCF-CRIME [33] is a large-scale dataset with 1,610 untrimmed surveillance videos for training and 290 for testing, totaling 128 hours. This dataset includes 13 types of anomalous events, spanning both indoor and outdoor settings and providing broad coverage of real-world scenarios.
+
+Evaluation Metrics. For anomaly detection, we employ standard metrics from previous works [33, 41]. Specifically, for UCF-CRIME, we compute AUC, which captures the trade-off between true positive and false positive rates. For XD-VIOLENCE, we report AP, reflecting the balance between precision and recall. For anomaly categorization, we report Top-1 accuracy on anomalous test videos from both datasets. These metrics are provided for all categories combined, as well as separately for base and novel categories, denoted by the subscripts b and n, respectively.
+
+Implementation Details. We implement our model in PyTorch and train it on an RTX 4090 with a 256-frame limit. Using the AdamW optimizer [17] with a learning rate of  $2 \times 10^{-5}$  and a batch size of 32, we train for 16 and 64 epochs in two phases. We use the pre-trained CLIP (ViT-B/16) model. The MLP module contains 2 fully connected layers with GeLU activation. The fusion weight  $\alpha$  is 1 during training and 2 during testing.  $K$  is 25 for XD-VIOLENCE and 5 for UCF-CRIME. Score weight  $\beta$  is 1 on XD-VIOLENCE (0 for base categories) and 0.5 on UCF-CRIME (0 for novel categories). Loss weight  $w_{i}$  follows the normal-to-anomaly ratio per iteration.
+
+# 4.2. Comparison with State-of-the-Art Methods
+
+In Tab. 1, we compare the performance of our method with prior VAD methods, ensuring that all methods use the same
+
+<table><tr><td>Method</td><td>ACC</td><td>ACCb</td><td>ACCN</td><td>ACC</td><td>ACCb</td><td>ACCN</td></tr><tr><td>Wu et al. [42]</td><td>64.68</td><td>89.31</td><td>30.90</td><td>41.43</td><td>49.02</td><td>37.08</td></tr><tr><td>Ours</td><td>90.29</td><td>92.37</td><td>87.43</td><td>47.14</td><td>56.86</td><td>41.57</td></tr></table>
+
+Table 2. Top-1 Accuracy (%) Comparisons on XD-VIOLENCE (left) and UCF-CRIME (right).
+
+visual features from CLIP and adopt an open-set setting. On XD-VIOLENCE, we achieve the best performance, with an increase of  $2.78\%$  overall and  $8.21\%$  on novel cases, demonstrating the effectiveness of our method in reducing detection ambiguity. On UCF-CRIME, our method achieves competitive results, likely due to the lightweight temporal encoder and segmented training, which limits optimization for the detection branch. Since other studies focus solely on traditional VAD without categorization, we compare our method's categorization performance with a leading study [42] in Tab. 2. Our method shows significant improvements, with a  $25.61\%$  gain on XD-VIOLENCE and  $5.71\%$  on UCF-CRIME, as well as further improvements of  $56.53\%$  and  $4.49\%$  on novel cases, highlighting its effectiveness in reducing categorization confusion.
+
+# 4.3. Ablation Studies
+
+Effectiveness of Lightweight Temporal Encoder. The experiments confirm the importance of temporal information in video-level tasks. Tab. 3 shows that the dynamic stream, with temporal encoding, provides useful temporal cues and complements the static stream effectively. While relying solely on temporal information performs poorly due to noise, the dynamic stream becomes more effective with loss weighting and text augmentation. Tab. 4 shows that adding the temporal encoder improves performance on base cases, but without further guidance, the lightweight encoder still introduces confusion for novel anomalies.
+
+Effectiveness of Group-Guided Text Encoding Mechanism. Comparisons in Tab. 4 between the second and third rows, or the fourth and fifth rows, on both datasets show that textual encodings based on group descriptions outperform the baseline, demonstrating the importance of our text encoding mechanism.
+
+Effectiveness of Text Augmentation. As shown in Tab. 3, text augmentation in both dynamic and static streams generally reduces detection ambiguity by compensating for the limitations of visual features. The dynamic stream with only text augmentation shows a slight drop on UCF-CRIME, suggesting noise in the temporal encodings. However, when combined with the loss weight, it demonstrates the importance of text, as shown in Rows 6 and 7.
+
+Effectiveness of Integrating Dynamic and Static Streams. Tab. 3 shows that integrating the two streams is generally more effective than using them independently, as
+
+<table><tr><td colspan="3">\(M_{\text{sta}}\)</td><td colspan="3">\(M_{\text{dyn}}\)</td><td rowspan="2">ST</td><td colspan="3">XD-VIOLENCE</td><td colspan="3">UCF-CRIME</td></tr><tr><td>visual</td><td>text</td><td>\(w_i\)</td><td>visual</td><td>text</td><td>\(w_i\)</td><td>AP (%)</td><td>\(\mathbf{AP}_b\) (%)</td><td>\(\mathbf{AP}_n\) (%)</td><td>AUC (%)</td><td>\(\mathbf{AUC}_b\) (%)</td><td>\(\mathbf{AUC}_n\) (%)</td></tr><tr><td>✓</td><td>×</td><td>×</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>54.75</td><td>46.30</td><td>76.61</td><td>48.47</td><td>47.72</td><td>50.05</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>59.65</td><td>56.41</td><td>75.29</td><td>52.21</td><td>59.18</td><td>48.45</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>59.26</td><td>57.20</td><td>74.28</td><td>84.26</td><td>92.06</td><td>86.86</td></tr><tr><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>×</td><td>✓</td><td>47.19</td><td>36.87</td><td>69.79</td><td>26.93</td><td>17.39</td><td>25.73</td></tr><tr><td>×</td><td>×</td><td>×</td><td>✓</td><td>✓</td><td>×</td><td>✓</td><td>54.98</td><td>57.79</td><td>69.40</td><td>23.06</td><td>14.68</td><td>19.74</td></tr><tr><td>×</td><td>×</td><td>×</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>54.16</td><td>56.03</td><td>68.19</td><td>83.21</td><td>91.94</td><td>85.43</td></tr><tr><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>✓</td><td>✓</td><td>48.55</td><td>51.15</td><td>59.93</td><td>80.97</td><td>90.71</td><td>83.63</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>✓</td><td>✓</td><td>×</td><td>✓</td><td>64.92</td><td>52.93</td><td>79.91</td><td>52.37</td><td>59.44</td><td>48.61</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>58.22</td><td>58.58</td><td>72.31</td><td>84.52</td><td>92.62</td><td>86.52</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>69.31</td><td>57.37</td><td>84.24</td><td>84.49</td><td>93.00</td><td>87.05</td></tr></table>
+
+Table 3. Effectiveness of Dynamic  $M_{\mathrm{dyn}}$  and Static  $M_{\mathrm{sta}}$  Streams with Text-Augmented Visual Data, Additional Loss Weight  $w_i$ , and Segmented Training (ST) on XD-VIOLENCE (left) and UCF-CRIME (right). In  $M_{\mathrm{sta}}$ , the visual data is the original visual feature output by CLIP, while in  $M_{\mathrm{dyn}}$ , it is derived from a lightweight temporal encoder.  
+
+<table><tr><td rowspan="2">Etem</td><td rowspan="2">Mgroup</td><td rowspan="2">Ffus</td><td rowspan="2">Lsep</td><td rowspan="2">ST</td><td colspan="3">XD-VIOLENCE</td><td colspan="3">UCF-CRIME</td></tr><tr><td>ACC (%)</td><td>ACCb (%)</td><td>ACcn (%)</td><td>ACC (%)</td><td>ACCb (%)</td><td>ACcn (%)</td></tr><tr><td>×</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>45.92</td><td>74.81</td><td>6.28</td><td>35.71</td><td>56.86</td><td>23.60</td></tr><tr><td>✓</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>53.42</td><td>92.37</td><td>0</td><td>25.71</td><td>70.59</td><td>0</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>×</td><td>✓</td><td>56.07</td><td>92.75</td><td>5.76</td><td>27.86</td><td>68.63</td><td>4.49</td></tr><tr><td>✓</td><td>×</td><td>✓</td><td>×</td><td>✓</td><td>56.51</td><td>94.66</td><td>4.19</td><td>27.14</td><td>74.51</td><td>0</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>✓</td><td>90.07</td><td>91.98</td><td>87.43</td><td>46.43</td><td>56.86</td><td>40.45</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>89.95</td><td>91.98</td><td>86.91</td><td>46.43</td><td>52.94</td><td>42.70</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>90.29</td><td>92.37</td><td>87.43</td><td>47.14</td><td>56.86</td><td>41.57</td></tr></table>
+
+they complement and constrain each other, which is evident from the comparisons in the third, sixth, and last rows.
+
+Effectiveness of Additional Loss Design. Tab. 3 emphasizes the importance of loss weight  $w_{i}$ , especially when training dynamic and static streams together. On XD-VIOLENCE, adding  $w_{i}$  slightly degrades single-stream training but significantly benefits integrated streams. Besides, Tab. 4 shows that adding separation loss  $\mathcal{L}_{\mathrm{sep}}$  improves performance, effectively addressing class imbalance.
+
+Effectiveness of Segmented Training. Results in Tab. 3 and Tab. 4 show that segmented training generally outperforms single-phase training, especially for novel cases, confirming that single-phase training may cause optimization conflicts and increase overfitting risks. On UCF-CRIME, single-phase training shows slightly better categorization performance on novel categories, likely due to randomness caused by optimization conflicts, as reflected in the poor performance on base categories.
+
+# 4.4. Qualitative results
+
+Fig. 4 presents qualitative results for anomaly detection, featuring two base and two novel categories from each dataset to cover all label groups. The comparison between the blue predicted score lines and the pink rectangles for ground truth demonstrates the effectiveness of our model in detecting anomalies. Notably, our method demonstrates
+
+Table 4. Effectiveness of the Lightweight Temporal Encoder  $E_{\mathrm{tem}}$ , Group-Guided Text Encoding Mechanism  $M_{\mathrm{group}}$ , Fusion Function  $F_{\mathrm{fus}}$ , Additional Separation Loss  $\mathcal{L}_{\mathrm{sep}}$ , and Segmented Training (ST) on XD-VIOLENCE (left) and UCF-CRIME (right).  
+
+<table><tr><td rowspan="2">Test Train</td><td colspan="2">XD-VIOLENCE</td><td colspan="2">UCF-CRIME</td></tr><tr><td>AP (%)</td><td>ACC (%)</td><td>AUC (%)</td><td>ACC (%)</td></tr><tr><td>XD-VIOLENCE</td><td>69.31</td><td>90.29</td><td>81.69</td><td>45.71</td></tr><tr><td>UCF-CRIME</td><td>66.16</td><td>85.87</td><td>84.68</td><td>47.14</td></tr></table>
+
+Table 5. Cross-Dataset Detection and Categorization Results.
+
+its capability to handle novel cases with minimal detection ambiguity, highlighting the strong support of the text-augmented dual stream.
+
+Fig. 5 shows similarity matrices of textual encodings, where labels indicated by the same dot are grouped together. Fig. 5(a) and (c) show results from encoding text using only label text, where visually similar anomalies lack corresponding textual similarity, revealing the limitations of relying solely on pre-trained models. Fig. 5(b) and (d) present results after being guided, where textual similarities within groups are enhanced to better align with visual similarities. This demonstrates the benefit of establishing label connections to guide encoding.
+
+# 4.5. Adaptability and Generalization
+
+Analysis of Cross-Dataset Ability. Tab. 5 shows that training on one dataset in an open-set manner and testing on another achieves results comparable to direct training on the target dataset, highlighting the adaptability of our method.
+
+![](images/5b796be25f6a4e8fe91ffe042636d69ebc9c9a3e62e00c24cf496caa3087280c.jpg)  
+base / fighting
+
+![](images/65f5cc03f5421d9ecf1a5678c0a538f6d859caf27d4f618fdd7079b334e367a0.jpg)  
+base / car accident
+
+![](images/9e01b9402e5cf06e75d071a00ebe4eb5afdb6a351b8d87606b3688b8f23e1473.jpg)  
+novel / riot
+
+![](images/c1ed70e91071fd6f43ec208797d2cde4941362feb3b5e5bcfc6a532311f384f8.jpg)
+
+![](images/c63eb57c9cd3a61fa0cafbc1ec8583ba01e1c0a377c3d18728005d064d73ff93.jpg)
+
+![](images/884ea2a278f3c00e9ad4d30372aedf6792836357bf5a12f82a06f9c34f7e8116.jpg)  
+base / assault
+
+![](images/b2cc56e13b2a49698e1e8bb9a8210a67bc7965e39c549835cfdddcc25fe204d4.jpg)
+
+![](images/29f9a1dccd30d3fbcb2702313be6149e9f49a889bd9199a774d367cbd2bbb7ae.jpg)  
+base / burglary
+
+![](images/34c47fdec4aea91b7557b7db448118d692bb92497ae4bcbb7a56e690f5647cd2.jpg)
+
+![](images/000d395c61396a059bd9d3e4c3ea74a7cea003300eadb78163b0b3680bb7bb90.jpg)  
+novel / arrest
+
+![](images/293cfccc3cb5a8955496ca1d148bd565aafcfb2b37a589627b85dd30647a0dd0.jpg)  
+novel / explosion
+
+![](images/07b22ae16a39cd71730b8e1626be81aadbbcbb1beaff8096da5262b0395ef1f8.jpg)  
+novel / arson
+
+![](images/96587b3384780d89d46858abd1c1125df064840758750261bfea0ff751d6829c.jpg)  
+Figure 4. Qualitative Results for Anomaly Detection. The first and second rows present results on XD-VIOLENCE and UCF-CRIME respectively. Red boxes and rectangles highlight the ground-truth anomalous frames, while blue lines represent predicted anomaly scores.  
+(a) XD-Violence origin  
+Figure 5. Similarity Matrices of Textual Encoding. (a) and (c) depict results using encodings from the original label data, while (b) and (d) show improvements achieved with the group-guided text encoding mechanism.
+
+![](images/2e92149ed0198b46be10ea414c2cefe10b8b880156f0245d1bc865da5b9f07d3.jpg)  
+(b) XD-Violence refine
+
+![](images/ded214b96cbdcfed284b73f04c603b582398521d4773b60e67fd8ba3f66d5ba3.jpg)  
+(c) UCF-Crime origin
+
+![](images/44f3333a838054f37166638a1bb32a9cfabf78f26f3c1cc86a1d203d4701d417.jpg)  
+(d) UCF-Crime refine
+
+<table><tr><td>Setting</td><td>ACC (%)</td><td>ACCb (%)</td><td>ACCn (%)</td></tr><tr><td>orig.</td><td>90.29</td><td>92.37</td><td>87.43</td></tr><tr><td>+ shoplifting</td><td>90.51</td><td>92.37</td><td>88.21</td></tr><tr><td>+ arrest</td><td>89.96</td><td>92.37</td><td>86.73</td></tr><tr><td>+ arson</td><td>88.77</td><td>92.37</td><td>84.08</td></tr><tr><td>+ assault</td><td>87.28</td><td>87.40</td><td>87.11</td></tr><tr><td>+ labels</td><td>85.21</td><td>86.64</td><td>83.25</td></tr><tr><td>orig.</td><td>47.14</td><td>56.86</td><td>41.57</td></tr><tr><td>+ riot</td><td>65.69</td><td>56.86</td><td>68.09</td></tr><tr><td>+ labels</td><td>45.00</td><td>54.90</td><td>39.33</td></tr></table>
+
+Table 6. Impact of Data Addition on Top-1 Accuracy for XD-VIOLENCE (top) and UCF-CRIME (bottom). "+" shoplifting" denotes the addition of both videos and labels, while "+" labels" indicates adding new labels only.
+
+Analysis of Open Vocabulary Ability. The open vocabulary ability is demonstrated by stable categorization performance after adding novel anomaly data, which we further validate by evaluating top-1 accuracy with the added data, as shown in Tab. 6. The additional data for one dataset is sourced from another. On XD-VIOLENCE, incorporating both same-group (e.g., arson) and different-group data (e.g., shoplifting) leads to stable performance, though assault shows the clearest decline due to confusion
+
+with similar labels like fighting. On UCF-CRIME, incorporating riot leads to notable improvement, with most instances accurately categorized despite being grouped with four other labels. Although the addition of new labels introduces some confusion, the performance remains robust across both datasets.
+
+# 5. Conclusion
+
+We propose the Anomize framework to address detection ambiguity and categorization confusion in open vocabulary video anomaly detection (OVVAD). By augmenting visual encodings with anomaly-related text through a dual-stream mechanism, Anomize improves the detection of unfamiliar samples and resolves ambiguity. Additionally, a group-guided text encoding mechanism enhances multimodal alignment and reduces categorization confusion. Experiments on XD-VIOLENCE and UCF-CRIME demonstrate the effectiveness of our method.
+
+Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grants 62171325, 62271361), the Hubei Provincial Key Research and Development Program (Grant 2024BAB039), and the supercomputing system at Wuhan University.
+
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\ No newline at end of file
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+![](images/9adc3f34e899ce15df33a9f5337edc9f5538671e8d82a5eafcb2556198440b80.jpg)
+
+# Antidote: A Unified Framework for Mitigating LVLM Hallucinations in Counterfactual Presupposition and Object Perception
+
+Yuanchen Wu $^{1,2,*}$  Lu Zhang $^{2}$  Hang Yao $^{1}$  Junlong Du $^{2}$  Ke Yan $^{2,\dagger}$  Shouhong Ding $^{2}$  Yunsheng Wu $^{2}$  Xiaojiang Li $^{1,\dagger}$
+
+$^{1}$  School of Computer Engineering & Science, Shanghai University  $^{2}$  Tencent YouTu Lab
+
+{yuanchenwu, yaohang, xqli}@shu.edu.cn {xluzhang, jeffdu, kerwinyan, ericshding, simonwu}@tencent.com
+
+# Abstract
+
+Large Vision-Language Models (LVLMs) have achieved impressive results across various cross-modal tasks. However, hallucinations, i.e., the models generating counterfactual responses, remain a challenge. Though recent studies have attempted to alleviate object perception hallucinations, they focus on the models' response generation, and overlooking the task question itself. This paper discusses the vulnerability of LVLMs in solving counterfactual presupposition questions (CPQs), where the models are prone to accept the presuppositions of counterfactual objects and produce severe hallucinatory responses. To this end, we introduce "Antidote", a unified, synthetic data-driven posttraining framework for mitigating both types of hallucination above. It leverages synthetic data to incorporate factual priors into questions to achieve self-correction, and decouple the mitigation process into a preference optimization problem. Furthermore, we construct "CP-Bench", a novel benchmark to evaluate LVLMs' ability to correctly handle CPQs and produce factual responses. Applied to the LLaVA series, Antidote can simultaneously enhance performance on CP-Bench by over  $50\%$ , POPE by  $1.8 - 3.3\%$ , and CHAIR & SHR by  $30 - 50\%$ , all without relying on external supervision from stronger LVLMs or human feedback and introducing noticeable catastrophic forgetting issues.
+
+# 1. Introduction
+
+Recently, Large Vision-Language Models (LVLMs) have achieved significant advancements, showing promising performance across various tasks, such as image caption, visual question answering (VQA), and visual dialogues [5, 23, 43, 45]. Despite their capabilities and versatility, the hallucination, characterized by generating counterfactual information, remains a significant challenge. It undermines their
+
+![](images/08957d682dacb5edc56f239622ab0abd592256b3f8275933120c9a28d1b089f4.jpg)  
+Figure 1. The hallucination responses induced by CPQ. Though recent hallucination mitigation methods improves LVLMs in object perception, while their models can still be easily deceived by CPQs and induce severe hallucinatory responses.
+
+reliability and limits applications in sensitive domains like healthcare and autonomous systems. In LVLM, studies of hallucination mainly focus on "object perception", including "object existence" and "image description" [17, 47, 50]. The former refers to whether the mentioned objects are actually non-existent, while the latter further evaluates whether the models output counterfactual attributes or relationships between objects. To alleviate the above types of hallucinations, recent works improve the instruction tuning process [15, 20], post-calibrate the model response via experts or decoding strategies [17, 46], and conduct posttraining of models [41, 50]. They have manifested effectiveness in alleviating object hallucinations on popular benchmarks, such as POPE [18] and CHAIR [32].
+
+However, a phenomenon emerges in Figure 1: for a simple question about the existence of a "car", the LVLMs with recent hallucination mitigation methods (HACL [15] as an example) can confirm its absence. When we implicitly presuppose its existence and pose a relevant question "What is the brand of the car?", the model suddenly outputs hallucinatory responses. This issue is particularly notable when querying about objects that are absent in the current image but frequently appear in similar visual con
+
+![](images/4063cb13a5cffa77539d819ff165357fcfb6664a448e0bfb80bcfeaf01b41a2e.jpg)  
+Figure 2. Performance comparison of LVLMs on benchmarks of general capabilities (MMBench [26]), hallucination of object perception (POPE [18]) and CPQ (the proposed CP-Bench). Higher values indicate better performance on corresponding benchmarks.
+
+texts, underscoring a potential limitation of existing hallucination alleviation techniques. We call this type of question "Counterfactual Presupposition Question (CPQ)". Compared to the conventional "object perception" hallucination focusing on response generation, CPQ further requires the model's judgment of presuppositions grounded by images. It is more challenging and evaluates the severity of hallucination in practical VQA scenarios where the validity of the presupposition cannot be guaranteed. Additionally, we investigate recent advanced open-source LVLMs (e.g., InternVL-2 [5] and Qwen2-VL [38] that have demonstrated superior capabilities on general tasks and anti-hallucination on object perception, surpassing closed-source models such as GPT-4o [29] and Claude-3.5 [3]. However, as illustrated in Figure 2, we observe that they still suffer from CPQs and output hallucinatory responses as shown in Figure 3a. To this end, we make attempts towards two following aspects to address the CPQ challenge and meanwhile addressing object perception hallucination:
+
+1) We introduce a unified, synthetic data-driven posttraining framework called "Antidote". We reckon that a primary cause of the above hallucinations is the object co-occurrence and over-learning of instructions. Hence, we aim to obtain images where the statistically co-occurring objects/scenes are decoupled (e.g., a speedboat without bridges in the background) and construct QA pairs targeted on these decoupled, non-existent objects (e.g., bridge), as presented in Figure 3b. We develop an automated data synthesis pipeline, comprising steps of image caption curation, visual scene understanding, factual verification, and sample construction. It allows us to derive factual priors for each sample, and then incorporate them into the prompt for models' self-correction. This process reformulates hallucination mitigation as a preference optimization problem, where the original response is treated as a "rejected" sample, and the corrected response as a "preferred" sample. By employing Antidote, LVLMs learn a
+
+preference constraint during training, enabling them to discriminate counterfactual presuppositions and generate factual responses well. Extensive experiments demonstrate its effectiveness on CPQ and object perception hallucinations.
+
+2) We construct "CP-Bench", a benchmark evaluating LVLMs' ability to discern counterfactual presuppositions and generate factual responses. It is composed of two parts, the synthetic validation (dev) set and the manually annotated test set. The dev set is automatically constructed from the data synthetic pipeline of Antidote. The CPQs in test set can be categorized into four categories in daily scenarios, i.e., item, knowledge, scene, and activity. The evaluations on recent advanced closed-sourced and open-sourced LVLMs highlights the critical gap in current models' ability to discern counterfactual presuppositions, providing a new insight into hallucinations of LVLMs.
+
+# 2. Related Work
+
+Hallucination in LVLMs. Recently, many large vision-language models (LVLMs) have emerged [5, 23, 27], extending the reasoning brain of LLMs to the vision modality. This enables LVLMs to complete various tasks, such as visual question answering and general visual dialogue. However, the hallucination, stemming from the inherent nature of LLMs [11], modality misalignment [5], and the quality of instruction turning data [20], raises concerns about their reliability and applicability. To evaluate the severity of hallucinations in LVLMs, POPE [18] identifies hallucinations related to object existence, while CHAIR [32] evaluates the proportion of hallucinated objects in image descriptions. To further broaden the scope of evaluation to include categories, attributes, and emotions within image descriptions, SHR [50], a GPT-assisted evaluation metric, has been proposed. This paper discusses LVLMs' hallucinations in counterfactual presupposition questions and introduce a corresponding benchmark, CP-Bench, to evaluate the severity of this issue. Our findings reveal that recent open-source LVLMs largely overlook this critical issue.
+
+Hallucination Mitigation. Previous works mitigating hallucinations of LVLMs primarily focus on object existence and image descriptions, i.e., object perception hallucination. Three mainstream approaches have emerged for mitigating these hallucinations: supervised fine-tuning (SFT), post-calibration, and post-training. SFT aims to fine-tune with the hallucination-free data [47], such as LRV [20] and InstructBLIP [6]. Post-calibration conducts additional post-processing techniques to model outputs, such as contrastive decoding strategies [17, 36, 39] and leveraging existing tools or expert models [46]. Post-training focuses on improving the hallucination of off-the-shelf LVLMs, which commonly employ retraining or preference optimization to alleviate hallucination [41, 50, 51]. In contrast, the pro
+
+![](images/b4dd6ce06add50236a56d5ff1e59b0564c27bf15d4eb4fac1c9917570fe9a0d9.jpg)
+
+# CP-BENCH:
+
+![](images/fb7299e39d1906f8622321a6654f825b3e3d78e2ef34b58313dee32643982992.jpg)  
+1 Item
+
+![](images/7e5862af1eaeb0cb044fa41fffa046d3a962d84a4d4334b044f07548f097f926.jpg)  
+#2 Knowledge
+
+![](images/6c8421eb133c7c0d35a2c43715a67ed36e78687345bf33eec6e2fba89daa5be2.jpg)  
+#3 Scene
+
+![](images/745a1234c5164cc3c6b38cdcb2cf16b3c56efd44c4a3106a1d80494609d9ea60.jpg)  
+#4 Activity
+
+Q1: What does the label on the beer show? -- THE LABEL IS ON RED WINE Answer [Qwen2-VL-72B]: The label on the beer shows "Coste A Preola."  
+Q2: What is the brand of Coke? -- MOUNTAIN DEW IS NOT COKE Answer [InternVL2-72B]: The brand in the image is Mountain Dew.  
+Q3: Is the bus moving or stationary? -- NO BUS IN THE SCENE  
+Answer [InternVL2-26B]: The bus in the image appears to be stationary ...  
+Q4: What is the player's number? -- NO INFORMATION OF THE NUMBER  
+Answer [LLaVA-Next-Mistral7B]: The player's number is 10.
+
+(a) CPQ samples from the proposed CP-Bench.
+
+![](images/9e2da5102d79aea3f119226447fd9129c48f4087752c000e591be43435aa82d7.jpg)
+
+# ANTIDOTE:
+
+![](images/84d4ea66e5bab720449da9e2e4b330c8ee073095c5bc0391ca21b370c5710a96.jpg)
+
+Image caption:
+
+a carving depicting a religious leader surrounded by his sons.
+
+Hallucination candidate:
+
+["altar", "church"]
+
+Question / Query samples:
+
+What is the significance of the altar in the carving?  
+Is an altar in the image?  
+- Please describe the church on the carving.
+
+![](images/e9bf0df830e2a7fe29bd7d61fdf5a850561d482304c5247615d267859d26dea0.jpg)  
+Figure 3. Examples of hallucination induced by CPQs and the synthetic samples of Antidote. The CPQs are selected from the test set of the proposed CP-Bench, which will be introduced in Section 4. "Hallucination candidates" are the non-existent objects that commonly appear in similar scenes. More examples can be viewed in Appendix.
+
+Image caption:
+
+a speedboat is traveling in the open water near a city.
+
+Hallucination candidate:
+
+["bridge", "seagull", "island"]
+
+Question / Query samples:
+
+What is the bridge made of in the background?  
+How many seagulls are on the speedboat?  
+- Please describe the seagulls flying above the water.
+
+(b) Training samples from Antidote's pipeline.
+
+posed Antidote not only effectively improves object perception hallucinations but also further overcomes the hallucinations induced by CPQs. It adopts the preference optimization paradigm but differs in that it does not rely on any expert models (e.g., GPT-4V) [50] to generate preference samples or exclusively utilize dis-preferred data [51]. Instead, we fully leverage the advantages of our synthetic data pipeline, seamlessly utilizing factual information without additional cost to enable the model to self-correct its responses.
+
+# 3. Our Post-training Framework: Antidote
+
+# 3.1. Motivation
+
+As illustrated in Figure 3a, two key issues can be observed: (1) LVLMs tend to blindly follow the instruction in the task query (Image #1 and Image #2). When asking "what does the label on the beer show?" for Image #1, the model ignores the existence of the subject in the question (i.e., the beer) and directly follows the instruction to identify the text on the label. (2) LVLMs overfit to similar scene-based QA patterns (Image #3 and Image #4). When asking "what is the player's number?" in a scenario where the player has no number on the uniform, the model generates a hallucinated answer that is usually in the VQA tasks with similar scenes. Based on the above observation, we aim to obtain the images where statistically co-occurring objects are decoupled (e.g., a car without wheels) and construct queries targeting these decoupled, non-existent objects (e.g., wheel), aiming at calibrating the bias of LVLMs. Thanks to the advancements in image generation models [7, 30] and LLMs [37, 44], we can synthesize the images and corresponding questions in a controlled manner (Figure 4). Then, with the factual prior dur
+
+ing the above process, we incorporate them into the models' prompt for self-correction. Finally, the self-correction process reformulates hallucination mitigation as a preference optimization problem, and we conduct direct preference optimization (DPO) to post-train the LVLMs.
+
+# 3.2. Data Synthesis Pipeline
+
+Step 1: Construction of Caption Pool. The caption pool is critical for enhancing the diversity and richness of the training set for Antidote. Captions can be sourced either from web-crawled datasets or generated by LLMs. Here, we collect the captions from CC3M [35] to build our pool. Since CC3M contains many noisy or unsuitable captions for image and question generation, DeepSeek-V2 [19] is adopted to perform a re-captioning and filtering process. To enhance the pool's diversity, we employ a fuzzy dedduplication strategy through MinHash and LSH algorithms [13].
+
+Step 2: Visual Scene Understanding. First, we prompt DeepSeek-V2 with instructions, such as "removing abstract concepts and specific terms" and "limit to less than 15 words", to rewrite captions  $\mathcal{C}_{img}$  for subsequent image generation. Second, we utilize DeepSeek-V2's comprehension and reasoning capability to identify the objects  $\mathcal{O}_{pre}$  within the scenes described by captions. Third, we leverage DeepSeek-V2's world knowledge to generate objects  $\mathcal{O}_{hallu}$  that typically occur in similar scenes. These objects will be served as hallucination candidates that will not be present in the generated images. The prompt template  $\mathbf{P1}$  in this step is detailed in Appendix. Inspired by recent self-reflection strategies [14, 42], each triplet  $<\mathcal{C}_{img}, \mathcal{O}_{pre}, \mathcal{O}_{hallu}>$  is sent back again to DeepSeek-V2, verifying whether each element conforms to their rules in  $\mathbf{P1}$ , such as "the number of generated objects", "generating objects with visible entities", and
+
+![](images/b7b3e70f1257d48c934cee5e688f995542300ad205bd2e2efcfe0c4b5ac088b2.jpg)  
+Figure 4. The data synthesis pipeline for Antidote. The pipeline consists of three stages: (a) construction of caption Pool; (b) visual scene understanding; (c) data synthesis.
+
+"avoiding conflicts in  $\mathcal{O}_{pre}$  and  $\mathcal{O}_{hallu}$ ".
+
+Step 3: Data Synthesis. In image generation,  $\mathcal{C}_{img}$  serves as the prompt and  $\mathcal{O}_{hallu}$  as the negative prompt. Benefiting from recent image generation models [7, 30], the generated images exhibit a high degree of photorealism and diverse content. This paper adopts Stable-Diffusion-3 [7] as the generator. However, it cannot ensure that the generated objects can fully align with  $\mathcal{O}_{pre}$  while suppressing the existence of  $\mathcal{O}_{hallu}$ . Hence, we introduce "Factual Assessor" driven by an open-set grounding model, Grounding-DINO [24]. It checks the presence of  $\mathcal{O}_{pre}$  and  $\mathcal{O}_{hallu}$  in the generated images. If an object in  $\mathcal{O}_{pre}$  is not detected, it will be removed. Similarly, detected objects in  $\mathcal{O}_{hallu}$  will also be removed. If either  $\mathcal{O}_{pre}$  or  $\mathcal{O}_{hallu}$  is  $\emptyset$ , the corresponding triplet will be discarded. Finally, the remaining triplets are sent to DeepSeek-V2 to generate task queries, such as CPQs and description queries.
+
+In early experiments, we note that the LLMs tend to generate similar questions when facing choosing the same main object (e.g., frequently focusing on "color" or "brand" when selecting "car" in  $\mathcal{O}_{pre}$  or  $\mathcal{O}_{hallu}$ ), degrading the diversity of task queries in the generated dataset. Thus, a key-value memory bank is maintained to save processed captions and corresponding queries. The captions are extracted to sentence embedding using BGE-m3 [4] as the key of the memory bank. For each  $<\mathcal{C}_{img}, \mathcal{O}_{pre}, \mathcal{O}_{hallu}>$ , we retrieve questions whose captions are semantically close to  $\mathcal{C}_{img}$  through the memory bank. These are then integrated to the prompt "Do not generate questions similar to the following: ..." to mitigate redundancy in generation.
+
+# 3.3. Self-Correction via Preference Alignment
+
+Antidote is a universal post-training framework for alleviating hallucination in CPQs, object existence, and image description. The overview of post-training is presented in Figure 5. Through the data synthetic pipeline, we construct the three types of task queries for post-training:
+
+1) Presupposition Questions: We prompt DeepSeek-V2 to generate CPQs based on  $\mathcal{O}_{hallu}$  using P2 in Appendix.
+
+In early experiments, we observed that only post-training with CPQs makes the baseline model overly "cautious" in responding to questions. Thus, we construct a True Presupposition Question (TPQ) set based on  $\mathcal{O}_{pre}$ . For the Antidote for presupposition questions, we prompt the baseline model with "Given the fact that there is  $\{\text{facts of } \mathcal{O}_{pre} / \mathcal{O}_{hallu}\}$ , please answer:  $\{\text{CPQ/TPQ}\}$ " to self-correct the original answer. For CPQs and TPQs, their self-corrected answer will be used as the positive response  $y_{pos}$ , while the original answer will be used as negative response  $y_{neg}$ .
+
+2) Object Existence: We randomly select objects in  $\mathcal{O}_{pre}$  and  $\mathcal{O}_{hallu}$  as the object candidate to build the training set of the object existence. The question prompts are generated by DeepSeek-V2, such as "Is / Are there {object} in the image?" and "Can you see {object} in the image?". For the Antidote for object existence, we prompt the model with "Given the fact that there is / isn't {object}, please answer: {question}" to self-correct its response.  
+3) Image Description: We generate task queries of image description by DeepSeek-V2, such as "Please describe the image in detail." and "Can you describe what you see in the image thoroughly?" For the Antidote of image description, we integrate \(<\mathcal{C}_{img}, \mathcal{O}_{pre}, \mathcal{O}_{hallu}>\) into the query and prompt the model to self-correct its response: "Given the hint of the image: the image caption: \(\{\mathcal{C}_{img}\}\), the object(s) you can see: \(\{\mathcal{O}_{pre}\}\), the object(s) you cannot see: \(\{\mathcal{O}_{hallu}\}\), please \(\{\text{query}\}".
+
+Response Filtering: Since not all model responses contain hallucinations, especially in object existence queries, such samples are unhelpful for hallucination mitigation and even lead to difficulty in optimization [40]. Thus, we compare the original and self-corrected responses and filter out samples with similar answers. In our experiments, we extract the embeddings of both responses using BGE-m3 [4] and calculate their cosine similarity to perform the filtering.
+
+Preference Optimization: By direct preference optimization (DPO) [31], we encourage the model to favor corrected positive response and reject hallucinatory negative response without building an implicit reward model [34]. Given the above constructed preference pairs  $\mathcal{D}$ , the policy model  $\pi_{\theta}$  (i.e., the post-trained LVLMs with Antidote) is optimized by maximizing the log-likelihood of the preferred response  $y_{pos}$  while minimizing the likelihood of the hallucinated response  $y_{neg}$ . The training objective function is given by:
+
+$$
+\begin{array}{l} \mathcal {L} _ {d p o} \left(\pi_ {\theta}; \pi_ {r e f}\right) = - \mathbb {E} _ {\mathcal {D}} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\theta} \left(y _ {p o s} \mid [ x _ {T} , x _ {I} ]\right)}{\pi_ {r e f} \left(y _ {p o s} \mid [ x _ {T} , x _ {I} ]\right)}\right) \right. \\ \left. - \beta \log \frac {\pi_ {\theta} \left(y _ {n e g} \mid [ x _ {T} , x _ {I} ]\right)}{\pi_ {r e f} \left(y _ {n e g} \mid [ x _ {T} , x _ {I} ]\right)}\right) \Bigg ], \tag {1} \\ \end{array}
+$$
+
+where  $x_{T}$  and  $x_{I}$  represent the text task prompt (without factual prior) and image, and  $\pi_{ref}$  denotes the reference
+
+![](images/37370bd2ba5bb76f87dbb3877d19169b8380194db3ddaca60137c9eae2d4222e.jpg)
+
+# Question (CPQ):
+
+What is the brand of the car?
+
+![](images/4259f02e61af436007bd736f59756c519d483d747b103c73d47f94efd16954cf.jpg)
+
+# Antidote:
+
+Given the fact that there is no car in image, ...
+
+# Original response: The car is a BMW.
+
+Self-corrected response : There is no car in the image, so it is not possible to determine the brand of the car.
+
+![](images/db1dc8139508b875f15f01b603528f61ac04a65130953be2b79fc6bbb6c979b3.jpg)  
+Figure 5. Overview of the proposed Antidote post-training. The factual information from the synthetic data is seamlessly integrated into the input task prompt. The LVLMs can utilize this information to self-correct the responses as "positive" samples. For the original responses, they are regarded as "negative" samples to achieve preference alignment for hallucination alleviation.
+
+# Question (description):
+
+Please describe the image in detail.
+
+![](images/70df7d591c11168d62a9c7227dc4332d4a56bf137069aaafb729c2d76f5d68cf.jpg)
+
+# Antidote:
+
+Given the hint of image:
+
+$\checkmark$  Caption:  
+hot air balloons flying over ancient structures at sunrise  
+$\checkmark$  Object(s) you can see: 'hot air balloons', 'ancient structures', 'sunrise'  
+$\checkmark$  Object(s) you cannot see: ... Please describe the image in detail.
+
+Original response: The image depicts a vibrant scene with hot air balloons and kites of various shapes and colors soaring above a stone city, adding to the lively atmosphere. A person in the bottom left corner seems to be admiring the view of the balloons and kites in the sky ...
+
+Self-corrected response: The image captures a beautiful scene of hot air balloons flying over ancient structures at sunrise. There are several hot air balloons in the sky, each with different colors and shapes, adding a vibrant touch to the scene. The ancient structures consist of a series of buildings, likely part of a castle or historical site. The sun is rising, casting a warm glow over the scene, and illuminating the structures below.
+
+# Question:
+
+What is the brand of the car?
+
+# Question with Antidote:
+
+Given there is no car in image, what is the brand of the car?
+
+# question
+
+![](images/2113daf526bafa28e38ff4fc487bb495640fd72e0847e5a70f300c2494f4dde1.jpg)
+
+# Large VLMs
+
+# response
+
+Hallucinated Answer: The car is a BMW.
+
+![](images/f9bedc99804024d547a49a3967aa5247290de635d8f5d4866ab07edc9bb4ca27.jpg)
+
+![](images/beb18feb3763e943d1ce0ffd0ee75cba2a4c06588fed714e5a330a35a03fd657.jpg)
+
+# Self-correction:
+
+There is no car in the image, so it is not possible to know the brand of the car.
+
+model (i.e., the original baseline LVLMs). The function  $\sigma$  is the log-sigmoid, and  $\beta$  is a hyperparameter controlling the preference margin. In the above preference optimization process, the reward margin is defined as:
+
+$$
+\hat {r} \left(x _ {T}, x _ {I}, y\right) = \beta \log \frac {\pi_ {\theta} \left(y _ {p o s} \mid \left[ x _ {T} , x _ {I} \right]\right)}{\pi_ {r e f} \left(y _ {p o s} \mid \left[ x _ {T} , x _ {I} \right]\right)}. \tag {2}
+$$
+
+Through maximizing the reward margin between the self-corrected response  $y_{pos}$  and the hallucinated response  $y_{neg}$ , we ensure that the model increasingly favors non-hallucinated samples over hallucinatory ones, leading to a robust self-correction process.
+
+# 4. CP-Bench: Evaluate Hallucination of CPQ
+
+Motivation. Recent hallucination benchmarks primarily focus on response generation, including object existence, attributes, and relations, while overlooking the textual semantics within queries. Figure 3a illustrates the vulnerability of recent LVLMs in solving counterfactual presupposition questions. To address this gap, CP-Bench is developed to quantify the LVLMs' ability to judge the correctness of presuppositions and generate factual responses.
+
+Details. CP-Bench includes of two subsets: a validation (dev) set and a test set. For the dev set, the images and questions are generated using the above data synthetic pipeline of Antidote. For the test set, the images are sampled from the CC3M dataset [35]. The corresponding queries are constructed by the following steps: object candidates are first obtained via an open-set grounding model, followed by generating query candidates via DeepSeek-V2 using prompt P2. Challenging candidates are manually selected as the fi
+
+nal task queries. Both sets consist of 1,000 curated samples, equally split into 500 CPQs and 500 true presupposition questions (TPQs). All counterfactual candidates in CPQs of CP-Bench are chosen from objects commonly associated with similar semantics or scenes, such as "railroad" in train-related contexts. This increases the benchmark's complexity, as prior research has shown that LVLMs often suffer from inherent statistical biases in their pre-training or fine-tuning datasets [18, 47]. The samples in CP-Bench can be classified into four categories in daily scenarios: item, knowledge, scene, and activity. More statistical details of CP-Bench can be viewed in Figure 6.
+
+Evaluation. Given the open-ended responses of LVLMs, GPT-4o [2] is introduced to convert responses into a binary classification task, assessing whether the models correctly recognize the correctness presupposition and output factual responses. CPQ labeled as "positive" class, while TPQs are labeled as "negative" samples. For CPQs, GPT-4o evaluates whether the models accurately identify the presence of the objects and generate corresponding responses. For TPQs, GPT-4o evaluates whether the models can discriminate and the reveal counterfactual information implicit in presuppositions. The primary evaluation metrics are the F1-score, Recall, Accuracy, and Precision. The prompt P3 used for CP-Bench evaluation is provided in Appendix.
+
+# 5. Experiment
+
+# 5.1. Implement Setup
+
+Experiment Baselines: We post-trained LLaVA series with the proposed Antidote, including LLaVA-1.5-Vincuna7B/13B [23], and LLaVA-Next-Mistral-7B [22]. All mod
+
+![](images/a6ca7a77ea66a145d10144b7560cbb0f828daf37baeb2c064248d7e77a1d0e2e.jpg)  
+Figure 6. The statistical details of CP-Bench (test) and CPQ examples. CP-Bench includes four types (i.e., scene, knowledge, item, and activity) of CPQs and TPQs from different scenes. It can comprehensively evaluate the LVLMs' ability to discriminate the correctness of presuppositions and generate factual responses.
+
+els above have been fully tuned on their collected visual instruction data before post-training. In practical implementation, we adopt LoRA [10] for training efficiency. The LoRA's dimension (rank)  $r$  is 64,  $\alpha$  is 128, and the scale parameter  $\beta$  in direct preference optimization is 0.1. More hyper-parameter setting can be viewed in Appendix.
+
+Evaluation Benchmarks. Besides CP-Bench, we assess the effectiveness of Antidote using three popular hallucination benchmarks and four general benchmarks. POPE [18] is used for evaluating object existence, while CHAIR [32] and SHR [50] are served to evaluate the hallucinations in image descriptions. Compared to CHAIR, which focuses on evaluating object-related hallucinations in responses, SHR focuses on sentence-level hallucinations with the introduction of LLMs. To further validate the catastrophic forgetting issue, we verify the general capability (such as visual reasoning, perception, and cross-domain generalization) of models trained with Antidote, including Science-QA [33], MMBench [25], MMVet [48], and LLaVA-Wild [23].
+
+Data Composition. The training set of Antidote is built by the data synthetic pipeline introduced in Section 3.2. Initially, we generated  $14k$  triplets of  $\langle C_{img},\mathcal{O}_{pre},\mathcal{O}_{hallu}\rangle$  and filtered out approximately  $4k$  triplets with Factual Accessor. Then, we generated the queries of CPQs, TPQs, object existence, and image descriptions of each remaining triplet. For each baseline LVLM, we applied response filtering after their inference and self-correction, discarding around  $15\%$  of the total samples. Finally, we sample 5,000
+
+CPQs, 5,000 TPQs, 2,000 questions of object existence, and 8,000 image description queries, i.e., a total of  $20k$  samples, for post-training. The discussion of data proportion settings can be viewed in Appendix.
+
+# 5.2. Main Results
+
+How does Antidote improve LVLMs' ability to discriminate presuppositions? In Table 1, we compare the performance of closed-sourced models, open-sourced models, and baseline models post-trained with Antidote on CP-Bench. The results reveal that the closed-source LVLMs significantly outperform the open-source models in distinguishing CPQ and outputting factual responses. The optimal performance is achieved by Claude-3.5-Sonnet and GPT-4o, which recall nearly  $90\%$  of CPQs on the test set. For open-source models, LLaVA-Next-Vicuna-13B stands out, achieving an F1-score of  $56.0\%$  and a recall of  $41.6\%$ . Notably, Antidote brings substantial improvements. For example, it boosts LLaVA-1.5 7B and 13B models' F1-scores from 5.7 and 17.3 to 78.4 and 83.5, respectively. As illustrated in Figure 8, we can observe that these models after Antidote can produce factual responses such as "I cannot answer ... as there is no ..." These results highlight Antidote's efficacy in enhancing model accuracy in recognizing presuppositions, pushing open-source models closer to closed-source counterparts on this challenging task.
+
+Does model size affect the ability to discriminate the correctness of presuppositions? (1) With identical architectures and training data, larger model sizes enhance the judgment of presupposition correctness. For instance, as Qwen2-VL [38] scales from 7B to 72B parameters, the recall increases from  $13.2\%$  to  $33.3\%$ , with a similar trend observed in the InternVL2 series. (2) Across different models, however, model size is not a decisive factor. Notably, MiniCPM-V2.5 [45], with only 8B parameters, achieves a recall that is  $8.5\%$  higher than Qwen2-VL-72B, demonstrating superior performance in recognizing CPQs. Moreover, InternVL2 [5] and Qwen2-VL, which surpass closed-source models in general performance, do not perform well on the VPF-Bench. Both models have utilized large-scale instruction fine-tuning datasets to enhance visual capabilities. We believe that their performance on the VPF-Bench is strongly correlated with over-learning of instruction tuning.
+
+How do LVLMs with Antidote perform on typical hallucination benchmarks? Here, we compare various types of mitigation approaches, including contrastive decoding (e.g., VCD [23] and VDD [49]), auxiliary learning (e.g., HACL [15]), and post-training (e.g., Volcano [16] and SeVA [51]). 1) For object existence, we assess POPE, where the results (Table 2) are averaged across three evaluation sets: the random, popular, and adversarial sets (the results for each set can be found in Appendix. On LLaVA 1.5-7B, we improved its original F1-score from 86.07 to
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">CP-Bench-Test</td><td>CP-Bench-Dev</td></tr><tr><td>F1-Score</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1-Score</td></tr><tr><td colspan="6">Closed-sourced(API)</td></tr><tr><td>Claude-3-5-Sonnet [3]</td><td>86.0</td><td>85.3</td><td>82.4</td><td>90.0</td><td>94.3</td></tr><tr><td>GPT-4o-0806 [29]</td><td>85.5</td><td>85.0</td><td>82.5</td><td>88.8</td><td>84.2</td></tr><tr><td>GPT-4o-mini-0718 [29]</td><td>77.6</td><td>75.9</td><td>72.6</td><td>83.3</td><td>81.8</td></tr><tr><td>GLM-4v [8]</td><td>79.7</td><td>80.3</td><td>82.1</td><td>79.7</td><td>88.2</td></tr><tr><td>GPT-4v-0409 [2]</td><td>71.6</td><td>75.8</td><td>86.6</td><td>61.0</td><td>86.0</td></tr><tr><td>InternVL-2-Pro [5]</td><td>64.2</td><td>70.5</td><td>81.5</td><td>53.0</td><td>60.3</td></tr><tr><td colspan="6">Open-sourced</td></tr><tr><td>LLaVA-Next-Vicuna-13B [22]</td><td>56.0</td><td>67.3</td><td>85.5</td><td>41.6</td><td>65.1</td></tr><tr><td>MiniCPM-V2.5-8B [45]</td><td>55.2</td><td>66.1</td><td>81.3</td><td>41.8</td><td>37.0</td></tr><tr><td>Qwen2-VL-72B [38]</td><td>48.8</td><td>65.0</td><td>90.7</td><td>33.3</td><td>42.6</td></tr><tr><td>LLaVA-Next-Vicuna-7B [22]</td><td>47.0</td><td>63.6</td><td>86.1</td><td>32.3</td><td>48.7</td></tr><tr><td>InternVL2-26B [5]</td><td>38.5</td><td>59.6</td><td>80.8</td><td>25.3</td><td>41.2</td></tr><tr><td>InstructBLIP-7B [6]</td><td>35.6</td><td>47.4</td><td>45.9</td><td>29.1</td><td>17.8</td></tr><tr><td>InternVL2-8B [5]</td><td>34.3</td><td>58.4</td><td>81.8</td><td>21.7</td><td>47.1</td></tr><tr><td>Cogglm2-19B [9]</td><td>34.2</td><td>57.4</td><td>75.3</td><td>22.1</td><td>42.8</td></tr><tr><td>Phi-3-Vision [1]</td><td>26.1</td><td>54.0</td><td>66.4</td><td>16.3</td><td>38.8</td></tr><tr><td>Qwen2-VL-7B [38]</td><td>22.7</td><td>54.9</td><td>80.3</td><td>13.2</td><td>33.7</td></tr><tr><td colspan="6">Baseline + Post-training / Decoding Strategies</td></tr><tr><td>LLaVA-v1.5-7B [21]</td><td>5.7</td><td>50.5</td><td>60.0</td><td>3.0</td><td>12.4</td></tr><tr><td>+ HA-DPO [50]</td><td>4.7</td><td>50.6</td><td>66.7</td><td>2.4</td><td>13.1</td></tr><tr><td>+ VCD [51]</td><td>6.1</td><td>50.7</td><td>64.0</td><td>3.2</td><td>12.0</td></tr><tr><td>+ SeVa [51]</td><td>24.1</td><td>55.1</td><td>78.0</td><td>14.3</td><td>25.4</td></tr><tr><td>+ Antidote (ours)</td><td>78.4 (+72.7)</td><td>84.5 (+34.0)</td><td>73.1 (+13.1)</td><td>73.1 (+70.1)</td><td>82.9 (+70.5)</td></tr><tr><td>LLaVA-v1.5-13B [21]</td><td>17.3</td><td>53.8</td><td>82.8</td><td>9.6</td><td>12.0</td></tr><tr><td>+ Antidote (ours)</td><td>83.5 (+66.2)</td><td>84.5 (+31.3)</td><td>89.5 (+6.7)</td><td>78.3 (+69.7)</td><td>88.0 (+66.0)</td></tr><tr><td>LLaVA-Next-Mistral-7B [22]</td><td>26.7</td><td>54.8</td><td>70.7</td><td>16.5</td><td>43.6</td></tr><tr><td>+ Antidote (ours)</td><td>76.8 (+50.1)</td><td>77.5 (+22.7)</td><td>79.4 (+8.7)</td><td>74.3 (+58.8)</td><td>84.4 (+40.8)</td></tr></table>
+
+Table 1. Performance Comparison on CP-Bench (test and dev). The detailed evaluation results of the dev set are provided in Appendix.  
+
+<table><tr><td>Method</td><td>Accuracy (%)</td><td>F1-Score (%)</td></tr><tr><td>LLaVA-1.5-7B</td><td>85.18</td><td>86.07</td></tr><tr><td>+ VDD [23]</td><td>86.47</td><td>85.13</td></tr><tr><td>+ HACL [15]</td><td>86.66</td><td>86.20</td></tr><tr><td>+ Volcano [16]</td><td>86.96</td><td>86.67</td></tr><tr><td>+ HA-DPO [50]</td><td>86.63</td><td>86.87</td></tr><tr><td>+ SeVa [51]</td><td>86.69</td><td>86.66</td></tr><tr><td>+ Antidote (ours)</td><td>88.09 (+3.75)</td><td>87.89 (+1.82)</td></tr><tr><td>LLaVA-1.5-13B</td><td>84.15</td><td>85.67</td></tr><tr><td>+ Volcano [16]</td><td>87.02</td><td>87.17</td></tr><tr><td>+ Antidote (ours)</td><td>88.93 (+4.78)</td><td>88.99 (+4.32)</td></tr></table>
+
+Table 2. Hallucination evaluation (POPE) on object existence. The performance is the average of the results across the three subsets.  
+
+<table><tr><td>Method</td><td>CHAIR_s ↓</td><td>CHAIR_i ↓</td><td>SHR ↓</td></tr><tr><td>LLaVA-1.5-7B</td><td>19.4</td><td>6.1</td><td>36.7</td></tr><tr><td>+ SeVa [51]</td><td>18.4</td><td>5.7</td><td>34.9</td></tr><tr><td>+ VCD [23]</td><td>17.9</td><td>5.8</td><td>34.2</td></tr><tr><td>+ OPERA [11]</td><td>15.6</td><td>5.7</td><td>34.1</td></tr><tr><td>+ HA-DPO [50]</td><td>18.0</td><td>5.9</td><td>34.0</td></tr><tr><td>+ SID [12]</td><td>15.1</td><td>5.4</td><td>33.1</td></tr><tr><td>+ Antidote</td><td>9.4 (-10.0)</td><td>3.3 (-2.8)</td><td>18.1 (-18.6)</td></tr><tr><td>LLaVA-1.5-13B</td><td>30.0</td><td>5.5</td><td>37.2</td></tr><tr><td>+ Antidote (ours)</td><td>12.6 (-17.4)</td><td>4.3 (-1.2)</td><td>21.3 (-15.9)</td></tr><tr><td>LLaVA-Next-Mistral-7B</td><td>13.0</td><td>4.6</td><td>28.4</td></tr><tr><td>+ Antidote (ours)</td><td>10.7 (-2.3)</td><td>3.5 (-1.1)</td><td>19.7 (-8.7)</td></tr></table>
+
+Table 3. Hallucination evaluation on image description, CHAIR and SHR. Max new tokens is set as 64 for each model. Smaller values correspond to fewer hallucinations.
+
+87.89 (+1.82%), with an even greater improvement on its 13B version, from 85.67 to 88.99 (+3.32%). Notably, we observed significant improvements on the adversarial subset, where objects are first ranked based on co-occurrence frequencies, and the top-k frequent objects are sampled. On the original 7B and 13B versions, Antidote improves by 2.58% and 4.12%, respectively. This demonstrates that Antidote can effectively mitigate the statistical biases inherent in LVLMs, which substantially contribute to object hallucination issues [18]. 2) For image description, we first evaluated on CHAIR (Table 3), which quantifies the hallucination by calculating the ratio of objects mentioned in the description that are not present in the ground-truth. On the LLaVA-1.5 series, we observed a substantial reduction in hallucinations, decreasing its hallucination rates by over 50%. For the 7B version, we reduced CHAIR_s from the prior best score of 15.1 to 9.4. We also tested on LLaVA-Next-Mistral-7B, further improving its CHAIR_s and CHAIR_i scores to 10.7 and 3.5, respectively. Additionally, we evaluated SHR [50], an advanced benchmark that uses detailed object-level descriptions from the Visual-Genome dataset as factual information and relies on GPT-4 to judge hallucinations in descriptions. Similarly, Antidote significantly reduces hallucinations in comparison to base
+
+line models on this metric as well.
+
+# 5.3. Analysis
+
+Catastrophic Forgetting. Since Antidote is a post-training method that fine-tunes the baseline models' parameters, we evaluated whether Antidote causes catastrophic forgetting by assessing the general capability of the post-trained LLaVA-1.5 series. From Table 4, it is evident that performance on these benchmarks did not significantly degrade and even improved on some benchmarks, such as  $2.8\%$  and  $2.6\%$  increase on Science-QA [28]. This suggests suppressing object perception hallucinations and enhancing CPQ discrimination can generalize to improvements in overall capabilities. There was a slight decrease in performance on LLaVA-Wild [23], where we observed that the post-trained version was "cautious" when answering uncertain/challenging questions compared to the baseline model, which is not preferred by its GPT-4 evaluator.
+
+Attention Visualization. We empirically investigate how attention from visual tokens contributes to important object-related text tokens before and after applying the proposed Antidote. We visualize some representative instances during training in Figure 7. For instance, when asked a CPQ:
+
+<table><tr><td>Method</td><td>POPE</td><td>CP-Bench</td><td>SHR (↓)</td><td>Science-QA</td><td>MMBench</td><td>MMVet</td><td>\( \mathbf{{LLaVA}}{}^{\mathbf{W}} \)</td></tr><tr><td>LLaVA-1.5-7B</td><td>85.92</td><td>12.4</td><td>36.7</td><td>66.8</td><td>64.3</td><td>30.5</td><td>65.4</td></tr><tr><td>+ Antidote (ours)</td><td>87.89</td><td>81.2</td><td>18.1</td><td>69.6</td><td>65.4</td><td>31.4</td><td>64.0</td></tr><tr><td>LLaVA-1.5-13B</td><td>85.67</td><td>12.0</td><td>37.2</td><td>71.6</td><td>67.7</td><td>35.4</td><td>70.7</td></tr><tr><td>+ Antidote (ours)</td><td>88.99</td><td>88.0</td><td>21.3</td><td>74.2</td><td>69.5</td><td>35.5</td><td>70.2</td></tr></table>
+
+Table 4. The evaluation on the benchmark of LVLMs' general capabilities.  
+
+<table><tr><td colspan="5">Question: What is the fork made of in the image? 
+Answer (LLaVa-1.5-7B): The fork in the image is made of metal.</td><td colspan="3">There is no fork in the image. Instead, there is a plate of food with shrimp and vegetables, specifically noodles.</td></tr><tr><td>Image</td><td>Attn (token-avg)</td><td>Attn (&#x27;fork&#x27;)</td><td>Attn (&#x27;medal&#x27;)</td><td>→</td><td>Attn (token-avg)</td><td>Attn (&#x27;shrimp&#x27;)</td><td>Attn (&#x27;vegetables&#x27;)</td></tr><tr><td colspan="5">Question: What is the vase made of in the image?? 
+Answer (LLaVa-1.5-7B): The vase in the image is made of wood.</td><td colspan="3">There is no vase in the image. The focus is on the bouquet of flowers and the background, so it can be inferred that there might not be a vase present in the image.</td></tr><tr><td>Image</td><td>Attn (token-avg)</td><td>Attn (&#x27;vase&#x27;)</td><td>Attn (&#x27;wood&#x27;)</td><td>→</td><td>Attn (token-avg)</td><td>Attn (&#x27;bouquet&#x27;)</td><td>Attn (&#x27;flowers&#x27;)</td></tr></table>
+
+<table><tr><td>r</td><td>a</td><td>CP-Bench</td><td>POPE</td><td>SHR (↓)</td><td>MMBench</td></tr><tr><td colspan="2">Baseline</td><td>12.4</td><td>86.07</td><td>36.7</td><td>64.3</td></tr><tr><td colspan="2">SFT</td><td>67.8</td><td>85.14</td><td>25.9</td><td>59.6</td></tr><tr><td>32</td><td>64</td><td>12.7</td><td>86.68</td><td>28.5</td><td>64.1</td></tr><tr><td>64</td><td>128</td><td>82.9</td><td>87.89</td><td>18.1</td><td>65.4</td></tr><tr><td>128</td><td>256</td><td>87.8</td><td>85.67</td><td>23.9</td><td>47.3</td></tr><tr><td>256</td><td>512</td><td colspan="4">Model Collapse</td></tr></table>
+
+Table 5. The effect of hyper-parameter in LoRA during the post-training and the SFT alternative. The baseline LVLM is LLaVA-1.5-7B. F1-score is adopted in CP-Bench and POPE.
+
+![](images/c8eac1189db45d1dbc9181232bbb3e05456e0bc3d675345846f0e0872c4dc2c0.jpg)  
+Figure 7. Attention visualization between the text tokens and vision tokens. The intensity of each text token's background indicates the attention weight magnitude of image tokens, with darker highlights representing higher attention. The attention values above the 0.995th quantile are shown with the highest color intensity (such as shrimp and vegetables).  
+Figure 8. Comparison of model responses before and after Antidote post-training. The cases are selected from the proposed CP-Bench benchmark.
+
+"What is the fork made of in the image?", we observe that the original LLaVA-1.5, while outputting "fork", does not significantly focus on visual tokens, and incorrectly attends to visual token information when outputting "metal". However, after training with Antidote, the model's attention to visual tokens becomes more accurate, focusing on the exact areas of the image corresponding to object-related text tokens, such as "shrimp" and "flowers".
+
+Compare with SFT. A straightforward alternative to Antidote's preference optimization is direct supervised fine-tuning (SFT) using the self-corrected responses in Antidote. As shown in Table 5, while SFT shows effectiveness in addressing model hallucinations for CPQs and image descriptions, it significantly underperforms compared to Antidote, particularly on POPE and MMBench, and suffers from catastrophic forgetting to some extent. Unlike SFT, which merely increases the probability of self-corrected responses, Antidote's preference alignment can be viewed as a form of contrastive learning (more discussions can be viewed in Appendix), where the model is trained to distinguish between self-corrected and hallucinatory responses. It exploits the preference information by increasing the model's probability of self-corrected responses relative to hallucinatory ones, guiding the model to suppress hallucinations while reducing over-fitting to preference samples.
+
+LoRA Fine-tuning. We evaluate the LoRA setting for Antidote. In parameter-efficient learning, this parameter determines the extent to which the model's knowledge can be
+
+altered during post-training. As presented in Table 5, a relatively higher rank  $r$  signifies greater flexibility in adjusting the model's knowledge. However, a larger  $r$  can lead to catastrophic forgetting (when  $r = 128$ ) and even cause overoptimization of Antidote, resulting in model collapse (when  $r = 256$ ). In conclusion, we set the rank  $r$  to 64 and the scaling factor  $a$  to 128 ( $2 \times r$  as default) in experiments.
+
+# 6. Conclusion
+
+This paper addresses the hallucinations in Large Vision-Language Models (LVLMs), focusing both on Counterfactual Presupposition Questions (CPQs) and object perception. The primary contribution of this work is Antidote, a synthetic data-driven post-training framework that significantly mitigates hallucinations by enhancing LVLMs' capability to discern counterfactual presuppositions and objects. To complement this, we introduce CP-Bench, a novel benchmark tailored to evaluate LVLMs' performance on CPQs. Extensive experiments demonstrate that Antidote not only significantly improves performance in recognizing counterfactual presuppositions but also enhances performance across a range of hallucination-related benchmarks, including POPE, CHAIR, and SHR, all without inducing catastrophic forgetting. These results underscore the promise of Antidote as a robust solution for enhancing the reliability of LVLMs in diverse vision-language tasks.
+
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+# Any-Resolution AI-Generated Image Detection by Spectral Learning
+
+Dimitrios Karageorgiou $^{1,2}$  Symeon Papadopoulos $^{1}$  Ioannis Kompatsiaris $^{1}$  Efstratos Gavves $^{2,3}$
+
+<sup>1</sup>Information Technologies Institute, CERTH, Greece
+
+$^{2}$ University of Amsterdam, The Netherlands
+
+<sup>3</sup>Archimedes/Athena RC, Greece
+
+{dkarageo,papadop,ikom}@iti.gr {d.karageorgiou,e.gavves}@uva.nl
+
+# Abstract
+
+Recent works have established that AI models introduce spectral artifacts into generated images and propose approaches for learning to capture them using labeled data. However, the significant differences in such artifacts among different generative models hinder these approaches from generalizing to generators not seen during training. In this work, we build upon the key idea that the spectral distribution of real images constitutes both an invariant and highly discriminative pattern for AI-generated image detection. To model this under a self-supervised setup, we employ masked spectral learning using the pretext task of frequency reconstruction. Since generated images constitute out-of-distribution samples for this model, we propose spectral reconstruction similarity to capture this divergence. Moreover, we introduce spectral context attention, which enables our approach to efficiently capture subtle spectral inconsistencies in images of any resolution. Our spectral AI-generated image detection approach (SPAI) achieves a  $5.5\%$  absolute improvement in AUC over the previous state-of-the-art across 13 recent generative approaches, while exhibiting robustness against common online perturbations. Code is available on https://mever-team.github.io/spai.
+
+# 1. Introduction
+
+Generative AI technology advances at an outstanding pace [18]. Early AI approaches for image synthesis, primarily based on Generative Adversarial Networks (GANs) [12], have recently been superseded by Diffusion Models (DMs) [10], capable of producing high-fidelity imagery, while supporting advanced conditioning schemes [4]. Recent methods for efficient training [33, 37] have further lowered the barrier for creating new generative models. In this landscape of numerous accessible high-performing commercial and open-source models, making strong assumptions about safeguards implemented at the model level [44] seems intractable, leading to an increasing numbers of harmful syn
+
+![](images/81f33a4d6716d61e8bf866dd0f913fb986af17778a119efe4e5565968f82a8ad.jpg)  
+Figure 1. SPAI employs spectral learning to learn the spectral distribution of real images under a self-supervised setup. Then, using the spectral reconstruction similarity it detects AI-generated images as out-of-distribution samples of this learned model.
+
+thetic imagery on the Internet [16], which calls for robust AI-generated Image Detection (AID) approaches.
+
+To this end, the image forensics community has established that generative models introduce subtle artifacts to the generated images [61, 66, 70] and proposed several AID methods for capturing them [46]. However, even generators with minimal differences introduce significantly different artifacts [1, 68]. Consequently, existing detectors poorly generalize to images originating from generators not seen during training [9, 68], while, due to the large number of available generative models, it is very difficult, if not intractable, to maintain an exhaustive up-to-date training dataset. Thus, current AID approaches perform poorly when tested outside of lab-controlled environments [16, 36].
+
+Recently, the idea of modeling the distribution of real images emerged as an alternative to learning to capture the artifacts introduced by specific detectors [9]. Under this
+
+new paradigm, synthetic images can be considered as out-of-distribution samples with respect to a model of real images. Early attempts to implement this idea mostly focused on modeling the spatial relationships among pixels of real images [9, 30]. However, several works found that real and AI-generated images are better distinguishable in the spectral domain [1, 45]. A fundamental principle of computer vision suggests looking for the most suitable invariant patterns for the task to be solved [22]. In the case of the AID task we argue that the spectral distribution of real images is such a suitable invariant pattern as it is not directly affected by the introduction of specific generative models, while it provides significant discriminative power. In this paper, we present Spectral AI-generated Image detection (SPAI) that introduces both a modeling approach for the spectral distribution of real images as well as an architecture for capturing instances that deviate from this learned distribution.
+
+To learn a spectral model of the real images we show that the pretext task of frequency reconstruction is an effective approach for modeling their frequency distribution, under a self-supervised training setup that uses only real images. Then, to detect AI-generated images as out-of-distribution samples of this model, we exploit the observation that a frequency reconstruction model trained on real images will reconstruct their frequencies more accurately, compared to the generated ones. We introduce the concept of spectral reconstruction similarity for estimating the divergence of the reconstructed frequencies from the ones actually present in the image under question.
+
+Moreover, capturing subtle clues in images is crucial for effectively distinguishing among real and AI-generated ones [7]. However, most computer vision models, having been designed for semantic-based tasks, cannot efficiently scale to the native resolution of modern photos [75], i.e. many megapixels. Therefore, pre-processing operations are required [38], effectively dropping a significant amount of discriminative information. To utilize all the spectral information present in the image we introduce the spectral context attention that enables us to efficiently process any-resolution images without prior pre-processing. We evaluate our approach across a set of 13 recently proposed generative approaches and five sources of real images, and achieve a  $5.5\%$  absolute improvement over state-of-the-art, while achieving superior robustness to common online perturbations. Fig. 1 presents an overview of the paper.
+
+In summary, our contributions include the following:
+
+- We introduce the spectral distribution of real images as a suitable invariant pattern for distinguishing between real and AI-generated images and we propose the use of masked spectral learning for modeling it.  
+- We show that the pretext task of frequency reconstruction is an effective approach for modeling the spectral distribution of real images under a self-supervised setup.
+
+- We introduce Spectral Reconstruction Similarity (SRS) for detecting AI-generated images as out-of-distribution samples of our learned spectral model of real images.  
+- We introduce Spectral Context Attention (SCA) to capture subtle spectral details in any-resolution images.  
+- We show a  $5.5\%$  performance increase compared to the state-of-the-art across a set of 13 generative models, while our approach exhibits superior robustness against several perturbations encountered online.
+
+# 2. Related Work
+
+Image Generation: Image generation approaches have rapidly evolved from the generation of low-quality imagery [27] to that of photorealistic visual content of any topic [19, 55]. Early approaches, primarily based on GANs [25, 26], established the capability of conditionally generating visual content from random noise, using additional textual [67, 73, 79] or visual [6, 54, 78] inputs to control the process. More recently, the introduction of DMs [32, 64] for image synthesis has set new standards to the quality of the generated content, using architectures that learn to reverse the diffusion process, either in the spatial [32] or in the latent [59] domain. As such, DMs have mostly superseded GANs in generative modeling, with only a few exceptions that adopt ideas introduced for DMs to GANs [35]. Moreover, recent works greatly increased the resolution of the generated images [19, 55], while techniques such as the Low-Rank Adaptation [28, 33] significantly enhanced the efficiency of adapting generative models to any domain. As a consequence, a large and continuously increasing arsenal of open-source and commercial image generation approaches is currently available [2, 19, 76].
+
+AI-Generated Image Detection: In response, several approaches have been proposed for distinguishing real from AI-generated (synthetic) images, either by detecting semantic inconsistencies or by capturing low-level artifacts introduced by the generative models. In the former group, recent approaches detect inconsistencies in facial geometry [3] as well as in shadows [61], perspective [21] and lighting [20] of the image. However, as improved generative models get released, such visible inconsistencies cease to exist. To this end, recent works have established that generative models introduce low-level artifacts and proposed approaches for capturing them either in the spatial [7, 70] or in the spectral [1, 17, 45] domain. However, such artifacts significantly differ even between models with minimal differences [1]. In pursuit of artifacts that better generalize across different generators, others have proposed architectures for capturing inconsistencies in texture-rich image regions [34, 48, 77], gradient differences [65] or artifacts introduced by the upscaling layers of the generative models [66] as well as spectral augmentation approaches [14]. Moreover, several recent works have employed features from pre-trained
+
+![](images/c5feaf283d28e4bec2faa0ad99dfc5017e9dd246a511348df7f2abfd2b83f88c.jpg)  
+Figure 2. Overview of the SPAI approach. We learn a model of the spectral distribution of real images under a self-supervised setup using masked spectral learning. Then, we use the spectral reconstruction similarity to measure the divergence from this learned distribution and detect AI-generated images as out-of-distribution samples of this model. Spectral context vector captures the spectral context under which the spectral reconstruction similarity values are computed, while spectral context attention enables the processing of any-resolution images for capturing subtle spectral inconsistencies.
+
+CLIP [56] encoders for capturing both low-level and semantic artifacts [8, 39, 52, 63, 74]. Common ground in all the aforementioned works is the attempt to model artifacts introduced by the generative approaches, with the intention of using them for the AID task. As such, they fail to generalize on unseen generators that introduce artifacts different than the ones present in the training set.
+
+Modeling Real Images: To better generalize on unseen generative models the direction of modeling the distribution of real images has recently emerged as an alternative solution to the AID task. The key idea is that AI-generated images constitute out-of-distribution samples with respect to a model of real (authentic) images. Early approaches towards this direction noticed that generative models cannot reconstruct real images as accurately as AI-generated ones [5, 58, 71]. Recently, He et al. [30] found that noise perturbations on generated images introduce more variance to the features extracted by a pre-trained encoder, compared to real images, while Cozzolino et al. [9] observed a smaller error on the reconstruction of real images using a super-resolution model. Such works do not take into account the fact that most artifacts introduced by the generative models are better visible in the frequency domain [1, 7, 45].
+
+In this paper, we argue that modeling the spectral distribution of real images is crucial for detecting AI-generated ones, as it constitutes a pattern that remains invariant to the introduction of new generative approaches, while providing significant discriminative capability. To the best of our knowledge, we are the first to employ frequency reconstruction [72] as a pretext task for learning such a model. To detect synthetic images as out-of-distribution samples of
+
+the aforementioned model, we introduce the spectral reconstruction similarity to measure the divergence between the reconstructed and the actual frequencies of an image in the latent space. Furthermore, by introducing spectral context attention we retain all the spectral information of the image, by processing it at its original resolution.
+
+# 3. Spectral AI-Generated Image Detection
+
+Distinguishing between AI-generated and real content, while generalizing to unknown generative models, requires capturing invariant features that remain distinctive across different generators and image transformations. While for AI-generated images, significant differences are visible in the frequency domain in the form of spectral artifacts introduced by the generators, their distribution significantly differs among different generative models. Instead, the spectral distribution of real images is not directly related to the introduction of specific generative approaches, but to long-term technological advances [40, 50], constituting an invariance for our task. Thus, our key idea is to build a spectral model of the real content and detect generated content as out-of-distribution samples of this model. To build such a detection pipeline we introduce i) a modeling approach for the spectral distribution of real images, ii) an architecture for capturing instances that deviate from this learned distribution. An overview of our architecture is shown in Fig. 2.
+
+# 3.1. Masked Spectral Learning
+
+To build a spectral model of real images we propose using the pretext task of frequency reconstruction under a self-supervised learning setup, using only real images. In par
+
+ticular, we randomly mask the low- or high-frequency component of the input images and train the model  $\mathcal{G}$  under the objective of reconstructing the missing frequencies.
+
+Frequency Masking: To obtain the low- and high-frequency components of input image  $x \in \mathbb{R}^{H \times W}$ , we use the 2D Discrete Fourier Transform  $\chi = \mathcal{F}(x) \in \mathbb{R}^{H \times W}$  where  $\chi(u, v)$  defines the complex frequency value at coordinates  $(u, v)$ . Next, inspired by [72], we define a mask  $M$  for masking parts of the spectrum according to a fixed radius  $r$  from its center, that we denote as  $(c_H, c_W)$ , with  $d(\cdot, \cdot)$  denoting the Euclidean distance:
+
+$$
+M (u, v) = \left\{ \begin{array}{l l} 0 & , d ((u, v), \left(c _ {H}, c _ {W}\right)) <   r \\ 1 & , \text {o t h e r w i s e} \end{array} \right. \tag {1}
+$$
+
+We then define the low- and high-frequency components as:
+
+$$
+x ^ {h} = \mathcal {F} ^ {- 1} (\chi \odot M) \tag {2}
+$$
+
+$$
+x ^ {l} = \mathcal {F} ^ {- 1} (\chi \odot (\mathbf {1} - M)) \tag {3}
+$$
+
+where  $\mathbf{1}$  defines an all-ones matrix,  $\odot$  point-wise multiplication and  $\mathcal{F}^{-1}$  the Inverse 2D Discrete Fourier Transform.
+
+To train  $\mathcal{G}$  we use an auxiliary decoding head  $\mathcal{H}$  to predict from its output the reconstructed image  $\hat{x} = \mathcal{H}(\mathcal{G}(\mathcal{B}(x^l, x^h)))$ , where  $\mathcal{B}(\cdot, \cdot)$  randomly samples one of its inputs according to a binomial distribution. We train the combination of  $\mathcal{G}$  and  $\mathcal{H}$  using the objective  $\mathcal{L}_{rec} = \mathcal{D}(\mathcal{F}(x), \mathcal{F}(\hat{x}))$ , where  $\mathcal{D}$  defines the frequency distance introduced in [72].  $\mathcal{H}$  is discarded after training.
+
+# 3.2. Spectral Reconstruction Similarity
+
+Up to this point,  $\mathcal{G}$  has learned to reconstruct the spectral distribution of real images given their low- or high-frequency components. Here, we introduce an approach to detect the out-of-distribution samples of  $\mathcal{G}$ . In the rest of the text, we assume that  $\mathcal{G}$  is a Vision Transformer (ViT) [15].
+
+We apply ViT's tokenization procedure to process the input image:  $x$  is split into  $L = H \cdot W / p^2$  tokens of size  $p \times p$ . Each token is embedded to a space of size  $d$  through a linear projection to formulate ViT's input sequence  $z_0 \in \mathbb{R}^{L \times d}$ . Moreover,  $\mathcal{G}$  comprises  $N$  transformer [69] blocks. We denote the output of the  $n$ -th transformer block as:
+
+$$
+z _ {n} = \mathcal {G} _ {n} \left(z _ {0}\right) \in \mathbb {R} ^ {L \times d}, n = \{1, \dots , N \} \tag {4}
+$$
+
+We encode  $x$ ,  $x^h$  and  $x^l$  into  $z_n$ ,  $z_n^h$  and  $z_n^l$  respectively, using Eq. (4). Then, we use  $N$  projection operators, denoted  $\mathbf{P}_n: R^d \to R^D$ , one per block of  $\mathcal{G}$ , to project the three aforementioned groups of representations from the feature space of  $\mathcal{G}$  to one that facilitates the similarity operations that we define next. Each projection operator comprises a series of linear projection, layer normalization [43] and GELU activation layers [31]. Further details regarding their
+
+structure are provided in the supplementary material. We use them to project  $z_{n}, z_{n}^{h}$  and  $z_{n}^{l}$  into  $\bar{z}_{n}, \bar{z}_{n}^{h}$  and  $\bar{z}_{n}^{l}$ , all belonging to the space of  $\mathbb{R}^{L \times D}$ . In the rest of our approach we only use these latter representations.
+
+As  $\mathcal{G}$  constitutes a spectral model of real images, it is expected to better reconstruct their missing frequencies compared to the ones of AI-generated images. Therefore, we expect bigger distances between  $\bar{z}_n$ ,  $\bar{z}_n^h$  and  $\bar{z}_n^l$  for AI-generated images. As such, we expect the similarity among the features of the original image, the low- and the high-frequency components to indicate the alignment of the spectral distribution of an image with the learned distribution of  $\mathcal{G}$ . To measure this divergence we introduce the concept of Spectral Reconstruction Similarity (SRS). For two representations  $z^A$  and  $z^B$  in space  $\mathbb{R}^{L\times D}$  we define SRS as:
+
+$$
+\lambda \left(z ^ {A}, z ^ {B}\right) = \frac {z ^ {A} \cdot z ^ {B}}{\| z ^ {A} \| \| z ^ {B} \|} \in [ - 1, 1 ] ^ {L \times 1}. \tag {5}
+$$
+
+Then, using Eq. (5) we define i) the SRS between the representations of the original image and the low-pass filtered one  $\omega_{n}^{ol} = \lambda (\bar{z}_{n},\bar{z}_{n}^{l})$  , ii) between the original image and the high-pass filtered one  $\omega_{n}^{oh} = \lambda (\bar{z}_{n},\bar{z}_{n}^{h})$  and iii) between the low and high-pass filtered components  $\omega_{n}^{lh} = \lambda (\bar{z}_{n}^{l},\bar{z}_{n}^{h})$
+
+Each of the SRS vectors  $\omega_{n}^{ol},\omega_{n}^{oh},\omega_{n}^{lh}$  includes  $L$  values, i.e. one for each of the  $L$  tokens of the ViT that capture information of a  $p\times p$  region of the image. We then calculate their mean and standard deviation, resulting in two scalars for each SRS vector. We concatenate these six values computed for the  $N$  blocks of  $\mathcal{G}$  into  $z^{\lambda}\in [-1,1]^{6N}$ .
+
+# 3.3. Spectral Context Vector
+
+Intuitively, we expect different values of  $z^{\lambda}$  to be useful for the discrimination of images with different levels of spectral information. For example, on images without significant high-frequency content, SRS values that relate to the reconstruction of high frequencies should provide little value. To capture this information, the network needs access to the context where the values of  $z^{\lambda}$  have been computed. To this end, we introduce the Spectral Context Vector (SCV)  $z^{C} \in \mathbb{R}^{D}$  that summarizes the representations of the original image from the  $N$  blocks of  $\mathcal{G}$ . In particular, starting from the projected representations  $\bar{z}_n$  defined in Sec. 3.2, we compute their mean and standard deviation over the  $L$  different ViT's tokens. Then, we concatenate these two derivative representations of dimensionality  $D$  from all the  $N$  transformer blocks into the vector  $z' \in \mathbb{R}^{N \times 2D}$ .
+
+Next, we define a learnable spectral map  $C \in \mathbb{R}^{N \times D}$  and two projection functions  $\mathcal{P}_1(\cdot): R^{2D} \to R^D$  and  $\mathcal{P}_2(\cdot): R^D \to R^D$ . Further details regarding the structure of  $\mathcal{P}_1$  and  $\mathcal{P}_2$  are provided in supplementary material. Using these three components the network learns to construct the SCV by attending to the most useful of the  $2D$  feature values for
+
+each of the  $N$  transformer blocks of  $\mathcal{G}$  as following:
+
+$$
+C ^ {\prime} = \mathcal {P} _ {2} \left(\operatorname {s o f t m a x} (C) \odot \mathcal {P} _ {1} \left(z ^ {\prime}\right)\right) \in \mathbb {R} ^ {N \times D} \tag {6}
+$$
+
+$$
+z ^ {C} = \sum_ {n = 1} ^ {N} C _ {n} ^ {\prime} \in \mathbb {R} ^ {D} \tag {7}
+$$
+
+where  $C_n^\prime$  denotes the  $n$ -th row of  $C^\prime$ . Finally, we concatenate  $z^C$  and  $z^{\lambda}$  into the spectral vector:
+
+$$
+z ^ {S} = \left[ z ^ {C}; z ^ {\lambda} \right] \in \mathbb {R} ^ {D + 6 N}. \tag {8}
+$$
+
+# 3.4. Spectral Context Attention
+
+In practice, the height and width of the input image  $x$  may receive arbitrarily large values, i.e. images of many megapixels. While ViTs in theory can scale to inputs of arbitrary size, their quadratic computational complexity w.r.t the length of their token sequence practically prohibits their use on such large inputs. Similar limitations are faced by convolutional neural networks. Thus, a typical approach in most computer vision tasks that rely on the semantic information of the image is to resize it to a fixed size. However, in verification tasks, such as AID, the ability to capture anomalies in subtle details of the image is crucial [7]. So, a resizing operation, that effectively discards the high-frequency information of the image, is problematic. To tackle this issue, we introduce the concept of Spectral Context Attention (SCA), for combining the most discriminative SRS values computed for different patches of the image, according to their respective SCV and a learnable spectral reconstruction importance vector  $q \in \mathbb{R}^{D_h}$ .
+
+Initially, we split the original image into  $K$  patches of size  $h \times w$ , forming the patched representation of the image  $x^{P} \in \mathbb{R}^{K \times h \times w}$ , while  $x_{k}$  denotes the  $k$ -th patch of this sequence. For each patch, we construct its spectral vector  $z_{k}^{S}$  following the approach introduced throughout the previous paragraphs. Next, following the transformer's attention notation [69] we define the weight matrices  $W_{K}, W_{V} \in \mathbb{R}^{(D + 6N) \times D_{h}}$  and  $W_{O} \in \mathbb{R}^{D_{h} \times (D + 6N)}$ . Conveniently, we define  $\bar{z}^{S} \in \mathbb{R}^{K \times (D + 6N)}$  as the concatenation of spectral vectors for all  $K$  image patches. Then, we fuse them into the image-level spectral vector  $\mathbf{z}^{S}$  through the following:
+
+$$
+\mathcal {A} = \operatorname {s o f t m a x} \left(\frac {q * \left(\bar {z} ^ {S} * W _ {K}\right) ^ {\intercal}}{\sqrt {D _ {h}}}\right) \in (0, 1) ^ {1 \times K} \tag {9}
+$$
+
+$$
+\mathbf {z} ^ {S} = \left(A * \left(\bar {z} ^ {S} * W _ {V}\right)\right) * W _ {O} \in \mathbb {R} ^ {D + 6 N} \tag {10}
+$$
+
+The computational complexity of SCA is  $O(K)$ .
+
+Classification Head: For the final prediction  $\hat{y} \in (0,1)$ , we use a three-layer MLP on  $\mathbf{z}^S$ , with RELU activations on the first two layers and a sigmoid activation at the final one.
+
+# 3.5. Training Process and Implementation
+
+We train the network in an end-to-end manner with the objective of minimizing the binary cross-entropy between the predicted  $\hat{y}$  and the ground-truth  $y$  values for each image, i.e.  $\mathcal{L}_{cls} = BCE(\hat{y}, y)$ .
+
+Augmented Views Training: To train our network, including the SCA module, under a single training stage, we would require images that comprise several  $(h \times w)$  patches. However, this would limit us on the type of training data that we could use, while any resizing or cropping approach would introduce unwanted biases. To this end, we train our network with a fixed number of patches  $K_{\text{training}}$ , that we construct as random views of the input image  $x$ , using a random augmentation policy. Thus, any image can be used for training, while this also enables an efficient implementation of the training pipeline. Instead, during inference, we use the actual number of patches  $K$  included in each image.
+
+Spectral Model: As our spectral model of real images  $\mathcal{G}$  we use a ViT-B/16 transformer [15] pre-trained on ImageNet [13] by Xie et al. [72], using a masking radius  $r = 16$ . We keep its weights frozen throughout the training of the components introduced in Secs. 3.2 to 3.4.
+
+# 4. Evaluation
+
+# 4.1. Evaluation Setup
+
+Implementation Details: We train our architecture for 35 epochs, with a learning rate  $(lr)$  of  $5e - 4$ , cosine decay and five epochs of linear warmup, using the AdamW [49] optimizer and batch size of 72. We set  $D = 1024$ ,  $K_{training} = 4$  and, to align with the pretext task,  $r = 16$ . The number of transformer blocks in the ViT we use for  $\mathcal{G}$  is  $N = 12$ , its latent dimensionality is  $d = 768$ , while the size of each of the  $K$  patches is  $h = w = 224$  pixels and empirically we set  $D_h = 1536$ . We train our model by applying random resizing, cropping, rotation, Gaussian blur, Gaussian noise and JPEG compression augmentations. The SRS, SCV and SCA are trained on a single Nvidia L40S 48GB GPU.
+
+Datasets: Following [7, 39], we train our approach on the  $180\mathrm{k}$  low resolution images of size  $256\times 256$  from a single latent diffusion model [59], introduced along with  $180\mathrm{k}$  real images by Corvi et al. [7]. Then, to evaluate our approach, we compose a representative set of images originating from recently introduced generative models. In particular, we employ images from [1] for Glide [51], Stable Diffusion 1.3 (SD1.3) and Stable Diffusion 1.4 (SD1.4), representing some early popular text-to-image synthesis approaches, primarily generating low-resolution images, i.e.  $< 0.5$  megapixels. Next, we collect from [1] images for DALLE2 [57], Stable Diffusion 2 (SD2) and Stable Diffusion XL (SDXL) [55]. Also, we employ the online sources of [24, 42] to collect images generated by Flux and Stable Diffusion 3 (SD3) [19] respectively. We also include images
+
+<table><tr><td rowspan="2">Image Size Approach</td><td colspan="3">&lt; 0.5 MPixels</td><td colspan="6">0.5 - 1.0 MPixels</td><td colspan="4">&gt; 1.0 MPixels</td><td rowspan="2">AVG</td></tr><tr><td>Glide</td><td>SD1.3</td><td>SD1.4</td><td>Flux</td><td>DALLE2</td><td>SD2</td><td>SDXL</td><td>SD3</td><td>GigaGAN</td><td>MJv5</td><td>MJv6.1</td><td>DALLE3</td><td>Firefly</td></tr><tr><td>NPR [66]</td><td>72.2</td><td>89.6</td><td>60.5</td><td>19.8</td><td>3.9</td><td>12.5</td><td>18.1</td><td>60.6</td><td>83.2</td><td>15.3</td><td>19.8</td><td>97.1</td><td>38.0</td><td>45.4</td></tr><tr><td>Dire [71]</td><td>33.3</td><td>59.9</td><td>61.3</td><td>45.7</td><td>52.2</td><td>68.5</td><td>46.9</td><td>49.2</td><td>36.3</td><td>41.9</td><td>50.3</td><td>65.2</td><td>49.9</td><td>50.8</td></tr><tr><td>CNNDet. [70]</td><td>59.2</td><td>59.0</td><td>61.2</td><td>39.8</td><td>71.5</td><td>57.5</td><td>67.4</td><td>30.2</td><td>73.4</td><td>48.8</td><td>56.7</td><td>23.5</td><td>73.4</td><td>55.5</td></tr><tr><td>FreqDet. [23]</td><td>43.6</td><td>92.3</td><td>92.7</td><td>36.5</td><td>47.4</td><td>42.5</td><td>66.5</td><td>69.8</td><td>63.2</td><td>36.9</td><td>27.5</td><td>42.2</td><td>80.9</td><td>57.1</td></tr><tr><td>Fusing [34]</td><td>63.0</td><td>62.8</td><td>62.2</td><td>57.5</td><td>76.7</td><td>66.9</td><td>62.1</td><td>38.8</td><td>80.4</td><td>64.0</td><td>74.0</td><td>25.2</td><td>76.3</td><td>62.3</td></tr><tr><td>LGrad [65]</td><td>76.5</td><td>82.4</td><td>83.4</td><td>74.9</td><td>85.7</td><td>60.7</td><td>70.2</td><td>12.7</td><td>89.9</td><td>69.2</td><td>79.6</td><td>30.0</td><td>42.0</td><td>65.9</td></tr><tr><td>UnivFD [52]</td><td>63.3</td><td>80.8</td><td>81.2</td><td>36.3</td><td>91.4</td><td>84.3</td><td>78.3</td><td>28.6</td><td>86.2</td><td>57.1</td><td>60.5</td><td>31.0</td><td>95.5</td><td>67.3</td></tr><tr><td>GramNet [48]</td><td>78.2</td><td>83.9</td><td>84.3</td><td>78.6</td><td>85.2</td><td>66.7</td><td>77.8</td><td>19.2</td><td>85.0</td><td>63.8</td><td>84.9</td><td>42.9</td><td>38.0</td><td>68.4</td></tr><tr><td>DeFake [63]</td><td>86.1</td><td>64.2</td><td>63.6</td><td>90.5</td><td>41.4</td><td>66.2</td><td>52.3</td><td>87.7</td><td>71.7</td><td>67.0</td><td>87.5</td><td>93.3</td><td>39.4</td><td>70.1</td></tr><tr><td>PatchCr. [77]</td><td>78.4</td><td>95.7</td><td>96.2</td><td>86.9</td><td>81.8</td><td>95.7</td><td>96.7</td><td>33.8</td><td>98.0</td><td>79.0</td><td>96.1</td><td>28.1</td><td>79.1</td><td>80.4</td></tr><tr><td>DMID [7]</td><td>73.1</td><td>100.0</td><td>100.0</td><td>97.2</td><td>54.3</td><td>99.7</td><td>99.6</td><td>67.9</td><td>67.9</td><td>99.9</td><td>94.4</td><td>41.3</td><td>90.2</td><td>83.5</td></tr><tr><td>RINE [39]</td><td>95.6</td><td>99.9</td><td>99.9</td><td>93.0</td><td>93.0</td><td>96.6</td><td>99.3</td><td>39.1</td><td>92.9</td><td>96.4</td><td>81.2</td><td>41.8</td><td>82.9</td><td>85.5</td></tr><tr><td>SPAI (Ours)</td><td>90.2</td><td>99.6</td><td>99.6</td><td>83.0</td><td>91.1</td><td>96.5</td><td>97.4</td><td>75.9</td><td>85.4</td><td>94.5</td><td>84.0</td><td>90.2</td><td>96.0</td><td>91.0</td></tr></table>
+
+Table 1. Comparison against state-of-the-art. Average AUC over 5 sources of real images is reported. Lower values are highlighted in red, while higher values are highlighted in green. Best overall average value is highlighted in bold, while second best is underlined. Our approach generalizes across all the considered generative approaches, even on ones producing imagery of extreme fidelity, such as SD3, where the single method [63] that scores better was required to explicitly train on relevant data.  
+
+<table><tr><td>Backbone</td><td># Training Data</td><td>AUC</td></tr><tr><td>CLIP ViT-B/16 [53]</td><td>400 million</td><td>87.6</td></tr><tr><td>DINOv2 ViT-B/14 [56]</td><td>142 million</td><td>87.5</td></tr><tr><td>MFM ViT-B/16 (Ours) [72]</td><td>1.2 million</td><td>91.0</td></tr></table>
+
+Table 2. Evaluation of different backbones. Average AUC over 5 sources of real images and 13 generative models is reported. Best value is highlighted in bold.
+
+generated and provided by GigaGAN [35], which constitutes one of the few recently proposed GAN-based generators. These approaches represent a group of recent methods, capable of producing images up to 1 megapixel. Finally, we collect images for Midjourney-v5 (MJv5), DALLE3 [2] and Firefly from [1], as well as for Midjourney-v6.1 (MJv6.1) from [60]. For each model we collect 1k images, with the exception of MJv6.1 for which we use 631 publicly available images. Regarding the real images we employ 1k samples from each of RAISE [11] and FODB [29], as representative sources of images captured by DSLR cameras and smartphones respectively. We include another 1k images from the test sets of ImageNet [13], COCO [47] and Open Images [41] that represent a general collection of online images, an object-focused database and a collection of high-resolution Web images respectively. These datasets have been collected before the advent of capable generative AI approaches and thus can be safely assumed to be real.
+
+Detection Approaches: We compare our approach against several recent methods proposed to tackle the issue of generalization on generative models not seen during training. We considered 12 approaches with publicly available code and weights. In particular, we employed CNNDetect [70], FreqDetect [23], GramNet [48], Fusing [34], LGrad [65], DMID [7], UnivFD [52], De
+
+Fake [63], DIRE [71], PatchCraft [77], NPR [66] and RINE [39] on their default setups. To facilitate our experiments we used the SIDBench framework [62]. In total, for the 12 considered methods, we evaluated 25 different weight checkpoints. We report best results per method.
+
+# 4.2. Comparison Against State-of-the-Art
+
+We compare against the considered detectors and report the obtained AUC scores for each of the 13 considered generative models in Tab. 1, averaged over all the sources of real images. While almost all competitors successfully distinguish AI-generated images from specific generators, in some cases even achieving near-perfect performance, they catastrophically fail to others. For example, while in the case of Firefly images our method achieves the best performance, in the case of DALLE3 images NPR [66] performs best. However, NPR underperforms in all the rest generative approaches, overall scoring the worst among the considered detectors. This highlights the inability of detectors that learn to capture specific types of artifacts to generalize to generators that introduce different types of inconsistencies. Instead, our approach, exhibits consistently high detection performance across all the generative models, achieving an absolute average improvement of  $5.5\%$  over the second best method, even with the later using a much larger ViT-L backbone pre-trained on the 400 million images of CLIP.
+
+Robustness Against Online Perturbations: To understand the robustness of our network against common perturbations encountered online we study five different types of perturbations. In particular, we study the effects of JPEG and WebP compression with quality factors  $Q = 85, 70, 50$  as well as Gaussian Blur with kernel size  $k = 3, 5, 7$ , Gaussian Noise with standard deviation  $\sigma = 1, 3, 5$  and resizing with scaling factors of  $85, 70, 50\%$ . To better isolate the ef
+
+![](images/0471debd96403cbbed8b484f843e6f133df8b1c0131de0e75af4a1ed62e349f1.jpg)  
+Figure 3. Robustness evaluation on common perturbations. Average AUC is presented over the perturbed versions of two sources of real images from smartphones and DSLR cameras respectively and 13 generative models.
+
+<table><tr><td colspan="2">Ablation</td><td>AUC</td></tr><tr><td colspan="2">SPAI (Ours)</td><td>91.0</td></tr><tr><td rowspan="6">Components</td><td>w/o spectral pretraining</td><td>52.5</td></tr><tr><td>w/o SRS</td><td>71.0</td></tr><tr><td>w/o SCV</td><td>84.9</td></tr><tr><td>w/o SCA</td><td>83.2</td></tr><tr><td>w/o SCA + TenCrop (mean)</td><td>85.3</td></tr><tr><td>w/o SCA + TenCrop (max)</td><td>84.2</td></tr><tr><td rowspan="5">Augm.</td><td>w/o JPEG compression</td><td>89.1</td></tr><tr><td>w/o distortions</td><td>84.2</td></tr><tr><td>w/o JPEG comp. &amp; distortions</td><td>87.7</td></tr><tr><td>with WebP compression</td><td>89.3</td></tr><tr><td>with chromatic augmentations</td><td>80.5</td></tr></table>
+
+fect of each perturbation, in this study we use only the sets of real images originating directly from DSLR and smartphone cameras, i.e. from RAISE and FODB respectively, and present the results in Fig. 3. For illustration purposes we limit the results to the two best competitor approaches, as indicated by Tab. 1. We see that in all cases our approach outperforms the competing methods.
+
+# 4.3. Ablation Studies
+
+Pretraining Approach: We evaluate the importance of the frequency reconstruction pretext task for learning the spectral distribution of real images. To this end, we replace our spectral learned ViT backbone and retrain our network using the CLIP [56] and DINOv2 [53], that have been trained using visual-text alignment and spatial alignment respectively. We report results in Tab. 2 and find that our ViT leads to clearly higher performance, while being trained only on a fraction of the data used for training CLIP and DINOv2.
+
+Architectural Components: To verify their significance we remove each of them and retrain the network. We report the respective AUC scores in Tab. 3. First, we
+
+Table 3. Ablation studies of the key components and augmentations. Average AUC over 5 sources of real images and 13 generative models is reported. Best value is highlighted in bold.  
+
+<table><tr><td>r</td><td>AUC</td><td>D</td><td>AUC</td><td>lr</td><td>AUC</td></tr><tr><td>8</td><td>82.4</td><td>768</td><td>86.4</td><td>1e-3</td><td>84.1</td></tr><tr><td>16</td><td>91.0</td><td>1024</td><td>91.0</td><td>5e-4</td><td>91.0</td></tr><tr><td>24</td><td>83.1</td><td>1536</td><td>88.8</td><td>1e-4</td><td>85.6</td></tr><tr><td>32</td><td>85.0</td><td>2048</td><td>85.3</td><td>5e-5</td><td>82.7</td></tr></table>
+
+Table 4. Hyperparameters tuning. Average AUC over 5 sources of real images and 13 generative models is reported. Best value is highlighted in bold.
+
+train the backbone along with the rest of the network from scratch, without using pretrained weights. As expected, performance plunges, highlighting the importance of learning the spectral distribution of real images first. Then, we remove SRS, SCV and SCA. For the latter, we evaluate using center cropping of the images as well as ten-crop along with mean and max fusion of the subsequent outputs. In all cases performance drops, highlighting the importance of these components in detecting AI-generated images as out-of-distribution samples to the underlying spectral model.
+
+Augmentations: We evaluate our augmentation policy by removing the noise and blur distortions, the JPEG compression as well as both and report performance in Tab. 3. Performance drops in all cases, highlighting their value. To evaluate whether further augmentations could benefit performance, we also train our network using WebP compression and chromatic augmentations. However, we found that this led to a decrease in the overall performance.
+
+Hyperparameters Tuning: We examined different values for the masking radius  $r$ , the learning rate  $lr$  and the size of the latent dimensionality  $D$  and we report the corresponding results in Tab. 4. We see that  $lr = 5e - 4$  was optimal for our network, as well as  $D = 1024$ . Regarding the masking radius, the optimality of  $r = 16$  highlights the importance of the alignment between the pretext task and the later use of this underlying spectral model for AID.
+
+# 4.4. Analysis of Spectral Context Attention
+
+We perform a qualitative evaluation of spectral context attention and present two samples in Fig. 4, where we
+
+![](images/4e52b9a51e5ecafc03aa29fc44383691d1d1b38a78c429a76cea6b892e117b0c.jpg)  
+(a) 6-finger case correctly spotted.
+
+![](images/2bdc8b23aa01e4819cae1c60d8517e9185cec8504fdc715dd7c326e2bf105dc9.jpg)  
+(b) Attending texture-rich regions.
+
+overlay the normalized attention score for each patch of the image. In the first one, depicting an AI-generated image of a human subject possessing a six fingers hand, our attention mechanism identified this patch as significant for the final decision. In the second case, we observe that spectral context attention predicts higher values for patches depicting some complex scenes, in contrast to patches with flat textures, aligning with our original intuition for building it.
+
+# 4.5. Failure Cases
+
+While our method, based on spectral learning, exhibits superior generalization performance both w.r.t state-of-the-art approaches as well as on robustness against online perturbations, it still cannot claim to fully solve the AID task. As Dufour et al. [16] highlighted, AI-generated images often appear online in the form of derivative images, i.e. parts of synthetic images appearing in screenshots, memes, or even in photographs of computer screens and in printed material. This intermediate medium, either fully digital, or involving analog parts in the case of external photographs and printings, distorts the spectral distribution of the AI-generated image signal. Thus, the subtle inconsistencies introduced by the generative approaches, become indistinguishable in this later noisy signal. Case in point, we present two AI-generated images in Fig. 5 that have been recently shared online. While our method successfully detects their early-shared copies, it fails to detect two of their derivative copies. This highlights some potential future directions on combining spectral learning with semantic context understanding.
+
+# 5. Conclusion
+
+In this paper we introduced the key idea that the spectral distribution of real images constitutes an invariant and highly-discriminative pattern for AI-generated image detection and proposed masked spectral learning to model it. To detect
+
+![](images/7491d59ac65028f07f79df76da311f9939acf6133f95935641d50bcabe0aef67.jpg)  
+Detection:  $86\%$
+
+![](images/301167cc475b6811e6804da8a72d2a877191e18fd1906c3bcaa81ea25174ba98.jpg)  
+Detection:  $79\%$
+
+![](images/7d2316b58df83c1aaae5482b875737da60c405f8a0d795b6ae4116085093c0ae.jpg)  
+Figure 4. Qualitative analysis of spectral context attention. A cool-warm overlay has been applied on each patch. Red color indicates significant patches for deciding whether the image is AI-generated (high attention values), while blue color indicates irrelevant patches (low attention values). The attention values have been normalized in [0, 1].  
+Detection:  $0\%$  
+(b) Derivative AI-generated images failed to be detected. The distortion introduced by the intermediate medium makes indistinguishable the spectral artifacts that were previously captured correctly.  
+Figure 5. Failures in detecting derivative AI-generated images. Similar to Fig. 4, spectral context attention is depicted in overlay.
+
+![](images/0a97c1a2d9675b320ed2e44ba4883349f393c5775e5fa63b69cf49e2d256df59.jpg)  
+(a) Accurately detected AI-generated images shared online. Spectral context attention correctly identifies artifacts in the hand and the texture of the jacket (left), as well as on the face and the ear (right).  
+Detection:  $2\%$
+
+generated images as out-of-distributions samples of this model, we introduced the concept of spectral reconstruction similarity for capturing the divergence of the spectral distribution of an image from the one learned by the underlying model. Furthermore, we introduced spectral context attention for detecting subtle spectral inconsistencies in images of any resolution. Using our approach we achieved a significant improvement in state-of-the-art performance, while achieving robustness against common online perturbations. By introducing our work we believe to contribute in reducing the malicious exploitation of generative AI as well as in providing the research community with useful ideas and building blocks for subsequent works in the field.
+
+Limitations: Detecting subtle spectral inconsistencies in AI-generated images requires this information to pass through the medium transmitting the image. Instead, compression algorithms that discard information not stimulating the human eye as well as noisy digital and analog channels corrupt this useful information. This ultimately constrains what any detector relying on the image signal can detect. Yet, we believe that our work constitutes a contribution towards better approaching these theoretical limitations.
+
+# Acknowledgments
+
+This work was partly supported by the Horizon Europe projects ELIAS (grant no. 101120237) and vera.ai (grant no. 101070093). The computational resources were granted with the support of GRNET.
+
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+# Any3DIS: Class-Agnostic 3D Instance Segmentation by 2D Mask Tracking
+
+![](images/159a63400fb33b7cee5a84c603c8d867b40e8ca73d16adddb6f5eca010d256ff.jpg)
+
+![](images/6d285d3c408c76f9b99e8748afdc531031896845d62a90259c255adc2f9304ef.jpg)  
+Figure 1. Comparison of our proposed approach, Any3DIS, with existing 3D instance segmentation methods such as Open3DIS [19]. Open3DIS frequently encounters over-segmentation issues, generating redundant 3D proposals due to its unsupervised merging process. In contrast, our approach leverages robust guidance from 2D mask tracking to maintain consistent object segmentation across video frames, effectively enhancing segmentation accuracy and being 10 times faster than Open3DIS.
+
+# Abstract
+
+Existing 3D instance segmentation methods frequently encounter issues with over-segmentation, leading to redundant and inaccurate 3D proposals that complicate downstream tasks. This challenge arises from their unsupervised merging approach, where dense 2D instance masks are lifted across frames into point clouds to form 3D candidate proposals without direct supervision. These candidates are then hierarchically merged based on heuristic criteria, often resulting in numerous redundant segments that fail to combine into precise 3D proposals. To overcome these limitations, we propose a 3D-Aware 2D Mask Tracking module that uses robust 3D priors from a 2D mask segmentation and tracking foundation model (SAM-2) to ensure consistent object masks across video frames. Rather than merging all visible superpoints across views to create a 3D mask, our 3D Mask Optimization module leverages a dynamic programming algorithm to select an optimal set of views, refin
+
+ing the superpoints to produce a final 3D proposal for each object. Our approach achieves comprehensive object coverage within the scene, significantly reduces unnecessary proposals by half, and lowers the average runtime by a factor of 10, mitigating potential negative impacts on downstream applications. Evaluations on ScanNet200 and ScanNet++ confirm the effectiveness of our method, with improvements across Class-Agnostic, Open-Vocabulary, and Open-Ended 3D Instance Segmentation tasks.
+
+# 1. Introduction
+
+3D Instance Segmentation (3DIS) is a core task in computer vision and robotics, with applications spanning autonomous navigation [2], augmented reality [1], and scene understanding [5]. Fully supervised 3DIS approaches [25, 29, 30]
+
+![](images/744c7bcb2a5f76f8de76de898e2ba32a893bc7b908a6b127c59da7dd2cd00854.jpg)  
+Figure 2. Difference between Open3DIS [19] and our Any3DIS. Open3DIS segments all 2D masks across views first, then lifts them to 3D proposals for merging, whereas our approach tracks all 2D masks across views, lifts them directly to 3D proposals, and then refines these proposals through optimization.
+
+rely on extensive manual annotation of 3D point clouds for each semantic class. Although these methods deliver high-quality segmentation results in a closed-set setting [26, 34], they struggle to generalize to previously unseen objects.
+
+Recent research has explored class-agnostic 3D instance segmentation (3DIS) to overcome this limitation. Training-based approaches [10, 12] leverage pseudo labels generated by 2D foundation models such as SAM [15] to train a 3D instance segmenter. These methods use point-pixel mapping to lift 2D masks directly into 3D pseudo masks. However, they are constrained by the quality of the pseudo labels, which are usually non-reliable. Alternatively, training-free or unsupervised-merging during testing methods [17, 19, 31, 33, 35] tackle this issue by lifting 2D segmentation masks to 3D space without additional training and merging the lifted masks using heuristic criteria to generate 3D proposals for novel objects. While promising, these methods encounter notable challenges. The 3D scene segmentation is prone to over-segmentation due to dense and inconsistent mask predictions across multiple views as shown in Fig. 1. Additionally, the computational cost is high, as the lack of guided merging criteria necessitates retaining all possible mask combinations for safety.
+
+To address these limitations, we introduce a novel approach termed 3D Instance Segmentation by 2D Mask Tracking which is compared to the previous method Open3DIS [19] in Fig. 2. This method leverages the 2D segmentation and tracking capabilities of the foundation model SAM 2 [23], generating comprehensive 2D mask tracks from an input RGB-D sequence. Each track can then be transformed into a potential 3D proposal, simplifying the complex merging process to a straightforward task of 2D mask tracking. However, directly applying SAM 2 on RGB frames alone is suboptimal, as it disregards valuable 3D information from the accompanying point cloud. To overcome this, we propose 3D-Aware 2D Mask Tracking,
+
+which integrates geometric cues from the 3D point cloud to enhance the robustness and accuracy of 2D mask tracking.
+
+Next, we lift the 2D mask tracks to 3D by aggregating superpoints whose 2D projections overlap with any of the track's 2D masks above a given threshold. However, directly selecting all such 3D superpoints may lead to suboptimal results, as it overlooks each superpoint's multi-view consistency. Specifically, while a superpoint might substantially overlap with a 2D mask in one view, it may have minimal or no overlap in other views. To address this, we propose 3D Proposal Refinement via Optimization approach, selectively assigning superpoints to a 3D proposal based on their cumulative overlap across all views. Although this optimization is NP-hard, we present a dynamic programming algorithm to obtain a fast and effective solution.
+
+We evaluate our method on both the ScanNet200 [24] and ScanNet++ [34] datasets. Our approach demonstrates substantial improvements in class-agnostic segmentation, outperforming Open3DIS and other fully supervised models on both datasets. Furthermore, our method achieves enhanced results on Open-Vocabulary [19, 27] and OpenEnded [18] 3D Instance Segmentation tasks, establishing a scalable solution adaptable to diverse, real-world applications and capable of handling various object classes and scene complexities.
+
+Our contributions can be summarized as follows:
+
+- We propose a 3D-Aware 2D Mask Tracking module that leverages strong 3D cues from a 2D foundation mask-tracking model, effectively producing consistent object-level masks across video frames using SAM-2.  
+- We introduce a 3D Proposal Refinement via Optimization process that employs dynamic programming to generate high-quality 3D proposals, significantly minimizing redundant 3D proposals.  
+- We validate the effectiveness of our method on the ScanNet200 [5] and ScanNet++ [34] datasets, achieving SOTA performance on Class-Agnostic, Open-Vocabulary, and Open-Ended 3D Instance Segmentation tasks.
+
+# 2. Related Work
+
+Fully-Supervised 3D Instance Segmentation methods, such as SoftGroup [30], Mask3D [25], and ISBNet [29], trained on closed-set datasets [1, 24, 26, 34], are well-regarded for delivering reliable 3D segmentation results. These approaches use 3D convolutional neural networks [4, 20, 21] to capture detailed semantic information from 3D point cloud scenes, employing clustering [6, 13] or kernel prediction [11, 29] techniques to generate final 3D instance segmentations. While these methods achieve high-quality, fine-grained 3D proposals, they have a critical limitation: they cannot detect or localize objects beyond the training set, which restricts their utility in open-world environments.
+
+Class-Agnostic 3D Instance Segmentation tries to segment all possible 3D object masks regardless of their semantic labels. The approaches can be broadly classified into two categories: training-based and training-free methods. Training-based methods leverage 3D annotations and pseudo labels from 2D foundation models to train an instance decoder. For example, Segment3D [12] uses pseudo labels generated by SAM [15] in conjunction with ground-truth masks to guide a two-stage training process with Minkowski's Unet [4] and a MaskFormer [3] decoder. Similarly, SAM-Graph [10] initializes its Graph Neural Network with SAM [15] and CropFormer [16] pseudo labels. However, these methods are fine-tuned using ground-truth masks, which limits their ability to segment unseen object classes. Training-free approaches seek to overcome this limitation by directly generating 3D proposals from 2D segmentation masks produced by 2D foundation models. Methods like OVIR-3D [17], SAM3D [33], SAI3D [35], MaskClustering [32], SAMPro3D [31], and Open3DIS [19] utilize models such as SAM to produce dense mask predictions for every 2D RGB-D frame, which are then aggregated into a unified set of 3D proposals. While these methods improve the quality of mask predictions, inconsistencies in 2D segmentation across RGB-D frames hinder their robustness, as they rely on heuristic merging criteria.
+
+Open-Vocabulary 3D Instance Segmentation (OV-3DIS) focuses on segmenting 3D objects from classes introduced during testing, rather than those seen during training. Methods like OpenMask3D [27] and Lowis3D [7] use 3D instance segmentation (3DIS) networks [25, 29] to produce class-agnostic proposals. In contrast, approaches such as SAI3D [35], MaskClustering [32], and OVIR-3D [17] employ 2D segmenters to generate masks for each view, which are then lifted into 3D space. Each method has its strengths and limitations: 3DIS networks excel at capturing large geometric structures but may miss small or rare objects due to class imbalance, while 2D segmenters are better at detecting small regions but struggle to maintain object consistency when projecting their results into 3D. Open3DIS [19] combines both 3D and 2D segmentation branches, leveraging the strengths of each to capture small objects while preserving larger structures through superpoint-level masks. However, OV-3DIS still relies on a predefined vocabulary during testing, requiring human intervention and limiting its use in truly autonomous systems that must operate without prior knowledge of object classes.
+
+Open-Ended 3D Instance Segmentation (OE-3DIS) was introduced by prior work [18] to enable object recognition without relying on predefined class labels during training or testing. This method uses Multimodal Large Language Models (MLLMs) to generate features in 2D space, which are then projected into the 3D point cloud. The results show
+
+that OE-3DIS can outperform Open3DIS, the current state-of-the-art in OV-3DIS, on the ScanNet++ dataset, without requiring ground-truth class names.
+
+# 3. Any3DIS
+
+Problem Definition: Given a 3D point cloud scene  $\{\mathbf{P}_i\}_{i=1}^N \in \mathbb{R}^{N \times 6}$  with  $N$  points, each point is defined by its spatial coordinates and color values  $(x,y,z,r,g,b)$ . Additionally, we have  $T$  RGB-D frames with the shape of  $(H,W)$ , each consisting of a color image  $\{\mathbf{I}_t\}_{t=1}^T$  and a depth image  $\{\mathbf{D}_t\}_{t=1}^T$ , where  $\mathbf{I}_t \in \mathbb{R}^{H \times W \times 3}$  and  $\mathbf{D}_t \in \mathbb{R}_+^{H \times W}$ . Every frame  $t$  also has the extrinsic matrix  $\mathbf{E}_t$  and shares the same intrinsic matrix  $\mathbf{K}$  to support the calculation of corresponding pixel projections from the point cloud. Our goal is to segment all  $Q$  3D object binary masks, represented as  $\{\mathbf{M}_q\}_{q=1}^Q$ , where each mask is a binary mask  $\mathbf{M}_q \in \{0,1\}^N$ . To facilitate the segmentation as in [12, 19, 29, 35], we further perform a normal-based graph cut algorithm [9] to partition the point cloud into a set of  $L$  superpoints  $\{\mathbf{S}_l\}_{l=1}^L$ , where each  $\mathbf{S}_l \in \{0,1\}^N$ .
+
+Overview: An overview of Any3DIS is shown in Fig. 3. Our approach leverages the concept of 3D instance segmentation by 2D mask tracking. First, in Sec. 3.1, we aim to find the tracks of all possible objects across frames by sampling superpoints. For each sampled superpoint, the 3D-Aware Instance Tracking module is applied to track consistent 2D segmentation masks across  $T$  frames for the corresponding object. In Sec. 3.2, these tracks are then lifted into 3D mask candidates by selecting superpoints whose projections sufficiently overlap with the 2D masks of these tracks. Finally, the 3D candidates are refined using the Mask Optimization module to retain the most relevant superpoints for the final 3D proposals.
+
+# 3.1. 3D-Aware 2D Mask Tracking
+
+The goal of this step is to track all possible objects across the RGB-D sequence. However, obtaining complete tracks for each object is challenging, as objects vary in appearance across frames in both spatial and temporal dimensions. For instance, if we begin tracking all visible objects in the first frame and continue until they disappear, we risk missing objects that appear in later frames. Additionally, the object's initial mask in the first frame does not often represent its largest visible area, which can reduce tracking quality.
+
+To address these challenges, we propose a novel approach to retrieve comprehensive tracks of all objects in the 3D scene by leveraging precomputed superpoints  $\{\mathbf{S}_l\}_{l=1}^L$  as 3D cues representing potential 3D proposals. To begin, we use the Farthest Point Sampling (FPS) [8] technique to select  $Q_1$  initial superpoints ( $Q_1 \ll L$ ). For each selected superpoint, we estimate the most suitable view called pivot view to initiate tracking for the corresponding 3D object,
+
+![](images/cc2f4a406d3090c54864153c0779598040f17428ae4492fd953fba036bd519b2.jpg)  
+Figure 3. Overview of Any3DIS. We propose a novel class-agnostic approach for 3D instance segmentation through 2D mask tracking. Specifically, we identify each selected superpoint's "pivot view" within the RGB-D frame sequence, where it is most visible. Using the SAM 2 model [23], we then obtain the 2D segmentation of this superpoint in the pivot view and track this 2D segmentation across other views. For each 2D mask obtained, we generate a 3D mask candidate by aggregating all 3D superpoints whose projections intersect with any of the 2D masks. These superpoints are then subjected to mask optimization to produce the final refined 3D mask proposal, which is added to the class-agnostic 3D instance segmentation bank, ready for downstream tasks.
+
+using its projected points as the query to obtain the 2D segmentation in that pivot view and tracking in other views.
+
+Pivot view selection. For each sampled superpoint  $\mathbf{S}_l$ , we generate a track of masks for the corresponding object across a sequence of  $T$  frames. First, we calculate the histogram of projected points for the superpoint  $\mathbf{S}_l$  across these  $T$  views, yielding  $\{\psi_t^l\}_{t=1}^T$ , i.e., counting the number of projected points that can be seen in each view  $t$ . Particularly, for superpoint  $\mathbf{S}_l$ , its 2D set of projected points  $\rho_t^l$  on frame  $t$  is obtained by projecting function  $\Pi(\cdot)$  using the camera parameters  $\mathbf{K}$ ,  $\mathbf{E}_t$  and depth  $\mathbf{D}_t$  as:
+
+$$
+\rho_ {t} ^ {l} = \Pi (\mathbf {S} _ {l}, \mathbf {K}, \mathbf {E} _ {t}, \mathbf {D} _ {t}). \tag {1}
+$$
+
+Furthermore, for a 3D superpoint  $\mathbf{S}_l$  in a view  $t$ , its neighboring superpoints (retrieved by the KNN algorithm using Euclidean distances between centroids) provide valuable context information to help decide whether that view is suitable for the pivot view for tracking. In other words, if any of the  $\kappa$  neighboring superpoints  $\mathbf{S}_k$  of  $\mathbf{S}_l$  are invisible in the current view, signified by low  $|\rho_t^k| / N_{\mathbf{S}_k}$ , where  $N_{\mathbf{S}_k}$  and  $|\rho_t^k|$  are the number of 3D points of superpoint  $\mathbf{S}_k$  and its number of projected points in view  $t$ , this will indicate that the view is not suitable even if most of the points of  $\mathbf{S}_l$  are visible, and vice versa. This motivates us to multiply the number of projected points of the superpoint in that view by
+
+a scale factor  $s_t^l \in [0,1]$ , computed as:
+
+$$
+s _ {t} ^ {l} = \frac {\sum_ {k \in \operatorname {K N N} \left(\mathbf {S} _ {l}\right)} \left| \rho_ {t} ^ {k} \right| / N _ {\mathbf {S} _ {k}}}{\kappa}. \tag {2}
+$$
+
+The final histogram of projected points of superpoint  $\mathbf{S}_l$  in view  $t$  is:  $\psi_t^l = |\rho_t^l| \cdot s_t^l$ . Next, we pick the view with the highest value from the histogram as the 'pivot view' for superpoint  $\mathbf{S}_l$ , denoted as  $\mathrm{pivot}(l) = \mathrm{argmax}_t \psi_t^l$ .
+
+Segmentation in pivot view and tracking in other views. After choosing the pivot view, we simply sample three projected points from  $\rho_{\mathrm{pivot}(l)}^l$  using FPS as the point prompting queries for SAM 2 [23], a 2D foundation model for segmentation and tracking, to leverage its powerful tracking capability. We obtain the 2D mask with score  $o_l$  in the pivot frame and use it as the mask prompting query for tracking in other views. Specifically, we construct two tracking sequences: one backward  $[\mathbf{I}_{\mathrm{pivot}(l)}:\mathbf{I}_0]$  and one forward  $[\mathbf{I}_{\mathrm{pivot}(l)}:\mathbf{I}_T]$ . It is worth noting that an object can disappear and later reappear in subsequent frames. SAM 2 can track these reappearing objects within a predefined memory window of 7 frames; after this, SAM 2 forgets them and treats them as new objects. To address this, we sample a projected point of superpoint  $\mathbf{S}_l$  at the reappearance view  $t$  from  $\rho_t^l$  as an additional point query for SAM 2, enabling consistent tracking of the target object over a longer sequence.
+
+At the end of this step, we obtain  $Q_{1}$  2D binary mask tracks  $\{\mathbf{m}_q^t\}_{t\in [1..T],q\in [1..Q_1]}$  with scores  $\{o_q\}_{q\in [1..Q_1]}$  from the RGB-D sequence, representing  $Q_{1}$  possible 3D objects.
+
+# 3.2. 3D Proposal Refinement via Optimization
+
+The goal of this step is to generate a final 3D mask proposal for each 2D mask track composed of 3D superpoints.
+
+Lifting 2D mask track to 3D mask candidate. For each 2D mask track  $\mathbf{m}_q$  of 3D object  $q$ , we lift it to 3D by grouping all superpoints  $\mathbf{S}_l$  whose projections overlap with any 2D mask  $\mathbf{m}_q^t$  in any view  $t$  by more than a threshold  $\tau$ . We first compute the binary value  $\overline{\mathbf{M}}_q^{t,l}$  indicating the visibility of superpoint  $\mathbf{S}_l$  in view  $t$  as follows:
+
+$$
+\overline {{\mathbf {M}}} _ {q} ^ {t, l} = \left\{ \begin{array}{l l} 1, & \text {i f I O U} \left(\rho_ {t} ^ {l}, \mathbf {m} _ {q} ^ {t}\right) \geq \tau \\ 0, & \text {o t h e r w i s e} \end{array} \right. \text {f o r} l \in [ 1.. L ]. \tag {3}
+$$
+
+Note that  $\overline{\mathbf{M}}_q^t\in \{0,1\} ^L$  is binary vector over all superpoints and  $\overline{\mathbf{M}}_q$  is the 3D mask candidate of object  $q$  by merging all visible superpoints in  $\overline{\mathbf{M}}_q^t$  over all views. Nevertheless, selecting all these superpoints may lead to suboptimal outcomes, as it overlooks the multi-view consistency of each superpoint. Notably, while a superpoint  $\mathbf{S}_l$  might significantly overlap with a 2D mask in one view, it could have little to no overlap in other views. To tackle this issue, we further refine all superpoints  $\mathbf{S}_l$  of 3D mask candidate  $\overline{\mathbf{M}}_q$  to form the final 3D mask proposal  $\mathbf{M}_q$  which maximizes the alignment with all 2D masks  $\mathbf{m}_q^t$  in all views.
+
+Refining 3D mask candidate to final 3D mask proposal. To this end, we introduce an unconstrained binary optimization problem to decide the membership  $\theta = \{0,1\}^{L}$  of all superpoints visible in  $\mathbf{S}_l\in \overline{\mathbf{M}}_q$  in the final 3D mask proposal  $\mathbf{M}_q$  as follows:
+
+$$
+\max  _ {\theta} \mathcal {L} (\theta) = \max  _ {\theta} \sum_ {t} \underbrace {\rho_ {t} ^ {\theta} \otimes \mathbf {m} _ {t} ^ {q}} _ {\text {(A) I n s i d e 2 D M a s k}} - \underbrace {\rho_ {t} ^ {\theta} \otimes \left(\mathbf {1} _ {H \times W} - \mathbf {m} _ {t} ^ {q}\right)} _ {\text {(B) O u t s i d e 2 D M a s k}}. \tag {4}
+$$
+
+where  $\rho_t^\theta$  represents the projection of the current solution  $\theta$  in view  $t$ , computed by projecting the 3D mask  $\mathbf{M}_{\theta}$  formed by merging all superpoints  $\mathbf{S}_l$  where  $\theta^l = 1$  (i.e.,  $\mathbf{M}_{\theta} = \{\mathbf{S}_l|\theta^l = 1\}$ ) onto view  $t$ . Additionally,  $a \otimes b$  counts the number of points in  $a$  that belong to  $b$ . The objective is to maximize the number of points from the current solution  $\theta$  that lie within a mask (part (A) in Eq. (4)) and minimize the number of points that lie outside the mask (part (B) in Eq. (4)) across all views. In other words, the 3D mask  $\mathbf{M}_{\theta}$  formed by  $\theta$  should align well with the 2D masks in every view to form the optimal final mask  $\mathbf{M}_q$ .
+
+Solving the binary optimization problem in Eq. (4) is NP-hard since we need to try all possible configurations of  $\theta$  to find the optimal solution, which cannot run in polynomial time. Instead, we propose a simple, yet effective
+
+Algorithm 1 Algorithm of 3D Mask Optimization.  
+Input: Visibility vector  $\overline{\mathbf{M}}_q^t$  in Eq. (3)  
+1: initialize: Objective value  $\mathbf{C}_0 = \mathbf{0}$  and current solution  $\theta_0 = 0$ .  
+2: for  $t = 1$  to  $T$  do  
+3: Option 1 - Retain current solution:  $\theta_t^1 = \theta_{t-1}, \quad \mathbf{C}_t^1 = \mathbf{C}_{t-1}$   
+4: Option 2 - Add all superpoints in  $\overline{\mathbf{M}}_q^t$  to current solution:  $\theta_t^2 = \theta_{t-1} \vee \overline{\mathbf{M}}_q^t$ ,  $\mathbf{C}_t^2 = \mathcal{L}(\theta_t)$  in Eq. (4)  
+5: If  $\mathbf{C}_t^1 > \mathbf{C}_t^2$  then:  $\theta_t = \theta_t^1$ ,  $\mathbf{C}_t = \mathbf{C}_t^1$  else:  $\theta_t = \theta_t^2$ ,  $\mathbf{C}_t = \mathbf{C}_t^2$   
+6: end for  
+7: return  $\theta_T$
+
+dynamic programming algorithm to obtain a fast and efficient solution. Concretely, for each 2D mask track  $\mathbf{m}_q$  of the  $q$ -th 3D object, we pre-compute its binary vector  $\overline{\mathbf{M}}_q^t$  as in Eq. (3) indicating the visibility of all superpoints in view  $t$ . Let  $\theta_t \in \{0,1\}^L$  be the current solution up to view  $t$  and  $\mathbf{C}_t \in \mathbb{N}$  be the objective value  $\mathcal{L}(\theta_t)$  of the current solution  $\theta_t$  from Eq. (4). We then traverse all views, and at each view  $t$ , we have two choices: (1) retain the current solution, or (2) add all superpoints in  $\overline{\mathbf{M}}_q^t$  to the current solution. We select the option that yields the better objective value  $\mathcal{L}(\theta_t)$  and proceed to the next view. The complete algorithm is outlined in Algorithm 1. Note that at each view, we choose to either add all newly visible superpoints or none, rather than selectively adding individual superpoints, partial inclusion of superpoints is not considered. Thus, this approach may not guarantee a globally optimal solution, however, it produces high-quality solutions that outperform previous methods in practice as shown in experiments.
+
+Iterative 3D object sampling. At the end of this stage, we obtain an initial set of  $Q_{1}$  binary masks  $\{\mathbf{M}_q\}_{q=1}^{Q_1}$  with corresponding 2D mask scores  $\{o_q\}_{q=1}^{Q_1}$  for evaluation. Some superpoints, however, remain unassigned to any 3D mask and may represent new 3D objects. To capture these additional objects, we repeat the process in Sec. 3.1 and Sec. 3.2  $n$  times iteratively until no free superpoints remain, yielding the  $Q$  final 3D mask proposals  $\{\mathbf{M}_q\}_{q=1}^Q$  and its score  $\{o_q\}_{q=1}^Q$ , where  $Q = Q_1 + Q_2 + \ldots + Q_n$ .
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets: To evaluate the effectiveness of our proposed method, we conduct experiments on two widely-used 3D instance segmentation datasets: ScanNet200 [5] and ScanNet++ [34]. ScanNet200 comprises approximately 1201 training scenes and 312 validation scenes, annotated with
+
+<table><tr><td>Method</td><td>2D Segmenter</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{25} \)</td></tr><tr><td>Segment3D [12]</td><td></td><td>19.0</td><td>29.7</td><td>41.6</td></tr><tr><td>SAM-Graph [10]</td><td></td><td>15.3</td><td>27.2</td><td>44.3</td></tr><tr><td>SAM3D [33]</td><td rowspan="2">SAM-HQ</td><td>8.3</td><td>17.5</td><td>33.7</td></tr><tr><td>SAMPro3D [31]</td><td>16.9</td><td>31.7</td><td>48.6</td></tr><tr><td>SAI3D [35]</td><td></td><td>17.1</td><td>31.1</td><td>49.5</td></tr><tr><td>Open3DIS [19]</td><td></td><td>20.7</td><td>38.6</td><td>47.1</td></tr><tr><td>Open3DIS [19]</td><td>SAM2-L</td><td>17.9</td><td>30.4</td><td>39.7</td></tr><tr><td>Any3DIS (ours)</td><td>SAM2-L</td><td>22.2</td><td>35.8</td><td>47.0</td></tr><tr><td>Any3DIS (ours)</td><td>SAM2.1-L</td><td>23.1</td><td>37.1</td><td>49.9</td></tr></table>
+
+Table 1. Class-Agnostic 3DIS on ScanNet++ with 1,554 classes.  
+
+<table><tr><td>Method</td><td>2D Segmenter</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{25} \)</td></tr><tr><td>OVIR-3D [17]</td><td rowspan="2">SAM-HQ</td><td>14.4</td><td>27.5</td><td>38.8</td></tr><tr><td>Open3DIS [19]</td><td>31.5</td><td>45.3</td><td>51.1</td></tr><tr><td>Open3DIS [19]</td><td rowspan="2">SAM2-L</td><td>26.7</td><td>40.2</td><td>53.8</td></tr><tr><td>Any3DIS (ours)</td><td>32.5</td><td>45.2</td><td>55.0</td></tr><tr><td>Open3DIS [19]</td><td>3D + SAM-HQ</td><td>41.5</td><td>51.6</td><td>56.3</td></tr><tr><td>Any3DIS (ours)</td><td>3D + SAM2-L</td><td>42.5</td><td>51.2</td><td>54.5</td></tr></table>
+
+200 object categories, facilitating detailed 3D semantic and instance segmentation. ScanNet++ offers posed RGB-D images and high-quality 3D geometry obtained via advanced laser scanning technology, including 360 training scenes and 50 validation scenes with annotations spanning up to 1,659 semantic classes. We evaluate our method on the validation sets across the three settings including class-agnostic, open-vocab, and open-ended 3DIS.
+
+Evaluation metrics: We evaluate our method using the primary metric of AP over IoU thresholds from  $50\%$  to  $95\%$  in  $5\%$  increments. Also, we report the metric at IoU thresholds of  $50\%$  and  $25\%$ , denoted as  $\mathbf{AP}_{50}$  and  $\mathbf{AP}_{25}$ . For OV-3DIS settings on the ScanNet200 dataset, we further report category group-specific metrics:  $\mathbf{AP}_{\mathrm{head}}$ ,  $\mathbf{AP}_{\mathrm{com}}$ , and  $\mathbf{AP}_{\mathrm{tail}}$ , as commonly presented in prior work.
+
+Implementation details: For 2D-3D image-point occlusion depth threshold, we use 0.1 for both datasets. For 3D lifting, we use  $\tau = 0.5$ . We perform RGB-D sampling at an interval of 10 views, following the approach in [19, 27, 35]. For class-agnostic 3D instance segmentation, we utilize the latest model of Segment Anything Model 2 (ViT-L) [23]. For OV-3DIS setting, we employ the OpenAI CLIP ViT-L/14@336px model [22] as described in [27] for pointwise feature extraction [19], and for OE-3DIS, we leverage the OSM [36] for aggregating point cloud feature tokens [18], with Vicuna-7B as the LLM decoder.
+
+# 4.2. Comparison to prior work
+
+Setting 1: Class-Agnostic 3D Instance Segmentation. We begin by evaluating our method in the class-agnostic
+
+Table 2. Class-Agnostic 3DIS on ScanNet200 with 198 classes.  
+
+<table><tr><td>Method</td><td>2D Segmenter</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{25} \)</td></tr><tr><td>OVIR-3D [17]</td><td></td><td>3.6</td><td>5.7</td><td>7.3</td></tr><tr><td>Segment3D [12]</td><td>SAM-HQ</td><td>10.1</td><td>17.7</td><td>20.2</td></tr><tr><td>Open3DIS [19]</td><td></td><td>11.9</td><td>18.1</td><td>21.7</td></tr><tr><td>Open3DIS [19]</td><td rowspan="2">SAM2-L</td><td>9.8</td><td>15.7</td><td>18.6</td></tr><tr><td>Any3DIS (ours)</td><td>12.9</td><td>19.0</td><td>21.9</td></tr></table>
+
+Table 3. Open-Vocabulary 3DIS on ScanNet++ with 100 classes.  
+
+<table><tr><td>Method</td><td>Segmenter</td><td>AP</td><td>APh</td><td>APc</td><td>APt</td></tr><tr><td>Search3D [28]</td><td rowspan="2">Mask3D [25]</td><td>14.3</td><td>16.1</td><td>13.6</td><td>12.9</td></tr><tr><td>OpenMask3D [27]</td><td>15.4</td><td>17.1</td><td>14.1</td><td>14.9</td></tr><tr><td>SAI3D [35]</td><td rowspan="3">SAM-HQ</td><td>12.7</td><td>12.1</td><td>10.4</td><td>16.2</td></tr><tr><td>OVIR-3D [17]</td><td>11.2</td><td>12.6</td><td>11.5</td><td>10.3</td></tr><tr><td>Open3DIS [19]</td><td>18.2</td><td>18.9</td><td>16.5</td><td>19.2</td></tr><tr><td>Open3DIS [19]</td><td rowspan="2">SAM2-L</td><td>16.4</td><td>16.9</td><td>14.3</td><td>17.1</td></tr><tr><td>Any3DIS (ours)</td><td>19.1</td><td>17.5</td><td>17.2</td><td>23.3</td></tr><tr><td>Open3DIS [19]</td><td>3D + SAM-HQ</td><td>23.7</td><td>27.8</td><td>21.2</td><td>21.8</td></tr><tr><td>Any3DIS (ours)</td><td>3D + SAM2-L</td><td>25.8</td><td>27.4</td><td>23.8</td><td>26.4</td></tr></table>
+
+Table 4. Open-Vocab 3DIS on ScanNet200 with 198 classes.
+
+3D instance segmentation setting, where the objective is to detect and segment instances without relying on predefined semantic categories. Tab. 1 and Tab. 2 present the performance comparison between our approach and existing methods on the ScanNet++ and ScanNet200 datasets, respectively. For ScanNet++ (Tab. 2), Any3DIS achieves an AP of 22.2, surpassing the previous state-of-the-art method Open3DIS [19], which attained an AP of 17.9 (using the same segmenter, SAM2-L) and 20.7 (with the higher-quality segmenter SAM-HQ [14]). This improvement underscores the effectiveness of our method in handling a wide variety of object categories. Furthermore, we evaluate Any3DIS using the new SAM2.1-L backbone, achieving a higher AP score of 23.1. This shows that the performance of our approach can be further enhanced by using improved versions of SAM2. For ScanNet200 (Tab. 2), our method achieves an AP of  $32.5\%$  using SAM2-L, outperforming both OVIR-3D [17] and Open3DIS [19], which utilize SAM-HQ [14] for generating 3D proposals from 2D masks alone. By integrating with 3D proposals from ISB-Net [29], Any3DIS further boosts the AP to 42.5, surpassing existing methods. These results highlight the advantage of our approach over previous methods.
+
+Setting 2: Open-Vocabulary Instance Segmentation. We next evaluate our method in an open-vocabulary setting, where the model must segment instances from previously unseen categories. Following the challenge setup, we assess our approach on the 100-class subset of ScanNet++. On this dataset (Tab. 3), Any3DIS achieves an AP of 12.9, outperforming Open3DIS[19], which scored an AP of 11.9, demonstrating improved generalization to
+
+<table><tr><td>Method</td><td>Setting</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{25} \)</td></tr><tr><td>Large-Vocab [18]</td><td>21K+ classes</td><td>7.3</td><td>11.9</td><td>15.2</td></tr><tr><td>Image-Tagging [18]</td><td>RAM++</td><td>9.1</td><td>15.5</td><td>19.1</td></tr><tr><td>Mask-Wise [18]</td><td>OSM</td><td>16.3</td><td>24.8</td><td>29.0</td></tr><tr><td>Point-Wise [18]</td><td>OSM</td><td>18.4</td><td>29.4</td><td>33.6</td></tr><tr><td>Any3DIS (ours)</td><td>OSM</td><td>20.1</td><td>30.4</td><td>35.5</td></tr></table>
+
+Table 5. Open-Ended 3DIS on ScanNet++ with 100 classes.  
+
+<table><tr><td>Method</td><td>Setting</td><td>AP</td><td>APh</td><td>APc</td><td>APt</td></tr><tr><td>Large-Vocab [18]</td><td>21K+ classes</td><td>8.5</td><td>9.9</td><td>7.2</td><td>8.3</td></tr><tr><td>Image-Tagging [18]</td><td>RAM++</td><td>10.7</td><td>11.6</td><td>11.0</td><td>9.3</td></tr><tr><td>Mask-Wise [18]</td><td>OSM</td><td>14.4</td><td>18.9</td><td>13.5</td><td>10.2</td></tr><tr><td>Point-Wise [18]</td><td>OSM</td><td>16.0</td><td>20.0</td><td>14.3</td><td>13.2</td></tr><tr><td>Any3DIS (ours)</td><td>OSM</td><td>19.1</td><td>18.2</td><td>16.9</td><td>22.8</td></tr></table>
+
+the challenging ScanNet++ dataset. On the ScanNet200 dataset (Tab. 4), our method achieves an AP of 25.8 when using 3D proposals combined with SAM2-L, surpassing Open3DIS and other baseline methods. Even with only 2D proposals, our approach reaches an AP of 19.1, exceeding previous methods under comparable conditions and underscoring our method's strength without relying on class name information in 3D proposals. Moreover, our method maintains robust performance across different category frequency groups, as demonstrated by the  $\mathrm{AP}_{\mathrm{head}}$  and  $\mathrm{AP}_{\mathrm{com}}$  metrics. The  $\mathrm{AP}_{\mathrm{tail}}$  also achieves notable results, indicating that our approach is effective in providing consistent and fine-grained segmentation
+
+Setting 3: Open-Ended Instance Segmentation. Finally, we assess our method in the open-ended setting [18], where the model must segment and recognize instances without predefined class labels during testing. Tab. 5 and Tab. 6 present the performance of our approach alongside baseline methods proposed in [18] on the ScanNet++ and ScanNet200 datasets, respectively. On ScanNet++ (Tab. 5), our approach achieves an AP of 20.1, surpassing prior baselines like Point-Wise, which achieved an AP of 18.4. This improvement highlights our method's capability to handle diverse object categories without a constrained vocabulary. For ScanNet200 (Tab. 6), our method achieves an AP of 19.1, outperforming Point-Wise by a margin of 3.1 AP. This demonstrates our approach's effectiveness in the open-ended setting across category frequency groups.
+
+Qualitative results. In our qualitative results on the ScanNet++ validation set (Fig. 4), we compare the segmentation performance of Any3DIS with Open3DIS and ground truth (GT). The leftmost column shows the input 3D point clouds, followed by GT masks, Open3DIS results, and our approach's results. Unlike Open3DIS, which frequently exhibits over-segmentation and struggles to accurately group
+
+Table 6. Open-Ended 3DIS on ScanNet200 with 198 classes.  
+
+<table><tr><td>3D-AMT</td><td>MaskOpt</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{25} \)</td><td>RC</td><td>\( RC_{50} \)</td><td>\( RC_{25} \)</td></tr><tr><td></td><td></td><td>17.0</td><td>30.1</td><td>42.6</td><td>30</td><td>50.7</td><td>67.8</td></tr><tr><td>✓</td><td></td><td>17.9</td><td>31.2</td><td>45.1</td><td>32.6</td><td>53.1</td><td>69.5</td></tr><tr><td></td><td>✓</td><td>20.3</td><td>33.7</td><td>44.5</td><td>35.8</td><td>56.9</td><td>71.9</td></tr><tr><td>✓</td><td>✓</td><td>22.2</td><td>35.8</td><td>47.0</td><td>40.8</td><td>63.8</td><td>80.8</td></tr></table>
+
+Table 7. Study on each module with Class-agnostic, ScanNet++.  
+
+<table><tr><td>No.</td><td>Strategy</td><td>AP</td><td>AP50</td><td>AP25</td></tr><tr><td>1</td><td>all lifted superpoints</td><td>17.9</td><td>31.2</td><td>45.1</td></tr><tr><td>2</td><td>superpoints in top-1 view</td><td>19.8</td><td>31.4</td><td>42.9</td></tr><tr><td>3</td><td>superpoints in top-5 views</td><td>20.6</td><td>33.6</td><td>44.9</td></tr><tr><td>4</td><td>superpoints in top-10 views</td><td>20.8</td><td>33.5</td><td>44.4</td></tr><tr><td>5</td><td>optimization (ours)</td><td>22.2</td><td>35.8</td><td>47.0</td></tr></table>
+
+Table 8. Study on different strategies for Mask Optimization.  
+
+<table><tr><td>Method</td><td>AP↑</td><td>Runtime (s) ↓</td><td>#Proposals</td></tr><tr><td>SAI3D [35]</td><td>17.1</td><td>4,122</td><td>616</td></tr><tr><td>OVIR-3D [17]</td><td>13.2</td><td>3,911</td><td>723</td></tr><tr><td>Open3DIS [19]</td><td>20.7</td><td>4,226</td><td>931</td></tr><tr><td>Any3DIS</td><td>22.2</td><td>488</td><td>484</td></tr></table>
+
+Table 9. Performance and Runtime analysis on Scannet++.
+
+object instances, Any3DIS produces more coherent segmentation, capturing object boundaries and structures with greater fidelity. Our method reduces redundancy and enhances segmentation accuracy across a variety of challenging indoor scenes. These results underscore Any3DIS's ability to achieve more precise and consistent segmentation through the 3D-Aware 2D Mask Tracking, which maintains continuity and precision across frames. This improvement is particularly evident in complex environments with multiple objects and diverse spatial arrangements, showing our method's robustness in producing high-quality 3DIS.
+
+# 4.3. Ablation study
+
+In this section, we conduct ablation studies on ScanNet++ [34] to analyze the impact of each component of our proposed method on the class-agnostic 3DIS performance.
+
+Study on the effect each component, 3D-Aware 2D Mask Tracking (3D-AMT) and Mask Optimization (MaskOpt), is presented in Tab. 7. The baseline method, which chooses the first frame as the pivot frame (excluding 3D-AMT) and utilizes all lifted superpoints without refinement (excluding MaskOpt), achieves an AP of 17.0. Incorporating 3D-AMT raises the AP to 17.9, highlighting that 3D-AMT enhances image feature representation for 3D segmentation. Adding MaskOpt alone significantly boosts the AP to 20.3, showcasing the impact of refining the mask selection process. Using both 3D-AMT and MaskOpt together results in the highest AP of 22.2, confirming that these components effectively complement each other to enhance performance.
+
+![](images/80449e4ba14befd61834fe28bb4147b8d98cc1d5808aed651f1fb8c63cc6a607.jpg)  
+Point Cloud
+
+![](images/d452e92add8d00822bc865ec98c8ba6ac07726ebe50a9fee76b0826dc8daefe3.jpg)  
+Ground Truth
+
+![](images/02b1be82a3926f24475a5c65af13976eee2530882fe5cdcd2c43ddc8ef130f1a.jpg)  
+Open3DIS
+
+![](images/d7fb84de933eea54edd1642244c162a38cb0cefe0ae5b8dd477a7c443041d68c.jpg)  
+Any3DIS (Ours)
+
+![](images/5f43a5bf675938d1d2a4c7ef01f74674a971c2f8f60f688eebdda17c2eb488e5.jpg)
+
+![](images/25bfd543465da4315fb355c6bd372fc5a56478e79f4f04c27f7a624a6b1725d9.jpg)  
+Figure 4. Qualitative Result on ScanNet++ Validation Set.: From left to right we show the input point cloud of 3D scenes, GT segmentation, Open3DIS [19], and Any3DIS (ours) results. Our approach achieves more accurate and consistent segmentation than Open3DIS.
+
+![](images/9d16a8e3373fdb3f9c59a61823e014f8365ce3e83b387352fccf3c15e7e5e9b6.jpg)
+
+![](images/84330f344bb0387625f7d84438c4f06d0c2b0f03024fed9bdb1a2cf9b311b93f.jpg)
+
+![](images/8c656be8f0cfb0811df6b77cb3310b70ddac3751f5f62d946b4f2b6f47e363be.jpg)
+
+![](images/ad883340664b62436898b0f1c67a84d71980ad7736eae9c37f1ea79b307391ff.jpg)
+
+![](images/6f7279240fb0035062eab5383e78329312e88e1cf7fab5b90bf087bd354ccd57.jpg)
+
+![](images/4863c0624fb3af8a563f730ef8acbe5d41b14e853201ec97b08fa4b639d498d1.jpg)
+
+Mask optimization strategies. We evaluate various strategies for mask optimization in Tab. 8. Using all lifted superpoints without any refinement (No. 1) achieves an AP of 17.9. In Eq. (4), rather than using all views in our proposed Algorithm 1, an alternative approach is to focus on the top views with the highest objective values,  $\mathcal{L}(\theta)$ . We then exhaustively explore all possible configurations of superpoints visible in these selected views to determine the optimal configuration  $\theta$ . A top-1 view selection strategy (No. 2) slightly raises the AP to 19.8. Choosing the top-5 (No. 3) and top-10 (No. 4) views further improves APs to 20.6 and 20.8, respectively. Our optimization approach (No. 5) achieves the highest AP of 22.2, confirming its effectiveness in identifying a good combination of superpoints.
+
+Performance analysis. Tab. 9 presents the runtime analysis and the average number of predicted 3D proposals for each method. Any3DIS achieves state-of-the-art performance while reducing the runtime by a factor of 10 and generating a sufficient number of 3D proposals.
+
+# 5. Conclusion
+
+In this paper, we have introduced Any3DIS, a novel class-agnostic 3D instance segmentation method that leverages 2D mask tracking to segment objects in point clouds. By identifying pivot views for sampled superpoints and using SAM 2 for 2D segmentation and tracking, our method effectively transfers 2D foundation model capabilities to 3D. Further proposal refinement via optimization improves segmentation quality. Extensive experiments on the ScanNet200 and ScanNet++ datasets demonstrate that Any3DIS consistently outperforms existing methods across various settings, including class-agnostic, open-vocabulary, and open-ended 3D instance segmentation, validating the effectiveness of our framework. In the future, we anticipate that further improvements in SAM 2's segmentation and tracking accuracy could enhance Any3DIS's performance. Also, advancements in quantum computing could enable optimal solutions to the proposed unconstrained binary optimization problem.
+
+# References
+
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+[2] J. Behley, M. Garbade, A. Milioto, J. Quenzel, S. Behnke, C. Stachniss, and J. Gall. SemanticKITTI: A Dataset for Semantic Scene Understanding of LiDAR Sequences. In Proc. of the IEEE/CVF International Conf. on Computer Vision (ICCV), 2019. 1  
+[3] Bowen Cheng, Alexander G. Schwing, and Alexander Kirilov. Per-pixel classification is not all you need for semantic segmentation. In NeurIPS, 2021. 3  
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+[8] Yuval Eldar, Michael Lindenbaum, Moshe Porat, and Yehoshua Y Zeevi. The farthest point strategy for progressive image sampling. IEEE transactions on image processing, 6(9):1305-1315, 1997. 3  
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+[11] Tong He, Chunhua Shen, and Anton van den Hengel. DyCo3d: Robust instance segmentation of 3d point clouds through dynamic convolution. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2  
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+[13] Li Jiang, Hengshuang Zhao, Shaoshuai Shi, Shu Liu, Chi-Wing Fu, and Jiaya Jia. Pointgroup: Dual-set point group
+
+ing for 3d instance segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 2  
+[14] Lei Ke, Mingqiao Ye, Martin Danelljan, Yifan Liu, Yu-Wing Tai, Chi-Keung Tang, and Fisher Yu. Segment anything in high quality. In NeurIPS, 2023. 6  
+[15] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al. Segment anything. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4015-4026, 2023. 2, 3  
+[16] Qi Lu, Jason Kuen, Shen Tiancheng, Gu Jiumiang, Guo Weidong, Jia Jiaya, Lin Zhe, and Yang Ming-Hsuan. High-quality entity segmentation. In ICCV, 2023. 3  
+[17] Shiyang Lu, Haonan Chang, Eric Pu Jing, Abdeslam Boullarias, and Kostas Bekris. Ovir-3d: Open-vocabulary 3d instance retrieval without training on 3d data. In Conference on Robot Learning, pages 1610–1620. PMLR, 2023. 2, 3, 6, 7  
+[18] Phuc DA Nguyen, Minh Luu, Anh Tran, Cuong Pham, and Khoi Nguyen. Open-ended 3d point cloud instance segmentation. arXiv preprint arXiv:2408.11747, 2024. 2, 3, 6, 7  
+[19] Phuc D. A. Nguyen, Tuan Duc Ngo, Evangelos Kalogerakis, Chuang Gan, Anh Tran, Cuong Pham, and Khoi Nguyen. Open3dis: Open-vocabulary 3d instance segmentation with 2d mask guidance. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 1, 2, 3, 6, 7, 8  
+[20] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652-660, 2017. 2  
+[21] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Advances in neural information processing systems, 30, 2017. 2  
+[22] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PMLR, 2021. 6  
+[23] Nikhila Ravi, Valentin Gabeur, Yuan-Ting Hu, Ronghang Hu, Chaitanya Ryali, Tengyu Ma, Haitham Khedr, Roman Radle, Chloe Rolland, Laura Gustafson, et al. Sam 2: Segment anything in images and videos. arXiv preprint arXiv:2408.00714, 2024. 2, 4, 6  
+[24] David Rozenberszki, Or Litany, and Angela Dai. Language-grounded indoor 3d semantic segmentation in the wild. In Proceedings of the European Conference on Computer Vision (ECCV), 2022. 2  
+[25] Jonas Schult, Francis Engelmann, Alexander Hermans, Or Litany, Siyu Tang, and Bastian Leibe. Mask3d: Mask transformer for 3d semantic instance segmentation. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 8216-8223. IEEE, 2023. 1, 2, 3, 6
+
+[26] Julian Straub, Thomas Whelan, Lingni Ma, Yufan Chen, Erik Wijmans, Simon Green, Jakob J Engel, Raul Mur-Artal, Carl Ren, Shobhit Verma, et al. The replica dataset: A digital replica of indoor spaces. arXiv preprint arXiv:1906.05797, 2019. 2  
+[27] Aycca Takmaz, Elisabetta Fedele, Robert W. Sumner, Marc Pollefeys, Federico Tombari, and Francis Engelmann. OpenMask3D: Open-Vocabulary 3D Instance Segmentation. In Advances in Neural Information Processing Systems (NeurIPS), 2023. 2, 3, 6  
+[28] Ayca Takmaz, Alexandros Delitzas, Robert W Sumner, Francis Engelmann, Johanna Wald, and Federico Tombari. Search3d: Hierarchical open-vocabulary 3d segmentation. arXiv preprint arXiv:2409.18431, 2024. 6  
+[29] Khoi Nguyen Tuan Duc Ngo, Binh-Son Hua. Isbnet: a 3d point cloud instance segmentation network with instance-aware sampling and box-aware dynamic convolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023. 1, 2, 3, 6  
+[30] Thang Vu, Kookhoi Kim, Tung M. Luu, Xuan Thanh Nguyen, and Chang D. Yoo. Softgroup for 3d instance segmentation on 3d point clouds. In CVPR, 2022. 1, 2  
+[31] Mutian Xu, Xingyilang Yin, Lingteng Qiu, Yang Liu, Xin Tong, and Xiaoguang Han. Sampro3d: Locating sam prompts in 3d for zero-shot scene segmentation. arXiv preprint arXiv:2311.17707, 2023. 2, 3, 6  
+[32] Mi Yan, Jiazhao Zhang, Yan Zhu, and He Wang. Maskclustering: View consensus based mask graph clustering for open-vocabulary 3d instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 28274-28284, 2024. 3  
+[33] Yunhan Yang, Xiaoyang Wu, Tong He, Hengshuang Zhao, and Xihui Liu. Sam3d: Segment anything in 3d scenes. arXiv preprint arXiv:2306.03908, 2023. 2, 3, 6  
+[34] Chandan Yeshwanth, Yueh-Cheng Liu, Matthias Nießner, and Angela Dai. Scannet++: A high-fidelity dataset of 3d indoor scenes. In Proceedings of the International Conference on Computer Vision (ICCV), 2023. 2, 5, 7  
+[35] Yingda Yin, Yuzheng Liu, Yang Xiao, Daniel Cohen-Or, Jingwei Huang, and Baoquan Chen. Sai3d: Segment any instance in 3d scenes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024. 2, 3, 6, 7  
+[36] Qihang Yu, Xiaohui Shen, and Liang-Chieh Chen. Towards open-ended visual recognition with large language model. In ECCV, 2024. 6
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+# Any6D: Model-free 6D Pose Estimation of Novel Objects
+
+Taeyeop Lee $^{1}$  Bowen Wen $^{2}$  Minjun Kang $^{1}$  Gyuree Kang $^{1}$  In So Kweon $^{1}$  Kuk-Jin Yoon $^{1}$ $^{1}$ KAIST  $^{2}$ NVIDIA
+
+# Abstract
+
+We introduce Any6D, a model-free framework for 6D object pose estimation that requires only a single RGB-D anchor image to estimate both the 6D pose and size of unknown objects in novel scenes. Unlike existing methods that rely on textured 3D models or multiple viewpoints, Any6D leverages a joint object alignment process to enhance 2D-3D alignment and metric scale estimation for improved pose accuracy. Our approach integrates a render-and-compare strategy to generate and refine pose hypotheses, enabling robust performance in scenarios with occlusions, non-overlapping views, diverse lighting conditions, and large cross-environment variations. We evaluate our method on five challenging datasets: REAL275, ToyotaLight, HO3D, YCBINEOAT, and LM-O, demonstrating its effectiveness in significantly outperforming state-of-the-art methods for novel object pose estimation. Project page: https://taeyeop.com/any6d
+
+# 1. Introduction
+
+Object 6D pose estimation is a crucial problem in computer vision and robotics, focusing on determining the rigid 6D transformation, comprising both 3D orientation and 3D translation, between reference and camera coordinates. This task has numerous practical applications, such as robotic manipulation [4, 13, 64, 69, 73, 78] and augmented reality [43, 44, 55]. In recent years, significant progress has been made in this field [3, 13, 20, 33], and research is ongoing.
+
+Research in 6D object pose estimation can be broadly categorized into three approaches: instance-level [22, 51, 62, 68], category-level [26-28, 32, 61, 65], and category-agnostic methods [47, 48, 71, 77]. Instance-level methods provide high precision but come with significant limitations. They rely on exact RGB-textured CAD models for estimating object poses, which restricts their effectiveness to only those objects seen during training. A major drawback is their inability to handle new objects without additional fine-tuning. Category-level methods partially
+
+![](images/8994cdf6f316cb1701adffa5eda2b5dbd9b437a769b950aa7ad756dc87cb66ae.jpg)  
+Anchor Image
+
+![](images/f71d958da33fab8983480eb7609a2221c5bb90fd4cffed12ab3f044627dd7e31.jpg)
+
+![](images/39027efae3032d5871bb3c8af81ff1dec54e9fa84a26590629c876fbdad845e3.jpg)  
+Object Alignment
+
+![](images/5bf82d337294b3a854bcacaa4b1cb51a3aaac37d7a18aacf320da835ed6d7504.jpg)  
+Query Image  
+6D Object Pose  
+Figure 1. Our method accurately estimates 6D object pose for novel objects on drastically different scenes and viewpoints using only a single RGB-D anchor image. We achieve robust pose estimation without requiring precise CAD models or posed multi-view reference images.
+
+mitigate these limitations by using category-specific prior knowledge, but they are still restricted to predefined object categories. Moreover, they face considerable challenges in acquiring comprehensive training datasets due to the complexity of aligning canonical poses. In contrast, category-agnostic methods aim to generalize across different objects without being limited to specific instances or categories, offering a more flexible approach to 6D pose estimation.
+
+Recent research has shifted toward category-agnostic approaches [25, 30, 47, 47, 52, 58, 70, 71] to address the limitations of both category-level and instance-level pose estimation. These efforts can be broadly divided into two directions: model-based methods [30, 47, 52], which require textured RGB 3D CAD models at test time, and model-free methods [16, 39, 59, 77], which utilize multiview reference images or video sequences of the target object during inference. Although both approaches show promising results, they still face significant practical limitations when dealing with unseen objects that are not physically accessible. In robotic manipulation scenarios, for example, these methods
+
+face difficulties when a robot encounters unexpected objects in a new environment without available 3D models or multiview images. This dependency on prior object data significantly limits their effectiveness in real-world applications.
+
+To address these challenges, Oryon [11] introduces a novel model-free approach for estimating the 6D pose of objects from a single reference RGBD image. Unlike earlier methods that rely heavily on detailed object data at test time, Oryon uses language guidance to perform pose estimation with just a single RGBD reference. This method demonstrates impressive adaptability, functioning effectively even when reference and target images come from entirely different environments. Oryon establishes correspondences between images using language cues and estimates the pose by aligning visible point clouds from the reference. However, its performance degrades when occlusions or minimal overlap object regions between the reference and target objects, limiting the number of matching points. Consequently, Oryon struggles in object manipulation scenarios involving human or robotic arms, particularly when targets are occluded, appear in non-overlapping views, or lack sufficient texture [15, 67], as shown in our experiments.
+
+To overcome these limitations, we present Any6DPose, a novel model-free approach for object pose estimation using a single anchor RGBD image. Inspired by recent advances in image-to-3D models [21, 36, 41, 72, 74, 76], our method estimates metric scale object shape for object pose estimation. Although existing 3D generation methods achieved promising photorealistic consistency between the input image and the generated 3D shape in normalized space, they often neglect critical aspects of 2D-3D alignment, especially the metric scale, which is crucial for accurate pose estimation and the subsequent downstream tasks. Therefore, we introduce a simple yet effective object alignment, jointly improving object size and pose estimation by alignment in 2D and 3D space. We generate multiple pose hypotheses and use a render and compare strategy to select the optimal one, building on previous work [71]. This enables our method to effectively handle disjoint views between query and anchor objects, as well as occlusions, diverse light conditions, and large cross-environment variations. We validate our approach across diverse scenarios on five public datasets: HO3D, YCBINEOAT, REAL275, ToyotaLight, and LM-O. Our Any6DPose significantly outperforms state-of-the-art methods in novel object pose estimation.
+
+The main contributions of our work are as follows:
+
+- We introduce Any6DPose, a novel framework that enables 6D pose and size estimation of novel objects in different scenes from only a single reference image.  
+- We propose a straightforward yet effective object alignment technique that addresses the challenges of existing 3D generation models, specifically improving 2D-3D
+
+alignment and size estimation for accurate pose estimation.  
+- We validate our approach through extensive experiments, demonstrating superior performance compared to state-of-the-art methods across five benchmark datasets.
+
+# 2. Related Works
+
+# 2.1. CAD Model-based Object Pose Estimation
+
+Instance-level pose estimation methods [17, 18, 24, 50, 64] rely on textured CAD models of specific objects, with training and testing conducted on the same instances. Category-level methods [8, 10, 31, 65, 79] generalize to novel instances within known categories but require expensive category annotations and remain constrained to predefined object classes. Category-agnostic methods [6, 9, 30] address these limitations by estimating the poses of arbitrary novel objects without category constraints. However, most still utilize ground-truth CAD models during inference, restricting their practical application in real-world scenarios where such models are unavailable. Some recent works [35, 54] try to retrieve CAD from existing databases.
+
+# 2.2. Model-Free Object Pose Estimation
+
+To overcome the limitations of CAD dependencies, model-free approaches have been developed that eliminate the need for explicit textured models by relying instead on a set of reference images of the target object. Gen6D [39], OnePose [60], and OnePose++[16] generate 3D point clouds from videos or multiple views using structure-from-motion (SfM) [57] and utilize these point clouds for pose estimation through 2D-3D matching [23, 29]. FS6D [77] and FoundationPose [71] extend this approach to RGB-D images, achieving promising results. However, these methods still depend on multiview images, with most requiring camera poses to merge these views, which is often impractical in real-world scenarios.
+
+Motivated by these challenges, recent work has focused on reducing these dependencies. For example, NOPE [46] estimates relative orientation using only a single anchor image. LoFTR [59] also contributes by using a transformer-based approach for feature matching, effectively enhancing the robustness of pose estimation from a single image. Similarly, Oryon [11] reduces the requirement to a single image by incorporating language guidance. However, these partial matching methods [11, 12, 34, 38, 53, 59] struggle in scenarios with non-overlap regions or significant occlusions in the target image. GigaPose [47], closely related to our approach, utilizes image-to-3D (Wonder3D [41]) to estimate object pose but still requires an initial novel object pose to determine object size. Concurrently, HIPPo [40], OmniManip [49], and SceneComplete [1] explore model-free object pose estimation from an image using image-to-3D methods.
+
+![](images/726d0a031e02cf955c5cc60cdfc5a169c19f12526725754a885401d5f3b67371.jpg)  
+Figure 2. Overview of the Any6D framework for model-free object pose estimation. First, we reconstruct normalized object shape  $O_N$  from the image-to-3D model. Then, we estimate accurate object pose and size from anchor image  $I_A$  using the proposed object alignment (Sec. 3.1). Next, we use the query image  $I_Q$  to estimate the pose with the reconstructed metric-scale object shape  $O_M$  (Sec. 3.2).
+
+# 3. Method
+
+Given an RGB-D anchor image  $(I_A)$  and an RGB-D query image  $(I_Q)$ , our task is to estimate the relative pose between them. The query images may capture the same object from drastically different viewpoints and scenes from the single anchor image. We formulate the problem as a relative pose estimation task [2, 11, 53, 59]. Our method aims to estimate the relative 6D pose  $\mathbf{T}_{A\rightarrow Q}\in \mathrm{SE}(3)$  between  $I_{A}$  and  $I_{Q}$  where  $\mathbf{T}_{A\to Q}$  is defined as the rigid transformation  $[R\mid t]$ , consisting of a rotation  $R\in \mathrm{SO}(3)$  and a translation  $t\in \mathbb{R}^3$
+
+Previous approaches have attempted matching using either visible RGB images [56, 59] or point clouds [2, 53]. While effective with significant overlap, these methods struggle in scenarios with occlusions or large viewpoint variations, as partial-to-partial matching lacks sufficient shared features. To address these challenges, our method adopts a full-to-partial matching strategy by reconstructing a complete 3D object shape, ensuring robust alignment even under little overlap. Accurate pose estimation is achieved through a render-and-compare pipeline [71], effectively handling occluded or partially visible objects. The benefits of our approach are confirmed through extensive experiments (Sec. 4.3), demonstrating superior performance in low-overlap scenarios.
+
+We introduce Any6D, a framework for estimating the relative pose  $\mathbf{T}_{A\rightarrow Q}$  between an anchor image  $I_{A}$  and a query image  $I_{Q}$ . Our framework comprises two components: first, we reconstruct the normalized object shape  $O_{N}$  from the anchor image using an image-to-3D model, without considering real-world scale or pose, and then estimate the metric-scale object shape  $O_{M}$  by determining both the
+
+actual object size  $s \in \mathbb{R}^3$  and the pose  $T_{O_M \to A}$ , aligning it properly in 2D and 3D space (Sec. 3.1). Next, we use the reconstructed metric-scale object shape and the query image to estimate the pose, deriving the relative transformation  $\mathbf{T}_{A \to Q}$  by combining  $T_{O_M \to A}$  and  $T_{O_M \to Q}$  (Sec. 3.2). The complete workflow of our Any6D framework is illustrated in Fig. 2.
+
+# 3.1. Coarse Object Alignment
+
+To our knowledge, there is no reliable existing solution for single-view metric-scale reconstruction from RGB-D that can handle diverse objects effectively. Given the recent advancements in RGB-based single-view reconstruction [21, 37, 76], we thus resort to InstantMesh [76] which has shown promising results across various objects. One key limitation, however, is the 3D object reconstruction only yields a shape with a normalized scale  $O_N$ , in the range [-1, 1] for each XYZ axis, meaning the resulting meshes are not properly scaled or positioned relative to the actual scene. This limitation prevents us from obtaining accurate pose alignment further, thus motivating our object alignment step, where we first estimate a coarse size of the object shape  $O_M$  and then refine this size by jointly solving accurate pose  $T_{O_M \to A}$ . Our approach involves estimating and aligning object shapes in both 3D and 2D spaces between  $I_A$  and  $O_N$ , including  $\mathbf{T}_a \in \mathrm{SE}(3)$ , and size  $s \in \mathbb{R}^3$ .
+
+Specifically, we estimate the object size  $s$  in a coarse-to-fine manner using  $I_{A}$ . We first initialize the coarse object size by comparing point clouds between  $I_{A}$  and  $O_{N}$  from their respective object centers. While the mean of points is a straightforward approach for center estimation, it becomes unreliable due to partial viewpoint and noisy outlier
+
+points in the anchor image, as shown in Fig. 3-(a, b). Using a simple axis-aligned bounding box also leads to inaccurate center estimation due to the partial observability, as shown in Fig. 3-(c). Therefore, we propose using an oriented bounding box to determine the object center, as shown in Fig. 3-(d), which yields a more reliable coarse center estimate for  $I_{A}$ . For the axis alignment, we align the oriented bounding box with the XYZ axis. We then sample various rotation angles and calculate the IoU between the rotated bounding boxes of  $I_{A}$  and  $O_{N}$  across different angles. The combination of rotation and scale that leads to the highest IoU is used to transform  $O_{N}$  into a coarsely aligned object shape, updating it to an initial object shape  $O_{M'}$ , which is subsequently used for accurate pose and size estimation.
+
+# 3.2. Fine Object Alignment
+
+Our framework aims to determine the relative pose  $\mathbf{T}_{A\rightarrow Q}$  between an anchor image  $I_{A}$  and a query image  $I_{Q}$ . This process involves multiple steps, starting with the reconstruction of a coarse object shape  $O_{M^{\prime}}$  and subsequently refining it to obtain the final metric-scale object shape  $O_{M}$ . Given the coarsely scaled initial shape  $O_{M^{\prime}}$ , we jointly refine both the pose and the object size through our object and size refinement.
+
+To refine the object shape and pose, we draw inspiration from FoundationPose [71] for its effective pose generation, refinement, and selection capabilities. However, it either requires ground-truth metric-scale object CAD for its model-based setup or multiple posed reference images in its model-free setup. This prevents its direct application in our considered setup, where only a single RGBD reference image is provided. We thus develop a joint module that injects the size estimation task into its pose refinement process. This allows us to estimate both the metric-scale size and pose reliably simultaneously.
+
+Our refinement pipeline involves three primary modules: pose estimation, size estimation, and axis alignment—all of which work together in a unified process by alternating between the task of size refinement and pose refinement. We begin by estimating an initial pose using  $O_{M'}$  and simultaneously refining the object size. In FoundationPose [71], sampling for pose hypothesis generation was only performed in  $SO(3)$  without considering size variations. Instead, we additionally sample different sizes, together with  $SO(3)$  sampling. In particular, the size samples are drawn in the range of  $\Delta s \in [s_0, s_1]$  (we empirically set  $s_0 = 0.6$ ,  $s_1 = 1.4$ ) along each axis. We then refine the sampled pose hypothesis using the refinement module provided by [71] and render them to compare with the query image observation. The optimal pose hypothesis is selected based on the comparison score indicated by the pose selection module in [71]. Once the optimal size is determined, we scale the object shape and switch to the pose refinement
+
+![](images/25971b877db07c716cd9e3cffc1244895a29aad0ccaba57ea962a6aac28634cd.jpg)  
+(a) Center of Raw Point Cloud
+
+![](images/5af908f40bb496b1f3cdef74fd498b3f165dbac53db996eed4061f3def086003.jpg)  
+(b) Center of Filtered Point Cloud
+
+![](images/b596e3dafa39f90c85e71989e69556d5df10a28eb2f484828a08161b2032e140.jpg)  
+(c) Center of Bounding Box of Filtered Points  
+(d) Center of Oriented Bounding Box of Filtered Points
+
+![](images/0768a492fe302ea52691fd38ca8c01b31df51b2518b7c2b507c8851bc410e8d8.jpg)  
+Figure 3. Visualization of each point clouds and center of mustard object.
+
+stage, including an axis alignment step for more precise accuracy. This updated alignment leverages the joint estimation of size and pose, leading to greater accuracy than traditional IoU-based methods.
+
+After refining the object parameters, we determine the final object pose  $T_{O_M\to A}$ , which provides an accurate alignment of the reconstructed object shape. With the anchor image  $I_A$ , query image  $I_Q$ , and metric-scale object shape  $O_M$ , we estimate the relative pose  $\mathbf{T}_{A\rightarrow Q}$  by composing two transformations: from the object to the anchor  $(\mathbf{T}_{O_M\to A})$  and from the object to the query  $(\mathbf{T}_{O_M\to Q})$ . The relative pose can be expressed as follows:
+
+$$
+\mathbf {T} _ {A \rightarrow Q} = \left(\mathbf {T} _ {O _ {M} \rightarrow A}\right) ^ {- 1} \cdot \mathbf {T} _ {O _ {M} \rightarrow Q} \tag {1}
+$$
+
+For pose selection, we employ a two-level render-and-compare strategy. Initially, a pose ranking network evaluates each hypothesis by comparing its rendered view to the cropped observation, producing an embedding to quantify alignment quality. Then, we apply self-attention to the concatenated embeddings of all hypotheses, incorporating global context to generate final scores for selecting the optimal pose.
+
+# 4. Experiments
+
+# 4.1. Datasets
+
+We evaluate our method on five diverse real-world datasets: HO3D [15], YCBIInEOTA [67], Toyota-Light [19], REAL275 [65], and LM-O [5]. Each dataset presents unique challenges in object pose estimation under various interaction scenarios and environmental conditions.
+
+HO3D [15] captures close-range RGB-D images of human-hand object interactions. Using the latest HO3D-V3 version, we evaluate our method on 4 objects across 13 video sequences, totaling 2K images. The dataset presents large variations in viewpoints and significant hand-based occlusions. We sample pair images from the DexYCB [7] dataset.
+
+Table 1. Model-free pose estimation results measured by AUC of ADD, and ADD-S, AR on HO3D dataset.  
+
+<table><tr><td rowspan="3">Modality Metrics</td><td colspan="3">Oryon [11]</td><td colspan="3">LoFTR [59]</td><td colspan="3">Gedi [53]</td><td colspan="3">Ours RGB-D</td></tr><tr><td colspan="3">RGB-D &amp; Language</td><td colspan="3">RGB-D</td><td colspan="3">Depth</td><td colspan="3">RGB-D</td></tr><tr><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td></tr><tr><td>AP10</td><td>23.8</td><td>0.0</td><td>0.4</td><td>22.5</td><td>0.0</td><td>1.2</td><td>94.4</td><td>1.9</td><td>3.5</td><td>100.0</td><td>16.2</td><td>22.2</td></tr><tr><td>AP11</td><td>25.6</td><td>0.0</td><td>1.3</td><td>59.4</td><td>15.6</td><td>14.8</td><td>100.0</td><td>55.0</td><td>32.3</td><td>100.0</td><td>73.8</td><td>59.0</td></tr><tr><td>AP12</td><td>21.2</td><td>0.0</td><td>1.4</td><td>12.5</td><td>1.2</td><td>2.1</td><td>99.4</td><td>30.6</td><td>20.3</td><td>100.0</td><td>48.8</td><td>28.3</td></tr><tr><td>AP13</td><td>26.2</td><td>0.0</td><td>0.6</td><td>31.9</td><td>1.9</td><td>1.9</td><td>100.0</td><td>13.1</td><td>8.8</td><td>100.0</td><td>74.4</td><td>45.0</td></tr><tr><td>AP14</td><td>8.1</td><td>0.0</td><td>0.0</td><td>25.0</td><td>0.0</td><td>0.0</td><td>76.2</td><td>0.0</td><td>0.6</td><td>100.0</td><td>35.6</td><td>29.7</td></tr><tr><td>SM1</td><td>24.7</td><td>0.0</td><td>1.1</td><td>52.8</td><td>3.4</td><td>1.9</td><td>82.0</td><td>0.0</td><td>1.6</td><td>86.5</td><td>34.8</td><td>27.8</td></tr><tr><td>SB11</td><td>46.1</td><td>0.0</td><td>2.4</td><td>75.4</td><td>8.4</td><td>15.6</td><td>96.4</td><td>13.8</td><td>12.1</td><td>100.0</td><td>86.8</td><td>68.9</td></tr><tr><td>SB13</td><td>29.9</td><td>0.0</td><td>4.2</td><td>33.5</td><td>0.0</td><td>1.9</td><td>98.2</td><td>11.4</td><td>9.4</td><td>99.4</td><td>64.1</td><td>54.6</td></tr><tr><td>MPM10</td><td>8.3</td><td>0.0</td><td>0.2</td><td>13.4</td><td>0.0</td><td>0.3</td><td>29.9</td><td>0.0</td><td>3.1</td><td>98.7</td><td>26.8</td><td>31.3</td></tr><tr><td>MPM11</td><td>33.8</td><td>0.0</td><td>0.1</td><td>26.1</td><td>0.0</td><td>0.0</td><td>35.0</td><td>0.0</td><td>0.6</td><td>100.0</td><td>3.2</td><td>32.4</td></tr><tr><td>MPM12</td><td>17.2</td><td>0.0</td><td>0.1</td><td>5.1</td><td>0.0</td><td>0.0</td><td>42.0</td><td>0.0</td><td>0.4</td><td>100.0</td><td>1.3</td><td>23.5</td></tr><tr><td>MPM13</td><td>24.2</td><td>0.0</td><td>0.4</td><td>10.2</td><td>0.0</td><td>0.3</td><td>45.2</td><td>0.0</td><td>1.3</td><td>100.0</td><td>15.9</td><td>30.9</td></tr><tr><td>MPM14</td><td>9.6</td><td>0.0</td><td>1.4</td><td>15.9</td><td>0.0</td><td>2.0</td><td>35.7</td><td>0.0</td><td>1.5</td><td>98.7</td><td>43.9</td><td>44.0</td></tr><tr><td>MEAN</td><td>23.0</td><td>0.0</td><td>1.0</td><td>29.5</td><td>2.3</td><td>3.2</td><td>71.9</td><td>9.7</td><td>7.4</td><td>98.7</td><td>40.4</td><td>38.3</td></tr></table>
+
+YCBCInEOTA [67] features mid-range RGBD images of dual-arm robot manipulations. The dataset includes three types of interactions: single-arm pick-and-place, within-hand manipulation, and pick-and-place with handoff between arms. We evaluate our method on 5 objects across 9 videos, totaling 749 frames, with pair images sampled from DexYCB [7]. The dataset presents diverse viewpoints and robot arm occlusions.
+
+Toyota-Light [19] focuses on single-object pose estimation under challenging lighting conditions. It features significant lighting variations between scenes, which present crucial challenges. Following Oryon[11], we evaluate our method on 2K image pairs.
+
+REAL275 [65] consists of RGBD images captured across different scenes, featuring six object categories with three instances per category. The dataset exhibits limited viewpoint variations and includes scenarios with minor occlusions. Following Oryon[11], we evaluate our method on 2K image pairs selected from the original real-world test set.
+
+LM-O [5] consists of RGBD images captured in cluttered scenes, featuring 12 distinct textureless objects. The dataset has viewpoint variations and realistic occlusion scenarios. We follow GigaPose[47] of input image, segmentation, and image-to-3d methods for comparison.
+
+# 4.2. Metrics
+
+Our primary evaluation metrics are based on the Average Distance of Model Points (ADD) [64, 75], which computes the mean distance between corresponding 3D model points under-predicted and ground truth poses. For asymmetric objects, we use ADD directly, while for symmetric objects, we employ ADD-S, which calculates the average distance to the closest model point. We report the Area Under the Curve (AUC) and the recall rate at a threshold of 0.1 times the object diameter [16, 77]. Additionally, we evaluate using the metrics established in the BOP challenge [20], including the Average Recall (AR) of Visual Surface Discrep
+
+ancy (VSD), Maximum Symmetry-aware Surface Distance (MSSD), and Maximum Symmetry-aware Projection Distance (MSPD). These metrics provide complementary perspectives on pose accuracy by evaluating recalls over multiple thresholds.
+
+# 4.3. Comparison with State-of-the-art
+
+The evaluation is conducted on 5 challenging datasets: HO3D, YCBCInEOTA, Toyota-Light, REAL275, and LM-O, each presenting unique challenges for pose estimation. For evaluation, we align the relative pose  $T_{A\rightarrow Q}$  with the object pose  $T_{O\rightarrow Q}$  by multiplying it with  $T_{O\rightarrow A}$ , following the approach used in Oryon [11]. We use ground-truth segmentation masks to evaluate the HO3D, YCBCInEOTA, Toyota-Light, and REAL275 datasets.
+
+We compare our approach against several recent state-of-the-art methods, including Oryon [11], a multi-modal object pose estimation method, and single-image matching baselines such as LoFTR [59], Gedi [53], and ObjectMatch [14]. For LoFTR, we use matched point clouds combined with pose optimization [63] to estimate accurate object poses. ObjectMatch leverages SuperGlue [56] for match estimation, as outlined in Oryon [11]. These baselines cover a range of approaches to pose estimation, from traditional feature matching to recent learning-based methods.
+
+Table 1 summarized the results on HO3D dataset. The experimental results on the HO3D dataset demonstrate that our proposed method significantly outperforms state-of-the-art approaches across all evaluation metrics. Specifically, our method achieves mean scores of  $98.7\%$ ,  $40.4\%$ , and  $38.3\%$  for ADD-S, ADD, and AR metrics, respectively, substantially surpassing previous methods, including Oryon  $(4.1\%, 0\%, 0.2\%)$ , LoFTR  $(29.5\%, 2.3\%, 3.2\%)$ , and Gedi  $(71.9\%, 9.7\%, 7.4\%)$ . These results are particularly notable given our method's consistent performance across object instances, even in challenging scenarios involving human-hand interactions and occlusions. The exceptional improve
+
+Table 2. Model-free pose estimation results measured by AUC of ADD, ADD-S, and AR on YCBINEOAT dataset.  
+
+<table><tr><td rowspan="3">Modality Metrics</td><td colspan="3">Oryon [11]</td><td colspan="3">LoFTR [59]</td><td colspan="3">Gedi [53]</td><td colspan="3">Ours RGB-D</td></tr><tr><td colspan="3">RGB-D &amp; Language</td><td colspan="3">RGB-D</td><td colspan="3">Depth</td><td colspan="3">RGB-D</td></tr><tr><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td><td>ADD-S</td><td>ADD</td><td>AR</td></tr><tr><td>sugar_box1</td><td>44.0</td><td>0.0</td><td>1.1</td><td>47.3</td><td>0.0</td><td>0.1</td><td>95.6</td><td>0.0</td><td>1.7</td><td>96.7</td><td>14.3</td><td>11.3</td></tr><tr><td>sugar_box_yalehand0</td><td>34.7</td><td>3.0</td><td>5.2</td><td>41.6</td><td>0.0</td><td>0.1</td><td>82.2</td><td>6.9</td><td>21.5</td><td>89.1</td><td>75.2</td><td>44.4</td></tr><tr><td>mustard0</td><td>48.6</td><td>0.0</td><td>3.5</td><td>47.3</td><td>20.3</td><td>15.2</td><td>100</td><td>0.0</td><td>19.1</td><td>100</td><td>23</td><td>32.4</td></tr><tr><td>mustard_easy_00_02</td><td>36.2</td><td>0.0</td><td>0.3</td><td>23.2</td><td>0.0</td><td>1.9</td><td>78.3</td><td>0.0</td><td>20.2</td><td>78.3</td><td>53.6</td><td>39.2</td></tr><tr><td>bleach0</td><td>10.4</td><td>0.0</td><td>1.5</td><td>55.2</td><td>0.0</td><td>0.9</td><td>74.6</td><td>0.0</td><td>7.7</td><td>98.5</td><td>68.7</td><td>56</td></tr><tr><td>bleach_hard_00_03_chaitanya</td><td>24.4</td><td>6.7</td><td>6.1</td><td>60</td><td>15.6</td><td>18.7</td><td>66.7</td><td>62.2</td><td>35.5</td><td>73.3</td><td>51.1</td><td>37.7</td></tr><tr><td>tomato_soup_can_yalehand0</td><td>32.8</td><td>0.0</td><td>4.5</td><td>10.7</td><td>0.0</td><td>6.8</td><td>60.3</td><td>0.0</td><td>7.8</td><td>70.2</td><td>0</td><td>14.1</td></tr><tr><td>cracker_box_reorient</td><td>13.2</td><td>0.0</td><td>0</td><td>26.3</td><td>0.0</td><td>0</td><td>97.4</td><td>0.0</td><td>1.8</td><td>100</td><td>60.5</td><td>44.2</td></tr><tr><td>cracker_box_yalehand0</td><td>15.0</td><td>0.0</td><td>1.2</td><td>22.6</td><td>0.0</td><td>0.2</td><td>89.5</td><td>0.0</td><td>10.4</td><td>97.7</td><td>63.9</td><td>58.2</td></tr><tr><td>MEAN</td><td>28.8</td><td>1.1</td><td>2.6</td><td>37.1</td><td>4</td><td>4.9</td><td>82.7</td><td>7.7</td><td>14.0</td><td>89.3</td><td>45.6</td><td>37.5</td></tr></table>
+
+Table 3. Model-free pose estimation results measured by AUC of ADD(-S), AR, MSSD, MSPD, and VSD on the Toyota-Light (TOYL) dataset.  
+
+<table><tr><td>Method</td><td>ADD(-S)</td><td>AR</td><td>MSSD</td><td>MSPD</td><td>VSD</td></tr><tr><td>SIFT [42]</td><td>14.1</td><td>30.3</td><td>39.6</td><td>44.1</td><td>7.3</td></tr><tr><td>Obj. Mat. [14]</td><td>5.4</td><td>9.8</td><td>13.0</td><td>14.0</td><td>2.4</td></tr><tr><td>Oryon [11]</td><td>22.9</td><td>34.1</td><td>42.9</td><td>45.5</td><td>13.9</td></tr><tr><td>Ours</td><td>32.2</td><td>43.3</td><td>55.8</td><td>58.4</td><td>15.8</td></tr></table>
+
+Table 4. Model-free pose estimation results measured by AUC of ADD(-S), AR, MSSD, MSPD, and VSD on the REAL275 dataset.  
+
+<table><tr><td>Method</td><td>ADD(-S)</td><td>AR</td><td>MSSD</td><td>MSPD</td><td>VSD</td></tr><tr><td>SIFT [42]</td><td>16.4</td><td>34.1</td><td>37.9</td><td>48.0</td><td>16.5</td></tr><tr><td>Obj. Mat. [14]</td><td>13.4</td><td>26.0</td><td>31.7</td><td>30.8</td><td>15.5</td></tr><tr><td>Oryon [11]</td><td>34.9</td><td>46.5</td><td>50.9</td><td>56.7</td><td>32.1</td></tr><tr><td>Ours</td><td>53.5</td><td>51.0</td><td>56.5</td><td>65.3</td><td>31.1</td></tr></table>
+
+ment in ADD-S metrics, approaching  $100\%$  in most cases, validates our method's robustness and accurate pose estimation under dynamic conditions.
+
+For the YCBCInEOAT dataset (Table 2), our approach achieves superior performance with mean scores of 89.3, 45.6, and 37.5 for ADD-S, ADD, and AR, significantly surpassing the corresponding scores of Gedi, which are 82.7, 7.7, and 14.0. The substantial improvement in ADD metrics particularly highlights our method's capability in precise pose estimation. These results validate our method's effectiveness in challenging scenarios with occlusions and nonoverlapping viewpoints, which are critical for real-world robotic applications.
+
+On the Toyota-Light dataset (Table 3), our method demonstrates substantial improvements across all metrics. We achieve  $32.2\%$  in ADD(-S),  $43.3\%$  in AR,  $55.8\%$  in MSSD, and  $58.4\%$  in MSPD, consistently outperforming Oryon by significant margins  $(9.3\%, 9.2\%, 12.9\%, \text{and} 12.9\%$  respectively). Our approach shows particular robustness under varying lighting conditions, which often pose significant challenges for existing methods. The consistent performance across all metrics demonstrates the stability of our approach in handling different lighting scenarios.
+
+On the REAL275 dataset (Table 4), our method demonstrates remarkable performance, achieving  $53.5\%$  in ADD(-S),  $51.0\%$  in AR,  $56.5\%$  in MSSD, and  $65.3\%$  in MSPD. These results significantly surpass previous methods, par
+
+Table 5. Model-free pose estimation results measured by AUC of AR, MSSD, MSPD, and VSD on the Linemod Occlusion (LM-O) dataset.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Segmentation</td><td rowspan="2">Image-to-3D</td><td colspan="4">Metrics</td></tr><tr><td>AR</td><td>MSPD</td><td>MSSD</td><td>VSD</td></tr><tr><td>GigaPose [47]</td><td>CNOS [45]</td><td>Wonder3D [41]</td><td>17.5</td><td>35.8</td><td>9.0</td><td>7.6</td></tr><tr><td>Ours</td><td>CNOS [45]</td><td>Wonder3D [41]</td><td>28.6</td><td>36.1</td><td>32.0</td><td>17.6</td></tr><tr><td>Ours</td><td>CNOS [45]</td><td>InstantMesh [76]</td><td>25.2</td><td>29.5</td><td>27.4</td><td>18.7</td></tr></table>
+
+ticularly showing substantial improvements over Oryon in most metrics (improvements of  $18.6\%$ ,  $4.5\%$ ,  $27.1\%$ , and  $33.8\%$ , respectively). While maintaining competitive performance in VSD ( $31.1\%$  versus Oryon's  $32.1\%$ ), our method excels in all other metrics, demonstrating superior generalization across various object categories and poses. This comprehensive evaluation validates the robustness and versatility of our approach in handling diverse real-world scenarios.
+
+Finally, on the Linemod Occlusion (LM-O) dataset (Table 5), we compare the estimation of the pose with a 3D model predicted from a single image. We compare the same input images, segmentation [45], and image-to-3D [41] followed by GigaPose [47] for fair comparison. Our method outperforms GigaPose under the same settings. Note that Gigapose is an RGB-based method but requires the initial pose to determine object size, while our method estimates object size from a single RGB-D image.
+
+These extensive experiments across multiple datasets demonstrate that our method consistently outperforms existing approaches, often by significant margins. The strong performance across different metrics and various challenging scenarios validates the effectiveness and reliability of our approach for real-world applications.
+
+# 4.4. Qualitative Results
+
+Fig. 4 shows qualitative results of our method compared to Oryon [11], LoFTR [59], and Gedi [53] on the HO3D dataset. Given the anchor image (left), we overlay the object contours in pink, along with the rendered object and rotation axes, to visualize the pose estimation results. The query images are selected to have no overlapping parts with the anchor images, creating a challenging scenario for pose estimation. While Oryon, LoFTR, and Gedi struggle under
+
+![](images/9755090e78bfb1b6fc49f395867bcb524fde0ac5ce5495ca6283288eba67b6f6.jpg)  
+Figure 4. Qualitative comparison of state-of-the-art methods on the HO3D Dataset. In this challenging scenario, the left anchor image shows only partially visible objects, while the query images are not visible due to occlusion or different viewing angles. This represents the most challenging case for matching. Gedi, being a depth-based method, shows ambiguity when dealing with RGB-based non-symmetric objects.
+
+these conditions due to their reliance on partial anchor information, our method effectively reconstructs complete object shapes, allowing for robust pose estimation even when parts of the object are occluded or not visible in the anchor view.
+
+The first example features a white cleanser object where only a portion is visible in the anchor image, with a significantly different viewpoint in the query image. Our method accurately estimates the pose, while others fail to handle the limited visibility of key features. In the second example with a SPAM can, the anchor image shows only the back view, while the query image captures the logo side partially occluded by a hand. Despite these challenging conditions, our method successfully estimates the correct pose, while competing methods fail to align due to their reliance on limited anchor information. The final example shows a blue pitcher where Gedi roughly estimates the center position but fails to capture the correct orientation. In contrast, our method successfully aligns rotational and translational components, closely matching the ground truth pose.
+
+Fig. 5 demonstrates our pose estimation results in robotic manipulation scenarios on the YCBCInEOAT dataset. We compare our method with Oryon, LoFTR, and Gedi across various examples of robot-object interaction. In the first example with a red cracker box, our method accurately aligns both position and orientation, while other methods struggle with pose estimation. Notably, the anchor image only shows the front cheese logo, yet our method successfully handles the back view in the query image. The second example involves a yellow mustard bottle manipulated by two dual robot arms. Our method maintains accurate pose estimation throughout the interaction, proving robust to occlusions from the gripper. In the final example with a yel
+
+low sugar box, our method achieves precise pose estimation despite minimal visible information in the anchor image, while competing methods fail to handle the challenging viewpoint variations. These qualitative results highlight our method handles challenging scenarios involving significant occlusions and viewpoint changes, consistently outperforming existing approaches in pose estimation accuracy.
+
+# 4.5. Ablation Studies
+
+In this section, we conduct ablation studies to evaluate our object shape and alignment estimation.
+
+Object Shape. We evaluate different object reconstruction approaches for pose estimation, including a comparison with a partial view-based baseline. For this baseline, given a camera-to-object pose  $T_{C \rightarrow O}$  and a reference RGB-D image  $I_r$ , we train an object-centric NeRF [70] model and use marching cubes [66] to extract a textured mesh. This baseline relies on ground-truth poses to train NeRF with aligned object coordinates, ensuring a fair comparison with the same pose estimation setup. It follows the single image version of FoundationPose [71]. As shown in Fig. 6, our reconstructed shapes differ significantly from the baseline, which exhibits missing regions in rear and diagonal views, leading to ambiguity in rendering and pose estimation. Table 6 presents the pose estimation results and mesh quality evaluation using Chamfer Distance (CD). The CD between our reconstructions and ground-truth meshes indicates that lower values correspond to better accuracy. Additionally, we found that improper axis alignment leads to distortions in the X, Y, and Z ratios, highlighting the importance of precise axis alignment.
+
+Object Alignment. We evaluate our simple but effective
+
+![](images/1a0bc487b301290be50a3c25cbaac866e5be35bbf38ea61e84eb4b291f8e6422.jpg)  
+Figure 5. Qualitative comparison of state-of-the-art methods on the YCBIInEOAT Dataset. In this challenging scenario, the left anchor image shows only partially visible objects, while the query images are not visible due to occlusion or different viewing angles. This represents the most challenging case for matching. Gedi, being a depth-based method, shows ambiguity when dealing with RGB-based non-symmetric objects.
+
+![](images/b7fbb3e199be0349b797faa0a0b45a031805c4600760471d73e0704e90b2f47a.jpg)  
+Figure 6. Comparison of shape quality between baseline method and ours.
+
+Table 6. Ablation Studies of Size Estimation on the HO3D dataset.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Object Alignment</td><td colspan="4">Metrics</td></tr><tr><td>Coarse Size</td><td>Refinement</td><td>Axis Align</td><td>ADD-S (↑)</td><td>ADD (↑)</td><td>AR (↑)</td><td>CD (↓)</td></tr><tr><td>Baseline</td><td>X</td><td>X</td><td>X</td><td>28.6</td><td>0.00</td><td>0.20</td><td>1.02</td></tr><tr><td>(1)</td><td>X</td><td>X</td><td>X</td><td>0.0</td><td>0.0</td><td>0.0</td><td>1.47</td></tr><tr><td>(2)</td><td>X</td><td>✓</td><td>✓</td><td>98.0</td><td>25.5</td><td>26.8</td><td>0.53</td></tr><tr><td>(3)</td><td>✓</td><td>X</td><td>✓</td><td>83.7</td><td>26.6</td><td>22.5</td><td>0.92</td></tr><tr><td>(4)</td><td>✓</td><td>✓</td><td>X</td><td>92.3</td><td>23.6</td><td>24.9</td><td>0.66</td></tr><tr><td>Ours</td><td>✓</td><td>✓</td><td>✓</td><td>98.7</td><td>40.4</td><td>38.3</td><td>0.49</td></tr></table>
+
+object alignment module: coarse size estimation, size and pose refinement and axis alignment. The results of our ablation study on these components are presented in Table 6. First, as shown in Table 6-(1), using raw object shape estimation without any alignment steps leads to failure in accurately estimating the object's rotation and translation, with all metrics showing subpar performance. This underscores the importance of size alignment as a foundational step in pose estimation. In Table 6-(2) and in our full method, incorporating coarse size estimation substantially improves the ADD metric. This shows that even a basic size esti
+
+mation allows the model to approximate the object's pose better. Next, Table 6-(3) demonstrates that incorporating axis alignment further enhances performance, particularly on the ADD-S and AR metrics. This process not only improves object shape estimation but also yields significant gains in pose accuracy by aligning the object's axes to avoid distortion in its proportions along the x, y, and z directions. Finally, our full method, incorporating coarse size estimation, refinement, and axis alignment, achieves the best results across all metrics. Specifically, as shown in Table 6, our method reaches an ADD of 40.4 and an AR of 38.3, outperforming the other configurations. These results validate the effectiveness of our alignment approach in enhancing object pose estimation.
+
+# 5. Conclusion
+
+We introduce Any6D, a novel framework for model-free object pose estimation that reduces dependence on CAD models and multi-view images, particularly in challenging object manipulation scenarios. Our method proposes an efficient object alignment method for precise pose and size estimation. Extensive experiments demonstrate that Any6D significantly outperforms state-of-the-art methods for occlusions and varying viewpoints. While our method shows promising results on pose and size estimation through image-to-3D alignment, it has limitations when the initial 3D shape is inaccurate, as our approach does not incorporate shape updating. A future direction would be to refine shape to enhance robustness and applicability in scenarios with inaccurate initial shapes.
+
+# Acknowledgment
+
+This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF2022R1A2B5B03002636), the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government (MSIT) (Artificial Intelligence Innovation Hub) under Grant 2021-0-02068, and KAIST Cross-Generation Collaborative Lab Project.
+
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+# AnyCam: Learning to Recover Camera Poses and Intrinsics from Casual Videos
+
+Felix Wimbauer $^{1,2,3}$
+
+Weirong Chen $^{1,2,3}$
+
+Dominik Muhle $^{1,2}$
+
+Christian Rupprecht<sup>3</sup>
+
+Daniel Cremers<sup>1,2</sup>
+
+<sup>1</sup>Technical University of Munich
+
+$^{2}$  MCML  $^{3}$  University of Oxford
+
+felix.wimbauer@tum.de cremers@tum.de
+
+![](images/45136acaa304cf7cc474c430d14670b5bb979b797f9ae262aae83c8e97b590c6.jpg)  
+Figure 1. AnyCam. Given a casual video and pretrained monocular depth estimation (MDE) and optical flow networks, AnyCam outputs camera poses, camera intrinsics, and uncertainty maps in a single forward pass. The uncertainty maps represent probable movement in the scene. By using a novel loss formulation, AnyCam can be trained on a large corpus of unlabelled videos mostly obtained from YouTube.
+
+![](images/a880a3e8fc2428642cd2903298ef658627df9f9090947d1fe12d59587c85be14.jpg)
+
+# Abstract
+
+Estimating camera motion and intrinsics from casual videos is a core challenge in computer vision. Traditional bundle-adjustment based methods, such as SfM and SLAM, struggle to perform reliably on arbitrary data. Although specialized SfM approaches have been developed for handling dynamic scenes, they either require intrinsics or computationally expensive test-time optimization and often fall short in performance. Recently, methods like Dust3r have reformulated the SfM problem in a more data-driven way. While such techniques show promising results, they are still 1) not robust towards dynamic objects and 2) require labeled data for supervised training. As an alternative, we propose AnyCam, a fast transformer model that directly estimates camera poses and intrinsics from a dynamic video sequence in feed-forward fashion. Our intuition is that such a network can learn strong priors over realistic camera poses. To scale up our training, we rely on an uncertainty-based loss formulation and pre-trained depth and flow networks instead of motion or trajectory supervision. This allows us to use diverse, unlabelled video datasets obtained mostly from YouTube. Additionally, we ensure that the predicted trajectory does not accumulate drift over time through a lightweight trajectory refinement step. We test AnyCam on established datasets, where it delivers accurate camera poses and intrinsics both qualitatively and quantitatively. Furthermore, even with trajectory refinement, AnyCam is significantly faster than existing works for SfM in
+
+dynamic settings. Finally, by combining camera information, uncertainty, and depth, our model can produce high-quality 4D pointclouds. For more details and code, please check out our project page: fwmb.github.io/anycam
+
+# 1. Introduction
+
+Estimating camera motion and intrinsics from a casual, dynamic video is a long-standing problem in 3D computer vision. Such scene parameters serve as the basis for a plethora of more complex applications, ranging from novel view synthesis to reconstruction. In particular, an efficient and robust solution to this problem would unlock the huge corpus of online video data from sources like YouTube to train 3D foundation models. To this day, the availability of 3D data is one of the main limitations when creating general-purpose 3D models. [33]
+
+Traditional SfM (and SLAM) systems like COLMAP [32] excel at reconstruction in settings where a static scene is captured from many well-distributed camera angles. However, they generally fail when there are dynamic parts in the scene, the camera follows a suboptimal trajectory, or the image quality suffers from artifacts. This makes them unsuitable for casual videos. Recently, a number of works have proposed to incorporate certain deep learning-based components into or instead of the classic SfM pipeline to make it more robust. For example, Dust3r [44] proposes a network to predict dense 3D pointmaps from multiple
+
+views. Camera pose and intrinsics can then be recovered by aligning the point maps from every view. FlowMap [34] reformulates the problem by learning per-frame depth and aligning them based on flow and point tracks. While these proposed approaches show promising results, they are still restricted to static scenes and fail when dynamic objects are too prominent. There are methods specifically designed to deal with dynamic scenes, e.g. LeapVO [5] and ParticleSfM [56]. However, they are generally trained in a supervised way and require calibrated camera intrinsics. Given the general lack of intrinsics information in casual videos, the applicability of such methods in this domain is limited.
+
+This work presents AnyCam, a novel method targeted explicitly for robust camera motion and intrinsic estimation in dynamic casual videos. Unlike most existing approaches, we utilize a transformer-based model to directly predict relative camera poses and intrinsics for a sequence of video frames. Crucially, this end-to-end formulation allows our network to learn strong priors over plausible camera poses and to become robust towards imperfect inputs. Additionally, we design a training scheme that can ingest raw videos and does not require any labels. Our formulation effectively models data uncertainty and automatically filters out dynamic objects. This enables training on a collection of datasets obtained from YouTube and other casual video sources, resulting in strong generalization capabilities. Furthermore, we present a lightweight test-time refinement step to avoid long-term drift.
+
+Our experiments thoroughly test AnyCam's zero-shot capabilities in camera pose estimation and intrinsics recovery. We achieve state-of-the-art results on several challenging dynamic benchmarks and perform on par with methods trained fully supervised with labeled data. Additionally, by combining camera information, uncertainties, and depth maps, we can create high-fidelity 4D pointclouds.
+
+# 2. Related Work
+
+# 2.1. Foundational Models for Depth and Flow
+
+In the tasks of monocular depth (MDE) and flow estimation, well-generalizable foundation models have replaced early deep learning approaches [8, 12, 13] in the last years. For MDE, DepthAnything [50] uses a data engine to construct a large corpus of automatically annotated data to learn relative depth estimation. Additional fine-tuning allows for metric depth estimates. DepthAnythingV2 [51] finetunes the previous model using synthetic data for better performance. Metric3D [53] and Metric3Dv2 [16] transform images to canonical camera intrinsics with a fixed focal length. DepthPro [1] proposes a two-stage training curriculum with a second stage solely on synthetic data to sharpen boundary predictions. DepthCrafter [17] leverages a conditional diffusion model to predict temporally consistent depth maps
+
+for videos. In this work, we utilize UniDepth [28] for metric MDE, which uses a geometric invariance loss on different image augmentation to enforce consistency.
+
+RAFT [38] presented the state of the art for optical flow estimation for a long time. It improved previous methods by introducing a recurrent look-up operator on correlation volumes to iteratively refine flow predictions without needing coarse-to-fine flow pyramids. GMFlow [46] avoids correlation volumes and instead leverages the properties of transformers for global matching on feature maps. This removes the need for iterative steps to improve runtime performance. UniMatch [47] extends GMFlow network by tasks of disparity and depth prediction to enable cross-task transfer learning of a single transformer network.
+
+We rely on both off-the-shelf MDE and Optical Flow networks to benefit from strong geometric priors during training and inference.
+
+# 2.2. SfM and SLAM
+
+For many decades, the problem of recovering camera parameters and geometry from images has been formulated as the Structure-from-Motion (SfM) pipeline [14, 24, 26]. While many different implementations of the SfM pipeline exist, COLMAP [32] has emerged as the standard due to its robustness and flexibility. One of the drawbacks of SfM methods is their high computational cost. Simultaneous Location and Mapping (SLAM) [9, 10, 22, 23] approaches employ a similar pipeline to SfM but focus on the efficient processing of consecutive video frames. In recent years, these classical optimization-based approaches were enhanced by learned components [2, 7, 19, 21, 29-31, 52]. However, relying on epipolar geometry [15] or photometric consistency [10] makes them susceptible to high error on highly dynamic scenes. The strong focus on self driving data provided datasets with mostly static environments [4, 11, 36], an assumption that does not hold for casual videos.
+
+# 2.3. Learning Based SfM and SLAM
+
+Largely learning-based methods started to replace classical SLAM and SfM systems due to improved robustness [39]. DROID-SLAM extends the framework of RAFT [38] by an update operator on both depth and pose estimates. A final differentiable bundle adjustment (BA) layer produces the final pose estimates. ParticleSfM [56] utilizes dense correspondences inside a BA framework to optimize poses. The dense correspondences are initialized from optical flow, and dynamic points are filtered using trajectory-based motion segmentation. CasualSAM [55] predicts both depth and movement from images to get frame-to-frame motion. A global optimization aligns the scale of the prediction and refines the poses. Dust3R [44] is a dense multi-view stereo method that regresses point coordinates between an image pair. This allows it to be extended to either SfM or
+
+SLAM. FlowMap [34] proposes to reconstruct a scene by overfitting a depth network to it and aligning depth maps via correspondences from flow or point tracking. LEAP-VO [5] combines visual and temporal information of video sequences to improve the tracking accuracy of points and identify occluded and dynamic points. A sliding window bundle adjustment then optimizes the poses. The concurrent work of MonST3R [54] finetunes Dust3r on mostly synthetic data to generalize it to dynamic scenes. While these works achieve impressive progress, they generally obtain poses from aligning depth and point maps or by optimizing them per-scene. This makes it hard to inject prior information about camera motion. In contrast, our method uses a neural network to predict a trajectory, which can effectively learn priors over realistic camera motions.
+
+# 3. Method
+
+In the following, we first describe our transformer-based model AnyCam, which directly predicts camera pose and intrinsics for video sequences. Further, we introduce an uncertainty-based training scheme, which enables training on large-scale dynamic video datasets without any ground truth labels, and a lightweight test-time refinement strategy.
+
+# 3.1. Preliminaries
+
+As input, our pipeline receives a sequence of  $n$  video frames  $\mathbf{I}^i\in ([0,1]^3)^\Omega ,i\in N$ , where  $N = \{1,\ldots ,n\}$  denotes the set of frame indices and  $\Omega = \{1,\dots ,H\} \times \{1,\dots ,W\}$  denotes the pixel lattice. Using off-the-shelf depth and optical flow predictors, we further obtain dense depth maps  $\mathbf{D}^i\in \mathbb{R}_+^{1\times H\times W}$ , as well as dense optical flows  $\mathbf{F}^{i\rightarrow j}\in \mathbb{R}^{2\times H\times W}$  from any frame  $i$  to  $j$ . We generally assume a simplified pinhole model that is constant for the duration of a sequence. Therefore, camera intrinsics for a video are modeled via a single focal length  $f\in \mathbb{R}_{+}$ . Let  $\pi_f(\mathbf{x}):\mathbb{R}^3\to \mathbb{R}^2$  be the corresponding projection function that maps a point  $\mathbf{x}\in \mathbb{R}^3$  in the camera's coordinate system to the respective pixel  $\mathbf{p}\in \mathbb{R}^2$  on the image plane parametrized by focal length  $f$ . Accordingly,  $\pi_f^{-1}(\mathbf{p},d):( \mathbb{R}^2,\mathbb{R}_+)\to \mathbb{R}^3$  denotes the unprojection function where  $d$  is the depth value for  $\mathbf{p}$ . Let  $\mathbf{P}^{i\rightarrow j}\in \mathrm{SE3}$  describe the relative camera pose, consisting of a rotation and translation, between frames  $i$  and  $j$ . To map a pixel location  $\mathbf{p}$  from frame  $i$  to frame  $j$  given the pixel's depth value  $d_{\mathbf{p}}$  in frame  $i$ , we write:
+
+$$
+\mathbf {p} ^ {\prime} = \pi_ {f} \left(\mathbf {P} ^ {i \rightarrow j} \pi_ {f} ^ {- 1} (\mathbf {p}, d _ {\mathbf {p}})\right) \tag {1}
+$$
+
+# 3.2. Transformer for Camera Prediction
+
+Camera pose and intrinsics are crucial for many 3D tasks. While SfM and SLAM can be highly accurate in well-posed, static environments, they are very sensitive to outliers. Therefore, dynamic objects pose a significant challenge to them. Not only do they make convergence to the
+
+correct solution more difficult, but they also often lead to catastrophic failures like loss of tracking or degenerate solutions. Different techniques were introduced to make the underlying optimizations more robust. These range from robust cost functions and RANSAC, to filtering out objects that could possibly move using off-the-shelf segmentation models. Nevertheless, these techniques are either hand-crafted, struggle to generalize across many domains, or present a significant computational overhead.
+
+This paper aims to build a robust camera pose estimation system that can readily be applied to any casual video. We base our design on three key insights:
+
+1. The space of plausible camera poses in videos is much more constrained than in general multi-view settings.  
+2. Strong, data-driven priors can help resolve ambiguities introduced by dynamic objects.  
+3. Incorporating information from all pixels instead of selected keypoints makes detecting outliers easier.
+
+Pose from a feed-forward network. For a natural video captured by a single camera, the space of plausible camera movements is well-constrained and continuous. This is especially true when also considering the temporal context of videos. However, this prior information is hard to inject into classical SfM and SLAM approaches [45]. Hand-crafted priors often fail to generalize to different domains and struggle to capture the full variety of plausible motions. On the other hand, when trained on large and diverse datasets, neural networks can learn strong priors over the distribution of plausible camera poses. This knowledge makes them robust to small outliers or noisy measurements and provides reliable generalization abilities. Therefore, we choose a neural network for the prediction of frame-to-frame poses.
+
+We rely on a transformer architecture, which as input receives frames  $\mathbf{I}^i$ , depth predictions  $\mathbf{D}^i$ , and flow predictions  $\mathbf{F}^{i\rightarrow i + 1}$  for a short sequence. First, a backbone extracts features for each timestep separately. Stacked self-attention layers allow the model to then exchange information between the frames, producing  $n - 1$  pose tokens  $\phi^{i\rightarrow i + 1}, i\in \{1,\dots ,n - 1\}$  and updated feature maps. Additionally, a single sequence token  $\phi^{\mathrm{seq}}$  is predicted.
+
+To decode the features, a frame prediction head  $\mathcal{H} = (\mathcal{H}^{\mathbf{P}},\mathcal{H}^{\sigma})$  outputs the 6DOF camera poses  $\mathbf{P}^{i\rightarrow i + 1}$  and pixel-wise uncertainty maps  $\sigma^i\in \mathbb{R}_+^\Omega$  for every timestep. A sequence head  $\mathcal{H}^{\mathrm{seq}}$  additionally determines a single set of camera intrinsics for the video. In the following, we explain how to robustly design these decoder heads.
+
+Robust intrinsics hypotheses. Camera intrinsics, which in our case are parametrized by focal length  $f$ , are notoriously difficult to disentangle from the camera movement. For example, the same motion pattern in the optical flow can be described by mostly rotation if the camera has a
+
+![](images/ee6863a0600c39347291f470d361e99bfc885f951a680973cd857d26feb881d9.jpg)  
+Figure 2. Architecture. AnyCam processes a sequence of frames from a casual video with corresponding depth maps and optical flow. A backbone extracts feature maps per image. Information sharing between frames is enabled by multiple attention layers that process the features of all sequence images. The transformer architecture outputs one pose token  $\phi^{i\rightarrow j}$  per timestep and an additional sequence token  $\phi^{\mathrm{seq}}$ . The pose tokens are processed using multiple intrinsic hypotheses  $f\in \{f_1,\dots ,f_m\}$ , parametrized by frame prediction heads  $(\mathcal{H}_f^{\mathbf{P}},\mathcal{H}_f^\sigma)$ . The sequence head  $\mathcal{H}^{\mathrm{seq}}$  predicts the likelihood scores of the different hypotheses. The model is trained end-to-end via a reprojection loss, a pose consistency loss between forward and backward pose predictions, and a KL-divergence loss.
+
+wide field of view or by mostly translation, if the field of view is narrow. Because camera intrinsics have such a major effect, designing a robust system to recover them is vital. While focal length could, in principle, also be predicted by the network directly, we find that it makes training unstable, and the network does not converge to a meaningful result
+
+Instead of considering the focal length as a free variable during training, we reformulate it as a property of the model itself. Considering a fixed set of  $m$  candidate focal lengths  $\{f_1,\dots ,f_m\}$ , we train  $m$  individual frame prediction heads  $\{\mathcal{H}_{f_1},\ldots ,\mathcal{H}_{f_m}\}$ . Every head  $\mathcal{H}_f$  predicts pose  $\mathbf{P}^{i\rightarrow i + 1}$  and uncertainty map  $\sigma_f^i$  under the assumption that the given sequence was captured with a camera of focal length  $f$ . For every candidate prediction, we later compute an individual loss. The sequence head  $\mathcal{H}^{\mathrm{seq}}$  learns likelihood scores  $\mathcal{P} = (\rho_{f_1},\dots ,\rho_{f_m})$  for the different candidates. The focal length and corresponding poses with the highest likelihood are the final output of the model.
+
+$$
+f _ {\text {f i n a l}} = \underset {f \in \left(f _ {1}, \dots , f _ {m}\right)} {\arg \max } \mathcal {P} \tag {2}
+$$
+
+This idea is similar to [34], but we use candidates as part of the model itself rather than only at the loss level.
+
+# 3.3. Dynamics-aware Pose Training
+
+We aim to train our model on large, unlabelled datasets. Here, our loss formulation follows two main objectives:
+
+1. Leveraging multi-view information to recover local camera motion between adjacent frames.  
+2. Using the context of longer sequences to learn realistic long-range camera motion patterns.
+
+Uncertainty-aware flow loss. Using the predicted relative pose  $\mathbf{P}_f^{i\rightarrow j}$  between two frames  $i$  and  $j$ , and the corresponding depth map  $\mathbf{D}^i$ , we can project all pixel locations
+
+$\mathbf{p}_{uv}$  from frame  $i$  into frame  $j$ . Subtracting the original pixel locations from the projected pixels locations  $\mathbf{p}_f^\prime$  yields the induced optical flow  $\hat{\mathbf{F}}_f^{i\rightarrow j}$ :
+
+$$
+\begin{array}{l} \hat {\mathbf {F}} _ {f, u v} ^ {i \rightarrow j} = \mathbf {p} _ {f, u v} ^ {\prime} - \mathbf {p} _ {u v} \tag {3} \\ = \pi_ {f} \left(\mathbf {P} ^ {i \rightarrow j} \pi_ {f} ^ {- 1} (\mathbf {p} _ {u v}, d _ {u v})\right) - \mathbf {p} _ {u v} \\ \end{array}
+$$
+
+Assuming a static world, the induced flow  $\hat{\mathbf{F}}_f^{i\rightarrow j}$  will match the reference optical flow  $\mathbf{F}^{i\rightarrow j}$  optimally if the predicted pose  $\mathbf{P}_f^{i\rightarrow j}$  and depth  $\mathbf{D}^i$  is as close to the real pose as possible. However, dynamic objects lead to inconsistencies in the reference optical flow, which would deteriorate gradients during optimization. From a statistical point of view, these inconsistencies cannot be captured via our flow induction formulation. Thus, we choose to model them via so-called aleatoric uncertainty and use the predicted uncertainty map  $\mathbf{U}_i$ . For a pair of frames  $i$  and  $j$ , this leads us to the following loss function:
+
+$$
+\ell_ {f, u v} ^ {\mathbf {F} ^ {i \rightarrow j}} = \left\| \hat {\mathbf {F}} _ {f, u v} ^ {i \rightarrow j} - \mathbf {F} _ {u v} ^ {i \rightarrow j} \right\| _ {1} \tag {4}
+$$
+
+$$
+\mathcal {L} _ {f} ^ {\sigma \mathbf {F} ^ {i \rightarrow j}} = - \frac {1}{| \Omega |} \sum_ {u v \in \Omega} \ln \frac {1}{\sqrt {2} \sigma_ {f , u v} ^ {i}} \exp - \frac {\sqrt {2} \ell_ {f , u v} ^ {\mathbf {F} ^ {i \rightarrow j}}}{\sigma_ {f , u v} ^ {i}} \tag {5}
+$$
+
+which is then summed up over every pair of neighboring frames within the sequence:
+
+$$
+\mathcal {L} _ {f} ^ {\sigma \mathbf {F}} = \sum_ {i = 1} ^ {n - 1} \mathcal {L} _ {f} ^ {\sigma \mathbf {F} ^ {i \rightarrow i + 1}} \tag {6}
+$$
+
+Intuitively, the model learns to downweight areas in the input frame where there will likely be a high loss, i.e. dynamic objects. In turn, the pose supervision signal mostly comes from areas that can likely be captured via the induced
+
+flow, i.e. static parts. In practice, the uncertainty map does not only make pose training more stable, but it can also be used in downstream tasks as a motion segmentation map. Finally, due to its dense nature, the loss is robust to small outliers, such as local inaccuracies of the reference flow.
+
+Learning camera motion patterns. While the flow loss  $\mathcal{L}_f^{\sigma \mathbf{F}}$  provides a strong training signal per frame, the model could, in theory, minimize the loss without considering adjacent frames. However, it is important for the model to also rely on the context of the entire sequence when predicting camera poses. For example, optical flow predictions for some frames could be inaccurate, or dynamic objects could occlude the relevant static part. We introduce an additional loss term and a dropout training strategy to make the model consider the entire sequence.
+
+We first leverage the fact that when reversing the sequence, the relative poses  $\mathbf{P}_f^{j\rightarrow i}$  between frames are the same as the inverted poses of the original sequence  $(\mathbf{P}_f^{i\rightarrow j})^{-1}$ . The model becomes more robust towards inaccurate inputs by enforcing consistency between the forward and backward pose predictions during training. We rely on a simple L1 loss, where  $\mathbf{I}_4$  is the  $4\times 4$  identity matrix:
+
+$$
+\mathcal {L} _ {f} ^ {\uparrow \downarrow} = \sum_ {i = 1} ^ {n - 1} \left\|\left(\mathbf {P} _ {f} ^ {i \rightarrow i + 1}\right) ^ {- 1} \mathbf {P} _ {f} ^ {i + 1 \rightarrow i} - \mathbf {I} _ {4} \right\| _ {1, 1} \tag {7}
+$$
+
+Furthermore, we utilize the temporal dependency of poses within a sequence. Given the overall trajectory, the model should learn strong motion priors. To encourage this, we apply a dropout scheme during training by setting values in the pose tokens to zero with probability  $p_{drop}$ . This encourages the network to exchange information between frames in the self-attention layers. The network needs to learn realistic motion patterns to overcome the noise injected by dropout. Note that applying dropout on the pose tokens does not affect the uncertainty map.
+
+Finding the best candidate. While the flow loss  $\mathcal{L}_f^{\sigma \mathbf{F}}$  is very effective for learning pose and uncertainty, it also serves as a helpful proxy. It indicates how well the model can reconstruct the observed optical flow using the predicted poses  $\mathbf{P}_f^{i\rightarrow j}$  and corresponding focal length  $f$ . After the model has converged during training, it will predict (close to) the optimal poses assuming focal length  $f$ .  $\mathcal{L}_f^{\sigma \mathbf{F}}$  now is mainly dependent on  $f$ . Thus, the magnitude of  $\mathcal{L}_f^{\sigma \mathbf{F}}$  during training reflects how close  $f$  is to the true but unknown actual focal length. We leverage this fact and train the sequence head  $\mathcal{H}^{\mathrm{seq}}$  to predict which of the focal candidates will yield the lowest flow loss.
+
+In practice, we find that, while correct on average, arg min on the different loss terms is too noisy to enable stable training. Therefore, we first convert the (inverted)
+
+flow loss terms to probability scores using softmax and then optimize the Kullback-Leibler divergence  $\mathbf{KL}_{\mathrm{div}}$ . Let  $\mathcal{P} = (\rho_{f_i},\dots,\rho_{f_m})$  be the output of  $\mathcal{H}^{\mathrm{seq}}$ :
+
+$$
+\mathcal {L} ^ {\text {I n t r}} = \mathbf {K L} _ {\mathrm {d i v}} \left(\mathcal {P}, \operatorname {s o f t m a x} \left(- \mathcal {L} _ {f _ {1}} ^ {\sigma \mathbf {F}}, \dots , - \mathcal {L} _ {f _ {m}} ^ {\sigma \mathbf {F}}\right)\right) \tag {8}
+$$
+
+Final loss. By combining all loss terms, we obtain the final training objective, through which our model learns poses, uncertainties, and intrinsic from unlabelled video sequences:
+
+$$
+\mathcal {L} = \sum_ {k = 1} ^ {m} \left(\lambda_ {\sigma \mathbf {F}} \mathcal {L} _ {f _ {k}} ^ {\sigma \mathbf {F}} + \lambda_ {\uparrow \downarrow} \mathcal {L} _ {f _ {k}} ^ {\uparrow \downarrow}\right) + \lambda_ {\text {I n t r}} \mathcal {L} ^ {\text {I n t r}} \tag {9}
+$$
+
+# 3.4. Test-time Refinement
+
+Our model predicts relative camera poses for a sequence of frames. This allows our model to be directly used as a visual odometry system by chaining the relative poses together:
+
+$$
+\mathbf {P} ^ {j} = \prod_ {i = 1} ^ {j} \mathbf {P} ^ {i \rightarrow i + 1} \tag {10}
+$$
+
+While this works well for short to medium-length sequences, it is prone to accumulating drift over a longer time. Small inaccuracies in earlier relative poses will propagate throughout the trajectory.
+
+We perform lightweight test-time refinement using bundle adjustment (BA) [41] to overcome this issue. By chaining multiple optical flow maps  $\mathbf{F}^{1\rightarrow i + 1}$ ,  $\mathbf{F}^{1 + 1\rightarrow i + 2}$ , ..., pixels can be tracked through multiple frames. We initialize the BA system with our predicted trajectory and then optimize over coarse pixel tracks in a sliding-window fashion. Crucially, the BA optimization requires the predicted uncertainty maps to downweigh pixel tracks on dynamic objects. For more details on the BA optimization, please refer to the supplementary material.
+
+# 4. Experiments
+
+In the following, we thoroughly evaluate the overall performance of our model regarding camera pose estimation and intrinsics recovery. We put a special focus on testing the zero-shot generalization capabilities of our network. Further, we also validate and demonstrate the effectiveness of our design choices.
+
+# 4.1. Setup
+
+Data. Our training formulation requires no labeled data and is robust towards dynamic objects and suboptimal image quality. This is a key benefit of our method, as dynamic videos with 3D labels are scarce. To highlight this strength, we rely on a diverse mix of datasets (YouTube-VOS [48], RealEstate10K [57], WalkingTours [42], OpenDV [49],
+
+<table><tr><td rowspan="2">Category</td><td rowspan="2">Method</td><td rowspan="2">No 
+Supervis.</td><td rowspan="2">Approx. 
+Runtime</td><td colspan="3">Sintel</td><td colspan="3">TUM-RGBD (dynamics)</td></tr><tr><td>ATE↓</td><td>RPEtrans ↓</td><td>RPErot ↓</td><td>ATE↓</td><td>RPEtrans ↓</td><td>RPErot ↓</td></tr><tr><td rowspan="3">w/ intrinsics*</td><td>DROID-SLAM [39]</td><td></td><td>&lt;2min</td><td>0.175</td><td>0.084</td><td>1.912</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DPVO [40]</td><td></td><td>&lt;2min</td><td>0.115</td><td>0.072</td><td>1.975</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LeapVO [5]</td><td></td><td>&lt;2min</td><td>0.089</td><td>0.066</td><td>1.250</td><td>0.068</td><td>0.008</td><td>1.686</td></tr><tr><td rowspan="4">w/o intrinsics</td><td>ParticleSfM [56]</td><td></td><td>&lt;20min</td><td>0.129</td><td>0.031</td><td>0.525</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MonST3R† [54]</td><td></td><td>&lt;2min</td><td>0.108</td><td>0.042</td><td>0.732</td><td>0.063</td><td>0.009</td><td>1.217</td></tr><tr><td>Robust-CVD [18]</td><td>✓</td><td>?</td><td>0.360</td><td>0.154</td><td>3.443</td><td>0.153</td><td>0.026</td><td>3.528</td></tr><tr><td>CasualSAM [55]</td><td>✓</td><td>&gt;1h</td><td>0.141</td><td>0.035</td><td>0.615</td><td>0.071</td><td>0.010</td><td>1.712</td></tr><tr><td></td><td>Ours w/o ref.</td><td>✓</td><td>&lt;20sec</td><td>0.099</td><td>0.045</td><td>0.567</td><td>0.095</td><td>0.025</td><td>1.050</td></tr><tr><td></td><td>Ours</td><td>✓</td><td>&lt;2min</td><td>0.078</td><td>0.031</td><td>0.427</td><td>0.056</td><td>0.005</td><td>0.927</td></tr></table>
+
+Table 1. Pose estimation in dynamic environments. Absolute trajectory error (ATE) and relative pose error for translation  $(\mathrm{RPE}_{\mathrm{trans}})$  and rotation  $(\mathrm{RPE}_{\mathrm{rot}})$  on the Sintel and TUM-RGBD (dynamics) datasets. We compare against other learning-based VO/SLAM systems. AnyCam achieves competitive performance against systems trained in a supervised manner as well as methods that have ground truth camera intrinsics available. We consistently outperform Robust-CVD and are on par with CasualSAM, which has a significantly higher runtime than AnyCam. *excluded from the evaluation. † concurrent work. Many measurements are taken over from [54].  
+
+<table><tr><td></td><td>Dataset</td><td>Source</td><td>Domain</td><td>Dyn.</td><td>Seq.</td><td>Frames</td></tr><tr><td rowspan="5">Train</td><td>YouTube-VOS</td><td>YouTube</td><td>Diverse</td><td>✓</td><td>3471</td><td>87K</td></tr><tr><td>RealEstate10K</td><td>YouTube</td><td>Indoor</td><td>✗</td><td>6929</td><td>90K</td></tr><tr><td>WalkingTours</td><td>YouTube</td><td>Outdoor</td><td>✓</td><td>278</td><td>53K</td></tr><tr><td>OpenDV</td><td>YouTube</td><td>Driving</td><td>✓</td><td>532</td><td>105K</td></tr><tr><td>EpicKitchens</td><td>GoPro</td><td>Ego</td><td>✓</td><td>167</td><td>100K</td></tr><tr><td rowspan="5">Test</td><td>Sintel</td><td>Blender</td><td>Synthetic</td><td>✓</td><td>14</td><td>629</td></tr><tr><td>TUM-RGBD</td><td>MoCap</td><td>Indoor</td><td>✓</td><td>8</td><td>720</td></tr><tr><td>Davis</td><td>YouTube</td><td>Diverse</td><td>✓</td><td>90</td><td>6118</td></tr><tr><td>Aria EA</td><td>Glasses</td><td>Ego</td><td>✓</td><td>30</td><td>19200</td></tr><tr><td>Waymo</td><td>Sensor Rig</td><td>Driving</td><td>✓</td><td>64</td><td>3067</td></tr></table>
+
+Table 2. Dataset Mix: We train our method on a diverse dataset mix obtained mostly from YouTube. Evaluation happens on unseen datasets. For many datasets, custom splits were used.
+
+EpicKitchens [6]) based on YouTube or individual GoPro capture, as shown in Tab. 2. None of the datasets has ground truth 3D labels (note that for some, Colmap was later applied to obtain proxy labels, but we do not use them). Following existing works on pose estimation in dynamic environments [5, 54, 56], we perform evaluation on the Sintel [3] and the dynamic subset of TUM-RGBD [35]. Furthermore, we test AnyCam qualitatively on three other datasets: Davis [27] (diverse videos from YouTube), Waymo [37] (autonomous driving), and Aria Everyday Activities [20].
+
+Implementation details. We rely on the recent UniDepth [28] and UniMatch [47] methods to obtain depth and flow maps. Our model is implemented in PyTorch and is initialized with a pretrained DinoV2 [25] ViT backbone. We train AnyCam in two stages with different sequence lengths, first 2 and then 8 frames. All frames are sampled at a resolution of  $336 \times 336$  from the videos in the datasets. During inference, we crop the input video to squares of 336 and pass sequences of up to 100 frames to the model at once. The model is configured to use 32 focal length candidates
+
+ranging from  $0.1H$  to  $3.5H$  where  $H$  is the image height. Training converges after 250k iterations at a batch size of 16 (seq. len 2) and 4 (seq. len 8) per GPU, and takes around two days on two NVIDIA A100 40GB GPUs per stage. For a video of 50 frames, it takes around 1) 15 seconds to obtain flows and depths, 2) 5 seconds for AnyCam to predict a trajectory, and 3) 90 seconds for test-time refinement. For more implementation details and hyperparameters, please refer to the supplementary material.
+
+# 4.2. Camera Pose Estimation
+
+We first test AnyCam's ability to recover camera trajectory in challenging environments and compare it to state-of-the-art methods in that domain. We group methods by the amount of data they require both during training and test time. SLAM and SfM systems for dynamic environments, like DPVO [40] and LeapVO [5], are trained with ground truth motion or trajectory data and mostly require camera intrinsics during test time. Methods like CasualSAM [55] require neither special training data nor intrinsics but are slow because they rely on much more costly test-time optimization. In comparison, AnyCam works in a feed-forward way, and optional test-time refinement is very lightweight.
+
+Our model achieves strong quantitative results throughout all benchmarks as shown in Tab. 1. The low relative pose errors for translation  $(\mathrm{RPE}_{\mathrm{trans}})$  and rotation  $(\mathrm{RPE}_{\mathrm{rot}})$ , even without test-time refinement, confirm that our model learns meaningful motion priors during training and generalizes to other datasets. In particular, this is noteworthy compared to specialized SLAM systems like LeapVO, which result in significantly higher local pose errors.
+
+However, when only relying on feed-forward predictions, our model can suffer from drift, denoted by a slightly higher absolute trajectory error (ATE). This is a result of chaining the predicted relative poses  $\mathbf{P}^{i\rightarrow j}$ , where small errors in earlier frames accumulate over time. Our test-time
+
+![](images/a74a28f1dfcd97863883182b03a452a0da041ae001667bcfd1d5e4ced04ccad3.jpg)
+
+![](images/cf934c304fba0bbf92d31c40d21216fe5f1a1f85c3727122270753d77b7b3d57.jpg)  
+Figure 3. Qualitative results on various datasets. Red: forward-pass prediction, Green: refined trajectory, Yellow: GT (if available). AnyCam is able to predict high-quality pose estimates on challenging scenes in dynamic environments. The uncertainty maps show objects with a high likelihood of movement, such as persons or cars, that would produce inconsistencies in the induced optical flow. Pose refinement with bundle adjustment further aligns the trajectory towards reducing the error compared to the ground truth poses.
+
+![](images/1670195153177f44a617052c3e349cc259e73152d489bc9090802311ef110fba.jpg)  
+Aria Everyday Activities
+
+![](images/b7f0a6b25511e3e0d8b73760b0bb12bc06f662cd5fd1ab8d80239e07882acecc.jpg)
+
+refinement effectively corrects for this by leveraging longer-range dependencies between frames. As a result, the drift is reduced, and AnyCam matches the ATE for some SLAM systems like LeapVO, which requires camera intrinsics.
+
+As can be seen in Tab. 1, AnyCam also generalizes to different domains like autonomous driving or egocentric vision. In particular, it works well in settings where classical SfM or SLAM systems are difficult to operate in. For example, in the first sequence of Aria Everyday Activities, a person enters a house via an opening door. Not only does the lighting change drastically, but also the 3D environment transforms as the door opens. Still, the camera motion trajectory is recovered correctly. During the second Waymo sequence, a vehicle moves in stop-and-go traffic. As can be observed in the uncertainty maps, AnyCam correctly identifies the moving vehicles on the left side as moving, while the uncertainty for the bus on the right is low. This indicates that the model actually relies on motion cues and not only on semantics, which would be the case when filtering out (potentially) moving objects with segmentation models.
+
+<table><tr><td>Method</td><td>AFEpx) ↓</td><td>RFE(%) ↓</td></tr><tr><td>UniDepth</td><td>447.4</td><td>0.357</td></tr><tr><td>Dust3r</td><td>434.0</td><td>0.364</td></tr><tr><td>Ours</td><td>252.2</td><td>0.181</td></tr></table>
+
+Table 3. Camera intrinsics estimation. We measure the mean absolute focal error (AFE) and mean relative focal error (RFE) across all sequences of the Sintel dataset.
+
+# 4.3. Infrinnsics Recovery
+
+For most casual videos, particularly when they originate from the internet, camera intrinsics are not available. Nevertheless, they are crucial for high-quality pose estimation and reconstruction. Therefore, we also evaluate the accuracy of the recovered focal length and report the results in Tab. 3. UniDepth predicts depth maps and focal length from a single image. Our superior performance against UniDepth (which provides the depth maps for AnyCam) suggests that our video-based training and inference offer benefits for fo
+
+![](images/788660635deadf209ad1488fc6e7ce439e8a2b1ffb775789043174696280dc73.jpg)
+
+![](images/c1740783c9db783838a8b1aed9e9faa81b9f00c7ea399f9c1a501a593dbdafbf.jpg)
+
+![](images/c7cce8ca69e68156aff9824ae69e221d30d29de49c07ef7e5029c5d11960a7b1.jpg)
+
+![](images/81f764015782da9982d531fe2bdaea95d9b4c02ea9cfc1840704cee1a0e78e36.jpg)
+
+![](images/aea83b9c2d318ec4f9674fd44032bc50cdd5618979b5547ed381a9c4f651842e.jpg)
+
+![](images/b0577599e686ff9d676a989ee4547911a63d293681f6dd5d2f1f49caf438c889.jpg)  
+Figure 4. Focal length candidates. Predicted likelihood and computed flow loss for different focal candidate (FL) hypotheses for two sequences of the Davis dataset. Below: Estimated trajectories for selected FL hypotheses increasing from left to right. Red trajectory shows the trajectory for the FL with the highest likelihood. The predicted likelihood tends to be more stable than the loss when estimating the best candidate.
+
+cal length recovery. While Dust3r also processes sequential frames, it is trained on classical multi-view settings and fails to generalize well to challenging dynamic scenarios.
+
+Additionally, we test our approach of training several prediction heads assuming different focal length candidates. As seen in Fig. 4, the individual heads predict significantly varying pose trajectories. For higher focal lengths on the right side, motion is modeled more through translation and only small rotations. The lower the focal length, the more the network predicts strong rotation. This highlights the importance of selecting the correct focal length candidate.
+
+In both examples, the predicted likelihood scores seem to pick a candidate that is very close to the actual focal length, and the selected trajectory is plausible. While the calculated loss is a very good indicator of which focal length is optimal, it can be noisy and is not guaranteed to always be correct. In the second example, the field-of-view is narrow, indicating a high focal length. However, the minimal loss is achieved for a fairly low focal length. We hypothesize that
+
+<table><tr><td colspan="2">Seq. len.</td><td colspan="2">Refinement</td><td colspan="3">Sintel</td></tr><tr><td>Train</td><td>Infer</td><td>Simple</td><td>Uncert</td><td>ATE↓</td><td>RPEtrans↓</td><td>RPErot↓</td></tr><tr><td>2</td><td>2</td><td></td><td></td><td>0.134</td><td>0.045</td><td>0.393</td></tr><tr><td>2</td><td>≥8</td><td></td><td></td><td>0.179</td><td>0.052</td><td>0.537</td></tr><tr><td>8</td><td>2</td><td></td><td></td><td>0.182</td><td>0.053</td><td>0.617</td></tr><tr><td>8</td><td>≥8</td><td></td><td></td><td>0.099</td><td>0.045</td><td>0.567</td></tr><tr><td>8</td><td>≥8</td><td>✓</td><td></td><td>0.136</td><td>0.036</td><td>0.440</td></tr><tr><td>8</td><td>≥8</td><td></td><td>✓</td><td>0.078</td><td>0.031</td><td>0.427</td></tr></table>
+
+Table 4. Model ablation on Sintel: We test the effect of 1) sequence length during training and inference, and 2) enabling refinement with or without uncertainty.
+
+the model learned to effectively filter out this noise, leading to a more stable and more accurate predictor compared to selecting the candidate with the lowest loss.
+
+# 4.4. Model Ablations
+
+Finally, we evaluate the design choices that went into our model and report the results in Tab. 4. First, we test whether AnyCam can learn meaningful priors from sequences. For this, a second model  $\text{AnyCam}_2$  trained only on sequences of length 2 (i.e. pairs of frames) is used as comparison. This model only predicts a single relative pose between the two frames and does not learn to use the context of longer sequences. The  $\text{RPE}_{\text{trans}}$  and  $\text{RPE}_{\text{rot}}$  metrics indicate that AnyCam can still perform accurate prediction between pairs of frames. However, the poor ATE results show that it leads to a noticeably higher drift. When passing a longer sequence to  $\text{AnyCam}_2$  at test time, the model cannot use this additional information and even gets confused, leading to overall poor results. Similarly, the final trajectory will suffer from drift when training with sequences of 8 frames but only passing pairs of frames to the model at inference. Only provided longer sequences, the model can utilize the learned priors, leading to improved overall scores.
+
+Additionally, we verify the effectiveness of our refinement strategy. Naive bundle adjustment struggles to provide an improvement, even when initialized with the predicted trajectory and focal length. Only when also weighing the pixel tracks through AnyCam's uncertainty, bundle adjustment can improve the overall trajectory quality.
+
+# 5. Conclusion
+
+AnyCam demonstrates that pose estimation and intrinsics recovery can effectively be performed by a feed-forward network with lightweight test-time refinement. It is possible to achieve competitive performance with supervised learning methods in the tasks of SfM and SLAM. Through a novel training pipeline, AnyCam can be trained on a large corpus of casual video data.
+
+Acknowledgements: This work was funded by the ERC Advanced Grant "SIMULACRON" (agreement #884679), the GNI Project "AI4Twinning", and the DFG project CR 250/26-1 "4D YouTube".
+
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+the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10371-10381, 2024. 2  
+[51] Lihe Yang, Bingyi Kang, Zilong Huang, Zhen Zhao, Xiaogang Xu, Jiashi Feng, and Hengshuang Zhao. Depth anything v2. arXiv preprint arXiv:2406.09414, 2024. 2  
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\ No newline at end of file
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+# AnyDressing: Customizable Multi-Garment Virtual Dressing via Latent Diffusion Models
+
+Xinghui Li<sup>1</sup> Qichao Sun<sup>1</sup> Pengze Zhang<sup>1</sup> Fulong Ye<sup>1</sup> Zhichao Liao<sup>2</sup>
+
+Wanquan Feng $^{1\dagger}$  Songtao Zhao $^{1\dagger}$  Qian He $^{1}$
+
+<sup>1</sup>Bytedance Intelligent Creation Tsinghua University
+
+https://crayon-shinchan.github.io/AnyDressing/
+
+![](images/a1fc0e7b5fb856c4c13d18df9ec43d868ec598a6241c625fb1190a1b6fcccb3d.jpg)  
+"A girl, red hair, wearing a hat, by a fence"
+
+![](images/64ce7b1dbaccfba9c822ca863b0e1ac0b3afbf9379eba47d6d914317745c57f5.jpg)  
+"A man with sunglasses, in the mountains"
+
+![](images/8a8ebf56db484b7362688797357e9ada7604379301557c4cfc98733e300c5132.jpg)  
+Reliability  
+"A girl, in front of the Eiffel Tower"
+
+![](images/f649ae447ef7f5118a94b654cc71072a05461582fbb685e8ff4798b6a0f05362.jpg)  
+Realistic Scenes
+
+![](images/278a2ff25ba7cc5657aa6ff729450239e2cedcaef7d8e4bd788681a0750d0126.jpg)
+
+![](images/8fa45db334a1e9724bff870319bd94042a349abc23286525b341451fb3453987.jpg)  
+"A girl, in the gym"
+
+![](images/f6c3ab0e6a0cfa5d9b7c62d80ddd1499c23e9a7e784ed81c4734e3424711275f.jpg)  
+"A girl in the forest"
+
+![](images/9ac7b510413cabef6a80cac152a952aece28b71c36deeecaacca919fd3be1afa.jpg)  
+"A girl, holding flowers"
+
+![](images/95c5ec3d3a95328c0fe55b96a5eb427daac89aa60344c8d6c5fb590e946b0294.jpg)
+
+![](images/99c2e04cf5543ddb443c7233b7c3537f5be9b74c7bca69ed60aa3cc85be27de3.jpg)
+
+![](images/cc334f93f9ffbc355dc5a984f728dba0868207b24df8b75025c1c73d2c9f73df.jpg)
+
+![](images/3dd3971ddf3e88853d89cbb344798028ae7335f419d9784772a27f86afd459a7.jpg)
+
+![](images/b6f7445e86cefcdfeaf2253d2d650fde7416a18359cd291c76f8b1d82d996e66.jpg)  
+Stylized Scenes  
+"A girl, yellow hair, in the city"
+
+![](images/85f68214063ea8096700206c94a0591df0c6f46aae7aa016605b8152c4300499.jpg)
+
+![](images/97db270f1f0016a40f6df4c6589df4e5528c4c0a5a3586ad56a487810f86c888.jpg)  
+"A girl, in the playground, holding the balloons"
+
+![](images/7070ad1948f27d1ef929aad5550323a71a7d578a2f7f842b3ace999b034fab5b.jpg)  
+"A girl, sitting in the hallway"
+
+![](images/9a9f478aaa624beb2dde77b87c8d1d5c34a1ff85d70f6ddbc5ab5ed8a9fa7cd4.jpg)  
+Complex Garment
+
+![](images/6fa21f17c0d12f458af471e46e0416cb74125d432b893131674d283ec7dc3c18.jpg)
+
+![](images/e671e43b6faa1dee6d00fc09c2a779cfd084e0fd9a94cdc07c826ddb8202e243.jpg)  
+"A girl, in the snow"
+
+![](images/b1894f45e348e0b962a3fc47333cb3f5231ba49ec71141088754a10ffb5a979b.jpg)  
+with ControlNet & IP-Adapter-FaceID  
+Compatibility  
+"A man, sky, in a field of flowers"  
+Figure 1. Customizable virtual dressing results of our AnyDressing. Reliability: AnyDressing is well-suited for a variety of scenes and complex garments. Compatibility: AnyDressing is compatible with LoRA [16] and plugins such as ControlNet [55] and FaceID [54].
+
+![](images/5ab999475d4081be0ae628d930923d9762da5912728e9a6938d4c4c1b3acb633.jpg)
+
+![](images/ff1b746ddd03af767ba8b46e0cc80a081c98df57904818efd640acf6e5d09ba3.jpg)  
+"A man, on the moon"
+
+![](images/9a853a730c88b5fa0de1bc4b2de083c29d04812355dbf1266b3837616ef32efb.jpg)
+
+![](images/e60241fe322cdc58abc82baaa2b119c5423040d6c796dcae2e99c1e844a98a9e.jpg)  
+"A girl with a bag in the classroom"
+
+![](images/904b6abf59a0da5fdb85ab808e5bf3a98024372936529b336823213b28af46f6.jpg)
+
+![](images/bd1cfdfa608315037285efd99b6a11bc9dac0178358bfb64754b42af9d3eb407.jpg)
+
+![](images/51965a199ab2f72dac77caa246935e348d551b0ff3c32b75692005f3b47ff968.jpg)
+
+![](images/63b499535008229aeb85f09bb06c1da6e01b881c1a07e66830214b89cc2389ef.jpg)  
+with LoRA  
+"Saiyans, sitting, in the city"  
+$\frac{1 + u}{1} - \frac{u}{1} = \frac{\left( {1 + u}\right) u}{1} < \frac{u}{1} = u$
+
+![](images/b4079508d9e13eeb2df56c32302c2fc1aaa5f393369cf2b9de5440094d072e0f.jpg)
+
+![](images/eae509692ba0b76308120ace9d3b1b727f963ecc393decc77d8625449bdd4701.jpg)  
+"Crayon Shin-chan, doll"
+
+# Abstract
+
+Recent advances in garment-centric image generation from text and image prompts based on diffusion models are impressive. However, existing methods lack support for various combinations of attire, and struggle to preserve the garment details while maintaining faithfulness to the text prompts, limiting their performance across diverse scenarios. In this paper, we focus on a new task, i.e., Multi-
+
+Garment Virtual Dressing, and we propose a novel AnyDressing method for customizing characters conditioned on any combination of garments and any personalized text prompts. AnyDressing comprises two primary networks named GarmentsNet and DressingNet, which are respectively dedicated to extracting detailed clothing features and generating customized images. Specifically, we propose an efficient and scalable module called Garment-Specific Feature Extractor in GarmentsNet to individually encode garment textures in parallel. This design prevents garment confusion while ensuring network efficiency. Meanwhile,
+
+we design an adaptive Dressing-Attention mechanism and a novel Instance-Level Garment Localization Learning strategy in DressingNet to accurately inject multi-garment features into their corresponding regions. This approach efficiently integrates multi-garment texture cues into generated images and further enhances text-image consistency. Additionally, we introduce a Garment-Enhanced Texture Learning strategy to improve the fine-grained texture details of garments. Thanks to our well-craft design, AnyDressing can serve as a plug-in module to easily integrate with any community control extensions for diffusion models, improving the diversity and controllability of synthesized images. Extensive experiments show that AnyDressing achieves state-of-the-art results.
+
+# 1. Introduction
+
+In recent years, the field of image generation has experienced transformative advancements [3, 9, 21], particularly with methods based on Latent Diffusion Models (LDMs) achieving remarkable success in text-to-image generation tasks [10, 15, 37, 38, 40, 41, 45]. Considering only textual information is inadequate for image customization, numerous approaches incorporate reference images with textual descriptions for image generation [24, 39, 49]. Specially, the Virtual Dressing (VD) task of generating garment-centric human images based on the reference garments has sparked considerable research interest [4, 42, 48], due to its significant potential in e-commerce and creative design.
+
+VD is used to be regarded as a subtask of traditional subject-driven image customization, prior approaches [11, 19, 24, 30, 39, 43, 46, 57] simply integrate the features of reference image into the text embeddings without fully exploiting the information from the reference image. Several subsequent works [32, 54] more comprehensively utilize the features of the reference image by training additional cross-attention layers to integrate reference image features into the diffusion model. However, these methods struggle to preserve the intricate textures of the garment. Recently, some methods [4, 42, 48] focus on garment-centric image generation. Most of them leverage a full copy of diffusion U-Net as the garment encoder named ReferenceNet to maintain fine-grained garment information. DreamFit [29] proposes a lightweight encoder, which utilizes trainable LoRA layers to extract garment features instead of finetuning a full copy of the UNet. Nevertheless, these methods are tailored exclusively to single items of clothing and lack support for multiple conditions, thus hindering the ability to freely dress in any combination of various garments.
+
+In this work, our focus is on a new task Multi-Garment Virtual Dressing, personalizing a character wearing any combination of target garments according to the customized text prompt or other controls. The task poses several chal
+
+lenges, including: 1) Garment fidelity: preventing confusion among multiple garments while preserving the intricate textures of each; 2) Text-Image consistency: minimizing the influence of multiple garments on irrelevant regions to ensure the faithfulness of the generated images to the text prompts; 3) Plugin compatibility: enabling seamless integration with community control plugins for LDMs.
+
+To address the aforementioned issues, we propose AnyDressing, a novel approach that customizes characters conditioned on any combination of garments and any personalized text prompts. AnyDressing primarily comprises two primary networks named GarmentsNet and DressingNet. The GarmentsNet leverages a core Garment-Specific Feature Extractor (GFE) module to extract multi-garment detailed features, which utilizes parallelized self-attention layers within a shared U-Net architecture to individually encode garment textures. And we employ LoRA mechanism within the self-attention layers to further reduce the parameter increase associated with the added garments. The GFE module not only avoids clothing blending but also ensures network efficiency, allowing for easy scalability to any number of garments. The DressingNet employs a Dressing-Attention (DA) mechanism to seamlessly integrate multigarment features into the denoising process. To ensure that each garment instance focuses specifically on its corresponding region, we further introduce a novel Instance-Level Garment Localization (IGL) learning strategy in DA. This avoids influencing other irrelevant regions in the synthetic image, thus improving fidelity to customized text prompts. Additionally, to enhance texture details, we design a Garment-Enhanced Texture Learning (GTL) strategy that strengthens the supervision of attire by imposing constraints from perceptual features and high-frequency information.
+
+Extensive experiments show that AnyDressing has certain advantages in the quantitative and qualitative results compared to state-of-the-art methods. Especially, AnyDressing can serve as a plugin compatible with various finetuned LDMs, customized LoRAs [16], and other extensions such as ControlNet [55] and IP-Adapter [54], enhancing the diversity and controllability of synthetic images. In summary, our contributions are as follows:
+
+- We propose a novel GarmentsNet to efficiently capture multi-garment textures in parallel by employing a core Garment-Specific Feature Extractor.  
+- We design a novel DressingNet incorporating a Dressing-Attention mechanism and an Instance-Level Garment Localization Learning strategy to accurately inject multi-garment features into their corresponding regions.  
+- We introduce a Garment-Enhanced Texture Learning strategy to effectively enhance the fine-grained texture details in synthetic images.  
+- Our framework can seamlessly integrate with any community control plugins for diffusion models. Both quan
+
+titative and qualitative experimental results demonstrate the superiority of our AnyDressing.
+
+# 2. Related Work
+
+Latent Diffusion Models. Latent Diffusion Models (LDMs) [33, 38] have become widely used in text-to-image generation tasks. Recent advancements have focused on making generated content more stable and controllable. For instance, ControlNet [55] and T2I Adapter [36] introduced additional conditioning modules injecting control into the denoising U-net via extra branches, such as edges and pose. Additionally, large model fine-tuning methods like LoRA [16] have significantly enhanced LDMs' generative capabilities in specific scenarios. In this work, we can integrate with various fine-tuned LDMs and customized LoRAs to enhance the diversity of generated images.
+
+Subject-Driven Image Generation. Subject-driven generation aims to produce content that aligns with the visual features of a reference image. Methods for this task can be categorized into Tuning-based methods [11, 13, 24, 39] and Tuning-free methods [18, 22, 26, 28, 32, 50, 51, 54, 56]. Tuning-based methods, such as DreamBooth [39] and Custom-Diffusion [24] require optimizing specific text tokens to represent target concepts using a limited set of subject images. On the other hand, Tuning-free methods generally encode the reference image into feature embeddings. FastComposer [51] integrates image features into text embeddings, while IP-Adapter[54] and SSR-Encoder[56] integrate image features into the denoising U-net through a decoupled cross-attention mechanism. However, these methods struggle to preserve the fine-grained texture.
+
+Virtual Try-On. Virtual Try-On (VTON) aims to synthesize an image of a specific person wearing a desired garment. Early methods [5, 14, 20, 25, 27, 34, 47, 52] utilize generative adversarial networks (GANs) with two-stage strategy, which rely on an explicit warping module and struggle to handle complex backgrounds. Recent studies [6, 12, 23, 35, 53] have used pre-trained LDMs as priors for VTON tasks. LADI-VTON [35] and DCI-VTON [12] explicitly deform the clothes and then use diffusion models to fuse and refine them. Rencent works [6, 23, 53] employ parallel U-Nets for clothing feature extraction and inject features into a denoising U-Net. However, VTON is essentially a localized image editing task and requires an existing model image, lacking flexibility in application scenarios.
+
+Virtual Dressing. Virtual Dressing (VD) [4, 42, 48] aims to generate freely editable human images with reference garments and optional conditions. StableGarment [48] and IMAGDressing [42] leverage a garment U-Net for extracting fine-grained clothing features and a denoising U-Net with a hybrid attention module to incorporate garment features into denoising process. Magic Clothing [4] additionally proposes a joint classifier-free guidance to balance the
+
+control of garment features and text prompts. DreamFit [29] proposes a lightweight garment encoder based on trainable LoRA layers to streamline model complexity and memory usage. However, existing approaches are limited to processing single items of clothing, and difficult to maintain fidelity to text prompts. In contrast, our method allows for freely dressing multiple garments and produces coherent and attractive images following customized text prompts.
+
+# 3. Preliminaries
+
+Stable Diffusion. The Diffusion Model belongs to a class of generative models that generate data through iterative denoising from random noise. In this paper, we specifically employ Stable Diffusion [38]. Stable Diffusion is a latent diffusion model that operates in the latent space of an autoencoder  $\mathcal{D}(\mathcal{E}(\cdot))$ , where  $\mathcal{E}$  and  $\mathcal{D}$  represent the encoder and decoder, respectively. For a given image  $\mathbf{x}_0$  with its corresponding latent feature  $\mathbf{z}_0 = \mathcal{E}(\mathbf{x}_0)$ , the diffusion forward process is defined as:
+
+$$
+\mathbf {z} _ {t} = \sqrt {\alpha_ {t}} \mathbf {z} _ {0} + \sqrt {1 - \alpha_ {t}} \epsilon , \tag {1}
+$$
+
+where  $\alpha_{t} = \prod_{s=1}^{t}(1 - \beta_{s})$ ,  $\epsilon \sim \mathcal{N}(0,1)$ , and  $\beta_{s}$  is the pre-defined variance schedule at timestep  $s$ .
+
+In the diffusion backward process, a U-Net  $\epsilon_{\theta}$  is trained to predict the noise. Given the textual condition  $\mathbf{C}$ , the training objective  $\mathcal{L}_{LDM}$  is defined as follows:
+
+$$
+\mathcal {L} _ {L D M} = \mathbb {E} _ {\mathbf {z} _ {0}, \epsilon , \mathbf {C}, t} \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, \mathbf {C}, t) \| _ {2}. \tag {2}
+$$
+
+# 4. Methodology
+
+Given  $N$  target garments, the proposed AnyDressing aims to generate a new image  $x_{dr}$ , showcasing a customized character dressed in multiple target garments across various scenes, styles and actions based on the text prompt. As illustrated in Fig. 2, AnyDressing comprises two primary networks: GarmentsNet and DressingNet. The GarmentsNet leverages the GFE module to extract detailed features from multiple garments (Sec. 4.1). Meanwhile, the DressingNet integrates these features for virtual dressing using a DA module and an IGL learning mechanism (Sec. 4.2). Additionally, a GTL strategy is designed further to enhance crucial texture details in the synthesis images (Sec. 4.3). Next, we will introduce the aforementioned modules, along with training and inference processes (Sec. 4.4), in detail.
+
+# 4.1. GarmentsNet
+
+Previous methods [4, 42, 48] leverage a full copy of diffusion U-Net [2, 17] as garment encoding network, ensuring precise preservation of clothing details. However, these methods are limited to handling a single garment and face
+
+![](images/167385e22d73882a9401c6eae1289be95e7edb545be48e8ce1ce0f2136745979.jpg)  
+Figure 2. Overview of AnyDressing. Given  $N$  target garments, AnyDressing customizes a character dressed in multiple target garments. The GarmentsNet leverages the Garment-Specific Feature Extractor (GFE) module to extract detailed features from multiple garments. The DressingNet integrates these features for virtual dressing using a Dressing-Attention (DA) module and an Instance-Level Garment Localization Learning mechanism. Moreover, the Garment-Enhanced Texture Learning (GTL) strategy further enhances texture details.
+
+significant garment confusion issues when applied to multi-garment virtual dressing, as shown in Fig. 3. A straightforward approach to dress multiple garments is to simply duplicate several garment encoding networks to manage different conditions. However, this method would result in a substantial increase in the number of parameters, making it computationally impractical.
+
+Drawing inspiration from the successful practice of the aforementioned reference mechanisms, we observe that self-attention layers are crucial for the implicit warping of features, enabling the effective matching of input garments to the appropriate body parts. Meanwhile, other layers are typically responsible for general feature extraction and can be shared across different garments without compromising the model's performance. Building on this insight, we innovatively design a simple yet effective architecture named GarmentsNet, which employs a core GFE module to encode features for each garment utilizing individual self-attention layers within a shared U-Net framework. Inspired by [29], we integrate LoRA [16] mechanism into self-attention layers, minimizing the increase in parameters associated with the added garments. As a result, this design significantly avoids garment blending while maintaining network efficiency. As illustrated in Fig. 2, the GFE module employs a parallelized self-attention mechanism to extract detailed features of multiple garments. Specifically, for each garment condition  $\mathbf{F}_i$ , we define the proprietary self-attention LoRA matrix  $\triangle \hat{\mathbf{W}}_i = \{\triangle \hat{\mathbf{W}}_q^i,\triangle \hat{\mathbf{W}}_k^i,\triangle \hat{\mathbf{W}}_v^i\}$
+
+where  $\triangle \hat{\mathbf{W}}_q^i$ ,  $\triangle \hat{\mathbf{W}}_k^i$  and  $\triangle \hat{\mathbf{W}}_v^i$  represent LoRA layers for the query, key and value projections of self-attention layers. We then concatenate self-attention results of each garment condition to obtain the aggregated garment features  $\mathbf{F}_{new}$ :
+
+$$
+\mathbf {F} _ {n e w} ^ {i} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {i} \left(\mathbf {K} _ {i}\right) ^ {\top}}{\sqrt {d}}\right) \mathbf {V} _ {i}, \tag {3}
+$$
+
+$$
+\mathbf {F} _ {n e w} = \operatorname {C o n c a t} \left(\mathbf {F} _ {n e w} ^ {1}, \mathbf {F} _ {n e w} ^ {2}, \dots , \mathbf {F} _ {n e w} ^ {N}\right), \tag {4}
+$$
+
+where  $\mathbf{Q}_i = \mathbf{F}_i(\hat{\mathbf{W}}_q + \triangle \hat{\mathbf{W}}_q^i)$ ,  $\mathbf{K}_i = \mathbf{F}_i(\hat{\mathbf{W}}_k + \triangle \hat{\mathbf{W}}_k^i)$ ,  $\mathbf{V}_i = \mathbf{F}_i(\hat{\mathbf{W}}_v + \triangle \hat{\mathbf{W}}_v^i)$ , only  $\triangle \hat{\mathbf{W}}$  is trainable and  $N$  represents the number of reference garments.
+
+Thanks to the multi-garment parallel processing design of our GFE module, GarmentsNet can seamlessly scale to any number of garments. Notably, this expansion requires only some newly added LoRA matrix  $\triangle \hat{\mathbf{W}}$ , and significantly minimizes both training and inference time compared with duplicating the entire garment encoding network. Considering the capability of GFE module to individually encode each garment, we excise the cross-attention modules in GarmentsNet to further reduce redundancy.
+
+# 4.2. DressingNet
+
+To incorporate multi-garment features during the diffusion process, we meticulously design the DressingNet, which serves as the main denoising net and primarily includes an adaptive Dressing-Attention mechanism and an Instance-Level Garment Localization Learning strategy.
+
+# 4.2.1 Adaptive Dressing-Attention
+
+In the VD task, the main denoising network is typically kept frozen during training [4, 42] to preserve its original editing and generation capabilities as much as possible. To incorporate reference garment features into latent features, we design an adaptive Dressing-Attention (DA) mechanism to efficiently integrate multi-garment texture cues into synthetic images, inspired by [54]. As shown in Fig. 2, the Dressing-Attention module includes a frozen self-attention module and a learnable cross-attention module. Let  $\{\mathbf{F}_1,\mathbf{F}_2,\dots ,\mathbf{F}_N\}$  denote  $N$  garment features output by the GarmentsNet at corresponding positions, we first concatenate these features along the spatial dimension to obtain the final garment features:  $\mathbf{F}_{all} =$  Concat  $(\mathbf{F}_1,\mathbf{F}_2,\dots ,\mathbf{F}_N)$ . We then introduce two trainable linear projection layers  $\mathbf{W}_k^{\prime}$  and  $\mathbf{W}_v^\prime$  to align garment features with latent feature  $\mathbf{Z}$ . Formally, the output of Dressing-Attention  $\mathbf{Z}_{new}$  is:
+
+$$
+\mathbf {Z} _ {\text {n e w}} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top}}{\sqrt {d}}\right) \mathbf {V} + \lambda * \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \left(\mathbf {K} ^ {\prime}\right) ^ {\top}}{\sqrt {d}}\right) \mathbf {V} ^ {\prime} \tag {5}
+$$
+
+where  $\lambda$  is a hyperparameter ensuring the flexibility of incorporating garment features, and  $\mathbf{Q} = \mathbf{Z}\mathbf{W}_q$ ,  $\mathbf{K} = \mathbf{Z}\mathbf{W}_k$ ,  $\mathbf{V} = \mathbf{Z}\mathbf{W}_v$ ,  $\mathbf{K}' = \mathbf{F}_{all}\mathbf{W}_k'$ ,  $\mathbf{V}' = \mathbf{F}_{all}\mathbf{W}_v'$ . Here,  $\mathbf{W}_q$ ,  $\mathbf{W}_k$  and  $\mathbf{W}_v$  are frozen self-attention layers. To accelerate the coverage, we initialize the  $\mathbf{W}_k'$ ,  $\mathbf{W}_v'$  with  $\mathbf{W}_k$ ,  $\mathbf{W}_v$ .
+
+# 4.2.2 Instance-Level Garment Localization Learning
+
+Although the above Dressing-Attention (DA) mechanism facilitates the integration of multi-garment features, it may result in text-image inconsistency. We argue that this results from the garment's attention map covering the entire image in the DA module, thereby injecting garment cues into the other irrelevant regions incorrectly. To tackle this issue, we introduce an Instance-Level Garment Localization (IGL) learning strategy, ensuring that each garment instance focuses solely on its corresponding region. Specifically, for each garment feature, we obtain its attention map  $A$  with the latent noise in each layer of the DA module:
+
+$$
+P = \operatorname {S o f t m a x} \left(\mathbf {Q} \left(\mathbf {K} ^ {\prime}\right) ^ {\top} / \sqrt {d}\right), \tag {6}
+$$
+
+$$
+A = \sum_ {j = 1} ^ {L} P _ {j}, \tag {7}
+$$
+
+where  $L$  denotes the length of corresponding garment features. Then, a regularization term  $L_{loc}$  is applied to explicitly learn attention localization for each garment instance:
+
+$$
+\mathcal {L} _ {l o c} = \frac {1}{N} \sum_ {k = 1} ^ {N} \| A _ {k} - M _ {k} \| _ {2}, \tag {8}
+$$
+
+where  $N$  is the number of garments in the reference image, and  $M_{k}$  represents the reference garment's segmentation mask. It is worth noting that the proposed IGL learning strategy is applied exclusively during the training phase and does not introduce any additional cost during inference.
+
+# 4.3. Garment-Enhanced Texture Learning
+
+Generally, diffusion models are merely optimized relying on the mean-squared loss defined in Eqn. 2, which treats all regions of the synthetic image equally, resulting in a struggle to maintain garment consistency, especially in cases of small text and intricate patterns. To synthesize fine-grained textures, we design a Garment-Enhanced Texture Learning (GTL) strategy to strengthen the supervision of attire details in image space, incorporating a perceptual loss  $\mathcal{L}_{\text{perc}}$  and a high-frequency loss  $\mathcal{L}_{\text{high-freq}}$ .
+
+Before introducing the proposed two losses, we define the generated image as:  $\hat{I} = \mathcal{D}(\hat{\mathbf{z}}_0)$ , where  $\mathcal{D}$  denotes the VAE decoder, and  $\hat{\mathbf{z}}_0$  is estimated through a single step of inference from the latent  $\mathbf{z}_t$ :
+
+$$
+\hat {\mathbf {z}} _ {0} = \frac {\mathbf {z} _ {t} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\theta}}{\sqrt {\alpha_ {t}}}. \tag {9}
+$$
+
+Considering the one-step inference may produce noisy and flawed images, the proposed losses are only applied at less noisy timestep  $(t\leq \eta)$ . To sum up, GTL can be defined as:
+
+$$
+\mathcal {L} _ {\text {t e x t u r e}} = \left\{ \begin{array}{l l} \mathcal {L} _ {\text {p e r c}} + \mathcal {L} _ {\text {h i g h - f r e q}}, & t \leq \eta \\ 0, & t > \eta \end{array} . \right. \tag {10}
+$$
+
+Perception Loss To simultaneously enhance structural consistency and pattern similarity with reference garments, we employ a perceptual loss based on the Deep Image Structure and Texture Similarity (DISTS) metric [7]. Specifically, we use the reference garment's segmentation mask to isolate the attire in both the generated and ground truth images, averaging their structural and textural inconsistencies within a perceptual feature space, defined as:
+
+$$
+\mathcal {L} _ {p r e c} = \frac {1}{N} \sum_ {k = 1} ^ {N} \mathcal {D I S T S} (\hat {I} \odot M _ {k}, I \odot M _ {k}), \tag {11}
+$$
+
+where  $\odot$  signifies element-wise multiplication.
+
+High-Frequency Loss As intricate details in the dressing garments typically appear as high-frequency components with rich edge information, we use edge detection to extract this high-frequency information, aiming to strengthen the constraints on detailed patterns. Specifically, we utilize Canny operator [8] to capture these rich-texture regions, the high-frequency loss  $\mathcal{L}_{high - freq}$  is defined as:
+
+$$
+\mathcal {L} _ {\text {h i g h - f r e q}} = \frac {1}{N} \sum_ {k = 1} ^ {N} \| \hat {I} \odot M _ {k} ^ {\prime} - I \odot M _ {k} ^ {\prime} \| _ {2}, \tag {12}
+$$
+
+where  $M_k' = M_k \odot P$ ,  $P$  is the extracted edge map of  $I$ .
+
+<table><tr><td rowspan="3">Method</td><td colspan="8">Single Grament</td><td colspan="4">Multiple Graments</td></tr><tr><td colspan="4">VITON-HD [5]</td><td colspan="4">Proprietary Dataset</td><td colspan="4">Dressing-Pair</td></tr><tr><td>CLIP-T ↑</td><td>CLIP-I ↑</td><td>CLIP-AS ↑</td><td>DINO ↑</td><td>CLIP-T ↑</td><td>CLIP-I ↑</td><td>CLIP-AS ↑</td><td>DINO ↑</td><td>CLIP-T ↑</td><td>CLIP-I* ↑</td><td>CLIP-AS ↑</td><td>DINO* ↑</td></tr><tr><td>IP-Adapter [54]</td><td>0.268</td><td>0.644</td><td>5.674</td><td>0.500</td><td>0.272</td><td>0.632</td><td>5.678</td><td>0.460</td><td>0.277</td><td>0.523</td><td>5.795</td><td>0.350</td></tr><tr><td>StableGarment [48]</td><td>0.285</td><td>0.583</td><td>5.781</td><td>0.522</td><td>0.281</td><td>0.587</td><td>5.648</td><td>0.510</td><td>0.284</td><td>0.556</td><td>5.735</td><td>0.412</td></tr><tr><td>MagicClothing [4]</td><td>0.288</td><td>0.640</td><td>5.703</td><td>0.363</td><td>0.298</td><td>0.619</td><td>5.784</td><td>0.340</td><td>0.266</td><td>0.583</td><td>5.540</td><td>0.290</td></tr><tr><td>IMAGDressing [42]</td><td>0.202</td><td>0.734</td><td>5.077</td><td>0.553</td><td>0.230</td><td>0.684</td><td>5.133</td><td>0.453</td><td>0.242</td><td>0.614</td><td>5.291</td><td>0.378</td></tr><tr><td>Ours</td><td>0.289</td><td>0.741</td><td>5.881</td><td>0.571</td><td>0.296</td><td>0.710</td><td>5.931</td><td>0.559</td><td>0.296</td><td>0.734</td><td>5.874</td><td>0.674</td></tr></table>
+
+# 4.4. Training and Inference
+
+In training, we average  $\mathcal{L}_{loc}$  across all  $m$  layers and define overall loss  $\mathcal{L}$  as follows:
+
+$$
+\mathcal {L} _ {L D M} = \mathbb {E} _ {\mathbf {z} _ {0}, \epsilon , \mathbf {C} _ {t}, \mathbf {C} _ {g}, t} \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, \mathbf {C} _ {t}, \mathbf {C} _ {g}, t) \| _ {2}, \tag {13}
+$$
+
+$$
+\mathcal {L} = \mathcal {L} _ {L D M} + \frac {\lambda_ {1}}{m} \mathcal {L} _ {l o c} + \lambda_ {2} \mathcal {L} _ {t e x t u r e}, \tag {14}
+$$
+
+where  $\mathbf{C}_t$  and  $\mathbf{C}_g$  represent text condition and clothing condition respectively. In the inference stage, we apply classifier-free guidance during the denoising process:
+
+$$
+\hat {\epsilon} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {C} _ {t}, \mathbf {C} _ {g}, t\right) = \omega \epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {C} _ {t}, \mathbf {C} _ {g}, t\right) + (1 - \omega) \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t\right). \tag {15}
+$$
+
+# 5. Experiments
+
+# 5.1. Setup
+
+Dataset. Notably, a dataset comprising image triplets that include model images paired with multiple laid-out garments is currently lacking. Therefore, we utilize a HumanParsing model to extract clothing items from DressCode [34] and an additional proprietary dataset collected from the internet, forming triplet data pairs (upper garment, lower garment, person image). In these triplets, one garment is an original laid-out image, while the other is a segmented image from the person's image. Finally, we construct 26,114 public triplets from Dresscode and 37,065 triplets from proprietary dataset to train AnyDressing. For model evaluation, we introduce two benchmarks to evaluate the model on single-garment and multi-garment dressing respectively. Specifically, for single-garment evaluation, we select 300 reference garments from VITON-HD [5] encompassing various styles and colors, and additionally collect 300 diverse garments with intricate textures from the internet. For multi-garment evaluation, we meticulously gather 25 lowers from the internet and pair each with 10 different uppers, resulting in 250 pairs named Dressing-Pair.
+
+Implementation Details. In our experiments, we initialize the weights of GarmentsNet and DressingNet with the weights of the U-Net in Stable Diffusion v1.5 [38]. Our model is trained on paired images at the resolution of  $768 \times 576$ . The trainable parameters are GarmentsNet and the cross-attention layers in Dressing-Attention module. During training, We adopt AdamW [31] optimizer with
+
+Table 1. Quantitative comparisons with baseline methods for both single-garment and multi-garment evaluation.  
+
+<table><tr><td>Method</td><td>Texture Consistency</td><td>Align with Prompt</td><td>Image Quality</td><td>Comprehensive Evaluation</td></tr><tr><td>IP-Adapter [54]</td><td>0.45%</td><td>6.65%</td><td>11.95%</td><td>2.20%</td></tr><tr><td>StableGarment [48]</td><td>1.60%</td><td>4.85%</td><td>2.65%</td><td>2.05%</td></tr><tr><td>MagicClothing [4]</td><td>2.05%</td><td>9.00%</td><td>9.70%</td><td>3.75%</td></tr><tr><td>IMAGDressing [42]</td><td>2.10%</td><td>2.50%</td><td>3.90%</td><td>1.70%</td></tr><tr><td>Ours</td><td>93.80%</td><td>77.00%</td><td>71.80%</td><td>90.30%</td></tr></table>
+
+Table 2. User study with baseline methods.
+
+a fixed learning rate of 5e-5. The model is trained for 100k steps on 8 NVIDIA A100 GPUs with a batch size of 4. During inference, we use DDIM [44] sampler with 30 steps and set guidance scale  $\omega$  to 6.0. Please refer to the supplementary materials for more details.
+
+Baselines. We compare our method against the following state-of-the-art image synthesis method: IP-Adapter [54], MagicClothing [4], StableGarment [48] and IMAGDressing [42]. We use the official model parameters from their official implementations. For a fair comparison, all experiments are conducted with the resolution of  $768 \times 576$ .
+
+Evaluation Metrics. We follow previous methods to adopt three metrics for evaluation: CLIP-T for text-image similarity, CLIP-I and DINO for garment consistency, and CLIP Aesthetic Score (CLIP-AS) for overall generation quality. Especially, to better evaluate multi-garment dressing, we introduce new metrics  $\mathrm{CLIP - I^{*}}$  and  $\mathrm{DINO^{*}}$  to assess texture consistency by leveraging OpenPose [1] to obtain the matching partitions of the reference garments in the synthesized image and averaging their corresponding metrics.
+
+# 5.2. Qualitative Analysis
+
+Since the compared methods lack multi-garment support, we obtain baseline results by concatenating multiple garments along the spatial dimension as input. Fig. 3 presents visual comparisons between our method and baseline approaches. AnyDressing maintains superior consistency in clothing style and texture, and exhibits better text fidelity, while other methods struggle to balance garment preservation and prompt faithfulness. In particular, baselines encounter significant background contamination and garment confusion in multi-garment dressing results, whereas our method demonstrates exceptional reliability, which is attributed to our designed GarmentsNet and DressingNet architectures. And Fig. 4 presents the results of AnyDressing as a plug-in module combined with other extensions and
+
+![](images/a036bf551052b3398fb18c089be94c1f9a9471fcd409695c0b8a8c8e3d229e3a.jpg)  
+Figure 3. Qualitative comparisons with state-of-the-art methods. Please zoom in for more details.
+
+customized LoRAs, demonstrating its powerful compatibility. Please refer to the supplementary for more results.
+
+# 5.3. Quantitative Comparisons
+
+Metric Evaluation. Tab. 1 shows the quantitative results of our methods against baselines. For single-garment evaluation, extensive experiments conducted on VITON-HD [5] and proprietary dataset prove the superiority of AnyDressing compared with all baselines. And our method significantly surpasses all baselines across all metrics in multi-garment virtual dressing results, fully demonstrating AnyDressing's reliability in handling both single-garment and
+
+multi-garment virtual dressing tasks.
+
+User Study. We conduct a user study to evaluate the generation quality of our model. We use all test garments and prompts in our dataset and randomly show the users 25 single-garment results and 25 multi-garment results from the baselines and our method. Each participant is asked to select the most preferred result under four criteria: texture consistency, alignment with the text prompt, image quality and comprehensive evaluation. In the end, we receive valid responses from 40 users. The collected preferences are reported in Tab. 2. In terms of four criteria, our method is preferred by most participants, with percentages reaching
+
+![](images/e3d010e6edc57aecc0d840c4cc12ceb85182414f736eb6fcec8c4ca6d65a36e1.jpg)  
+Figure 4. Examples of plug-in results of AnyDressing.
+
+<table><tr><td>GFE</td><td>IGL</td><td>GTL</td><td>CLIP-T ↑</td><td>CLIP-I* ↑</td><td>CLIP-AS ↑</td></tr><tr><td>×</td><td>×</td><td>×</td><td>0.260</td><td>0.625</td><td>5.572</td></tr><tr><td>✓</td><td>×</td><td>×</td><td>0.265</td><td>0.718</td><td>5.627</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>0.289</td><td>0.722</td><td>5.790</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>0.296</td><td>0.734</td><td>5.874</td></tr></table>
+
+Table 3. Ablation study of AnyDressing.
+
+93.80%, 77.00%, 71.80% and 90.30% respectively.
+
+# 5.4. Ablation Studies
+
+GFE & IGL. To validate the effectiveness of our proposed architecture, we employ traditional ReferenceNet [17] to encode multiple garments concurrently and then incorporate them into the denoising U-Net similar to [42] as our base model. As illustrated in Fig. 5, Base+GFE significantly reduces garment confusion and improves garment consistency compared to Base, which is attributed to the multi-garment parallel processing design of the GFE module. Base+GFE+IGL shows better fidelity to the text prompts and further mitigates background contamination, which demonstrates IGL mechanism effectively constrains garment features to attend to the correct regions. The quantitative comparison in Tab. 3 further proves the effectiveness of each module, with GFE primarily improving the CLIP-I* and IGL enhancing both CLIP-T and CLIP-AS.
+
+GTL. Fig. 6 intuitively demonstrates the effectiveness of our proposed GTL strategy, encouraging the model to enhance detail preservation, particularly in small text and in
+
+![](images/d109dd1c765f4b09fe890f10b155b04d04e0d53d4cc766baea92451e193af063.jpg)  
+Figure 5. Ablation results on GFE and IGL modules.
+
+![](images/7654ad6ba94d466ffbf2c6c40f0e2b03a5fe6575b6fc30e477274f9e2730be44.jpg)  
+Figure 6. Ablation results on GTL module.
+
+tricate patterns. And quantitative result in Tab. 3 also verifies that our designed GTL improves texture consistency.
+
+# 6. Conclusion
+
+This paper presents AnyDressing comprising two core networks named GarmentsNet and DressingNet to focus on a new task, i.e., Multi-Garment Virtual Dressing. The GarmentsNet employs a Garment-Specific Feature Extractor module to efficiently encode multi-garment features in parallel. The DressingNet integrates these features for virtual dressing using a Dressing-Attention module and an Instance-Level Garment Localization Learning mechanism. Additionally, we design a Garment-Enhanced Texture Learning strategy to further enhance texture details. Our approach can seamlessly integrate with any community control plugins. Extensive experiments show that AnyDressing achieves state-of-the-art results.
+
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+# AnyEdit: Mastering Unified High-Quality Image Editing for Any Idea
+
+Qifan Yu $^{1*}$  Wei Chow $^{1*}$  Zhongqi Yue $^{2}$  Kaihang Pan $^{1}$  Yang Wu $^{3}$  Xiaoyang Wan $^{1}$  Juncheng Li $^{1\dagger}$  Siliang Tang $^{1}$  Hanwang Zhang $^{2}$  Yueting Zhuang $^{1\dagger}$
+
+$^{1}$ Zhejiang University,  $^{2}$ Nanyang Technological University,  $^{3}$ Ant Group
+
+{yuqifan, 3210103790, kaihangpan, junchengli, siliang, yzhuang}@zju.edu.cn
+
+nickyuezhongqi@gmail.com, wy306396@antgroup.com
+
+https://dcd-anyedit.github.io/
+
+# Abstract
+
+Instruction-based image editing aims to modify specific image elements with natural language instructions. However, current models in this domain often struggle to execute complex user instructions accurately, as they are trained on low-quality data with limited editing types. We present AnyEdit, a comprehensive multi-modal instruction editing dataset, comprising 2.5 million high-quality editing pairs spanning over 20 editing types and five domains. We ensure the diversity and quality of the AnyEdit collection through three aspects: initial data diversity, adaptive editing process, and automated selection of editing results. Using the dataset, we further train a novel AnyEdit Stable Diffusion with task-aware routing and learnable task embedding for unified image editing. Comprehensive experiments on three benchmark datasets show that AnyEdit consistently boosts the performance of diffusion-based editing models. This presents prospects for developing instruction-driven image editing models that support human creativity.
+
+# 1. Introduction
+
+With the development of multi-modal datasets [26, 40] and generative frameworks [11, 17], recent text-to-image generation (T2I) models [2, 3, 32, 37-39, 48, 51] have shown promising results in generating high-fidelity photo-realistic images. To enhance the controllability of generated images, image editing [7, 10, 19, 27, 42, 61] aims to modify desired target elements and retain unrelated contents, which has achieved significant improvements for T2I models. More recently, instruction-based image editing [5, 6, 10, 19, 48] pave the way to conveniently edit images using natural language instructions without complex descriptions or region
+
+specific masks. However, the scarcity of high-quality instruction editing datasets makes it difficult to develop powerful instruction-guided image editing models.
+
+Despite several prior works [5, 14, 15, 41, 49, 54, 57] showcasing promising instruction-following editing datasets and achieving effective results, they still struggle with drawbacks due to limited editing types and low data quality. These methods lack support for editing instructions based on complex multi-modal perception (e.g., spatial composition [59], viewpoint [53], commonsense understanding [4]) and reference-based editing instructions (e.g., customization [8, 47], image transfer [55]), limiting the model's ability to understand interleaved editing instructions and robustly execute a wide variety of editing tasks. To address the above limitations, this work, AnyEdit, first provides a comprehensive catalog of editing instructions and systematically introduces a unified editing framework for various editing tasks. As shown in figure 1, AnyEdit is divided into five classes based on editing capabilities, with each class containing multiple task types. Regarding the general editing scenarios in previous work [15, 54, 57], AnyEdit categorizes them into Local Editing and Global Editing based on their granularity to construct more precise instructions. To accommodate the editing intentions for spatial perception, we further include Camera Movement Editing. For commonsense understanding, we introduce Implicit Editing, which replaces direct intentions with more complex instructions that require imaginative thinking. In addition, to accommodate reference inputs from the visual modality, we incorporate Visual Editing to construct multi-modal editing instructions.
+
+Although AnyEdit has enriched editing types, there exist three principal challenges for high-quality dataset collection: (1) First, we observe that current editing datasets overlook inherent data biases when preparing initial imagedataset pairs [13, 31, 50], leading to an imbalance of concepts within the dataset. For instance, "change the tree in the
+
+![](images/69ea06b3d49977bd3d80158b140f5aa2dd53ececed04574cacaca1b1fef2f913.jpg)  
+Local Editing  
+Erase the tower near the bridge  
+Replace the bicycle with a scooter
+
+![](images/9172ccdd1eeccc5afdb3986396371ccfd920f73c5ae2128c000cb90f723f4c12.jpg)
+
+![](images/c2af2061797dfae289703d969c2aa3f2ccba1103e343a5fa02e7b6da8b623c66.jpg)  
+Include a bike in front of the garage
+
+![](images/05f7fb7b09391019be0ff01904be7a58e85111d4dd3bbc41fb352b2a2f72ad45.jpg)  
+Make the bus a fire truck
+
+![](images/9cfa3d6e4faa69ac22e2be884ef54ff810aed1c534794c55841bccc20c24c37b.jpg)  
+Chan of ze  
+ge the action bra to jumping
+
+![](images/57bc89594b19df7258643db762d7adb962ad9d3be95bd1a2fbc3043fefbf5ad0.jpg)  
+Replace 'EAT' with 'DINE
+
+![](images/47b96dd1b3bb02334670543f0f1e9e23461709d8d3f88ef517af988f7f3d7b8a.jpg)  
+Turn the TV to pink
+
+![](images/b0277a570d05609d56b50b6bcb0b477d2b7ba48eea7223e6c996ee6814183895.jpg)  
+Increase pears from two to three  
+Change the material of elephants like leather.
+
+![](images/1dccfcab8e97f2fc7bf3ab341dbe2592410deee33de70daaca1b6b7c1416c500.jpg)
+
+![](images/fb1dcff3802d1c6d161d7966126373a4b5ce68b9585d95bd3732fa0a9167da5c.jpg)  
+Visual Editing  
+Material Transfer  
+Change the material of the hat as [V*]
+
+![](images/495643af38d5979eba2fef7807f28304383f38ccdff750f04e5f72e73fe2580b.jpg)  
+Visual Reference  
+Replace the child with a  $[V^{*}]$
+
+![](images/713c8a47d3b06f527ce4aa17f997f61c61008419ae15b7952a306493d930bc48.jpg)  
+Visual Depth  
+Make the image follow the depth map [V*]
+
+![](images/98529e7f6b2114de354fc4ee4ec907e166a39e112db40d2aba84c2c792cedfba.jpg)  
+Visual Sketch  
+Alter the dog with sketch  $[\mathbf{V}^{*}]$  as object
+
+![](images/395d8de8bcc06abaf8ac81452f78fe1ab3658643a87d09dfe232b4065ecbef61.jpg)  
+Visual Segment  
+Erase the bench like segment image [V*]
+
+![](images/f115c13795a478a756b07302d2f4cc762aa2291badc5e42b05bda0eacefd8046.jpg)  
+Visual Scribble  
+Follow the given scribble  $[V^{*}]$  to replace the cat
+
+![](images/eabe757b64f9868657af28d23148f7923d7182c247ba932737f508ba9e5e0918.jpg)  
+Visual Layout  
+Follow the given layout  $[V^{*}]$  to erase the object
+
+![](images/17074adab43a83901698462cf90c99840b697d2c86c320e291c3f8b77592e3a3.jpg)  
+Camera Movement Editing  
+Move the man in the image
+
+![](images/581646b31287b88427dbb555cb9b6ec9e85b9222f0b8ef371589ae0714b5757a.jpg)  
+Complete the image as possible you can
+
+![](images/d23babdfe394908ac6f636bf588d5f788d463e13e693c38847bff3bada7ec803.jpg)  
+Turn the vessel clockwise
+
+![](images/1cd6d9e79deec951528320e1da589f3345d36e048254f00268910c1d2f64ed7b.jpg)  
+Minify the giraffe in the image
+
+![](images/c3a3ad5193c0fb3a35e99ea8aa57e5e324c4dfe1ed1f9e64e547a9d1d6f9838d.jpg)  
+Global Editing  
+Turn the background to prosperous city
+
+![](images/426cf42b0d1714a85452fc86401d50a4da5afff19871675e27141331ab5cca80.jpg)  
+Change the weather to foggy  
+1. p.
+
+![](images/979cf3b67a7efa24a441df7cb2582ed74842898afdf6e6aecc46fae1bde9bcf5.jpg)  
+Change to Chinese watercolor painting
+
+![](images/982c76fe6bb132fcba923b1ebf7dda7e5781c6bdff5d156bab3a87ca9b7b7596.jpg)  
+Implicit Change  
+Relation Change  
+Switch the location of the cat and dog  
+(a) AnyEdit Dataset Collection Visualization Examples
+
+![](images/55309b8f1bd03e49c1f4258ca236020845543752c6ae019c6736a37170a6a301.jpg)  
+Implicit Change  
+What will happen if the man can't catch the wave?
+
+![](images/30c93c6e0d8ee0d72ddc87a6e05d02518aef9add88f291870901c29059c2af87.jpg)  
+(b) AnyEdit Dataset Collection Distribution  
+Figure 1. Examples of AnyEdit at scale. We comprehensively categorize image editing tasks into 5 groups based on different editing capabilities: (a) Local Editing which focuses on region-based editing (green area); (b) Global Editing which focuses on the full range of image rendering (yellow area); (c) Camera Move Editing which focuses on viewpoints changing instead of scenes (gray area); (d) Implicit Editing which requires commonsense knowledge to complete complex editing (orange area); (e) Visual Editing which encompasses additional visual inputs, addressing the requirements for multi-modal editing (blue area).
+
+park to a camel' may bring undesired sand because "sand" and "camel" frequently co-occur in the training data. Thus, we introduce counterfactual synthetic scenes to enrich realworld data with tail concepts and their diverse combinations, achieving a balanced distribution of concepts in the dataset and enhancing generalization in editing tasks. (2) Secondly, current data collection methods struggle to accommodate diverse input formats and editing requirements due to the shared pipeline for all instructions. Therefore, we propose an adaptive editing pipeline that automatically selects the appropriate data pipeline for each task. (3) Third, there exist inherent drawbacks in the collected triplets of original images, edit instructions, and edited images due to the randomness of generation (i.e., low resolution [40], high noise [18], and misalignment between text and images [43, 45]). Thus, we develop an instruction validation pre-filter and image assessment post-filter strategy to filter out unsatisfactory results. In this way, AnyEdit automatically comprises  $2.5\mathrm{M}$  high-quality editing data across 25 distinct editing types (c.f., Tab. 1), showing a  $28.9\%$  improvement in visual similarity and  $18.8\%$  in semantic sim
+
+ality over SOTA datasets (c.f., Tab. 3). This automated process opens up the possibility of scaling the high-quality editing dataset in a low-resource manner.
+
+To fully harness the potential of AnyEdit's high-quality editing data, we propose a novel AnyEdit Stable Diffusion approach (AnySD) that employs task-aware routing and learnable task embeddings to support various editing types within AnyEdit, thereby constructing a robust instruction-based editing model for handling diverse editing requests. The task-aware routing mechanism leverages AnyEdit's diverse data to adjust the granularity of editing (e.g., local object or global style), while the learnable task embedding coordinates the inherent complexity across tasks within AnyEdit. In this way, AnySD fully harnesses the comprehensive and diverse data from AnyEdit to set new records on the MagicBrush and Emu-Edit benchmarks.
+
+Furthermore, to facilitate a comprehensive evaluation of instruction-based image editing, we manually curate a challenging benchmark, AnyEdit-Test, from our automatically collected AnyEdit dataset, comprising 1,250 high-quality editing pairs in diverse scenarios, across 25 distinct cate
+
+<table><tr><td rowspan="2">Editing Dataset</td><td rowspan="2">#Size</td><td rowspan="2">#Types</td><td colspan="5">Instruction Type</td><td colspan="3">Target Scenario</td><td rowspan="2">Open Source</td></tr><tr><td>Local</td><td>Global</td><td>Camera Movement</td><td>Implicit</td><td>Visual</td><td>Real Image</td><td>Synthetic Image</td><td>Synthetic Scene</td></tr><tr><td>MagicBrush [54]</td><td>10K</td><td>5</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>×</td><td>✓</td></tr><tr><td>InstructPix2Pix [5]</td><td>313K</td><td>4</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>✓</td></tr><tr><td>EMU-Edit [41]</td><td>-</td><td>8</td><td>✓</td><td>✓</td><td>×</td><td>✓</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>×</td></tr><tr><td>HQ-Edit [21]</td><td>197K</td><td>6</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>✓</td></tr><tr><td>SEED-Data-Edit [15]</td><td>3.7M</td><td>6</td><td>✓</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>✓</td><td>✓</td><td>×</td><td>✓</td></tr><tr><td>EditWorld [49]</td><td>8.6K</td><td>1</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>×</td><td>✓</td><td>×</td><td>×</td><td>✓</td></tr><tr><td>UltraEdit [57]</td><td>4M</td><td>9</td><td>✓</td><td>✓</td><td>×</td><td>×</td><td>×</td><td>✓</td><td>✓</td><td>×</td><td>✓</td></tr><tr><td>AnyEdit</td><td>2.5M</td><td>25</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+gories (50 per category). We notice that (1) Existing models often fail to properly modify or cause distortions in complex tasks (e.g., action change shown in Fig. 5), exposing the limitations of current benchmarks for complex tasks. (2) Even for common tasks in AnyEdit-Test, some previous SOTA models show a notable performance drop compared to existing benchmarks (e.g., DINO's decline in global editing in Tab. 5), revealing the limitations of current benchmarks in multi-scene editing. This highlights the critical role of AnyEdit-Test in thoroughly assessing the capabilities of editing models. We will release it for public research.
+
+Our main contributions are summarized as follows:
+
+- We systematically categorize various editing instructions in a novel perspective and innovatively introduce a unified editing framework that leverages an adaptive editing pipeline to automatically collect diverse high-quality editing data across different scenarios in a scalable way.  
+- We construct a multi-type, multi-scene dataset, AnyEdit, and its corresponding benchmark AnyEdit-Test for instruction-based editing in various scenarios, comprising 25 distinct and complex editing types to accommodate broader requirements of real-world editing.  
+- We use our proposed AnySD to fully unlock the potential of AnyEdit, achieving SOTA improvements in instruction adherence and image fidelity across diverse editing types.
+
+# 2. Related Work
+
+Table 1 compares the existing Instruction-based image editing datasets including InstructPix2Pix [5], MagicBrush [54], EMU-Edit [41], HQ-Edit [21], SEED-DataEdit [15], EDITWORLD [49], and UltraEdit [57]. Among these, the first four datasets use automatic methods to collect data, while the latter three incorporate human curation. InstructPix2Pix [5] utilizes P2P [19] for image editing, which makes it only suitable for synthetic images. MagicBrush [54] hires crowd workers to annotate images from the MSCOCO [26] dataset manually but only includes 10K editing pairs due to expensive labor expenses. HQ-Edit[21] also lacks fine-grained details and realism due to its diptych generation though it exploits GPT-4V [1] and DALLE [3] to enhance descriptions. Both of them are lack of generalization. With the advancements in multi-modal understanding [22-25, 33-35, 52] and generation [9, 16, 36, 46],
+
+Table 1. Comparison of existing image editing datasets. "Real Image" means the original images are from real world, "Synthetic Image" means they are from T2I models, "Synthetic Scene" indicates both images and captions are generated to address the inherent data bias.  
+
+<table><tr><td>Dataset</td><td>#Samples</td><td>#Concepts</td><td>License</td><td>Annotator</td></tr><tr><td colspan="5">Real World Image Caption Paired Dataset</td></tr><tr><td>MS COCO [26]</td><td>123,287</td><td>80</td><td>CC BY 4.0</td><td>Human</td></tr><tr><td>MVIImgNet [53]</td><td>31,783</td><td>238</td><td>CC BY 4.0</td><td>Human</td></tr><tr><td>LLaVA-CC3M-Pretrain [28]</td><td>519,176</td><td>31423</td><td>Custom</td><td>GPT-4V</td></tr><tr><td colspan="5">Counterfactual Synthetic Scene Pair Dataset</td></tr><tr><td>AnyEdit-Composition</td><td>22,936</td><td>500</td><td>Custom</td><td>Composition</td></tr></table>
+
+Table 2. Data preparation details for AnyEdit dataset collection.
+
+SEED-Data-Edit [15] and UltraEdit [57] have been recently introduced to enrich the types and turns of image editing. However, they only focus on traditional editing tasks, neglecting more complex and customized editing needs. Although EMU-Edit [41] and EditWorld [49] endeavor to simulate physical world editing, they lack a unified definition of implicit editing. Moreover, these datasets fail to incorporate viewpoint changes and support multi-modal inputs. In AnyEdit, we combine five distinct groups of data, covering 25 editing types, which will be released to help the community. It is worth noting that AnyEdit is the only dataset that considers the data bias and introduces counterfactual synthetic scenes to balance the distribution of the dataset.
+
+# 3. AnyEdit
+
+# 3.1. Editing Type Definition
+
+To equip instruction-based editing models with comprehensive capabilities to follow any creative ideas, we compiled a multi-modal image editing dataset AnyEdit for instruction-based image editing, consisting of 2.5M high-quality editing pairs across five primary domains, as illustrated in Fig. 1. The dataset comprises editing tasks divided into five main categories, each containing various editing types: (1) Local editing: add, remove, replace, color alter, appearance alter, material change, action change, textual change, and counting. (2) Global editing: background change, tone transfer, and style change. (3) Camera movement editing: rotation change, out-painting, movement, and resize. (4) Implicit editing: implicit change and relation change. (5) Visual editing: visual reference, material transfer, and visual conditions (i.e., depth, segmentation, scribble, sketch, mask). Specifically, local editing targets specific areas of an image without altering unrelated semantic content, while global editing affects the entire image. Camera movement editing extends this concept by manipulating the viewpoint of specific objects or the whole content within the scene. Furthermore, implicit editing involves hidden changes in
+
+![](images/b826e2e7e44b6fffac872e0924913f9b1145acfdebdf1c5e96909600374d2a60.jpg)  
+Figure 2. The comprehensive construction pipeline of AnyEdit. We summarize the general pipeline into five steps: (1) General data preparation from real-world image-text pairs and synthetic scenes. (2) Diverse instruction generation using LLM to produce high-quality editing instructions. (3) Pre-filtering for instruction validation. (4) Adaptive editing pipeline tailors specific editing methods for each edit type to generate high-quality edited images. (5) Image quality assessment ensures high-quality editing pairs for the AnyEdit Dataset.
+
+state or interaction patterns that require comprehension. Visual editing, on the other hand, incorporates additional visual inputs as references alongside editing instructions. Figure 1(a) shows examples of various editing types in each category and their detailed definitions are in Appendix B.1.
+
+# 3.2. Automatic Dataset Collection
+
+General Data Preparation. Previous studies have demonstrated that high-quality initial images facilitate the diversity of editing image creation [15, 57]. To address real-world user demands for image editing in complex scenarios, we collect  $\sim 680\mathrm{K}$  real-world image-caption pairs from annotated datasets (i.e., MSCOCO [26], LLaVACC3M-Pretrain [28]) and multi-view image datasets (i.e., MVImgNet [53]). Then, we enrich those brief captions by MLLMs (e.g., VILA [25]) for the completeness of the descriptions. However, these image-text pairs suffer from inherent data bias, leading to the model falling short in domains not well covered by general knowledge [13, 31]. Thus, we introduce the Counterfactual Synthetic Scene Pair Dataset to balance the data distribution of the initial imagedtext pairs. Specifically, we collect infrequent tail concepts from internet data and combine multiple concepts and contexts to generate a description by LLaMA-3B [12]. Subsequently, we invoke off-the-shelf T2I models to produce the initial images. In this manner, we enrich the original dataset by incorporating rare concept combinations, resulting in  $\sim 700\mathrm{K}$  high-quality and diverse image-caption pairs for the AnyEdit dataset collection, as illustrated in Table 2.
+
+Diverse Instruction Generation. It aims to create varied editing instructions and corresponding edited caption outputs based on the caption of the initial image. As illustrated in Figure 2, we leverage the public Llama3-8b [12] model to convert original captions to diverse editing instructions. To address the limitations in instruction diversity and consistency when generating editing instructions, we integrate intuitive type constraints with LLM generation and employ in-context examples to develop a task-specific agent tailored to each editing type. Furthermore, we integrate the generated editing instructions with the original captions to create
+
+instruction pairs, which serve as in-context examples for iterative self-enhancement, thereby gradually increasing the diversity and complexity of the instructions. Details of the prompt constraints and examples are in Appendix B.2.
+
+Adaptive Editing Pipelines. Traditional instruction-editing datasets [41, 57] rely on fixed pipelines [19] or time-consuming manual filtering, making it difficult to efficiently generate high-quality edited images for complex editing types and various input formats. Here we propose an adaptive view of editing pipelines that customizes the edited image according to the specific type of editing. Specifically, we design 9 core pipelines for generating local, global, camera movement, implicit, and visual editing data. During image editing generation, we input editing instruction pairs along with the original images and their variants into the adaptive editing pipeline. The pipeline dynamically selects tailored solutions based on the editing type to generate images that align with the intended edits. Additionally, we incorporate extra constraints (e.g., dilated masks, layouts, and geometry guidance) into the U-Net layers within the diffusion process to achieve more precise semantic alignment and artifact reduction. Full details of the image construction process for each editing type can be found in Appendix B.3.
+
+Data Quality Enhancement. Since the quality of editing data is critical for robust editing model training in AnyEdit, we further introduce a comprehensive filtering strategy for data quality enhancement. It consists of two steps: instruction validation pre-filter and image quality post-filter.
+
+(i) Instruction Validation Pre-filter. We notice that partial editing instructions from LLMs sometimes introduce ambiguities that adversely impact the edited image (e.g., changing appearance in "color alter" editing or changing action of the static desk in "action change" editing). Simultaneously, low-quality initial images (e.g., low resolution, bad aspect ratio, lack of aesthetics) consistently lead to unsatisfactory editing results, even after time-consuming rounds of selection. Thus, we employ task-specific heuristic rules to validate various instructions, ensuring consistency and performing aesthetic evaluations to guarantee that aesthetically
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="2">Semantic Similarity</td><td colspan="2">Visual Similarity</td></tr><tr><td>CLIPin</td><td>CLIPout</td><td>SSIM</td><td>DINOv2</td></tr><tr><td>IP2P [5]</td><td>0.2650</td><td>0.2694</td><td>0.5826</td><td>0.6859</td></tr><tr><td>UltraEdit [57]</td><td>0.2834</td><td>0.3049</td><td>0.6401</td><td>0.7231</td></tr><tr><td>AnyEdit (Ours)</td><td>0.3288</td><td>0.3133</td><td>0.6638</td><td>0.9053</td></tr></table>
+
+Table 3. Overall dataset quality comparison between AnyEdit and other datasets using automatic semantic and visual metrics.
+
+balanced images are used for the editing process.
+
+(ii) Image Quality Post-filter. After collecting all the editing results, we conducted an automatic data evaluation to filter out unsatisfactory images that did not meet the criteria for data generation. First, we utilize CLIP filtering metrics [41, 57] to assess the alignment between edited images  $I_{e}$  and their output captions  $T_{e}$ , ensuring consistency with editing instructions and desired modifications in target regions. Subsequently, we utilize CLIP image similarity to compare the original image  $I_{o}$  and the edited image  $I_{e}$ , ensuring the fidelity of unedited image elements at the pixel level. Additionally, we compute the L1 distance between  $I_{o}$  and  $I_{e}$  to maintain the global structure of the original images. Finally, we employ CLIP directional similarity [54], which quantifies the alignment between modifications in images and the associated changes in captions, to verify the AnyEdit's instruction-following capability. We further apply the object detector to validate the presence of edited objects (in Local Editing) and the VLM to assess the modification of global images (in Global Editing).
+
+# 3.3. Characteristics and Statistics
+
+Benefiting from our promising automated dataset collection approach, AnyEdit comprises 2.5 million high-quality editing pairs across 25 distinct editing types. AnyEdit encompasses a broader range of domains, including complex editing tasks such as viewpoint editing, implicit editing, and visual editing, and it incorporates a richer variety of scenes, including conceptually rich synthetic scenes (c.f., Tab. 1). Moreover, the data distribution of AnyEdit in Fig. 1(b) reflects a broad variety of edit types, with coverage across domains. Quantitatively, we assess AnyEdit's data quality based on semantic similarity and visual similarity metrics (c.f., Tab. 3). The significant improvement  $(+25.2\%)$  in DINOv2 and  $+16.0\%$  in CLIPin compared to the UltraEdit shows AnyEdit's effectiveness in maintaining pixel-level consistency and accurately reflecting editing instructions.
+
+# 4. Method
+
+# 4.1. Architecture
+
+Since AnyEdit contains a wide range of editing instructions across various domains, it holds promising potential for developing a powerful editing model to address high-quality editing tasks. However, training such a model has
+
+![](images/c430c39d6a5820cbf4f0488689bd605c5d769fd23df0ea730c19c02679473ccb.jpg)  
+Figure 3. Architecture of AnySD. AnySD is a novel architecture to supports three conditions (original image, editing instruction, visual prompt) for various editing tasks.
+
+three extra challenges: (a) aligning the semantics of various multi-modal inputs; (b) identifying the semantic edits within each domain to control the granularity and scope of the edits; (c) coordinating the complexity of various editing tasks to prevent catastrophic forgetting. To this end, we propose a novel AnyEdit Stable Diffusion approach (AnySD) to cope with various editing tasks in the real world. As illustrated in Figure 3, AnySD includes three designs: visual prompt projector, task-aware routing, and learnable task embedding. Then, we will introduce each AnySD design.
+
+Visual Prompt Projector. To align the semantics of multimodal inputs, we first use a visual prompt projector to align these image features  $z_{V}$  from the frozen CLIP image encoder with the instruction embeddings to obtain visual prompt  $c_{V}$ . We then integrate these embeddings into the timestep embeddings of the UNet through cross-attention interactions to provide visual prompt conditioning during general image editing diffusion [5]. The diffusion objective is then adjusted as follows:
+
+$$
+L = \mathbb {E} _ {\mathcal {E} (x), \mathcal {E} \left(c _ {I}\right), c _ {T}, c _ {V}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, \mathcal {E} \left(c _ {I}\right), c _ {T}, c _ {V}\right)) \| _ {2} ^ {2} \right] \tag {1}
+$$
+
+where  $\epsilon \in N(0,1)$  is the noise added by the diffusion process and  $[x,c_I,c_T,(c_V)]$  is a quadruple of editing instruction, with  $c_{V}$  only being applicable for visual editing.
+
+Task-aware Routing. Since each editing type exhibits different granularities and scopes of edits, we propose a task-aware routing strategy with Mixture of Experts (MoE) [29] blocks to meet task-specific editing requirements. Specifically, the visual condition  $c_V$  is integrated into the frozen UNet layers with decoupled cross-attention to avoid disrupting the edit instruction condition. Each MoE block shares the same text attention layer but has diverse visual attention weights for  $c_V$  by the router based on the task embedding. Therefore, we introduce a cross-attention layer for each expert and add the distributed results from all experts to the output of text cross-attention as follows,
+
+$$
+\mathbf {Z} ^ {\text {n e w}} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {\top}}{\sqrt {d}}\right) \mathbf {V} + \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \left(\mathbf {K} ^ {\prime}\right) ^ {\top}}{\sqrt {d}}\right) \mathbf {V} ^ {\prime} \tag {2}
+$$
+
+where  $\mathbf{K}' = c_v\mathbf{W}_k'$  is the query matrix from the visual
+
+<table><tr><td rowspan="2"></td><td colspan="4">EMU-Edit Test</td><td colspan="4">MagicBrush Test</td></tr><tr><td>CLIPim ↑</td><td>CLIPout ↑</td><td>L1 ↓</td><td>DINO ↑</td><td>CLIPim ↑</td><td>CLIPout ↑</td><td>L1 ↓</td><td>DINO ↑</td></tr><tr><td>PnP [44]</td><td>0.521</td><td>0.089</td><td>0.089</td><td>0.304</td><td>0.568</td><td>0.101</td><td>0.289</td><td>0.220</td></tr><tr><td>Null-Text [30]</td><td>0.761</td><td>0.236</td><td>0.075</td><td>0.678</td><td>0.752</td><td>0.263</td><td>0.077</td><td>0.664</td></tr><tr><td>InstructPix2Pix [5]</td><td>0.834</td><td>0.219</td><td>0.121</td><td>0.762</td><td>0.837</td><td>0.245</td><td>0.093</td><td>0.767</td></tr><tr><td>EMU-Edit [41]</td><td>0.859</td><td>0.231</td><td>0.094</td><td>0.819</td><td>0.897</td><td>0.261</td><td>0.052</td><td>0.879</td></tr><tr><td>UltraEdit (SD3) [57]</td><td>0.845</td><td>0.283</td><td>0.071</td><td>0.794</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SD1.5 w/ MagicBrush [54]</td><td>0.838</td><td>0.222</td><td>0.100</td><td>0.776</td><td>0.883</td><td>0.261</td><td>0.058</td><td>0.871</td></tr><tr><td>SD1.5 w/ AnyEdit (Ours)</td><td>0.866 (+3.3%)</td><td>0.284 (+27.9%)</td><td>0.095 (-5.0%)</td><td>0.812 (+4.6%)</td><td>0.892 (+1.0%)</td><td>0.273 (+4.6%)</td><td>0.057 (-1.7%)</td><td>0.877 (+0.7%)</td></tr><tr><td>AnySD w/ AnyEdit (Ours)</td><td>0.872 (+4.1%)</td><td>0.285 (+28.4%)</td><td>0.070 (-30.0%)</td><td>0.821 (+5.8%)</td><td>0.898 (+1.7%)</td><td>0.275 (+5.4%)</td><td>0.051 (-12.1%)</td><td>0.881 (+1.1%)</td></tr></table>
+
+![](images/3be78daa94cc4e207098ffdfba7c277e2f5effef3aa335cc1ad4dbf905f31289.jpg)  
+Figure 4. Dataset scales effect.
+
+prompt and  $\mathbf{W}_k^{\prime}$  is the corresponding weight matrix.
+
+Learnable Task Embeddings. To guide the generation process toward the appropriate granularity for each editing task, we learn a task embedding  $v_{i}$  during training. Unlike previous work [41], we insert task embeddings before the MoE block rather than integrate them into the whole denoising process to alleviate query confusion between instructions and editing types. The task embedding  $v_{i}$  has two main roles: (1) It concatenates with  $z_{v}$  (set to zero when no visual prompt is provided) to form  $c_{V}$  for MoE blocks; (2) it inputs to the router [60], distributing weights across MoE experts. More details of architecture are in Appendix G.1
+
+# 4.2. Training and Inference
+
+To enhance AnySD's ability to handle diverse conditioning for editing, we introduce CFG [20] extending from Instruct-Pix2Pix [5] for three conditioning. Furthermore, we structure our training into two stages for AnySD, ensuring that the diffusion model can thoroughly understand general editing knowledge and develop fine-grained task-specific skills.
+
+Stage I: Instruction Understanding. In this phase, we freeze the task-aware router and only pre-train the UNet layer to align with editing instructions. Additionally, We set additional conditions to zero tensors by CFG to enhance the model's instruction-following capability.
+
+Stage II: Task Tuning. In this phase, we further fine-tune  $\mathbf{W}_k^{\prime}$  and  $\mathbf{W}_v^{\prime}$  within the MoE block, task-aware router, visual prompt projector, and task embeddings to adapt the model to the task-specific editing granularity.
+
+Inference. In the inference stage, we predict the editing type with LLMs (e.g., LLaMA-3) when given the input instruction. Then, we apply our AnySD for editing.
+
+# 5. Experiments
+
+In this section, we first assess AnyEdit and AnySD on popular standard editing benchmarks (§ 5.2), demonstrating the high quality of the AnyEdit dataset and the superiority of the AnySD architecture. Additionally, we extend the evaluation to the more challenging AnyEdit-Test benchmark (§ 5.3) to show the promising expandability of our approach, better aligning with the creative editing demands in real-world scenarios. We further present qualitative results (§ 5.4) and conduct in-depth analysis (§ 5.5) to illustrate the
+
+Table 4. Comparison of methods on EMU-Edit [41] and MagicBrush [54] benchmark. We show performance improvements over SOTA models of the same architecture, with only training data differences.  
+
+<table><tr><td></td><td></td><td>CLIPim ↑</td><td>CLIPout ↑</td><td>L1 ↓</td><td>DINO ↑</td></tr><tr><td rowspan="7">Local</td><td>Null-Text [30]</td><td>0.773</td><td>0.270</td><td>0.245</td><td>0.641</td></tr><tr><td>InstructPix2Pix [5]</td><td>0.753</td><td>0.274</td><td>0.164</td><td>0.562</td></tr><tr><td>MagicBrush [54]</td><td>0.823</td><td>0.293</td><td>0.120</td><td>0.698</td></tr><tr><td>HIVEw [56]</td><td>0.814</td><td>0.294</td><td>0.184</td><td>0.651</td></tr><tr><td>HIVEc [56]</td><td>0.845</td><td>0.299</td><td>0.114</td><td>0.766</td></tr><tr><td>UltraEdit (SD3) [57]</td><td>0.831</td><td>0.308</td><td>0.112</td><td>0.731</td></tr><tr><td>AnyEdit (Ours)</td><td>0.863</td><td>0.297</td><td>0.094</td><td>0.788</td></tr><tr><td rowspan="7">Global</td><td>Null-Text [30]</td><td>0.753</td><td>0.277</td><td>0.270</td><td>0.613</td></tr><tr><td>InstructPix2Pix [5]</td><td>0.747</td><td>0.261</td><td>0.180</td><td>0.523</td></tr><tr><td>MagicBrush [54]</td><td>0.731</td><td>0.278</td><td>0.233</td><td>0.493</td></tr><tr><td>HIVEw [56]</td><td>0.762</td><td>0.287</td><td>0.196</td><td>0.579</td></tr><tr><td>HIVEc [56]</td><td>0.787</td><td>0.294</td><td>0.253</td><td>0.576</td></tr><tr><td>UltraEdit (SD3) [57]</td><td>0.772</td><td>0.297</td><td>0.191</td><td>0.619</td></tr><tr><td>AnyEdit (Ours)</td><td>0.788</td><td>0.301</td><td>0.159</td><td>0.647</td></tr><tr><td rowspan="6">Camera Movement</td><td>InstructPix2Pix [5]</td><td>0.700</td><td>-</td><td>0.178</td><td>0.477</td></tr><tr><td>MagicBrush [54]</td><td>0.765</td><td>-</td><td>0.170</td><td>0.589</td></tr><tr><td>HIVEw [56]</td><td>0.779</td><td>-</td><td>0.175</td><td>0.619</td></tr><tr><td>HIVEc [56]</td><td>0.838</td><td>-</td><td>0.171</td><td>0.739</td></tr><tr><td>UltraEdit (SD3) [57]</td><td>0.802</td><td>-</td><td>0.340</td><td>0.514</td></tr><tr><td>AnyEdit (Ours)</td><td>0.833</td><td>-</td><td>0.110</td><td>0.745</td></tr><tr><td rowspan="6">Implicit</td><td>InstructPix2Pix [5]</td><td>0.794</td><td>0.288</td><td>0.190</td><td>0.558</td></tr><tr><td>MagicBrush [54]</td><td>0.865</td><td>0.280</td><td>0.149</td><td>0.711</td></tr><tr><td>HIVEw [56]</td><td>0.821</td><td>0.284</td><td>0.161</td><td>0.635</td></tr><tr><td>HIVEc [56]</td><td>0.862</td><td>0.284</td><td>0.137</td><td>0.728</td></tr><tr><td>UltraEdit (SD3) [57]</td><td>0.856</td><td>0.281</td><td>0.135</td><td>0.703</td></tr><tr><td>AnyEdit (Ours)</td><td>0.867</td><td>0.289</td><td>0.130</td><td>0.733</td></tr><tr><td rowspan="2">Visual</td><td>Uni-controlnet [58]</td><td>0.717</td><td>0.249</td><td>0.260</td><td>0.442</td></tr><tr><td>AnyEdit (Ours)</td><td>0.801</td><td>0.258</td><td>0.145</td><td>0.628</td></tr></table>
+
+Table 5. Comparison of methods on AnyEdit-Test benchmark.
+
+scalability and broader applicability of AnyEdit.
+
+# 5.1. Experimental Setup
+
+Settings. For a fair comparison, we adopt Stable-Diffusion 1.5 [38] as the backbone and follow the settings of InstructPix2Pix [5] to train our AnySD. Notably, we only use data from AnyEdit for training, without incorporating any additional datasets. More details are in Appendix G.5.
+
+Benchmarks & Metrics. We access our method across two popular benchmarks: Emu Edit Test [41] and MagicBrush [54]. These standard benchmarks evaluate editing models by comparing edited results with ground truths. Additionally, we manually selected 50 high-quality editing data from each editing type in AnyEdit, creating AnyEdit-Test for a more challenging and comprehensive evaluation. Notably, AnyEdit-Test is not visible during training. See Appendix E for details of AnyEdit-Test. Following prior work [14, 41, 54], we adopt semantic similarity (i.e.,
+
+![](images/c592d93a930d3038e2a08c05a43dcde3ed3d7b59228e7442eb138cbb9a117e45.jpg)  
+(i)
+
+![](images/5f2dd37eb7b25f2a0315dc3c167ddfac0a84c9a062a22379d03b6d07d3899d11.jpg)  
+"Make Santa Claus laugh and wear a pair of glasses"  
+"Add a butterfly fluttering around the cat"
+
+![](images/8ba878d3e63846cba7a253cde60900092b47563f9567664cda1e8815b83d1600.jpg)
+
+![](images/71d88f6a381f0252409b85436aaba1ea08de0e3640a2b9fab56ffe26127cc45b.jpg)  
+"Make the bears wearing tiny hats of different colors"
+
+![](images/acd55334087e4607502c00900c9acb6f6c8e2d9de37b53d9bec40a11f98917f9.jpg)  
+"Turn the background to a garden"  
+Input  
+IP2P  
+Magic  
+Brush  
+H  
+三-c  
+Ultr  
+aEdit  
+Ours  
+Figure 5. Qualitative evaluation of 10 distinct and complex tasks on AnyEdit-Test, such as action change (i), appearance alter (iv), rotation change (viii), counting (ix), and outpainting (x), demonstrates that our method yields promising results across these editing tasks.
+
+![](images/209f89ed7986b2e561d2f6662810ffe0e56d9d4574a283c57db8fb57bae71692.jpg)  
+"Change the style of the image to bit style"  
+"Turn the color of dog to pink"
+
+![](images/33566f5f86612d0f7b14fa4bda836c57220826cfd501ad4ac996c98cad19a14b.jpg)
+
+![](images/34b85b5b568b8ff78c191e277f49d4d10d0a9c50b314bdd708936b85197d61a4.jpg)  
+"Rotate the table counterclockwise"  
+"Eliminate the moons from five to three"
+
+![](images/779b3e6783e9f56f942a3c47377ade3f5584778f932ff9fe601bbaccb93c9020.jpg)  
+"Complete the image as you can"
+
+![](images/c2358c35844e5569145dce4e3d322071d758d8b9250e85e53e2a685a2e6e47bf.jpg)  
+Input  
+IP2P  
+MagicBrush  
+HIVE-c  
+UltraEdit  
+Ours
+
+CLIPim and CLIPout) and visual similarity (i.e., DINO and L1 distance) metrics to evaluate the effectiveness of AnySD trained on AnyEdit for instruction-based image editing.
+
+Baselines. We use the following baselines: 1) specialized image editing methods: PnP [44], Null-Text [30]. 2) instruction-based methods: it directly edits images with natural language, including InstructPix2Pix [5], MagicBrush [54], HIVE [56], EMU-Edit [41], UltraEdit [57]. 3) visual condition methods: it targets visual editing, including Uni-controlnet [58]. More details are in Appendix G.6.
+
+# 5.2. Main Results on Standard Image Editing
+
+We report the standard image editing results of AnyEdit and other baselines on EMU-Edit Test and MagicBrush benchmarks in Table 4. Based on the experimental results, we have summarized the following conclusions: (i) Our SD1.5 with AnyEdit, which only changes the training data to AnyEdit, consistently demonstrates superior semantic performance in both edit alignment and content preservation compared to SOTA methods, even without additional mask supervision (0.872 for CLIPim and 0.285 for CLIPout on the EMU-Edit Test). It highlights AnyEdit's effectiveness in mastering high-quality image editing, validating its high-quality editing data with significant semantic alignment and underlying clear editing structure. (ii) Our AnySD model, trained on AnyEdit using the AnySD architecture, further surpasses SOTA methods in both semantic and visual similarity (0.872 of CLIPim on EMU-Edit Test and 0.881 of DINO on MagicBrush Test), setting new records
+
+on MagicBrush and Emu-Edit benchmarks. This demonstrates the superiority of AnySD in following editing instructions while preserving unchanged image elements, thanks to its task-aware architecture that learns task-specific knowledge from the diverse editing types in AnyEdit, enhancing the model's cross-task editing capabilities.
+
+# 5.3. Comparison on AnyEdit-Test Benchmark
+
+Table 5 presents the results of the AnyEdit-Test benchmark, where each instruction is designed to rigorously evaluate AnyEdit's adaptability across a wider range of challenging editing scenarios. We provide further results of each editing category in Appendix F. It can be observed that (i) most baselines struggle to effectively handle more complex editing tasks that are rarely in standard benchmarks (0.190 v.s. 0.121 on average L1), especially for implicit editing that requires reasoning abilities. This illustrates the importance of AnyEdit-Test for evaluating the performance of editing models on complex tasks. (ii) Even for common editing tasks, state-of-the-art models show a significant decline in consistency performance on AnyEdit-Test (-3.5% on CLIPim and -19.2% on DINO of UltraEdit). This underscores the limitations of existing benchmarks in evaluating multi-scene editing. (iii) In contrast, AnyEdit significantly outperforms SOTA methods across all editing categories, demonstrating its scalability and robustness in handling complex tasks across diverse scenarios. (iv) Traditional methods often struggle to handle visual editing effectively due to additional visual inputs. In such cases, even
+
+![](images/398024dd66a42e2bbf8c2522a5c25e1ba1eab25b8e8d699818f7707e0ccdb7c6.jpg)  
+Input & Visual condition
+
+![](images/084cb1b01e55c262ec70f384f58c81cd0207ef1540fdc1643b5aeecdaaf21a54.jpg)  
+Uni-controlnet
+
+![](images/5f9103f3e3c075a69d88bbfc4be4e292e73b2078c8d29a7d368ec92d46946c1c.jpg)  
+Ours
+
+![](images/8f7cec5f9a96a8da7d396679b0fe7f85a2b03e53475bd0fd8343500beeb126ca.jpg)  
+change the material of lady's cloth like the give image  $[V^{*}]$
+
+![](images/f755e625703cc40bf89687c7b540f5d8a3eb58449676d60b328b62b37f9aaa73.jpg)
+
+![](images/dc73320f3a6caddabf6047fc2f022c0509d291f76820547dab30603f108a75fa.jpg)
+
+![](images/0be560dc87fae60f8d4e3e4e91dcaa876b9a543d9b8d860a03588a27d17e8253.jpg)  
+Watch the given depth image  $[V^{*}]$  to remove basketball
+
+![](images/a7f6866c438759f71f5780a8172f6995525f42c0bef9c8aa4fc3f96386831ad0.jpg)  
+Follow the given bounding box  $[V^{*}]$  to erase the laptop
+
+![](images/909684226251a249ca47a27dd8a1547c433360f73fb7c4f4690dd48c2e0ad48a.jpg)  
+Figure 6. Comparison of our image editing method against Unicontrolnet [58] for visual editing tasks on AnyEdit-Test.
+
+when compared to Uni-ControlNet, which is pre-trained with diverse visual conditions, AnyEdit consistently performs better in visual editing tasks. It shows the efficacy of AnyEdit in handling vision-conditioned editing instructions. We provide more qualitative evidence in Sec. 5.4.
+
+# 5.4. Qualitative Evaluation
+
+Due to the limitations of quantitative metrics in evaluating editing tasks, we perform qualitative evaluations to further assess the effectiveness of our approach, as shown in Figure 5. Our key observations are: 1) Most baseline models, including the human-tuned HIVE-c[56] and the SOTA UltraEdit with its extensive training data[57], still suffer from over-editing or misalignment when handling complex fine-grained instructions (e.g., "facial distortion" and "missing glasses" in Fig. 5(ii)). 2) Due to the limited diversity and quality of current datasets, previous methods (i.e., ip2p [5], MagicBrush [54], and UltraEdit) struggle to generalize to novel editing types in diverse scenarios (e.g., failing to follow instructions in rotation change and counting tasks, or roughly altering objects instead of its fine-grained appearance in appearance alter task). 3) In contrast, our method can effectively ensure editing accuracy in target regions and maintain consistency in irrelevant areas even without any mask guidance (Fig. 5(i), (vii)). Also, our method can automatically distinguish between foreground and background to modify the background (Fig. 5(v)). Moreover, our method successfully executes more complex editing instructions (e.g., style change in Fig. 5(vi) and outpainting in Fig. 5(x)).
+
+Additionally, we visualize AnyEdit results on visual editing in Figure 6. In this challenging setting, UniControl can either reflect only the pixel information from the visual condition or retain the semantics of the original image without performing any edits. In contrast, for various visual instructions, AnyEdit consistently comprehends the pixel information in visual conditions and achieves reliable editing.
+
+<table><tr><td></td><td></td><td>CLIPim ↑</td><td>CLIPout ↑</td><td>L1 ↓</td><td>DINO ↑</td></tr><tr><td></td><td>AnySD w/ AnyEdit</td><td>0.872</td><td>0.285</td><td>0.070</td><td>0.821</td></tr><tr><td>1</td><td>w/o task-aware routing</td><td>0.838</td><td>0.275</td><td>0.154</td><td>0.757</td></tr><tr><td>2</td><td>w/o task emb</td><td>0.859</td><td>0.282</td><td>0.107</td><td>0.809</td></tr><tr><td>3</td><td>AnyEdit (w/o compsn.)</td><td>0.868</td><td>0.271</td><td>0.099</td><td>0.785</td></tr></table>
+
+Table 6. Ablation study of our method on EMU-Edit Test [41].
+
+These promising visualization results confirm the effectiveness and high quality of the diverse editing data in AnyEdit. More qualitative results are shown in Appendix H.2.
+
+# 5.5. In-depth Analysis
+
+AnySD Architecture. We investigate the effectiveness of each component and conduct the following experiments on EMU-Edit Test benchmark: (1) We remove the text-aware routing strategy in AnySD (c.f. Rows 1 of Tab. 6) and find that it leads to significant performance degradation (0.838 v.s. 0.872 in CLIPim and 0.154 v.s. 0.070 in L1), demonstrating its crucial role for adapting diverse image editing tasks. (2) We remove task embeddings in AnySD and observe that it has little impact on semantic alignment but significantly affects visual consistency (c.f. Rows 2 of Tab. 6), suggesting that task embeddings control the perceptual granularity of pixel information during cross-attention. Analysis of Data Scaling in AnyEdit. In Figure 4, we analyze the data scaling effect of AnyEdit on image editing capability. We observe: (1) For consistency metrics (i.e., CLIPim and DINO), performance improves progressively as data scale increases; (2) For editing accuracy metrics (i.e., CLIPout), we can achieve promising performance even with a small amount of data, indicating that AnyEdit excels in semantic alignment. (3) Furthermore, we remove the AnyEdit-Composition editing data in counterfactual synthesis scenarios, as shown in row 3 of Tab. 6, the lack of conceptual balance in AnySD hinders its ability to generalize, leading to a decline in semantic performance (-4.9% of CLIPout). This confirms the efficacy of counterfactual synthetic scenes to generalization in editing tasks.
+
+# 6. Conclusion
+
+In this work, we present a novel perspective for categorizing editing tasks and introduce a unified framework that exploits adaptive pipelines to construct high-quality data for diverse editing tasks in a low-resource manner. Building on this, we propose AnyEdit, a multi-type, multi-scene instruction-based editing dataset comprising 2.5M editing samples across 25 distinct types, along with its benchmark, AnyEdit-Test, enabling a more comprehensive paradigm for unified image editing. Furthermore, we develop the powerful AnySD, unlocking the full potential of AnyEdit. Extensive experiments on standard benchmarks and the challenging AnyEdit-Test demonstrate that our method excels in high-quality image editing across diverse tasks and scenarios, accurately executing complex instructions while preserving image consistency in unmodified elements.
+
+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), and the Zhejiang NSF (LRG25F020001). We thank all the reviewers for their valuable comments.
+
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+# AnyMap: Learning a General Camera Model for Structure-from-Motion with Unknown Distortion in Dynamic Scenes
+
+Andrea Porfiri Dal Cin
+
+Georgi Dikov
+
+Jihong Ju
+
+Mohsen Ghafoorian
+
+XR Labs, Qualcomm Technologies, Inc.
+
+{adalcin,gdikov,jihoju,mghafoor}@qti.QUALCOMM.com
+
+# Abstract
+
+Current learning-based Structure-from-Motion (SfM) methods struggle with videos of dynamic scenes captured by wide-angle cameras. We present AnyMap, a differentiable SfM framework that jointly addresses image distortion and motion estimation. By learning a general implicit camera model without predefined parameters, AnyMap handles lens distortion and estimates multi-view consistent 3D geometry, camera poses, and (un)projection functions. To resolve the ambiguity where motion estimation can compensate for undistortion errors and vice versa, we introduce a low-dimensional motion representation consisting of a set of learnable basis trajectories, which are interpolated to produce regularized motion estimates. Experimental results show that our method achieves accurate camera poses, excels in camera calibration and image rectification, and enables high-quality novel view synthesis. Our low-dimensional motion representation effectively disentangles undistortion from motion estimation, outperforming existing methods.
+
+# 1. Introduction
+
+Recent progress in Structure-from-Motion (SfM) has shifted to differentiable estimation of depth, camera poses, and intrinsics, enabling neural networks to implicitly model scene geometry [6, 16, 45, 51, 57]. Although learning-based methods produce results comparable to conventional methods like COLMAP [43, 44], they assume a pinhole camera model and lack support for lens distortion inherent to wide-angle or fisheye cameras. This limitation restricts their applicability on distorted videos, leaving COLMAP as the default solution for camera calibration and image rectification.
+
+Handling distortions in learning-based SfM is challenging. Zero-shot methods [16, 57, 62] that regress 3D geometry, poses, and intrinsics without optimization on input images underperform on distorted images (see Sec. 4.3). Scene coordinate regressors [6] also fail, as they rely on frozen pre-trained encoders to map image features to scene coor
+
+![](images/35181bfa1af83e3de5dbebf0a851234eadd96a8b4666f1deb3174c6957600ad7.jpg)  
+Figure 1. AnyMap: our differentiable SfM method leverages off-the-shelf correspondences and monodepths to learn the camera model, enabling calibration, pose estimation, 3D reconstruction, and image rectification from distorted videos of dynamic scenes.
+
+dinates; lens distortions introduce spatially varying image deformations, leading to inconsistent encoder performance across different image regions. Fine-tuning the image encoder, as in FlowMap [45], helps adapt to lens distortions and more effectively mapping distorted image patches to scene geometry. However, current optimization strategies for intrinsics struggle when parameterizing distortions. It has been shown in [13] that optimizing camera intrinsics directly is suboptimal due to ambiguities in distorted camera models—different parameter sets can represent equivalent cameras. This leads to optimization instability, with gradient descent oscillating between equivalent solutions without convergence. FlowMap estimates camera intrinsics as a function of scene geometry by selecting among candidate focal lengths and tentatively aligning unprojected point clouds for each candidate. However, for models like Fisheye624 [42], which involve numerous distortion coefficients, this approach becomes infeasible due to rapid growth in combinations and persistent camera model ambiguities.
+
+We address these challenges by introducing AnyMap, a differentiable SfM method that estimates multi-view consistent 3D geometry, camera poses, and (un)projection functions from an input video using a general camera model that accounts for lens distortion by mapping image points to their incoming light ray directions. Central to AnyMap is an invertible neural network (INN) [8] that learns this bidirectional mapping, eliminating predefined camera models in favor of a model-free framework. AnyMap is fully differentiable: scene geometry is obtained from a range network mapping planar image points to scalar distances to the corresponding unprojected 3D points in spherical coordinates; camera poses are computed by aligning unprojected point clouds, as in FlowCam [46]; and the (un)projection is computed differentiably via the INN. This enables end-to-end optimization with gradient descent and faster runtimes comparable to FlowMap. AnyMap induces a dense optical flow from estimated scene geometry, camera poses, and model, which we supervise for multi-view consistency by minimizing the distance to pairwise correspondences from off-the-shelf methods. However, since the (un)projection is estimated per-pixel, motion handling becomes critical. Dynamic objects violate epipolar constraints, introducing inconsistencies that adversely affect the reconstruction and camera calibration. To compensate for that, inspired by [56], we introduce a low-dimensional representation of scene motion, using learnable basis trajectories combined via per-pixel weights predicted by an MLP. As discussed in Sec. 4.4, this regularized representation helps calibrate distortions and estimate motion jointly, since unregularized motion often compensates for handled distortion instead of actual scene dynamics.
+
+In summary, our contributions are threefold:
+
+- We introduce a general camera model that accounts for lens distortion and is learned by an invertible neural network to compute the (un)projection functions differentiably. This model avoids common ambiguities in distorted camera models, enabling seamless embedding in end-to-end network optimization.  
+- We present AnyMap, a learning-based SfM method that supports distorted videos and eliminates the need for predefined camera models. It is fully differentiable, enabling high-quality results in downstream tasks like image rectification and novel view synthesis.  
+- We introduce a per-pixel, low-dimensional motion representation for AnyMap with the goal of regularizing motion estimation to improve performance when calibrating camera distortions in dynamic scenes.
+
+# 2. Related Work
+
+Conventional SfM methods rely on descriptor extraction, correspondence estimation, and bundle adjustment to opti
+
+mize camera parameters and 3D points, including intrinsic parameters and distortion coefficients. COLMAP [43] and its faster variant GLOMAP [37] are the standard for offline camera parameter estimation, supporting radial and tangential distortions. Bundle adjustment requires a close initialization; while pinhole cameras can exploit focal length assumptions for this, lens distortions introduce additional parameters that complicate finding a good starting point for optimization.
+
+Learning-based SfM methods [3, 11, 12, 28, 48, 49, 53, 58, 65], as well as recent ones like ACE0 [6] and MASt3R [16, 26, 57] generally assume a pinhole camera and lack support for image distortion. DROID-SLAM [51] estimates depths and camera poses from videos and supports lens distortion but requires ground-truth intrinsics and underperforms compared to COLMAP. FlowMap [45], closely related to our work, performs per-video gradient descent by minimizing the distance between optical flow induced by estimated depths, poses, and intrinsics under the pinhole camera model, but lacks support for distortion models. AnyMap fills this gap by introducing an integrated solution that supports lens distortion, enabling calibration, rectification, and SfM within a unified differentiable framework.
+
+Monocular Calibration and Rectification methods achieve performance close to multi-view approaches without optimization of camera parameters via bundle adjustment, but lack temporal consistency for videos. Geometric methods depend on handcrafted features [1, 30, 39, 41] but fail when these are absent. Reconstruction approaches use adversarial learning [18, 59] or diffusion [60] for image rectification. Regression methods infer intrinsics from a predefined camera model [5, 31, 55] or implicit representations like distortion [27] or viewing-angle maps [13]. Notably, [13] models radial distortion by mapping image points to viewing angles but is limited to radial distortions, ignores tangential distortions in fisheye lenses, and defines only an unprojection function. In contrast, our camera model implements both unprojection and projection functions, enabling use in SfM.
+
+Motion in SfM is tackled by various methods [7, 9, 10, 25, 32, 36, 52, 63] that produce consistently scaled depth in dynamic regions, often leveraging monocular depths to align moving objects with static backgrounds. CasualSAM [64] jointly optimizes depths, extrinsics, and focal length, learning dense motion masks for motion handling. Consistent Video Depth (CVD) [63] predicts per-pixel 3D motion vectors via an MLP but requires known camera parameters. MonST3R [62] is zero-shot and generates dynamic point clouds and camera poses from videos, and 3D Gaussian Splatting [22] has been extended to dynamic scenes [56]. However, these methods typically depend on known camera parameters and depth estimates, and lack support for lens distortion. AnyMap uniquely addresses these limitations and, to our knowledge, is the first to provide preprocessing for novel view synthesis in dynamic scenes with lens distortion.
+
+![](images/ec0e2218a9e898a9efef85f209976768a632f80d709d6331f1a1f69daa0fa554.jpg)  
+Figure 2. General Camera Model. The (un)projection functions are an invertible neural network. We illustrate the unprojection  $s_1 = \pi^{-1}(x_1)$  in cyan and the projection  $\pi(s_2) = x_2$  in green.
+
+# 3. Method
+
+We introduce our general camera model (Sec. 3.1), central to AnyMap—our learning-based SfM method supporting lens distortions. We then propose a low-dimensional motion parameterization to enable reconstruction and calibration in dynamic scenes (Sec. 3.3).
+
+# 3.1. General Camera Model
+
+We propose a general camera model that accommodates lens distortions—specifically radial and tangential—by avoiding fixed projection and unprojection equations. Instead, we define general (un)projection functions that can be effectively learned by an invertible neural network (INN).
+
+(Un)projection. Consider an image point  $x = (\rho, \theta)$  in polar coordinates  $\Omega$ , where  $\rho$  is the radial distance from the image center and  $\theta$  is the azimuthal angle. The unprojection function  $\pi^{-1} : \Omega \to \mathbb{S}^2$  maps  $x$  to the direction  $s = (\psi, \phi)$  of the incoming light ray on the unit sphere  $\mathbb{S}^2$  (see Fig. 2). Conversely, given a 3D point  $X = (r, \psi, \phi) \in \mathbb{R}^+ \times \mathbb{S}^2$  in spherical coordinates, where  $r$  is the range, the projection function  $\pi : \mathbb{S}^2 \to \Omega$  maps the azimuthal angle  $\psi$  and polar angle  $\phi$  of  $X$  to the image point  $x \in \Omega$ .
+
+When modeling only radial distortion, we exploit the symmetry  $\theta = \phi$  [13], reducing both  $\pi^{-1}$  and  $\pi$  to one-dimensional mappings:  $\pi^{-1}:\rho \mapsto \psi$  and  $\pi :\psi \mapsto \rho$ .
+
+Learning. We learn the unprojection function  $\pi^{-1}$  using an INN, termed the camera network, ensuring consistent computation of  $\pi$  via invertibility, so that  $x = \pi (\pi^{-1}(x))$  for all  $x\in \Omega$ . In SM A, we compare alternative strategies for computing  $\pi$  from  $\pi^{-1}$ , such as lookup tables. We demonstrate that using the INN offers a good trade-off between projection accuracy and computational efficiency.
+
+Having introduced our general camera model, we now detail AnyMap—a learning-based SfM method integrating the camera network to support videos captured with cameras exhibiting radial and tangential distortions.
+
+# 3.2. Differentiable SfM Framework
+
+For a video sequence of  $V$  frames  $\{\mathbf{I}_i\in \mathbb{R}^{H\times W\times 3}\}$  captured by a distorted camera with unknown but constant
+
+intrinsic, AnyMap outputs per-frame range maps  $\{\mathbf{R}_i\in$ $\mathbb{R}^{H\times W}\}$  , camera poses  $\mathbf{E}_i\in \mathbb{S}\mathbb{E}(3)$  , and the (un)projection functions  $\pi$  and  $\pi^{-1}$  in Sec. 3.1.
+
+We model the distance from the sensor to scene points using a neural network that maps each image  $\mathbf{I}_i$  to a range map  $\mathbf{R}_i$ . Unlike methods that learn the focal length [6] or soft-select it by aligning back-projected points [45], we learn the unprojection  $\pi^{-1}$  and, inversely, the projection  $\pi$  for our general camera model. This allows fine-tuning of both the range and camera networks on the input video, using supervision from pixel-wise correspondences obtained via optical flow or 2D point tracks. Given a pair of frames, their range maps, and relative pose, we reproject image points from the first frame to the second using  $\pi^{-1}$  and  $\pi$ , inducing an optical flow computed differentiably. By supervising the induced flow with known correspondences, AnyMap is optimized end-to-end to estimate consistent 3D geometry, camera extrinsics, and importantly, the (un)projection  $\pi$  and  $\pi^{-1}$  for the general camera model.
+
+Fig. 3 provides an overview of AnyMap. We now detail our parameterization of scene geometry, camera extrinsics, and the camera model.
+
+Range Map Unprojection. We unproject image points into 3D camera coordinates using the unprojection function  $\pi^{-1}$  learned by the camera network. For each image point  $x$  in frame  $\mathbf{I}_i$ , we compute its direction  $(\psi, \phi) = \pi^{-1}(x)$  and its range  $r = \mathbf{R}_i(x)$ , obtaining the 3D camera coordinate:
+
+$$
+X _ {i} ^ {\operatorname {c a m}} (x) = r \left[ \begin{array}{l l l} \sin (\psi) \cos (\phi) & \sin (\psi) \sin (\phi) & \cos (\psi) \end{array} \right] ^ {\top} \tag {1}
+$$
+
+Since intrinsics are constant, we compute  $\pi^{-1}(x)$  once for each  $x$  and reuse  $(\psi, \phi)$  across all frames, updating only when the camera network's weights change during fin-tuning. Our range map parameterization avoids numerical issues with cameras having a field of view  $\sim 180^{\circ}$ , where unprojection using depth is undefined at  $\psi = \pm 90^{\circ}$ , leading to numerical instability during gradient computation. $^{1}$
+
+Estimation of Camera Extrinsics. We estimate relative camera poses similarly to FlowCam [46], using a differentiable solution that aligns unprojected range maps via the orthogonal Procrustes problem [19], which has a closed-form, differentiable solution.
+
+For frame pair  $i,j$ , we unproject points in  $\mathbf{R}_i$  and  $\mathbf{R}_j$  using  $\pi^{-1}$  to obtain 3D points  $X_{i}^{\mathrm{cam}}$  and  $X_{j}^{\mathrm{cam}}$ . Using known correspondences, we obtain the subsets  $X_{i\leftrightarrow j}^{\mathrm{cam}}$  and  $X_{j\leftrightarrow i}^{\mathrm{cam}}$  of one-to-one matched 3D points between  $i\leftrightarrow j$  and  $j\leftrightarrow i$ , respectively. We seek the relative transformation  $\mathbf{E}_{ij}$  minimizing the sum of squared distances between matched points:
+
+$$
+\mathbf {E} _ {i j} = \underset {\mathbf {E}} {\operatorname {a r g m i n}} \| \mathcal {W} ^ {1 / 2} \left(X _ {j \leftrightarrow i} ^ {\mathrm {c a m}} - \mathbf {E} X _ {i \leftrightarrow j} ^ {\mathrm {c a m}}\right) \|, \tag {2}
+$$
+
+![](images/06960855ac4f0527734493d697247eb23147d3fdf66a50f4db5025bc8f50ceb6.jpg)  
+Figure 3. AnyMap framework. The reprojection loss  $\mathcal{L}^{2\mathrm{D}}$  for frame pair  $i,j$  is computed as the distance between known correspondences  $x_{i\rightarrow j}$  and induced correspondences  $\hat{x}_{i\rightarrow j}$  by ranges  $\mathbf{R}_i$ , (un)projection  $\pi^{-1}$  and  $\pi$ , and relative pose  $\mathbf{E}_{ij}$ . Relative pose is computed by Procrustes alignment of matched point sets unprojected from  $\mathbf{R}_i$  and  $\mathbf{R}_j$ , respectively.
+
+where  $\mathcal{W}$  contains correspondence weights predicted by an MLP from per-pixel features, as in FlowCam. We write  $\mathbf{E}_{ij} = \mathbf{E}_j^{-1}\mathbf{E}_i$ , setting  $\mathbf{E}_1 = \mathbb{I}_4$  as the world origin.
+
+Estimation of Camera Intrinsics. Optionally, AnyMap can explicitly estimate the focal length  $f$  and distortion coefficients  $\mathbf{k} = (k_{1},\dots,k_{n})$  that best fit the learned  $\pi^{-1}$  to the unprojection function  $\Psi^{-1}$  of a user-provided mathematical camera model by least squares fitting, as detailed in SM C.
+
+# 3.3. Handling Dynamic Scenes
+
+When dealing with dynamic scenes, inconsistencies in induced correspondences  $\hat{x}_{i\rightarrow j}$  can no longer be attributed solely to calibration errors; they also arise from unaccounted scene motion that violates the epipolar constraints governing the static portion of the scene. As distortion is progressively corrected during gradient descent, naively learning dense motion risks overfitting to the very distortion being removed, thereby hindering the estimation of both scene motion and the (un)projection functions  $\pi^{-1}$  and  $\pi$ , which depend on the estimated scene geometry.
+
+We resolve the ambiguity in scene motion and calibration by introducing a compact motion representation that serves as a regularizing prior. Specifically, we model scene motion with a low-dimensional set of 3D basis trajectories. At each time step  $i$ , we learn  $B$  basis trajectories  $\{\mathbf{T}_i^{(b)}\}_{b = 1}^B\subset \mathbb{S}\mathbb{E}(3)$ , which are shared among all 3D points to capture common motion components. For any image point  $x$ , we unproject it at time  $i$  to obtain its 3D world coordinates  $X_{i}(x) = \mathbf{E}_{i}X_{i}^{\mathrm{cam}}(x)$ . The motion of  $x$  from frame  $i$  to  $i + 1$  is represented by the transformation  $\mathbf{T}_i(x)$ , computed by combining trajectories:
+
+$$
+\mathbf {T} _ {i} (x) = \sum_ {b = 1} ^ {B} w _ {i} ^ {(b)} (x) \mathbf {T} _ {i} ^ {(b)}, \tag {3}
+$$
+
+where the weights  $\mathbf{w}_i(x) = [w_i^{(1)}(x),\dots,w_i^{(B)}(x)]$  are predicted by an MLP  $\mathcal{G}$  and satisfy  $\| \mathbf{w}_i(x)\| = 1$ .  $\mathcal{G}$  predicts weights from world coordinates and time step:
+
+$$
+\mathbf {w} _ {i} (x) = \mathcal {G} \left(X _ {i} (x), i\right). \tag {4}
+$$
+
+Including time step  $i$  allows  $\mathcal{G}$  to adapt weights over time, enabling dynamic point-to-trajectory assignments. For brevity, we will henceforth omit the explicit dependency of  $\mathbf{T}_i$  on  $x$ .
+
+To compute the cumulative transformation  $\mathbf{T}_{i\rightarrow j}$  over multiple frames  $(j - i > 1)$ , we iteratively apply per-frame motion transformations to the 3D point  $X_{i}(x)$ . At each time step  $k = i,\ldots ,j - 1$ , we update the point's position using:
+
+$$
+X _ {k + 1} (x) = \mathbf {T} _ {k} X _ {k} (x), \tag {5}
+$$
+
+where  $\mathbf{T}_k$  is computed as in (3). Recursively applying (5), the 3D position  $X_{j}(x)$  of  $x$  at frame  $j$  becomes:
+
+$$
+X _ {j} (x) = \left(\prod_ {k = i} ^ {j - 1} \mathbf {T} _ {k}\right) X _ {i} (x) = \mathbf {T} _ {i \rightarrow j} X _ {i} (x), \tag {6}
+$$
+
+with the product denoting sequential transformations.
+
+# 3.4. Optimization
+
+We optimize AnyMap end-to-end on the input video using a weighted sum of the loss terms described below.
+
+Reprojection loss  $\mathcal{L}^{2\mathrm{D}}$ . Using the predicted range  $\mathbf{R}_i(x)$ , world-to-camera extrinsics  $\mathbf{E}_i$ , and unprojection function  $\pi^{-1}$ , we unproject each image point  $x$  at frame  $i$  into world coordinates  $X_i(x)$ . Applying the transformation  $\mathbf{T}_{i\rightarrow j}$  from Eq. (6) yields the 3D position at frame  $j$ :
+
+$$
+X _ {j} (x) = \mathbf {T} _ {i \rightarrow j} X _ {i} (x). \tag {7}
+$$
+
+For static scenes, we fix  $\mathbf{T}_{i\rightarrow j} = \mathbb{I}_4$ . We project  $X_{j}(x)$  onto the image plane of frame  $j$  using the extrinsics  $\mathbf{E}_j$  and the projection  $\pi$ , obtaining the predicted correspondence:
+
+$$
+\hat {x} _ {i \rightarrow j} = \pi (\mathbf {E} _ {j} ^ {- 1} X _ {j} (x)). \tag {8}
+$$
+
+Given known correspondences  $x_{i\rightarrow j}$  the reprojection loss is:
+
+$$
+\mathcal {L} _ {i \rightarrow j} ^ {\mathrm {2 D}} = \sum_ {x} \| \hat {x} _ {i \rightarrow j} - x _ {i \rightarrow j} \| _ {\text {H u b e r}}, \tag {9}
+$$
+
+where the sum is over all points  $x$  in frame  $i$  and  $\| \cdot \|_{\mathrm{Huber}}$  denotes the Huber loss. This loss robustly minimizes the
+
+distance between predicted and known correspondences, promoting multi-view consistent estimation of ranges, extrinsics, (un)projection, and motion trajectories.
+
+Monocular Depth Loss  $\mathcal{L}^{\mathrm{m}}$ . While  $\mathbf{T}_{i\rightarrow j}$  minimizes  $\mathcal{L}^{2\mathrm{D}}$  by adjusting for inconsistencies between  $\hat{x}_{i\rightarrow j}$  and  $x_{i\rightarrow j}$ , without constraints on the predicted ranges  $\mathbf{R}_i$ , the loss does not penalize inaccuracies when  $\mathbf{T}_{i\rightarrow j}$  is large, nor does it ensure consistent scale reconstruction for moving objects relative to the static background. To address this, we convert the estimated ranges  $\mathbf{R}_i$  to depths  $\mathbf{D}_i$  at image points where depth unprojection is defined. We then compare estimated depths to monocular depths  $\mathbf{D}_i^{\mathrm{m}}$  using the ordinal loss from [29], which penalizes incorrectly ordered depth pairs  $(x_{1},x_{2})$  to promote linear consistency between  $\mathbf{D}_i$  and  $\mathbf{D}_i^{\mathrm{m}}$ .
+
+To down-weight the ordinal loss for static points, we compute a motion weight  $m_{ij}$  for the first sampled pixel  $x_{1}$ :
+
+$$
+m _ {i j} (x _ {1}) = \left\| X _ {j} \left(x _ {1}\right) - X _ {i} \left(x _ {1}\right) \right\| _ {2}, \tag {10}
+$$
+
+and compute the weighted ordinal loss:
+
+$$
+\mathcal {L} _ {i} ^ {\mathrm {m}} \left(x _ {1}, x _ {2}\right) = m _ {i j} \left(x _ {1}\right) \| \mathcal {R} \left(x _ {1}, x _ {2}\right) - \mathcal {R} ^ {\mathrm {m}} \left(x _ {1}, x _ {2}\right) \| \tag {11}
+$$
+
+$$
+\mathcal {R} \left(x _ {1}, x _ {2}\right) = \tanh  \left(\beta \left(\mathbf {D} _ {i} \left(x _ {1}\right) - \mathbf {D} _ {i} \left(x _ {2}\right)\right)\right) \tag {12}
+$$
+
+$$
+\mathcal {R} ^ {\mathrm {m}} \left(x _ {1}, x _ {2}\right) = \left\{ \begin{array}{l l} + 1, & \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {1}\right) > \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {2}\right) \\ - 1, & \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {1}\right) <   \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {2}\right) \\ 0, & \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {1}\right) = \mathbf {D} _ {i} ^ {\mathrm {m}} \left(x _ {2}\right) \end{array} \right. \tag {13}
+$$
+
+where  $\beta$  is a hyperparameter. By only considering  $m_{ij}(x_1)$  and not, e.g., the product of  $m_{ij}(x_1)$  and  $m_{ij}(x_2)$ , we avoid instances where  $x_1$  is not supervised due to  $x_2$  being static with a near-zero weight.
+
+Unprojection loss  $\mathcal{L}^{\mathrm{u}}$ . Learning the unprojection function  $\pi^{-1}$  per pixel can lead to inaccuracies in texture-less regions due to unreliable correspondences (see Sec. 5). To mitigate this, we introduce  $\mathcal{L}^{\mathrm{u}}$  to prevent the learned  $\pi^{-1}$  from deviating significantly from the unprojection function  $\Psi^{-1}$  of a parameterized camera model. Every  $U$  epochs, we fit the learned unprojection  $\pi^{-1}$  to the parameterized unprojection  $\Psi^{-1}$  using the least squares procedure detailed in SM C, resulting in a fitted function  $\bar{\Psi}^{-1}$ . The loss is then:
+
+$$
+\mathcal {L} ^ {\mathrm {u}} = \sum_ {x} \| \pi^ {- 1} (x) - \bar {\Psi} ^ {- 1} (x) \| _ {2}. \tag {14}
+$$
+
+This term encourages the learned unprojection to remain close to the parametric model, preventing divergence in regions with poor correspondences while still allowing fine-tuning to the specific input video sequence.
+
+Finally, we optimize AnyMap using the combined loss:
+
+$$
+\mathcal {L} = \mathcal {L} ^ {\mathrm {2 D}} + \lambda_ {\mathrm {m}} \mathcal {L} ^ {\mathrm {m}} + \lambda_ {\mathrm {u}} \mathcal {L} ^ {\mathrm {u}}. \tag {15}
+$$
+
+Initialization. We initialize AnyMap using a variant of [45]. For each candidate set  $\{f_k, \alpha_k\}$  of Unified Camera Model
+
+(UCM) [34] parameters, we solve for camera poses as in Sec. 3.2 and compute  $\mathcal{L}^{2\mathrm{D}}$  using UCM's (un)projection. We select the optimal  $f,\alpha$  using the softmax-weighted sum:
+
+$$
+f = \sum_ {k} w _ {k} f _ {k}, \quad \alpha = \sum_ {k} w _ {k} \alpha_ {k}, \quad w _ {k} = \frac {\exp \left(- \mathcal {L} _ {k} ^ {2 D}\right)}{\sum_ {l} \exp \left(- \mathcal {L} _ {l} ^ {2 D}\right)}. \tag {16}
+$$
+
+We optimize the network for 100 epochs using this initialization, utilizing the running mean of the estimated  $f$  and  $\alpha$  to initialize the camera network. We reset the range network to its initial weights and continue the optimization, now computing  $\mathcal{L}^{2\mathrm{D}}$  using the learned (un)projection  $\pi^{-1}$  and  $\pi$ .
+
+# 3.5. Implementation
+
+The range network uses a convolutional MiDAS [40] backbone, initialized with FlowMap [45] weights. The camera network is an INN with 3 nonlinear layers of dimension 8, implemented using [17]. We use ResFlow [8] for invertible transformations, as NICE [14] and RealNVP [15] lack sufficient representational power to model the camera. We optimize AnyMap for up to 8000 epochs, computing  $\mathcal{L}^{2\mathrm{D}}$  from RAFT [50] flow and CoTracker V1 [21] tracks. For  $\mathcal{L}^{\mathrm{m}}$ , we set  $\beta = 100$ . We enable  $\mathcal{L}^{\mathrm{u}}$  after 2000 epochs, re-fitting  $\Psi^{-1}$  every  $U = 100$  epochs. When only radial distortion is present,  $\Psi^{-1}$  is the unprojection of EUCM [23]; for both radial and tangential distortions, we use Fisheye624 [42]. We set  $\lambda_{\mathrm{m}} = 0.1$  and  $\lambda_{\mathrm{u}} = 0.05$ . The number of basis trajectories is  $B = 10$ , and  $\mathcal{G}$  applies a softmax with temperature  $t = 1.1$ . Under the static scene assumption, we do not optimize these basis trajectories or  $\mathcal{G}$ . Monodepth estimates come from Depth Pro [4]. Further details and INN comparisons can be found in SM E.
+
+# 4. Experiments
+
+We evaluate AnyMap in terms of camera calibration and image rectification (Sec. 4.2), downstream tasks like camera pose estimation and novel view synthesis (Sec. 4.3), and its performance in dynamic scenes with motion (Sec. 4.4).
+
+# 4.1. Experimental Setup
+
+We conduct experiments on an NVIDIA A100 GPU, and on real fisheye videos and synthetically distorted videos.
+
+Synthetic Distortion. To assess performance under varying distortion levels while maintaining consistent visual content, we synthetically distort videos using the six-parameter Kannala-Brandt model (KB6) [20]. We sample distortion coefficients  $k_{1}$  and  $k_{2}$  at equal intervals in the ranges  $[1/6, 1/3]$  and  $[1/8, 1/5]$ , respectively, generating five parameter tuples  $(k_{1}, k_{2})$  per sequence to simulate increasing distortions. We assume a unit aspect ratio and centered principal point.
+
+Datasets. We use real fisheye videos from Aria Everyday Activities (AEA) [33], featuring known radial and tangential distortions by the Fisheye624 [42] model, extracting
+
+![](images/f0eaec0720d3324a05c7bec132b5577190e7a57b20cfad47a7ab67465be738bf.jpg)  
+Figure 4. Qualitative Rectification Results. Comparisons to state-of-the-art monocular and multi-view image rectification methods illustrate the effectiveness of our method on MipNeRF-360 [2], LLFF [35], Tanks & Temples [24].
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">MipNeRF-360 [2] (3 scenes)</td><td colspan="5">LLFF [35] (5 scenes)</td><td colspan="5">Tanks &amp; Temples [24] (8 scenes)</td><td colspan="5">Aria Everyday Activities [33] (3 scenes)</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Re ↓</td><td>Δf ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Re ↓</td><td>Δf ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Re ↓</td><td>Δf ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Re ↓</td><td>Δf ↓</td></tr><tr><td>Auto-DC [1]</td><td>15.98</td><td>0.510</td><td>0.208</td><td>-</td><td>-</td><td>12.48</td><td>0.397</td><td>0.320</td><td>-</td><td>-</td><td>13.27</td><td>0.478</td><td>0.274</td><td>-</td><td>-</td><td>9.80</td><td>0.306</td><td>0.329</td><td>-</td><td>-</td></tr><tr><td>PCN [59]</td><td>20.46</td><td>0.634</td><td>0.139</td><td>-</td><td>-</td><td>15.29</td><td>0.482</td><td>0.143</td><td>-</td><td>-</td><td>15.30</td><td>0.530</td><td>0.156</td><td>-</td><td>-</td><td>15.04</td><td>0.498</td><td>0.172</td><td>-</td><td>-</td></tr><tr><td>GeoCalib [54]</td><td>16.20</td><td>0.588</td><td>0.171</td><td>5.01</td><td>2.12</td><td>13.26</td><td>0.420</td><td>0.197</td><td>8.97</td><td>3.05</td><td>14.27</td><td>0.501</td><td>0.189</td><td>7.85</td><td>2.98</td><td>14.92</td><td>0.476</td><td>0.179</td><td>8.02</td><td>3.11</td></tr><tr><td>Porfiri et al. [13]</td><td>21.09</td><td>0.685</td><td>0.093</td><td>3.29</td><td>1.54</td><td>15.90</td><td>0.498</td><td>0.130</td><td>7.05</td><td>2.47</td><td>18.48</td><td>0.602</td><td>0.115</td><td>6.39</td><td>2.29</td><td>13.24</td><td>0.428</td><td>0.160</td><td>9.21</td><td>2.85</td></tr><tr><td>GLOMAP [37]</td><td>22.23</td><td>0.730</td><td>0.054</td><td>1.50</td><td>0.84</td><td>18.05</td><td>0.550</td><td>0.098</td><td>3.21</td><td>1.17</td><td>21.06</td><td>0.704</td><td>0.069</td><td>2.87</td><td>1.03</td><td>17.20</td><td>0.587</td><td>0.124</td><td>4.94</td><td>1.26</td></tr><tr><td>COLMAP [43]</td><td>22.26</td><td>0.736</td><td>0.053</td><td>1.49</td><td>0.82</td><td>18.08</td><td>0.554</td><td>0.095</td><td>3.20</td><td>1.15</td><td>21.06</td><td>0.706</td><td>0.068</td><td>2.87</td><td>1.01</td><td>17.23</td><td>0.588</td><td>0.121</td><td>4.92</td><td>1.24</td></tr><tr><td>COLMAP MVS [44]</td><td>22.85</td><td>0.750</td><td>0.049</td><td>1.44</td><td>0.80</td><td>18.46</td><td>0.569</td><td>0.091</td><td>2.97</td><td>1.07</td><td>21.44</td><td>0.713</td><td>0.065</td><td>2.77</td><td>1.00</td><td>17.71</td><td>0.601</td><td>0.116</td><td>4.75</td><td>1.19</td></tr><tr><td>AnyMap</td><td>28.15</td><td>0.915</td><td>0.021</td><td>1.02</td><td>0.65</td><td>21.30</td><td>0.777</td><td>0.069</td><td>2.35</td><td>0.89</td><td>22.73</td><td>0.780</td><td>0.056</td><td>2.01</td><td>0.73</td><td>20.38</td><td>0.692</td><td>0.076</td><td>3.01</td><td>0.94</td></tr></table>
+
+Table 1. Rectification and Calibration Results. AnyMap surpasses monocular and multi-view methods on real sequences from Aria Everyday Activities [33] and synthetically distorted LLFF [35], MipNeRF-360 [2], Tanks & Temples [24].
+
+three 100-frame sequences. The sequences used for evaluation are detailed in SM D. $^{2}$  We synthetically distort the FlowMap [45] splits of MipNeRF-360 [2], LLFF [35], and Tanks & Temples (T&T) [24]. For dynamic scenes, we synthetically distort videos from the DAVIS [38] dataset. For T&T and DAVIS, we obtain pseudo ground-truth poses using COLMAP MVS [44], masking out dynamic objects.
+
+# 4.2. Camera Calibration and Image Rectification
+
+We compare AnyMap with monocular and multi-view calibration and rectification methods. For monocular, we include geometric Auto-DC [1], reconstruction-based PCN [59] (rectification only), and regression-based GeoCalib [54] and Porfiri et al.[13] (calibration and rectification). For multi-view, we evaluate COLMAP (MVS) [43, 44] and GLOMAP [37], configured with KB6 for radial distortions or Fisheye624 for both radial and tangential distortions in AEA [33]. To ensure fairness, we configure AnyMap as static, i.e.,  $\mathbf{T}_{i\rightarrow j} = \mathbb{I}_4$  for evaluation on static datasets.
+
+Metrics. To account for different camera models used by each method, we measure the relative focal length error
+
+$\Delta f$  and model-agnostic pixel reprojection error Re [13], normalized by image resolution. For image rectification, we use the usual PSNR, SSIM, and LPIPS.
+
+Discussion. Tab. 1 shows calibration results, with AnyMap outperforming the state-of-the-art monocular methods GeoCalib and Porfiri et al., as well as multi-view methods COLMAP (MVS) and GLOMAP. COLMAP and GLOMAP are evaluated under optimal conditions, using Fisheye624 for AEA and KB6 for the synthetic datasets. AnyMap also sets a new benchmark in image rectification (see Fig. 4), achieving the highest scores across all quality metrics.
+
+# 4.3. Pose Estimation & Novel View Synthesis
+
+We evaluate AnyMap for novel view synthesis using 3D Gaussian Splatting (3DGS) [22]. Specifically, we assess the Average Trajectory Error (ATE) of camera poses estimated by AnyMap, DROID-SLAM [51], MASt3R [16], and COLMAP (MVS) on distorted images, comparing them to pseudo ground-truth poses from COLMAP MVS on undistorted images, following [16, 45]. We use 3DGS Lightning [61] with rectified images from AnyMap and COLMAP (MVS). For AnyMap, we obtain the focal length by fitting the learned (un)projection (see Sec. 3 and SM C). DROID-SLAM requires known intrinsics and supports both KB6 and
+
+![](images/fd9896ac9af701d4894e4d029a856dc415f4a83f9086c76928d5f32c8d90876d.jpg)  
+Figure 5. Qualitative Novel View Synthesis and Pose Results. AnyMap produces superior results to COLMAP in 3DGS on LLFF [35] and Tanks & Temples [24]. AnyMap (orange) estimates camera poses from distorted images qualitatively similar to ground truth (cyan).
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">MipNeRF-360 [2] (3 scenes)</td><td colspan="5">LLFF [35] (5 scenes)</td><td colspan="5">Tanks &amp; Temples [24] (8 scenes)</td><td colspan="5">Aria Everyday Activities [33] (3 scenes)</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>ATE ↓</td><td>t ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>ATE ↓</td><td>t ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>ATE ↓</td><td>t ↓</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>ATE ↓</td><td>t ↓</td></tr><tr><td>MASt3R [16]</td><td>-</td><td>-</td><td>-</td><td>0.0612</td><td>1.1</td><td>-</td><td>-</td><td>-</td><td>0.0487</td><td>0.8</td><td>-</td><td>-</td><td>-</td><td>0.1092</td><td>1.7</td><td>-</td><td>-</td><td>-</td><td>0.0964</td><td>1.2</td></tr><tr><td>DROID-SLAM [37]</td><td>21.05</td><td>0.775</td><td>0.416</td><td>0.0428</td><td>0.6</td><td>19.05</td><td>0.698</td><td>0.420</td><td>0.0376</td><td>0.3</td><td>18.90</td><td>0.620</td><td>0.476</td><td>0.0943</td><td>0.8</td><td>16.54</td><td>0.574</td><td>0.452</td><td>0.0827</td><td>0.8</td></tr><tr><td>COLMAP [43]</td><td>28.22</td><td>0.910</td><td>0.174</td><td>0.0024</td><td>5.2</td><td>23.87</td><td>0.800</td><td>0.299</td><td>0.0045</td><td>1.3</td><td>24.76</td><td>0.777</td><td>0.304</td><td>0.0150</td><td>5.8</td><td>22.15</td><td>0.734</td><td>0.318</td><td>0.0128</td><td>8.7</td></tr><tr><td>COLMAP MVS [44]</td><td>28.77</td><td>0.918</td><td>0.170</td><td>0.0023</td><td>40.5</td><td>23.98</td><td>0.803</td><td>0.297</td><td>0.0042</td><td>12.8</td><td>24.98</td><td>0.781</td><td>0.298</td><td>0.0142</td><td>49.0</td><td>22.35</td><td>0.738</td><td>0.310</td><td>0.0120</td><td>35.2</td></tr><tr><td>AnyMap</td><td>32.08</td><td>0.932</td><td>0.169</td><td>0.0022</td><td>10.3</td><td>23.32</td><td>0.820</td><td>0.290</td><td>0.0034</td><td>6.4</td><td>26.33</td><td>0.814</td><td>0.262</td><td>0.0092</td><td>18.4</td><td>25.03</td><td>0.789</td><td>0.278</td><td>0.0101</td><td>9.5</td></tr></table>
+
+Fisheye624 models. We initialize 3DGS with point clouds from each method and optimize scenes using  $90\%$  of the views for training and  $10\%$  for testing. PSNR, SSIM, and LPIPS are computed against the original undistorted images.
+
+Discussion. As shown in Tab. 2, AnyMap outperforms COLMAP and DROID-SLAM on average across all datasets in terms of ATE, albeit with about 2.8 times the runtime of COLMAP. For novel view synthesis, AnyMap surpasses DROID-SLAM in all metrics and exceeds COLMAP in all metrics except PSNR on the LLFF dataset, where COLMAP leads by about  $2\%$ . MAST3R performs poorly on distorted sequences, yielding the lowest scores among the evaluated methods. As illustrated in Fig. 5, our method also achieves superior qualitative results in novel view synthesis for distorted videos compared to COLMAP.
+
+# 4.4. Dynamic Scenes
+
+We evaluate AnyMap on synthetically distorted videos from the DAVIS [38] dataset, featuring prominent moving foreground objects. Since existing learning-based methods do not handle unknown extrinsics, intrinsics, and depths with lens distortion, we assess MonST3R [62] (zero-shot) and CasualSAM [64], fine-tuned per video under a pinhole camera model with unknown extrinsics. To enable CasualSAM to handle lens distortion and test our camera model's adaptability, we replace its pinhole (un)projection with our camera network learning  $\pi^{-1}$ , creating the variant CasualSAM+CN, which now supports distortion. We then evaluate the full AnyMap framework and two variants: (i) AnyMap (static),
+
+Table 2. Pose Estimation and Novel View Synthesis Results. AnyMap outperforms MAST3R, DROID-SLAM, and COLMAP (MVS) in pose estimation and 3DGS quality on distorted datasets. While 2.8 times slower than COLMAP, AnyMap is 3.1 times faster than COLMAP MVS, with better results in most view synthesis quality metrics. Time  $t$  is in minutes.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="8">DAVIS [38] (3 scenes)</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Repx ↓</td><td>ATE ↓</td><td>Abs Rel ↓</td><td>δ&lt;1.25 ↑</td><td>t ↓</td></tr><tr><td>CasualSAM [64]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.228</td><td>0.581</td><td>39.04</td><td>369</td></tr><tr><td>CasualSAM*</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.130</td><td>0.455</td><td>58.02</td><td>369</td></tr><tr><td>MonST3R [62]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.214</td><td>0.548</td><td>42.54</td><td>50</td></tr><tr><td>MonST3R*</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.121</td><td>0.440</td><td>59.05</td><td>50</td></tr><tr><td>Porfiri et al. [13]</td><td>15.09</td><td>0.520</td><td>0.188</td><td>9.23</td><td>-</td><td>-</td><td>-</td><td>3</td></tr><tr><td>CasualSAM + CN</td><td>16.78</td><td>0.568</td><td>0.165</td><td>8.47</td><td>0.137</td><td>0.466</td><td>56.36</td><td>391</td></tr><tr><td>AnyMap (static)</td><td>12.28</td><td>0.402</td><td>0.210</td><td>11.03</td><td>0.238</td><td>0.627</td><td>32.01</td><td>489</td></tr><tr><td>AnyMap+CVD</td><td>17.05</td><td>0.589</td><td>0.148</td><td>8.21</td><td>0.130</td><td>0.480</td><td>55.61</td><td>612</td></tr><tr><td>AnyMap</td><td>22.54</td><td>0.701</td><td>0.082</td><td>3.20</td><td>0.106</td><td>0.432</td><td>59.27</td><td>603</td></tr></table>
+
+Table 3. Rectification, Calibration, Pose, and Depth Estimation Results on dynamic scenes from the DAVIS [38] dataset. Methods marked with * are evaluated on undistorted images for reference. Time is measured in seconds.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">MipNeRF-360 [2]</td><td colspan="3">LLFF [35]</td><td colspan="3">T&amp;T [24]</td><td colspan="3">AEA [33]</td></tr><tr><td>LPIPS</td><td>Re</td><td>ATE</td><td>LPIPS</td><td>Re</td><td>ATE</td><td>LPIPS</td><td>Re</td><td>ATE</td><td>LPIPS</td><td>Re</td><td>ATE</td></tr><tr><td>AnyMap (w/o Lna)</td><td>0.035</td><td>1.22</td><td>0.0024</td><td>0.080</td><td>2.69</td><td>0.0042</td><td>0.059</td><td>2.39</td><td>0.0138</td><td>0.087</td><td>3.69</td><td>0.0112</td></tr><tr><td>AnyMap (dynamic)</td><td>0.023</td><td>1.04</td><td>0.0024</td><td>0.073</td><td>2.42</td><td>0.0040</td><td>0.057</td><td>2.03</td><td>0.0110</td><td>0.080</td><td>3.05</td><td>0.0109</td></tr><tr><td>AnyMap (parametric)</td><td>0.078</td><td>2.21</td><td>0.0032</td><td>0.104</td><td>3.15</td><td>0.0061</td><td>0.085</td><td>3.06</td><td>0.0196</td><td>0.130</td><td>5.20</td><td>0.0138</td></tr><tr><td>AnyMap</td><td>0.021</td><td>1.02</td><td>0.0022</td><td>0.069</td><td>2.35</td><td>0.0034</td><td>0.056</td><td>2.01</td><td>0.0092</td><td>0.076</td><td>3.01</td><td>0.0101</td></tr></table>
+
+Table 4. AnyMap variants show the impact of design choices in our method. For all metrics, lower is better. Full table in SM F.
+
+setting  $\mathbf{T}_{i\rightarrow j} = \mathbb{I}_4$ ; and (ii) AnyMap+CVD, replacing our low-dimensional motion representation with dense motion prediction as in CVD [63]. In this variant, our MLP  $\mathcal{G}$  is replaced by  $\mathcal{H}$ , which directly predicts motion vectors for each 3D point and time frame instead of using weights to interpolate basis trajectories. Practically, this modifies Eq. (7) to:  $X_{j}(x) = X_{i}(x) + \mathcal{H}(X_{i}(x),i)$ . For fairness, all methods use RAFT [50] and Depth Pro [4].
+
+Metrics. For calibration, rectification, and poses, we use the
+
+![](images/b99e741026620e4c83b29cdaac3762e800a7c71acdd5ef17376424c9f2523f8a.jpg)  
+Figure 6. Qualitative comparison of learning-based SfM methods handling scene motion and lens distortion.
+
+metrics from Sec. 4.2 and 4.3. Depth estimation performance is measured using the absolute relative error (Abs Rel) and percentage of inlier points  $(\delta_{<1.25})$ , as in [62], against pseudo ground-truth depths from Shape of Motion [56], provided with COLMAP MVS-extrinsics and intrinsics.
+
+Discussion. Tab. 3 shows dynamic scenes results. AnyMap (static) shows poor performance in calibration, pose, and depth estimation. Similarly, CasualSAM and MonST3R achieve subpar pose and depth results. CasualSAM+CN, which integrates our camera network, outperforms both CasualSAM and the baseline monocular rectification method by Porfiri et al.[13], demonstrating the effectiveness of our camera network within existing frameworks. CasualSAM tends to predict compensating motion, especially at image borders, due to high correspondence uncertainty from inadequate distortion handling, leading to significant rectification artifacts (see Fig.6). AnyMap+CVD performs better than CasualSAM+CN but is outperformed by our full AnyMap with a low-dimensional motion representation across all metrics, despite having slower runtimes. Although our method is  $56\%$  slower than CasualSAM on average, it achieves higher accuracy. Furthermore, AnyMap provides superior pose estimation and comparable depth estimation compared to CasualSAM and MonST3R evaluated on undistorted images.
+
+# 5. Ablation Study
+
+We analyze the impact of AnyMap's design choices. Tab. 4 demonstrates the effectiveness of the unprojection loss  $\mathcal{L}^{\mathrm{u}}$  on real and synthetic datasets, showing performance regression when  $\mathcal{L}^{\mathrm{u}}$  is disabled. Notably, AnyMap outperforms COLMAP (MVS) even without  $\mathcal{L}^{\mathrm{u}}$ , indicating that the optimization remains stable and produces high-quality results without supervision of the learned  $\pi^{-1}$ . For synthetic images
+
+![](images/d7c5f1fd5dcd2728225ab4c9d081acf2d8a552527697a48e35356e7a9ade10cd.jpg)  
+Figure 7. Supervision of learned (un)projection leads to improved qualitative results in rectification in MipNeRF-360 (garden) [2].
+
+![](images/99a6f8e30451eab274b250e2ff9a9d106cc47ede3e4b5aa0454e61f9410ba701.jpg)
+
+![](images/9f3fea340d401f4f08dbed3e3c5b2425b56b7c7a1abc223536edbf999d42705b.jpg)
+
+![](images/781aacfaad53521c72854c4e2e85b16636d6fc682e83d0a7235bc27d124656a3.jpg)
+
+with KB6, we supervise  $\pi^{-1}$  by fitting it to the unprojection  $\Psi^{-1}$  of the EUCM model, ensuring we do not artificially benefit from matching the synthetic camera model to the fitted one. Fig. 7 shows a failure case without  $\mathcal{L}^{\mathrm{u}}$ , where rectification diverges at image edges due to unreliable correspondences; applying  $\mathcal{L}^{\mathrm{u}}$  corrects this, improving image rectification. We also ablate the effect of not enforcing the constraint  $\mathbf{T}_{i\rightarrow j} = \mathbb{I}_4$  in static scenes. Aside from a marginal performance regression in reprojection error Re of about  $1.8\%$  on average, we observe a  $24\%$  speedup for the static AnyMap, as  $\mathcal{G}$  is neither tasked with motion prediction nor optimized (see full table in SM F). Finally, in Tab. 4, we test the effectiveness of our camera network by replacing  $\pi^{-1}$  and  $\pi$  with parameterized (un)projection functions of the KB6 and Fisheye624 models, optimizing focal length and distortion parameters directly—this variant is called AnyMap (parameterized). Using the same initialization, this leads to a significant performance regression and optimization issues [13], yielding lower results than multiview methods.
+
+Additional evaluations in SM F show that our monocular depth loss  $\mathcal{L}^{\mathrm{m}}$  effectively prevents scale drift of moving objects; without it, scale drift occurs.
+
+# 6. Conclusion
+
+We introduced AnyMap, a gradient-descent-based SfM framework handling lens distortion and dynamic scenes. We show that AnyMap excels at calibration, rectification, pose estimation, and novel view synthesis. Being differentiable, AnyMap could serve as a foundation for self-supervised monodepth estimation and general novel view synthesis.
+
+Limitations. Our method is slower and more memory-intensive than scene coordinate regressors like ACE0 [6], although memory can be reduced by subsampling frames during gradient descent or using a compact image encoder. Relying on optical flow and point tracks, AnyMap operates only on video sequences. Like most dynamic SfM methods, inaccurate monodepths can hinder motion estimation accuracy, but our multi-view optimization mitigates this issue. In scenes with dominant motion, the reference frame may focus on dynamic objects, causing static backgrounds to be treated as moving—a problem mitigated by motion masks.
+
+# References
+
+[1] Miguel Aleman-Flores, Luis Alvarez, Luis Gomez, and Daniel Santana-Cedrés. Automatic lens distortion correction using one-parameter division models. Image Processing On Line, 4:327-343, 2014. 2, 6  
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\ No newline at end of file
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+# AnyMoLe: Any Character Motion In-between Leveraging Video Diffusion Models
+
+Kwan Yun Seokhyeon Hong Chaelin Kim Junyong Noh KAIST, Visual Media Lab
+
+{ yunandy, ghd3079, chaelin.kim, junyongnoh}@kaist.ac.kr
+
+# Abstract
+
+Despite recent advancements in learning-based motion in-between, a key limitation has been overlooked: the requirement for character-specific datasets. In this work, we introduce AnyMoLe, a novel method that addresses this limitation by leveraging video diffusion models to generate motion in-between frames for arbitrary characters without external data. Our approach employs a two-stage frame generation process to enhance contextual understanding. Furthermore, to bridge the domain gap between real-world and rendered character animations, we introduce ICAdapt, a fine-tuning technique for video diffusion models. Additionally, we propose a "motion-video mimicking" optimization technique, enabling seamless motion generation for characters with arbitrary joint structures using 2D and 3D-aware features. AnyMoLe significantly reduces data dependency while generating smooth and realistic transitions, making it applicable to a wide range of motion in-between tasks. The code and videos are available at project page.
+
+# 1. Introduction
+
+Keyframe interpolation is essential in the animation creation process, providing smooth and natural transitions between keyframes to achieve lifelike character movements. Traditionally, this process has been highly labor-intensive, often involving extensive manual adjustments to refine the animation. In recent years, while the adoption of motion capture (MOCAP) technologies has helped alleviate this manual burden, its high costs and infeasibility for certain characters and animals present significant challenges. To address these limitations, deep learning-based motion in-between methods have emerged, making notable advancements [12, 18]. These efforts have focused on developing sophisticated architectures [9, 13, 32, 33] and utilizing large datasets [18] to generate realistic motion sequences over long durations. Nevertheless, a major hurdle persists: training existing in-between models still demands vast amounts of MOCAP or manually keyframed
+
+Figure 1. AnyMoLe generates in-between motion from context frames and keyframes without requiring external training data.
+
+data for each character. This is a crucial issue, as motion in-between is not only valuable for well-documented characters but is even more essential for those that are difficult to capture with MOCAP or lack extensive keyframed data.
+
+Recent advancements in video generation models, trained on web-scale video datasets, have enabled the generation of realistic videos from arbitrary text [4-6, 16] or images [46, 56]. Additionally, some models have demonstrated the ability to interpolate between two images, naturally generating a range of transitioning scene elements or camera movements [10, 46, 47]. These capabilities align closely with the goal of motion in-betweening, as video generation models excel at creating smooth transitions and continuous motion. Therefore, these models can address data scarcity issues often encountered in 3D motion in-betweening and leverage the generation of realistic motions from rendered keyframes, which become the essential foundation of our motion in-betweening process.
+
+We propose a novel motion in-betweening method, AnyMoLe, which addresses the problem of scarcity of character-specific datasets. AnyMoLe leverages video diffusion models to generate in-betweening motion through a sequential process of rendering, video generation, and motion optimization. In this process, we observed that naively generating an interpolated video and reconstructing a 3D character often yielded unsatisfactory results due to: 1) limited contextual understanding, 2) domain gaps between real-world and rendered scenes, and 3) difficulties in accurately tracking motion from a generated video. To address these issues, we propose components specifically designed to overcome each challenge.
+
+Limited contextual understanding arises from the fixed input of video diffusion models, which only utilize the first and last frames, without direct knowledge of the intermediate or previous frames. To address this lack of contextual awareness, we condition frame generation on previous frames as motion context, treating the problem as frame inpainting by incorporating masked noise during the video generation process. Additionally, we employ a two-stage approach for smooth video generation: first, generating sparse frames to establish the motion structure, followed by dense frame generation to fill in the details.
+
+The domain gap stems from differences in the distributions between real-world videos and rendered scenes. Video diffusion models are typically trained on real-world videos, which often feature elements like motion blur and complex organic environments. In contrast, rendered scenes usually depict synthetic environments and virtual characters. To bridge this gap, we employ Inference-stage Context Adaptation (ICAdapt). This approach fine-tunes the video diffusion model by using only a short, 2-second segment of context motion. During this process, the spatial module is overfitted to accurately represent specific virtual characters, while the temporal module remains frozen to preserve the learned motion dynamics.
+
+To address the difficulty in tracking the motion of arbitrary rigged characters in the generated video, we propose a novel motion-video mimicking method. Motion-video mimicking is similar to 3D reconstruction with a difference in allowed degree of freedom, as it is for rigged characters with an arbitrary joint structure. For motion-video mimicking, we propose a sequential optimization approach that predicts the states of 3D joints to generate smooth transitions. The joint prediction is performed by our newly proposed scene-specific joint estimator, specifically designed for motion in-betweening in a few-shot setting, using only the context frames and keyframes for training.
+
+Table 1. Difference between AnyMoLe and baseline methods.  
+
+<table><tr><td>Methods</td><td>Characters</td><td>Training data</td><td>Output</td></tr><tr><td>AnyMoLe</td><td>Arbitrary</td><td>None</td><td>3D motion</td></tr><tr><td>TS [33]</td><td>Human</td><td>3D motion Dataset</td><td>3D motion</td></tr><tr><td>Deciwatch [53]</td><td>Human</td><td>video-3D poses Dataset</td><td>3D poses</td></tr></table>
+
+By integrating these techniques, AnyMoLe successfully performs the first motion in-betweening for arbitrary characters as shown in Figure 1. The differences between AnyMoLe and previous methods are highlighted in Table 1. Our contributions can be summarized as follows:
+
+- By utilizing a video diffusion model with two stage inference for contextual understanding, we propose the first motion in-betweening method for arbitrary characters without external data.  
+- We present ICA adapt, to bridge the domain gaps between real-world videos and rendered scenes by finetuning a video diffusion model.
+
+- We introduce a novel optimization technique for motion-video mimicking, which enables sequential motion optimization for arbitrary characters.  
+- We propose a new scene-specific joint estimator, specialized for a specific rendering scene, which utilizes 2D and 3D-aware features for effective 3D joint estimation.
+
+# 2. Related Work
+
+# 2.1. Motion In-betweening
+
+Motion in-between aims to generate smooth and natural motion transitions by a 3D character conditioned on a sparse set of keyframes. Early approaches mainly utilized optimization with space-time constraints [35, 45] or radial basis functions [36, 37] to interpolate keyframes. Other approaches leveraged motion graphs [26, 27] constructed from a given motion dataset, where optimal paths connecting two keyframes are found within these graphs [25]. Statistical models such as maximum a posteriori [7] and geostatistical models [30] were also employed for transition synthesis.
+
+With the rise of learning-based methods, neural network models have produced promising results for motion in-betweening. Specifically, Recurrent Neural Networks [17, 18, 23, 39, 40], Convolutional Neural Networks [19, 22, 28, 58], and Transformers [21, 32, 33] have been widely adopted. Recently, diffusion-based models have gained popularity for their ability to generate intermediate transitions by leveraging their generative capabilities [9, 24, 41]. Despite these advancements, performing motion in-betweening for diverse characters within a single model remains challenging, because preparing extensive animation data for each specific character is infeasible. In contrast, our method harnesses the capabilities of video diffusion models to create in-between frames for any characters with arbitrary joint structures, bypassing the need for preparing extensive motion data.
+
+# 2.2. Diffusion Based Video Interpolation Models
+
+Recent advancements in image-conditioned video diffusion models enable the generation of promising results for video frame interpolation, particularly addressing the limitations of traditional methods. Diffusion models, originally applied to large-scale text-to-video (T2V) generation [5, 20, 38, 44, 48], have been extended to image-to-video (I2V) synthesis [4, 15, 43, 46, 56]. Techniques such as SEINE [8] and PixelDance [54] leverage these models to generate image transitions, while DynamiCrafter [46] utilize them for frame interpolation between two input images. Most recently, ToonCrafter [47] finetuned a general interpolation model, to become cartoon interpolation model using a relatively small dataset of cartoon videos (a few hundred thousand samples compared to the original dataset of ten millions). Similarly, we finetune a video diffusion model but with only two seconds of context motion for single motion adaptation.
+
+![](images/59205df1a42911fa85034435f1a306520f28ceaf8a282107634b10dad81fd4d0.jpg)  
+Figure 2. Overview of AnyMoLe: First, the video diffusion model is fine-tuned without using any external data (Sec. 3.1) while the scene-specific joint estimator is trained (Sec. 3.3.1). Next, the fine-tuned video generation model produces an in-between video (Sec. 3.2), which is then refined through motion video mimicking to generate the final in-between motion (Sec. 3.3).
+
+# 3. Methods
+
+Given two seconds of context motion and target key frames for a 3D character, AnyMoLe performs 3D motion in-between using a video diffusion model, as illustrated in Figure 2. The process can be described as follows:
+
+1. Using the two seconds of context motion and target keyframes, render each frame from diverse views.  
+2. From the multi-view rendered images, finetune the video diffusion model and train a scene-specific joint estimator concurrently using both 2D and 3D-aware features.  
+3. The finetuned video diffusion model generates an inbetween video in a two stage auto-regressive manner: first, generate coarse frames from the given context and key frames, second, fill in the remaining frames.  
+4. Optimize character motion sequentially to align it motion with the generated video using a differentiable renderer and the trained joint estimator.
+
+In the following subsections, we will describe the ICA adapt (Sec. 3.1), two stage conditional video generation process (Sec. 3.2), and progressive optimization process for motion-video mimicking (Sec. 3.3).
+
+# 3.1. Inference-stage Context Adaptation
+
+We use DynamiCrafter [46], a state-of-the-art open-source video interpolation model as our baseline. While this video diffusion model has demonstrated robust motion understanding capability for live-action videos, there is a domain gap when applying it to rendered character animation. For example, rendered scenes contain virtual avatars and synthetic backgrounds that differ from the scenes observed in real-world videos, and they lack camera effects such as motion blur. Therefore, we finetune the video diffusion model at the start of inference, using the videos rendered from two seconds of given context motions. If we train the whole video diffusion model using a single motion, it will lead to catastrophic forgetting which was evident in Xing et al. [47]. Therefore, we finetune the spatial module and image projector of DynamiCrafter while preserving the original temporal module and fps embedding. This process ensures
+
+that finetuned model  $D_{adp}$  faithfully generates a video as it is rendered while keeping its ability to generate new motions.
+
+![](images/2c2e12e3fbf03f557e2246f8110784feebae4ba3c687c6f3cf10f3d195e6d9f6.jpg)  
+Context Motion  
+Figure 3. Overview of the ICA adapt training process. The spatial module and image injection module are trained, while the others are frozen.
+
+Specifically, for the input, we render two seconds of motion at 30 fps from  $N$  different views, resulting in  $N$  videos. Then, we sample images with intervals of 1, 2, and 3 frames, which becomes 30, 15, and 10 fps videos, respectively. We segment each video into 16 frame intervals using a sliding window to align with the output dimension of  $D_{adp}$ . As a result, the two seconds motion is converted to multiple video clips, each containing 16 frames, aligning with the output dimension of the diffusion model. Finetuning the spatial module and image projector with these clips ensures that the generated videos fall in the domain of rendering scene while preserving the details of the input character.
+
+Figure 3 shows the process for ICA adapt, whose objective function is defined as follows:
+
+$$
+\min  _ {\theta} \mathbb {E} _ {\mathcal {E} _ {v a e} (\mathbf {x}), t, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {z} _ {t}; I _ {0}, I _ {N}, \mathbf {t x t}, t, f p s\right) \| _ {2} ^ {2} \right], \tag {1}
+$$
+
+where  $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$  represents noise,  $I_0$  and  $I_N$  denote the first and last frames, txt is a text condition automatically generated from a pretrained video captioning model [51],
+
+![](images/dcc7d868804d9e115387368877e0e5c1a2159ada86576f143afe25b83fedf1c3.jpg)  
+Figure 4. Context frames guided video generation process.
+
+and  $fps$  refer to the frame rate. This training aims to capture the spatial information that remains constant (e.g., scene environment and character) while avoiding overfitting to the temporal information that may change (e.g., walking to running). The training is conducted in latent space, as  $D_{\text{adp}}$  is a latent diffusion model.
+
+# 3.2. Two-stage Video Generation
+
+With the finetuned video diffusion model  $D_{adp}$ , we can now generate an interpolated video for the target character, a recipe for our final in-betweened motion. Here, naively generating a video from keyframes would produce results with wrong context, as interpolation lacks contextual information about the previous motion. To generate a video that naturally reflects the given context, we first produce coarse frames by using context frames as guidance in an auto-regressive manner. Because  $D_{adp}$  is a video interpolation model that originally takes only the first and last images as input and cannot utilize additional context frames, we reformulate the task of interpolation with context frame guidance as a problem of latent inpainting during the diffusion process [3, 29]. Specifically,  $D_{adp}$  takes the rendered images  $I_0$  and  $I_N$  as input and generates  $I_n$  where  $\{n \in \mathbb{Z} \mid 1 \leq n \leq N - 1\}$ . With guidance frames  $I_m$  where  $\{m \in \mathbb{Z} \mid M_1 \leq m \leq M_2\}$ ,  $M_2 < N$ , we iteratively use these frames  $I_m$  during the backward denoising process. For example, at timestep  $t$  during denoising, noisy latents  $z_{n_t}$  are replaced with the encoded guidance frames combined with noise  $\epsilon_t$ , which is equivalent to producing them through the forward diffusion process. Please refer to Figure 4 for illustration that replaces corresponding parts of  $z_{n_t}$  with  $\mathcal{E}_{vae}(I_m) + \epsilon_t$  to produce  $z_{n_t}'$ . This process is carried out iteratively, regenerating  $I_m$  while ensuring that the interpolated results are correctly aligned with the distribution of  $D_{adp}$ .
+
+After the iterative generation, the interpolated sparse video is generated. Because this video is generated with a low frame-rate with large semantic jumps across neighbor
+
+ing frames, the resulting motion is unlikely to be smooth. To address this, we perform the second stage for fine video generation. Similar to the first stage, we use keyframes as input but with a smaller time interval. As we additionally have the frames generated in the first stage, they can be effectively used as guidance for the second stage. This process is shown in Figure 5. Blue boxes represent given frames, green boxes represent generated frames, and gray boxes represent the frames that are yet to be generated.
+
+![](images/94b79c8f0f58bbbfc35a2b8b3923e23130eb0616f05ebf3a274786b779d583e5.jpg)  
+Figure 5. Two stage inference of  $D_{adp}$ . First, at coarse stage, low frame-rate video is generated in auto regressive manner. Next, high frame-rate video is generated from low frame-rate video.
+
+# 3.3. Motion-video Mimicking
+
+The purpose of motion video mimicking is to elevate the generated video into 3D motion data, guided by keyframes, to produce the final motion output. We achieve this by optimizing the root position  $P$  and per-joint rotation  $R$ , starting from keyframes using our scene-specific 3D joint estimator  $\mathcal{E}_{\text{scene}}$ . We will first discuss the  $\mathcal{E}_{\text{scene}}$  in Sec 3.3.1 and the optimization process in Sec 3.3.2.
+
+# 3.3.1. Scene-specific Joint Estimator
+
+Accurate joint position estimation is a fundamental objective for optimizing motion in video analysis. Although there are few general-purpose 2D keypoint detection methods [49, 50], we observed that these approaches, typically trained on real images, often fail to generalize to unseen rendered characters. To address this limitation, we propose a 3D joint estimation network  $\mathcal{E}_{\text {scene }}$ , specialized in a specific scene. The training process is shown in Figure 6. We use the same dataset as in ICAdapt, supplemented with additional images for target keyframes, applying a weight  $w > 1$ . This weight is used to avoid overfitting to context frames, because the context frames are extracted at 30 fps, while the keyframes are at 1 fps. Moreover, we exclude images rendered from back views because only the front views will be used for motion-video mimicking. Training  $\mathcal{E}_{\text {scene }}$  with back views would confuse left-right information.
+
+Despite incorporating two seconds of context frames and keyframes, the available data remains relatively limited in size to train a 3D estimator from scratch. To bolster performance of  $\mathcal{E}_{\text {scene }}$  with limited data, we leverage
+
+![](images/d54f41749a089449da61f099ae0c9e2b90446fc726dde5e08a49a478128a31bc.jpg)  
+Figure 6. Overview of joint estimator training process.
+
+features from DINOv2 [31], which are trained with register tokens [11]. These features encapsulate rich semantic information through self-supervised training on extensive image datasets. Recognizing that DINOv2 effectively captures 2D semantic features but lacks an inherent understanding of 3D structures, we supplement DINOv2 features with FiT3D [52] features, a 3D-aware variant that provides structural guidance. The feature merger is achieved using lightweight convolutional layers and concatenation to prevent overfitting. The resultant fused feature  $F$  is subsequently decoded into heatmaps, facilitating precise 2D pose estimation.
+
+We pass the estimated 2D joint positions through MLP layers to predict depth for each joint. Building on recent findings [57] that emphasize the superiority of contextual features over large datasets for 3D pose estimation, we leverage  $F$  also for per joint depth estimation. Specifically, we sample the feature  $f_{x,y} \in \mathbb{R}^{1 \times 1 \times C}$  from  $F$ , which corresponds to the estimated 2D joint in spatial dimension. Then, the sampled feature  $f_{x,y}$  is concatenated with the estimated 2D joint position and passed through a Depth MLP for the estimation of a per joint depth value. The training objective of  $\mathcal{E}_{\text{scene}}$  is based on a MSE loss, defined as follows:
+
+$$
+L _ {\text {j o i n t}} = \left\| \mathcal {T} \left(G _ {\text {j o i n t}}, p _ {\text {c a m}}\right) - J _ {\text {e s t}} \right\| _ {2} ^ {2}, \tag {2}
+$$
+
+where  $G_{joint}$  indicates the ground-truth 3D joint positions in global space, automatically derived using context frames and keyframes,  $p_{cam}$  denotes the camera parameters,  $\mathcal{T}$  is an affine transformation that projects global positions onto screen space, and  $J_{est}$  indicates the estimated joint positions. Given that the depth is represented in normalized device coordinates (NDC) space, we denormalize it using the half of height to match the range of width-height and depth information.
+
+# 3.3.2. Optimization Process
+
+We initiate the optimization process using two keyframes, denoted as  $P_{k_1}, R_{k_1}$  and  $P_{k_2}, R_{k_2}$ , which represent the root positions and per-joint rotations at frames  $k_1$  and  $k_2$ , re
+
+spectively. From these keyframes, we iteratively optimize the motion parameters for interpolated frames by moving inwards toward the center. Specifically, we first optimize the parameters for the frames adjacent to the keyframes:  $P_{k_1 + 1}, R_{k_1 + 1}$  and  $P_{k_2 - 1}, R_{k_2 - 1}$  and for each subsequent frame, we initialize the optimization using the parameters from the nearest previously optimized frames. This optimization process continues as long as  $k_1 + f < k_2 - f$ , where  $f$  is the number of frames optimized from each keyframe. This sequential optimization ensures fast convergence and maintains temporal coherence with adjacent frames. Because the keyframes are the only ground truth data available, they serve as the initial poses during the optimization of the surrounding frames.
+
+In addition to 3D joint positions estimated using  $\mathcal{E}_{\text {scene }}$ , we utilize an image loss to minimize the image-wise difference between the rendered character and the generated video. This image loss captures subtle movements that the joint loss might miss. We also utilize two regularization losses,  $L_{reg}$ . Position regularization enforces the root position to be similar to the position of two nearest keyframes, while rotation regularization enforces the current rotation to be similar to that of the previous frame to stabilize the optimization process. To this end, the objective for Motion-Video Mimicking is defined as follows:
+
+$$
+\operatorname * {a r g m i n} _ {P, R} \| \mathcal {T} (\mathcal {M} (P, R), p _ {c a m}) - \mathcal {E} _ {\text {s c e n e}} (\hat {I}) \| _ {2} ^ {2} + \lambda_ {i m g} \| I _ {P, R} - \hat {I} \| _ {2} ^ {2} + L _ {r e g}
+$$
+
+$$
+\text {w h e r e} L _ {\text {r e g}} = \lambda_ {\text {p o s}} \| P _ {j} - P _ {\text {i n t p}} \| _ {2} ^ {2} + \lambda_ {\text {r o t}} \| R _ {j} - R _ {\text {p r e v}} \| _ {2} ^ {2}. \tag {3}
+$$
+
+Here,  $\hat{I}$  represents a single frame from the generated video,  $\mathcal{M}(P,R)$  represents the 3D positions of joints in the global coordinate system given the local rotation and global position,  $p_{cam}$  and  $\mathcal{T}$  follows the notations of Eq. 2. The terms  $\lambda_{img},\lambda_{pos}$ , and  $\lambda_{rot}$  denote the weights, and  $I_{P,R}$  represents the rendered image given the root position and rotation. Through this optimization process, we can obtain the final 3D positions and rotations of the target character, resembling the generated 2D video.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+We implemented AnyMoLe and conducted all training and inference on a computer with an Nvidia A6000 GPU. For ICA adapt, frames are rendered in four different views ( $N = 4$ ; front, left, right, and back), while the back view is discarded for  $\mathcal{E}_{\text{scene}}$ . ICA adapt was conducted for 500 steps with a batch size of 16, while  $\mathcal{E}_{\text{scene}}$  was trained for 3,500 steps with a batch size of 32. Weight  $w$  for keyframes in Figure 6 was set to 3. For two-stage inference, the first stage generated a 5fps video, while the second stage generated a 15fps video. After optimization on the 15fps video, we upsampled the video to 30fps for evaluation by apply
+
+![](images/b8364c19bbe82431461e599fb2da5e7e82a87e11715a17a36dc58a9f5b80e9aa.jpg)  
+Figure 7. Results of baseline comparison. Our method generated in-between frames similar to the ground truth, while SinMDM and SinMDM* generated out-of-context motion (blue box). TST generated partially out-of-context footsteps (blue box) and out-of-style motion (red box). ERD-QV generated motion that has a different style, with a stiff back and sharp hand positions (red box).
+
+Table 2. Quantitative results compared with the baselines. Ours outperformed all competitors with by margin.  
+
+<table><tr><td>Character</td><td colspan="8">Humanoid</td><td colspan="7">Non-humanoid</td></tr><tr><td>Methods</td><td>HL2Q↓</td><td>L2Q↓</td><td>L2P↓</td><td>NPSS↓</td><td>LPIPS↓</td><td>CLIP↑</td><td>SSIM↑</td><td>HL2Q↓</td><td>L2Q↓</td><td>L2P↓</td><td>NPSS↓</td><td>LPIPS↓</td><td>CLIP↑</td><td>SSIM↑</td><td></td></tr><tr><td>Ours</td><td>0.0015</td><td>0.0011</td><td>0.0063</td><td>0.0726</td><td>0.0547</td><td>0.9711</td><td>0.9343</td><td>0.0019</td><td>0.0021</td><td>0.0299</td><td>0.1863</td><td>0.0433</td><td>0.9675</td><td>0.9531</td><td></td></tr><tr><td>SinMDM</td><td>0.0971</td><td>0.0386</td><td>0.3733</td><td>1.7148</td><td>0.1007</td><td>0.9393</td><td>0.9185</td><td>0.2465</td><td>0.1710</td><td>0.1382</td><td>4.4324</td><td>0.0816</td><td>0.9536</td><td>0.9362</td><td></td></tr><tr><td>SinMDM*</td><td>0.0981</td><td>0.0390</td><td>0.3991</td><td>1.7584</td><td>0.1053</td><td>0.9287</td><td>0.9161</td><td>0.2467</td><td>0.1713</td><td>0.1973</td><td>4.4076</td><td>0.0943</td><td>0.9495</td><td>0.9332</td><td></td></tr><tr><td>TST</td><td>0.0028</td><td>0.0106</td><td>0.0209</td><td>4.3509</td><td>0.0953</td><td>0.9606</td><td>0.9148</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>ERD-QV</td><td>0.0028</td><td>0.0109</td><td>0.0098</td><td>4.3801</td><td>0.0693</td><td>0.9656</td><td>0.9272</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr></table>
+
+ing a Gaussian filter and slerp. Weights  $\lambda_{img}$ ,  $\lambda_{pos}$ , and  $\lambda_{rot}$  in Eq.3 were set to 50, 7,000, and 30,000, respectively. For all of our experiments, we used the first two seconds of the input motion as the context motion and sampled the remaining portion of the motion at one-second intervals for the target keyframes.
+
+# 4.2. Evaluation Metrics
+
+For evaluation metrics, we measured the rotation, position, and rendered image similarity, all compared with ground-truth motion. For rotation, we used L2Q and NPSS metrics. L2Q is the L2 distance in local quaternion space compared to ground truth, while NPSS is the angular frequency similarity proposed in Gopalakrishnan et al. [14]. Because the joints that are near the root have a larger impact on overall character motion compared to leaf joints, we also propose to use an adjunctive metric, Hierarchy-filtered L2Q (HL2Q). We conducted the filtering process using the known skeletal hierarchy. In our experiments, we used the child joints only up to  $50\%$  of the depth from the root joint in the skeleton hierarchy. Additional results with varying filtering thresholds are presented in the supplementary material. For positional differences, we used L2P, which measures the L2 distance between the global joint position and ground truth. Lastly, we used LPIPS [55] for perceptual similarity, CLIP [34] for
+
+semantic similarity, and SSIM for structural similarity of rendered characters, compared with the ground truth under the same camera setting.
+
+# 4.3. Comparison with Baselines
+
+We conducted comparisons with three different baselines: ERD-QV [18], TST [33], and SinMDM [57]. ERD-QV and TST are motion in-betweening methods trained on large MOCAP datasets, while SinMDM is a motion generation method trained on single motions, which demonstrated motion in-betweening as its application. For ERD-QV and TST, their original MOCAP datasets [18] were used, while SinMDM was trained using the same context frames as our method. We also made a variant of SinMDM, SinMDM* that preserves keyframes by omitting region-of-interest (ROI) blending. This adjustment was made because ROI blending was originally designed for settings involving multiple target frames.
+
+In our experiments, we used 20 different motions of diverse characters, including both humanoid characters and non-humanoid characters (e.g., birds, snakes, and dinosaurs). The humanoid characters were sourced from Mixamo [1], while the non-humanoid characters were obtained from Truebones Zoo [42]. Because the ERD-QV and TST methods were trained for a single character, we retargeted
+
+![](images/7820935d5e0919f4a4f6783c072ff10e1f3e85aa10bfe7639b06d827f7ce6666.jpg)  
+Figure 8. Ablation results on video generation. Without applying ICA adapt, each frame of the video exhibited inconsistencies, such as generating noticeable style shifts (blue box). Omitting the fine-stage process resulted in a low frame rate, making identical or significant jumps between frames.
+
+their motions to target humanoid characters using the commercial software MotionBuilder [2]. However, as these methods cannot generate motions for non-humanoid characters such as snakes, comparison for non-humanoid characters was not performed.
+
+Comparison results are shown in Figure 7. While our method faithfully generated frames following the style of the input keyframes, SinMDM and SinMDM* resulted in motion that was out of context due to the method overfitting to the given context frames. This is because the original SinMDM trains the model with a full motion; the context frames may not contain all the motions that will be used for the motion in-between task. For ERD-QV and TST, while these models generated the foot motion better than SinMDM, they failed to follow the style of the given motion, such as upper body tilt or hand positions. Quantitative results are presented in Table 2. In all metrics, our method outperformed competitors by large margin.
+
+# 4.4. Ablation Study
+
+Video Generation The first stage of AnyMoLe is to generate a video by filling in the motion in 2D using the knowledge of a large video diffusion model. In this paper, we proposed ICA adapt to bridge the gap between real-world videos and rendered scenes. Additionally, we implemented a two-stage generation process to achieve a higher frame rate, ensuring smooth motion optimization, as frame-wise similarity aids in optimizing between neighboring frames. We conducted an ablation study without these components. As shown in Figure 8, when ICA adapt was not used, spatial information—such as the style of horse-changed (blue box). When the fine-stage was not used, a low frame rate video was produced, with identical nearby frames. In contrast, our method produced results with smooth transitions and no visual artifacts.
+
+Table 3. Quantitative results of ablation study.  
+
+<table><tr><td>Methods</td><td>HL2Q↓</td><td>L2Q↓</td><td>L2P↓</td><td>NPSS↓</td><td>LPIPS↓</td><td>CLIP↑</td><td>SSIM↑</td></tr><tr><td>Ours</td><td>0.00169</td><td>0.00158</td><td>0.01811</td><td>0.1295</td><td>0.04901</td><td>0.9693</td><td>0.9437</td></tr><tr><td>w/o ICAdapt</td><td>0.00210</td><td>0.00181</td><td>0.02640</td><td>0.1413</td><td>0.07115</td><td>0.9619</td><td>0.9340</td></tr><tr><td>w/o fine stage</td><td>0.00200</td><td>0.00171</td><td>0.02204</td><td>0.1345</td><td>0.06037</td><td>0.9653</td><td>0.9385</td></tr><tr><td>w XPose</td><td>0.00174</td><td>0.00167</td><td>0.01976</td><td>0.1288</td><td>0.06004</td><td>0.9678</td><td>0.9421</td></tr><tr><td>w/o data select</td><td>0.00799</td><td>0.00421</td><td>0.15460</td><td>0.2434</td><td>0.12735</td><td>0.9061</td><td>0.9211</td></tr></table>
+
+To verify whether degraded video quality indeed negatively impacts the generated motion, we conducted a quantitative evaluation on the full process without these components. For this quantitative ablation study, we used the same dataset and metrics as in the baseline comparison, but this time the resulting values for humanoid and non-humanoid characters were averaged for simplification. As shown in the results for  $w/o$  ICA adapt and  $w/o$  fine stage in Table 3, the final motion extracted from lower-quality videos led to lower performance on all metrics. This occurred because the degraded video quality negatively affects the optimization process by making joint estimation more challenging for  $w/o$  ICA adapt and causing larger motion gaps between adjacent frames for  $w/o$  fine stage.
+
+Motion Video Mimicking For Motion Video Mimicking, we first trained our scene-specific joint estimator and sequentially optimized 3D joint positions to estimate the character motion. We compared our joint estimator with general pose estimation method XPose [50]. As shown in Table 3, ours outperformed in all the metrics except NPSS. This is because XPose, trained with real images, sometimes failed to estimate the positions correctly when the appearance of the character is somewhat stylized. We additionally conducted a study on our data selection process, which differs from the training dataset used for ICA adapt. Specifically, we
+
+Table 4. Perceptual study results on ground-truth similarity, target keyframe faithfulness, and motion naturalness. The number indicates the percentage of selections.  
+
+<table><tr><td>Character</td><td colspan="3">Humanoid</td><td colspan="3">Non-humanoid</td></tr><tr><td>Methods</td><td>Similar</td><td>Faithful</td><td>Natural</td><td>Similar</td><td>Faithful</td><td>Natural</td></tr><tr><td>Ours</td><td>60.12</td><td>63.10</td><td>64.88</td><td>90.48</td><td>92.46</td><td>91.67</td></tr><tr><td>SinMDM</td><td>13.10</td><td>14.29</td><td>7.74</td><td>3.97</td><td>3.17</td><td>3.57</td></tr><tr><td>SinMDM*</td><td>5.36</td><td>4.17</td><td>5.95</td><td>5.56</td><td>4.37</td><td>4.76</td></tr><tr><td>TST</td><td>16.07</td><td>12.50</td><td>16.67</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ERD-QV</td><td>5.36</td><td>5.95</td><td>4.76</td><td>-</td><td>-</td><td>-</td></tr></table>
+
+included rendered keyframes with weight  $w$  but excluded back-view images when training the scene-specific joint estimator. This data choice was crucial because excluding keyframes led to worse results due to overfitting to context frames as indicated by the last row in Table 3. Additionally, because motion video mimicking was performed only in the frontal view, training with an in-domain dataset helped improve performance.
+
+# 4.5. User Study
+
+We conducted a user study with 21 participants, 11 female and 10 male aged 27.1 on average to evaluate motion in-between results based on human perception. Each participant was presented with three questions on each of 20 motions and asked to choose the one that is: 1) most similar to the ground-truth motion (Similar), 2) best follows the last target keyframe (Faithful), and 3) most smooth and natural (Natural). The scores reported in Table 4 represent the percentage of selections for each category. Our method received higher scores compared to the baseline methods for both humanoid and non-humanoid characters.
+
+# 5. Applications
+
+AnyMoLe can extend its capabilities from single character motion in-between to handling multi-object scenarios, such as two ball simulation. By leveraging video diffusion models with contextual understanding, it ensures smooth transitions between objects while maintaining coherent spatial relationships. This is achieved with simple modification to  $\mathcal{E}_{\text {scene }}$  and optimization process, to estimate and optimize all positions of objects instead of the joints. As shown in Figure 9, AnyMoLe smoothly generates two ball simulation with different bounciness.
+
+# 6. Discussion and Conclusion
+
+We proposed a novel motion in-betweening method to overcome the limitations posed by requirements of datasets. While our method requires training only a lightweight pose estimator using pretrained feature extractors and finetuning the video diffusion model on a small dataset, the overall process still necessitates five to six hours to complete the
+
+![](images/60bc93669da4ed33cbf7a9a8ac780868cb199580f9512d4ba159febe0a3f082c.jpg)  
+Figure 9. From understanding of the context, AnyMoLe can naturally generate in-between frames in a multi-object scenario.
+
+![](images/2ef2de027f2fed5432f1a2efcc311fa82cfbc12b4cc4307ae48910d52dd27bb9.jpg)  
+Figure 10. Visualization of a generated frame from a fast turnaround, showing ambiguity that can hinder joint estimation.
+
+entire process. Additionally, for motions with fast or complex dynamics as shown in Figure 10, rapid movements can blur the generated videos, causing ambiguity—especially in distinguishing left from right joints—and thus hampering motion estimation. One possible direction to mitigate time requirements and improve robustness against a few ambiguous frames in generated videos is to train a context-informed, character-agnostic 3D joint estimator. If such pretraining can be achieved without sacrificing performance, it would significantly reduce computational time for training Scene-specific joint estimator and ensure robustness, even when encountering blurry frames, due to its contextual understanding.
+
+In this paper, we introduced a novel method for motion in-betweening that effectively leverages video diffusion models to overcome the limitation of requiring character-specific dataset, which has been overlooked. To achieve this, we first identified three primary challenges associated with the naive application of these video diffusion models to motion in-betweening tasks: 1) limited contextual understanding, 2) domain gaps, and 3) difficulties in tracking motion from generated videos. To address these challenges, we introduced a two-stage video generation process using context frames, the ICAdapt method, motion-video mimicking, and a scene-specific joint estimator. By addressing these key challenges, our approach is the first to successfully achieve motion in-betweening for arbitrary characters without the need for external data. We believe that our contributions broaden the use of video generation models and will stimulate further research in 3D character motion synthesis, particularly for characters that are challenging to capture with MOCAP or to animate manually.
+
+# Acknowledgements
+
+This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2024-00333478).
+
+# References
+
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