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+# DisCoPatch: Taming Adversarily-driven Batch Statistics for Improved Out-of-Distribution Detection
+
+Francisco Caetano $^{1,*}$ , Christiaan Viviers $^{1,*}$ , Luis A. Zavala-Mondragon $^{1}$ , Peter H.N. De With $^{1}$ , Fons van der Sommen $^{1}$ $^{1}$ Eindhoven University of Technology, The Netherlands
+*Equal contribution
+
+# Abstract
+
+Out-of-distribution (OOD) detection holds significant importance across many applications. While semantic and domain-shift OOD problems are well-studied, this work focuses on covariate shifts - subtle variations in the data distribution that can degrade machine learning performance. We hypothesize that detecting these subtle shifts can improve our understanding of in-distribution boundaries, ultimately improving OOD detection. In adversarial discriminators trained with Batch Normalization (BN), real and adversarial samples form distinct domains with unique batch statistics - a property we exploit for OOD detection. We introduce DisCoPatch, an unsupervised Adversarial Variational Autoencoder (VAE) framework that harnesses this mechanism. During inference, batches consist of patches from the same image, ensuring a consistent data distribution that allows the model to rely on batch statistics. DisCoPatch uses the VAE's suboptimal outputs (generated and reconstructed) as negative samples to train the discriminator, thereby improving its ability to delineate the boundary between in-distribution samples and covariate shifts. By tightening this boundary, DisCoPatch achieves state-of-the-art results in public OOD detection benchmarks. The proposed model not only excels in detecting covariate shifts, achieving $95.5\%$ AUROC on ImageNet-1K(-C), but also outperforms all prior methods on public Near-OOD $(95.0\%)$ benchmarks. With a compact model size of 25MB, it achieves high OOD detection performance at notably lower latency than existing methods, making it an efficient and practical solution for real-world OOD detection applications. The code is available at github.com/caetas/DisCoPatch.
+
+# 1. Introduction
+
+Out-of-distribution (OOD) detection consists of identifying whether a given test sample significantly deviates from the
+
+known information of in-distribution (ID) data. It is often employed as a preliminary step in image-based systems, aiming to mitigate the risks associated with feeding OOD inputs to a model. Besides safeguarding a system against erroneous predictions, it also facilitates the safe handling of OOD samples, either by rejection or transfer to human intervention. However, the significance of OOD lies not only in bolstering the reliability of image processing systems, but also in its standalone role for anomaly and fault detection. A simple example of this use case can be found in the visual inspection of industrial image data, where it is easy to acquire imagery of normal samples yet virtually impossible to define the expected defects [50]. In the OOD context, these anomalies can be broadly classified into two types: (1) anomalous objects in images which refer to unexpected or rare items appearing in the frame, and (2) faulty equipment or products which refer to malfunctions or irregularities in the machinery or products under inspection. As a consequence, this task is typically cast as an OOD classification problem.
+
+OOD detection comprises various types of shifts in data. (a) Semantic shifts, such as encountering unseen classes, and (b) domain shifts, like distinguishing between real images and drawings, have easily established boundaries and are well-defined in literature [19, 32]. On the other hand, (c) covariate shifts, which involve perturbations in data or subtle changes in its expected variability, are often conflated with domain shifts [69]. It is essential to differentiate covariate shifts, since they pose unique challenges requiring tailored detection mechanisms.
+
+Figure 1 illustrates the proposed framework for interpreting shifts in a data distribution. In our definition, the ID range covers an expected semantic shift, containing a pre-defined number of different classes, as exemplified by ImageNet-1K [51], along with some degree of variability in terms of domain and covariate shifts. For instance, introducing a novel class such as bagpipes in NINCO [3] represents an OOD semantic shift, as ImageNet-1K lacks such examples. An extreme change in domain, such as
+
+
+Figure 1. Diagram illustrating data distribution shifts. Variations in the z-axis define semantic shifts, domain shifts represent new contexts like sketches with unchanged semantics and variability, and covariate shifts indicate changes within the same domain and semantic content, such as image perturbations (e.g., blurring).
+
+a hand-drawn representation of a plane from the Sketch dataset [12], is considered OOD, despite the retaining of semantic relevance. Additionally, substantial covariate shifts, such as a blurred horse image from ImageNet-1K(-C) [18], are also classified as OOD, even though there are no explicit alterations in semantic or domain concepts.
+
+Various unsupervised OOD detection methods have been explored that utilize generative models, including Variational Autoencoders (VAEs) [46], Generative Adversarial Networks (GANs) [54], Normalizing Flows (NFs) [26] and more recently Denoising Diffusion Probabilistic Models (DDPMs) [63]. The detection of anomalous data is usually performed by assessing whether they deviate from the learned representation manifold, or by comparing the reconstructed and original images in pixel space. DDPMs exhibit superior mode coverage compared to GANs and VAEs, albeit with much slower sampling/detection rates [66]. NFs present a good framework for OOD detection, but it is well documented that they often assign a higher likelihood to OOD samples than the ID data [25].
+
+This paper proposes that the batch statistics extracted by Batch Normalization (BN) [23] layers can be used to improve OOD detection. It has been hypothesized that in adversarial networks trained with BN, clean and adversarial images are drawn from two distinct domains, with each domain exhibiting different means and variances in the BN layers [67]. This has been empirically proved by examining feature statistics at different layers of a discriminator, thus validating that these stem from separate underlying distributions [62]. This "two-domain hypothesis" points to BN's inherent ability to separate ID and OOD samples based on batch statistics. However, BN increases adversarial vulnerability by shifting model reliance towards non-robust features rather than robust ones [1]. To mitigate this, we propose utilizing a patch-based strategy for both training and
+
+inference. During training, partitioning images into patches encourages the model to focus on robust features that persist across diverse regions of the same image. During inference, processing batches of patches from a single image allows the model to ensure that the batch statistics correspond to the same underlying distribution.
+
+In this paper, we demonstrate this effect can be leveraged by training a discriminator in an Adversarial VAE framework with DisCoPatch, using both reconstructed and generated images as OOD samples; this model yields an excellent OOD detector with an efficient and compact design. This approach not only excels in detecting covariate shifts but also proves effective against semantic OOD samples, all while significantly accelerating detection speed compared to prior methods. Since DisCoPatch is trained end-to-end, the quality of generated counterfactual samples becomes less critical; the VAE's outputs naturally enhance the discriminator's boundary-setting ability as training progresses. This method achieves high OOD detection performance with a compact and low-latency model, offering a practical solution for real-time applications. The main contributions of this work are as follows:
+
+- A novel analysis of Batch Normalization's inherent bias toward batch statistics, demonstrating how this mechanism can be leveraged for effective OOD detection by structuring batches with patches from the same image.
+- DisCoPatch, a lightweight, unsupervised framework specifically designed for OOD detection.
+- State-of-the-art performance in Covariate Shift and Near-OOD detection, along with competitive results in Far-OOD detection, all while achieving significantly lower latency than existing methods.
+
+# 2. Related Work
+
+# 2.1. Semantic Shift and Covariate Shift OOD
+
+OOD detection literature predominantly focuses on semantic shift and typically falls into two categories: (a) supervised, which requires labels or OOD data, and (b) unsupervised, which relies solely on ID data [69]. Given the nature of the OOD detection problem, OOD data are often not sufficiently representative, as OOD samples can come from a wide variety of unknown distributions. As such, unsupervised methods are generally preferred. Covariate shift occurs when images have consistent semantic and domain content, but are recorded under deviating imaging settings and conditions, or corrupted in a post-processing step. Although increasing the degree of variance under these conditions can deteriorate semantic and domain content, this study focuses on covariate shifts within the same domain, as these subtle distribution shifts can cause significant drops in the classification performance of machine learning models [18].
+
+# 2.2. Generative-based Methods
+
+A widely used and initially intuitive approach for OOD detection involves fitting a generative model $p(x; \theta)$ to a data distribution $x$ and evaluating the likelihood of unseen samples under this model, assuming that OOD samples will have lower likelihoods [2]. However, this assumption has been challenged, with various generative models assigning higher likelihoods to certain OOD samples [20, 42]. To address this, different approaches have been proposed, including using the Watanabe-Akaike Information Criterion (WAIC) [5], specific likelihood ratios [55, 65], and hierarchical VAEs [16]. These methods aim to correct for likelihood estimation errors, population-level background statistics, and model feature dominance. Another approach suggests labeling samples as OOD if their likelihoods fall outside the typical range of a model [4, 60], i.e., a sample may be classified as OOD not only if its likelihood is lower than that of ID data, but also if it is higher [41].
+
+# 2.3. Reconstruction-based Methods
+
+Reconstruction-based methods involve training a model $R$ to reconstruct inputs $x$ from the training distribution, such that we obtain $\hat{x} = R(x)$ . The rationale is that if $R$ has an information bottleneck, it will struggle to accurately reconstruct OOD inputs. However, these methods face practical challenges, including difficulty in tuning the information bottleneck size [9, 45]. If it is too small, ID samples may not be faithfully reconstructed; if it is too large, the model can learn the identity function, allowing OOD samples to be reconstructed with low error. Some approaches address these issues by using the Mahalanobis distance in the Autoencoder's feature space as an OOD metric [9], or by introducing a memory module to discourage OOD sample reconstruction [13]. However, none of these methods fully resolve the bottleneck selection issue. To tackle this limitation, DDPMs have been employed, leveraging noise bottlenecks [63] and reconstructions from a range of noise values without the need for dataset-specific tuning [15] or of corrupted inputs [39].
+
+# 2.4. Feature-based and Logit-based Methods
+
+Several scoring functions have been devised to differentiate between ID and OOD examples, leveraging characteristics of ID samples, but not represented in OOD ones, and vice versa. These functions primarily stem from three sources: (1) probability-based measures, such as maximum softmax probabilities [19], and minimum Kullback-Leibler (KL) divergence between softmax and mean class-conditional distributions [21]; (2) logit-based functions, including maximum logits [21], and the use of the logsumexp function computed over logits [38]; (3) feature-based functions, involving the norm of the residual between a feature and its low-dimensional embeddings [43], as well as mini
+
+mum Mahalanobis distance between a feature and class centroids [31]. Some hybrid methods combine both logit and feature scores for OOD detection [61], while more recent works have introduced masked image modeling pretraining into OOD detection with promising results [33, 34]. However, the detection speed of these methods is severely constrained by their large transformer-based backbones.
+
+# 2.5. Adversarial Variational Autoencoders
+
+The VAE [24] consists of an encoder that predicts the parameters $\mu$ and $\sigma$ of the variational distribution of the input data, and a decoder that takes a sample from this distribution to reconstruct the input. VAEs are trained to maximize the Evidence Lower Bound (ELBO), which balances reconstruction fidelity with the latent space regularization to ensure that it follows a predefined probability distribution. Using latent space as a bottleneck restricts the information that can pass through, leading to uncertainty and blurriness in the reconstructions [8]. Additionally, the pixel-wise reconstruction error and the high dimensionality of natural image manifolds pose challenges for VAEs in generating high-quality and realistic samples. While natural images are assumed to lie on low-dimensional manifolds due to local scale redundancy [28], local details exist in higher-dimensional manifolds, making them difficult to capture.
+
+GANs [14] consist of two neural networks with adversarial objectives: the generator learns to map a random vector to the data space; the discriminator acts as a classifier trained to differentiate real samples from generated ones. Despite their success in generation tasks, GANs suffer from two primary limitations compared to VAEs. The first is mode collapse, which occurs when the generator produces only a few different types repeatedly, making it easily recognizable by the discriminator. Consequently, the discriminator's feedback lacks useful information [58]. Additionally, GANs lack an encoder network, which restricts their ability to reconstruct an input or manipulate its latent representation. AnoGAN [54] tries to circumvent this by optimizing a random latent vector to match a test sample and determining an anomaly score based on reconstruction quality and the discriminator's output.
+
+The VAE and GAN have been combined by incorporating a discriminator to enhance the realism of VAE reconstructions [30]. Alternatively, the BiGAN [11] architecture features an encoder, generator, and discriminator, aiming for good unsupervised feature representations but tends to produce less accurate reconstructions. Other approaches have adapted this VAE/GAN combination to fully utilize the strengths of each architecture to improve the realism of the images produced by the model [47]. DisCoPatch aims to retain the adversarial benefits and the mode coverage of the hybrid strategy, without the final goal of image generation, thereby reducing computational requirements.
+
+
+Figure 2. Overview of the DisCoPatch architecture. During inference, only the Discriminator is used.
+
+# 2.6. Batch Normalization
+
+Batch Normalization [23] is a widely used technique to speed up the training process of deep neural networks. It became popular for GAN architectures after being utilized in the DCGAN model [48] for both the generator and the discriminator. Essentially, BN takes a batch of feature samples $\{x_{1}, x_{2}, \ldots, x_{m}\}$ and computes
+
+$$
+y _ {i} = \frac {x _ {i} - \mu_ {R}}{\sigma_ {R}} \cdot \gamma + \beta , \tag {1}
+$$
+
+where, during training, $\mu_R$ and $\sigma_R$ are the running mean and the running standard deviation, which are updated according to the input batch statistics $\mu_B$ and $\sigma_B$ with a nontrainable momentum parameter $m$ by
+
+$$
+\left[ \begin{array}{c c} \mu_ {R} & \sigma_ {R} \end{array} \right] = (1 - m) \left[ \begin{array}{c c} \mu_ {R} & \sigma_ {R} \end{array} \right] + m \left[ \begin{array}{c c} \mu_ {B} & \sigma_ {B} \end{array} \right]. \quad (2)
+$$
+
+Here, $\gamma$ and $\beta$ are learned parameters. It should be noted that when the BN layer is set to evaluation mode, $\mu_R$ and $\sigma_R$ are fixed to the values learned throughout training (i.e. parameter $m$ in Eq. (2) is set to zero).
+
+Compared to models without normalization, BN accelerates training in the early stages and leads to better performance in GANs. However, the distinct distributions of clean and adversarial samples have hindered BN's effectiveness in adversarial settings [62, 67], as models trained with BN can still suffer from instability and low generalizability [64]. Alternative normalization approaches, such as Weight Normalization [52] and Spectral Normalization [40], have demonstrated improved performance for image generation and benefits in training stability, while still accelerating GAN training.
+
+# 3. DisCoPatch
+
+# 3.1. Overview
+
+A prevalent generative-based approach for OOD detection involves utilizing the trained generator to evaluate the likelihood of unseen samples. However, in adversarial setups, some information about the ID boundary will be incorporated into the discriminator, as it learns to assess the probability of a sample being real (ID) or synthetic (OOD). As
+
+mentioned in Section 1, we exploit the observation that BN can help an adversarially trained discriminator to separate underlying data distributions by recognizing that clean and adversarial images are drawn from two distinct domains (i.e. ID and OOD). Instead of solely estimating likelihoods, DisCoPatch clusters ID features while excluding OOD samples by employing an Adversarial VAE that generates and reconstructs samples to enhance feature separation. The discriminator penalizes poorly generated and reconstructed images, reinforcing the distinction between ID and OOD and refining the decision boundary.
+
+It is on this premise that we propose a Discriminative Covariate Shift Patch-based Network, DisCoPatch. DisCoPatch is an Adversarial VAE-inspired architecture, as shown in Figure 2, in which both the VAE and the discriminator are trained adversarially. Adversarily trained discriminators have been previously used for OOD detection [27]. DisCoPatch's approach combines generative and reconstruction-based strategies to distill information about the ID set and OOD boundaries to the discriminator during training in an unsupervised manner. Unlike traditional adversarial methods, DisCoPatch's focus is on leveraging the generator's output as a tool to refine the discriminator. DisCoPatch's discriminator only utilizes the current batch's (of patches) statistics in the BatchNorm2D layer (i.e. parameter $m$ in Eq. (2) is set to one). Subsection 4.6 details extensive ablation experiments to demonstrate its effectiveness.
+
+# 3.2. Training
+
+The VAE is trained to reduce the standard ELBO loss, while also producing samples (generated patches using the VAE decoder) that can fool the discriminator. The discriminator is trained to not only distinguish between generated and real patches, as in the standard GAN setup, but also reconstructed patches. Reconstructed patches from VAEs typically lack detail, i.e., they have a sub-optimal high-frequency representation [36], which can be found in certain types of covariate shifts, such as blurriness. On the other hand, images generated from GANs often exhibit severe high-frequency differences, leading the discriminator to focus excessively on these components [35]. This focus can hinder the generator's ability to capture low-frequency components. By
+
+
+Figure 3. Covariate shifts can be simulated by reconstructed and generated patches. Encouraging more realism helps to tighten the border between the ID and the OOD sets.
+
+training the discriminator on reconstructions and generations, and encouraging both to appear more realistic, the discriminator's boundaries of the ID frequency spectrum become tighter, strengthening its ability to detect OOD samples, as illustrated in Figure 3.
+
+The VAE in DisCoPatch's framework remains unchanged compared to the traditional VAE, with parameters $\theta$ and composed of an encoder $\mathcal{E}_{\theta_{\mathrm{E}}}$ and a decoder $\mathcal{G}_{\theta_{\mathrm{G}}}$ responsible for generating an image output. The VAE is a parameterized model given by $q_{\theta_{\mathrm{E}}} (z | x^{(i)}) = \mathcal{N}(z; \mu^{(i)}, \sigma^{2(i)} \mathbf{I})$ , where $\mu^{(i)}$ and $\sigma^{2(i)}$ are outputs of $\mathcal{E}_{\theta_{\mathrm{E}}}$ . The prior distribution of the latent codes is $p(z) = \mathcal{N}(z; 0, \mathbf{I})$ . The VAE loss function combines a reconstruction term and a latent space regularization term, as demonstrated in the original paper by [24] and adversarial implementations [47]. The reconstruction term optimizes the encoding-decoding process, while the regularization term aligns the encoder distributions with a standard Gaussian. The latter is represented by the KL-divergence between the predicted distribution and the prior distribution. Both terms are represented in Figure 2 and can be written as
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {V A E}} = \left\| x ^ {(i)} - \mathcal {G} _ {\theta_ {\mathrm {G}}} (z) \right\| ^ {2} \\ - \frac {1}{2} \sum_ {j = 1} ^ {\dim (z)} \left(1 + \log \left(\sigma_ {j} ^ {2 (i)}\right) - \mu_ {j} ^ {2 (i)} - \sigma_ {j} ^ {2 (i)}\right). \tag {3} \\ \end{array}
+$$
+
+An additional model, the discriminator $\mathcal{D}$ , parameterized by $\phi$ , is added to the traditional VAE architecture. It has two main goals, as shown in Figure 2. First, it must discern between real patches and patches either reconstructed from $z_{\mathrm{real}}$ or generated from random noise $z_{\mathrm{fake}}$ . This can be
+
+achieved by minimizing the cross-entropy function
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {D}} = \mathbb {E} _ {x \sim p (x)} [ \log (1 - \mathcal {D} _ {\phi} (x)) ] \\ + \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x | z _ {\text {r e a l}})} [ \log (\mathcal {D} _ {\phi} (x)) ] \tag {4} \\ + \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x | z _ {\text {f a k e}})} [ \log (\mathcal {D} _ {\phi} (x)) ]. \\ \end{array}
+$$
+
+This suggests that in addition to the discriminator's initial goal of improving generated patches (sampled from random noise), it also pushes the reconstructions toward more realism. Therefore, an adversarial loss term, which encourages the VAE to generate or reconstruct patches that fool the discriminator, is added to the loss function, so that
+
+$$
+\begin{array}{l} \begin{array}{l} \mathcal {L} _ {\mathrm {A d v}} = \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x \mid z _ {\text {r e a l}})} [ 1 - \log (\mathcal {D} _ {\phi} (x)) ] \\ \quad \cdot \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x \mid z _ {\text {r e a l}})} [ 1 - \log (\mathcal {D} _ {\phi} (x)) ] \end{array} \tag {5} \\ + \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x | z _ {\mathrm {f a k e}})} [ 1 - \log (\mathcal {D} _ {\phi} (x)) ]. \\ \end{array}
+$$
+
+The final DisCoPatch loss function is thus a weighted combination of both the Vanilla VAE loss and the adversarial loss, which results in
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {D C P}} = \left\| x ^ {(i)} - \mathcal {G} _ {\theta_ {\mathrm {G}}} (z) \right\| ^ {2} \\ - \frac {\omega_ {\mathrm {K L}}}{2} \sum_ {j = 1} ^ {\dim (z)} \left(1 + \log \left(\sigma_ {j} ^ {2 (i)}\right) - \mu_ {j} ^ {2 (i)} - \sigma_ {j} ^ {2 (i)}\right) \tag {6} \\ + \omega_ {\operatorname {R e c}} \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x | z _ {\text {r e a l}})} [ 1 - \log (\mathcal {D} _ {\phi} (x)) ] \\ + \omega_ {\text {G e n}} \mathbb {E} _ {x \sim p _ {\theta_ {\mathrm {G}}} (x | z _ {\text {f a k e}})} [ 1 - \log (\mathcal {D} _ {\phi} (x)) ]. \\ \end{array}
+$$
+
+# 3.3. Patching Strategy
+
+The patching strategy begins by taking a high-resolution input image, typically a standard $256 \times 256$ resolution, and cropping it into $N$ random patches, each of size $64 \times 64$ . This approach allows the model to capture fine-grained details in different image regions. During training, batches are composed of patches sourced from multiple images rather than from a single one. This setup accelerates training and ensures that the model learns consistent and robust ID features across a range of images, minimizing the potential for overfitting on individual image characteristics.
+
+In this setup, using the standard BatchNorm2D layer constrains batch processing during inference to a single image, since normalization must be applied only to features from the same distribution; mixing ID and OOD samples in a batch would distort the statistics and hinder effective separation. Therefore, we introduce a custom layer, PatchNorm2D, which retains the weights and biases of BatchNorm2D but enables the simultaneous normalization of multiple groups of patches. Specifically, each batch consists of several groups of $N$ patches, where each group contains patches from the same image that are normalized together. This ensures that the model produces independent results per image while maintaining the benefits of batch normalization. The final anomaly score for an image is the
+
+
+Figure 4. Different patching strategies employed by the model. Training normalizes patches from multiple images, while inference normalizes patches per image.
+
+mean of the scores of all patches within that same image. For the remainder of the paper, we refer to the model as DisCoPatch- $N$ , indicating the number of patches per image used during inference. Both strategies are illustrated in Figure 4.
+
+# 4. Experiments & Methodology
+
+# 4.1. Datasets
+
+In OOD detection benchmarks, the conventional approach involves designating an entire dataset as ID and then compiling multiple datasets that lack any semantic overlap with the ID categories to act as OOD sets. To ensure consistency in the benchmarking process, we adhere to the methodology proposed by OpenOOD [70]. Our evaluation encompasses three tasks: (1) Near-OOD, which exhibits slight semantic variation compared to ID datasets; (2) Far-OOD, which encompasses both semantic and domain shifts; and (3) Covariate Shift OOD, involving corruptions within the ID set. ImageNet-1K [51] was defined as the ID dataset. Further details on the datasets are summarized in Appendix A.
+
+# 4.2. Evaluation Metrics
+
+The evaluation metrics employed in OpenOOD by [70] are adopted for this work. These two main evaluation metrics are: (1) AUROC, which measures the area under the Receiver Operating Characteristic (ROC) curve, and displays the relationship between True Positive Rate (TPR) and False Positive Rate (FPR); and (2) FPR95, which measures the FPR when the TPR is equal to $95\%$ , with lower scores indicating better performance. The full results are provided in the form "AUROC/FPR $95\%$ ". In addition to these quantitative metrics, a UMAP visualization of the extracted features is included as a qualitative evaluation, providing insight into the separability of ID and OOD samples in the learned feature space.
+
+# 4.3. Baseline Models
+
+For the ImageNet-1K benchmark, we compare our method, DisCoPatch, against SOTA public models, such
+
+as MOODv2 [34], NNGuide [44], SCALE [68], Rank-Feat&Weight [57], ASH [7], and FDBD [29], all of which have demonstrated SOTA performance on Near-OOD and Far-OOD detection for these datasets. These models employ feature-based and logit-based strategies to perform OOD detection. In the case of NNGuide, we evaluate three of its available backbones to assess performance across different model types: the top-performing RegNet [49], a more efficient ResNet-50 [17], and the lightweight MobileNetV2 [53].
+
+# 4.4. DisCoPatch Implementation & Compute
+
+Appendix B contains the implementation specifics of DisCoPatch. The computational resources for training and evaluating models are detailed in Appendix C.
+
+# 4.5. Experimental Significance
+
+To support the main claims of this work, we perform five random runs to validate DisCoPatch's performance on the OOD benchmarks and compute the average performance.
+
+# 4.6. Batch Normalization Bias Analysis
+
+We conduct various supplemental experiments to investigate the effect of Batch Normalization's reliance on the batch statistics $\mu_B$ and $\sigma_B$ (Eq. 2) during training. We conduct the experiments using the complete ImageNet-1K dataset, center-cropped and resized to $256 \times 256$ pixels, within the DisCoPatch framework. Unlike our main experiments that rely on patch-based batches, here we evaluate the model's sensitivity to batch-level statistics across the full-resolution images. This model was used with the standard BatchNorm2D parameters, with track_runting.stats set to True and the default momentum of 0.1.
+
+In the first experiment, the model is analyzed in evaluation mode, as described in Subsection 2.6. In this mode, the model utilizes the running mean, $\mu_R$ , and variance, $\sigma_R$ , learned during training and neglects the statistics of the current batch. As mentioned in Section 1, this paper hypothesizes that the batch statistics of the batch being evaluated can be a powerful feature for OOD detection. Consequently, we also introduce an additional model, in which the track_runting.stats option in PyTorch's BatchNorm2D layer is set to False. This setting causes the model to disregard the running mean and variance obtained during training, and instead, it employs solely the statistics $\mu_B$ and $\sigma_B$ of the batch being tested for normalization. This configuration does not modify the layer weights and is solely used to illustrate dependency on batch-level statistics during inference. For a comprehensive analysis, refer to Appendix D. Alternative normalization strategies are covered in Appendix E.
+
+Table 1. OOD benchmark results for models trained on ImageNet-1K. Results are obtained from the respective research papers where available or recomputed $(^{*})$ and reported following the OpenOODv1.5 benchmark as AUROC/FPR95.
+
+
| Model | Near-OOD | Far-OOD | Covariate Shift |
| SSB-hard | NINCO | iNaturalist | DTD | OpenImage-O | ImageNet-1K(-C) |
| MOODv2 [34] (BEiTv2) | 85.0/58.1* | 92.7/38.2* | 99.6/1.8 | 94.3/24.7 | 97.4/13.6 | 70.5/73.9* |
| SCALE [68] (ResNet-50) | 77.4/67.7 | 85.4/51.8 | 98.0/9.5 | 97.6/11.9 | 94.0/28.2 | 83.3/54.1* |
| NNGuide [44] (RegNet) | 84.7/54.7* | 93.7/28.9* | 99.9/1.8 | 95.8/17.0 | 97.7/10.8 | 78.5/61.6* |
| NNGuide [44] (ResNet-50) | 71.5/82.8* | 80.5/69.8* | 96.9/14.3 | 90.4/27.4 | 92.4/35.4 | 78.6/58.7* |
| NNGuide [44] (MobileNetV2) | 64.3/90.3* | 75.5/80.2* | 80.2/70.2 | 88.3/40.6 | 82.9/63.3 | 78.1/61.4* |
| RankFeat [56] (ResNetv2-101) | 89.4/47.9* | 90.0/39.3* | 96.0/13.0 | 95.0/25.4 | 92.4/33.3* | 91.3/38.7* |
| ASH [10] (ResNet-50) | 74.1/80.6* | 83.0/64.2* | 97.9/11.5 | 97.6/11.9 | 92.8/32.7* | 84.7/51.3* |
| FDBD [37] (ResNet-50) | 68.4/83.4* | 81.4/66.1* | 97.6/12.4 | 98.0/10.7 | 91.7/35.6* | 82.2/57.8* |
| DisCoPatch-64 (Proposed) | 95.8/19.8 | 94.3/39.0 | 99.1/3.6 | 96.4/18.9 | 94.4/29.7 | 97.2/10.6 |
+
+# 5. Results
+
+Table 1 shows that DisCoPatch-64 surpasses state-of-the-art methods in Near-OOD and Covariate Shift benchmarks, with a particularly large performance gap in the Covariate Shift OOD detection task. Although DisCoPatch does not achieve SOTA performance in any of the Far-OOD benchmarks, it is close to matching the best performers on the iNaturalist and DTD tasks and attains competitive performance in OpenImage-O, whilst being a much smaller model. Detailed performance analysis for Covariate Shift can be found in Appendix G.
+
+
+Figure 5. AUROC on Near-OOD detection vs. latency of the models. Circumference size is equivalent to relative model size.
+
+The superiority of DisCoPatch extends beyond raw detection performance. As illustrated in Figure 5, DisCoPatch outperforms all other models in Near-OOD detection performance while reducing latency by up to an order of magnitude. Even with only 16 patches per image, DisCoPatch outperforms all other models tested. Appendix F offers a detailed examination of the performance of additional patch counts. However, increasing the patch count beyond 64 did not result in any noticeable performance improvements. The performance gap between DisCoPatch and the second fastest model, NNGuide (MobileNetV2), is near $25\%$ .
+
+
+Figure 6. AUROC on Far-OOD detection vs. latency of the models. Circumference size is equivalent to relative model size.
+
+Although DisCoPatch does not achieve the highest performance in Far-OOD detection, Figure 6 shows that it is surpassed only by the two largest and slowest models, MOODv2 and NNGuide with a RegNet backbone, with a marginal gap of just $1\%$ , while being at least ten times faster. DisCoPatch also exceeds the performance of NNGuide (MobileNetV2), the next smallest model, by $12\%$ . Again, increasing the number of patches per image beyond 64 yielded no further significant improvements in detection performance. Table 4 in the supplementary material provides details on model size and latency.
+
+Figure 7 presents a UMAP visualization of the average features extracted by the discriminator from 64 patches per image. The results show that samples from Near-OOD datasets (NINCO, SSB-hard) cluster closer to the ID set (ImageNet-1K), while Far-OOD samples (OpenImageO, DTD, iNaturalist) are mapped farther away. While the proposed method effectively structures the feature space into distinct clusters, the decision boundary remains suboptimal. This highlights the potential for integrating post-hoc feature-based methods to further enhance OOD separation.
+
+
+Figure 7. UMAP visualization of discriminator-extracted features, each point corresponding to the mean features of image patches.
+
+# 6. Discussion
+
+Covariate Shift OOD. Validation on ImageNet-1K(-C) reveals that DisCoPatch achieves a substantial improvement over other models in this task. As hypothesized in Section 3, and supported by recent findings [35, 36], training a discriminator with VAE reconstructions enhances sensitivity to corruptions that diminish the high-frequency spectrum. This effect arises because reconstructed images generally lack high-frequency content, prompting the discriminator to classify this lack of content as "fake" and its presence as "real." In contrast, training the discriminator with generated images strengthens its ability to detect high-frequency amplification. DisCoPatch's unique unsupervised training approach, which exposes the discriminator to generated and reconstructed patches, enables robust detection of low- and high-frequency perturbations, leading to consistent performance across various corruptions.
+
+Near-OOD and Far-OOD. The covariate shift-focused training strategy effectively tightens the boundary between ID and OOD samples, improving detection performance on both Near-OOD and Far-OOD datasets. DisCoPatch outperforms existing models, achieving SOTA performance in Near-OOD detection. Although the same does not occur for Far-OOD, DisCoPatch's performance is competitive, and the model is only beaten by far larger and slower models.
+
+Deployment. There are generally two main deployment scenarios for OOD detection algorithms: (1) The OOD detection algorithm is the primary focus, deployed as a standalone application. (2) The OOD detection algorithm operates alongside a main image processing algorithm, ensuring its safe and effective use. An OOD algorithm must be practical and effective in real-world scenarios, delivering strong detection performance while being highly deployable. Deployability should be assessed in the following aspects: (a) Accessibility, evaluated by the compute requirements necessary for the algorithm; (b) Development Cycle, measured by the time required for model training and deployment; (c) Inference Speed, which reflects the time it
+
+takes for the algorithm to make predictions during deployment; and (d) Accuracy, denoting the ability of the algorithm to provide highly accurate OOD detection.
+
+An ideal OOD detection algorithm excels in all these dimensions, ensuring that it can be used effectively in various practical applications. As detailed in our results and Appendix C, DisCoPatch excels in all criteria. The model achieves SOTA OOD detection results, while utilizing a substantially smaller and faster model. Table 4 indicates that DisCoPatch is 1 order of magnitude faster than the other evaluated models; being up to 12 times faster than MOODv2 and up to 19 times quicker than NNGuide. Training a tailored model is also efficient and flexible, as demonstrated in Table 3, making it a strong candidate for applications that require fast development cycles.
+
+# 7. Limitations & Future Work
+
+Comprehensive benchmarking of Covariate Shift detection across diverse architectures is vital to advance the field. While DisCoPatch shows promise for generative-based setups, evaluating more models will clarify how architecture impacts detection performance. Covariate Shift detection is particularly critical in fields like medical imaging, where identifying distribution shifts is crucial to ensuring trustworthy predictions. Expanding such evaluations to high-stakes domains could broaden the relevance of DisCoPatch and similar models for robust, real-world applications.
+
+While current results demonstrate the effective use of batch statistics for OOD detection, a signal-processing-focused analysis of feature propagation and suppression at each layer could provide key insights, improving model interpretability. The planned extensions include the integration of several ResNet-based architectures that use BatchNorm2D layers. Beyond discriminator architectures, future work should also assess more robust reconstructors (e.g., VQ-GAN) and generators (e.g., DDPMs).
+
+# 8. Conclusion
+
+This paper introduces DisCoPatch, an unsupervised lightweight framework for OOD detection. DisCoPatch, unlike traditional VAE or GAN training objectives, uses a combination of reconstructed and generated images to address a wide range of frequency-spectrum perturbations. Furthermore, this study highlights the inherent bias in Batch Normalization toward batch statistics. DisCoPatch effectively exploits this bias for competitive OOD detection, particularly for Covariate Shift and Near-OOD detection. DisCoPatch sets a new state-of-the-art in public OOD detection benchmarks, with $95.5\%$ AUROC on Covariate Shift detection and $95.0\%$ on Near-OOD detection, while maintaining low latency and a compact 25MB model, which makes it well suited for real-time, resource-constrained applications.
+
+# Acknowledgments
+
+This work used the Dutch national e-infrastructure with the support of the SURF Cooperative using grant no. EINF-10021. This research was funded by the European Xecs Eureka TASTI Project.
+
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+# DisCoRD: Discrete Tokens to Continuous Motion via Rectified Flow Decoding
+
+
+
+
+Figure 1. Continuous methods generate smooth motions, but lack faithfulness (red text) to conditioning signals. In contrast, discrete methods demonstrate high faithfulness (blue words) but often produce less natural results such as unexpressive motion and frame-wise noise (red box). We present a novel discrete token decoding method, DisCoRD, that generates smooth, dynamic motion (blue box) while faithfully adhering to the conditioning signal. The plotted lines represent left-hand trajectories of generated motions for visual comparison.
+
+
+
+
+
+# Abstract
+
+Human motion is inherently continuous and dynamic, posing significant challenges for generative models. While discrete generation methods are widely used, they suffer from limited expressiveness and frame-wise noise artifacts. In contrast, continuous approaches produce smoother, more natural motion but often struggle to adhere to conditioning signals due to high-dimensional complexity and limited training data. To resolve this "discord" between discrete and continuous representations we introduce DisCoRD: Discrete Tokens to Continuous Motion via Rectified Flow Decoding, a novel method that leverages rectified flow to decode discrete motion tokens in the continuous, raw motion space. Our core idea is to frame token decoding as a conditional generation task, ensuring that DisCoRD captures fine-grained dynamics and achieves smoother, more natural motions. Compatible with any discrete-based framework, our method enhances naturalness without compromising faithfulness to the conditioning signals on diverse
+
+settings. Extensive evaluations demonstrate that DisCoRD achieves state-of-the-art performance, with FID of 0.032 on HumanML3D and 0.169 on KIT-ML. These results establish DisCoRD as a robust solution for bridging the divide between discrete efficiency and continuous realism. Project website: https://whwjdqs.github.io/discord-motion/
+
+# 1. Introduction
+
+Human motion generation controlled by diverse signals has become an emerging area in computer vision, driven by its vast applications in virtual reality to animation, gaming, and human-computer interaction. The ability to generate realistic human motions that are precisely aligned with input conditions—such as textual descriptions [11, 12, 51, 60], human speech [28, 30, 62], or even music [10, 25, 46]—is essential for creating immersive and interactive experiences. Two critical qualities define the success of such systems [56]: faithfulness, ensuring that the generated motion accurately reflects the conditioning signal, and naturalness, producing smooth and lifelike motions that are comfortable and convincing to human observers. Deficiencies in faithfulness
+
+
+Figure 2. Concept of DisCoRD. Discrete quantization methods encode multiple motions into a single quantized representation. While existing methods directly decode from this quantized representation, DisCoRD iteratively decodes the discrete latent in a continuous space to recover the inherent continuity and dynamism of motion. To assess the gap between reconstructed and real motion, prior work primarily used FID as the metric. Here, we additionally propose symmetric Jerk Percentage Error (sJPE) to evaluate the differences in naturalness between reconstructed and real motion.
+
+cause misaligned motions, while slight unnaturalness disrupts immersion and triggers the uncanny valley [36] effect.
+
+Since human motion is inherently continuous, generation based on continuous representations is naturally well-suited for producing smooth and realistic motion [38, 51, 60, 65]. However, due to the high dimensionality of continuous representation, they often encounter challenges with cross-modal mapping ambiguity [49, 61] which can result in low faithfulness. This issue becomes especially pronounced in data-constrained settings, such as motion capture datasets [32], where limited examples lead to difficulty of learning consistent mappings between signals and motions. On the other hand, discrete quantization methods [12, 41, 64] utilize motion VQ-VAEs [55] to discretize motion representation, simplifying the learning of high-dimensional data mappings by reformulating it as a classification task. This discretization enables more efficient learning and can be particularly beneficial when dealing with limited data, improving faithfulness [12, 40, 41]. However, motion VQ-VAEs face two main challenges. First, under-reconstruction occurs when fine-grained motion details, which are essential for generating dynamic movements, are lost during token discretization. Second, frame-wise noise arises from directly decoding discrete tokens, introducing unnatural artifacts that disrupt motion smoothness and diminish user immersion. These challenges make it difficult to generate motion that is both smooth and natural while maintaining high faithfulness.
+
+In this paper, we propose DisCoRD, a novel approach that bridges discrete and continuous motion generation to achieve both faithfulness and naturalness. Our key insight is to leverage the strong faithfulness of discrete generation methods [12, 40, 64] by utilizing rectified flow models [26,
+
+[29] to translate pretrained discrete tokens back into raw motion space. This enhances naturalness while preserving alignment with the conditioning signals.
+
+Our method offers two primary advantages over traditional discrete decoding methods, as shown in Figure 2. First, instead of directly decoding discrete tokens into motion space, we use them as conditioning signals to guide motion generation within the continuous motion space. This reduces fine-grained noise and results in smoother, more natural motion. Second, rather than relying on a one-step decoding process, we employ an iterative refinement approach using a rectified flow model [5, 67], which progressively improves reconstruction quality. This enables the generation of dynamic and complex movements that conventional methods struggle to capture. Moreover, DisCoRD is framework-agnostic, making it adaptable to any discrete generation method (e.g., autoregressive [64] or bidirectional [12]), regardless of the conditioning signal type (e.g., text, music, or speech), thereby improving performance.
+
+Although our method improves motion naturalness, evaluating this quality remains challenging. Traditional metrics such as MPJPE do not correlate well with human perception [9, 18], and FID fails to capture subtle, frame-wise noise, as illustrated in Figure 4. These limitations reduce the reliability of existing metrics in accurately assessing reconstructed motion naturalness. To address this, we introduce a novel sample-wise metric, the symmetric Jerk Percentage Error (sJPE), which evaluates reconstructed motion by simultaneously detecting under-reconstruction and fine-grained artifacts. Our experiments demonstrate the effectiveness of DisCoRD in enhancing sample-wise naturalness without suffering from under-reconstruction. Extensive evaluations across text-to-motion, co-speech gesture, and music-to-dance generation demonstrate that our method achieves state-of-the-art naturalness, consistently outperforming existing approaches. Our contributions are as follows:
+
+1. We introduce DisCoRD, a novel method for decoding discrete tokens in continuous motion space, improving the naturalness of generated motions while preserving faithfulness across various models and tasks.
+2. We propose a novel evaluation scheme, the symmetric Jerk Percentage Error (sJPE), designed to evaluate both under-reconstruction and frame-wise noise, which are often overlooked but critical for motion generation.
+3. Our extensive experiments demonstrate that our methods achieve state-of-the-art performance on existing human motion generation scenarios.
+
+# 2. Related Work
+
+Human Motion Generation from Diverse Signals. Generating natural and controllable 3D human motion remains a long-standing task. Early approaches prioritized motion naturalness [2, 13, 22], while recent advances in deep learn
+
+ing expand capabilities to generate motion conditioned on diverse signals. Recent advances of text-to-motion datasets [11, 42] have driven progress in text-conditioned motion synthesis, while music-motion datasets [25, 48] have enabled music-driven dance generation. Speech-motion datasets [27, 28, 62] extends motion control by synthesizing gestures from speech. As most recent methods rely on discrete representations [10, 12, 30], our work enhances motion naturalness for all discrete methods, regardless of the task, by addressing the discrete token decoding problem.
+
+Continuous Human Motion Generation. Early approaches to signal-to-motion generation employ regression-based mapping of control signals to motion within a continuous representation space. These works leverage Variational Autoencoders (VAE) [11, 21, 39], GANs [14], or CLIP features [43, 50] to generate natural motion. More recently, with the success of diffusion models [15, 47], motion generation models have achieved unprecedented generation quality [52, 53, 65]. Follow-up works explore continuous latent spaces for efficient motion generation [8, 60], incorporate physical constraints to improve realism [63], and integrate retrieval mechanisms to enhance generalization [66]. Their ability to generate smooth, natural motion makes them well-suited for not only motion synthesis but also for a generative prior [37, 45]. However, due to the lack of scalability in current motion datasets, the high complexity of continuous representations often makes it difficult to establish reliable cross-modal mappings between control signals and generated motions, leading to suboptimal performance.
+
+Discrete Human Motion Generation. Recently, to simplify the complex mapping between control signals and motions, some methods have reformulated the generation task as a discrete token classification problem, achieving notable performance in motion generation [46, 62, 64]. These approaches often employ VQ-VAEs [54] and its variants [24] to create motion tokens, which are then used to generate motion sequences via autoregressive [17, 35, 40, 59, 62, 64], or masked [12, 19, 28, 30] token prediction. More recently, discrete diffusion models have been introduced to directly denoise these discrete tokens [7, 31]. While these methods effectively bypass complex signal-to-motion mapping challenges, their inherent characteristics—such as quantization errors and discreteness result in unnatural artifacts, including under-reconstruction and frame-wise noise.
+
+# 3. Method
+
+In this section, we introduce DisCoRD, a novel method for decoding pretrained discrete representations in the raw motion domain using rectified flow. This approach enables motion generation that is both smooth and dynamic: (1) decoding in the raw motion domain preserves natural motion smoothness, and (2) utilizing rectified flow enhances
+
+expressiveness, capturing fast-paced movements. We begin by introducing rectified flow models and motion tokenization, followed by an explanation of our condition projection, conditional rectified flow decoder, and training details.
+
+# 3.1. Preliminaries
+
+Rectified Flow. Diffusion models [15, 47] have demonstrated remarkable performance due to their iterative denoising formulation, which enhances their ability to capture complex data variations and generate high-dimensional samples. However, they typically require a large number of denoising steps to produce high-quality outputs. In contrast, rectified flow [29] provides a more direct approach by framing sample generation as a transport problem, addressed through a flow matching algorithm [1, 26, 29]. Flow matching algorithm aims to construct a transport map denoted as $T: \mathbb{R}^d \to \mathbb{R}^d$ , that effectively transfers observations from the source distribution $x_0 \sim \pi_0$ on $\mathbb{R}^d$ to the target distribution $x_1 \sim \pi_1$ on $\mathbb{R}^d$ . This transport process is formalized as the following ordinary differential equation (ODE):
+
+$$
+d x _ {t} = v \left(x _ {t}, t\right) d t. \tag {1}
+$$
+
+Here, $v$ represents the vector field, and $x_{t}$ denotes the trajectory parameterized over $t \in [0,1]$ . Rectified flow follows the formulation of the forward process in diffusion models [20], but its specific parameterization enables a more direct mapping between distributions and improves efficiency. Specifically, its forward process can be expressed as:
+
+$$
+x _ {t} = t x _ {1} + (1 - t) x _ {0}, \tag {2}
+$$
+
+where $v$ is defined as $x_{1} - x_{0}$ . Then, the model is trained to learn a causal approximation of $v$ , denoted as $v_{\theta}$ , by solving the following least squares regression problem:
+
+$$
+\min _ {v} \int_ {0} ^ {1} \mathbb {E} \left[ \| \left(x _ {1} - x _ {0}\right) - v \left(x _ {t}, t\right) \| ^ {2} \right] d t. \tag {3}
+$$
+
+Once trained, samples from the target distribution $\pi_1$ can be generated by solving Equation (1) using an ODE solver, where the initial conditions are drawn from the source distribution $\pi_0$ . Unlike conventional diffusion models, which require many denoising steps, rectified flow follows a nearly straight trajectory, enabling more efficient transport with much fewer denoising steps.
+
+Motion Tokenization. The objective of generative models based on discrete quantization methods is to reformulate the regression problem into a classification problem. These models typically undergo a two-stage training process. In stage 1, a VQ-VAE is trained to encode a motion sequence $\mathbf{X} = [\mathbf{x}_1,\mathbf{x}_2,\dots ,\mathbf{x}_T]$ where $\mathbf{x}_t\in \mathbb{R}^{d_{motion}}$ using an encoder $\mathcal{E}$ , into a sequence of discrete tokens $\mathbf{Z} = [\mathbf{z}_1,\mathbf{z}_2,\dots ,\mathbf{z}_{T / q}]$ . Each token $\mathbf{z}_t$ is retrieved from
+
+
+Pretrained Quantizer
+Inference
+
+
+DisCoRD
+
+
+Pretrained Token Generator
+
+
+DisCoRD
+Figure 3. An overview of DisCoRD. During the Training stage, we leverage a pretrained quantizer to first obtain discrete representations (tokens) of motion. These tokens are then projected into continuous features $\mathbf{C}$ , which are concatenated with noisy motion $\mathbf{X}_t$ . This concatenated feature is used to train a vector field $v$ . During the Inference stage, we use a pretrained token prediction model based on the pretrained quantizer to first generate tokens from the given control signal. These generated tokens are then projected into continuous features $\hat{\mathbf{C}}$ , concatenated with Gaussian noise $\mathbf{X}_0 \sim \mathcal{N}(0, I)$ , and iteratively decoded through the learned vector field $v_\theta$ into motion $\hat{\mathbf{X}}_1$ .
+
+the codebook $\mathcal{Z} = \{\mathbf{z}_k\in \mathbb{R}^{d_{code}}\}_{k = 1}^N$ , and $T$ represents the length of the original motion sequence while $q$ is the downsample factor. Then a decoder $\mathcal{D}$ reconstructs the motions $\mathbf{X}_{recon}$ from $\mathbf{Z}$ , with the network trained using a reconstruction loss and a commitment loss. In stage 2, the index sequence $\mathbf{S} = [\mathbf{s}_1,\mathbf{s}_2,\dots ,\mathbf{s}_{T / q}]$ , representing the one-hot encoded codebook indices of the discrete token sequence $\mathbf{Z}$ is used to train a next-index prediction model conditioned on various signals.
+
+After training both stages, generating a new motion sequence $\hat{\mathbf{X}}$ from a given condition $\mathbf{C}$ involves two steps: first, the stage 2 model produces a sequence of predicted indices $\hat{\mathbf{S}}$ , which is then converted into discrete tokens $\hat{\mathbf{Z}}$ using the learned codebook. Finally, $\mathcal{D}$ reconstructs the motion sequence $\hat{\mathbf{X}}$ from $\hat{\mathbf{Z}}$ , yielding the desired motion output.
+
+# 3.2. DisCoRD
+
+Directly decoding discrete tokens using traditional feedforward decoders $\mathcal{D}$ suffer from limited expressiveness and propagate token discreteness into decoded motions, resulting in under-reconstructed and noisy outputs (Figure 5). To address these issues, we propose decoding pretrained tokens in continuous space by replacing $\mathcal{D}$ with an expressive rectified
+
+flow model. Specifically, we first extract frame-wise conditioning features from discrete tokens through a Condition Projection module, and then use these features as frame-wise conditions for a Rectified Flow Decoder that synthesizes human motion from Gaussian noise. The overall pipeline of DisCoRD is depicted in Figure 3.
+
+Condition Projection. To enable our decoder to generate expressive motion, we first extract frame-wise conditioning features from discrete tokens $\mathbf{Z} = [\mathbf{z}_1,\dots ,\mathbf{z}_{T / q}]$ . Since each token $\mathbf{z}_t$ encodes information spanning $q$ consecutive motion frames, we must extract $q$ distinct, frame-specific features from each token. A naive upsampling and linear projection would result in same $q$ features from each token, and upconvolution layers would disregard the temporal correspondence between each tokens and frames. To mitigate these issues, we first repeat each token $\mathbf{z}_t\in \mathbb{R}^{1\times d_{code}}$ $q$ times to restore the original temporal resolution, resulting in $\mathbf{z}_t^{\text{repeat}}\in \mathbb{R}^{q\times d_{code}}$ . Then we stack into a tensor $\mathbf{z}_t^{\text{stacked}}\in \mathbb{R}^{1\times (q\times d_{code})}$ and project to $\mathbf{z}_t^{\text{project}}\in \mathbb{R}^{1\times (q\times d_{feat})}$ . Finally, we unstack the projected tensor to $\mathbf{z}_t^{\text{final}}\in \mathbb{R}^{q\times d_{feat}}$ where each vector $\mathbf{c}_i\in \mathbb{R}^{d_{feat}}$ (for $i\in [1,\ldots ,q]$ ) are frame-wise conditioning features. This process is applied to every token in $\mathbf{Z}$ , resulting in $\mathbf{C} = [\mathbf{c}_1,\dots ,\mathbf{c}_T]$ . This approach maintains the
+
+correspondence between tokens and motion frames by explicitly extracting $q$ features from each token, ensuring that the resulting frame-wise conditioning features are well-suited for the motion decoding. Moreover, we found that our projection method enhances motion generation on unseen token sequences on stage 2.
+
+Rectified Flow Decoder. Our goal is to decode discrete tokens into natural motion while operating within a continuous space. Therefore, we do not directly map discrete tokens back into motion, but treat discrete tokens as a signal to guide motion decoding in the raw motion space. Given the frame-wise conditioning features $\mathbf{C}$ extracted from discrete tokens by the condition projection module, we train a conditional rectified flow model to reconstruct the original motion. Specifically, given a motion data distribution $P_{\mathbf{X}}$ , we define the transport process from Gaussian noise $\mathbf{X_0} \sim \mathcal{N}(0,I)$ to motion $\mathbf{X_1} \sim P_{\mathbf{X}}$ , guided by frame-wise conditioning features $\mathbf{C}$ , formulated as:
+
+$$
+\min _ {v} \int_ {0} ^ {1} \mathbb {E} \left[ \| \left(\mathbf {X} _ {1} - \mathbf {X} _ {0}\right) - v \left(\mathbf {X} _ {t}, t, \mathbf {C}\right) \| ^ {2} \right] d t, \tag {4}
+$$
+
+with $\mathbf{X}_t = t\mathbf{X}_1 + (1 - t)\mathbf{X}_0$
+
+We concatenate frame-wise features $\mathbf{C}$ along the channel dimension, similar to image generation methods [16, 67], allowing each motion frame to be conditioned independently. This formulation ensures that decoding remains in the continuous space, enabling more expressive decoding. During inference, features $\hat{\mathbf{C}}$ are first extracted from tokens generated by a pretrained token generation model. This extracted features are then iteratively decoded into $\hat{\mathbf{X}}_1$ by solving a conditional ODE using the Euler method, progressively improving generation quality.
+
+Training. In variants of diffusion models, training is performed over the entire data instance with fixed sequence lengths, such as 196 frames in HumanML3D [11], a standard in motion generation [51, 60]. While this approach improves reconstruction quality in stage 1, our results indicate that these improvements do not translate effectively to generation quality in stage 2. To address this limitation and improve generalization to unseen motion sequences during inference, we train our rectified flow model on sliding windows of motion frames rather than max length spans. Additionally, although conventional U-Net diffusion models often incorporate attention mechanisms to enhance performance [44], we found this strategy to be suboptimal in our context, resulting in a performance degradation.
+
+# 4. Experiments
+
+In this section, we evaluate the effectiveness of DisCoRD in achieving motion naturalness compared to other discrete methods. We begin by assessing the naturalness of reconstructed motions to highlight the expressive capabilities of
+
+
+Figure 4. sJPE and FID response to frame-wise gaussian noise. We introduce Gaussian noise with varying standard deviations (x-axis) to ground-truth motion data and evaluate its effect on sJPE and FID. Noise sJPE is highly sensitive to subtle frame-wise perturbations, whereas Static sJPE remains low. FID is highly insensitive to frame-wise noise. Note that FID scale (y-axis, right) is very small compared to sJPE scale (y-axis, left).
+
+our rectified flow decoder. Then, we examine how this naturalness carries over to stage 2, generating natural motions while preserving faithfulness. We focus on text-to-motion generation due to its complex motions and diversity, but also evaluate our approach on other motion generation tasks, including co-speech gesture generation and music-to-dance generation, demonstrating the flexibility of our method.
+
+# 4.1. Dataset and Evaluation
+
+Datasets. For text-to-motion, we use HumanML3D [11] and KIT-ML [42]. HumanML3D is a 3D motion dataset with language annotations, including 14,616 motion sequences paired with 44,970 text descriptions. Sourced from motion capture data, motions are standardized to a template, scaled to 20 FPS, and cropped to 10 seconds if longer. KIT-ML is a smaller dataset with 3,911 motion sequences paired with 6,278 text descriptions. Motion capture data are downsampled to 12.5 FPS, with 1–4 descriptions per sequence. For co-speech gesture generation, we utilize the SHOW [62] dataset, while a mixed version of AIST++ [25] and HumanML3D is used for music-to-dance generation. Further dataset details are provided in the Supplementary Section B.
+
+Evaluation. We evaluate DisCoRD on both motion reconstruction and motion generation separately. For motion reconstruction, the primary objective is to assess how effectively the decoder reconstructs motion from tokens. This is measured by Fréchet Inception Distance (FID), which assesses motion realism by comparing the feature distributions of generated and ground truth motions, and Mean Per Joint Position Error (MPJPE), which quantifies positional accuracy. For text-to-motion generation, we follow [51] and employ several established metrics: FID, R-Precision, Multimodal Distance (MM-Dist), and Multimodality (MModality). For co-speech gesture generation, we employ Fréchet Gesture Distance (FGD) [33], and for music-to-dance generation, following [53], we utilize $\mathrm{Dist}_k$ and $\mathrm{Dist}_g$ to assess the quality of generated motions by comparing the distributional spread
+
+
+Figure 5. Under-reconstruction and frame-wise noise. We visualize fine-grained motion trajectories (top), and corresponding jerk graphs (bottom), where blue and red regions indicate noise and static sJPE, respectively. Compared to other methods, DisCoRD significantly reduces sJPE, resulting in smoother motion (fewer blue regions) and greater dynamism (fewer red regions), as highlighted in green boxes.
+
+
+
+
+
+
+
+of generated and real motions. Additional specifics on these metrics are provided in the Supplementary Section B.
+
+Symmetric Jerk Percentage Error. Prior works [12, 60] rely on MPJPE and FID at stage 1. However, MPJPE has limited correlation with human perceptual preferences [9], while FID, being a model-level metric extracted from pretrained network features, fails to capture per-sample naturalness [57]. Our experiments further indicate that FID is particularly insensitive to subtle, fine-grained noise (see Figure 4), which critically affects immersive motion quality [58]. To overcome these limitations, we introduce the Symmetric Jerk Percentage Error (SJPE), a metric explicitly designed to assess both under-reconstructed motions and frame-level noise through jerk. Jerk, defined as the third derivative of position with respect to time, has proven to effectively quantify subtle deviations [4, 7] and kinetic inconsistencies in motion [3, 23], being a critical measure for detecting unnatural artifacts in generated motion.
+
+Let $J_{\mathrm{pred},t}$ and $J_{\mathrm{true},t}$ denote the predicted and ground truth jerk, respectively, at time $t$ over $n$ time points. Then sJPE, capturing the symmetric mean absolute percentage error [34] between predicted and ground truth jerk values, is defined as
+
+$$
+\mathrm {s J P E} = \frac {1}{n} \sum_ {t = 1} ^ {n} \frac {\left| J _ {\text {p r e d} , t} - J _ {\text {t r u e} , t} \right|}{\left| J _ {\text {t r u e} , t} \right| + \left| J _ {\text {p r e d} , t} \right|}. \tag {5}
+$$
+
+Within sJPE, we identify two components: Noise sJPE and Static sJPE. Noise sJPE corresponds to instances where $J_{\mathrm{pred},t} > J_{\mathrm{true},t}$ , indicating an overestimation of jerk in the predicted motion, which reflects the presence of fine-grained noise. This effect is evident in discrete-based methods, where discrete tokens introduce frame-wise noise, as shown in Figure 5. Static sJPE captures instances where $J_{\mathrm{pred},t} \leq J_{\mathrm{true},t}$ , indicating underestimation of jerk, or insufficiently dynamic predicted motion, highlighted by green boxes in Figure 5. Together, these components provide a comprehensive measure
+
+| Dataset | Methods | FID ↓ | MPJPE ↓ | sJPE ↓ |
| H-ML3D | MLD [60] (cont.) | 0.017 | 14.7 | 0.404 |
| T2M-GPT [64] | 0.089 | 60.0 | 0.564 |
| +DisCoRD(Ours) | 0.031(+65%) | 71.5 | 0.488(+13%) |
| MMM [41] | 0.097 | 46.9 | 0.517 |
| +DisCoRD(Ours) | 0.020(+79%) | 56.8 | 0.429(+17%) |
| MoMask [12] | 0.019 | 29.5 | 0.512 |
| +DisCoRD(Ours) | 0.011(+42%) | 33.3 | 0.385(+25%) |
| KIT-ML | T2M-GPT [64] | 0.470 | 46.4 | 0.526 |
| +DisCoRD(Ours) | 0.284(+40%) | 58.7 | 0.395(+25%) |
| MoMask [12] | 0.113 | 37.5 | 0.384 |
| +DisCoRD(Ours) | 0.103(+9%) | 33.0 | 0.359(+7%) |
+
+Table 1. Quantitative results on motion reconstruction. DisCoRD enhances naturalness as a decoder for discrete models, shown by improvements over base models on FID and sJPE (blue). H-ML3D stands for HumanML3D and cont. for continuous.
+
+of prediction accuracy, capturing both over- and underestimations of jerk within a unified score. Additional details and results are in Supplementary Section C.
+
+# 4.2. Quantitative results
+
+Natural Motion Reconstruction. We evaluate DisCoRD's effectiveness in reconstructing natural motions from discrete models. Existing discrete methods often struggle to generate natural motions, as indicated by higher sJPE and FID values. While MoMask achieves competitive FID, its high sJPE suggests significant frame-wise noise and poor reconstruction quality compared to continuous models like MLD. Our proposed DisCoRD decoder substantially improves motion quality, as shown by reduced FID and sJPE metrics, overcoming the typical limitations of discrete models and producing smoother, more natural motions. Note that MPJPE measures only positional accuracy, and does not reflect motion naturalness or align with human perception [18].
+
+| Datasets | Methods | R Precision ↑ | FID ↓ | MM-Dist↓ | MultiModality ↑ |
| Top 1 | Top 2 | Top 3 |
| Human ML3D | MDM [52] | - | - | 0.611±.007 | 0.544±.044 | 5.566±.027 | 2.799±.072 |
| MLD [6] | 0.481±.003 | 0.673±.003 | 0.772±.002 | 0.473±.013 | 3.196±.010 | 2.413±.079 |
| MotionDiffuse [65] | 0.491±.001 | 0.681±.001 | 0.782±.001 | 0.630±.001 | 3.113±.001 | 1.553±.042 |
| ReMoDiffuse [66] | 0.510±.005 | 0.698±.006 | 0.795±.004 | 0.103±.004 | 2.974±.016 | 1.795±.043 |
| MMM [41] | 0.504±.003 | 0.696±.003 | 0.794±.002 | 0.080±.003 | 2.998±.007 | 1.164±.041 |
| T2M-GPT [64] | 0.491±.003 | 0.680±.003 | 0.775±.002 | 0.116±.004 | 3.118±.011 | 1.856±.011 |
| + DisCoRD (Ours) | 0.476±.008 | 0.663±.006 | 0.760±.007 | 0.095±.011 (+18%) | 3.121±.009 | 1.831±.048 |
| BAMM [40] | 0.525±.002 | 0.720±.003 | 0.814±.003 | 0.055±.002 | 2.919±.008 | 1.687±.051 |
| + DisCoRD (Ours) | 0.522±.003 | 0.715±.005 | 0.811±.004 | 0.041±.002 (+25%) | 2.921±.015 | 1.772±.067 |
| MoMask [12] | 0.521±.002 | 0.713±.002 | 0.807±.002 | 0.045±.002 | 2.958±.008 | 1.241±.040 |
| + DisCoRD (Ours) | 0.524±.003 | 0.715±.003 | 0.809±.002 | 0.032±.002 (+29%) | 2.938±.010 | 1.288±.043 |
| KIT-ML | MDM [52] | - | - | 0.396±.004 | 0.497±.021 | 9.191±.022 | 1.907±.214 |
| MLD [6] | 0.390±.008 | 0.609±.008 | 0.734±.007 | 0.404±.027 | 3.204±.027 | 2.192±.071 |
| MotionDiffuse [65] | 0.417±.004 | 0.621±.004 | 0.739±.004 | 1.954±.062 | 2.958±.005 | 0.730±.013 |
| ReMoDiffuse [66] | 0.427±.014 | 0.641±.004 | 0.765±.055 | 0.155±.006 | 2.814±.012 | 1.239±.028 |
| MMM [41] | 0.404±.005 | 0.621±.006 | 0.744±.005 | 0.316±.019 | 2.977±.019 | 1.232±.026 |
| T2M-GPT [64] | 0.398±.007 | 0.606±.006 | 0.729±.005 | 0.718±.038 | 3.076±.028 | 1.887±.050 |
| + DisCoRD (Ours) | 0.382±.007 | 0.590±.007 | 0.715±.004 | 0.541±.038 (+25%) | 3.260±.028 | 1.928±.059 |
| MoMask [12] | 0.433±.007 | 0.656±.005 | 0.781±.005 | 0.204±.011 | 2.779±.022 | 1.131±.043 |
| + DisCoRD (Ours) | 0.434±.007 | 0.657±.005 | 0.775±.004 | 0.169±.010 (+17%) | 2.792±.015 | 1.266±.046 |
+
+Table 2. Quantitative results on motion generation. ± indicates a 95% confidence interval. +DisCoRD indicates that the baseline model's decoder is replaced with DisCoRD. Bold indicates the best result, while underscore refers the second best. DisCoRD improves naturalness, as evidenced by FID improvements shown in blue, while preserving faithfulness, demonstrated by R-Precision.
+
+| Methods | sJPE↓ | FGD↓ |
| TalkSHOW [62] | 0.284 | 74.88 |
| + DisCoRD(Ours) | 0.077 | 43.58 |
| ProbTalk [30] | 0.406 | 5.21 |
| + DisCoRD(Ours) | 0.349 | 4.83 |
+
+Table 3. Quantitative results on each method's SHOW test set. DisCoRD outperforms baseline models on sJPE and FGD.
+
+| Methods | sJPE↓ | Distk→ (9.780) | Distg→ (7.662) |
| TM2D [10] | 0.275 | 8.851 | 4.225 |
| +DisCoRD(Ours) | 0.261 | 9.830 | 8.519 |
+
+Table 4. Quantitative results on the AIST++ test set. DisCoRD outperforms baseline model on sJPE, $\mathrm{Dist_k}$ and $\mathrm{Dist_g}$ .
+
+Natural Motion Generation. To evaluate DisCoRD's effectiveness in decoding predicted tokens, we use models trained in stage 1 to assess their performance in decoding tokens generated by pretrained token predictors. As shown in Table 2, our method consistently outperforms baseline models, particularly in terms of FID, achieving state-of-the-art performance in naturalness. We observe that for T2M-GPT, which employs a vanilla VQ-VAE with limited representational capacity, there is a slight decline in faithfulness, as a single token can map to multiple motions in DisCoRD. However, with RQVAEs [24], a popular quantization method on recent works [12, 40], DisCoRD performs on par and even increase
+
+faithfulness, shown by R-Precision and MM-Dist. These results indicate that when paired with a decent tokenizer, DisCoRD can significantly boost naturalness without sacrificing faithfulness, highlighting its potential as a default decoder replacement for discrete motion generation models.
+
+Performance on Various Tasks. To validate our approach as a general method for enhancing naturalness in discrete-based human motion generation, we train DisCoRD on co-speech gesture and music-driven dance generation, conducting a comparative analysis against baseline models. As shown in Table 3 and Table 4, our method consistently outperforms baseline models across both tasks, achieving superior performance on sJPE and standard evaluation metrics. We present additional evaluation results in Supplementary Section D.
+
+Effect of Sample Steps. By selecting the rectified flow algorithm from among the various diffusion model variants, we exploit its efficient transport mechanism to achieve inference speeds comparable to baseline models. As shown in Figure 6, we evaluated the decoding times for both MoMask and our model on tokens generated by a pretrained token generator. At the default setting of 16 sampling steps, our model achieves decoding speeds on par with MoMask while delivering superior sJPE, stage 1 FID, and stage 2 FID. Furthermore, by reducing the sampling steps, our method can decode tokens significantly fasterer than MoMask, maintaining comparable or enhanced FID and sJPE performance. Additionally, although it was not the primary focus of this
+
+
+Figure 6. Decoding efficiency comparison. We report the average decoding time for a batch of 32 token sequences on an NVIDIA RTX 4090 Ti, averaged over 20 trials on the HumanML3D test set. DisCoRD achieves more better performance on motion naturalness at a comparable decoding speed to MoMask and can even decode significantly faster while maintaining superior performance.
+
+| Methods | Recon | Generation |
| FID↓ | FID↓ | RP@1↑ | RP@2↑ | RP@3↑ |
| MoMask-R0 | 0.125 | 0.082 | 0.505 | 0.696 | 0.793 |
| +Ours | 0.061(+51%) | 0.068(+17%) | 0.491(-2.8%) | 0.682(-2.0%) | 0.782(-1.4%) |
| MoMask-R1 | 0.066 | 0.058 | 0.517 | 0.710 | 0.805 |
| +Ours | 0.024(+64%) | 0.037(+36%) | 0.510(-1.4%) | 0.703(-1.0%) | 0.800(-0.6%) |
| MoMask-R2 | 0.046 | 0.053 | 0.520 | 0.712 | 0.806 |
| +Ours | 0.018(+61%) | 0.031(+42%) | 0.517(-0.6%) | 0.709(-0.4%) | 0.806(-0.0%) |
| MoMask-R4 | 0.024 | 0.047 | 0.519 | 0.711 | 0.807 |
| +Ours | 0.011(+54%) | 0.032(+32%) | 0.520(+0.2%) | 0.711(0.0%) | 0.806(-0.1%) |
| MoMask-R5 | 0.019 | 0.045 | 0.521 | 0.713 | 0.807 |
| +Ours | 0.011(+42%) | 0.032(+29%) | 0.524(+0.6%) | 0.715(+0.3%) | 0.809(+0.2%) |
+
+experiment, we observed that sJPE responds more sensitively to changes in sampling steps compared to FID, further confirming that our sJPE metric effectively captures subtle variations in motion quality. Detailed decoding times are reported in the Supplementary Table E.
+
+Effect of Residual Quantization. We evaluate the impact of the representational capacity of motion tokens on DisCoRD by varying the residual quantization (RQ) levels in MoMask. As shown in Tab. 5, while DisCoRD consistently improves FID across all RQ levels, its R-Precision gains over each MoMask baseline increase with higher RQ levels, suggesting that DisCoRD better leverages richer token representations. This result is consistent with Table 2 where R-Precision drops for T2M-GPT (based on standard VQ-VAE) but maintains performance for MoMask and BAMM.
+
+Ablation Studies. We conduct ablation studies on DisCoRD's each component shown in Table 6. First, we compare our decoding strategy with post refinement methods which refine output motions from MoMask's decoder. Feedforward convolution layers show little improvement and
+
+Table 5. Effect of residual quantization levels (R). in MoMask on DisCoRD performance. Higher R yields greater R-Precision (RP) gains, indicating better use of richer representations.
+
+| Methods | Reconstruction | Generation |
| FID↓ | sJPE↓ | FID↓ | MM-Dist↓ |
| MoMask | 0.019±.001 | 0.512 | 0.051±.002 | 2.957±.008 |
| + Post Refinement (FF model) | 0.028±.000 | 0.481 | 0.044±.002 | 2.962±.006 |
| + Post Refinement (RF model) | 0.013±.000 | 0.489 | 0.035±.002 | 2.955±.008 |
| + DisCoRD (Ours) | 0.011±.000 | 0.385 | 0.032±.002 | 2.938±.010 |
| Ours (Upconv) | 0.010±.000 | 0.375 | 0.039±.003 | 2.943±.006 |
| Ours (Repeat & Linear) | 0.011±.001 | 0.342 | 0.038±.001 | 2.947±.008 |
| Ours (w/ Attention) | 0.020±.000 | 0.384 | 0.043±.002 | 2.983±.009 |
| Ours (w/ Full Motion Sequence) | 0.008±.000 | 0.385 | 0.038±.002 | 2.952±.009 |
+
+Table 6. Ablation studies. Evaluation on the HumanML3D test set assessing the impact of decoding strategies, projection methods, and training strategies. FF and RF denote feedforward and rectified flow model, respectively.
+
+rectified flow post refinement falls short in all metrics compared to ours. Second, we examine alternative projection mechanisms. While up-convolution or repeat followed by a linear layer show strong reconstruction performance, they fail to decode natural motion from generated token sequences (unseen at training) shown by low FID. Additionally, incorporating attention into the U-Net backbone and using full motion sequences instead of windowed motion segments result in performance degradation. This indicates that focusing on localized motion segments enhances the model's generalization capability, particularly in stage 2.
+
+# 4.3. Qualitative Results
+
+We visualize motion trajectories in Figure 5, where DisCoRD, unlike discrete methods, produces smooth and expressive motion with low sJPE. Extensive visualizations are provided in Supplementary Sections C.3 and E.1 with supporting user studies in Sections C.4 and E.2.
+
+# 5. Conclusion and Discussion
+
+In this paper, we present DisCoRD, a novel approach that decodes discrete motion tokens to natural, dynamic human motion using rectified flow. To demonstrate gains in naturalness, we also introduce symmetric Jerk Percentage Error (sJPE), specifically designed to capture subtle artifacts that were overlooked by traditional metrics. Extensive experiments across text-to-motion, co-speech gesture, and music-to-dance tasks demonstrate that DisCoRD consistently achieves state-of-the-art performance, providing a versatile solution adaptable to various discrete-based motion generation frameworks. While we experimented only on human motion generation, a promising direction would be to expand our framework to discrete talking face, hand motion, or even whole body motion generation.
+
+Acknowledgments. This study was supported by the Institute of Information Communications Technology Planning Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2024-00457882, Artificial Intelligence Research Hub Project). This work was also supported by the Culture, Sports and Tourism R&D Program through the Ko
+
+rea Creative Content Agency, funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name: Development of multimodal UX evaluation platform technology for XR spatial responsive content optimization, Project Number: RS-2024-00361757). T.-H. Oh was partially supported by the IITP grant funded by the Korea government (MSIT) (No. RS-2023-00225630, Development of Artificial Intelligence for Text-based 3D Movie Generation).
+
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+# DisTime: Distribution-based Time Representation for Video Large Language Models
+
+Yingsen Zeng $^{1*}$ , Zepeng Huang $^{1*}$ , Yujie Zhong $^{1\dagger}$ , Chengjian Feng $^{1}$ , Jie Hu $^{1}$ , Lin Ma $^{1}$ , Yang Liu $^{2}$ $^{1}$ Meituan Inc.
+
+$^{2}$ Wangxuan Institute of Computer Technology, Peking University
+
+{yingsen_2, huang_zpeng}@163.com jaszhong@hotmail.com yangliu@pku.edu.cn
+
+# Abstract
+
+Despite advances in general video understanding, Video Large Language Models (Video-LLMs) face challenges in precise temporal localization due to discrete time representations and limited temporally aware datasets. Existing methods for temporal expression either conflate time with text-based numerical values, add a series of dedicated temporal tokens, or regress time using specialized temporal grounding heads. To address these issues, we introduce DisTime, a lightweight framework designed to enhance temporal comprehension in Video-LLMs. DisTime employs a learnable token to create a continuous temporal embedding space and incorporates a Distribution-based Time Decoder that generates temporal probability distributions, effectively mitigating boundary ambiguities and maintaining temporal continuity. Additionally, the Distribution-based Time Encoder re-encodes timestamps to provide time markers for Video-LLMs. To overcome temporal granularity limitations in existing datasets, we propose an automated annotation paradigm that combines the captioning capabilities of Video-LLMs with the localization expertise of dedicated temporal models. This leads to the creation of InternVIDTG, a substantial dataset with 1.25M temporally grounded events across 179k videos, surpassing ActivityNet-Caption by 55 times. Extensive experiments demonstrate that DisTime achieves state-of-the-art performance across benchmarks in three time-sensitive tasks while maintaining competitive performance in Video QA tasks. DisTime is released at https://github.com/josephzpng/DisTime.
+
+# 1. Introduction
+
+With Large Language Models (LLMs) displaying powerful comprehension abilities, significant efforts have been made to bridge the gap between language and vision, en
+
+
+Figure 1. Comparison of temporal expression paradigms in Video-LLMs: (a) Text-Modal Discretization: time represented via text/number hybrids, (b) Multi-Token Discretization: dedicated temporal tokens, (c) Specialized Temporal Heads: utilizing temporal grounding models for direct regression, and (d) DisTime: distribution-based time decoder for temporal localization.
+
+abling LLMs to tackle visual tasks. As a result, Image-LLMs [6, 7, 19, 27, 34, 57] have achieved breakthroughs in image-related tasks. In the realm of video tasks, which contain richer information, numerous Video-LLMs [6, 18, 20, 47, 49, 53] have also made substantial progress in areas such as reasoning, captioning, and summarization. However, for temporal comprehension, these models typically manage temporal information by capturing the sequence of events rather than the precise timing of their occurrence. This leads to significant shortcomings in time-sensitive tasks, such as moment retrieval [9, 12, 16, 25, 39–41], dense video captioning [16, 56], and grounded video question answering [3, 46], etc.
+
+Temporal expression poses a significant challenge in time-sensitive Video-LLMs. The simplest approach is to express time using numbers, either alone or with markers, within the text modality. Models like GroundingGPT [24], VTimeLLM [15], and TimeMarker [4] employ this strategy. However, these methods force time and numbers to share the same decision boundary, complicating the classification process, as illustrated in Fig. 1a. To address modal
+
+confusion, some methods like Momentor [35] and VTGLLM [13] introduce extra tokens specifically for time expression, as shown in Fig. 1b. This approach, however, heavily depends on the classification of these new tokens and the balanced distribution of time data during training. Some tokens may receive insufficient training due to long-tailed distributions in the dataset. Both approaches share the drawback that using tokens for time expression is inherently discrete, resulting in insufficient precision for time representation (e.g., expressing decimals) and lacking explicit modeling of relationships between adjacent numerical values. The third approach, exemplified by InternVideo2.5 [44] and shown in Fig. 1c, creates trainable task tokens and a specialized temporal perception head to assist in time point decoding. These modules (e.g. CGDETR [33]) are typically designed for temporal grounding, containing numerous parameters and requiring the re-input of visual information.
+
+To improve the representation of temporal positions in LLMs, we propose DisTime, a method using an additional learnable token to indicate event time spans. This token creates a continuous embedding space for timestamps, thus avoiding confusion with numerical text values. As shown in Fig. 1d, DisTime utilizes the Distribution-based Time Decoder to convert the time token into start and end timestamps. Inspired by DFL [22], which acknowledges the inherent ambiguity in boundary detection, temporal boundaries face similar challenges, making direct regression to absolute time values difficult. Decoding the time token into a distribution provides flexibility when event boundaries are unclear, thereby reducing complexity in model prediction. Our method first converts the time token into a probability distribution, and then integrates this distribution to produce specific values. Unlike the approach in Fig. 1c, our decoder utilizes a minimal number of parameters (almost negligible) and without re-inputting original/encrypted images.
+
+Another challenge for time-sensitive Video-LLMs is the scale of temporal-aware datasets. Current video training datasets [2, 21, 51] predominantly focus on captioning, summarizing, and reasoning, often neglecting temporal awareness. The labor costs of annotating large volumes of time-sensitive data are significant. Although methods like VTimeLLM [15], InternVid-MR [11], and Momentor [35] propose unsupervised approaches to expand temporal grounding data, they share a common limitation: temporal granularity constraint, referring to reliance on shot boundaries and coarse fixed temporal intervals. VTimeLLM uses detected shot boundaries as time points, making event localization prone to errors within single shots, as simple boundaries do not accurately capture event timing. InternVid-MR divides videos into 2-second segments, determining event boundaries based on visual-text similarity, which often results in low labeling accuracy, par
+
+ticularly for short-duration events. Momentor merges segments by assessing the consistency of character instances between consecutive shots, but it still depends on the temporal boundaries of shots, ignoring static objects like scenery.
+
+To expand temporal-aware video data, we propose an annotation paradigm that overcomes temporal granularity constraints for event boundaries. Our method harnesses the captioning abilities of Video-LLMs for event extraction and employs the fine-grained localization capabilities of dedicated models for event boundary detection. Drawing on expertise from well-annotated data, the pseudo labels break free from shot-boundary constraints, making them more suitable for temporal grounding tasks. We employ three dedicated models: UniMD [52] for traditional in-domain temporal grounding, Mr.Blip [32] for high-precision localization with LLMs, and TFVTG [55] for zero-shot settings without training. A scoring strategy evaluates the grounding results, selecting the highest-scoring model output as the ensemble result for each event. Ultimately, we generated 1.25 million event annotations, over 55 times larger than the ActivityNet-Caption [16] dataset.
+
+To summarize, this paper makes three contributions:
+
+- We propose DisTime, a method that uses a single token for temporal expression in Video-LLMs. This approach transforms the token into a distribution via a distribution-based time decoder, which addresses event boundary uncertainty and enables continuous time modeling.
+- We propose an automated annotation paradigm that combines the captioning capabilities of LLMs with the fine-grained grounding abilities of dedicated temporal grounding models. With this paradigm, we create the InternVid-TG dataset, featuring 179K videos and 1.25M events.
+- Experiments demonstrate that DisTime enhances the fine-grained grounding abilities of Video-LLMs across three time-sensitive tasks. Notably, on Charades-STA [9], our model surpasses all dedicated models and current Video-LLMs in R@1iou=0.3 score, even in a zero-shot setting.
+
+# 2. Related Work
+
+Time-sensitive video understanding. Time-sensitive video understanding tasks require interpreting a video as a sequence of interconnected events and locating them in a temporally grounded manner. Moment Retrieval [9, 12, 16] focuses on identifying the timing of a specific event within a video. Dense Video Captioning [16, 56] involves describing and summarizing all events with their temporal information along the video timeline. Grounded Video Question Answering [3, 46] demands understanding questions while addressing the embedded temporal information. Thus, these tasks challenge models to have strong temporal sensitivity. Vision language models. With advancements in Large Language Models (LLMs), there is a growing focus on extending their capabilities from natural language process
+
+
+Figure 2. Overview of the Video-LLM with DisTime. Our DisTime method employs a single token (denoted as ) to represent continuous time, transformed by a distribution-based time decoder and time encoder. Initially, sampled timestamps are converted into time tokens and integrated into the LLM's input sequence. During autoregressive generation, when a is encountered, its corresponding LLM last-layer embedding is decoded into start and end times. These timestamps are then re-encoded to update the temporal context for subsequent autoregressive steps. In the final output sequence, the decoded times replace the . This approach enables the Video-LLM to explicitly model time, thereby enhancing its time-sensitive capabilities.
+
+ing to the visual domain, enhancing functions such as question answering, description, and summarization based on visual information. Recent Vision Language Models [6, 7, 19, 27, 57] incorporate learnable modules to integrate language and vision, primarily targeting image-level perception and comprehension. As multimodal research has progressed, Video-LLMs [18, 21, 23, 53] have emerged, showing strong performance in tasks like video question answering and captioning. However, these approaches largely concentrate on visual-level task requirements and exhibit limitations in high-level temporal perception.
+
+Temporal-awareness video language models. To tackle the challenges of time-sensitive tasks, recent VideoLLMs have focused on constructing time-sensitive data and enhancing temporal awareness in their architectures. GroundingGPT [24] improves performance by generating time-sensitive datasets and integrating multimodal data. VtimeLLM [15] enhances temporal perception through optimized training strategies, enriched datasets, and tailored instruction. TimeChat [37] and TimeMarker [4] incorporate temporal information from the current video frame into the multimodal input, enabling systems to perceive and interpret temporal dynamics effectively. However, these methods model time using textual representation, sharing decision boundaries with regular numerical values, thereby complicating classification and introducing quantization errors. Momentor [35] and VTG-LLM [13] introduce special tokens for timestamp modeling. Momentor uses a temporal perception module to ensure time continuity, while VTGLLM incorporates absolute-time tokens to manage timestamp information, reducing quantization errors. Despite
+
+this, these methods rely heavily on numerous new tokens for representing time absolutely, often overlooking time continuity and boundary fuzziness. We aim to maintain time continuity while addressing boundary fuzziness attentively.
+
+# 3. Method
+
+This section delves into the proposed DisTime, a method that uses a single token to represent continuous time in large language models (LLMs), enabling transformation between time tokens and timestamps via Distribution-based Time Encoder-Decoder. In Sec. 3.1, we present an overview of our approach to time-sensitive video understanding. Sec. 3.2 details the rationale and strategy for modeling time as a distribution in LLMs. We then introduce the Iterative Time Refinement mechanisms (Sec. 3.3) that update the temporal context during the autoregression process. Finally, Sec. 3.4 outlines the objective function and training methodology for optimizing the time token, time decoder, and time encoder.
+
+# 3.1. Overview
+
+The architecture of our time-sensitive video-LLM with DisTime is illustrated in Fig. 2, comprising five core components: a visual encoder with a projector, a text encoder, a LLM, a time decoder $(\Phi_{\mathrm{time - dec}})$ and a time encoder $(\Phi_{\mathrm{time - enc}})$ . First, a certain number of video frames are uniformly sampled from the video. Then, the visual encoder encodes the video frames, and the projector maps them into the language space to obtain visual tokens $\{V_i\}_{i = 1}^T$ , where $T$ is the number of sampled time steps in the video. Then, we derive a sequence of temporal representations $\{\tau_i\}_{i = 1}^T$
+
+by processing the timestamps through the time encoder, as:
+
+$$
+\tau_ {i} = \Phi_ {\text {t i m e - e n c}} (t _ {i}), i = 1, 2, \dots , T \tag {1}
+$$
+
+where $t_i \in [0,1]$ is the relative timestamp normalized to the video duration. Subsequently, the time tokens $\{\tau_i\}_{i=1}^T$ and visual tokens $\{v_i\}_{i=1}^T$ are interleaved and jointly input to the LLM with the user's instruction text tokens $\{Q_i\}_{i=1}^N$ , as:
+
+$$
+\text {I n p u t} = \operatorname {C o n c a t} \left(\tau_ {1}, v _ {1}, \dots , \tau_ {T}, v _ {T}, Q _ {1}, \dots , Q _ {N}\right), \tag {2}
+$$
+
+where $\{Q_i\}$ is encoded via text encoder. We use a dedicated time token, termed Distribution-based Time Token, to represent continuous time. This token is instantiated in the vocabulary as $<\text{TIME_STAMP}>$ . The autoregressive generation process includes both standard vocabulary tokens and the dedicated time token. When the LLM outputs $<\text{TIME_STAMP}>$ , we extract the corresponding hidden state $\mathbf{h}_{\text{time}}$ from the final layer and pass it to the time decoder to obtain continuous timestamps, as follows:
+
+$$
+\operatorname {s t}, \operatorname {e t} = \Phi_ {\text {t i m e - d e c}} (\mathbf {h} _ {\text {t i m e}}), \tag {3}
+$$
+
+where $st \in [0,1]$ and $et \in [0,1]$ denote the decoded start time and end time. These timestamps are then reprocessed through the time encoder to refresh the temporal context for subsequent autoregressive steps. The is replaced with the re-encoded time token, establishing explicit temporal referencing that functions as video timeline pointers. Finally, the is replaced with corresponding decoded timestamps $(st, et)$ , which are concatenated with generated text tokens (e.g. event_2) to form the LLM's complete output. This produces time-sensitive predictions with explicit timestamps.
+
+Our method is compatible with mainstream Video-LLMs (e.g. InternVL2.5 [5], LLaVA-OneVision [18]) that retain temporal-aligned input token sequences while being incompatible with the models using global temporal aggregation (e.g. LinVT [10], BLIP3-Video [38]).
+
+# 3.2. Modeling Time as Distribution
+
+DisTime to LLMs. Current Video-LLMs excel in global video understanding but often struggle with time-sensitive tasks due to imprecise event timing modeling. Existing solutions either (1) express time in text modality (complicating the classification for time and numbers), (2) use numerous learnable tokens (suffering from long-tailed distributions and temporal discontinuity), or (3) employ heavy temporal modules (adding extra high computational costs). The representation of time remains a critical optimization target for time-sensitive modeling.
+
+Furthermore, inspired by [22], we recognize the inherent ambiguity in event boundary detection. For instance, the query "A person is drinking water from a cup" introduces annotation uncertainty, such as whether to include the cup-picking action in the temporal segment. This ambiguity makes direct regression to absolute timestamps susceptible
+
+
+Figure 3. The illustration of time decoder and time encoder.
+
+to precision errors. Holistic analysis of multiple boundary hypotheses is essential to mitigate uncertainty.
+
+To address these limitations, we propose DisTime - a time modeling paradigm that represents time as probability distributions within LLMs. Our framework achieves continuous temporal representation through two key innovations: (1) Single-Token Constraint: This encapsulates continuous temporal information within a dedicated token using a lightweight encoder $(\Phi_{\mathrm{time - enc}})$ and decoder $(\Phi_{\mathrm{time - dec}})$ , enabling precise temporal grounding with minimal computational overhead. (2) Distribution-Aware Decoding: This resolves boundary ambiguity through probabilistic times-tamp generation, where final temporal coordinates are derived from weighted combinations of multiple hypotheses.
+
+Distribution-based time token. The dedicated time token in LLMs is termed Distribution-based Time Token (denoted as ), distinctly separating it from numerical text tokens in the vocabulary. When the LLM generates a , a lightweight decoder with a softmax function transforms it into a latent probability distribution, with each dimension of the latent embedding corresponding to an anchor point on the normalized time axis. These probability distributions enable continuous value representation.
+
+Time decoder. The time decoder is used to decode the into continuous timestamps, as shown in Fig. 3. Specifically, we partition the normalized temporal axis into $reg_{max} + 1$ discrete bins, each linked to an anchor point representing the probability of the timestamp being localized at that position. Formally, the temporal distribution is represented as a vector $\mathbf{e} = [\mathbf{e}_{st},\mathbf{e}_{et}]$ , where $\mathbf{e}\in \mathbb{R}^{2\times (reg_{max} + 1)}$ , and $\mathbf{e}_{st}$ and $\mathbf{e}_{et}$ denote the start and end time distributions, respectively. A lightweight MultiLayer Perceptron (MLP) followed by a softmax activation maps the to distribution vectors $\mathbf{e}$ , as:
+
+$$
+\mathbf {e} = \Phi_ {\text {t i m e - d e c}} \left(\mathbf {h} _ {\text {t i m e}}\right) = \operatorname {s o f t m a x} \left(\operatorname {M L P} \left(\mathbf {h} _ {\text {t i m e}}\right)\right). \tag {4}
+$$
+
+Continuous timestamps of start time and end time are derived via anchor-weighted summation, as:
+
+$$
+s t = \sum_ {i = 0} ^ {r e g _ {m a x}} \mathbf {e} _ {s t} ^ {(i)} \cdot a _ {i}, \quad e t = \sum_ {i = 0} ^ {r e g _ {m a x}} \mathbf {e} _ {e t} ^ {(i)} \cdot a _ {i}, \tag {5}
+$$
+
+where $\{a_{i}\}_{i = 0}^{reg_{max}}$ are anchors defined as: $a_{i} = i / reg_{max}$
+
+Time encoder. As shown in Fig. 3, the time encoder acts as the inverse of the decoder, translating continuous timestamps $(st, et) \in [0,1]$ into a time token $\tau$ . Firstly, each
+
+
+Figure 4. The autoregression of text token and time token.
+
+timestamp is projected into a Gaussian-regularized distribution to model annotation ambiguity, as: $p_{st} \sim \mathcal{N}(st, \delta^2)$ , $p_{et} \sim \mathcal{N}(et, \delta^2)$ , where $\delta$ controls the distribution spread. Here $\delta = 1$ for boundary uncertainty. The continuous distributions $p_{st}$ and $p_{et}$ are then discretized into $reg_{max} + 1$ uniformly spaced bins spanning [0, 1] to obtain the discretized distributions $\hat{\mathbf{e}}_{st}$ and $\hat{\mathbf{e}}_{et}$ . Next, a MLP projects the concatenated distributions $[\hat{\mathbf{e}}_{st}, \hat{\mathbf{e}}_{et}]$ into LLM-compatible time tokens $\tau$ , as:
+
+$$
+\tau = \operatorname {M L P} \left(\left[ \hat {\mathbf {e}} _ {s t}, \hat {\mathbf {e}} _ {e t} \right]\right). \tag {6}
+$$
+
+The encoding process operates through two stages: (1) time token injection during input visual sequence composition, and (2) LLM autoregressive processing. In the former stage, we set $st = et$ to model instantaneous temporal positions. In the latter stage, we utilize timestamps decoded by the time decoder and replace the with the encoded token $\tau$ for refined temporal representation.
+
+# 3.3. Iterating Time Refinement
+
+Time token re-encoding. The hidden embedding of inherently capture event boundary ambiguity (e.g. multi-modal distributions). In the autoregressive generation paradigm of LLMs, retaining raw time tokens across iterations can propagate errors due to representation uncertainty. To address this, we use probability-weighted timestamps from the decoder output to refine the LLM's temporal context. As shown in Fig. 3, we re-encode the decoded timestamps into fixed-variance Gaussian distributions via the time encoder. This re-encoded time token serves dual purposes: it transforms ambiguous temporal token interpretations into well-defined Gaussian-distributed representations and ensures distributional alignment across all time tokens. Through this method, arbitrary decoded distributions are normalized into standardized Gaussian forms, enabling consistent temporal representation and enhancing the LLM's temporal comprehension capability.
+
+Time token autoregression. The time token autoregression operates in a similar fashion to text tokens, as depicted in Fig. 4. Both token types undergo explicit decoding: text tokens map to vocabulary indices, while time tokens decode to continuous timestamps $(st, et)$ . The decoded results are then transformed into embeddings for subsequent iterations via domain-specific encoding: an embedding layer for text tokens and a time encoder for time tokens.
+
+# 3.4. Training Strategy
+
+Training Object. The loss function comprises three components: distribution focal loss $\mathcal{L}_{dist}$ for temporal distribution learning, 1d-IoU regression loss $\mathcal{L}_{reg}$ to directly optimize temporal grounding, and next token prediction loss $\mathcal{L}_{ntp}$ for autoregressive generation. The distribution focal loss [22] is key for training the distribution-based time token and time decoder, as it learns the underlying general distribution without introducing additional priors. The unified training objective is formulated as: $\mathcal{L} = \lambda_1 \cdot \mathcal{L}_{ntp} + \lambda_2 \cdot \mathcal{L}_{reg} + \lambda_3 \cdot \mathcal{L}_{dist}$ , where we set $\lambda_1 = \lambda_2 = \lambda_3 = 1$ for balanced multi-task optimization.
+
+Training Recipe. Based on the Video-LLMs that have been trained for general understanding capabilities, our method trains only one stage for enhancing temporal grounding ability. During this stage, the vision backbone and intermediate layers are frozen, and LoRA [14] is employed for efficient fine-tuning of the LLM. Additionally, the parameters of the LLM token embedding, LLM head, and the time encoder and decoder are fully trained.
+
+# 4. InternVid-TG
+
+Existing large-scale video training datasets primarily emphasize captioning, summarization, and reasoning tasks while lacking temporal awareness. Furthermore, though some automated annotation methods [11, 15, 35] attempt to scale supervision, they remain constrained by shot boundaries or coarse fixed temporal intervals. To expand time-aware supervision and overcome these constraints, we propose a temporal-aware data expansion framework that synergistically combines the summarization capabilities of large multimodal models with the fine-grained localization capabilities of temporal dedicated models. Fig. 5 illustrates the proposed annotation paradigm, which comprises four steps: event capturing, event boundary detection, scoring and ensemble processes, and instruction writing. Ultimately, we automate the annotation of InternVid-FLT [42] video data, transitioning from the original video-text alignment data to temporal grounding data, named InternVid-Temporal-Grounding (InternVid-TG).
+
+# 4.1. Generation pipeline
+
+Event capturing. Video-LLMs are trained on a large amount of video caption data, which endows them with powerful descriptive capabilities. We leverage this to extract event descriptions present in videos. First, we obtain the untrimmed sources from InternVid-FLT. We maintain the original resolution of the video and decode it at 1 fps to form an image sequence, which serves as the visual input for GPT-4o [1]. Next, we use the query "please identify the events that occur in the video" to prompt the model. In response, GPT-4o generates dense video captions in the
+
+
+Figure 5. The pipeline of our temporal-aware data expansion paradigm, which utilizes multimodal LLM and dedicated temporal models to generate temporal grounding annotations.
+
+format of “(start time, end time, event description)”. Here, we disregard the segment information in the response and use the event description as the extracted event. Finally, we obtain $\approx 7.0$ events per video.
+
+Event boundary detection using dedicated models. In the step of automatically annotating time points, to eliminate the dependency on shot segmentation, we directly use three models specifically designed for visual temporal grounding to perform the annotation. These models include UniMD [52], Mr.Blip [32], and TFVTG [55].
+
+UniMD is a traditional method specialized for temporal grounding. We retrain it using the visual features from InternVideo2 [43] as input because the training data for the visual encoder of InternVideo2 includes videos from InternVid-FLT. This adaptation makes UniMD more suited to the domain of InternVid-FLT. Mr.Blip is a dedicated Video-LLM trained for temporal grounding, and it is one of the state-of-the-art (SOTA) models in the Charades-STA [9], ANet-Caption [16], and QVHighlight [17] benchmarks. In QVHighlight, it achieves a top-1 recall at $50\%$ IoU $(R@1_{iou=0.5})$ of $74.77\%$ , demonstrating a high degree of overlap in event localization. TFVTG is a train-free video grounding model adapted for zero-shot scenarios. In zero-shot situations, it achieves a top-1 recall at $30\%$ IoU $(R@1_{iou=0.3})$ of $67.04\%$ on the Charades-STA benchmark, showing competitiveness with the fine-tuned SOTA LDDETR [54] which achieves $73.92\%$ R@1_{iou=0.3}.
+
+By inputting the extracted event descriptions and the videos, we independently input them into these three dedicated models to obtain the time segment for each event.
+
+Similarity scoring and ensemble. To evaluate the segment output from step two, we introduce a similarity scoring strategy. This score subsequently serves as the basis for assembling the segments from these three models. We utilize InternVideo2 [44] as our scoring model. Initially, each video segment is trimmed, and the video encoder of Intern-
+
+| Dataset | annotator | #videos | Avg Dura. (s) | #events | #events/vid |
| Ego4d [12] | Human | 2k | 472 | 18.4k | 9.2 |
| Charades-STA [9] | Human | 10k | 30 | 68k | 6.8 |
| ANet-caption [16] | Human | 15k | 118 | 22.5k | 1.5 |
| VTimeLLM [15] | LLM | 146k | 52 | 353k | 2.4 |
| InternVid-MR [11] | LLM | - | - | 150k | - |
| Momentor [35] | LLM | 65k | 403 | 1460k | 22.5 |
| InternVid-TG (ours) | LLM+ dedicated | 179k | 55 | 1250k | 7.0 |
+
+Table 1. Comparison among InternVid-TG, existing human-annotated datasets, and unsupervised datasets.
+
+Video2 is employed to extract visual features. Concurrently, the textual feature of each event caption is derived using InternVideo2's text encoder. The cosine similarity between these features is computed to assess text-video relevance. For each event, the temporal result with the highest score is selected as the ensemble output. In the supplementary materials, we present evidence supporting the effectiveness of our scoring strategy and ensemble approach. Additionally, we use the human-annotated InternVid-TG-1k, comprising 1,000 queries, to assess the quality of the pseudo labels.
+
+Instruction writing. We design 5 dialogue templates to convert temporal grounding annotations into single-turn conversations, which require identifying timestamps for the given event descriptions in the video.
+
+# 4.2.Impact
+
+Scale. Tab. 1 presents our dataset's data distribution. InternVid-TG annotates 1.25M events from 179k videos, originating from the same source as VTimeLLM and InternVid-MR. However, we extract more events, resulting in the largest video count among these datasets. Overall, our method provides a scalable data expansion approach. Since InternVid-FLT includes 4 million videos, we can expand further to incorporate more videos if needed.
+
+# 5. Experiment
+
+In this section, we begin by detailing the experimental setup (Sec. 5.1) and benchmarks (Sec. 5.2). Following this, in
+
+| Dataset | Task |
| VideoChat2 [21] (232k) | General Video Understanding |
| ANet-Caption [16] (37k) | Moment Retrieval |
| ANet-Caption [16] (9.8k) | Dense Video Captioning |
| YouCook2 [56] (2k) | Dense Video Captioning |
| ET-Instruct [28] (126k) | Multi-Event |
| InternVid-TG (1250k) | Moment Retrieval |
+
+Sec. 5.3, we conduct ablation studies to examine the time distribution representation, time token re-encoding, and the effectiveness of our proposed dataset. Finally, in Sec. 5.4, we provide further comparisons with current Video-LLMs for time-sensitive and general QA tasks. Additional ablation studies, qualitative analyses, and further benchmarks are included in the supplementary material.
+
+# 5.1. Implementation Details
+
+The proposed DisTime is integrated into two current Video-LLMs, InternVL2.5 [5] and LLaVA-OneVision [18], to enhance its performance on time-sensitive tasks. We use InternVL2.5-1B, LLaVA-OneVision-7B, and InternVL2.5-8B as baselines, with ablation studies conducted on InternVL2.5-1B. For visual input, both Video-LLMs sample frames at equal intervals: InternVL2.5 samples 16 frames, while LLaVA-OneVision samples at most 32 frames. The MLP for the time encoder and decoder consists of three fully connected layers with ReLU functions. The time decoder and encoder are parameter-efficient, collectively comprising just $0.36\%$ of InternVL2.5-1B, $0.34\%$ of LLaVA-OneVision-7B and $0.84\%$ of InternVL2.5-8B. The specific training data are detailed in Tab. 2.
+
+# 5.2.Benchmarks
+
+The comprehensive evaluation covers three time-sensitive tasks: Moment Retrieval (MR), Dense Video Captioning (DVC), and Grounded Video Question Answering (Grounded-VQA). For MR, we use the Charades-STA [9], ANet-Caption [16], and QVHighlights [17]. For DVC, we evaluate on ANet-Caption and YouCook2 [56]. For Grounded-VQA, we employ the NExT-GQA [46] dataset. Additionally, we assess our model's performance on general video understanding tasks using MVBench [21], VideoMME [8], and LongVideoBench [45].
+
+# 5.3. Ablation Study
+
+Roles of distribution representation. The comparison between directly predicting timestamps (denoted as "Direct") and obtaining timestamps through distribution prediction (denoted as "Dist.") is presented in Tab. 3. Utilizing distribution representation for time enhances the model's performance across all metrics in the MR task's Charades-STA dataset and the DVC task's YouCook2 dataset. Notably, YouCook2 exhibits a significant improvement, with the F1 score increasing from $2.2\%$ to $16.3\%$ .
+
+Table 2. Details of the training data covering both general video understanding and time-sensitive comprehension.
+
+| Direct | Dist. | Re-Enc. | Charades-STA (MR) | YouCook2 (DVC) |
| R@1(IoU=0.3) | R@1(IoU=0.5) | R@1(IoU=0.7) | mIoU | SODA_c | CIDEr | F1 Score |
| ✓ | | | 76.6 | 51.9 | 24.9 | 49.5 | 0.6 | 0.9 | 2.2 |
| ✓ | | 77.0 | 53.5 | 26.7 | 50.1 | 0.9 | 4.0 | 16.3 |
| ✓ | ✓ | 78.1 | 56.3 | 29.7 | 51.6 | 4.2 | 15.6 | 20.5 |
+
+Table 3. Ablation study of different components in the time tokenizer. "Direct" indicates that the decoder directly predicts timestamps, while "Dist." means the decoder first predicts a distribution and then aggregates it into timestamps. "Re-Enc." denotes the use of time token re-encoding for the next step of autoregression.
+
+| Training Data | Charades-STA (MR) | QVHighlights (MR) |
| R@1(IoU=0.3) | R@1(IoU=0.5) | R@1(IoU=0.7) | mIoU | R@1(IoU=0.3) | R@1(IoU=0.5) | mAP@.5 | mAP@.75 |
| Baseline | 77.4 | 51.4 | 22.9 | 48.7 | 38.7 | 17.7 | 34.8 | 12.5 |
| w/ VTimeLLM [15] | 76.2 | 51.9 | 25.0 | 49.3 | 51.0 | 25.8 | 46.0 | 18.8 |
| w/Momentor [35] | 76.6 | 50.6 | 21.6 | 47.8 | 39.7 | 17.8 | 35.1 | 12.5 |
| w/ Intern Vid-TG1 | 77.8 | 55.5 | 28.0 | 51.0 | 52.2 | 26.4 | 46.2 | 18.9 |
| w/ Intern Vid-TG | 78.1 | 56.3 | 29.7 | 51.6 | 54.1 | 27.8 | 47.9 | 19.2 |
+
+Table 4. The effectiveness of the LLM-generating time-sensitive datasets. Baseline refers to the basic training data, which includes general video understanding and time-sensitive datasets excluding the datasets used for comparison. InternVid-TG† denotes a subset that includes videos overlapping with those in VTimeLLM.
+
+Roles of time token re-encoding. As shown in Tab. 3, time token re-encoding ("Re-Enc") enhances distribution representation effectiveness, particularly in the high-precision metrics required for the MR task on Charades-STA, where $\mathrm{R} @ 1_{\mathrm{iou}=0.7}$ improves by $3\%$ . This underscores the importance of time token re-encoding for high-precision temporal expressions. Furthermore, in the YouCook2 dataset for the DVC task, "Re-Enc" leads to an increase of $11.6\%$ in the CIDEr score and a boost of $4.2\%$ in the F1 score.
+
+The effectiveness of InternVid-TG. We assess our proposed dataset's effectiveness on two MR benchmarks: Charades-STA and QVHighlights. For a fair comparison with VTimeLLM, we used a subset (InternVid-TG†) that shares overlapping videos with VTimeLLM, totaling ≈90k videos. As Tab. 4 shown, compared to VTimeLLM and Momentor, the model with InternVid-TG† shows improvements on both benchmarks, even though Momentor contains more events than InternVid-TG†. Notably, annotation noise can decrease metrics, as seen with Momentor, where the model's performance on Charades dropped. Finally, utilizing our full InternVid-TG dataset, expanding from 90k to 179k videos, further boosts performance.
+
+# 5.4. Main Results
+
+Moment Retrieval. As shown in Tab. 5, our model is compared to dedicated methods and time-sensitive Video-LLMs for the MR task on the Charades-STA, ANet-Caption benchmarks. Our DisTime-InternVL and DisTime-LLaVAOV models outperform all others in $R@1_{\mathrm{iou}=0.3}$ , even in a zero-shot setting. Among Video-LLMs optimized for MR tasks (i.e. excluding InternVL2.5 and LLaVA-OneVision), DisTime demonstrates robust time-sensitivity. In Charades-STA, DisTime-InternVL-1B surpasses others across all metrics, notably outperforming TimeMarker by $+4.4\%$ in $R@1_{\mathrm{iou}=0.5}$ . The DisTime-InternVL-8B model
+
+| Model | Size | Charges-STA | ANetCaption |
| R@1(IoU=0.3) | R@1(IoU=0.5) | R@1(IoU=0.7) | mIoU | R@1(IoU=0.3) | R@1(IoU=0.5) | R@1(IoU=0.7) | mIoU |
| Dedicated |
| UniVTG [26] | - | 72.6 | 60.2 | 38.6 | 52.2 | - | - | - | - |
| UniMD [52] | - | - | 63.9 | 42.2 | - | - | 42.7 | 25.1 | - |
| Mr.BLIP [32] | 3B | - | 69.3 | 49.3 | 58.6 | - | 53.92 | 35.6 | - |
| LLaVA-MR [30] | 3B | - | 70.7 | 49.6 | 59.8 | - | - | - | - |
| Video-LLMs |
| Momentor [35] | 7B | 42.6 | 26.6 | 11.6 | 28.5 | 42.9 | 23.0 | 12.4 | 29.3 |
| ChatVTG [36] | 7B | 52.7 | 33.0 | 15.9 | 34.9 | 40.7 | 22.5 | 9.4 | 27.2 |
| VTimeLLM [15] | 13B | 55.3 | 34.3 | 14.7 | 34.6 | 44.8 | 29.5 | 14.2 | 31.4 |
| TimeChart [37] | 7B | - | 32.2 | 13.4 | - | - | - | - | - |
| VTG-LLM [13] | 7B | - | 33.8 | 15.7 | - | - | - | - | - |
| InternVideo2.5 [44] | 7B | - | 43.3 | - | 41.7 | - | - | - | - |
| TimeMarker [4] | 8B | 73.5 | 51.9 | 26.9 | 48.4 | 67.4 | 50.7 | 33.0 | 49.5 |
| InternVL2.5* [5] | 1B | 3.1 | 1.5 | 0.7 | 5.1 | 5.3 | 2.9 | 1.5 | 5.5 |
| LLaVA-OneVision*[18] | 7B | 20.8 | 7.2 | 2.2 | 14.5 | 24.8 | 14.0 | 9.0 | 20.5 |
| InternVL2.5* [5] | 8B | 27.9 | 10.9 | 4.2 | 18.2 | 21.1 | 12.7 | 8.6 | 17.2 |
| DisTime-InternVL | 1B | 78.1 | 56.3 | 29.7 | 51.6 | 67.1 | 45.4 | 23.1 | 45.2 |
| DisTime-LLAVOV | 7B | 76.3 | 52.0 | 19.8 | 47.4 | 57.6 | 34.3 | 13.7 | 37.1 |
| DisTime-InternVL | 8B | 81.0 | 60.3 | 30.8 | 53.1 | 72.9 | 53.2 | 30.3 | 50.5 |
+
+Table 5. Comparison with various models on Moment Retrieval task in Charades-STA and ANet-Caption. "Dedicated" refers to the model fine-tuned with benchmark-specific training data. \*\* indicates results from our supplementary testing of the model. Notably, in Charades-STA, our DisTime is in a zero-shot setting.
+
+| Model | Size | YouCook2 | ANet-Caption |
| SODA_c | CIDEr | F1 Score | SODA_c | CIDEr | METEOR |
| Valley [31] | 7B | 0.1 | 0.0 | 1.5 | 0.3 | 1.8 | 0.8 |
| Momentor [35] | 7B | - | - | - | 2.3 | 14.9 | 4.7 |
| VTimeLLM [15] | 13B | - | - | - | 5.9 | 27.2 | 6.7 |
| TimeChat [37] | 7B | 1.2 | 3.4 | 12.6 | - | - | - |
| VTG-LLM [13] | 7B | 1.5 | 5.0 | 17.5 | - | - | - |
| DisTime-InternVL | 1B | 4.2 | 15.6 | 20.5 | 4.5 | 17.9 | 4.7 |
| DisTime-LLaVAOV | 7B | 5.4 | 21.8 | 19.5 | 4.9 | 21.3 | 4.9 |
| DisTime-InternVL | 8B | 6.9 | 31.0 | 26.4 | 4.1 | 17.8 | 5.8 |
+
+further widens this gap to $+8.4\%$ . In ANet-Caption, our 8B model excels in $\mathrm{R}@\mathrm{l}_{\mathrm{iou}=0.3}$ and mIoU, trailing slightly behind Mr.BLIP, which is dedicated to ANet-Caption, but remains competitive in $\mathrm{R}@\mathrm{l}_{\mathrm{iou}=0.5}$ . Compared to the baseline InternVL2.5, DisTime significantly enhances the MR task performance. The 1B model demonstrates an improvement in $\mathrm{R}@\mathrm{l}_{\mathrm{iou}=0.3}$ on Charades-STA, increasing from $3.1\%$ to $78.1\%$ . This validates our method's superior ability to express temporal information in LLMs and to enhance their skills in temporal localization. Furthermore, incorporating DisTime into LLaVA-OneVision considerably increases its temporal sensitivity, showcasing the generalizability and scalability of our method.
+
+Dense Video Captioning. As shown in Tab. 6, in the stepwise dense video captioning task, both DisTime-InternVL and DisTime-LLaVAOV significantly outperform all VideOLLMs on the YouCook2 benchmark. This improvement is attributed to our proposed Iterative Time Refinement mechanism, which clarifies the output time token through reencoding, thereby more accurately conveying the timing of the previous event in each subsequent autoregressive step. For the ANet-Caption benchmark, our method surpasses Valley and Momentor but falls short of VTimeLLM. It is important to note that, unlike VTimeLLM, which relies on 100-frame inputs, our method uses fewer input frames, with DisTime-InternVL using 16 frames and DisTime-LLaVAOV using 32 frames. Capturing nuanced event progression in ANet-Caption may require richer visual context from additional frames.
+
+Grounded Video Question Answering. The results for the grounded video question answering task on the NExT-GQA
+
+Table 6. Comparison with LLM-based models on the Dense Video Captioning task in ANet-Caption and YouCook2.
+
+| Model | Size | NExT-GQA |
| Acc@QA | Acc@GQA | mIoP | IoP@0.3 | IoP@0.5 | mIoU | IoU@0.3 | IoU@0.5 |
| SeViLA [50] | 3B | 68.1 | 16.6 | 25.7 | 34.7 | 22.9 | 21.7 | 29.2 | 13.8 |
| Temp [46] | 150M | 60.2 | 16.0 | 25.7 | 31.4 | 25.5 | 12.1 | 17.5 | 8.9 |
| FrozenBILM [48] | 1B | 70.8 | 17.5 | 24.2 | 28.5 | 23.7 | 9.6 | 13.5 | 6.1 |
| DisTime-InternVL | 1B | 65.9 | 17.0 | 33.5 | 42.9 | 23.7 | 31.1 | 41.0 | 21.8 |
| DisTime-LLaVAOV | 7B | 75.8 | 22.8 | 36.3 | 48.4 | 28.7 | 31.9 | 45.6 | 23.5 |
| DisTime-InternVL | 8B | 80.3 | 28.1 | 40.5 | 55.1 | 33.8 | 35.9 | 52.0 | 28.8 |
+
+Table 7. Comparison with models on the Grounded Video Question Answering task in NExT-GQA.
+
+| Model | Size | MVBench avg | Video-MME (wo sub)) | LongVideoBench (val total)) |
| TimeChat | 7B | 38.5 | 34.7 | - |
| TimeMarker | 8B | 67.4 | 57.3 | 56.3 |
| InternVideo2.5 | 7B | 75.7 | 65.1 | 60.6 |
| InternVL2.5 | 1B | 64.3 | 50.3 | 47.9 |
| LLaVA-OneVision | 7B | 56.7 | 58.2 | 56.3 |
| InternVL2.5 | 8B | 72.0 | 64.2 | 60.0 |
| DisTime-InternVL | 1B | 62.6 | 47.4 | 49.0 |
| DisTime-LLaVAOV | 7B | 59.0 | 54.4 | 55.4 |
| DisTime-InternVL | 8B | 72.0 | 59.6 | 60.0 |
+
+Table 8. Comparison with models on the General Video Understanding tasks in short (MVBench and Video-MME) and long (LongVideoBench) video benchmarks.
+
+benchmark are shown in Tab. 7. This task not only evaluates the understanding of question answering but also requires the ability to temporally locate events. Among the compared methods, DisTime-InternVL-1B surpasses them in most metrics (except for Acc@GQA and IoP@0.5). When scaled up to DisTime-InternVL-8B, it achieves the top performance across all metrics.
+
+General Video Understanding. The results of the general video understanding task are shown in Tab. 8. Without any targeted optimization of general understanding capabilities, our methods exhibit diverse performance improvements across various benchmarks. In MVBench, DisTime-LLaVAOV-7B outperforms LLaVA-OneVision by $2.3\%$ , while DisTime-InternVL-8B maintains consistent performance metrics. In LongVideoBench, DisTime-InternVL-1B shows a improvement of $1.1\%$ . Despite a decline in performance on VideoMME, both DisTime-InternVL and DisTime-LLaVAOV remains competitive when compared to other models. For example, DisTime-InternVL-8B significantly outpaces TimeMarker with the same parameter size, and DisTime-InternVL-1B surpasses TimeChat, which has a much larger parameter size. The integration of DisTime primarily aims to enhance time-sensitive tasks, while still maintaining competitiveness in general understanding tasks.
+
+# 6. Conclusion
+
+This paper proposes DisTime, a lightweight paradigm for enhancing temporal expression in Video-LLMs by using a single token to regress continuous timestamps through distribution prediction. Additionally, we propose an automated annotation paradigm that leverages LLMs and specialized temporal grounding models. Video-LLMs equipped with DisTime achieve improved temporal comprehension through efficient continuous time modeling and scalable data generation, providing practical solutions for applications requiring fine-grained video understanding.
+
+# Acknowledgment
+
+This work was supported by the grants from the National Natural Science Foundation of China 62372014 and Beijing Natural Science Foundation 4252040.
+
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+[57] Deyao Zhu, Jun Chen, Xiaogian Shen, Xiang Li, and Mohamed Elhoseiny. Minigpt-4: Enhancing vision-language understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 1, 3
\ No newline at end of file
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+# Discontinuity-aware Normal Integration for Generic Central Camera Models
+
+Francesco Milano $^{1\star}$ Manuel López-Antequera $^{2}$ Naina Dhingra $^{2}$ Roland Siegwart $^{1}$ Robert Thiel $^{2}$ ETH Zurich, $^{2}$ Meta
+
+# Abstract
+
+Recovering a 3D surface from its surface normal map, a problem known as normal integration, is a key component for photometric shape reconstruction techniques such as shape-from-shading and photometric stereo. The vast majority of existing approaches for normal integration handle only implicitly the presence of depth discontinuities and are limited to orthographic or ideal pinhole cameras. In this paper, we propose a novel formulation that allows modeling discontinuities explicitly and handling generic central cameras. Our key idea is based on a local planarity assumption, that we model through constraints between surface normals and ray directions. Compared to existing methods, our approach more accurately approximates the relation between depth and surface normals, achieves state-of-the-art results on the standard normal integration benchmark, and is the first to directly handle generic central camera models.
+
+# 1. Introduction
+
+The problem of reconstructing a 3D surface from its surface normal map, also known as normal integration, has long been studied in computer vision. Its importance lies in its several applications for shape reconstruction, in particular as a necessary step to recover the surface from the output of photometric stereo [34] or shape-from-shading [20] techniques, which estimate normals from image shading.
+
+Classically, normal integration has been studied predominantly under the assumption that the surface to be reconstructed is smooth [28]. This assumption, however, breaks in the presence of depth discontinuities, which naturally arise due to occlusions. While a number of methods for discontinuity-preserving integration have been proposed, these tend to introduce simplifying assumptions on the statistics of the discontinuities [3, 29] or model their magnitude only implicitly [1, 7, 35]. Moreover, the vast majority of the existing methods for discontinuity-preserving normal integration tackle the case of orthographic projection [3, 29, 36]; an exception is represented by the recently
+
+proposed methods of BiNI [7] and of Kim et al. [24], which allow handling normals observed by an ideal pinhole camera, which more closely resembles real-world scenarios.
+
+All the leading methods are derived from partial differential equations (PDEs) which relate normals to the depth map describing the surface, and typically base their formulation on functionals that discretely approximate these PDEs [7, 21, 24, 28]. In this work, we propose a novel formulation not derived from differential constraints, but based instead on the simple assumption that the surface is composed of local planes separated by discontinuities. We model this assumption through conditions between the surface normal and the ray direction associated with each pixel. We show experimentally that this results in a more accurate approximation of the ground-truth relation between depth and normals. Additionally, by relying on ray directions, our approach is to the best of our knowledge the first to directly handle generic central camera models, thereby extending the case of an ideal pinhole. Furthermore, our mathematical formulation explicitly takes discontinuities into account.
+
+In order to recover both the depth map and the discontinuity values, we adopt an iterative optimization process based on the bilateral weighting scheme of BiNI. In particular, we adapt their semi-smooth assumption to our formulation and extend its optimization scheme to iteratively estimate depth and discontinuities. We additionally provide important novel insights on the optimization convergence, in light of our formulation. Experimental results show that our method captures discontinuities more accurately than existing methods and sets a new state of the art in the standard normal integration benchmark [31]. We provide extensive ablations on the hyperparameters of our method and further demonstrate it on normal maps from non-ideal pin-hole cameras and real-world data, showing effective surface reconstruction also under these conditions.
+
+In summary, our main contribution is a novel formulation for discontinuity-aware normal integration based on a local planarity assumption and ray directions, that: (i) more accurately describes the relation between depth and surface normals, (ii) achieves state-of-the-art results on the standard normal integration benchmark, and (iii) shows for the first time direct applicability to generic central camera models.
+
+# 2. Related work
+
+In the following Section, we briefly review the main existing approaches for normal integration. For a more extensive summary, we refer the reader to the surveys [28, 29].
+
+The majority of normal integration methods proposed in the literature are derived from discrete approximations to PDEs relating depth and surface normals. One category of approaches, pioneered by Horn and Brooks [21], are based on constraints between the partial derivatives of the depth and the gradient field computed from the normal map [2, 3, 11, 15, 29]. More recently, an alternative differential formulation has been proposed by Zhu and Smith [37] and later extended by Cao et al. [7] that instead enforces an orthogonality constraint between the normals and the tangent plane to the surface, showing improved numerical stability. Our method is derived from a similar orthogonality constraint, but proposes a more general formulation that is applicable to generic central camera models and explicitly takes discontinuities into account.
+
+To handle depth discontinuities, two main categories of approaches have been proposed that extend the PDE-based formulations above. One category of methods modify their functionals with robust estimators that reduce the effect of large residuals [3, 11, 27]. Another line of approaches instead introduce weights in the terms of the PDEs. Among these, single-analysis methods use weights defined before the optimization based on error residuals or input gradients [1, 13, 23, 33, 36]. Since the weights are kept fixed, these approaches might fail to correct wrong discontinuities during the optimization. To address this issue, alternative approaches have been proposed that iteratively optimize the weights. Typically, this is achieved by alternatively updating depth and parameters controlling the location of the discontinuities [2, 29, 35]. Recently, Cao et al. [7] significantly advanced the state of the art by proposing an iterative weight-update approach based on the assumption that the target surface is one-sided differentiable. At each iteration, the terms in its functional are scaled by relatively weighting the residuals on the two sides of each point, resulting in effective discontinuity preservation for the first time also for the perspective, ideal pinhole case. Kim et al. [24] later proposed to explicitly model gradients across discontinuities through auxiliary edges, showing more accurate detection of small discontinuities. In our approach, we adopt the bilateral weighting scheme of [7] and extend it to our formulation, which explicitly models discontinuities and handles generic central cameras.
+
+# 3. Discontinuity-aware normal integration
+
+Formally, the objective of normal integration is to recover a surface, in the form of a depth map, from a single-view per-pixel normal map and known camera parameters. Our
+
+method tackles this problem by explicitly modeling surface discontinuities while solving for the unknown depth values. Additionally, unlike previous methods that are designed for orthographic and pinhole cameras, our approach allows modeling the broader category of central cameras.
+
+In the following Section, we first derive the general formulation of our method for discontinuity-aware surface normal integration for arbitrary central cameras (Sec. 3.1). We then describe the general optimization framework to estimate solutions from our proposed formulation (Sec. 3.2). Finally, in Section 3.3 we provide specific details on how we perform the optimization and retrieve discontinuities by extending and generalizing the bilateral assumption of [7].
+
+# 3.1. Proposed formulation
+
+Let us consider a generic central camera, that is, any camera that models a central projection [16], and let us denote with $\pmb{\tau}:\pmb{u}\in \mathbb{R}^2\mapsto \pmb{\tau}(\pmb{u}) = (\tau_x(\pmb{u}),\tau_y(\pmb{u}),1)^{\mathrm{T}}\in \mathbb{R}^3$ the mapping from a point $\mathbf{u} = (u,v)^{\mathrm{T}}$ on its image plane to its corresponding ray direction vector $\pmb{\tau}(\pmb{u})$ . The elements $\tau_{x}(\pmb{u})$ and $\tau_{y}(\pmb{u})$ represent the tangent of the viewing angle, corresponding to the ray passing through $\pmb{u}$ , respectively along the $x$ and $y$ axes of the camera coordinate frame. For a generic point $\pmb{p}(\pmb{u})$ along the ray, with camera coordinates $(x(\pmb{u}),y(\pmb{u}),z(\pmb{u}))^{\mathrm{T}}\in \mathbb{R}^{3}$ , these can be expressed as $\tau_{x}(\pmb{u}) = \frac{x(\pmb{u})}{z(\pmb{u})}$ and $\tau_{y}(\pmb{u}) = \frac{y(\pmb{u})}{z(\pmb{u})}$ . In the specific case of a pinhole camera with focal lengths $f_{x}$ and $f_{y}$ and principal point $(c_{x},c_{y})$ , the mapping $\pmb{\tau}$ is affine in the image coordinates and can be written as $\pmb{\tau}(\pmb{u}) = \left(\frac{u - c_x}{f_x},\frac{v - c_y}{f_y},1\right)^{\mathrm{T}}$ .
+
+When the camera observes a fully-opaque surface, each ray that intersects the surface is in one-to-one correspondence both with the visible 3D point $\pmb{p} = (x,y,z)^{\mathrm{T}}\in \mathbb{R}^{3}$ at which it intersects the surface and with the normal vector $\pmb {n}(\pmb {p}) = (n_x,n_y,n_z)^{\mathrm{T}}\in S^2\subset \mathbb{R}^3$ at that point. It follows that it is possible to define injective mappings from image coordinates to visible surface points and normal vectors.
+
+Our general formulation for normal integration, makes use of: (i) a local planarity approximation to handle pixel discretization, (ii) explicit discontinuity modelling, and (iii) the general definition of ray direction vectors. In particular, let $a$ and $b$ be two neighboring pixels in the input normal map, with corresponding image coordinates $\boldsymbol{u}_a = (u_a, v_a)^\top$ and $\boldsymbol{u}_b = (u_b, v_b)^\top$ . In our main experiments, we define neighborhood based on 4-connectivity, although other connectivities can also be considered. Furthermore, let $m$ denote a subpixel location along the line segment connecting pixel $a$ and $b$ on the image plane (Fig. 1) and let $\boldsymbol{\tau}_i = (\tau_{x_i}, \tau_{y_i}, 1)^\top$ , $\boldsymbol{p}_i = (x_i, y_i, z_i)^\top$ , and $\boldsymbol{n}_i = (n_{ix}, n_{iy}, n_{iz})^\top$ denote respectively the ray direction vector, the unknown visible surface point, and the known normal vector corresponding to (sub)pixel $i \in \{a, b, m\}$ . Our method assumes that at the location of both $a$ and $b$ the sur
+
+
+Figure 1. Visualization of our local planarity assumption on the image plane. For each pair of neighboring pixels $a$ and $b$ , a subpixel $m$ is selected on the line segment connecting $a$ and $b$ , here chosen to be equidistant from the pixel centers. Along both the directions $m \rightarrow b$ and $m \rightarrow a$ , the surface is assumed to be locally planar, with a discontinuity at the location of $m$ .
+
+face can be locally approximated by a plane segment perpendicular to the normal vector. More precisely, as illustrated in Fig. 2, we assume that the point $\pmb{p}_m$ can be found at the intersection between the ray $\tau_m$ and the plane tangent to the surface at $\pmb{p}_b$ . To model a depth discontinuity at $\pmb{p}_m$ , we further assume that the plane tangent to the surface at point $\pmb{p}_a$ can be intersected by moving from $\pmb{p}_m$ by $\varepsilon_{b\to a}$ units along the positive direction of the $z$ camera axis.
+
+The assumptions described above can be modeled through the following system of 6 independent equations, where we define $dx_{ij} \coloneqq x_i - x_j$ , $dy_{ij} \coloneqq y_i - y_j$ , $dz_{ij} \coloneqq z_i - z_j$ , with $i,j \in \{a,b,m\}$ , and use a right-hand convention for camera coordinates $(x,y,$ and $z$ axes pointing respectively to the right, bottom, and front):
+
+$$
+\left\{\begin{array}{l}\tau_ {x _ {m}} = \frac {x _ {b} + d x _ {m b}}{z _ {b} + d z _ {m b}}\\\tau_ {y _ {m}} = \frac {y _ {b} + d y _ {m b}}{z _ {b} + d z _ {m b}}\\\tau_ {x _ {a}} = \frac {x _ {b} + d x _ {m b} - d x _ {m a}}{z _ {b} + d z _ {m b} - d z _ {m a}}\\\tau_ {y _ {a}} = \frac {y _ {b} + d y _ {m b} - d y _ {m a}}{z _ {b} + d z _ {m b} - d z _ {m a}}\\n _ {b x} \cdot d x _ {m b} + n _ {b y} \cdot d y _ {m b} + n _ {b z} \cdot d z _ {m b} = 0\\n _ {a x} \cdot d x _ {m a} + n _ {a y} \cdot d y _ {m a} + n _ {a z} \cdot \left(d z _ {m a} + \varepsilon_ {b \rightarrow a}\right) = 0\end{array}\right. \tag {1}
+$$
+
+The first four equations in the system follow from the definition of ray direction vector, while the last two model the perpendicularity constraint between the two plane segments and the normal vectors $\pmb{n}_a$ , $\pmb{n}_b$ , taking into account the depth discontinuity $\varepsilon_{b\rightarrow a}$ .
+
+Solving (1) for $dx_{ma}, dx_{mb}, dy_{ma}, dy_{mb}, dz_{ma}, dz_{mb}$ , and plugging the solutions back into the definitions of these quantities yields the following condition on $z_{a}, z_{b}$ , and $\varepsilon_{b \to a}$ :
+
+$$
+z _ {a} = \omega_ {\varepsilon_ {a}} \cdot \varepsilon_ {b \rightarrow a} + \omega_ {b \rightarrow a} \cdot z _ {b}, \tag {2}
+$$
+
+
+Figure 2. Visualization of our local planarity assumption in 3D. We assume that the surface can be modeled as piecewise-planar and define the plane endpoints as the intersection between the surface and the rays from the camera center of projection $O$ along the ray directions $\tau_{a}$ , $\tau_{b}$ , and $\tau_{m}$ . We explicitly model a discontinuity $\varepsilon_{b\rightarrow a}$ along the $z$ camera axis in line with $p_m$ .
+
+where
+
+$$
+\omega_ {\varepsilon_ {a}} = \frac {n _ {a z}}{\boldsymbol {n} _ {\boldsymbol {a}} ^ {\top} \boldsymbol {\tau} _ {\boldsymbol {a}}}
+$$
+
+$$
+\omega_ {b \rightarrow a} = \frac {\boldsymbol {n} _ {a} ^ {\top} \boldsymbol {\tau} _ {m} \cdot \boldsymbol {n} _ {b} ^ {\top} \boldsymbol {\tau} _ {b}}{\boldsymbol {n} _ {a} ^ {\top} \boldsymbol {\tau} _ {a} \cdot \boldsymbol {n} _ {b} ^ {\top} \boldsymbol {\tau} _ {m}}. \tag {3}
+$$
+
+We provide a full derivation of (3) in Appendix A.
+
+It should be noted that all the quantities in (3) are known by hypothesis, except for $\tau_{m}$ (or equivalently the location of the subpixel $m$ on the image plane), the choice of which controls the local planarity approximation (Fig. 2). In our main experiments, we assume for simplicity that $\tau_{m} = (\tau_{a} + \tau_{b}) / 2$ , which for mappings $\pmb{\tau}$ that are affine in the image coordinates corresponds to $m$ having image coordinates given by the average of the pixel coordinates of $a$ and $b$ , i.e., $\pmb{u}_{m} = (\pmb{u}_{a} + \pmb{u}_{b}) / 2$ . However, alternative choices for obtaining $\tau_{m}$ are possible, including through linear interpolation $\pmb{\tau}_{m} = \pmb{\tau}_{a} + \lambda_{m}(\pmb{\tau}_{b} - \pmb{\tau}_{a})$ , with $\lambda_{m} \in [0,1]$ (of which the above is a special case, with $\lambda_{m} = 0.5$ for all pixel pairs). We refer the reader to Appendix D in the Supplementary Material for a more detailed analysis and for ablations on the choice of $\tau_{m}$ .
+
+We furthermore note that the coefficients in (3) depend on terms of the form $n^{\top}\tau$ , which relate surface normals to ray directions through a dot product. This dot product relationship has previously been studied in the literature, famously by Marr [26] and more recently by Bae and Davison [4]. As previously noted in these works, a necessary condition for a surface point to be visible is that the angle between its corresponding ray direction vector and surface normal vector is greater than $90^{\circ}$ , i.e., $n^{\top}\tau < 0$ , with equality being attained in the limit of the point lying on an occluding boundary. It follows that, assuming valid surface normals, the terms $n_a^{\top}\tau_a$ and $n_b^{\top}\tau_b$ in (3) are strictly negative. On the other hand, the terms $n_a^{\top}\tau_m$ and $n_b^{\top}\tau_m$ are
+
+negative if the points of intersection between the ray direction $\tau_{m}$ and the two local planes containing $p_a$ and $p_b$ , respectively, are visible by the camera when approximating the surface as local planes. As we discuss more in detail in Appendix C, when choosing $\tau_{m}$ to linearly interpolate $\tau_{a}$ and $\tau_{b}$ the latter condition is fulfilled for all but very specific corner cases, and is always verified in practice for $\tau_{m} = (\tau_{a} + \tau_{b}) / 2$ . From (3), it follows that under these settings the $\omega_{b\to a}$ terms are always positive. While this condition is not strictly necessary, it allows a convenient reformulation of (2), as detailed in the next Section.
+
+# 3.2. General solution framework
+
+Similarly to previous methods [7, 24], our formulation allows estimating the unknown depth values by solving a least-squares optimization problem. In particular, the set of conditions (2) for all valid choices of neighboring pixels $(a,b)$ , $(a,c)$ , etc. can be rewritten in the form of a system of linear equations $\mathbf{A}\mathbf{z} = \mathbf{b}$ , where
+
+$$
+\begin{array}{l} \mathbf {A} = \left[\begin{array}{c c c c}1&- \omega_ {b \rightarrow a}&0&\dots\\1&0&- \omega_ {c \rightarrow a}&\dots\\\vdots&\vdots&\vdots&\ddots\\- \omega_ {a \rightarrow b}&1&0&\dots\\\vdots&\vdots&\vdots&\ddots\end{array}\right], \tag {4} \\ \mathbf {z} = \left[ \begin{array}{c} z _ {a} \\ z _ {b} \\ z _ {c} \\ \vdots \end{array} \right], \text {a n d} \mathbf {b} = \left[ \begin{array}{c} \omega_ {\varepsilon_ {a}} \cdot \varepsilon_ {b \to a} \\ \omega_ {\varepsilon_ {a}} \cdot \varepsilon_ {c \to a} \\ \vdots \\ \omega_ {\varepsilon_ {b}} \cdot \varepsilon_ {a \to b} \\ \vdots \end{array} \right]. \\ \end{array}
+$$
+
+The optimization problem then reads as:
+
+$$
+\min _ {\mathbf {z}} \left(\mathbf {A} \mathbf {z} - \mathbf {b}\right) ^ {\top} \mathbf {W} \left(\mathbf {A} \mathbf {z} - \mathbf {b}\right), \tag {5}
+$$
+
+where $\mathbf{W}$ is an optional diagonal matrix that can assign different weights to the equations. The unknown depth values $\mathbf{z}$ can then be found by applying an iterative conjugate gradient method [7, 18] on the normal equation of (5), $\mathbf{A}^{\mathrm{T}}\mathbf{W}\mathbf{A}\mathbf{z} = \mathbf{A}^{\mathrm{T}}\mathbf{W}\mathbf{b}$ . However, since our formulation explicitly takes discontinuities into account, the term $\mathbf{b}$ in (5) depends on the values $\varepsilon_{b\rightarrow a}$ , $\varepsilon_{c\rightarrow a}$ , etc. We note that if the ground-truth values of these quantities - hence of the term $\mathbf{b}$ - were known, the conditions expressed by the system $\mathbf{A}\mathbf{z} = \mathbf{b}$ would model exactly the relationship between the ground-truth depth values at the different pixels, and as we show in Section 4.3, the optimization would be able to recover the ground-truth depth values with close-to-perfect accuracy. Since, however, the ground-truth values for $\varepsilon_{b\rightarrow a}$ are unknown, in our optimization we not only iteratively update the depth values, but also optimize the term $\mathbf{b}$ , so that it progressively models the ground-truth term more closely.
+
+More in detail, upon initialization we assume the surface to be smooth everywhere, thereby setting all discontinuities $\varepsilon_{b\to a}$ to 0. As a consequence, the system of equations (4) is initially homogeneous; knowing that depth values are positive and following a common practice in the literature [7, 28], we therefore introduce the change of variable $\tilde{z} := \log z$ . To allow rewriting (2) as a condition on $\tilde{z}_a$ and $\tilde{z}_b$ , we additionally express the discontinuity values as relative discontinuities, by introducing the terms $\alpha_{b\to a} := \varepsilon_{b\to a} / z_b$ , so that
+
+$$
+\varepsilon_ {b \rightarrow a} = \alpha_ {b \rightarrow a} \cdot z _ {b}. \tag {6}
+$$
+
+Using (6) and applying the logarithm to both sides of (2), we can rewrite our condition (2) as
+
+$$
+\tilde {z} _ {a} ^ {(t)} = \log \left(\omega_ {\varepsilon_ {a}} \cdot \alpha_ {b \rightarrow a} ^ {(t)} + \omega_ {b \rightarrow a}\right) + \tilde {z} _ {b} ^ {(t)}, \tag {7}
+$$
+
+where we additionally use the superscript ${}^{(t)}$ to indicate that the variables are evaluated at iteration $t$ of the optimization.
+
+We note that upon initialization the terms inside the logarithm in (7) coincide with $\omega_{b\rightarrow a}$ , having set $\varepsilon_{b\rightarrow a}^{(0)} = 0$ and therefore $\alpha_{b\rightarrow a}^{(0)} = 0$ . As noted in Section 3, when choosing the subpixel locations $m$ to interpolate between $a$ and $b$ , the terms $\omega_{b\rightarrow a}$ are positive, which ensures that the logarithm is always defined. Similarly to [7, 24], we initialize the log-depth values $\tilde{z}_a^{(t)},\tilde{z}_b^{(t)}$ , etc. to 0, which corresponds to a planar surface of unit depth. At each iteration $t$ , we first optimize the log-depth values using the system of equations $\tilde{\mathbf{A}}\tilde{\mathbf{z}} = \tilde{\mathbf{b}}$ that can be derived from (7) with the same procedure used to write (4) from (2); then, we update the terms $\alpha_{b\rightarrow a}^{(t)}$ , as we detail in the next Section.
+
+# 3.3. Discontinuity-aware bilateral formulation
+
+In order to guide the optimization of the log-depth values as well as to iteratively update the discontinuity values, we adopt the semi-smooth assumption of BiNI [7], which we extend to our formulation and briefly summarize below.
+
+For a pinhole camera with focal lengths $f_{x}$ and $f_{y}$ and principal point $(c_{x}, c_{y})$ , BiNI makes use of the following discrete PDE, here expressed in our notation:
+
+$$
+\gamma_ {b \rightarrow a} \left(\tilde {z} _ {a} - \tilde {z} _ {b}\right) = \delta_ {b \rightarrow a}, \tag {8}
+$$
+
+where neighboring pixels $b$ are defined according to 4-connectivity, and the terms $\gamma_{b\to a}$ and $\delta_{b\rightarrow a}$ are defined as:
+
+$$
+\gamma_ {b \rightarrow a} = n _ {a x} \left(u _ {a} - c _ {x}\right) + n _ {a y} \left(v _ {a} - c _ {y}\right) + n _ {a z} f, \tag {9}
+$$
+
+with $f = f_{x}$ , $\delta_{b\to a} = \pm n_{ax}$ for neighboring pixels $b$ s.t. $(u_b,v_b) = (u_a\pm 1,v_a)$ and $f = f_y$ , $\delta_{b\to a} = \pm n_{ay}$ for neighboring pixels $b$ s.t. $(u_b,v_b) = (u_a,v_a\pm 1)$ . Their method then assumes the surface to be semi-smooth, that is,
+
+to contain at most one-sided discontinuities. This assumption is modeled by weighting each equation (8), at each optimization iteration $t$ , by a term
+
+$$
+w _ {b \rightarrow a} ^ {\operatorname {B i N I} (t)} = \sigma_ {k} \left(\left(\operatorname {r e s} _ {- b \rightarrow a} ^ {(t)}\right) ^ {2} - \left(\operatorname {r e s} _ {b \rightarrow a} ^ {(t)}\right) ^ {2}\right), \tag {10}
+$$
+
+where $\mathrm{res}_{b\to a}^{(t)}\coloneqq \gamma_{b\to a}\left(\tilde{z}_a^{(t)} - \tilde{z}_b^{(t)}\right)$ is a residual that encodes the extent to which the surface is discontinuous between $\pmb{p_b}$ and $\pmb{p_a}$ , $\sigma_k(\cdot)$ is the sigmoid function $\sigma_{k}(x) = (1 + e^{-kx})^{-1}$ , and where we denote with $-b$ the neighbor of $a$ opposite to $b$ , i.e. s.t. $\pmb{u}_{-b} - \pmb{u}_{a} = -(u_{b} - u_{a})$ . By properties of the sigmoid function, $w_{b\rightarrow a}^{\mathrm{BiNI}(t)}\in [0,1]$ and $w_{-b\rightarrow a}^{\mathrm{BiNI}(t)} = 1 - w_{b\rightarrow a}^{\mathrm{BiNI}(t)}$ , with $w_{b\rightarrow a}^{\mathrm{BiNI}(t)}\approx 0$ indicating that the estimated surface is discontinuous between $\pmb{p_b}$ and $\pmb{p_a}$ but continuous between $\pmb{p}_{-b}$ and $\pmb{p_a}$ , and $w_{b\rightarrow a}^{\mathrm{BiNI}(t)}\approx w_{-b\rightarrow a}^{\mathrm{BiNI}(t)}\approx 0.5$ that the surface is continuous on both sides.
+
+We note that, up to the multiplicative constant $\gamma_{b\to a}$ , the formulation of BiNI (8) has the same functional form as our formulation. While (8) could be rewritten as $\tilde{z}_a - \tilde{z}_b = \delta_{b\to a} / \gamma_{b\to a}$ , as noted in Sec. 2 of the Supplementary of BiNI [9] the factor $\gamma_{b\to a}$ proves to be crucial to improving their numerical stability during optimization. We empirically verify that the same holds true for our formulation, and we therefore rewrite our formulation as follows, by multiplying both sides of (7) by $\gamma_{b\to a}$ and rearranging:
+
+$$
+\gamma_ {b \rightarrow a} \left(\tilde {z} _ {a} - \tilde {z} _ {b}\right) = \gamma_ {b \rightarrow a} \log \left(\omega_ {b \rightarrow a} + \omega_ {\varepsilon_ {a}} \cdot \alpha_ {b \rightarrow a}\right). \tag {11}
+$$
+
+Following BiNI, we furthermore define our weighting matrix $\mathbf{W}$ based on (10). Importantly, we additionally note that $\gamma_{b\rightarrow a}$ can be rewritten (up to the differences between $f_{x}$ and $f_{y}$ ) as
+
+$$
+\gamma_ {b \rightarrow a} = f \cdot \boldsymbol {n} _ {\boldsymbol {a}} ^ {\top} \boldsymbol {\tau} _ {\boldsymbol {a}}, \tag {12}
+$$
+
+which for generic central cameras we generalize as
+
+$$
+\gamma_ {b \rightarrow a} = \| \boldsymbol {u} _ {\boldsymbol {b}} - \boldsymbol {u} _ {\boldsymbol {a}} \| / \| \boldsymbol {\tau} _ {\boldsymbol {b}} - \boldsymbol {\tau} _ {\boldsymbol {a}} \| \cdot \boldsymbol {n} _ {\boldsymbol {a}} ^ {\top} \boldsymbol {\tau} _ {\boldsymbol {a}}. \tag {13}
+$$
+
+In light of this observation, we present a thorough analysis of the impact of the terms in (13) in Appendix B, providing important novel findings about their effect on convergence and shedding light on the role of $\gamma_{b\to a}$ in the optimization.
+
+While the above procedure allows optimizing the log-depth values, as noted in Sec. 3.2 we would like to additionally update our discontinuity terms $\alpha_{b\to a}^{(t)}$ , to model discontinuities with increasingly higher accuracy. To this purpose, we invert (7) to derive the following update scheme:
+
+$$
+\alpha_ {b \rightarrow a} ^ {(t + 1)} \leftarrow \left(\exp \left(\tilde {z} _ {a} ^ {(t)} - \tilde {z} _ {b} ^ {(t)}\right) - \omega_ {b \rightarrow a}\right) / \omega_ {\varepsilon_ {a}}, \tag {14}
+$$
+
+with $\alpha_{b\to a}^{(0)} = 0$ for all valid pairs $(a,b)$ . However, applying this update to all pairs would cause the optimization to converge in one iteration to a suboptimal solution, since its objective (5) would evaluate to 0. To avoid this, we introduce
+
+
+Figure 3. Discontinuity activation term (16) for $q = 50.0$ and $\rho = 0.25$ . The term $\beta_{b\to a}^{(t)}$ progressively incorporates discontinuities in our formulation, which correspond to $w_{b\rightarrow a}^{\mathrm{BiNI}(t - 1)} < 0.5$ .
+
+an additional term $\beta_{b\to a}^{(t)}\in [0,1]$ in (11), which selectively activates the discontinuity terms, as follows:
+
+$$
+\gamma_ {b \rightarrow a} \left(\tilde {z} _ {a} ^ {(t)} - \tilde {z} _ {b} ^ {(t)}\right) = \gamma_ {b \rightarrow a} \log \left(\omega_ {b \rightarrow a} + \omega_ {\varepsilon_ {a}} \cdot \alpha_ {b \rightarrow a} ^ {(t)} \cdot \beta_ {b \rightarrow a} ^ {(t)}\right). \tag {15}
+$$
+
+The rationale for $\beta_{b\to a}^{(t)}$ is the following: If the surface is estimated to be continuous between pixels $a$ and $b$ , one can approximate $\alpha_{b\rightarrow a}\approx 0$ , so the influence of the discontinuity term should be negligible. On the other hand, the more the surface is estimated to be discontinuous between $a$ and $b$ , the more the term $\alpha_{b\rightarrow a}$ would increase the accuracy of (11), and thus the more it should be taken into account. We note that the weights $w_{b\to a}^{\mathrm{BiNI}}$ naturally model this relationship. Indeed, as the optimization identifies with increasing confidence that a discontinuity is present between $a$ and $b$ the corresponding term $w_{b\to a}^{\mathrm{BiNI}}$ increasingly approaches 0. Viceversa, if the optimization identifies the surface to be continuous between $a$ and $b$ , or at least equally discontinuous in the directions of the two opposite pixels $b$ and $-b$ , the term $w_{b\to a}^{\mathrm{BiNI}}$ is greater or equal than 0.5 ( $w_{b\to a}^{\mathrm{BiNI}}\to 1$ in the first case and $w_{b\to a}^{\mathrm{BiNI}}\approx 0.5$ in the latter). We therefore define the discontinuity activation terms as
+
+$$
+\beta_ {b \rightarrow a} ^ {(t)} = \sigma \left(q \cdot \left(\rho - w _ {b \rightarrow a} ^ {\mathrm {B i N I} ^ {(t - 1)}}\right)\right), \tag {16}
+$$
+
+where we set $q = 50.0$ and $\rho = 0.25$ , which guarantees that $\beta_{b\to a}^{(t)}$ tends smoothly to 1 as $w_{b\rightarrow a}^{\mathrm{BiNI}^{(t - 1)}}\to 0$ and smoothly to 0 as $w_{b\rightarrow a}^{\mathrm{BiNi}(t - 1)}\to 0.5^{-}$ (cf. Fig. 3). We study the impact of the hyperparameters $q$ and $\rho$ in Appendix E.
+
+# 4. Experiments
+
+This Section provides the experimental evaluation of our method, describing our experimental setup (Sec. 4.1), comparing the accuracy of its formulation to that of existing ones (Sec. 4.2), evaluating its normal integration accuracy on a standard benchmark (Sec. 4.3), and demonstrating its applicability to generic central cameras (Sec. 4.4) and real-world input normals (Sec. 4.5). Readers can find ablations, additional experimental results, and a discussion of the limitations of our method in the Supplementary Material.
+
+# 4.1. Experimental settings
+
+Baselines. We compare our method to the state-of-the-art BiNI [7] and Kim et al. [24] on the DiLiGenT benchmark [31]. As no source code is publicly available for [24], in the remaining evaluations we only compare our method to BiNI, setting its hyperparameter to its default value.
+
+Hardware and timing. We run all our evaluations on a standard CPU-only machine, on which our unoptimized implementation takes between 50 and 120 seconds for 1200 iterations with an input normal map of size $512 \times 612$ .
+
+# 4.2. Comparison of formulation accuracy
+
+Before examining the quality of the reconstruction produced by our optimization, we assess how accurately our formulation approximates the ground-truth relation between depth and surface normals compared to existing PDE-derived formulations. To this end, we compute for both our method and BiNI the absolute residual emerging from the respective formulations; as previously noted, this has for both the same functional form $|\gamma_{b\to a}(\tilde{z}_a - \tilde{z}_b) - \mathrm{RHS}|$ , where RHS denotes the right-hand side of (8) for BiNI and of (11) for our method. We evaluate this quantity on the DiLiGenT dataset [31], assuming for fairness unknown discontinuity values, thereby setting the terms $\alpha_{b\rightarrow a}$ in our formulation to 0. As shown in Tab. 1, our method achieves mean error lower by one or two orders of magnitude on all but one object. We provide additional comparisons using relative residuals in Appendix G, where we find similar results.
+
+# 4.3. Benchmark experiments
+
+We evaluate the reconstruction accuracy of our normal integration method compared to the state-of-the-art approaches [7] and [24] on the standard DiLiGenT benchmark [31], which provides ground-truth normal maps produced by an ideal pinhole camera. As shown by Fig. 5 and Tab. 2, our method without discontinuity computation (i.e., setting $\alpha_{b\rightarrow a} = 0$ ) achieves accuracy that is state-of-the-art for 7 out of 9 objects, comparable for 1 object, and worse for a single object. This result shows that the higher accuracy of our formulation can effectively translate into better reconstruction quality through the optimization process. This is further confirmed by verifying that using coefficients based on discontinuity values $\alpha_{b\rightarrow a}$ from the ground-truth surface, the optimization results in an extremely low error for virtually all the objects. We note that our method converges more slowly than BiNI, and we therefore run it for a larger number of iterations (1200); however, after the same number of iterations necessary for BiNI to achieve convergence (150) our method already achieves better results than the other approaches on most objects. Iterative computation of the terms $\alpha_{b\rightarrow a}$ allows more accurately capturing discontinuities (Fig. 6) and further reduces the reconstruc
+
+
+Figure 4. Reconstructions of our method from real-world data. From the left, the third and fourth column show our reconstruction based on normals respectively from photometric stereo [22] (first column) and from DSINE [4] (second column).
+
+tion error, resulting in state of the art on virtually all objects. Further, object-specific improvements can be obtained by tuning the hyperparameters of our discontinuity activation term (cf. Appendix E).
+
+# 4.4. Experiments with non-ideal pinhole cameras
+
+To verify the applicability of our method to generic central camera models, we synthetically render normal maps (and depth for evaluation) observed by a pinhole camera with Brown-Conrady lens distortion [5], using BlenderProc [10]. Since to our knowledge no other methods are available that can directly handle normals from non-ideal pinhole cameras, we show, for illustration purposes only, the output of BiNI for such distorted maps; we remark that a quantitative evaluation is unfair, since BiNI assumes normals from an ideal pinhole camera. We additionally render the normal and depth maps observed by an ideal pinhole camera with intrinsics resulting from undistortion and resolution matching the original one. As shown in Fig. 7, our method effectively handles the case with lens distortion both for scene-level maps of medium complexity and for object-level ones, while the reconstruction from BiNI suffers from noticeable distortion, as expected. The undistorted reconstructions show comparable results between the two methods, with slightly better accuracy for ours, but at the cost of a reduced field of view, due to barrel distortion.
+
+# 4.5. Experiments with real-world data
+
+Figure 4 shows qualitative examples of the reconstructions produced by our method using normals obtained from real-world images [22], both through a recent photometric stereo approach [22] and through prediction by a state-of-the-art learning-based normal estimation method [4]. The results indicate that our method can be applied effectively to real-world normal maps, producing reasonably accurate reconstructions also for the overly smooth normals of [4].
+
+| Method | bear | buddha | cat | cow | harvest | pot1 | pot2 | reading | goblet |
| BiNI [7] | (3.72 ± 2.71) × 10-1 | (4.57 ± 9.21) × 10-1 | (0.54 ± 1.09) × 100 | (4.46 ± 3.58) × 10-1 | (0.52 ± 2.71) × 100 | (4.18 ± 5.63) × 10-1 | (3.96 ± 4.26) × 10-1 | (0.50 ± 1.24) × 100 | (0.43 ± 1.33) × 100 |
| Ours | (0.82 ± 7.39) × 10-2 | (0.90 ± 9.12) × 10-1 | (0.03 ± 1.27) × 100 | (0.19 ± 1.61) × 10-1 | (0.22 ± 2.80) × 100 | (0.09 ± 2.72) × 100 | (0.39 ± 3.11) × 10-1 | (0.08 ± 1.21) × 100 | (0.06 ± 1.20) × 100 |
+
+Table 1. Absolute formulation accuracy on the ground-truth log-depth map, DiLiGenT dataset [31]. For both methods, we report mean and standard deviation across the pixels of the absolute residual $|\gamma_{b\rightarrow a}(\tilde{z}_a - \tilde{z}_b) - \mathrm{RHS}|$ computed on the ground-truth log-depth map, where RHS denotes the right-hand side of (8) for BiNI and (11) for Ours. We use $\tau_{m} = (\tau_{a} + \tau_{b}) / 2$ and $\alpha_{b\rightarrow a} = 0$ for Ours.
+
+| Method | bear | buddha | cat | cow | harvest | pot1 | pot2 | reading | goblet* |
| BiNI [7] – From paper | 0.49 | 0.86 | 0.11 | 0.07 | 2.73 | 0.62 | 0.22 | 0.34 | 8.53 |
| BiNI [7] – From code [8], 1200 iterations† | 0.33 | 1.06 | 0.07 | 0.06 | 1.84 | 0.64 | 0.22 | 0.26 | 9.00 |
| Kim et al. [24] | 0.45 | 0.67 | 0.24 | 0.06 | 2.44 | 0.57 | 0.19 | 0.15 | 9.02 |
| Ours w/o αb→a computation, 150 iterations | 0.08 | 0.30 | 0.06 | 0.09 | 4.98 | 0.52 | 0.13 | 0.21 | 6.46 |
| Ours w/o αb→a computation, 1200 iterations | 0.07 | 0.26 | 0.06 | 0.08 | 4.83 | 0.50 | 0.13 | 0.12 | 6.56 |
| Ours, 150 iterations | 0.03 | 0.37 | 0.06 | 0.08 | 1.35 | 0.50 | 0.14 | 0.15 | 5.98 |
| Ours, 1200 iterations | 0.03 | 0.24 | 0.06 | 0.08 | 0.73 | 0.49 | 0.13 | 0.17 | 4.72 |
| Ours with known discontinuity values | 0.01 | 0.10 | 0.03 | <10-2 | 0.34 | 0.04 | 0.03 | 0.08 | 0.11 |
+
+Table 2. Mean absolute depth error (MADE) [mm] on the DiLiGenT benchmark [31]. For each object, bold and underlined denote respectively the best and the second-best result across the methods. The results of Kim et al. are taken from [24]. *This object contains a full depth discontinuity. † BiNI achieves full convergence already after 150 iterations.
+
+
+Figure 5. Comparison on the DiLiGenT benchmark [31]. First row: Ground-truth surfaces. Second and third row: Surface reconstructed by BiNI [7]; absolute depth errors maps (in mm). Fourth and fifth row: Surface reconstructed by our method with explicit discontinuity computation; absolute depth error maps. The color map is the same for the first eight columns. Below each absolute depth error map is the corresponding mean value (MADE) in mm. The absolute depth error maps are displayed from the viewpoint of the input normal map.
+
+# 5. Conclusions
+
+We presented a novel formulation for normal integration based on a local planarity assumption modeled through ray directions and explicit discontinuity terms. Compared to existing methods, our approach more accurately approximates the relation between depth and surface normals and
+
+achieves state-of-the-art results on the standard benchmark for normal integration. Furthermore, thanks to its formulation based on ray directions, our method allows for the first time handling normals from generic central cameras.
+
+Acknowledgements. The authors thank Lionel Ott and Yu-jie Wei for their feedback on the manuscript draft and the anonymous reviewers for their constructive comments.
+
+
+Ground truth
+
+
+BiNI [7]
+
+
+Ours
+
+
+Figure 6. Detail of the reconstructed surfaces. Our formulation allows capturing discontinuities with higher accuracy than the previous method of BiNI [7]. Top and bottom rows show respectively objects harvest and pot1 from the DiLiGenT benchmark [31].
+
+
+
+
+
+
+Figure 7. Reconstructions for non-ideal pinhole normal maps. From the left, first three columns: input normal map with Brown-Conrady distortion, reconstruction of our method, and reconstruction of BiNI; last three columns: undistorted input normal map, reconstruction of our method, reconstruction of BiNI. Below each reconstruction are the corresponding mean relative depth error (RE) and mean depth error relative to the average depth of the scene (ERA), both expressed as percentages. Note that undistortion causes part of the scene to be cropped. Source of the mesh models from the top to the bottom row: [12], [19], [14] [32].
+
+
+RE: 2.08, ERA: 1.99
+
+
+RE: 2.94, ERA: 3.02
+
+
+RE:8.20,ERA:7.04
+
+
+RE: 0.27, ERA: 0.30
+
+
+RE: 8.01, ERA: 6.47
+
+
+RE: 4.44, ERA: 4.29
+
+
+RE: 13.32, ERA: 10.09
+
+
+RE: 1.16, ERA: 1.29
+
+
+
+
+
+
+
+
+
+
+
+
+RE: 2.26, ERA: 2.07
+RE: 2.49, ERA: 2.48
+
+
+RE: 8.35, ERA: 6.85
+
+
+RE: 0.16, ERA: 0.19
+
+
+
+
+RE: 2.30, ERA: 2.09
+RE: 2.63, ERA: 2.61
+
+
+RE: 8.69, ERA: 6.73
+
+
+RE: 0.17, ERA: 0.21
+
+# References
+
+[1] Amit Agrawal, Rama Chellappa, and Ramesh Raskar. An Algebraic Approach to Surface Reconstruction from Gradient Fields. In ICCV, 2005. 1, 2
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+
+Is the Range of Surface Reconstructions from a Gradient Field? In ECCV, 2006. 2
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+Biases for Surface Normal Estimation. In CVPR, 2024. 3, 6
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+[18] Magnus R. Hestenes and Eduard Stiefel. Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(6):409-436, 1952. 4
+[19] Vladyslav Holhanov. Mesh “Office”. https://sketchfab.com/3d-models/office-28fd69ff714343f2bd278a2572774323, 2021. CC BY 4.0.8
+[20] Berthold K.P Horn. Obtaining Shape from Shading Information. The Psychology of Computer Vision, pages 115-155, 1975. 1
+
+[21] Berthold K.P Horn and Michael J Brooks. The Variational Approach to Shape from Shading. Computer Vision, Graphics, and Image Processing, 33(2):174-208, 1986. 1, 2
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\ No newline at end of file
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+# Discovering Divergent Representations between Text-to-Image Models
+
+Lisa Dunlap $^{1*}$ Joseph E. Gonzalez $^{1}$ Trevor Darrell $^{1}$ Fabian Caba Heilbron $^{2}$
+Josef Sivic $^{2,3}$ Bryan Russell $^{2}$ $^{1}$ University of California, Berkeley $^{2}$ Adobe Research $^{3}$ CIIRC CTU
+
+
+Figure 1. Discovering divergent representations with CompCon. Left: CompCon takes as input a pair of text-to-image models and outputs a diverging prompt description to produce a diverging visual attribute appearing in one model but not the other. Right: We show the discovered diverging visual attribute 'flames' appearing in PixArt but not SDXL-Lightning over different diverging prompts.
+
+Output: divergent representation
+
+Diverging visual attribute: "Flames"
+
+Diverging prompt description:
+prompts with representations of strong emotions such as rage, grief, and resilience.
+
+# PixArt
+
+Digital art of an enraged opera singer
+
+
+
+A poem narrating the tempest within an artist's heart.
+
+
+
+Oil painting of the fervor of a evolutionary speech.
+
+
+
+An abstract representation of existential dread
+
+
+
+A fierce display of a protector's unwavering courage.
+
+
+
+# SDXL-Lightning
+
+
+
+
+
+
+
+
+
+
+
+# Abstract
+
+In this paper, we investigate when and how visual representations learned by two different generative models diverge from each other. Specifically, given two text-to-image models, our goal is to discover visual attributes that appear in images generated by one model but not the other, along with the types of prompts that trigger these attribute differences. For example, 'flames' might appear in one model's outputs when given prompts expressing strong emotions, while the other model does not produce this attribute given the same prompts. We introduce CompCon (Comparing Concepts), an evolutionary search algorithm that discovers visual attributes more prevalent in one model's output than the other, and uncovers the prompt concepts linked to these visual differences. To evaluate CompCon's ability to find diverging representations, we create an automated data generation pipeline to produce $ID^2$ , a dataset of 60 input-dependent differences, and compare our approach to several LLM- and VLM-powered baselines. Finally, we use CompCon to compare popular text-to-image models, finding divergent representations such as how PixArt depicts prompts mentioning loneliness with wet streets and Stable Diffusion 3.5 depicts African American people in media professions.
+
+# 1. Introduction
+
+Generative models develop unique representations of semantic concepts – for instance, happy scenes contain warm colors, or dogs are found outside. While many of these representations are shared across models, understanding when representations diverge can reveal stylistic differences between models. In this work, we explore how to uncover such divergent representations by identifying input-dependent differences between two text-to-image models. Specifically, we aim to discover pairs of semantic concepts and visual attributes where prompts containing a semantic concept cause one model to generate images displaying the corresponding visual attribute, while the other does not. For example, prompts that mention strong emotions result in images with flames in one model but not the other (Fig. 1).
+
+Discovering divergent representations is beneficial for both model developers and users. For developers, it can help decide which model to deploy to production based on any problematic discovered divergent representations, and for evaluating against competitor models. For users, it can help in selecting the model that best aligns with their own interpretations and needs. Manually performing this task is labor-intensive, as it requires sifting through hundreds or thousands of images to find visual attribute differences; once identified, additional effort is needed to determine the types of input prompts that trigger these differences.
+
+When comparing text-to-image models, the evaluation typically focuses on metrics such as image quality and prompt adherence [22, 24-26, 30, 37, 40]. While these metrics indicate how well models perform, they often overlook what the models actually learn. For example, what defines 'cute' versus 'ugly'? What characteristics make something appear 'futuristic'? What does 'emotion' look like? As we will show, models trained on different data, using different encoders or training procedures, can learn distinct interpretations of the same concept. For instance, one model may associate 'ancient' with the Paleolithic Era while the other associates it with the Roman Empire.
+
+To address the task of discovering divergent representations, we make the following contributions. First, we introduce CompCon (Comparing Concepts), an evolutionary search algorithm designed to uncover input-dependent differences in model representations. CompCon first discovers pairwise differences in model outputs, generates a description of the prompts that cause this difference, and iteratively refines this description by analyzing existing prompts and generating new ones likely to highlight these differences. As shown in Figure 1, CompCon can generate prompts that result in model behaviors like putting flames behind opera singers for one model but not the other.
+
+Second, we create $\mathrm{ID}^2$ (Input-Dependent Differences), a dataset of 60 semantic-visual representations to evaluate the efficacy of our method. Using this dataset, we compare CompCon to LLM, TF-IDF, and VisDiff [17] baselines. As our third contribution, we apply CompCon to compare the PixArt and SD-Lightning text-to-image models, finding, for example, that prompts mentioning anger result in depictions of 'flames' in PixArt, prompts mentioning sadness and solitude result in 'wet streets' in PixArt, and abstract prompts with cosmic motifs result in 'mandala circular designs' in SD-Lightning. We also uncover bias, such as PixArt generating older men for prompts mentioning traditional professions. These findings demonstrate how CompCon can systematically reveal subtle differences between generative models, helping developers and users better understand and leverage these models' unique behaviors.
+
+# 2. Related Work
+
+Evaluating Text-to-Image Models. The evaluation of text-to-image models has advanced significantly in recent years. Traditional quality measures such as FID [25], Inception core [40], CLIP score [24], and CLIP-R score [37] have been complemented by newer metrics like TAIM [22] and TIFA [26], which leverage vision-and-language models to assess prompt adherence. Holistic benchmarks such as HEIM and others [10, 30, 39, 47] aggregate multiple axes of evaluation, including quality, prompt adherence, style, and efficiency. While these approaches excel in measuring overall model performance, they focus on objective
+
+qualities and often overlook fine-grained, subjective differences between models. Our work complements these efforts by targeting input-dependent differences, particularly in semantic interpretations and stylistic variations, which are crucial for understanding model-specific behaviors.
+
+Interpreting Diffusion Models. Several works have explored ways of interpreting the internal representations of generative vision-language models. Bau et al. [4], Dravid et al. [15], Gandelsman et al. [19, 20] explore how to describe the function of certain neurons and attention heads in natural language,, and Tong et al. [44] discovers how image and text representations differ in latent space to better understand CLIP failures. We see our work as a data-driven approach to attain similar insights into model behavior.
+
+Discovering Bias in Diffusion Models. Uncovering and mitigating biases in text-to-image models has been well explored, with many works focus on finding and mitigating a predefined set of biases related to gender, race, and geography [5, 11, 18, 21, 23, 45, 46]. Recently, a line of works have emerged that aim to automatically discover biases from the data, rather than using a predefined list. Many of these approaches [13, 14] discover bias by prompting a large language model (LLM) to propose potential biases from image captions, generating prompts that may indicate a bias in models (e.g., "a doctor") and using a VLM to check if this bias exists. Liu et al. [34] builds on this by clustering generated images based on concepts like gender, while Chinchure et al. [8] extends bias discovery to counterfactual examples, eliminating the need for a large caption pool. In contrast, our work focuses on model comparison, rather than single-model auditing, which better reflects many real-world evaluations where success is measured by improvement relative to other models. Additionally, while previous methods [13, 14] identify biases from input captions, CompCon analyzes generated images directly using VLMs. This enables discovery of subtler, more nuanced differences in visual representation, including social biases and stylistic or conceptual divergences between models. Further discussion is in Sections 5.4 and G.1 of the Appendix.
+
+Describing Differences in Image Sets. Several works have aimed to describe differences in sets of images using natural language. For example, VisDiff [17] generates visual attributes distinguishing two sets of images by analyzing captions and refining them using cross-modal embeddings. Similarly, Chiquier et al. [9] train interpretable CLIP classifiers that evolve based on LLM-generated attributes. While these approaches focus on dataset-level differences, they do not address input-dependent variation. We adapt and extend VisDiff's methodology for pairwise comparison, focusing on prompt-specific divergences and refining attribute discovery to capture subtler differences. Additionally, our method introduces a novel iterative search for prompt descriptions that cause these differences.
+
+# 3. Divergent Representation Discovery
+
+Let $P$ be a set of text prompts, and $\mathcal{I}_1^{(P)}$ and $\mathcal{I}_2^{(P)}$ be sets of images generated by two text-to-image models given the input prompts $P$ . We call the natural language descriptions of the prompt set $P$ and any visual differences between the two generated image sets $\mathcal{I}_1^{(P)}$ and $\mathcal{I}_2^{(P)}$ a divergent representation (see Figure 1). These divergent representations take the form of a pair of natural language descriptions $(a, d_{P_a})$ , where $a$ is a description of a visual attribute seen more often in one model than the other (e.g., "flames"), and $d_{P_a}$ is a description of the concepts present in text prompts $P_a$ eliciting this difference (e.g., "strong emotions"). We refer to $a$ as a diverging visual attribute, $d_{P_a}$ as a diverging prompt description, and $P_a$ as diverging prompts.
+
+Given a pair of text-to-image models $\Theta = (\theta_{1},\theta_{2})$ , we aim to discover differences in the images generated by the two models as well as a description of the types of input text prompts that trigger these differences. Let $\mathcal{P}$ be the set of all possible text prompts and $\mathcal{A}$ be the set of all possible diverging visual attributes. Our goal is to find the mapping $\mathcal{F}_{\Theta}$ from text prompts in $\mathcal{P}$ to diverging visual attributes in $\mathcal{A}$ given the model pair $\Theta$ ,
+
+$$
+\mathcal {F} _ {\Theta}: \mathcal {P} \mapsto \mathcal {A}. \tag {1}
+$$
+
+Note that this mapping is not a bijection as multiple text prompts may map to a single diverging visual attribute. Moreover, multiple diverging visual attributes may be depicted for a given set of diverging prompts.
+
+Our approach for computing the mapping $\mathcal{F}_{\Theta}$ comprises two steps, illustrated in Figure 2. First, given the text-to-image model pair $\Theta$ and a large set of initial prompts $\mathcal{P}_0 \subset \mathcal{P}$ , we compute a set of diverging visual attributes $\mathcal{A}_0 \subset \mathcal{A}$ (Section 3.1). Next, for each diverging visual attribute $a \in \mathcal{A}_0$ , we optimize an objective to find the set of diverging prompts $\mathcal{P}_a \subset \mathcal{P}$ resulting in the diverging visual attribute $a$ (Section 3.2). We next describe each of these steps.
+
+# 3.1. Discovering Diverging Visual Attributes
+
+Our goal is, given a text-to-image model pair $\Theta$ and a large set of initial text prompts $\mathcal{P}_0$ , to compute a set of diverging visual attributes $\mathcal{A}_0$ over images generated given the prompts. This task is challenging as a system must identify any consistent visual differences between the two models' generated image sets. These differences are often subtle and difficult to spot over the large generated image collection. We address this challenge by prompting an off-the-shelf vision-language model (VLM) for this task.
+
+For the text-to-image model pair $\Theta$ and a text prompt $p$ , let $\mathcal{G}(\Theta, p) = \left\{\mathcal{I}_1^{(p)}, \mathcal{I}_2^{(p)}\right\}$ denote the two sets of images generated by each model given prompt $p$ . We first sample a batch of prompts $\mathcal{P}_{batch} \subset \mathcal{P}_0$ and, for each prompt $p \in \mathcal{P}_{batch}$ , we construct a two-row image grid by tiling the
+
+images in $\mathcal{I}_1^{(p)}$ on the top row and $\mathcal{I}_2^{(p)}$ on the bottom row. Using this image grid, we instruct a VLM to find diverging visual attributes appearing more in images of $\mathcal{I}_1^{(p)}$ compared to $\mathcal{I}_2^{(p)}$ (see Appendix for our instruction prompt). Our resulting diverging visual attribute list $\mathcal{A}_0$ is the aggregation of discovered attributes across $\mathcal{P}_{batch}$ .
+
+Next, we rank each diverging visual attribute $a \in \mathcal{A}_0$ by assigning a score indicating how well attribute $a$ can distinguish image sets $\mathcal{I}_1^{(\mathcal{P}_0)}$ and $\mathcal{I}_2^{(\mathcal{P}_0)}$ . For each set of images generated by prompt $p \in \mathcal{P}_0$ , we define a divergence score $z(a, \mathcal{I}_1^{(p)}, \mathcal{I}_2^{(p)}) \to \{0, 1\}$ that indicates whether image set $\mathcal{I}_1^{(p)}$ contains attribute $a$ while $\mathcal{I}_2^{(p)}$ does not.
+
+Using cross-modal similarity, here CLIP [38], we compute the cosine similarity $s(\cdot)$ between diverging visual attribute $a$ and each image in sets $\mathcal{I}_1^{(p)}$ and $\mathcal{I}_2^{(p)}$ . Using these similarities, we define the divergence score as the product of two indicated conditions,
+
+$$
+\begin{array}{l} z \left(a, \mathcal {I} _ {1} ^ {(p)}, \mathcal {I} _ {2} ^ {(p)}\right) = \mathbb {1} \left[ s \left(a, \mathcal {I} _ {1} ^ {(p)}\right) > t \right] \times \tag {2} \\ \mathbb {1} \left[ s (a, \mathcal {I} _ {1} ^ {(p)}) - s (a, \mathcal {I} _ {2} ^ {(p)}) > \delta \right] \\ \end{array}
+$$
+
+where $t$ and $\delta$ are hyperparameters that determine if $\mathcal{I}_1^{(p)}$ contains attribute $a$ and $\mathcal{I}_2^{(p)}$ does not contain $a$ .
+
+Using this divergence score, we define the overall score for attribute $a$ as the mean divergence score over prompts in the initial prompt set: $\frac{1}{|\mathcal{P}_0|}\sum_{p\in \mathcal{P}_0}z(a,\mathcal{I}_1^{(p)},\mathcal{I}_2^{(p)})$ . A score of 1 means that all images generated by model $\theta_1$ contain attribute $a$ and none of the images generated by $\theta_2$ contain $a$ . A score of 0 indicates that $a$ never appears more often in images generated by $\theta_1$ . Note that we are not optimizing for scores close to 1, we are simply interested in any attribute $a$ that obtains a score sufficiently above zero. Finally, as many attributes $\mathcal{A}_0$ are semantically equivalent (e.g. "flames" and "fire") we prompt an LLM to remove similar attributes.
+
+# 3.2. Discovering Diverging Prompt Descriptions
+
+After we discover a set of diverging visual attributes $\mathcal{A}_0$ , for each attribute $a \in \mathcal{A}_0$ we aim to find a natural language description $d_{\mathcal{P}_a}$ of the diverging prompts that trigger this attribute. This task is challenging as the search space over all possible text prompts $\mathcal{P}$ is large, and we must not only find a set of prompts but a natural language description that completely covers this set.
+
+Let $\mathcal{L}(d_{\mathcal{P}_a})$ be the diverging prompts generated from description $d_{\mathcal{P}_a}$ . Our objective is to maximize the expected divergence score over the generated prompts:
+
+$$
+\max _ {d \mathcal {P} _ {a}} \mathbb {E} _ {p \sim \mathcal {L} (d \mathcal {P} _ {a})} [ z (a, \mathcal {I} _ {1} ^ {(p)}, \mathcal {I} _ {2} ^ {(p)}) ], \tag {3}
+$$
+
+where $z$ is the divergence score defined in Equation (2). That is, we want to maximize the number of prompts that have been generated by description $d_{\mathcal{P}_a}$ and confirmed to
+
+
+Discovering Divergent Visual Attributes
+
+
+Discovering Divergent Prompt Descriptions
+Figure 2. CompCon overview. We illustrate our approach for discovering diverging visual attributes (top) and diverging prompt descriptions (bottom). Given two text-to-image models and a set of prompts, we use a VLM to identify visual differences. For each diverging attribute, we iteratively refine diverging prompt descriptions by generating candidate prompts $\mathcal{P}_a^{can}$ from the description, classifying them as diverging ( $\mathcal{H}^{div}$ ) or non-diverging ( $\mathcal{H}^{non}$ ). The objective is to maximize the proportion of generated prompts classified as diverging.
+
+Algorithm 1 Discovering diverging prompt descriptions
+Output: Diverging prompt description $d_{\mathcal{P}_a}^\star$
+```txt
+Input: Model pair $\Theta$ , diverging visual attribute $a$ , initial set of prompts $\mathcal{P}_0$ , number of iterations $N$
+```
+
+```txt
+1: Initialize: prompt bank $\mathcal{H} \gets \emptyset$ , scores $\sigma \gets$ emptyArray(N), descriptions $d_{\mathcal{P}_a} \gets$ emptyArray(N)
+```
+
+```txt
+2: $\mathcal{P}_a\gets$ classifyDiverging(Theta,a,P)
+```
+
+```txt
+3: $\mathcal{H}^{div}\gets \mathcal{P}_a$
+```
+
+```txt
+4: $\mathcal{H}_a^{non} \gets \mathcal{P} \setminus \mathcal{P}_a$
+```
+
+```txt
+5: for $i$ in $1,\ldots ,N$ do
+```
+
+```txt
+6: $h_a^{div}, h_a^{non} \gets \text{sample}(\mathcal{H}^{div}, \mathcal{H}^{non})$
+```
+
+```txt
+7: $d_{\mathcal{P}_a}[i]\gets$ describeDiverging $(\mathcal{P}_a^{div},\mathcal{P}_a^{non},\mathcal{H})$
+```
+
+```latex
+8: $\mathcal{P}_a^{can} \gets \text{getNewDiverging}(d_{\mathcal{P}_a}[i], a, \mathcal{H})$
+```
+
+```txt
+9: $\mathcal{P}_a^{div},\mathcal{P}_a^{non}\gets$ classifyDiverging( $\Theta ,a,\mathcal{P}_a^{\text{can}})$
+```
+
+```txt
+10: $\sigma [i]\gets |\mathcal{P}_a^{div}| / |\mathcal{P}_a^{can}|$
+```
+
+```txt
+11: $\mathcal{H}^{non} = \mathcal{H}^{non}\cup \mathcal{P}_a^{non}$
+```
+
+```txt
+12: $\mathcal{H}^{div} = \mathcal{H}^{div}\cup \mathcal{P}_a^{div}$
+```
+
+```txt
+13: end for
+```
+
+```latex
+14: $d_{\mathcal{P}_a}^\star \gets d_{\mathcal{P}_a}[\arg \max (\sigma)]$
+```
+
+```txt
+15: return $d_{\mathcal{P}_a}^*$
+```
+
+be diverging. We explore two options for our prompt generator $\mathcal{L}$ . The first is to use an LLM to generate new prompts given $d_{\mathcal{P}_a}$ , and the second is to retrieve prompts from a large prompt bank using $d_{\mathcal{P}_a}$ .
+
+As the desired diverging prompt description $d_{\mathcal{P}_a}$ is discrete (natural language) and Objective (3) is not differen
+
+tiable, we optimize the objective via evolutionary search. To achieve this goal, for $N$ evolutionary search iterations, we use an LLM to generate description $d_{\mathcal{P}_a}$ given a bank of diverging and non-diverging prompts $\mathcal{H}^{div}$ and $\mathcal{H}^{non}$ , generate new prompts and images from $d_{\mathcal{P}_a}$ , add these new prompts to $\mathcal{H}^{div}$ and $\mathcal{H}^{non}$ , and evolve our description using these updated sets.
+
+We maintain a bank $\mathcal{H} = (\mathcal{H}^{div},\mathcal{H}^{non})$ of diverging and non-diverging text prompts, where diverging prompts are given by $\mathcal{H}^{div} = \{p\mid z(a,\mathcal{I}_1^{(p)},\mathcal{I}_2^{(p)}) = 1\}$ and non-diverging prompts are given by $\mathcal{H}^{non} = \{p\mid z(a,\mathcal{I}_1^{(p)},\mathcal{I}_2^{(p)}) = 0\}$ . We mutate the current description $d_{\mathcal{P}_a}$ by prompting an LLM (GPT-4o) to provide a description of what concepts are shared in $\mathcal{H}^{div}$ but not in $\mathcal{H}^{non}$ and score the mutation using Objective (3). The mutation prompt is provided in the Appendix.
+
+Algorithm 1 provides pseudocode for our evolutionary search algorithm, with its key functions described below.
+
+Mutation function describeDiverging. Given the bank of diverging and non-diverging text prompts $\mathcal{H}$ , we sample $B$ prompts from $\mathcal{H}^{div}$ and $\mathcal{H}^{non}$ and instruct an LLM to output a description $d_{\mathcal{P}_a}$ (the diverging prompt description) of what concepts are shared across diverging prompts which are not seen in non-diverging prompts. After the first iteration, prompts in $\mathcal{H}$ which were generated in the previous iteration are up-weighted when sampling.
+
+Mutation scoring. To score the current mutation, we first define a function getNewDiverging that, given the di
+
+verging prompt description $d_{\mathcal{P}_a}$ , diverging visual attribute $a$ , and prompt bank $\mathcal{H}$ , provides candidate prompts $\mathcal{P}_a^{can}$ that are likely to be diverging and do not directly relate to attribute $a$ . We explore two ways of obtaining $\mathcal{P}_a^{can}$ : generation and retrieval. In the generation setting, we prompt an LLM (GPT-4o) to generate a diverse set of $k$ new prompts that align with the description $d_{\mathcal{P}_a}$ , given random samples of prompts from $\mathcal{H}$ as a point of reference. The instruction prompt can be found in the Appendix. In the retrieval setting we use description $d_{P_a}$ to retrieve the top $k$ prompts from the prompt bank $\mathcal{H}$ excluding the $B$ sampled prompts used to generate the prompt description, having the highest text embedding similarity to $d_{P_a}$ . We show results of both of these approaches in Section 5 and provide further implementation details in 5.1.
+
+Next, we define a function classifyDiverging that, given the model pair $\Theta$ , visual attribute $a$ , and candidate prompts $\mathcal{P}_a^{can}$ , finds the diverging prompts $\mathcal{P}_a^{div} = \{p \in \mathcal{P}_a^{can} \mid z(a, \mathcal{I}_1^{(p)}, \mathcal{I}_2^{(p)}) = 1\}$ . If more than one image is generated per prompt, we define a prompt as diverging if the majority of the generated images result in a diverging score $z(a, i_1^{(p)}, i_2^{(p)}) = 1$ for $i_1^{(p)} \in \mathcal{I}_1^{(p)}$ and $i_2^{(p)} \in \mathcal{I}_2^{(p)}$ .
+
+Finally, we approximate the expectation in Objective (3) by the ratio of diverging to candidate prompts set sizes,
+
+$$
+\mathbb {E} _ {p \sim \mathcal {L} \left(d _ {\mathcal {P} _ {a}}\right)} [ z (a, \mathcal {I} _ {1} ^ {(p)}, \mathcal {I} _ {2} ^ {(p)}) ] = \frac {| \mathcal {P} _ {a} ^ {d i v} |}{| \mathcal {P} _ {a} ^ {c a n} |} \tag {4}
+$$
+
+where $|\cdot|$ denotes the size of the set. We return the diverging prompt description $d_{\mathcal{P}_a}$ with the highest ratio.
+
+# 4. $\mathbf{ID}^2$ Dataset and LLM Evaluation
+
+To systematically evaluate methods for discovering divergent representations, we created $\mathrm{ID}^2$ (Input-Dependent Differences), a benchmark dataset containing 60 divergent representations between text-to-image models. Each representation consists of a diverging visual attribute and its corresponding diverging prompt description. Moreover, we include for each diverging representation a set of prompts that align with the diverging prompt description and, for each prompt, pairs of generated images where the diverging visual attribute is depicted in one image but not the other.
+
+Creating such a benchmark is challenging because divergent representations between models are not known a priori, and manual annotation across the vast prompt space is impractical. To address this, we use a simulation approach: rather than comparing two distinct models, we use a single model (SD-3.5-Turbo [1]) and simulate differences by modifying input prompts to include specific visual attributes.
+
+For each divergent representation in $\mathrm{ID}^2$ , we generate paired prompts where one explicitly mentions the visual attribute while the other does not. Both prompts are processed by the same text-to-image model, creating image pairs that
+
+
+Figure 3. $\mathbf{ID}^2$ creation. Given a diverging prompt description $d_{p_a}$ and diverging visual attribute $a$ , we use an LLM to generate prompt pairs where one of the prompts mentions the diverging visual attribute. Both prompts are then passed to the same text-to-image model to generate image pairs with the visual difference $a$ .
+
+exhibit controlled, systematic differences. This simulation approach allows us to create ground truth data with known divergent representations against which we can evaluate discovery methods. To assess the quality of discovered representations, we developed an LLM-based evaluation framework that measures both attribute similarity and description accuracy compared to ground truth. This framework provides objective metrics to compare different approaches for identifying divergent representations between text-to-image models. We describe the dataset creation and evaluation process below and in Figure 3.
+
+$\mathbf{ID}^2$ Dataset Creation. Each divergent representation $(a, d_{P_a})$ in $\mathbf{ID}^2$ comprises a ground truth diverging visual attribute $a$ and ground truth diverging prompt description $d_{P_a}$ . We generate the diverging representations using either GPT-4o, Claude 3.5 Sonnet [3], or manually. Each diverging visual attribute $a$ is a short phrase, and diverging prompt description $d_{P_a}$ is a list of semantic concepts that a prompt should include. These representations cover diverse categories, such as related concepts ('red roses', ['love', 'romance}], abstract representations ('geometric shapes', ['efficiency', 'productive}], and bias ('overweight person', ['lazy', 'unmotivated']) The full list of diverging representations are located in the Appendix.
+
+Given a diverging representation $(a, d_{P_a})$ , we generate a corresponding set of prompts and generated images $\{(p, \mathcal{I}_1^{(p)}, \mathcal{I}_2^{(p)})\}$ such that each prompt $p$ aligns with diverging prompt description $d_{P_a}$ and the accompanying pair of generated images $\mathcal{I}_1^{(p)}$ and $\mathcal{I}_2^{(p)}$ has diverging visual at
+
+We illustrate the process for creating this set in Figure 3. First, we use GPT-4o to generate a prompt $p$ that aligns with diverging prompt description $d_{P_a}$ along with an altered prompt $p^{\mathrm{alt}}$ that contains attribute $a$ . Both prompts are then given to a diffusion model $\theta$ (SD-3.5-Turbo) to generate images such that $\mathcal{I}_1^{(p)} = \theta(p)$ and $\mathcal{I}_2^{(p)} = \theta(p^{\mathrm{alt}})$ . The authors manually inspect these generations to ensure the prompts align with the diverging prompt description $d_{P_a}$ , and that diverging visual attribute $a$ is seen in the majority of images corresponding to $\mathcal{I}_1^{(p)}$ but not $\mathcal{I}_2^{(p)}$ . We further validate these sets with human studies described later in the section.
+
+For each of the 60 diverging representations, we generate 3 image pairs per prompt across 50 prompts, resulting in two sets of 150 images. Finally, for each representation, we also include a set of distractors - image pairs from 200 randomly generated prompts where $\mathcal{I}_1^{(p)}$ and $\mathcal{I}_2^{(p)}$ are generated with the same prompt $p$ over different random seeds, resulting in image pairs with no discernible difference in visual attributes. The purpose of these distractors is to assess the methods' ability to generate descriptions and attributes in the presence of noise (no diverging visual attribute present). LLM Evaluation. When given ground truth representations $(a,d_{P_a})$ and predicted representations $(a',d_{P_a}')$ , we use an LLM-as-a-judge (GPT-4o) to compute an attribute score and a description score, which respectively measure the similarity of the predicted visual attribute and prompt description to the ground truth. The prompt given to the judge can be found in the Appendix.
+
+These scores range from 0 to 1, where 1 indicates perfect agreement, 0.5 indicates partial agreement, and 0 indicates no agreement. Partial agreement means that the predicted attribute or description is related to the ground truth. For example, the ground truth visual attribute is 'flames' and the predicted attribute is 'a red color palette' would be deemed a partial alignment. To maintain a fair evaluation with other baselines, we prompt our mutation LLM to structure descriptions $d_{P_a}$ as a short list of semantic concepts.
+
+Human Validation of $\mathbf{ID}^2$ and LLM Evaluation. We conducted a two-stage validation study with 4 PhD students, each annotating 10 randomly sampled sets from $\mathbf{ID}^2$ (2 annotations per set). Participants identified concepts appearing more frequently in one set versus another and concepts shared across prompts. They then assessed whether our ground truth diverging attribute and diverging prompt description aligned with their descriptions and with the images/prompts. Nearly all participants agreed with the ground truth: participants validated that all 40 visual attributes appeared in generated image pairs, and 36/40 provided free-form attributes that matched the ground truth (match validated by the participants). Similarly, for prompt descriptions, 39/40 validated the ground truth, and 34/40 provided free-form attributes that matched the ground truth.
+
+To validate our LLM scoring system, three participants scored 25 predictions using the same rubric given to the LLM judge. The weighted Cohen's kappa [12] between humans and the LLM was 0.635, comparable to inter-human agreement (0.667), confirming that LLM-as-a-judge scores align closely with human evaluation.
+
+# 5. Experiments
+
+We measure CompCon's ability to discover diverging visual attributes and diverging prompt descriptions in comparison to baselines on the $\mathrm{ID}^2$ (Section 5.3) and apply CompCon to compare two popular open source models, PixArt [6] and SD-Lighting [32] to find diverging representations and uncover age and gender bias (Section 5.4)
+
+# 5.1. Experimental Details
+
+For our experiments, we set the size of $\mathcal{P}_{\text {batch }}$ to be 50, $t = 0$ , and $\delta = 0.05$ for our diverging visual attribute discovery phase. In our diverging prompt description phase, we sample 25 prompts from $\mathcal{H}^{\text {div }}$ and $\mathcal{H}^{\text {non }}$ and generate $k = 25$ new prompts per iteration. For all experiments, each model generates 3 images per prompt across different seeds. We set $t = 0.2$ and $\delta = 0.05$ for our benchmark comparison. For the model comparison in Section 5.4, we manually inspect prompts labeled as diverging to set thresholds $t$ and $\delta$ . Hyperparameters for each discovered diverging representation, as well as all LLM and VLM prompts used for the method and baselines can be found in the Appendix.
+
+We use GPT-4o [36] as the LLM for CompCon's diverging visual attribute discovery and diverging prompt description discovery phases, as well as for the LLM-Only baseline described below. We use CLIP ViT-bigG-14 [7, 28, 38] trained on Laion2b [41] to classify diverging prompts and attributes and the instructor-xl [43] text embedding model for prompt retrieval. Our dataset generation and experiments were performed on two 80GB NVIDIA A100 GPUs.
+
+# 5.2. Baselines
+
+We compare CompCon to several baselines on the $\mathrm{ID}^2$ , including an end-to-end approach and approaches for the individual diverging visual attribute and diverging prompt description discovery phases.
+
+LLM-only (end-to-end). We select 50 random prompts $P_{\text{sample}}$ from each dataset $\mathcal{D}_a$ , caption the corresponding generated images and prompt an LLM (GPT-4o) to find any diverging representations.
+
+TF-IDF (diverging visual attribute discovery). We caption the generated images $\mathcal{I}_1^{(\mathcal{P}_{sample})}$ and $\mathcal{I}_2^{(\mathcal{P}_{sample})}$ . We then combine all captions produced for $\mathcal{I}_1^{(\mathcal{P}_{sample})}$ and $\mathcal{I}_2^{(\mathcal{P}_{sample})}$ into two separate documents and compute TF-IDF [42], taking the top-5 1-3 word phrases that appear more often in captions of $\mathcal{I}_1^{(\mathcal{P}_{sample})}$ than $\mathcal{I}_2^{(\mathcal{P}_{sample})}$ .
+
+VisDiff (diverging visual attribute discovery). We apply the VisDiff algorithm [17] for finding differences in image sets $\mathcal{I}_1^{(\mathcal{P}_{sample})}$ and $\mathcal{I}_2^{(\mathcal{P}_{sample})}$ .
+
+TF-IDF (prompt description discovery). Given a diverging visual attribute $a$ , we run classifyDiverging on $\mathcal{D}_a$ to obtain the diverging and non-diverging prompts and run TF-IDF to find which phrases appear more often in the diverging prompts compared to the non-diverging prompts. We report results using this method on the diverging visual attribute's discovered by CompCon.
+
+We use Llava 1.5-7b [33] for image captioning used in the VisDiff and TF-IDF baselines.
+
+# 5.3. Benchmark Results
+
+| Metric | Method | Top 1 | Top 5 |
| Attribute Score | CompCon | 0.60 | 0.68 |
| VisDiff | 0.47 | 0.62 |
| TF-IDF | 0.23 | 0.37 |
| LLM-only | 0.08 | 0.24 |
| Description Score | CompCon [5-iter] | 0.64 | 0.78 |
| CompCon [1-iter] | 0.59 | 0.72 |
| TF-IDF | 0.40 | 0.57 |
| LLM-only | 0.03 | 0.28 |
+
+Table 1. Visual attribute and prompt description scores on $\mathbf{{ID}}^{2}$ . Our approach outperforms all baselines on both diverging visual attribute and diverging prompt description discovery.
+
+We report diverging visual attribute and diverging prompt description discovery results in Table 1. CompCon obtains higher attribute and description scores than the baselines. An example output, along with their strengths and weaknesses, are shown in Figure 4. We find that:
+
+1. The LLM-only baseline performs poorly compared to the other methods, often outputting diverging representations that are completely unrelated to the ground truth. This result is due to the complexity of the task: the LLM must (1) find differences between each pair of captions, (2) uncover which differences are seen most often, and (3) summarize the prompts that have this difference in the captions.
+2. When discovering diverging visual attributes, VisDiff and TF-IDF often fail at identifying more fine-grained differences. This finding is likely due to the reliance on captions lacking fine-grained detail, especially when comparing images depicting similar contexts.
+3. While additional iterations offer modest gains in performance when generating diverging prompt descriptions, we see in Figure 4 that iterations are beneficial when the ground truth description is more fine-grained. This iterative refinement enables the model to evolve from describing general representations to fine-grained qualities.
+
+
+A cozy nook for intimate dinner gatherings
+Diverging Visual Attribute
+Ground Truth: 'venetian blinds'
+LLM-Only: 'onlookers'
+TF-IDF: 'natural light'
+VisDiff: 'wooden floor'
+CompCon: 'striped window blin
+Figure 4. $\mathbf{ID}^2$ example. Top: We show dataset prompts and corresponding generated images, where the second image row depicts the diverging visual attribute. Bottom: We show the ground truth diverging visual attribute and diverging prompt description, along with outputs from our approach and the baselines. Notice that our method produces outputs that better align with the ground truth.
+
+
+A compact arena furnished for casual family meals
+Diverging Prompt Description
+Ground Truth: 'small dining room', 'small living room'
+LLM-Only: 'Crowd', 'spectators', 'audience'
+TF-IDF: 'space', 'corner', 'compact'
+CompCon[1]: 'Indoor settings', 'Spatial organization', 'Design elements'
+CompCon[5]: 'Cozy environments', 'Multifunctional spaces', 'Compact Comfort'
+
+Attribute
+
+
+A snug corner for reading and relaxation
+
+
+A charming spot for private cocktails and conversations
+Description
+
+Additional experiments on the effects of iterations, the choice of LLM and VLM, and sensitivity analysis of the effects of LLM and VLM errors are in Section B.
+
+# 5.4. Qualitative Results
+
+Using CompCon we find divergent representations in several popular diffusion models: PixArt Alpha [6], SDXL-Lightning [32], Stable Diffusion 3.5 Large [1], and Playground 2.5 [31]. As listed in Section 3, we use an LLM to generate diverging prompts from the prompt description generated at each iteration. A subset of these generated diverging prompts are shown below. Additional prompts, experiments on other prompt sets and models, and a comparison to a single-model method are in the Appendix (A, G.1).
+
+Results on templated prompts. We run CompCon with an initial prompt bank covering different art styles, subjects, and descriptors and visualize results in Figure 5. CompCon discovers both diverging representations like negative emotions and empty urban environments produce "wet streets" in PixArt. Looking at the "flames" example in Figure 1, we also see diversity in the presentation of attributes, with flames taking the form of a burning podium to a fiery background to a large red cloud. Lastly, we see scenarios of poor prompt adherence in the "decay" divergence representation, where SD-Lightning does not produce visual elements that indicate rundown and abandoned places while PixArt associates abandonment with decay. Our findings demonstrate that CompCon can effectively uncover both concrete and abstract divergent representations in text-to-image models,
+
+
+Diverging Visual Attribute: Wet Streets
+The concepts indicative of diverging prompts are characterized by a consistent representation of bleakness, desolation, and an underlying tone of negative emotion such as sadness, anger, or emptiness in an urban environment.
+Figure 5. CompCon results comparing PixArt and SD-Lightning. PixArt associates negative emotions and desolation in urban environments with 'wet streets,' while SD-Lightning struggles to depict run-down or dilapidated scenes, where PixArt instead conveys 'decay.'
+
+
+A spotless, modern kitchen set up in the middle of an otherwise gutted and abandoned apartment.
+
+
+A lavish banquet set up on a long table in an otherwise empty and dilapidated mansion hall.
+
+
+A meticulously restored vintage car parked in front of a row of dilapidated, boarded-up homes.
+
+
+A bright, blooming flower garden surrounding a rundown, abandoned gas station.
+
+
+A diverging prompt is characterized by the stark contrast of elements associated with opulence, care, or newness placed within or against settings that are visibly deserted, neglected, or starkly barren.
+
+
+Diverging Visual Attribute: decay
+
+
+
+
+
+
+Figure 6. Finding bias. CompCon discovers racial bias in Stable Diffusion 3.5 images for prompts related to media professions.
+
+providing interpretable insights into their behavior. The template used to create the prompt bank, additional qualitative examples, and analysis on the effects of iterations are included in the Appendix. Additionally, the Appendix includes results of running CompCon on a dataset of prompts generated by LLMs, creating a fully automated pipeline.
+
+Detecting bias. We show that CompCon can be used for the crucial task of bias detection. As an initial prompt set, we take existing prompts from Luccioni et al. [35], which probe a model's gender bias when it comes to professions. This dataset contains 252 template prompts that uses a list of professions and interchanges "man", "woman", and "person" (e.g., "A man/woman/person who works as a baker"). In Figure 6, CompCon highlights differences in how professions are visually represented, with Stable Diffusion 3.5 generating significantly more African American people in media and communication-focused roles. More examples of CompCon detecting other biases in the Appendix (A.2).
+
+# 5.5. Limitations and Cost
+
+As CompCon relies on off-the-shelf LLMs and VLMs, it inherits their biases. While such biases can cause false negatives when discovering diverging representations, the descriptions found still align with human discovery. We validate this through user studies showing that our benchmark evaluation matches human annotation. Additionally, Section B shows that CompCon detects gender and age biases between diffusion models, and CompCon can find correct diverging representations even when the VLM or LLM fails part of the time.
+
+Cost. Using GPT-4o as the VLM and LLM costs $\sim$ 0.50 for attribute discovery plus $\sim$ 0.02 per attribute iteration. This can be cost-effective for comparing one model to $N$ others $(\mathcal{O}(N))$ . Running smaller open-source models like IDEFICS llama3-8b [29] cuts costs while maintaining competitive performance, still outperforming baselines. Additional open-model results are in the Appendix (Sec B).
+
+# 6. Conclusion
+
+We present CompCon, a method for systematically discovering divergent representations between text-to-image models. By identifying input-dependent differences in model outputs and uncovering the prompt concepts linked to these differences, CompCon provides a framework to understand how models interpret semantic concepts differently. Our results on our $\mathrm{ID}^2$ benchmark and in the comparison of PixArt and SD-Lighting, demonstrate CompCon effectiveness in revealing subtle model-specific behaviors. This opens the possibility of identifying and mitigating unwanted behavior-generated images and videos. Moreover, our approach can serve as a tool for probing the hypothesis that different models converge to the same representation [27].
+
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+# Discretized Gaussian Representation for Tomographic Reconstruction
+
+Shaokai Wu $^{1}$ , Yuxiang Lu $^{1}$ , Yapan Guo $^{4}$ , Wei Ji $^{2}$ , Suizhi Huang $^{1}$ , Fengyu Yang $^{3}$ , Shalayiding Sirejiding $^{1}$ , Qichen He $^{1}$ , Jing Tong $^{1}$ , Yanbiao Ji $^{1}$ , Yue Ding $^{1}$ , Hongtao Lu $^{1*}$ $^{1}$ Shanghai Jiao Tong University, $^{2}$ National University of Singapore, $^{3}$ Yale University, $^{4}$ Suzhou Xiangcheng People's Hospital
+
+{shaokai.wu, luyuxiang_2018, huangsuizhi, salaydin}@sjtu.edu.cn {ayombeach, tj19.hf, jiyanbiao, dingyue, htlu}@sjtu.edu.cn guo_yapan@outlook.com, jiwei@nus.edu.sg, fengyu.yang@yale.edu
+
+# Abstract
+
+Computed Tomography (CT) enables detailed cross-sectional imaging but continues to face challenges in balancing reconstruction quality and computational efficiency. While deep learning-based methods have significantly improved image quality and noise reduction, they typically require large-scale training data and intensive computation. Recent advances in scene reconstruction, such as Neural Radiance Fields and 3D Gaussian Splating, offer alternative perspectives but are not well-suited for direct volumetric CT reconstruction. In this work, we propose Discretized Gaussian Representation (DGR), a novel framework that reconstructs the 3D volume directly using a set of discretized Gaussian functions in an end-to-end manner. To further enhance efficiency, we introduce Fast Volume Reconstruction, a highly parallelized technique that aggregates Gaussian contributions into the voxel grid with minimal overhead. Extensive experiments on both real-world and synthetic datasets demonstrate that DGR achieves superior reconstruction quality and runtime performance across various CT reconstruction scenarios. Our code is publicly available at https://github.com/wskingdom/DGR.
+
+# 1. Introduction
+
+When a patient undergoes a Computed Tomography (CT) scan at a hospital, the initial output is not the familiar image seen on the screen, but rather a series of projection data generated by X-ray detectors [21]. This data is then processed by a CT reconstruction algorithm to transform the raw information into a 3D volume, which radiologists examine to assess the patient's condition. This task is challenging due to three key factors. Firstly, the ionizing radiation exposure from a complete CT scan poses significant health risks to
+
+
+Figure 1. I: CT imaging workflow: X-ray projections are acquired from multiple angles. II: Deep Learning-based Reconstruction (DLR): Networks are trained on paired projection-image datasets to reconstruct volumes, requiring extensive pre-training. III: Instance reconstruction (exemplified by 3DGS): Instance-adaptive optimization of 3D Gaussians via differentiable rendering, tailored for each instance without the need for training datasets.
+
+patients, limiting the projections that can be acquired [41]. Secondly, time constraints in emergency situations require fast reconstruction to enable timely diagnosis [3]. Thirdly, the method must be generalizable across various CT configurations, such as different scan geometries, to accommodate heterogeneous imaging protocols and patient populations.
+
+As illustrated in Figure 1, existing CT reconstruction methods broadly fall into two categories: Deep Learning-based Reconstruction (DLR) and instance reconstruction. Early DLR approaches, such as FBPCovNet [16] and RED-CNN [4], primarily focused on image denoising within the reconstructed domain. Subsequent methods
+
+like HDNet [15] advanced to joint optimization across both projection and image domains. More recently, advanced diffusion-based DLR methods, including Diffusion-MBIR [6] and SWORD [37], leverage score-based diffusion models to guide the reconstruction process. Despite these advancements, DLR methods face persistent challenges: high training costs and limited generalization across diverse CT scanner configurations. For instance, models trained on Cone-Beam CT data often perform poorly on Fan-Beam CT systems, and networks optimized for chest scans may show degraded performance on head scans.
+
+In response to these challenges, instance reconstruction methods have emerged, specifically designed to yield patient-specific results. Inspired by the success of scene reconstruction techniques, particularly Neural Radiance Fields (NeRF) [29] and 3D Gaussian Splatting (3DGS) [19], numerous adaptations have been proposed for CT reconstruction. Exemplars of NeRF-based methodologies, such as NAF [40], Intra-Tomo [39], and SAX-NeRF [2], implicitly represent the tomographic scene as a continuous function of 3D spatial coordinates and optimize a neural network within the projection domain. However, these methods typically require hours per reconstruction, which renders them impractical for real-time clinical deployment. On the other hand, 3DGS-based methodologies, such as 3DGR-CAR [8] and X-Gaussian [3], leverage explicit Gaussian functions to represent tomographic scenes. Nevertheless, directly applying 3DGS to CT leads to a strong integration bias [41] due to density inconsistency inherent in 3DGS. While $\mathbb{R}^2$ -Gaussian [41] attempts to mitigate these issues with a rectified 3DGS rasterizer and voxelizer, it introduces computational overhead stemming from the fundamental discrepancy between 3DGS's view-oriented rendering and the requirements of discretized tomographic reconstruction.
+
+These limitations highlight a critical gap: existing DLR methods are hindered by dataset dependency and training complexity, while instance reconstruction paradigms are not well-aligned with tomographic objectives. Motivated by these challenges, we rethink the framework's design based on three core principles: discretized representation, efficient reconstruction, and unified global optimization.
+
+From these foundational considerations, we propose our Discretized Gaussian Representation (DGR) method. For representation, given that the target volumetric grid is discretized, we directly model the 3D volume as a set of discretized Gaussian functions. To ensure differentiability and accurate preservation of continuous Gaussian contributions within local grid regions, we developed a novel alignment technique. For reconstruction, we advance beyond traditional voxelization with our highly parallelized Fast Volume Reconstruction method, which can reconstruct a $256 \times 256 \times 256$ volume from over 150,000 Gaussians in just 0.09 seconds per iteration. In terms of optimization,
+
+the synergy of our lightweight representation and fast reconstruction allows for joint optimization of all Gaussians, a departure from 3DGS-based methods that rely on selective view or block optimization. We evaluate DGR on three public CT datasets: FIPS [34], AAPM-Mayo LDCT [30], and FUMPE [27], covering both real-world and synthetic data. Comprehensive experiments across multiple reconstruction tasks demonstrate that DGR surpasses state-of-the-art DLR and instance reconstruction methods in both quantitative metrics and qualitative assessments.
+
+Our main contributions can be summarized as follows:
+
+- We propose DGR, an end-to-end CT reconstruction method that directly reconstructs 3D volumes by learning from discretized Gaussian functions.
+- We introduce a fast volume reconstruction technique that efficiently aggregates Gaussian contributions into a discretized volume using a highly parallelized approach, significantly reducing reconstruction time.
+- We demonstrate DGR's superior performance over both DLR and instance reconstruction methods through extensive experiments on real-world and synthetic datasets.
+
+# 2. Background
+
+# 2.1. Deep Learning Reconstruction
+
+Deep Learning Reconstruction (DLR) methods have consistently been a prominent area in CT reconstruction since the successful application of deep neural networks in image processing [32]. Conventional DLR approaches are primarily categorized into direct-learning and indirect-learning approaches [38]. Direct learning methods involve training networks to directly reconstruct images from projection data (sinograms). Prominent instances include AUTOMAP [42], which employs manifold approximation, and iRadonMAP [12], which utilizes learnable filtering and back-projection techniques. Conversely, indirect learning methods [4, 11, 16, 18] frame CT reconstruction as a high-level denoising problem. These methods first transform raw projection data into the image domain, typically via filtered back-projection (FBP) [1] or iterative reconstruction (IR), and subsequently train networks to map these noisy initial images to their clean counterparts. Certain indirect methods, such as HDNet [15], further integrate both projection and image domains' knowledge to guide the reconstruction.
+
+Recent advancements in DLR have led to the development of diffusion models that further guide the reconstruction process. Models like MCG [5], DiffusionMBIR [6], and SWORD [37] learn the score function as a prior, which helps manage noise and artifacts in the reconstructed images. However, diffusion-based methods are computationally more intensive than traditional DLR, limiting their practicality in clinical settings. Despite this, DLR methods can improve generalization and performance by training on large datasets with diverse imaging conditions.
+
+
+Figure 2. Pipeline of DGR. The 3D volume is initially represented by a set of continuous Gaussians, with each Gaussian's contribution confined to a local region surrounding the voxel. The Gaussians are then discretized onto the 3D grid, where their contributions are aligned to directly reconstruct the entire volume. Fast Volume Reconstruction technique gathers these contributions in a highly parallelized manner. Within each iteration, these Gaussians are reconstructed and then projected into the measurement domain for optimization.
+
+# 2.2. Instance Reconstruction
+
+Instance Reconstruction-based methods constitute another category of CT reconstruction techniques, focused on reconstructing images through solving an optimization problem. These methods are fundamentally rooted in iterative reconstruction (IR) [9], where an objective function balances data fidelity with regularization terms. These terms impose prior knowledge or constraints, such as sparsity, smoothness, or edge preservation, to guide the reconstruction. Common approaches like algebraic reconstruction techniques (ART) [13], simultaneous iterative reconstruction technique (SIRT) [35], and total variation (TV) [33] regularization are widely adopted to enhance image quality and reduce artifacts compared to direct analytical methods like filtered back projection (FBP) [1].
+
+Recent advancements for CT imaging have seen the adaptation of instance reconstruction methods, such as Neural Radiance Fields (NeRF) [29] and 3D Gaussian Splatting (3DGS) [19]. NeRF-based approaches like NAF [40] and Intra-Tomo [39] optimize by minimizing the difference between synthetic and ground-truth projections, incorporating both local and global geometric priors. SAX-NeRF [2] further enhances Sparse-View X-ray reconstruction through transformer-based structure-aware modeling. These NeRF-based methods typically require hours of inference time per instance [41], making them impractical for clinical use.
+
+Generally, 3DGS-based methods surpass NeRF-based methods in both speed and image quality. Following the original 3DGS, they represent the CT scene as a set of 3D Gaussians. 3DGR-CT [24, 25] integrates 3D Gaussians with a differentiable CT projector for Cone-Beam CT reconstruction. 3DGR-CAR [8] leverages a U-Net [32] to
+
+initialize Gaussian centers before employing 3DGS for final reconstruction. DIF-Gaussian [26] uses 3D Gaussians to model feature distributions for estimating attenuation coefficients. X-Gaussian [3] adapts 3DGS for novel view synthesis in X-ray imaging. However, these 3DGS-based methods are not ideal for direct 3D volume reconstruction. $\mathbb{R}^2$ -Gaussian [41] identified integration bias in the standard 3DGS formulation and proposed rectified rasterizer and differentiable voxelizer to mitigate this limitation.
+
+# 3. Preliminary
+
+Problem Formulation Clinical CT imaging involves capturing X-ray projections of the patient from various angles, which are then processed to reconstruct a 3D volume that represents the internal structures. The CT imaging system for a 2D image slice can be described as:
+
+$$
+y = A x + \beta , \tag {1}
+$$
+
+where $x \in \mathbb{R}^{w \times h}$ denotes the 2D image with width $w$ and height $h$ , and $y \in \mathbb{R}^{m \times n}$ represents the projection matrix, where $m$ is the number of projection views and $n$ is the number of detector elements per view. The matrix $A \in \mathbb{R}^{m \times n \times w \times h}$ is the Radon Transform [31] matrix, which maps the geometric relationship between the object and the X-ray source/detector system. The noise term $\beta \in \mathbb{R}^{m \times n}$ represents measurement noise.
+
+Optimization Goal. The goal of CT reconstruction is to accurately estimate the underlying image $x$ from measured projection data $y$ . While the Inverse Radon Transform theoretically offers a perfect mapping, real-world issues like data noise and the underdetermined nature of the inverse problem makes perfect reconstruction unattainable.
+
+The reconstruction process is commonly formulated as an optimization problem:
+
+$$
+x ^ {*} = \arg \min _ {x} \mathcal {E} (A x, y) + R (x), \tag {2}
+$$
+
+where $\mathcal{E}$ is the data fidelity term, which measures the discrepancy between the estimated measurement $Ax$ and the actual measurement $y$ , often using the L1 or L2 norm. The regularization term $R(x)$ enforces properties like smoothness or sparsity in the reconstructed image, with Total Variation (TV) [33] regularization being a popular choice [28].
+
+# 4. Methodology
+
+We illustrate our DGR framework in Figure 2. DGR aims to directly reconstruct the 3D tomographic volume in an end-to-end and efficient manner. We organize our method section into three parts: Discretized Gaussian Representation (Section 4.1), Fast Volume Reconstruction (Section 4.2), and Global Optimization (Section 4.3).
+
+# 4.1. Discretized Gaussian Representation
+
+Continuous Gaussian Representation We begin by introducing the basic formulation of the continuous Gaussian representation for tomographic volume reconstruction. We define the Gaussian function centered at $\mu$ with covariance $\Sigma$ as:
+
+$$
+G (p, \mu , \Sigma) = e ^ {- \frac {1}{2} (p - \mu) ^ {\top} \Sigma^ {- 1} (p - \mu)}, \tag {3}
+$$
+
+where $p \in \mathbb{R}^d$ , $d = 3$ is the 3D point in the scene (For clarity in the Einstein Summation representation presented in this section, we maintain the notation of a constant $d = 3$ ). The Gaussian function is bell-shaped and symmetric around the mean $\mu$ , with its spread controlled by the standard deviation $\sigma$ , determining its extent in 3D space. We utilize isotropic Gaussians rather than anisotropic ones to represent the 3D volume. This choice is justified by the isotropic attenuation properties of CT tissues, particularly soft tissues, which exhibit minimal directional dependence. As noted in [17], small distributed source elements can be treated as isotropic, consistent with tissue behavior.
+
+Direct Reconstruction Let the target volume be denoted by $V \in \mathbb{R}^{w \times h \times c}$ , where $w, h,$ and $c$ correspond to the width, height, and depth (or length) of the volume, respectively. The intensity of a voxel $V(p)$ at a spatial coordinate $p$ within this volume is expressed as the cumulative contribution from all $n$ constituent Gaussians:
+
+$$
+V (p) = \sum_ {i = 1} ^ {n} G \left(p, \mu_ {i}, \Sigma_ {i}\right) \cdot I _ {i}, \tag {4}
+$$
+
+where $I_{i}\in \mathcal{R}^{+}$ represents the scalar intensity value of the $i$ -th Gaussian, functioning as both its individual contribution to the voxel intensity and its weight. The quadratic form $(p - \mu)^{\top}\Sigma^{-1}(p - \mu)$ is recognized as the squared Mahalanobis distance, which quantifies the statistical distance of
+
+point $p$ from the Gaussian center $\mu$ , normalized by the distribution's shape. This quantity will be referred to as $D^2$ in subsequent discussions for conciseness.
+
+The direct computation of every Gaussian's contribution to the entire volume presents a significant challenge, leading to unacceptable computational expense (see Table 5). For a deeper understanding of this computational complexity, please refer to Appendix E.2. To mitigate this issue, we restrict each Gaussian's effect to a localized region around its assigned voxel, as detailed below.
+
+Gaussian Effect Confinement The influence of a Gaussian on a given voxel is known to attenuate with increasing distance from the Gaussian's centroid. Leveraging this principle, restricting the contributions to only those Gaussians within a specified proximity of each voxel can substantially accelerate the reconstruction process.
+
+To formalize this concept, we define the effective proximity for each Gaussian as a cuboid $w_0 \times h_0 \times c_0$ , where $w_0, h_0, c_0$ are all odd integers. This box is centered on the voxel, and we denote the set of all 3D coordinates within this cuboid as $B_0 \subset \mathbb{R}^3$ .
+
+Naturally, the specific coordinates within the cuboid $B_0$ depend on the Gaussian function's center $\mu$ . For a Gaussian centered at $\mu$ , its influence is evaluated at coordinates $B = B_0 - \mu$ , and $B$ is a constant tensor. This is because the coordinates within $B_0$ are relative to $\mu$ , meaning that subtracting $\mu$ yields a fixed pattern of offsets independent of its absolute position. Mathematically, this reflects the translation invariance of the Gaussian function's shape: shifting $\mu$ only changes the peak's location, not the function's overall form.
+
+Now, we can compute the squared Mahalanobis distance $D^2$ for a given relative coordinate in $B$ with respect to the Gaussian's mean (which is implicitly at the origin for these relative coordinates) as:
+
+$$
+D ^ {2} = B ^ {\top} C ^ {- 1} B. \tag {5}
+$$
+
+Here, $C$ denotes the covariance matrix of the Gaussian. The contribution of the $i$ -th Gaussian to the voxel intensity at a relative coordinate described by $B$ is then given by:
+
+$$
+e ^ {- \frac {1}{2} D ^ {2}} \cdot I _ {i}. \tag {6}
+$$
+
+While this localized confinement might lead to a loss of information from more distant Gaussians, it is worth noting that all Gaussians are trainable and can compensate for any missing information from more distant Gaussians.
+
+Discretize and Align In reconstructing a 3D volume $V$ , directly using the continuous mean $\mu$ for indexing and summing all Gaussian contributions presents a challenge: the gradient with respect to $\mu$ cannot propagate through this summation. This occurs because the discretized 3D volume $V$ relies on integer coordinates, while $\mu$ is continuous.
+
+Simply discretizing $\mu$ by rounding it to the nearest integer for indexing would render the reconstruction process non-differentiable, thereby hindering optimization. To circumvent this, rather than directly discretizing $\mu$ , we calculate each Gaussian's contribution at the discretized grid positions aligned with their floored integer coordinates. More precisely, we select the floored integer of the box's center as the indexing point, denoting this integer-centered box as $\lfloor B \rfloor$ .
+
+For enhanced clarity, we define the residual between the continuous center $\mu$ and its floored integer counterpart as:
+
+$$
+\Delta \mu = \mu - \lfloor \mu \rfloor , \tag {7}
+$$
+
+where $\lfloor \mu \rfloor$ signifies the floor function. This $\Delta \mu$ quantifies the offset between the continuous and discretized positions, thereby enabling precise alignment between the continuous Gaussian center and the discretized grid.
+
+Subsequently, we establish a relationship between the coordinates of the new box $\lfloor B\rfloor$ and the original box $B$ by accounting for this offset. The transformation from $B$ to $\lfloor B\rfloor$ is expressed as:
+
+$$
+\left\lfloor B \right\rfloor_ {n, w _ {0}, h _ {0}, c _ {0}, d} = B _ {w _ {0}, h _ {0}, c _ {0}, d} - \Delta \mu_ {n, 1, 1, 1, d}. \tag {8}
+$$
+
+Here, $\Delta \mu$ is implicitly broadcast across the dimensions of $B$ to enable element-wise subtraction. This adjustment guarantees that each Gaussian's contribution is accurately evaluated at its corresponding position on the discretized grid, relative to its floored mean. This 'Discretize and Align' procedure thus enables seamless optimization by ensuring the unimpeded flow of gradients through the aggregation of Gaussian contributions, thereby preserving the differentiability of the reconstruction pipeline.
+
+# 4.2. Fast Volume Reconstruction
+
+Parallel Computation To improve computational efficiency, we compute the squared Mahalanobis distance $D^2$ for each local region in parallel. For each voxel, $D^2$ is calculated using the discretized box $\lfloor B \rfloor$ , leading to:
+
+$$
+D ^ {2} = \lfloor B \rfloor^ {\top} C ^ {- 1} \lfloor B \rfloor . \tag {9}
+$$
+
+To represent this computation more clearly and compactly, we utilize the Einstein summation convention, which implicitly sums over repeated indices. The expression for $D^2$ thus becomes:
+
+$$
+D _ {n, w _ {0}, h _ {0}, c _ {0}} ^ {2} = \sum_ {d} \left\lfloor B \right\rfloor_ {n, w _ {0}, h _ {0}, c _ {0}, d} C _ {n, d, d} ^ {- 1} \left\lfloor B \right\rfloor_ {n, w _ {0}, h _ {0}, c _ {0}, d}.
+$$
+
+Once $D^2$ is computed, the contributions of all Gaussians are summed to form the reconstructed volume.
+
+Decomposition To further reduce computation in Equation 10, we decompose the computationally expensive Einstein summation into smaller, more manageable summations. The squared Mahalanobis distance $D^2$ can be explicitly decomposed into a combination of the following four
+
+smaller Einstein sums:
+
+$$
+B ^ {T} C ^ {- 1} B _ {n, w _ {0}, h _ {0}, c _ {0}} = \sum_ {d} B _ {w _ {0}, h _ {0}, c _ {0}, d} ^ {T} C _ {n, d, d} ^ {- 1} B _ {w _ {0}, h _ {0}, c _ {0}, d},
+$$
+
+$$
+B ^ {T} C ^ {- 1} \Delta \mu_ {n, w _ {0}, h _ {0}, c _ {0}} = \sum_ {d} B _ {w _ {0}, h _ {0}, c _ {0}, d} ^ {T} C _ {n, d, d} ^ {- 1} \Delta \mu_ {n, 1, 1, d},
+$$
+
+$$
+\Delta \mu^ {T} C ^ {- 1} B _ {n, w _ {0}, h _ {0}, c _ {0}} = \sum_ {d} \Delta \mu_ {n, 1, 1, d} ^ {T} C _ {n, d, d} ^ {- 1} B _ {w _ {0}, h _ {0}, c _ {0}, d},
+$$
+
+$$
+\Delta \mu^ {T} C ^ {- 1} \Delta \mu_ {n, 1, 1, 1} = \sum_ {d} \Delta \mu_ {n, 1, 1, d} ^ {T} C _ {n, d, d} ^ {- 1} \Delta \mu_ {n, 1, 1, d},
+$$
+
+Subsequently, we compute the squared Mahalanobis distance $D^2$ as:
+
+$$
+\begin{array}{l} D ^ {2} = \left(B ^ {\top} C ^ {- 1} B\right) - \left(B ^ {\top} C ^ {- 1} \Delta \mu\right) \\ - \left(\Delta \mu^ {\top} C ^ {- 1} B\right) + \left(\Delta \mu^ {\top} C ^ {- 1} \Delta \mu\right). \tag {10} \\ \end{array}
+$$
+
+The final contribution of the Gaussians within the local region is computed as:
+
+$$
+\Gamma = e ^ {- \frac {1}{2} D _ {n, w _ {0}, h _ {0}, c _ {0}} ^ {2}} \cdot I, \tag {11}
+$$
+
+where $\Gamma \in \mathbb{R}^{n\times w_0\times h_0\times c_0}$ represents the contributions of $n$ Gaussians within the local region. This decomposition allows us to calculate the contributions in a highly efficient manner, reducing time complexity without increasing space complexity. Specifically, $B_{w_0,h_0,c_0,d}$ is only $\frac{1}{n}$ the size of $\lfloor B\rfloor_{n,w_0,h_0,c_0,d}$ , enabling far more efficient computations. The quantitative evidence supporting this efficiency gain is presented in Table 5.
+
+Then we aggregate the contribution of each Gaussian into its corresponding voxels within the volume. Specifically, for each contribution $\Gamma_{i,x,y,z}$ from the $i$ -th Gaussian to the voxel located at position $(x,y,z)$ , the volume update proceeds as:
+
+$$
+V _ {x, y, z} \leftarrow V _ {x, y, z} + \Gamma_ {i, x, y, z}. \tag {12}
+$$
+
+This aggregation is performed for all Gaussians, guaranteeing the precise accumulation of their contributions at the appropriate locations within the reconstructed volume. A highly parallelized implementation of this update process is available in our codebase for further reference.
+
+Notably, our Fast Volume Reconstruction is a plug-and-play module that can be seamlessly integrated into existing methods leveraging 3D Gaussians. For instance, while X-Gaussian [3] originally focuses on novel view synthesis without volume reconstruction, integrating our module into its pipeline prior to loss computation enables it to perform volume reconstruction, as demonstrated in Table 1.
+
+# 4.3. Global Optimization
+
+Subsequent to reconstructing the 3D volume from the Gaussians, we adopt a joint optimization of the Gaussian param
+
+
+SAX-NerF
+
+
+PSNR: 37.07 SSIM:0.913 PSNR: 30.65 SSIM:0.872
+
+
+PSNR: 37.92 SSIM:0.990 PSNR: 32.53 SSIM:0.965
+
+
+
+
+PSNR:34.10 SSIM:0.921
+
+
+PSNR: 41.96 SSIM:0.985
+
+
+PSNR: 34.01 SSIM:0.923
+
+
+raannnnnne
+
+
+PSNR: 39.71 SSIM:0.937 PSNR: 31.83 SSIM:0.877
+
+
+PSNR: 42.46 SSIM:0.994 PSNR: 34.47 SSIM:0.977
+
+
+
+
+PSNR: 38.16 SSIM:0.957
+
+
+PSNR: 47.57 SSIM:0.990
+
+
+PSNR: 37.84 SSIM:0.951
+
+
+DGR
+
+
+PSNR: 39.77 SSIM:0.951 PSNR: 32.23 SSIM:0.919
+
+
+PSNR: 43.55 SSIM:0.996 PSNR: 37.34 SSIM:0.993
+
+
+
+
+PSNR: 41.08 SSIM:0.963
+
+
+PSNR: 50.91 SSIM:0.997
+
+
+
+
+Groun
+
+
+
+
+
+
+
+
+Figure 3. Qualitative Comparison of our DGR with previous state-of-the-art instance reconstruction methods SAX-NeRF and $\mathbb{R}^2$ -Gaussian, with major differences highlighted in Red boxes. Please zoom in for better visibility.
+
+
+
+
+PSNR: 41.26 SSIM:0.962
+
+eters within the projection space. Diverging from conventional 3DGS and its variants, which typically optimize parameters per selected view [3, 19] or local blocks [41], our global optimization strategy achieves convergence in fewer than 1K iterations, representing a substantial improvement over standard approaches (e.g., requiring 30K iterations).
+
+The initial phase of this optimization involves projecting the reconstructed 3D volume back into the projection domain. To accomplish this, we define a general geometry projection transformation $\mathcal{T}$ :
+
+$$
+\hat {P} = \mathcal {T} (V), \tag {13}
+$$
+
+where $\hat{P} \in \mathbb{R}^{m \times n \times p}$ denotes the estimated projection.
+
+This concise formulation is independent of specific CT acquisition geometries, demonstrating strong compatibility with various CT settings, including Fan-Beam or Cone-Beam CT, as well as Sparse-View or Limited-Angle CT. In each iteration, we optimize the Gaussian parameters to minimize the discrepancy between the estimated projection $\hat{P}$ and the reference projection $P$ . This optimization is guided by an objective function combining $\mathcal{L}_1$ loss, SSIM [36] loss $(\mathcal{L}_{SSIM})$ , and total variation [33] loss $(\mathcal{L}_{TV})$ :
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {1} (\hat {P}, P) + \lambda_ {2} \mathcal {L} _ {\text {S S I M}} (\hat {P}, P) + \lambda_ {3} \mathcal {L} _ {\text {T V}} (V), \tag {14}
+$$
+
+where $\lambda_{1} = 0.6$ , $\lambda_{2} = 0.2$ , and $\lambda_{3} = 1$ are the respective weights for the $\mathcal{L}_1$ , $\mathcal{L}_{\mathrm{SSIM}}$ , and $\mathcal{L}_{\mathrm{TV}}$ . We discuss the definition and usage of these loss functions in Appendix D.1.
+
+To further enhance the optimization process, we adopt the well-established adaptive density control for 3D Gaussians [19]. This involves cloning under-reconstructed Gaussians, splitting over-reconstructed ones into smaller Gaussians, and pruning those with near-zero gradient magnitudes. As this process is standard and not our core contribution, we provide full details in Appendix F.
+
+# 5. Experiments
+
+# 5.1. Experiment Settings
+
+Datasets and Evaluation Setup We conducted experiments using three distinct datasets: FIPS [34], AAPM-Mayo LDCT [30], and FUMPE [27]. To ensure a fair and reproducible evaluation, we maintained consistent settings for all compared methods and grouped them by task, as detailed below: For Cone-Beam Sparse-View CT, we evaluated on the FIPS [34] dataset, following the setup used by $\mathbb{R}^2$ -Gaussian [41]. This dataset includes both real-world and synthetic data. The real-world evaluation utilized three cases with 721 real projections, while the synthetic portion involved 15 real CT volumes encompassing a range of subjects from organisms to artificial objects. For Fan-Beam Sparse-View CT and Limited-Angle CT, we followed the evaluation protocols of SWORD [37] and Diffusion-MBIR [6], using the widely adopted AAPM-Mayo LDCT dataset. This dataset comprises 5388 slices with a $1\mathrm{mm}$
+
+Table 1. Comparisons of 75/50/25-view Sparse-View CT on FIPS dataset. Best in Bold.
+
+| Methods | 75-view | 50-view | 25-view |
| PSNR↑ | SSIM↑ | Time↓ | PSNR↑ | SSIM↑ | Time↓ | PSNR↑ | SSIM↑ | Time↓ |
| Real-World Dataset |
| FDK [7] | 30.03 | 0.535 | - | 27.38 | 0.449 | - | 23.30 | 0.335 | - |
| IntraTomo [39] | 36.79 | 0.858 | 2h25m | 36.99 | 0.854 | 2h19m | 35.85 | 0.835 | 2h18m |
| NAF [40] | 38.58 | 0.848 | 51m28s | 36.44 | 0.818 | 51m31s | 32.92 | 0.772 | 51m24s |
| SAX-NeRF [2] | 34.93 | 0.854 | 13h21m | 34.89 | 0.840 | 13h23m | 33.49 | 0.793 | 13h25m |
| X-Gaussian* [3] | 38.27 | 0.894 | 10m21s | 37.80 | 0.881 | 10m5s | 35.12 | 0.859 | 9m55s |
| R²-Gaussian (iter=10k) [41] | 38.10 | 0.872 | 3m39s | 37.52 | 0.866 | 3m37s | 35.10 | 0.840 | 3m23s |
| R²-Gaussian (iter=30k) [41] | 39.40 | 0.875 | 14m16s | 38.24 | 0.864 | 13m52s | 34.83 | 0.833 | 12m56s |
| DGR (iter=300) | 39.91 | 0.937 | 3m36s | 38.66 | 0.929 | 3m24s | 35.16 | 0.883 | 2m59s |
| DGR (iter=1000) | 41.28 | 0.952 | 13m14s | 39.27 | 0.940 | 11m48s | 34.58 | 0.870 | 8m54s |
| Synthesis Dataset |
| FDK [7] | 28.63 | 0.497 | - | 26.50 | 0.422 | - | 22.99 | 0.317 | - |
| IntraTomo [39] | 35.42 | 0.924 | 2h7m | 35.25 | 0.923 | 2h9m | 34.68 | 0.914 | 2h19m |
| NAF [40] | 37.84 | 0.945 | 30m43s | 36.65 | 0.932 | 32m4s | 33.91 | 0.893 | 31m1s |
| SAX-NeRF [2] | 38.07 | 0.950 | 13h5m | 36.86 | 0.938 | 13h5m | 34.33 | 0.905 | 13h3m |
| X-Gaussian* [3] | 38.22 | 0.955 | 9m58s | 37.50 | 0.946 | 9m50s | 35.18 | 0.924 | 9m51s |
| R²-Gaussian (iter=10k) [41] | 38.29 | 0.954 | 2m38s | 37.63 | 0.949 | 2m35s | 35.08 | 0.922 | 2m35s |
| R²-Gaussian (iter=30k) [41] | 38.88 | 0.959 | 8m21s | 37.98 | 0.952 | 8m14s | 35.19 | 0.923 | 8m28s |
| DGR (iter=300) | 38.71 | 0.957 | 2m24s | 38.05 | 0.954 | 2m17s | 35.76 | 0.930 | 2m14s |
| DGR (iter=1000) | 39.63 | 0.964 | 7m27s | 38.74 | 0.960 | 7m13s | 36.55 | 0.947 | 6m53s |
+
+thickness, commonly used in CT reconstruction research. Additionally, we performed evaluations on the FUMPE [27] dataset, which contains 8792 chest CT images. Following standard practice, we adopted Peak Signal-to-Noise Ratio (PSNR) [14] and Structural Similarity Index Measure (SSIM) [36] as our image quality metrics.
+
+Implementation Details We implemented DGR using PyTorch. Most experiments were trained on a single NVIDIA RTX 6000 GPU. However, for the 75/50/25-view Sparse-View CT experiments on the FIPS dataset, we utilized a single NVIDIA RTX 3090 GPU to ensure a fair comparison by maintaining the same training environment as $\mathbf{R}^2$ -Gaussian. We initialized the number of Gaussians to 150K and set the local box size to $17\times 17\times 17$ . The Adam optimizer [20] was employed with an initial learning rate of $3\times 10^{-4}$ , which decayed to $3\times 10^{-5}$ by the end of training. For Cone-Beam Sparse-View CT, the training process was limited to 1K iterations. For Fan-Beam Sparse-View CT, we did not set the iteration limit, and the training process is ceased when the validation loss converges in the projection domain.
+
+# 5.2. Experimental Results and Analysis
+
+# 5.2.1. Cone-Beam Sparse-View CT Reconstruction
+
+In Table 1, we present a comparison of DGR with advanced instance reconstruction methods on the FIPS dataset. Baselines include NeRF-based methods (IntraTomo [39],
+
+NAF [40], SAX-NeRF [2]) and 3DGS-based methods (X-Gaussian [3], $\mathbb{R}^2$ -Gaussian [41]), with X-Gaussian specifically implemented using our Fast Volume Reconstruction module. DGR demonstrates superior image quality and computational efficiency across all view counts, significantly outperforming previous instance reconstruction methods. Even with just 300 iterations, DGR surpasses most advanced methods while completing reconstruction in approximately 3 minutes.
+
+The faster reconstruction time achieved by DGR is attributed to the discretized representation, which is inherently well-aligned with the reconstruction task and avoids redundant computation. Furthermore, DGR's lightweight framework enables the joint optimization of all Gaussians, significantly reducing computation time without compromising reconstruction quality, as illustrated in Figure 3.
+
+# 5.2.2. Fan-Beam Sparse-View CT Reconstruction
+
+In Table 2, we compare DGR with leading DLR methods on the AAPM-Mayo LDCT dataset [30]. The term 'Data' in these tables refers to the number of images used to train the DLR methods, whereas our DGR optimizes without relying on additional training data. The baseline methods include traditional CNN-based approaches such as FBPCovNet [16], U-Net [23], and PLANet [38], alongside advanced diffusion-based methods like GMSD [10],
+
+Table 2. Comparisons of 180/120/90/60-view Sparse-View CT on AAPM-Mayo LDCT dataset. Best in Bold.
+
+| Method | Extra Data | 180-view | 120-view | 90-view | 60-view |
| PSNR↑ | SSIM↑ | PSNR↑ | SSIM↑ | PSNR↑ | SSIM↑ | PSNR↑ | SSIM↑ |
| FBP [1] | 0 | 31.69 | 0.882 | 28.30 | 0.787 | 26.20 | 0.701 | 23.18 | 0.595 |
| FBPCovNet [16] | 4839 | 42.23 | 0.988 | 39.45 | 0.983 | 37.11 | 0.976 | 35.63 | 0.966 |
| U-Net [23] | 4839 | 38.37 | 0.985 | 35.58 | 0.977 | 30.09 | 0.947 | 28.83 | 0.937 |
| PLANet [38] | 4176 | 42.76 | 0.965 | 41.67 | 0.962 | 40.99 | 0.957 | 38.97 | 0.941 |
| GMSD [10] | 4839 | 41.44 | 0.988 | 39.41 | 0.981 | 37.25 | 0.974 | 34.31 | 0.958 |
| SWORD [37] | 4839 | 45.08 | 0.994 | 42.49 | 0.990 | 41.27 | 0.986 | 38.49 | 0.978 |
| DGR | 0 | 46.13 | 0.997 | 44.64 | 0.994 | 43.23 | 0.992 | 40.25 | 0.985 |
+
+Table 3. Fan-Beam Limited-Angle CT $90^{\circ}$ reconstruction.
+
+| Method | Data | Axial | Coronal | Sagittal |
| PSNR ↑ | SSIM ↑ | PSNR ↑ | SSIM ↑ | PSNR ↑ | SSIM ↑ |
| FBP [1] | 0 | 14.91 | 0.397 | 17.07 | 0.411 | 15.46 | 0.403 |
| FBPCovNet [16] | 3142 | 26.76 | 0.879 | 25.77 | 0.874 | 22.92 | 0.841 |
| ADMM-TV [28] | 3142 | 23.19 | 0.793 | 22.96 | 0.758 | 19.95 | 0.782 |
| MCG [5] | 3839 | 26.01 | 0.838 | 24.55 | 0.823 | 21.59 | 0.706 |
| Lahiri et al. [22] | 3142 | 28.08 | 0.931 | 26.02 | 0.856 | 23.24 | 0.812 |
| DiffusionMBIR [6] | 3142 | 34.92 | 0.956 | 32.48 | 0.947 | 28.82 | 0.832 |
| DGR | 0 | 38.22 | 0.970 | 39.32 | 0.969 | 38.35 | 0.970 |
+
+and SWORD [37]. To ensure a fair comparison for 180/120/90/60-view Sparse-View CT, we replicated the settings used in SWORD [37]. Notably, DGR surpasses advanced DLR methods that incorporate prior knowledge in Fan-Beam Sparse-View CT reconstruction, despite requiring zero training data. This validates DGR's ability to address diverse CT reconstruction tasks without architectural modifications while achieving superior performance.
+
+# 5.2.3. Fan-Beam Limited-Angle CT Reconstruction
+
+In Table 3, we report the performance of Limited-Angle CT reconstruction experiments conducted on the AAPM-Mayo LDCT dataset [30], following the methodology of DiffusionMBIR [6]. The baseline methods include traditional CNN-based techniques such as FBPCovNet [16] and Lahiri et al. [22], alongside advanced diffusion-based approaches like MCG [5] and DiffusionMBIR [6]. For these evaluations, the angular data acquisition was restricted to a $90^{\circ}$ range within a total of $180^{\circ}$ . Without any prior knowledge, DGR still demonstrates a substantial improvement over these advanced DLR methods.
+
+# 5.2.4. Additional Evaluations and Visualizations
+
+Our DGR is further evaluated on the FUMPE dataset [27] for Fan-Beam 180/120/90/60-view chest CT reconstruction, with the quantitative results detailed in Appendix Table 9. Furthermore, iterative reconstruction visualizations of DGR are showcased in Appendix Figures 4, 5, and 6.
+
+# 5.3. Ablation Study
+
+In Table 4, we evaluate the impact of local box size on 60-view Sparse-View CT reconstruction using the AAPM-Mayo LDCT dataset. Each configuration was assessed over 1K iterations to ensure stable measurements of training time
+
+Table 4. Effect of Box Size on 60-view Sparse-View CT
+
+| Box-Size | 13 × 13 × 13 | 15 × 15 × 15 | 17 × 17 × 17 | 19 × 19 × 19 |
| Time (minutes) | 7.92 | 11.07 | 16.58 | 26.99 |
| V-Ram (GiB) | 10.70 | 13.29 | 16.87 | 21.32 |
| PSNR / SSIM | 35.99 / 0.960 | 38.90 / 0.973 | 40.25 / 0.985 | 40.98 / 0.987 |
+
+and video memory usage. We observe that performance improves with increasing box size; however, this comes at the cost of increased time consumption and video memory. Consequently, we chose $17 \times 17 \times 17$ as the default box size for our experiments, as it achieves an optimal balance between performance and efficiency.
+
+Effect of Fast Volume Reconstruction In Table 5, we compare the video memory and time consumption of our Fast Volume Reconstruction (denoted as FVR below) against the Direct reconstruction (Equation 4). We observe that Fast Volume Reconstruction achieves a significant reduction in video memory consumption. The decomposition further reduces the reconstruction time from 1.05s to 0.09s, thereby enabling the highly efficient reconstruction capabilities.
+
+Table 5. Video-Memory and Time Per Iteration
+
+| Method | VRAM (GiB) | Time (s) |
| Direct Reconstruction (estimated) | 16662.50 | / |
| FVR w/o Decomposition | 16.87 | 1.05 |
| FVR w/ Decomposition | 16.87 | 0.09 |
+
+Analysis of Loss Functions In Appendix Tables 6, 7, and 8, we discuss the usage of various loss functions. Results indicate that a combined use of $\mathcal{L}_1$ loss, SSIM loss ( $\mathcal{L}_{SSIM}$ ), and total variation loss ( $\mathcal{L}_{TV}$ ) yields the best performance. Analysis of Isotropic Gaussians and Voxelizer As detailed in Appendix Sections D.2 and D.3, our ablation studies demonstrate that DGR surpasses alternative designs in both image quality and reconstruction speed.
+
+# 6. Conclusion
+
+We present DGR, a novel framework that rethinks CT reconstruction through representation, reconstruction, and optimization. Evaluated on multiple datasets against both Deep Learning Reconstruction and instance reconstruction baselines, DGR achieves superior image quality and speed, demonstrating significant potential for clinical application.
+
+# Acknowledgments
+
+This research is supported by the Fundamental Research Funds for the Central Universities (project number YG2024ZD06), NSFC (No. 62176155), and Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102).
+
+# References
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+# DisenQ: Disentangling Q-Former for Activity-Biometrics
+
+Shehreen Azad Yogesh Singh Rawat
+
+Center for Research in Computer Vision
+
+University of Central Florida
+
+https://sacrcv.github.io/DisenQ-website/
+
+# Abstract
+
+In this work, we address activity-biometrics, which involves identifying individuals across diverse set of activities. Unlike traditional person identification, this setting introduces additional challenges as identity cues become entangled with motion dynamics and appearance variations, making biometrics feature learning more complex. While additional visual data like pose and/or silhouette help, they often struggle from extraction inaccuracies. To overcome this, we propose a multimodal language-guided framework that replaces reliance on additional visual data with structured textual supervision. At its core, we introduce DisenQ (Disentangling Q-Former), a unified querying transformer that disentangles biometrics, motion, and non-biometrics features by leveraging structured language guidance. This ensures identity cues remain independent of appearance and motion variations, preventing misidentifications. We evaluate our approach on three activity-based video benchmarks, achieving state-of-the-art performance. Additionally, we demonstrate strong generalization to complex real-world scenario with competitive performance on a traditional video-based identification benchmark, showing the effectiveness of our framework.
+
+# 1. Introduction
+
+Traditional person identification aims to recognize the same individual across different cameras, time and location [57], focusing on facial recognition [1, 38], gait analysis [16, 17, 33, 35], and whole-body biometrics [19, 32, 43, 58]. While effective in gait-based analysis, these approaches struggle when individuals engage in diverse daily activities beyond just standing or walking. Extending beyond conventional methods, activity-biometrics involves identifying individuals from their daily activities [3] by leveraging motion dynamics, making it more suitable for real-world applications like surveillance, healthcare, smart environments where recognition across diverse activities is crucial.
+
+Effective identification in activity biometrics requires disentangling biometric features from appearance-based non-biometric and motion cues to prevent identity bias and
+
+
+(a) Existing multimodal person identification approach
+
+
+(b) Our multimodal activity-aware person identification
+Figure 1. Comparison of existing and our activity-aware person identification framework: (a) Existing multimodal methods [32] lacking activity-awareness leads to misidentifications due to entangled biometrics and motion features. (b) Our model disentangles biometrics and motion features using language guidance, enabling activity-awareness and more accurate identification across diverse activities while being appearance invariant.
+
+fully leverage motion dynamics. Existing method [3] address this using additional visual modalities like silhouettes, but their reliance on accurate extraction limits reliability in real-world settings to aid feature separation. This highlights the need for an approach that ensures effective feature separation without additional visual data, improving generalization across varying conditions and activities.
+
+To reduce reliance on additional visual data, cross-modal learning using text has been explored with CLIP-based contrastive learning methods [22, 32, 58]. While effective in aligning global image-text associations, these methods lack identity-specific feature separation, leading to misidentifications due to appearance variation. Additionally, their failure to maintain temporal consistency makes them less suitable for video-based activity-biometrics where motion dynamics play a critical role (Figure 1). Multimodal Large
+
+Language Models (MLLMs) offer a generative alternative by leveraging structured textual reasoning to achieve better feature separation and robustness in complex scenarios [4, 5, 11, 31, 36, 47, 48]. However, existing MLLM-based person identification approaches [26, 50] rely on additional visual data and are image based, making them ineffective at capturing motion dynamics essential for activity-biometrics.
+
+To enhance activity-based person identification without relying on additional visual data, we introduce a multimodal Disentangling Querying (DisenQ) Transformer based framework that explicitly separates biometrics, nonbiometrics, and motion features. Unlike prior works that rely on additional visual modalities, our approach uses structured text descriptions generated from a frozen Vision-Language Model (VLM) to provide semantic supervision for cross-modal feature learning. These language descriptions serve as explicit guidance, enabling robust feature separation by distinguishing identity-related attributes from appearance and motion cues.
+
+At the core of our approach is our proposed DisenQ, a Disentangling Querying Transformer, that separates biometrics, non-biometrics and motion features using structured textual guidance while minimizing feature leakage. The disentangled features enhance similarity-based retrieval in a traditional identification pipeline. By leveraging language-driven supervision as an auxiliary modality, DisenQ eliminates the need for additional visual modalities, reduces reliance on biased visual cues, and improves generalization across diverse real-world activities.
+
+We evaluate our framework on three activity-based video benchmarks, demonstrating strong generalization across diverse activities. Additionally, to assess its broader applicability, we evaluate it on a large-scale traditional video-based identification benchmark. Our approach achieves state-of-the-art performance on most datasets and remains competitive on others, highlighting its robustness in real-world scenarios. Our main contributions are as follows:
+
+- We use language guidance for activity-biometrics to explicitly disentangle feature spaces, enabling cross-modal learning without additional visual data.
+- We introduce DisenQ (Disentangling Q-Former) that effectively separates biometrics, non-biometrics, and motion features for activity-aware person identification.
+- Our method achieves state-of-the-art performance on activity-based benchmarks and competitive performance on a traditional video-based person identification benchmark highlighting its generalization ability across diverse real-world scenarios.
+
+# 2. Related Works
+
+Visual modality based person identification. Traditional person identification primarily relies on image-based ap
+
+proaches [7, 23, 27, 40, 54], focusing on body shape, clothing, and appearance. While some works improve robustness with cloth-invariant representations [19, 20, 55], or additional modalities like silhouettes [29], skeletons [42, 45], or 3D shape [9], they lack spatiotemporal awareness. Videobased approaches [6, 8, 21, 25, 28, 37, 41, 43, 44, 51] integrate temporal cues but remain limited to walking-based identification, making them less effective for activity-based identification. The only prior activity-based identification method [3] relies on silhouette extraction, which is unreliable in challenging conditions. Instead, we leverage structured language supervision to enhance identity learning without requiring additional visual data.
+
+Language modality based person identification. Several CLIP based identification approaches [10, 22, 32, 34, 53, 56, 58] leverage image-text contrastive learning [46] for traditional image-based person identification. However, these methods lack temporal modeling and cannot disentangle motion from biometric features, making them unsuitable for activity-based identification. Similarly, large foundation models for image-based person identification [26, 50] incorporate language but rely on additional visual modalities, as well as lack temporal modeling capabilities. To address this, we leverage language guidance not just for cross-modal learning, but to explicitly disentangle video-based features, enabling a more robust and adaptable framework for activity-aware identification.
+
+Multimodal Large Language Models. Several works [2, 11, 30, 31, 46, 61] have been introduced to enhance image-text alignment by bringing visual features closer to language space. Among these, BLIP-2's Q-Former [31] is a lightweight approach that effectively aligns visual and language modalities. We build our proposed DisenQ based on this architecture to align visual features with language while disentangling biometrics, non-biometrics, and motion through structured textual guidance. To the best of our knowledge, this is the first work to leverage Q-Former for feature disentanglement.
+
+# 3. Method
+
+We propose a Disentangling Q-Former (DisenQ) based multimodal framework for activity-biometrics. Our framework consists of a visual encoder to extract visual features from an RGB video and a frozen VLM to generate a detailed prompt which is encoded via a text encoder (Section 3.1). To ensure robust feature disentanglement, DisenQ separates biometrics, non-biometrics, and motion features in the visual domain through language guidance (Section 3.2). Finally, an identification head performs person identification (Section 3.3), ensuring that biometrics features remain clothing-invariant while incorporating motion cues for improved identity matching. Given an RGB video $V$ , with ground truth actor and activity labels $(y_{ID}$ and $y_{Action})$
+
+
+(a) Framework Overview
+
+
+(b) DisenQ Overview
+
+
+(c) Structured Textual Description
+Figure 2. Framework overview: (a) Given an RGB video, our model performs language-guided activity-aware person identification using the proposed Disentangling Q-Former (DisenQ). (b) DisenQ disentangles biometrics, motion, and non-biometrics visual features using structured language guidance and dedicated learnable queries for each feature type. (c) The frozen VLM generates structured textual descriptions from the key-frame (red dotted line) to serve as language supervision for DisenQ. Here, $[F, T_x]$ denotes concatenation of $F$ and $T_x$ . During inference, only the components within the gray dashed box are utilized, removing the need for text generation.
+
+the framework aims to correctly match the identity of the person in a probe video to its corresponding identity in the gallery. The overall approach is illustrated in Figure 2.
+
+# 3.1. Feature Extraction
+
+Visual feature extraction. Given a sequence of frames from a video $V$ , each frame $v_{i} \in \mathbb{R}^{H \times W \times 3}$ , where $H$ and $W$ represent its height and width, is processed through a visual encoder to extract visual features $f_{i} \in \mathbb{R}^{N \times D}$ . Here, $N$ denotes the number of extracted visual tokens per frame, and $D$ is the hidden dimension of each token. Here, each visual feature $f_{i}$ has temporal ordering information associated with it through a position embedding layer. Finally, temporal attention pooling is applied on all frame features to get a global video-level feature $F$ .
+
+Prompt generation and textual feature extraction. To generate structured and semantically consistent language description, we use a frozen VLM to generate prompts from the key-frame of the input video during only training, without requiring the VLM during inference. These descriptions are categorized into three distinct components following pre-defined templates: Biometrics prompt $(P_b)$ , describing identity-specific traits such as body shape, posture, and no
+
+table physical characteristics; Motion prompt $(P_{m})$ describing the action label and movement; and Non-biometrics prompt $(P_{\hat{b}})$ , describing clothing, and accessories. To maintain consistency, biometrics descriptions are generated only once per unique identity and reused in all subsequent videos of the same actor by storing and iteratively refining it by updating the stored description using a running average. This prevents major description drift and ensures stable identity representation across varied activities and appearances.
+
+The generated prompts are then encoded using a pretrained frozen text-encoder to obtain textual embeddings $(T_{b}, T_{m}, T_{\hat{b}})$ which serve as language-driven supervision for visual feature disentanglement.
+
+# 3.2. DisenQ
+
+We introduce DisenQ (Disentangling Querying Transformer) to separate biometrics, motion and non-biometrics features in the visual domain by aligning visual representations with structured textual cues. Adapted from the original Q-Former [31], DisenQ introduces three separate sets of learnable queries: $z_{b}$ (biometrics), $z_{m}$ (motion) and $z_{\hat{b}}$ (non-biometrics); instead of a single query set, enabling explicit disentanglement. Each query set shares the same self
+
+attention and cross-attention layers while leveraging textual guidance, ensuring effective feature separation. However, they explicitly attend to different information without interaction, preserving distinct feature representations for biometrics, motion and non-biometrics. The learned queries are then utilized for activity-based person identification, improving the model's ability to distinguish individuals based on biometrics while leveraging motion cues and remaining invariant to non-biometrics attributes.
+
+Biometrics feature disentanglement. To extract identity-related features, the biometrics query $z_{b}$ attends to itself through self-attention to refine itself. Then the refined query performs cross-attention with the visual feature $F$ and biometrics textual supervision features $T_{b}$ with query, key and value being used as Equation 1.
+
+$$
+Q _ {b} = W z _ {b}, \quad K _ {b} = W [ F, T _ {b} ], \quad V _ {b} = W [ F, T _ {b} ]. \tag {1}
+$$
+
+Here, $[F,T_b]$ denotes concatenation of $F$ and $T_{b}$ , followed by a linear projection.
+
+Motion feature disentanglement. To extract motion-specific representations, the motion query $z_{m}$ , similar to biometrics query $z_{b}$ , first undergoes self-attention, ensuring it refines motion-related patterns independently. Subsequently, the motion query cross-attends to the visual feature $F$ and its corresponding textual feature $T_{m}$ with query, key and value acting as Equation 2.
+
+$$
+Q _ {m} = W z _ {m}, \quad K _ {m} = W [ F, T _ {m} ], \quad V _ {m} = W [ F, T _ {m} ]. \tag {2}
+$$
+
+Non-biometrics feature disentanglement. To separate non-biometrics features, the non-biometrics query $z_{\hat{b}}$ similar to others, also, first undergoes self-attention, refining itself without influence from other feature categories. Following this, the non-biometrics queries cross-attend to the visual feature $F$ and non-biometrics textual feature $T_{\hat{b}}$ with query, key and value acting as Equation 3.
+
+$$
+Q _ {\hat {b}} = W z _ {\hat {b}}, \quad K _ {\hat {b}} = W [ F, T _ {\hat {b}} ], \quad V _ {\hat {b}} = W [ F, T _ {\hat {b}} ]. \tag {3}
+$$
+
+# 3.3. Identification Head
+
+The learned query embeddings $z_{b}, z_{m}$ and $z_{\hat{b}}$ go through mean pooling to form single vectors, denoted as $F_{b}, F_{\hat{b}}$ , and $F_{m}$ , among which only $F_{b}$ and $F_{m}$ is used for final identification.
+
+Loss Functions. During training, the model is optimized to refine $F_{b}$ using a combination of standard cross-entropy $(\mathcal{L}_{ID})$ , and triplet loss $(\mathcal{L}_{Tri})$ following [3, 19]. These losses are defined as Equation 4 and Equation 5.
+
+$$
+\mathcal {L} _ {I D} = - y \log \hat {y} \simeq \mathcal {L} _ {A c t}, \tag {4}
+$$
+
+$$
+\mathcal {L} _ {T r i} = \max \left(\mathcal {D} \left(F _ {b} ^ {a}, F _ {b} ^ {p}\right) - \mathcal {D} \left(F _ {b} ^ {a}, F _ {b} ^ {n}\right) + m, 0\right), \tag {5}
+$$
+
+Here, $y$ and $\hat{y}$ denote the ground truth and predicted labels. $F_{b}^{p}$ and $F_{b}^{n}$ represent the positive and negative biometrics features for an anchor biometrics feature $F_{b}^{a}$ within the same batch. $\mathcal{D}(\cdot)$ computes the Euclidean distance, and $m$ is the margin in the triplet loss.
+
+Since the motion feature $F_{m}$ contributes to identity recognition, it is explicitly trained to preserve motion-related information while remaining independent of biometrics attributes. The model is optimized for $F_{m}$ using the cross-entropy loss $(\mathcal{L}_{Act})$ of Equation 4.
+
+Furthermore, to reinforce the independence of biometrics and non-biometrics features, an orthogonality constraint is imposed between $F_{b}$ and $F_{\hat{b}}$ as Equation 6.
+
+$$
+\mathcal {L} _ {\text {O r t h}} = \left\| F _ {b} ^ {T} F _ {\hat {b}} \right\|. \tag {6}
+$$
+
+The overall loss function is defined as Equation 7.
+
+$$
+\mathcal {L} = \lambda_ {1} \mathcal {L} _ {I D} + \lambda_ {2} \mathcal {L} _ {\text {T r i}} + \lambda_ {3} \mathcal {L} _ {\text {O r t h}} + \lambda_ {4} \mathcal {L} _ {\text {A c t}}. \tag {7}
+$$
+
+Here, $\lambda_{i\in 1,\dots,4}$ , is weighting factor for each loss term.
+
+Identity Similarity Computation. To enhance identity matching, we introduce an adaptive weighting mechanism that integrates motion features into the similarity calculation, unlike traditional methods that rely solely on biometrics. Instead of fixed weights, we use a lightweight MLP to dynamically adjust the contribution of biometrics and motion features based on their relevance. Given a probe identity $A$ and gallery identity $B$ , we compute cosine similarities for both biometrics and motion features, concatenate them, and pass them through the MLP with ReLU activations and a softmax function. This enables the model to leverage motion cues to guide biometrics matching, prioritizing motion when it provides meaningful identity information and relying more on biometrics when motion cues are less discriminative. The final similarity score is computed as Equation 8.
+
+$$
+\operatorname {S i m} (A, B) = \alpha_ {1} \operatorname {S i m} _ {b} (A, B) + \alpha_ {2} \operatorname {S i m} _ {m} (A, B). \tag {8}
+$$
+
+Here, $\alpha_{i\in 1,2}$ are the weighting factors.
+
+Inference. DisenQ operates without textual supervision during inference, relying solely on the learned query embeddings acquired during training. It utilizes self-attention to retain query-specific information and cross-attention to extract relevant visual features, ensuring effective disentanglement of biometrics, non-biometrics and activity features purely from visual embeddings.
+
+# 4. Experiments
+
+Datasets: We evaluate our model on NTU RGB-AB, PKU MMD-AB, and Charades-AB, following [3]. NTU RGB-AB consists of 106 actors performing 94 actions across
+
+Table 1. Performance comparison of activity-based person identification on NTU RGB-AB, PKU MMD-AB, Charades-AB on same activity (denoted by Same) and cross activity (denoted by Cross) evaluation protocol. R@1 denotes Rank 1 accuracy. † denotes results produced in our environment. Bold and underline denotes best and second best results.
+
+| Methods | Venue | NTU RGB-AB | PKU MMD-AB | Charades-AB |
| Same | Cross | Same | Cross | Same | Cross |
| R@1 | mAP | R@1 | mAP | R@1 | mAP | R@1 | mAP | R@1 | mAP | R@1 | mAP |
| Models with only visual modality |
| TSF [28] | AAAI 20 | 71.8 | 31.8 | 67.8 | 26.9 | 76.4 | 37.5 | 71.6 | 33.2 | 35.4 | 21.9 | 30.2 | 19.0 |
| VKD [44] | ECCV 20 | 67.4 | 35.6 | 66.3 | 31.5 | 78.4 | 38.5 | 72.2 | 34.3 | 36.3 | 20.7 | 31.9 | 18.8 |
| BiCnet-TKS [25] | CVPR 21 | 72.7 | 34.5 | 69.1 | 30.2 | 80.8 | 38.5 | 77.1 | 33.3 | 40.3 | 27.3 | 38.3 | 23.3 |
| PSTA [51] | ICCV 21 | 67.4 | 34.8 | 65.1 | 31.4 | 77.4 | 50.4 | 72.4 | 47.4 | 42.9 | 28.3 | 38.7 | 24.8 |
| STMN [15] | ICCV 21 | 73.0 | 35.1 | 70.2 | 30.1 | 76.6 | 47.9 | 71.5 | 42.2 | 38.7 | 24.5 | 33.9 | 20.8 |
| SINet [6] | CVPR 22 | 69.4 | 30.7 | 66.2 | 27.8 | 79.6 | 40.8 | 74.1 | 26.2 | 40.3 | 26.9 | 37.3 | 21.9 |
| CAL [19] | CVPR 22 | 73.8 | 28.4 | 70.3 | 24.0 | 81.3 | 49.4 | 78.3 | 43.4 | 43.8 | 25.8 | 40.1 | 21.2 |
| Video-CAL [19] | CVPR 22 | 75.5 | 39.9 | 73.3 | 31.7 | 79.6 | 49.4 | 77.3 | 45.7 | 43.9 | 28.5 | 41.5 | 25.8 |
| PSTR [7] | CVPR 22 | 69.1 | 34.1 | 68.3 | 32.5 | 84.3 | 47.5 | 78.0 | 41.2 | 37.2 | 24.7 | 35.1 | 20.3 |
| AIM [55] | CVPR 23 | 71.4 | 35.4 | 72.8 | 30.2 | 82.5 | 48.9 | 79.2 | 44.9 | 40.1 | 28.3 | 35.6 | 26.7 |
| SCNet [20] | ACM MM 23 | 69.9 | 31.5 | 68.8 | 26.3 | 79.5 | 43.6 | 73.9 | 39.7 | 31.7 | 21.9 | 27.4 | 17.6 |
| ABNet [3] | CVPR 24 | 78.8 | 40.3 | 77.0 | 37.6 | 86.8 | 57.3 | 81.4 | 51.8 | 45.8 | 31.6 | 44.8 | 28.8 |
| Models with visual + language modality |
| CLIP ReID [32] † | AAAI 23 | 77.1 | 40.2 | 75.2 | 33.7 | 82.3 | 52.1 | 81.2 | 50.8 | 44.2 | 31.3 | 42.1 | 27.7 |
| CCLNet [10] † | ACM MM 23 | 75.2 | 36.1 | 74.3 | 33.1 | 83.2 | 51.4 | 80.1 | 47.5 | 42.1 | 29.3 | 38.8 | 23.4 |
| TF-CLIP [58] † | AAAI 24 | 77.3 | 41.2 | 74.8 | 31.3 | 83.4 | 52.3 | 80.8 | 50.1 | 40.2 | 28.1 | 39.7 | 26.0 |
| TVI-LFM [26] † | NeurIPS 24 | 76.2 | 38.1 | 75.9 | 34.1 | 85.2 | 53.9 | 81.5 | 52.1 | 45.7 | 30.1 | 42.8 | 28.3 |
| Instruct-ReID [22] † | CVPR 24 | 78.2 | 41.5 | 75.9 | 33.4 | 84.3 | 53.1 | 81.7 | 52.3 | 44.8 | 28.3 | 40.1 | 25.3 |
| EVA-CLIP [49] † | | 71.2 | 35.1 | 69.1 | 28.3 | 73.8 | 46.2 | 67.4 | 39.4 | 38.1 | 26.1 | 31.3 | 21.8 |
| Ours | | 82.2 | 43.8 | 80.9 | 41.3 | 89.2 | 59.3 | 84.1 | 56.9 | 49.9 | 34.8 | 48.4 | 32.5 |
+
+88.7k samples, while PKU MMD-AB includes 66 actors, 41 actions, and 17k samples. Charades-AB features 267 actors with 157 actions across 9.8k videos, averaging 6.8 activities per video. To assess the generalization capability of our model on more challenging real-world scenarios, we evaluate it on MEVID [12], which includes 158 actors and 8k tracklets, incorporating greater viewpoint, distance, and lighting variations, making it a more complex benchmark for video-based identification.
+
+Evaluation Protocol and Metrics: We follow the same evaluation protocol and dataset splits as [3] for NTU RGB-AB, PKU MMD-AB, and Charades-AB, employing two evaluation protocols: same-activity and cross-activity. Additionally, due to view information explicitly being available for NTU RGB-AB and PKU MMD-AB, we evaluate including and excluding same-view settings too. For MEVID, we use the official protocol and splits. We report rank 1, rank 5 accuracies and mAP as evaluation metrics.
+
+# 4.1. Implementation Details
+
+We use 8 frames which are randomly selected with a stride of 4 from each original video to create RGB clip. Each frame is resized to $224 \times 224$ and horizontal flipping is used for data augmentation, following [3, 18]. We use pretrained ViT G/14 from EVA-CLIP [49] as the visual encoder and BERT [13] as the frozen text encoder. Additionally,
+
+we use LLaVA 1.5 7B [36] as the frozen VLM to generate prompts. We initialize DisenQ with pre-trained weights from InstructBLIP [11]. We train the model for 60 epochs with a batch size of 32 with each batch containing 8 person and 4 clips for each person. AdamW is used as the optimizer with weight decay of $5e - 2$ and base learning rate of $1e - 4$ with $\beta$ values as [0.9, 0.999]. The triplet loss margin $m$ is set to 0.3, $\lambda_{i} \in [1,..,4]$ in Equation 7 is set as 0.01.
+
+# 4.2. Results
+
+Performance on activity-biometrics benchmarks. Table 1 presents the performance comparison of our framework against other existing methods. Across all datasets, our model outperforms the previous best-performing approach, improving Rank-1 accuracy and mAP across all evaluation protocols on NTU RGB-AB, PKU MMD-AB, and Charades-AB. Notably, we observe an average Rank-1 accuracy improvement of $3.7\%$ , $2.4\%$ and $3.9\%$ respectively on NTU RGB-AB, PKU MMD-AB, and Charades-AB, demonstrating the effectiveness of our approach. We present more results in supplementary.
+
+Generalization to traditional video-based benchmark. Table 2 presents the identification results of our model compared to concurrent methods on MEVID, a large-scale traditional video-based identification dataset primarily focused on walking sequences. Unlike NTU RGB-AB, PKU
+
+Table 2. Performance comparison of traditional person identification on MEVID in general evaluation setting. R@1 and R@5 denote rank 1 and rank 5 accuracies. † denotes reproduced results.
+
+| Methods | Venue | R@1 | R@5 | mAP |
| Models with only visual modality |
| Attn-CL [43] | AAAI 20 | 42.1 | 56.0 | 18.6 |
| Attn-CL + rerank [43] | AAAI 20 | 46.5 | 59.8 | 25.9 |
| AP3D [18] | ECCV 20 | 39.0 | 56.0 | 15.9 |
| TCLNet [24] | ECCV 20 | 48.1 | 60.1 | 23.0 |
| BiCnet-TKS [25] | CVPR 21 | 19.0 | 35.1 | 6.3 |
| STMN [14] | ICCV 21 | 31.0 | 54.4 | 11.3 |
| PSTA [51] | ICCV 21 | 46.9 | 60.8 | 21.2 |
| PiT [59] | TII 22 | 34.2 | 55.4 | 13.6 |
| CAL [19] | CVPR 23 | 52.5 | 66.5 | 27.1 |
| ShARc [62] | WACV 24 | 59.5 | 70.3 | 29.6 |
| ABNet [3]† | CVPR 24 | 58.3 | 68.4 | 30.1 |
| Models with visual + language modality |
| CLIP ReID [32]† | AAAI 23 | 51.2 | 64.2 | 28.3 |
| CCLNet [10]† | ACM MM 23 | 50.8 | 60.3 | 27.1 |
| TVI-LFM [26]† | NeurIPS 24 | 49.2 | 61.8 | 23.7 |
| Instruct-ReID [22]† | CVPR 24 | 53.8 | 59.4 | 28.4 |
| EVA-CLIP [49]† | | 53.1 | 59.2 | 26.9 |
| Ours | | 60.7 | 70.3 | 30.4 |
+
+MMD-AB, and Charades-AB, which contain diverse activities, MEVID lacks activity variability, making activity-based identification less impactful. Despite this, our model remains competitive, achieving a $1.2\%$ improvement in Rank-1 accuracy. This demonstrates that while our framework is designed for activity-biometrics, it generalizes well to traditional video-based identification scenarios by effectively disentangling identity from appearance, ensuring robust performance even in real-world unconstrained settings.
+
+# 4.3. Ablation Studies
+
+We conduct ablation studies on NTU RGB-AB and Charades-AB datasets on the same activity, including same view evaluation protocol and present the results in Table 3. While NTU RGB-AB provides a controlled setting with diverse clothing and activity variations; Charades-AB contains much more real-world complexity, including varied lighting, occlusions, and higher appearance variations, which better tests model generalization.
+
+Contribution of each component is presented in Table 3 (top). A vision encoder alone struggles due to entangled identity, appearance, and motion features leading to poor performance. Introducing text supervision via cross-attention and projecting features into distinct spaces improves identity retention by mitigating the influence of appearance variability. However, the most substantial gains come from DisenQ, which explicitly separates biometrics, non-biometrics, and motion features. By aligning separate learnable queries with structured textual priors, DisenQ establishes a well-structured feature representation that sig
+
+Table 3. Ablation studies for each component. Here, $F_{b}$ , $F_{b}$ and $F_{m}$ denote biometrics, non-biometrics and motion features.
+
+| Method | NTU RGB-AB | Charades-AB |
| Rank 1 | mAP | Rank 1 | mAP |
| Contribution of each component |
| Vision encoder | 73.2 | 36.2 | 40.1 | 29.2 |
| + Text encoder | 77.7 | 40.6 | 46.5 | 31.8 |
| + DisenQ | 82.2 | 43.8 | 49.9 | 34.8 |
| Ablation of different type of feature disentanglement |
| No disentanglement | 74.2 | 38.2 | 42.3 | 29.9 |
| Fb and Fb | 76.6 | 40.9 | 44.7 | 31.9 |
| Fb and Fm | 79.2 | 41.1 | 48.2 | 32.9 |
| Fb, Fb and Fm | 82.2 | 43.8 | 49.9 | 34.8 |
| Performance of each disentangled feature |
| Biometrics | 80.4 | 43.0 | 48.1 | 32.0 |
| Non-biometrics | 3.8 | 1.2 | 1.3 | 0.1 |
| Motion | 76.3 | 39.4 | 44.2 | 27.1 |
| Biometrics + Motion | 82.2 | 43.8 | 49.9 | 34.8 |
+
+nificantly enhances activity-biometrics performance.
+
+Ablation of different type of feature disentanglement, illustrated in Table 3 (middle) presents their individual impact on performance. When biometrics and non-biometrics features are disentangled, the model effectively mitigates clothing bias but struggles with variations in motion, resulting in improved yet suboptimal performance across different actions. Disentangling biometrics and motion features enhances stability by preserving identity-specific movement patterns, which are crucial for reliable identification across activities. The most comprehensive performance is achieved when all three feature types are disentangled, ensuring that identity-related features remain distinct while controlling appearance and motion influences.
+
+Individual performance of each disentangled feature, illustrated in Table 3 (bottom), provides further insights into their discriminative power for activity-based identification. Biometrics features alone exhibit the highest performance among each individual feature types, highlighting their intrinsic value in accurately identifying individuals. In contrast, non-biometric features significantly degrade performance, indicating that our disentanglement was effective in removing identity-related information from this feature space. Motion features offer moderate performance, providing additional context but lacking the distinctiveness of biometrics attributes. The synergy between biometric and motion features yields the most effective results, leveraging both identity cues and dynamic movement patterns for robust identification across challenging scenarios.
+
+# 5. Analysis and Discussion
+
+Effect of disentanglement on feature space. Figure 3 presents the impact of DisenQ on feature disentanglement
+
+
+No Disentanglement
+
+
+Ineffective Disentanglement
+
+
+Effective Disentanglement
+
+
+Figure 3. Impact of DisenQ on feature disentanglement. The left plot shows the feature space of vision encoder with no feature disentanglement, resulting in poor identity clustering. The middle plot shows an ineffective disentanglement using cross-attention and projection, where biometrics features remain mixed with non-biometrics, causing improper clustering. In contrast, the right plot demonstrates DisenQ-enabled disentanglement, achieving well-separated biometrics clusters, distinctly isolated from non-biometrics and motion features. Colors represent five identities across two activity classes.
+Figure 4. Performance analysis across activities (top 5 best and worst) on NTU RGB-AB. Here, bars and dots respectively represent person identification and action recognition accuracy.
+
+by comparing feature spaces before and after its application. Without DisenQ, feature separation relies on simple cross-attention and projection, resulting in overlapping clusters where biometric features mix with non-biometrics from different identities wearing similar clothing. In contrast, DisenQ effectively separates biometrics, non-biometrics, and motion features into distinct spaces with clear boundaries. DisenQ's structured separation ensures that biometrics clusters remain identity-specific and free from confounding appearance-based cues, leading to robust identification.
+
+Impact of design choice for disentanglement. We explore different architectural variations of DisenQ to evaluate the trade-off between complexity and effectiveness. A variant using three independent Q-Formers—each learning biometrics, non-biometrics, or motion features separately—yields only a marginal $0.23\%$ Rank-1 accuracy gain on NTU RGB-AB while tripling the parameter count, suggesting that our original design is already sufficient for disentanglement. To test whether additional parameters could still be beneficial, a deeper DisenQ variant with the same parameter count as the three-Q-Former setup results in a $3.8\%$ drop due to overfitting, indicating that simply increas
+
+ing model capacity does not guarantee better feature separation. These findings highlight that structured learning is more critical than model size, and our DisenQ architecture strikes an optimal balance between effectiveness, and computational cost for activity-based person identification.
+
+Performance analysis across activities. To examine the impact of different activities on person identification, we analyze performance across activity classes by identifying the five best and worst-performing actions. While activities involving significant body movements (e.g., running, jumping) provide distinctive motion patterns that aid recognition, they can introduce biases if overemphasized. Conversely, subtle activities (e.g., minor hand/head gestures) may lower accuracy due to weaker motion cues. Our findings (Figure 4) show that fixed weighting $(\alpha_{1} = \alpha_{2} = 0.5$ in Equation 8) of biometric and motion features can negatively affect identification for low-motion activities, whereas adaptive weighting ensures motion features contribute only when beneficial, stabilizing performance. Notably, highly distinctive actions retain high person identification accuracy even without explicit motion cues, confirming that motion serves as a complementary rather than dominant factor. Likewise,
+
+Table 4. Similarity of generated prompts across multiple runs on NTU RGB-AB subset. Sim. and Std. Dev. denotes mean cosine similarity and standard deviation.
+
+| Ft. | Sim. | St. Dev. |
| Tb | 0.92 | 0.03 |
| Tb | 0.79 | 0.12 |
| Tm | 0.68 | 0.17 |
+
+
+Figure 5. Feature space of generated motion prompts across multiple runs (NTU RGB-AB subset).
+
+challenging activities do not inherently degrade identification performance, as the model prioritizes biometrics features when necessary, ensuring balanced identification.
+
+Utility and quality of the generated prompts. To assess the impact of accurate textual prompts on disentanglement, we replace non-biometrics descriptions with random clothing details, leading to a $9.2\%$ drop in Rank-1 accuracy on NTU RGB-AB, highlighting the necessity of precise appearance descriptions. Additionally, we assess prompt consistency by generating descriptions for the same key-frame over five runs on a subset of NTU RGB-AB (10 identities and 10 action classes) and report the average results in Table 4. Biometrics descriptions remain highly stable, as indicated by high cosine similarity and low standard deviation, ensuring reliable identity representation. Non-biometrics descriptions also exhibit relative consistency, with minor variations. Motion descriptions exhibit the most variability, as different textual descriptions may be generated for the same action label. Figure 5 confirms that semantically similar motion prompts still cluster in the same feature space, ensuring consistency in representation.
+
+Choice of vision encoder and VLM. Our model supports various vision encoder architectures. To identify the best performer, we evaluated three popular vision encoders: SigLIP-L [60], ViT-1B from InternVideo2 [52], and ViTG/14 from EVA-CLIP [49] and find ViT-G/14 to be the best performing model (Table 5 (top)). Additionally, we show robustness of our approach across various VLMs, where we observe that changing the VLM does not contribute to significant changes ((Table 5 (bottom))), thus we select LLaVA for its efficiency and open-source property.
+
+Qualitative results. Figure 6 compares the top-2 rank retrieval results of our model with ABNet, the only other existing activity-biometrics method. As shown, ABNet often misidentifies individuals when they perform the same activity, indicating an over-reliance on motion cues. In contrast, our model, with adaptive motion weighting and effective disentanglement of biometrics, non-biometrics, and motion features, accurately identifies individuals by prioritizing biometrics features over activities. We present more qualitative example in supplementary.
+
+Table 5. Performance comparison of different vision encoders and VLMs for NTU RGB-AB and Charades-AB datasets.
+
+| Model | Size | NTU RGB-AB | Charades-AB |
| R1 | mAP | R1 | mAP |
| Vision encoders |
| SigLIP-L [60] | 0.3B | 80.2 | 41.6 | 48.3 | 33.7 |
| ViT-1B [52] | 1B | 83.4 | 42.1 | 49.2 | 34.7 |
| ViT-G/14 [49] | 1.8B | 82.2 | 43.8 | 49.9 | 34.8 |
| Visual Language Models (VLMs) |
| GPT-4V [39] | - | 82.3 | 43.7 | 49.8 | 34.9 |
| InstructBLIP [11] | 7B | 82.1 | 43.8 | 49.7 | 34.8 |
| LLaVA 1.5 [36] | 7B | 82.2 | 43.8 | 49.9 | 34.8 |
+
+
+
+
+
+
+
+
+
+
+Figure 6. Top-2 rank retrieval comparison of our model and ABNet [3]. For a given probe image (left), the middle two images show incorrect matches retrieved by ABNet due to its overreliance on activities, while the right two images show correct matches retrieved by our model, which effectively disentangles biometrics features from motion cues.
+
+
+
+
+
+
+
+# 6. Conclusion
+
+In this work, we introduce a multimodal Disentangling Querying (DisenQ) Transformer based framework for activity-biometrics, where individuals are identified across diverse activities. Our framework leverages structured language guidance to disentangle biometrics, non-biometrics, and motion cues without additional visual modalities. By performing feature disentanglement, DisenQ ensures that biometrics features remain invariant to non-biometrics information, and motion cues enhance identification without overshadowing stable identity traits. An adaptive weighting mechanism dynamically balances biometrics and motion contributions for reliable identity retrieval. Our approach surpasses existing methods on activity-based benchmarks and generalizes well to traditional video-based identification, demonstrating the importance of effective feature disentanglement in activity-aware person identification.
+
+# 7. Acknowledgement
+
+This research is based upon work primarily supported by the National Science Foundation under Grant No. 2331319. Any opinions, findings, and conclusions or recommendations contained herein are those of the authors and should not be interpreted as necessarily representing the views, either expressed or implied, of the National Science Foundation.
+
+# References
+
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+# Disentangled Clothed Avatar Generation with Layered Representation
+
+Weitian Zhang $^{1}$ Yichao Yan $^{1\dagger}$ Sijing Wu $^{1}$ Manwen Liao $^{2}$ Xiaokang Yang $^{1}$ $^{1}$ MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University
+ $^{2}$ The University of Hong Kong
+
+1{weitianzhang, yanyichao, wusijing, xkyang}@sjtu.edu.cn
+
+2{manwen}@connect.hku.hk
+
+
+(a) Disentangled Clothed Avatar Generation
+
+
+
+
+(b) Animation
+
+
+Figure 1. We propose LayerAvatar to efficiently generate diverse clothed avatars with components fully disentangled. The generated avatars can be animated and synthesized in novel views. They can also be decomposed into body, hair, and clothes for component transfer.
+
+
+
+
+(c) Camera View Control
+
+
+
+
+
+
+
+
+(d) Decomposition
+
+
+(e) Component Transfer
+
+# Abstract
+
+Clothed avatar generation has wide applications in virtual and augmented reality, filmmaking, and more. While existing methods have made progress in creating animatable digital avatars, generating avatars with disentangled components (e.g., body, hair, and clothes) has long been a challenge. In this paper, we propose LayerAvatar, a novel feed-forward diffusion-based method capable of generating high-quality component-disentangled clothed avatars in seconds. We propose a layered UV feature plane representation, where components are distributed in different layers of the Gaussian-based UV feature plane with corresponding semantic labels. This representation can be effectively learned with current feed-forward generation pipelines, facilitating component disentanglement and en
+
+hancing details of generated avatars. Based on the well-designed representation, we train a single-stage diffusion model and introduce constrain terms to mitigate the severe occlusion issue of the innermost human body layer. Extensive experiments demonstrate the superior performances of our method in generating highly detailed and disentangled clothed avatars. In addition, we explore its applications in component transfer. The project page is available at https://olivia23333.github.io/LayerAvatar.
+
+# 1. Introduction
+
+The creation of digital avatars has various applications [2, 13] in virtual and augmented reality, filmmaking, and more. Traditional graphics-based pipelines require extensive effort from 3D artists to construct a single digital avatar. To reduce tedious manual labor and facilitate mass production, learning-based methods aiming at generating digital avatars
+
+automatically have been widely explored recently.
+
+Recent learning-based methods [3, 16, 77] mainly combine 3D representations [28, 39, 55, 64] with generation pipelines (e.g., 3D-aware GANs [4, 5, 43] and diffusion models [47, 52]) to create digital avatars. However, most of these methods often ignore the compositional nature of digital avatars and represent the human body, hair, and clothes as a whole, which limits their capabilities in digital avatar customization such as cloth transfer. Neural-ABC [7] and SMPLicit [14] provide parametric model with disentangled clothes and human body. However, modeling texture are leaved an un-explored problem. HumanLiff [23] proposes a layer-wise generation process that first generates clothed avatars in minimal clothes, then generates digital avatars wearing the next layer of clothing conditioned on the current layer. Nevertheless, the human body and clothes are not fully disentangled, which makes it difficult to extract the components of each layer, thus reducing the editing ability. In addition, some methods [15, 18, 59, 63, 66] follow the trend of DreamFusion [49] to achieve disentangled clothed avatar generation by learning each component of digital avatars separately through the prior knowledge of 2D diffusion models [52] in an optimization manner. These methods can generate clothed avatars with each component disentangled, however, they take hours to generate a single digital avatar, and the optimization time will increase linearly according to the number of components.
+
+In this paper, we propose LayerAvatar, a novel feedforward diffusion-based method that achieves (1) component disentanglement, enabling seamless transfer of individual components such as clothes, hair, and shoes; (2) high-quality results, with generated avatars exhibiting intricate facial details, distinct fingers, and realistic cloth wrinkles; and (3) efficiency, requiring only seconds to generate a single avatar. We choose 3D Gaussians [28] as the underlying representation due to its high-quality rendering results for intricate details, and strong representation capability for diverse cloth types. However, naively representing the disentangled clothed avatar using 3D Gaussians is impractical due to its unstructured nature that is incompatible with most current feed-forward generation pipelines [5, 52]. Therefore, we introduce a Gaussian-based UV feature plane, in which 3D Gaussians are projected into a predefined 2D UV space shared among subjects. The attributes of each 3D Gaussian are encoded as local geometry and texture latent features, which can be obtained from the 2D feature plane via bilinear interpolation. Furthermore, to achieve full disentanglement of avatar components (hair, shoes, upper cloth) and higher generation quality, we represent avatar components in separate layers of the UV feature plane which provides neighboring components with distinctive features from different layers to facilitate decomposition.
+
+To generate the layered representation in a feed-forward
+
+manner, we elaborately train a single-stage diffusion model [6] from multi-view 2D images. To fully disentangle each component and ensure plausible avatar generation results, we employ supervision both in the individual components and the entire compositional clothed avatar. Moreover, several prior losses are utilized to constrain the smooth surface and reasonable color of the severely occluded human body.
+
+We evaluate LayerAvatar on multiple datasets [9, 20, 74], demonstrating its superior performance in generating disentangled avatars. We also explore its application in component transfer. In summary, our main contributions are:
+
+- We introduce LayerAvatar, a novel feed-forward clothed avatar generation pipeline with each component disentangled, enhancing the controllability of avatar generation.
+- We propose a layered UV feature plane representation that enhances generation quality and facilitates the disentanglement of each component.
+- Our method achieves outstanding generation results on multiple datasets and support downstream applications such as component transfer.
+
+# 2. Related work
+
+Diffusion in 3D Generation. Encouraged by the success of diffusion model [52] in 2D image generation area, researchers have attempted to extend it to 3D generation tasks. These works can be divided into two categories, feed-forward and optimization-based methods. Optimization-based methods [8, 32, 33, 49, 50, 61, 67], represented by DreamFusion [49], utilize SDS loss to distill prior knowledge of 2D diffusion model to supervise 3D scenes. These methods often suffer from oversaturation and Janus problems. Thus, improved SDS loss [67] and camera-conditional [35] or multi-view diffusion models [56] are introduced to mitigate these problems. Moreover, optimization-based methods usually take hours to generate a single object, which hinders its application in real life. On the other hand, feed-forward methods [37, 69, 75, 78, 82] directly learn diffusion model for 3D representations, such as points [42, 76], voxels [51], meshes [37, 72], and implicit neural representations [22, 41, 57]. These methods can generate 3D objects in seconds. Several attempts [12, 25, 79, 80] have been made to adapt them to the field of digital human generation. Different from most previous works, we regard digital avatars as a composition of multiple components instead of a unified whole and learn a diffusion model on the proposed layered representation.
+
+Clothed Avatar Generation. Inspired by general 3D object generation, many methods [3, 12, 16, 21, 44, 81] introduce 3D-aware GANs [5] and diffusion models [52] for clothed avatar generation. These methods first learn clothed avatars in canonical space and then animate them to posed space using a deformation module. Following EG3D [5], some methods [77, 81] apply triplane features to represent
+
+
+Figure 2. Method overview. LayerAvatar learns a feed-forward diffusion model to generate clothed avatars with each component disentangled. The clothed avatars are represented as layered UV feature plane where components are represented separately. After decoding the feature plane into attribute maps, we can extract 3D Gaussians from them through SMPL-X-based templates. Generated clothed avatars are then transformed into targeted pose space for further supervision. Reconstruction loss and constraint loss are both utilized to facilitate the disentanglement and handle the severe occlusion of human body layer.
+
+clothed avatars for higher quality and utilize inverse skinning for animation. AG3D [16] introduces forward skinning technique [10, 11] to achieve robust animation including loose clothing. On the other hand, Chupa [30] and Avatar-Popup [31] apply diffusion models to learn front and back view image pairs and then lift them to 3D space. Despite their impressive success, most of these methods represent clothed avatars as an entity and fail to disentangle the human body and clothes. Recently, some optimization-based methods [15, 18] achieved success in generating cloth-disentangled avatars, however, the generating process takes hours to generate a single avatar.
+
+Compositional Avatar Representation. Instead of representing avatars [40, 68, 73] as a single entity, some methods represent clothed avatars as a combination of multiple submodules. COAP [38], Spams [45] and DANBO [58] consider human avatars as a composition of body parts, while EVA3D [21] and ENARF-GAN [44] follow this trend and utilize multiple neural networks to represent different body parts of the digital avatar, achieving more efficient and detailed generation results. Several methods [1, 23, 71] represent clothed avatars as separate layers to enable the expressiveness of various topologies. However, these methods ignore the disentanglement of human body and clothes, which makes each submodule less physically meaningful. Recently, some works [17, 34, 48, 70, 83] disentangle the human body and clothes by representing each component
+
+separately. During the rendering process, these components are combined through various compositional rendering techniques. Most of these methods are designed to optimize a single digital avatar. In this paper, we propose a novel layered UV feature plane representation that is compatible with feed-forward generation framework.
+
+# 3. Method
+
+We propose LayerAvatar, a feed-forward generative method for disentangled clothed avatar generation. The overview of our method is illustrated in Fig. 2. We provide a brief introduction for prior knowledge in Sec. 3.1. To achieve disentangled clothed avatar generation, we propose a novel layered UV feature plane representation (Sec. 3.2), which facilitates disentanglement and is compatible with current feed-forward generative pipelines. The clothed avatars are generated in canonical space and then deformed to targeted pose space via deformation module (Sec. 3.3). The training process is introduced in Sec. 3.4.
+
+# 3.1. Preliminary
+
+SMPL-X [46] is an expressive parametric human model that can produce naked human meshes $M(\beta, \theta, \psi)$ given shape parameter $\beta$ , pose parameter $\theta$ , and expression pa
+
+rameter $\psi$ . The producing process can be formulated as:
+
+$$
+T (\beta , \theta , \psi) = T _ {c} + B _ {s} (\beta ; s) + B _ {e} (\psi ; e) + B _ {p} (\theta ; p), \tag {1}
+$$
+
+$$
+M (\beta , \theta , \psi) = L B S (T (\beta , \theta , \psi)), J (\beta), \theta , \mathcal {W}),
+$$
+
+where a canonical human mesh $T$ is first calculated as a combination of the mean shape template $T_{c}$ and vertex displacements $(B_{s}(\beta ;s), B_{e}(\psi ;e), B_{p}(\theta ;p))$ computed by the blend shapes $s, e, p$ and their corresponding pose, shape, and expression parameters. The body template $T$ is then deformed to the given pose by linear blend skinning(LBS) based on the skinning weights $\mathcal{W}$ and joint locations $J(\beta)$ . 3D Gaussians [28] is a primitive-based explicit representation that combines the strengths of both previous explicit and implicit representations. It consists of a set of learnable 3D Gaussian primitive $\mathcal{G}_k$ where each contains five attributes: position $\mu$ , scaling matrix $\mathbf{S}$ , rotation matrix $\mathbf{R}$ , opacity $\alpha$ , and color $\mathbf{c}$ . In practice, we employ diagonal vector $\mathbf{s} \in \mathbb{R}^3$ and axis-angle $\mathbf{r} \in \mathbb{R}^3$ to represent $\mathbf{S}$ and $\mathbf{R}$ respectively. 3D Gaussians are represented as ellipses in 3D space defined by their position $\mu$ and covariance matrix $\boldsymbol{\Sigma} = \mathbf{R}\mathbf{S}\mathbf{S}^{T}\mathbf{R}^{T}$ . During the rendering process, these 3D Gaussians are projected to a 2D image plane where the pixel color $\mathbf{C}$ can be calculated as follows:
+
+$$
+\mathbf {C} = \sum_ {i = 1} ^ {N} \mathbf {c} _ {i} \sigma_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \sigma_ {j}), \tag {2}
+$$
+
+where $\mathbf{c}_i$ is the color of the $i$ -th 3D Gaussian on the ray, and $\sigma_i$ is the blending weight calculated with the opacity $\alpha$ .
+
+# 3.2. Layered UV Feature Plane Representation
+
+Previous methods mainly represent avatars as a single entity or depend on optimization-based schemes. As a result, the generated results often have difficulty with editing or are slow to create, typically taking hours to generate a single subject. To address these limitations, we propose a layered UV feature plane representation that can separate components of clothed avatars and is compatible with fast, feedforward generation pipelines. We employ 3D Gaussians as the base representation for efficient rendering along with easy animation and editing.
+
+To enable disentanglement, we consider clothed avatars as a composition of human body and exterior components.
+
+$$
+\mathcal {G} _ {\text {a v a t a r}} = \left\{\mathcal {G} _ {\text {b o d y}}, \mathcal {G} _ {\text {t o p}}, \mathcal {G} _ {\text {b o t t o m}}, \mathcal {G} _ {\text {h a i r}}, \mathcal {G} _ {\text {s h o e s}} \right\}. \tag {3}
+$$
+
+Each component is represented as a set of Gaussian primitives $\mathcal{G}_i$ parameterized with five attributes: 3D position $\pmb{\mu}_i\in \mathbb{R}^3$ , opacity $\alpha_{i}\in \mathbb{R}$ , rotation matrix $\mathbf{R}_i$ represented by axis angle $\mathbf{r}_i\in \mathbb{R}^3$ , scale matrix $\mathbf{S}_i$ represented by diagonal vector $\mathbf{s}_i\in \mathbb{R}^3$ and rgb color $\mathbf{c}_i\in \mathbb{R}^3$ . Inspired by existing works [24, 80] that initialize 3D Gaussians by attaching them to SMPL parametric model for geometry and animation prior. We initialize the 3D Gaussians of each component by attaching them to self-designed templates based
+
+on SMPL-X. For each component, we design a template that maximizes coverage of the region where the component may exist. To enhance generation quality, all templates are subdivided to support densified Gaussian primitives. Then, we initialize the positions of 3D Gaussians as the center points of faces on the densified template mesh. And the initial rotations of 3D Gaussians are set as the tangent frame of the faces, which consists of the normal vector of that face, the direction vector of one edge and their cross product.
+
+For compatibility with feed-forward generation pipelines, previous methods typically project 3D Gaussians into 2D space (e.g., multi-view image space [60, 62], UV space [80]). Unlike these methods, which represent the entire subject as a single entity and then employ a post-processing step for disentanglement, we directly model components separately by mapping their templates into a three-layer UV space, combined with semantic labels. The first layer represents the innermost part of the human body, the second layer represents the hair and shoes, and the third layer represents top and bottom clothes. Following [80], all Gaussian attributes are stored as local UV features to enhance generation quality. The UV features plane is first split into two parts in a channel-wise manner and then decoded by two light-weight shared MLP decoders $\mathcal{D}_g$ and $\mathcal{D}_t$ separately. $\mathcal{D}_g$ decodes the geometry-related attributes: position offset $\Delta \mu$ and opacity $\alpha$ of 3D Gaussians and $\mathcal{D}_t$ predicts texture-related attributes, color c and covariance-related rotation $\Delta \mathbf{r}$ and scale $\Delta s$ . Given the decoded attribute maps, we can extract the attributes for each 3D Gaussian $\mathcal{G}_i$ via bilinear interpolation. The opacity value $\alpha_{i}$ and color value $\mathbf{c}_i$ are obtained directly, and the other values are obtained via following formula based on their initial values:
+
+$$
+\boldsymbol {\mu} _ {i} = \boldsymbol {\mu} _ {i} ^ {0} + \Delta \boldsymbol {\mu} _ {i}, \quad \mathbf {s} _ {i} = \mathbf {s} _ {i} ^ {0} \cdot \Delta \mathbf {s} _ {i}, \quad \mathbf {r} _ {i} = \mathbf {r} _ {i} ^ {0} \cdot \Delta \mathbf {r} _ {i}, \tag {4}
+$$
+
+where $\pmb{\mu}_i^0$ , $\mathbf{s}_i^0$ , and $\mathbf{r}_i^0$ are initial position, scale, and rotation values for 3D Gaussians, respectively. $\Delta \pmb{\mu}_i$ , $\Delta \mathbf{s}_i$ and $\Delta \mathbf{r}_i$ are predicted residuals extracted from attribute maps. By collecting the attributes of 3D Gaussians with the same semantic label, we can obtain a canonical space representation of each component, and their composition forms the complete disentangled clothed digital avatar.
+
+# 3.3. Deformation
+
+Benefiting from the SMPL-X-based templates, our method supports deformation in body shapes and novel poses including gestures and facial expressions. To support training with multiple subjects in various body shapes, we disentangle the body shape factor by defining all the templates in a canonical space with neutral body shapes. The neutral body shape avatar and its corresponding components can be transformed into targeted body shape space via the follow-
+
+ing warping process:
+
+$$
+\bar {\boldsymbol {\mu}} = \boldsymbol {\mu} + B _ {s} (\beta , s, \boldsymbol {\mu}), \tag {5}
+$$
+
+where $\bar{\mu}$ represents the position of 3D Gaussians in the targeted $\beta$ body shape space and $B_{s}(\beta ,s,\pmb {\mu})$ are corresponding body shape related offsets extracted from the SMPL-X based templates via barycentric interpolation. We further add pose-dependent offsets $B_{p}(\theta ,p,\pmb {\mu})$ and facial expression offsets $B_{e}(\psi ,e,\pmb {\mu})$ in the same way to ensure accurate animation results.
+
+The animation of a generated avatar from the canonical T-pose to an arbitrary target pose can be regarded as transforming the 3D Gaussian attributes. During the animation process, the opacity $\alpha$ and color $\mathbf{c}$ of 3D Gaussians remain unchanged. Therefore, we only discuss the transformation of position $\mu$ , rotation matrix $\mathbf{R}$ and scale matrix $\mathbf{S}$ in this section. Using the LBS function, we can transform the position $\bar{\mu}$ of 3D Gaussians as:
+
+$$
+\boldsymbol {\mu} ^ {\prime} = \sum_ {i = 1} ^ {n _ {b}} w _ {i} \mathbf {B} _ {i} \bar {\boldsymbol {\mu}}, \tag {6}
+$$
+
+where $n_b$ represents the number of joints and $\mathbf{B}_i$ is the transformation matrix of the $i$ -th joint. For 3D Gaussians on the innermost human body layer, the corresponding blend skinning weights $w$ are obtained directly from SMPL-X-based templates through barycentric interpolation, as these regions usually undergo minimal topology changes. For 3D Gaussians representing the exterior components, we follow [16] to extract the skinning weights from a pre-computed low-resolution volumetric field of fused skinning weights, which is more stable for points that deviate significantly from the original template. $\mathbf{T} = \sum_{i=1}^{n_b} w_i \mathbf{B}_i$ is the blended transformation matrix, and the rotation matrix $\mathbf{R}$ is updated via $\mathbf{R}' = \mathbf{T}_{1:3,1:3} \mathbf{R}$ , where $\mathbf{T}_{1:3,1:3}$ is the rotational part of $\mathbf{T}$ . The scale matrix $\mathbf{S}$ is recalculated in the targeted pose space to fit deformed topology.
+
+# 3.4. Learning Disentangled Clothed Avatar
+
+To mitigate the impact of occlusion, we adopt a single-stage training scheme [6], which is more robust in occluded and sparse view situations. Specifically, the layered UV feature plane fitting and diffusion training process is conducted simultaneously, and the UV feature plane is jointly optimized by the fitting and diffusion loss. Similar to the SDS loss [49], the diffusion loss provides a diffusion prior for the UV feature plane, thereby facilitating the completion of unseen regions in the training images.
+
+Layered UV Feature Plane Fitting. Given multi-view images, we optimize the layered UV feature plane and shared decoders to reconstruct avatars with disentangled components. The objective function can be divided into reconstruction and constraint part. The reconstruction loss $\mathcal{L}_{\mathrm{recon}}$
+
+can be formulated as follows:
+
+$$
+\mathcal {L} _ {\text {r e c o n}} = \lambda_ {\text {c o l o r}} \cdot \mathcal {L} _ {\text {c o l o r}} + \lambda_ {\text {m a s k}} \cdot \mathcal {L} _ {\text {m a s k}} + \lambda_ {\text {p e r}} \cdot \mathcal {L} _ {\text {p e r}} + \lambda_ {\text {s e g}} \cdot \mathcal {L} _ {\text {s e g}}. \tag {7}
+$$
+
+To achieve the disentanglement between exterior components and human body, we not only minimize the color loss $\mathcal{L}_{\mathrm{color}}$ and mask loss $\mathcal{L}_{\mathrm{mask}}$ on the overall rendering result, but also perform supervision on each component. Specifically, we first render the 3D Gaussians corresponding to each component separately to obtain multi-view images of each component. Then, inspired by Clothedreamer [36], instead of blending the rendering results of these components via estimated depth order to obtain the rendering results of clothed avatars, we directly render all the 3D Gaussians to alleviate artifacts caused by the blending process. The silhouette masks of each component and the clothed avatar are obtained similarly. The ground truth of silhouette masks is estimated based on the semantic segmentation results predicted by Sapiens [29]. We apply Huber loss [26] for both $\mathcal{L}_{\mathrm{color}}$ and $\mathcal{L}_{\mathrm{mask}}$ following SCARF [17], due to its robustness to the estimated noisy segmentation results. To enhance the details of generated results, we also employ a perceptual loss $\mathcal{L}_{\mathrm{per}}$ [27] to minimize the difference between extracted features of rendered outputs and targeted images.
+
+Components in overlapping regions may learn inverted color or opacity values due to incorrect depth ordering. To address this, we render semantic segmentation maps of the clothed avatar by assigning the segmentation label of each Gaussian as its color. We then minimize the distance to the predicted semantic segmentation map using the Huber loss, $\mathcal{L}_{\mathrm{seg}}$ , to encourage accurate depth ordering.
+
+Due to the severe occlusion of the inner human body layer, we apply constraints on the geometry and texture of the human body to obtain reasonable results. Since the human body is always within the exterior layer, we employ the following constraints:
+
+$$
+\mathcal {L} _ {\text {m a s k i n}} = \lambda_ {\text {m a s k i n}} \operatorname {R e L U} \left(\mathcal {R} _ {m} ^ {b} \left(\mathcal {G} _ {\text {b o d y}}\right) - M _ {\mathrm {f g}}\right), \tag {8}
+$$
+
+where $\mathcal{R}_m^b (\mathcal{G}_{\mathrm{body}})$ represents the rendered silhouette of the human body, and $M_{\mathrm{fg}}$ is the estimated foreground silhouette mask. When rendering $\mathcal{R}_m^b (\mathcal{G}_{\mathrm{body}})$ , we detach the opacity values and set them to 1, only optimizing offset and covariance-related attributes, preventing the model from minimizing the loss via decreasing opacity on the boundary. Utilizing the prior that the occluded skin color should be similar to the color of hands, we introduce the following texture constraint:
+
+$$
+\mathcal {L} _ {\text {s k i n}} = \lambda_ {\text {s k i n}} \left(M _ {\text {o c}} \odot \left(\mathcal {R} _ {m} ^ {b} \left(\mathcal {G} _ {\text {b o d y}}\right) - \mathbf {C} _ {\text {s k i n}}\right)\right), \tag {9}
+$$
+
+where $\mathbf{C}_{\mathrm{skin}}$ is the average color of pixels in the hands region and $M_{\mathrm{oc}}$ is the mask of the occluded region. Other regularization terms are as follows:
+
+$$
+\mathcal {L} _ {\text {r e g}} = \lambda_ {\text {o f f s e t}} \mathcal {L} _ {\text {o f f s e t}} + \lambda_ {\text {s m o o t h}} \mathcal {L} _ {\text {s m o o t h}}. \tag {10}
+$$
+
+$\mathcal{L}_{\mathrm{offset}} = \|\Delta_{\mu}\|^2$ constrains the offset from being extremely large. $\mathcal{L}_{\mathrm{smooth}}$ is the total variational (TV) loss, which is used to minimize the average $L_2$ distance between neighboring pixels on attribute maps. This regularization term encourages smooth transitions between the neighboring attributes (e.g. offsets, rotation, and opacity), promoting the generation of reasonable texture and geometry surface.
+
+Disentangled Clothed Avatar Diffusion Model. To generate disentangled clothed avatars, we train a diffusion model that maps Gaussian noise to the layered UV latent space. Since diffusion models generally perform better on inputs with low channel dimensions [53], we concatenate our layered UV feature plane across widths instead of stacking them across channels. During training, we first obtain destructed UV feature plane $x_{t}$ by adding Gaussian noise $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ to the layered UV feature plane $x_{0}$ according to following noise schedule:
+
+$$
+\boldsymbol {x} _ {t} := \alpha (t) \boldsymbol {x} _ {0} + \sigma (t) \boldsymbol {\epsilon}, \tag {11}
+$$
+
+where $\alpha(t)$ and $\sigma(t)$ are predefined functions that control the intensity of added noise, and $t$ is the time step in the range of [0, 1]. To stabilize and accelerate training, we use v-prediction proposed in [54] to train the denoising UNet. The objective function for the diffusion model is:
+
+$$
+\mathcal {L} _ {\text {d i f f}} = \underset {t, \boldsymbol {x} _ {0}, \epsilon} {\mathbb {E}} \left[ \frac {1}{2} w (t) \| \hat {\boldsymbol {x}} _ {0} - \boldsymbol {x} _ {0} \| ^ {2} \right], \tag {12}
+$$
+
+where $w(t) = (\alpha (t) / \sigma (t))^{2\omega}$ , the $\omega$ is set to 0.5 following [6]. $\mathcal{L}_{\mathrm{diff}}$ is used to update not only the parameters of denoising UNet, but also the UV feature plane. It promotes the UV feature plane to adapt to the learned latent space, thereby providing priors for occluded regions.
+
+# 4. Experiments
+
+Baselines. To evaluate holistic generation quality, we compare our method with the state-of-the-art methods of animatable avatar generation (EVA3D [21], StructLDM [25], and E3Gen [80]) on THuman2.0 [74] dataset. We then evaluate the decomposition capability of our method by comparing the layer-wise generation results with the disentanglement-related method HumanLiff [23] on Tightcap [9] dataset. And we further evaluate the component generation quality against optimization-based methods: LAGA [18], SO-SMPL [63], and TELA [15]. Our method is trained on a composite dataset including CustomHuman [20], THuman2.0 [74], and THuman2.1 [74].
+
+Metrics. For holistic generation quality evaluation, we utilize FID [19] following previous works [5, 25, 80]. For layer-wise generation results, we adopt FID for overall generation quality evaluation and L-PSNR [23] for disentanglement capability evaluation, which calculates the PSNR between two layers with the adding component masked. Additionally, we conduct a user study with 20 participants to
+
+compare the generation quality and disentanglement quality of our methods with optimization-based methods.
+
+Dataset. For THuman2.0 [74], we sample 500 scans and render each from 54 camera views to obtain multi-view images. Then, we employ Sapiens [29] to estimate segmentation masks for these images, from which per-component silhouette masks can be extracted. This approach enables our method to learn directly from multi-view images without requiring separate meshes of each component, thereby simplifying the data collection process. Tightcap [9] contains 3D scans with separate meshes for cloth and shoe, which facilitates direct rendering of multi-view images and silhouette masks for each component. For a fair comparison, we use the preprocessed version provided by HumanLiff [23], which selects 107 samples from Tightcap. Each sample is rendered from 158 camera views, providing images and silhouette masks for both the entire avatar and each component. We also construct a composite dataset consisting of 1954 selected scans from THuman2.0 [74], THuman2.1 [74], and CustomHuman [20] datasets. Each scan is processed in the same way as the THuman2.0 data. Additionally, all SMPL-X parametric models are standardized to neutral gender with refinement in body shape parameters to ensure the body layer fits underneath the cloth surface.
+
+# 4.1. Evaluation of Generation Quality and Disentanglement Capability
+
+Disentanglement and Animation Capacities. The disentanglement and animation results are shown in Fig. 1. Our method successfully generates clothed avatars with full disentanglement of components such as hair, shoes, and clothes from the human body. Moreover, our method reconstructs the inner body layer with reasonable geometry and texture under severe occlusion. Benefiting from the SMPL-X-based templates within our layered Gaussian-based UV feature plane representation, each component can be easily deformed into novel poses.
+
+Comparisons. For holistic generation quality, we compare our method against representative feed-forward diffusion and 3D-aware GAN pipelines. The quantitative comparison results are shown in Tab. 1a. Our method outperforms all baselines on THuman2.0 [74] dataset, achieving the best FID score. The visual comparisons shown in Fig. 3 further enhance the superiority of our method. EVA3D [21] struggles with generating digital avatars with plausible texture and geometry. Compared to StructLDM [25] and E3Gen [80], our method exhibits finer details, such as distinctive fingers, realistic cloth wrinkles, and intricate faces.
+
+To evaluate disentanglement capability, we compare layer-wise generation results and disentangled avatar generation results of our method with state-of-the-art methods. For layer-wise generation, our method surpasses other methods in both FID and L-PSNR, as shown in Tab. 1b,
+
+| Methods | FID↓ |
| EVA3D [21] | 124.54† |
| StructLDM [25] | 25.22† |
| E3Gen [80] | 15.78★ |
| Ours | 12.50 |
+
+(a) Holistic Generation Quality.
+
+| Methods | FID↓ | L-PSNR↑ |
| EVA3D [21] | 61.58* | <20* |
| Rodin [65] | 56.57* | 18.12* |
| HumanLiff [23] | 54.39* | 28.57* |
| Ours | 17.37 | >40 |
+
+(b) Layer-wise Generation Quality.
+
+| Methods | Disentanglement↑ | Quality↑ | Time↓ |
| SO-SMPL [63] | 13.02 | 3.57/8.57 | 5h |
| LAGA [18] | 9.77 | 5.00/1.43 | 1.5h |
| TELA [15] | 19.07 | 14.29/8.57 | 6h |
| Ours | 58.14 | 77.14/81.43 | 2s |
+
+
+Figure 3. Qualitative comparison. The left part demonstrates our generation results on THuman2.0 dataset [74]. The middle part illustrates layer-wise generated results on Tightcap dataset [9]. Our method can generate more reasonable human bodies under severe occluded scenarios. The right part exhibits our component generation results compared with optimization-based methods.
+
+
+
+
+
+which indicates that our method achieves higher holistic generation results and can generate disentangled avatars without facing the identity shifting problem. The elimination of identity shifting demonstrates that our method achieves full disentanglement of components, since entangled components will result in shifting problems. As shown in Fig. 3, Rodin [65] struggles to maintain identity consistency during the generation process. Although Human-Liff [23] achieves correct layer-wise generation, it produces less smooth body geometry and exhibits subtle identity shifting, shown by the enlarged face region. Our method can generate each layer without shifting problems, demonstrating more complete disentanglement.
+
+For disentangled avatar generation, we compare our method with state-of-the-art optimization-based methods. As shown in Tab. 1c, our method generates clothed avatars in significantly less time and achieves a higher user preference. Qualitative comparisons are illustrated in Fig. 3. SO-SMPL [63] generates unrealistic, cartoonish colors and exhibits unnatural sawtooth on the border of generated com
+
+(c) Component Quality and Disentanglement Evaluation.
+Table 1. Quantitative comparison. Our method outperforms other methods in both holistic and layer-wise generation quality, as well as disentanglement capability. Due to the minor difference between the two masked layers, the L-PSNR value of our method is so large that we use $>40$ to express it. For component comparison, we show the quality preference in component quality preference/overall quality preference format. *, † and * denote results adopted from HumanLiff [23], StructLDM [25] and E3Gen [80] respectively.
+
+| Methods | FID↓ | KID ↓ |
| Two-stage | 19.06 | 15.40 |
| Pipeline (SLMO) | 30.83 | 30.18 |
| Pipeline (SLMN) | 28.95 | 29.21 |
| Full pipeline | 12.50 | 9.39 |
+
+Table 2. Ablation study on THuman2.0 Dataset. The full pipeline outperforms baselines on both FID and KID by a large margin.
+
+ponents (highlighted by orange circles). LAGA [18] and TELA [15] struggle with blurry fingers, oversaturated colors, and incomplete disentanglement from the body layer. In contrast, our method generates fully disentangled avatars with distinctive fingers and realistic color.
+
+# 4.2. Ablation Study
+
+# Layered vs. Single-Layer Representation.
+
+To demonstrate the effectiveness of our layered UV feature plane, we design two baselines that use single-layer UV feature plane to generate disentangled clothed avatars.
+
+
+Figure 4. Ablation study on THuman2.0 Dataset. Comparing randomly generated avatars and decomposition results, our method generates avatars with higher quality and better disentanglement.
+
+One baseline representation is SLMO (single-layer-multi-output), which utilizes a single pair of geometry and texture decoders $(\mathcal{D}_g$ and $\mathcal{D}_t)$ to predict attributes for all components. Another one is SLMN (single-layer multi-network), which employs different decoders to predict the attributes of Gaussian primitives for each component. Since they only contain a single-layer UV feature plane, attributes of different components will share one feature if they are initialized in the same location. As shown in Fig. 4, Fig.5 and Tab. 2, single-layer UV representations generate clothed avatars with lower quality both quantitatively and qualitatively. This is because our layered UV feature plane representation provides each component with an optimized UV distribution and independent feature space. Without the layered UV plane, which provides distinctive features for components in overlapping and neighboring regions, single-layer representations struggle to disentangle components, leading to blurred boundaries between components.
+
+Single Stage vs. Two Stage. We also compare the single-stage training scheme with the commonly used two-stage training scheme, shown in Tab. 2 and Fig. 4. The single-stage training can generate avatars with finer details, such as intricate faces.
+
+# 4.3. Applications
+
+Component Transfer. We further explore applications such as component transfer. Thanks to the component disentanglement and shared structure provided by our method, we can directly transfer clothes and other components be
+
+
+Figure 5. Zoom in comparison between E3Gen and LayerAvatar. Compared to single-layer representation, layered representation exhibits detailed faces and clear boundaries between components.
+
+
+Figure 6. Component transfer. Given the generated avatars in the first column, we can transfer the upper-clothes, pants, hair, and shoes of the avatars in the second to fifth column to them. The results are shown in the rightmost column.
+
+tween generated samples. The component transfer results are shown in Fig. 6. Our method can accurately transfer components across various body shapes while maintaining high-quality details of the transferred items.
+
+# 5. Conclusion
+
+In this paper, we propose LayerAvatar, a novel feedforward diffusion-based method for generating component-disentangled clothed avatars. Our method proposes a layered UV feature plane representation, which organizes 3D Gaussians into different layers, each corresponding to specific components of clothed avatars (e.g., body, hair, clothing). Leveraging this representation, we train a single-stage diffusion model to generate each feature plane, enabling the generation of fully disentangled clothed avatars. To ensure complete component disentanglement, we incorporate constraint terms into the model. Extensive experiments validate the superiority of LayerAvatar in generating fully disentangled clothed avatars and its effectiveness in component transfer tasks. Additional limitations and implementation details are discussed in the supplementary material.
+
+Acknowledgments. This work was supported in part by NSFC (62201342), and Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102).
+
+# References
+
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+# Disentangled World Models: Learning to Transfer Semantic Knowledge from Distracting Videos for Reinforcement Learning
+
+Qi Wang $^{1,2,3*}$ Zhipeng Zhang $^{4,5*}$ Bao Xie $^{2,3*}$ Xin Jin $^{2,3\dagger}$ Yunbo Wang $^{1}$ Shiyu Wang $^{5,6}$ Liaomo Zheng $^{5,6}$ Xiaokang Yang $^{1}$ Wenjun Zeng $^{2,3}$
+
+1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University
+$^{2}$ Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo, China
+3 Ningbo Key Laboratory of Spatial Intelligence and Digital Derivative, Ningbo, China
+
+4 University of Chinese Academy of Sciences
+
+5 Shenyang Institute of Computing Technology, Chinese Academy of Sciences
+
+Shenyang CASNC Technology Co., Ltd
+
+https://qiwang067.github.io/diswm
+
+# Abstract
+
+Training visual reinforcement learning (RL) in practical scenarios presents a significant challenge, i.e., RL agents suffer from low sample efficiency in environments with variations. While various approaches have attempted to alleviate this issue by disentangled representation learning, these methods usually start learning from scratch without prior knowledge of the world. This paper, in contrast, tries to learn and understand underlying semantic variations from distracting videos via offline-to-online latent distillation and flexible disentanglement constraints. To enable effective cross-domain semantic knowledge transfer, we introduce an interpretable model-based RL framework, dubbed Disentangled World Models (DisWM). Specifically, we pretrain the action-free video prediction model offline with disentanglement regularization to extract semantic knowledge from distracting videos. The disentanglement capability of the pretrained model is then transferred to the world model through latent distillation. For finetuning in the online environment, we exploit the knowledge from the pretrained model and introduce a disentanglement constraint to the world model. During the adaptation phase, the incorporation of actions and rewards from online environment interactions enriches the diversity of the data, which in turn strengthens the disentangled representation learning. Experimental results validate the superiority of our approach on various benchmarks.
+
+
+Figure 1. Overview of our proposed framework. The key idea is to leverage distracting videos for semantic knowledge transfer, enabling the downstream agent to improve sample efficiency on unseen tasks.
+
+# 1. Introduction
+
+Visual reinforcement learning (VRL) presents a promising approach for training agents within complex environments [11, 18, 20, 28, 45]. However, VRL frequently suffers from performance degradation in practical scenarios due to the complexity, volatility, and visual distractions in environments. Even minor environmental variations can result in significant pixel-level shifts, making the trained VRL policies ineffective or suboptimal [6, 7]. For instance, a slight change in lighting conditions can affect an object's appearance (e.g., color, shadow, or other visual attributes). Therefore, it is crucial to enhance models with interpretability, enabling them to perceive, learn, and understand the semantic environmental variations.
+
+Disentangled representation learning (DRL) presents a promising approach to addressing the interpretability challenges inherent in the "black-box" nature of deep learning algorithms. Fundamentally, DRL approaches mimic the cognitive processes of biological intelligence, where under
+
+Table 1. MuJoCo (downstream domain) vs. DMC (accessible distracting videos).
+
+ | Video: DMC | Target: MuJoCo | Similarity / Difference |
| Task | Reacher Easy | Pusher | Relevant robotic control tasks |
| Dynamics | Two-link planar | Multi-jointed robot arm | Different |
| Action space | Box(-1, 1, (2), float32) | Box(-2, 2, (7), float32) | Different |
| Reward range | [0, 1] | [-4.49, 0] | Different |
+
+standing the world is facilitated by decomposing observations into distinct and independent factors [2, 14, 38, 40, 41]. In this form, when a factor of variation is changed (e.g., color), only a small portion of features in the disentangled representation will be affected, enabling the agent to recover performance quickly. Several studies have explored the integration of DRL algorithms in the domain of VRL. For example, Higgins et al. [15] trained a $\beta$ -VAE offline to obtain disentangled representations for reinforcement learning. TED [7] adopts a self-supervised auxiliary task to learn temporally disentangled representations for reinforcement learning. Additionally, Dunion et al. [6] introduced conditional mutual information to achieve a disentangled representation with correlated data. However, existing methods typically learn the representations from scratch, lacking any prior knowledge of the world. These approaches often require extensive interactions with the environment to acquire desired behaviors.
+
+Towards this challenge, we introduce a model-based interpretable VRL framework, dubbed Disentangled World Models (DisWM), which leverages prior knowledge extracted from distracting videos to facilitate the learning of unseen downstream tasks through latent distillation. It is crucial to note that distracting videos refer to videos with visual distractions, which are beneficial for learning disentangled representations. Specifically, as depicted in Figure 1, our framework consists of two phases: first, we pretrain a DRL encoder to learn disentangled latent representations from distracting videos. By doing so, the pretrained DRL encoder is "knowledgeable" in terms of representation disentanglement. Subsequently, we finetune an orthogonally designed world model with dual constraints of disentanglement and distillation, leveraging semantic knowledge transferred from the pretrained model via offline-to-online latent distillation. Another benefit of disentangled world model adaptation is that incorporating actions and rewards from online interactions with the environment enriches the diversity of the visual observations, which in turn strengthens the process of disentangled representation learning. It is worth mentioning that, as a cross-domain framework, DisWM does not require the pretraining videos to originate from the same domain as the downstream tasks.
+
+Experimental results demonstrate the effectiveness of our proposed approach in improving the sample efficiency of VRL agents across our modified DeepMind Control and
+
+MuJoCo Pusher. The contributions of this work can be summarized as follows:
+
+- We frame the problem of learning interpretable VRL agents as a domain transfer learning problem. The key idea is to extract semantic knowledge from distracting videos and transfer this disentanglement capability to downstream control tasks.
+- We present DisWM, an approach that follows the pretraining-finetuning paradigm using distracting videos, incorporating specific techniques of offline-to-online latent distillation and flexible disentanglement constraints.
+
+# 2. Problem Setup
+
+We formulate visual reinforcement learning as a partially observable Markov decision process (POMDP) that uses DMC and MuJoCo Pusher as the test bench. Specifically, we concentrate on scenarios where videos without actions and rewards are accessible, enabling world knowledge transfer. The goal is to maximize the cumulative reward of the target POMDP $\langle \mathcal{O},\mathcal{A},\mathcal{T},\mathcal{R},\gamma \rangle$ by transferring the shared world knowledge from the videos. These notations correspond to the visual observation space, the action space, the transition probabilities, the reward function, and the discount factor, respectively.
+
+For instance, in one of the cross-domain experiments, we use MuJoCo as the downstream domain and the frames collected from DMC as the distracting video. Table 1 highlights the differences between the two domains in terms of visual appearances, physical dynamics, action spaces, and reward functions.
+
+# 3. Method
+
+# 3.1. Overview of DisWM
+
+In this section, we present the details of DisWM, which involves three main stages (see Figure 2):
+
+a) Disentangled representation pretraining: Pretrain a DRL-based video prediction model from distracting videos to extract disentangled features.
+b) Offline-to-online latent distillation: Transfer the semantic knowledge from the pretrained model to the world model via cross-domain latent distillation.
+c) Disentangled world model adaptation: Finetune the downstream agent with disentanglement constraints by incorporating the action and reward information.
+
+
+(a) Action-free disentangled representation pretraining
+
+
+(b) Action-conditioned world model finetuning
+Figure 2. Architecture of Disentangled World Models. (a) The action-free video prediction model with disentanglement constraints is pretrained on distracting videos offline for the well-disentangled latent variable $\mathbf{z}_{\mathrm{disen}}$ , which extracts semantic knowledge from the visual observations. The disentangled capability of $\mathbf{z}_{\mathrm{disen}}$ is then transferred to the world model through latent distillation. (b) The action-conditioned world model is finetuned through disentanglement regularization online, which encourages the factorized representation. Moreover, the incorporation of actions and rewards enriches the diversity of the data, which in turn strengthens the disentangled representation learning.
+
+# 3.2. Disentangled Representation Pretraining
+
+To extract well-disentangled representations that can be transferred to the downstream world model, we first train a video prediction model on distracting videos without incorporating action information (Lines 4-8 of Alg. 1). This model comprises three key components: (i) the posterior learner that encodes the observation $o_{t}$ to latent state $z_{t}$ via $\beta$ -VAE encoder1, which serves as a typical DRL framework to extract latent features $\mathbf{z}_{t}$ from observations, (ii) the prior module that predicts future latent states based on historical states, without directly relying on the current observation $o_{t}$ , and (iii) the $\beta$ -VAE-based decoder that reconstructs $\hat{o}_t$ from the latent state $z_{t}$ . Concretely, the model can be formulated as follows:
+
+$$
+\beta \text {- V A E e n c o d e r :} \quad \mathbf {z} _ {t} = e _ {\phi^ {\prime}} (o _ {t})
+$$
+
+$$
+\text {P o s t e r i o r} z _ {t} \sim q _ {\phi^ {\prime}} (z _ {t} \mid z _ {t - 1}, \mathbf {z} _ {t})
+$$
+
+$$
+\text {P r i o r s t a t e :} \quad \hat {z} _ {t} \sim p _ {\phi^ {\prime}} (\hat {z} _ {t} \mid z _ {t - 1}) \tag {1}
+$$
+
+$$
+\text {R e c o n s t r u c t i o n :} \quad \hat {o} _ {t} \sim p _ {\phi^ {\prime}} (\hat {o} _ {t} \mid z _ {t})
+$$
+
+Isotropic unit Gaussian: $p(\mathbf{z}) = \mathcal{N}(\mathbf{0},I)$
+
+where $\phi^{\prime}$ denotes the parameters of the model. The $\beta$ -VAE-based video prediction model is trained to minimize the fol
+
+lowing loss function:
+
+$$
+\begin{array}{l} \mathcal {L} \left(\phi^ {\prime}\right) = \mathbb {E} _ {q _ {\phi^ {\prime}}} \left[ \sum_ {t = 1} ^ {T} - \ln p _ {\phi^ {\prime}} \left(o _ {t} \mid z _ {t}\right) \right. \\ + \underbrace {\beta_ {1} \mathrm {K L} \left[ q _ {\phi^ {\prime}} \left(z _ {t} \mid z _ {t - 1} , o _ {t}\right) \| p _ {\phi^ {\prime}} \left(\hat {z} _ {t} \mid z _ {t - 1}\right) \right]} _ {\text {a c t i o n - f r e e K L l o s s}} \tag {2} \\ \underbrace {+ \beta_ {2} \operatorname {K L} \left[ q _ {\phi^ {\prime}} \left(\mathbf {z} _ {t} \mid o _ {t}\right) \| p (\mathbf {z} _ {t}) \right]} _ {\text {d i s e n t a n g l e m e n t l o s s}} \biggr ]. \\ \end{array}
+$$
+
+The variational posterior distribution $q_{\phi'}(\mathbf{z}_t \mid o_t)$ is encouraged to be close to the standard multivariate Gaussian distribution $\mathcal{N}(\mathbf{0}, I)$ to strengthen the orthogonality and disentanglement of the latent space. The importance of the disentanglement loss term is governed by $\beta_2$ .
+
+# 3.3. Offline-to-Online Latent Distillation
+
+After the offline pretraining with the distracting videos, the model is fine-tuned online to adapt to the downstream task by integrating actions and rewards (Lines 13 of Alg. 1). A straightforward approach to transfer disentangled features involves initializing the action-conditioned world model with checkpoints obtained from the pretrained video prediction model. Nevertheless, it may experience a potential mismatch issue caused by the discrepancies between the two domains in visual appearances and physical dynamics. Directly applying the pretraining-finetuning paradigm
+
+for downstream tasks tends to overwrite the disentangled information encoded in the pretrained latent features, leading to decreased performance when there are large domain discrepancies between the source and the target domains.
+
+Through comprehensive pretraining on distracting videos that contain diverse visual variations, the video prediction model thus builds an interpretable and orthogonality latent space. In this space, the latent variable $\mathbf{z}_{\mathrm{disen}}$ achieves a high degree of disentanglement. To exploit the prior semantic knowledge from the pretrained model and improve the sample efficiency of the downstream tasks, we introduce an offline-to-online latent distillation. This approach enables the disentangling capability of $\mathbf{z}_{\mathrm{disen}}$ from the pretrained model to be effectively transferred to the latent variable $\mathbf{z}_{\mathrm{task}}$ of the world model. Specifically, this is achieved by minimizing the Kullback-Leibler (KL) divergence between the latent distributions of the two domains. The corresponding distillation loss $\mathcal{L}_{\mathrm{distill}}$ can be formulated as follows:
+
+$$
+\mathcal {L} _ {\text {d i s t i l l}} = \mathrm {K L} \left(\mathbf {z} _ {\text {d i s e n}} \| \mathbf {z} _ {\text {t a s k}}\right) = \sum \mathbf {z} _ {\text {d i s e n}} \cdot \log \left(\frac {\mathbf {z} _ {\text {d i s e n}}}{\mathbf {z} _ {\text {t a s k}}}\right) \tag {3}
+$$
+
+# 3.4. Disentangled World Model Adaptation
+
+By obtaining well-disentangled representations of $\mathbf{z}_{\mathrm{disen}}$ and employing the latent distillation for knowledge transfer, we then propose a DRL-based world model $\mathcal{M}_{\phi}$ , designed to harness these features to enhance interoperability and robustness against environmental variations (Lines 14-15 of Alg. 1). The components of $\mathcal{M}_{\phi}$ can be detailed as follows:
+
+Recurrent transition: $h_t = f_\phi(h_{t-1}, z_{t-1}, a_{t-1})$
+
+$\beta$ -VAE encoder: $\mathbf{z}_t\sim e_\phi (o_t)$
+
+Posterior state: $z_{t}\sim q_{\phi}(z_{t}|h_{t},\mathbf{z}_{t})$
+
+Prior state: $\hat{z}_t\sim p_\phi (\hat{z}_t|h_t)$ (4)
+
+Reconstruction: $\hat{o}_t\sim p_\phi (\hat{o}_t|h_t,z_t)$
+
+Reward prediction: $\hat{r}_t\sim r_\phi (\hat{r}_t|h_t,z_t)$
+
+Discount factor: $\hat{\gamma}_t\sim p_\phi (\hat{\gamma}_t|h_t,z_t)$
+
+Isotropic unit Gaussian: $p(\mathbf{z}) = \mathcal{N}(\mathbf{0},I)$
+
+where $\phi$ represents the combined parameters of the world model. We train $\mathcal{M}_{\phi}$ on the sampled data from the replay buffer $\mathcal{B}$ with the following loss function:
+
+$$
+\begin{array}{l} \mathcal {L} (\phi) = \mathbb {E} _ {q _ {\phi}} \left[ \sum_ {t = 1} ^ {T} \underbrace {- \ln p _ {\phi} \left(o _ {t} \mid h _ {t} , z _ {t}\right)} _ {\text {i m a g e r e c o n s t r u c t i o n}} \underbrace {- \ln r _ {\phi} \left(r _ {t} \mid h _ {t} , z _ {t}\right)} _ {\text {r e w a r d p r e d i c t i o n}} \right. \\ \underbrace {- \ln p _ {\phi} (\gamma_ {t} \mid h _ {t} , z _ {t})} _ {\text {d i s c o u n t p r e d i c t i o n}} + \underbrace {\alpha \operatorname {K L} [ q _ {\phi} (z _ {t} \mid h _ {t} , o _ {t}) \| p _ {\phi} (\hat {z} _ {t} \mid h _ {t}) ]} _ {\text {K L d i v e r g e n c e}} \\ \underbrace {+ \beta \mathrm {K L} [ q _ {\phi} (\mathbf {z} _ {t} \mid o _ {t}) \| p (\mathbf {z} _ {t}) ]} _ {\text {d i s e n t a n g l e m e n t l o s s}} + \underbrace {\eta \mathcal {L} _ {\text {d i s t i l l}}} _ {\text {d i s t i l l a t i o n l o s s}}. \tag {5} \\ \end{array}
+$$
+
+where $\beta$ is a hyperparameter used to balance reconstruction quality and disentanglement capability. In this adaptation stage, $\eta$ serves as a hyperparameter that gradually decreases from 0.1 to 0.01. Intuitively, $\eta$ controls the progressive adaptation of the world model with the shared world knowledge transfer from the pretrained video prediction model.
+
+Through the comprehensive training processes of this framework, we equip the DisWM with the capability to learn and understand the underlying semantic representations. This enhancement enables the model to be less sensitive to environmental variations, such as changes in object colors, positions, and backgrounds. Furthermore, by incorporating actions and rewards during the finetuning phase, the world model can generate data with more diverse representations, thereby improving the disentangled representation learning. For behavior learning, we utilize the actor-critic method that is in line with DreamerV2 [10] (Lines 16-18 of Alg. 1). For more details of behavior learning, please refer to Supplementary Material B.
+
+# 4. Experiments
+
+# 4.1. Experimental Setups
+
+Benchmark We evaluate DisWM on DeepMind Control Suite (DMC) [34], MuJoCo Pusher [35], and Draw-erWorld [37]. DMC is a widely adopted benchmark with comprehensive and flexible robotic-control tasks. For DMC benchmark, we use 5 tasks, i.e., Walker Walk, Cheetah Run, Hopper Stand, Finger Spin, Cartpole Swingup. In MuJoCo Pusher, a multi-jointed robotic arm is employed to manipulate a target cylinder (object). The goal is to move the object to a designated target position using the robot's end effector (fingertip). The agent receives the negative reward, which is a combination of three components: the distance between the fingertip and the target, the distance between the object and the target goal position, and a penalty for large actions. DrawerWorld is a modified Metaworld [43] benchmark designed to evaluate texture adaptability in manipulation tasks. It includes five additional textures from realistic photos and grid texture. During training, we initially employ the grid texture and then change to the wood texture midway, while adopting the metal texture exclusively for evaluation. The corresponding results on Draw-erWorld are reported in Supplementary Material C.2. Furthermore, the introduction of compared baselines is given in Supplementary Material A.
+
+Implementation details. The visual observations of online finetuning stages are resized to $64 \times 64$ pixels. Inspired by APV [29], we build distracting video datasets with 1M frames using DreamerV2 [10] to interact with the environments with visual color distractors. This video datasets consist of the samples stored in the replay buffer throughout the
+
+Algorithm 1 The training pipeline of DisWM.
+1: Hyperparameters: $H$ : Horizon of latent imagination.
+2: Require: Distracting video dataset $\mathcal{D}$
+3: Initialize: Parameters of the model $\{\phi ,\psi ,\xi \}$
+4: for training step $t = 1,2,\ldots ,K_{1}$ do $\triangleright$ Disentangled representation pretraining
+5: Sample random minibatch $\{o_t\}_{t = 1}^T\sim \mathcal{D}$
+6: Obtain Gaussian prior $\mathbf{z}_t$ from Isotropic unit Gaussian $\mathcal{N}(\mathbf{0},I)$
+7: Pretrain the action-free video prediction model with disentanglement regularization by minimizing Eq. (2).
+8: end for
+9: Train the random agent and collect a replay buffer $\mathcal{B}$
+10: while not converged do
+11: for training step $t = 1,2,\dots ,K_2$ do
+12: Sample $\{(o_t,a_t,r_t)\}_{t = 1}^T\sim \mathcal{B}$
+13: Distill the disentangled features to the world model using Eq. (3). $\triangleright$ Offline-to-online latent distillation
+14: Obtain Gaussian prior $\mathbf{z}_t$ from Isotropic unit Gaussian $\mathcal{N}(\mathbf{0},I)$ . $\triangleright$ Disentangled world model adaptation
+15: Train the world model $\mathcal{M}_{\phi}$ with latent distillation and disentanglement constraints using Eq. (5).
+16: Generate $\{(\hat{z}_i,\hat{a}_i)\}_{i = t}^{t + H}$ using $\pi_{\psi}$ and $\mathcal{M}_{\phi}$ . $\triangleright$ Behavior learning
+17: Train the critic $v_{\xi}$ over $\{(\hat{z}_i,\hat{a}_i)\}_{i = t}^{t + H}$
+18: Train the actor $\pi_{\psi}$ over $\{(\hat{z}_i,\hat{a}_i)\}_{i = t}^{t + H}$
+19: end for
+20: $o_1\gets$ env reset () $\triangleright$ Environment interaction
+21: for time step $t = 1,2,\ldots ,T$ do
+22: Sample $\hat{a}_t\sim \pi_\psi (\hat{a}_t|\hat{z}_t)$
+23: $r_t,o_{t + 1}\gets$ env. step( $\hat{a}_t$ ).
+24: end for
+25: Append data to the replay buffer $\mathcal{B}$
+26: end while
+
+training process until the agent achieves maximum score. For tasks in the DMC benchmark, the training steps of the agent are limited to $1 \times 10^{6}$ environment steps. Each run of DisWM requires roughly 5GB of VRAM and takes around 16 hours to train on a single RTX 3090 GPU. The dimensions of well-disentangled latent $\mathbf{z}_{\mathrm{disen}}$ and downstream task latent $\mathbf{z}_{\mathrm{task}}$ are both set to 20 in our approach. In Figure 3, we showcase the example observations of various tasks with color distractors. We train the agent using a fixed set of colors, where the RGB values are varied within a restricted range around the original values. Furthermore, at the midpoint of the training process, we change to a different color scheme for varying distractors.
+
+# 4.2. Main Comparison
+
+We evaluate the sample efficiency and task performance for all the methods with the training curves of episode return. Figure 4 shows the performance of DisWM and all the baselines. Remarkably, it achieves better performance than TED [7], a method on top of RAD [17] and tailored for environments with distractors. For the offline-to-online finetuning models, DV2 Finetune achieves the second-best performance by transferring knowledge from the distracting videos. However, we observe a significant decline in sample efficiency, particularly in scenarios with large data distribution shifts between the source and target domains (e.g.,
+
+DMC $\rightarrow$ MuJoCo). These shifts can occur in various aspects, including visual observation, physical dynamics, reward definition, or the action space of the robots. Another crucial baseline is APV [29], which focuses on transferring knowledge obtained from videos with a stacked latent prediction model. Nevertheless, without environment-specific designs for visual distractors, directly training may eventually result in a decrease in performance in the downstream tasks. The CURL model struggles to learn effective behavior policies, especially in Hopper Stand. Additional results on the challenging DMC Humanoid Walk can be found in Supplementary Material C.1.
+
+Additionally, we present qualitative results in Figure 5 and Figure 6. Figure 5 shows the traversals of $\beta$ -VAE during the pretraining phase. In each row of traversals, a distinct attribute varies, while other attributes remain constant, indicating that the pretrained model has successfully disentangled and learned this attribute, thereby improving the sample efficiency of the RL agent. Figure 6 displays the fine-grained disentanglement results on MuJoCo Pusher during the finetuning phase, demonstrating that the world model can effectively disentangle the variations.
+
+# 4.3. Model Analyses
+
+Ablation studies. We conduct ablation studies to validate the effect of the latent distillation and disentanglement con
+
+
+
+
+
+
+(a) Walker Walk
+
+
+
+
+
+
+
+
+
+
+
+
+(b) Reacher Easy
+
+
+
+
+
+
+
+
+Figure 3. Example image observations of our modified DMC and MuJoCo Pusher with color distractors.
+
+
+
+
+(c)Pusher
+
+
+
+
+
+
+
+
+
+
+(a) Cheetah Run $\rightarrow$ Walker Walk
+
+
+(b) Reacher Easy $\rightarrow$ Cheetah Run
+
+
+(c) Cheetah Run $\rightarrow$ Hopper Stand
+
+
+(d) Finger Spin $\rightarrow$ Reacher Easy
+
+
+(e) Finger Spin $\rightarrow$ Cartpole Swingup
+
+
+(f) Reacher Easy $\rightarrow$ Pusher
+Figure 4. Comparison of DisWM against visual RL baselines, including DreamerV2 [10], APV [29], DV2 Finetune, TED [7], CURL [18].
+
+straints. Figure 7 (Left) shows corresponding results in the DMC Walker Walk $\rightarrow$ Cheetah Run. The green curve shows that removing the latent distillation of DisWM results in a decreased performance, which indicates that the latent
+
+distillation is essential during the early training stage. For the model represented by the blue curve, we do not adopt disentanglement constraints for both pretrain and finetune stages. It can be seen that the necessity of introducing DRL-
+
+
+Figure 5. Visualization of traversals of $\beta$ -VAE during the pretraining phase.
+
+
+Figure 6. Fine-grained disentanglement results on MuJoCo Pusher during world model adaptation phase. Each row in Pusher images displays the traversal results on a specific attribute.
+
+based training and disentangled representation significantly improves the learning efficiency of the agent.
+
+Sensitivity analyses. We conduct sensitivity analyses on DMC (Cheetah Run $\rightarrow$ Walker Walk). As shown in Figure 7 (Middle), we observe that when $\beta$ for the representation disentanglement is too small, the model learns entangled latent representations. When $\beta$ is too large, it will impede the reconstruction of the image, leading to a decline in performance. Latent distillation weight $\eta$ controls the cross-domain transfer scale. Intuitively, setting this hyperparameter too low may result in the downstream agent not getting enough knowledge from the pretrained mod
+
+els. Conversely, excessively high $\eta$ may result in the model overfitting to the pretrained model, which is not conducive to the learning of the downstream task. Additional sensitivity analyses on the latent space dimension are provided in Supplementary Material C.3.
+
+Effects of video domain. In Figure 8, we evaluate DisWM on DMC Cartpole Swingup by pretraining on alternative video datasets, including frames collected from Finger Spin, Reacher Easy, Walker Walk, and Hopper Stand. Interestingly, compared with the DreamerV2 agent without pretraining, DisWM can always benefit from pretraining via offline-to-online latent distillation. It obtains the semantic
+
+
+Figure 7. These figures illustrate the ablation studies and sensitivity analyses of DisWM on DMC Walker Walk $\rightarrow$ Cheetah Run. Left: Comparison with DisWM without cross-domain latent distillation or disentanglement constraints. Middle: The sensitivity analyses of cross-domain latent distillation weight. Right: The performance of DisWM with different disentanglement scale.
+
+
+
+
+
+knowledge from the pretrained model and strengthens the disentanglement capability during finetuning phase.
+
+
+Figure 8. Performance of DisWM on DMC Cartpole Swingup with different video datasets.
+
+# 5. Related Work
+
+Visual MBRL. Visual RL learns control policies from raw pixels, which has achieved remarkable performance in various tasks [3, 4, 31, 37], while prior RL studies focus on learning policies from low-dimensional states. Extant approaches can be divided into two main directions: model-free RL [18, 19, 24, 32, 42, 44, 47] and model-based RL [1, 8-10, 12, 20, 21, 23, 27, 30, 36, 46]. The following methods specifically address the variations of environments in visual MBRL. Pan [28] et al. decompose visual dynamics into controllable and uncontrollable states through the optimization of inverse dynamics. SeeX [16] proposed a bilevel optimization framework that adopts a separated world model and maximizes the task-relevant uncertainty. Orthogonal to these studies, our approach employs a DRL-based world model to alleviate the issue of visual variations.
+
+Transfer RL To facilitate the learning of unseen tasks, transfer RL [22, 24, 26, 33, 36, 48] leverages the knowledge learned from past tasks. One promising way is to transfer world knowledge from accessible videos to improve the downstream control. APV [29] established a pretraining-finetuning framework with a stacked latent prediction model and video-based intrinsic bonus. IPV [39] introduced contextualized world models that pretrained on diverse in-the-wild videos. It incorporates a context encoder that works alongside the latent dynamics model into the image encoder to capture rich contextual information. PreLAR [45] pretrained the world model with the derived meaningful actions from the action-free video using an inverse dynamics encoder. Different from these approaches, we propose a new solution to transfer world knowledge from distracting videos to improve the learning efficiency of downstream tasks via offline-to-online latent distillation.
+
+# 6. Conclusions and Limitations
+
+In this paper, we present a transfer RL dubbed DisWM, which addresses the challenge of environment variations in practical scenarios. Our key insight is to leverage the accessible distracting videos to facilitate the sample efficiency of downstream tasks to offer flexible disentanglement constraints. Specifically, we introduce disentangled representation pretraining, offline-to-online latent distillation, and disentangled world model adaptation to improve the downstream control. DisWM demonstrates superior performance than existing visual RL baselines across various benchmarks.
+
+One limitation of our approach is that disentangled representation learning encounters challenges in complex environments. Exploring the non-stationary environments with more intricate variations, such as time-varying background video distractions, could further highlight the potential of our approach for practical scenarios.
+
+Acknowledgements. This work was supported by Grants of NSFC 62302246 & 62250062, ZJNSFC LQ23F010008, Ningbo 2023Z237 & 2024Z284 & 2024Z289 & 2023CX050011 & 2025Z038, the Smart Grid National Science and Technology Major Project (2024ZD0801200), the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), the Fundamental Research Funds for the Central Universities, and the IDT Foundation of Youth Doctoral Innovation (S203.2.01.32.002). Additional support was provided by the project of Supporting Program for Young and Middle-aged Scientific and Technological Innovation Talents in Shenyang (Grant RC210488), the project of Provincial Doctoral Research Initiation Fund Program (Grant 2023-BS-214), the High Performance Computing Center at Eastern Institute of Technology, Ningbo, and Ningbo Institute of Digital Twin.
+
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\ No newline at end of file
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+# Disentangling Instance and Scene Contexts for 3D Semantic Scene Completion
+
+Enyu Liu* En Yu* Sijia Chen Wenbing Tao † Huazhong University of Science and Technology
+
+{eyliu,yuen,sijiachen,wenbingtao}@hust.edu.cn
+
+# Abstract
+
+3D Semantic Scene Completion (SSC) has gained increasing attention due to its pivotal role in 3D perception. Recent advancements have primarily focused on refining voxel-level features to construct 3D scenes. However, treating voxels as the basic interaction units inherently limits the utilization of class-level information, which is proven critical for enhancing the granularity of completion results. To address this, we propose Disentangling Instance and Scene Contexts (DISC), a novel dual-stream paradigm that enhances learning for both instance and scene categories through separated optimization. Specifically, we replace voxel queries with discriminative class queries, which incorporate class-specific geometric and semantic priors. Additionally, we exploit the intrinsic properties of classes to design specialized decoding modules, facilitating targeted interactions and efficient class-level information flow. Experimental results demonstrate that DISC achieves state-of-the-art (SOTA) performance on both SemanticKITTI and SScBench-KITTI-360 benchmarks, with mIoU scores of 17.35 and 20.55, respectively. Remarkably, DISC even outperforms multi-frame SOTA methods using only single-frame input and significantly improves instance category performance, surpassing both single-frame and multi-frame SOTA instance mIoU by $17.9\%$ and $11.9\%$ , respectively, on the SemanticKITTI hidden test. The code is available at https://github.com/Enyu-Liu/DISC.
+
+# 1. Introduction
+
+With the rapid development of autonomous driving [11, 37], accurate environmental perception is crucial for tasks like navigation and obstacle avoidance [15]. The 3D Semantic Scene Completion (SSC) task addresses these critical demands by jointly predicting scene geometry and semantics to enable comprehensive 3D scene understanding. SSC methods are primarily categorized into lidar-based [6, 31, 45] and vision-based approaches [2, 12, 13, 25, 28, 50].
+
+
+VoxFormer
+Figure 1. Comparative Analysis of Different Methods. Incorporating instance or scene specific information significantly improves prediction accuracy for their corresponding categories.
+
+
+Symphonies
+
+
+DISC(Ours)
+
+Owing to their lower memory consumption, vision-based methods have gained prominence. VoxFormer [25] pioneers a sparse-to-dense architecture that mitigates projection blurring, and subsequent advances enhance voxel feature learning through techniques like self-distillation [38], context priors [50], and implicit instance fusion [13]. Since all these methods utilize voxels as the basic units for feature interaction, we classify them as voxel-based methods.
+
+Although voxel-based methods have achieved remarkable performance, we observe distinct prediction flaws in instance and scene categories: instance categories suffer from class omission and semantic ambiguity due to occlusion and projection errors, while scene categories exhibit structural incoherence from out-of-view regions. Based on this analysis, we argue that fully leveraging class-level information can help address the divergent challenges of different categories. As shown in Fig. 1, compared to VoxFormer [25] (no category-specific priors) and Symphonies [13] (implicit instance priors), our method explicitly integrates both instance and scene information, achieving superior performance in completion details. Nevertheless, despite the proven benefits of class-level information, voxel-based works have not further extended the class-level concepts. We attribute this limitation to three critical challenges faced by voxel-based methods in leveraging class-level information: (1) Voxel construction process inherently disrupts the structural information of categories; (2) Voxel-based methods require a unified module to handle features across all categories, limiting the ability to address divergent challenges posed by instance and scene categories; (3)
+
+
+(a) Voxel-Based Method
+
+
+(b) Class-Based Method (Ours)
+Figure 2. Comparison of main architectures. The key differences between our Class-Based Method and the previous Voxel-Based Method are highlighted in red-brown. Our method initializes instance and scene queries with semantic and geometric priors, using a dual-stream structure and tailored modules for class-discriminative scene semantic completion.
+
+Voxel-based methods rely on 3D spatial feature interactions, which impose high computational costs and hinder further integration of class-level information.
+
+To overcome these challenges, we depart from conventional voxel-based paradigms and propose Disentangling Instance and Scene Contexts (DISC), a class-aware dual-stream architecture for discriminative reconstruction. As shown in Fig. 2(b), DISC operates in BEV space and introduces two core modules to leverage category-specific information: a Discriminative Query Generator (DQG) and a Dual-Attention Class Decoder (DACD). Our method addresses three critical issues: (1) Replaces voxel queries with independent instance and scene queries, preserving category-specific structural information while integrating richer geometric and semantic priors; (2) Employs tailored modules to resolve distinct instance and scene challenges; (3) Mitigates BEV's height-axis limitations by disentangling instance and scene contexts, thereby enabling efficient class-level integration with lower computational costs.
+
+Specifically, our DQG module first initializes independent queries with positional priors based on instance and scene properties, followed by aggregating contextual information to provide semantic priors. Moreover, we argue that feature disentanglement mitigates the BEV limitations in height-axis modeling. For example, road and pedestrian categories within the same BEV grid exhibit significant height disparities, causing vertical feature ambiguity during 3D reconstruction. However, disentangling instance and scene contexts alleviates such multi-height distributions in shared grids. Leveraging this insight, DISC adopts BEV
+
+space for query initialization and feature interaction, which significantly reduces memory usage. To address projection errors, we further propose a Coarse-to-fine BEV generation module to deliver precise semantic priors.
+
+Moreover, to design targeted solutions, we further analyze the root causes of instance and scene errors and their relationships. We identify that scene categories suffer from topological errors due to weak global reasoning (e.g., roads appearing in terrain), while instance categories exhibit semantic ambiguities from projection errors and occlusion-induced feature loss. Additionally, scene context aids instance reasoning, for example, pole-shaped objects on sidewalks are more likely to be traffic lights than trunks. Based on these analysis, our DACD decoder implements two specialized layers: the Adaptive Instance Layer (AIL) dynamically fuses image features and scene context to mitigate projection errors and recover occluded details, and the Global Scene Layer (GSL) establishes cross-region interactions to expand the scene's receptive field and ensure layout coherence. Both layers leverage class-specific properties to regulate feature propagation within their respective streams.
+
+Finally, we evaluate DISC on SemanticKITTI and SSCBench-KITTI-360 benchmarks, achieving state-of-the-art (SOTA) mIoU scores of 17.35 and 20.55 respectively. Notably, with only single-frame inputs, DISC outperforms multi-frame SOTA methods. Furthermore, DISC demonstrates substantial gains in instance-level understanding, improving instance mIoU by $17.9\%$ over SOTA methods, while simultaneously achieving SOTA scene mIoU performance on the SemanticKITTI hidden test set.
+
+In summary, our main contributions are the following:
+
+- We propose DISC, a novel class-based architecture for the SSC task, featuring a dual-stream structure that decouples instance and scene categories in the BEV plane to fully utilize class-level information.
+- We propose the Discriminative Query Generator (DQG) that provides geometric and semantic priors for both instance and scene queries, paired with the Dual-Attention Class Decoder (DACD) to address the distinct challenges of instance and scene categories, ensuring accurate and efficient feature interaction within each stream.
+- We achieve SOTA performance with DISC on both SemanticKITTI and SSCBench-KITTI-360 benchmarks. Moreover, DISC is the first to outperform multi-frame SOTA methods using only single-frame inputs.
+
+# 2. Related Works
+
+3D Semantic Scene Completion. The 3D Semantic Scene Completion (SSC) task, introduced by SSCNet [36], is an important task in computer vision [4, 5, 21, 47, 48] that aims to jointly estimate the complete geometry and semantics of a scene from sparse inputs, playing a crucial role in applications like autonomous driving and virtual reality.
+
+
+
+
+(a)
+(b)
+
+
+(c)
+Figure 3. The overall architecture. (a) DISC is a novel semantic scene completion method with a dual-stream framework for specialized instance and scene categories processing. (b) The Discriminative Query Generator (DQI) integrates geometric and contextual priors into instance and scene queries based on category attributes. (c) Details of the Adaptive Instance Layer (AIL) and the Global Scene Layer (GSL), which address the distinct challenges faced by instance and scene categories during the reconstruction process in a differentiated manner. For clarity, the Feed-Forward Network (FFN) and positional embedding are omitted in the figure.
+
+Early methods [6, 31, 45] focused on LiDAR for 3D semantic occupancy prediction, but camera-based approaches have gained prominence due to their cost efficiency. Recent voxel-based methods, such as MonoScene [2], TPV-Former [12], and VoxFormer [25], enhance semantic information for each voxel, using techniques like monocular image inputs, tri-perspective views, and deformable attention mechanisms. Other approaches like OccDepth [28] and VPOcc [16] improve geometric projection and address perspective distortion, while Symphonize [13] and CG-Former [50] focus on instance-level representations and enhanced voxel features. Voxel-based methods struggle to distinguish instance and scene features, while our approach employs class-aware modeling to resolve this divergence.
+
+BEV-based 3D Perception BEV-based methods have gained significant attention in 3D perception due to their compact scene representation [20]. These methods can be classified into transformer-based and frustum-based approaches, depending on how BEV maps are derived from camera images. Transformer-based methods [3, 7, 8, 14, 26, 44] project BEV grids onto camera images and pull features from neighboring points into the BEV space. Frustum-based methods [22, 23, 29, 30, 40, 51] lift image features into 3D frustums by predicting depth probabilities and then use voxel pooling to generate BEV features. In this work, we build upon the Lift-Splat-Shoot (LSS) method [29] and leverage depth information to reduce geometric ambiguity
+
+caused by depth estimation errors. While BEV cuts computational costs [10, 49] for 3D scene completion, it underperforms scene-based methods due to vertical coupling of instance and scene features in unified BEV representations. Our feature-decoupling modules resolve this height-dimension constraint, unlocking BEV's potential.
+
+# 3. Method
+
+# 3.1. Overall Architecture
+
+The overall architecture of DISC is shown in Fig. 3. A 2D backbone [13] extracts multi-scale feature maps $F^{2D}$ , followed by the Discriminative Query Generator (DQG) producing instance queries $\mathbf{Q}_{\mathrm{ins}} \in \mathbb{R}^{N_{\mathrm{ins}} \times C}$ and scene queries $\mathbf{Q}_{\mathrm{scn}} \in \mathbb{R}^{N_{\mathrm{scn}} \times C}$ in the BEV space, where $N_{\mathrm{ins}}$ and $N_{\mathrm{scn}}$ represent the number of initial queries (Sec. 3.2). These queries are processed by the Dual-Attention Class Decoder (DACD) for class-specific feature interaction (Sec. 3.3). Finally, the refined instance and scene features are fused in 3D space and passed through a prediction head to obtain the scene completion results (Sec. 3.4). Detailed descriptions of each component are provided in the following subsections.
+
+Depth Estimator. Following previous works [13, 19, 50], we employ a pretrained MobileStereoNet [35] to estimate the depth of the input image. The estimated depths are used to supervise depth predictions and compute the 3D positions
+
+of projected points from pixel coordinates.
+
+# 3.2. Discriminative Query Generator
+
+As shown in Fig. 3(b), we propose a category-aware query design that distinguishes between instance queries and scene queries to preserve their distinct geometric properties. Unlike uniform voxel queries, our approach integrates geometric and semantic priors into query initialization while maintaining computational efficiency. First, BEV features are derived by projecting 2D features $(F^{2D})$ onto the BEV plane, with projection errors mitigated through a Coarse-to-fine BEV Generation module. For instances, their sparse spatial distribution and projection errors make the image space more suitable for identifying potential positions. However, perspective distortion complicates uniform sampling across different distances. Therefore, we first locate potential instances in the image space and then refine them in the BEV space. For scene queries, we adopt a large-sized design to capture continuous spatial distributions while preserving structural coherence, thereby avoiding the segmentation artifacts caused by fine-grained voxel queries. Notably, all queries incorporate BEV positional embeddings (detailed in the appendix).
+
+Coarse-to-fine BEV Generation. To address projection errors in LSS [29], we first generate coarse voxel features $V_{\mathrm{coarse}} \in \mathbb{R}^{C \times X \times Y \times Z}$ via lifting, where $X$ , $Y$ , and $Z$ correspond to the scene grid dimensions. Depth-guided surface voxels are then refined using $F^{2D}$ , producing optimized $V_{\mathrm{fine}} \in \mathbb{R}^{C \times X \times Y \times Z}$ through feature fusion. Finally, BEV features $C \in \mathbb{R}^{C \times X \times Y}$ are obtained by Z-axis max pooling of $V_{\mathrm{fine}}$ . Further implementation details are provided in the supplementary materials.
+
+Instance Query. To improve the recall of instance categories, we detect potential instances through image-space segmentation and project candidate pixels to BEV. A parallelizable neighbor suppression strategy selects $N_{\mathrm{ins}}$ reference positions: $k \times k$ grids form voting blocks, with highest-probability candidates retained per block. This emphasizes small and long-tail objects while maintaining efficiency, expressed as:
+
+$$
+X _ {\text {i n s}} = \left\{\mathrm {C T} \left(\mathbf {g} _ {n}\right) \mid \mathbf {g} _ {n} \in \operatorname {T o p} - N \left(\left\{\operatorname {M a x} \left(B _ {k \times k} ^ {i}\right) \right\} _ {i = 1} ^ {s}\right) \right\} \tag {1}
+$$
+
+Here, $s$ denotes the number of blocks, and $B_{k\times k}^{i}$ represents the $i$ -th block of $k\times k$ grids, where $i$ ranges from 1 to $s$ . The Max operation selects the grid with the highest probability in each block as a candidate. $\mathbf{g}_n$ refers to the top-N selected candidate grids, and $\mathrm{CT}(\mathbf{g}_n)$ denotes their center coordinates, forming the reference set $X_{\mathrm{ins}}$ for instance queries. The features at these locations in BEV plane initialize the instance queries: $\mathbf{Q}_{\mathrm{ins}} = C[X_{\mathrm{ins}}]$ .
+
+Scene Query. For scene categories, we design a patch-based scene query generation strategy to enrich the informa
+
+
+Figure 4. Instance-Image Cross-Attention. For each instance query, we adaptively select a series of heights and combine them with its reference point coordinates on the BEV plane to project the query into the image space. This enables capturing image features across multiple height levels.
+
+tion in each individual query. Specifically, BEV features are divided into multiple equally sized patches, with the center point of each patch serving as the reference point for a scene query. Each patch is upsampled via convolution until the feature size reaches $1 \times 1$ , which is then used as the initialization feature for the scene query, expressed as:
+
+$$
+\mathbf {Q} _ {\mathrm {s c n}} = \operatorname {U p S a m p l e} (C) \tag {2}
+$$
+
+Here, UpSample represents the upsampling operation.
+
+# 3.3. Dual-Attention Class Decoder
+
+As discussed in Sec. 1, existing methods [13, 25, 50] employ a unified attention module for both instance and scene features, limiting targeted optimizations. Given the distinct characteristics between instances and scenes, this approach is suboptimal. In contrast, we design task-specific decoding layers tailored to each challenges, as shown in Fig. 3 (c). Prone to occlusion and projection errors, instances require multi-level geometric and semantic information for robust reasoning. For example, height direction features and contextual categories facilitate instance refinement and ambiguity reduction. Scene categories, with their continuous distribution, require global receptive fields to capture spatial relationships and maintain layout coherence. Based on these insights, we propose the Dual-Attention Class Decoder comprising an Adaptive Instance Layer and a Global Scene Layer. As follows, we will explain how they achieve targeted feature propagation and interaction.
+
+Adaptive Instance Layer. As shown in Fig. 4, to address the loss of height information in BEV space, the instance query is transformed into pillar-like queries. Given the significant height variance within instance classes (e.g., trucks and traffic signs are much taller than pedestrians), we use adaptive height sampling rather than uniform sampling. For
+
+each instance query $q_{\mathrm{ins}}$ , discrete candidate heights are initialized. A linear layer predicts probabilities for these candidates, and TOP-N selection identifies the most probable heights. These heights are combined with the reference coordinates $x_{\mathrm{ins}}$ to form reference points $P_{j} = (x_{\mathrm{ins}}, h_{j})$ . These points are then projected onto the image feature space, where nearby features are sampled using deformable cross attention. The weighted sum of these features is then used to update $q_{\mathrm{ins}}$ , expressed as:
+
+$$
+q _ {\text {i n s}} = \sum_ {j = 1} ^ {N} w _ {j} \mathrm {D A} \left(q _ {\text {i n s}}, F ^ {2 D}, \mathcal {T} ^ {W I} \left(x _ {\text {i n s}}, h _ {j}\right)\right) \tag {3}
+$$
+
+Here, $h_j$ represents a sampled height, with a total of $N$ heights, and $w_j$ is the corresponding sampling weight. $T^{WI}$ denotes the projection from the world coordinate system to image space for feature sampling. In practice, the 3D reference points are randomly offset within the voxel grid range to enhance the ability of $q_{\mathrm{ins}}$ to capture features.
+
+After that, the instance queries extract scene features from the region of interest through attention mechanism, which is formulated as:
+
+$$
+q _ {\text {i n s}} = \mathrm {D A} \left(q _ {\text {i n s}}, C _ {\text {s c n}}, x _ {\text {i n s}}\right) \tag {4}
+$$
+
+where $C_{\mathrm{scn}}$ represents scene features output by the GSL. We also utilize self attention to capture internal relationships among instance queries and recover lost information:
+
+$$
+\mathbf {Q} _ {\text {i n s}} = \operatorname {S e l f A t t n} \left(\mathbf {Q} _ {\text {i n s}}\right) \tag {5}
+$$
+
+Finally, instance features are propagated across the entire BEV plane using a UNet-like [32] network, yielding $C_{\mathrm{ins}}$ . Global Scene Layer. To enable each scene query to capture global information, we construct $\mathbf{Q}_{\mathrm{img}}$ following the same method as $\mathbf{Q}_{\mathrm{scn}}$ , obtained by the smallest scale image feature $F_s^{2D}$ . For each scene query $q_{\mathrm{scn}}$ , global semantic features are aggregated from $\mathbf{Q}_{\mathrm{img}}$ via cross attention, as shown below:
+
+$$
+q _ {\mathrm {s c n}} = \operatorname {C r o s s A t t n} \left(q _ {\mathrm {s c n}}, \mathbf {Q} _ {\mathrm {i m g}} ^ {\in \text {M a s k}}, \mathbf {Q} _ {\mathrm {i m g}} ^ {\in \text {M a s k}}\right) \tag {6}
+$$
+
+where Mask is a random mask that discards a portion of $\mathbf{Q}_{\mathrm{img}}$ , simulating information loss (e.g., occlusions), which aids the network in better inferring the scene layout.
+
+Then $\mathbf{Q}_{\mathrm{scn}}$ interact with BEV features through self attention, further expanding the global receptive field and propagating visible features from nearby areas to distant and unseen regions beyond the viewpoint, as expressed by:
+
+$$
+\mathbf {Q} _ {\mathrm {s c n}} = \operatorname {S e l f A t t n} \left(\mathbf {Q} _ {\mathrm {s c n}}\right) \tag {7}
+$$
+
+Finally, the queries are combined into BEV features based on the positions of the reference points, and $C_{\mathrm{scn}}$ is obtained through upsampling layers.
+
+# 3.4. Feature Fusion and Losses
+
+Feature Fusion. Prior BEV-based 3D reconstruction methods [10, 49] suffer from two limitations: (1) oversimplified height features and (2) coupled instance-scene feature interactions. When instance-class objects (e.g., pedestrians) and scene-class elements (e.g., roads) project onto the same BEV grid, their significant height variations create learning conflicts. We address this through category-decoupled height prediction:
+
+$$
+V = \left(C _ {\text {i n s}} \bigotimes H _ {\text {i n s}}\right) + \left(C _ {\text {s c n}} \bigotimes H _ {\text {s c n}}\right) \tag {8}
+$$
+
+where $H_{\mathrm{ins}}, H_{\mathrm{scn}} \in [0,1]^{X \times Y \times Z}$ are height distributions predicted via convolutional networks, and $\otimes$ denotes broadcasted element-wise multiplication.
+
+We enhance $V$ using a Local and Global Aggregator with Dynamic Fusion to produce the final 3D feature volume. Unlike CGFormer [50], only the left and front views are input to the Global Aggregator, as the BEV plane already contains sufficient detailed features for aggregation.
+
+Training Loss. Following prior works, we use the Scene-Class Affinity Loss $\mathcal{L}_{scal}$ from Monoscene [2] for both semantic and geometric predictions, while simultaneously optimizing precision, recall, and specificity. Additionally, a class-frequency weighted cross-entropy loss $\mathcal{L}_{ce}$ is applied, with the total loss for this part given by:
+
+$$
+\mathcal {L} _ {s s c} = \mathcal {L} _ {s c a l} ^ {g e o} + \mathcal {L} _ {s c a l} ^ {s e m} + \mathcal {L} _ {c e} \tag {9}
+$$
+
+Additionally, we introduce segmentation and height prediction losses for both instance and scene categories on the BEV plane to facilitate discriminative feature learning. Segmentation loss combines cross-entropy and dice loss [34], while height prediction uses focal loss [33]:
+
+$$
+\mathcal {L} _ {\text {a u g}} = \mathcal {L} _ {\text {s e g}} + \lambda_ {h} \mathcal {L} _ {\text {h e i g h t}} \tag {10}
+$$
+
+The $\mathcal{L}_{\mathrm{aug}}$ loss is applied at each decoder layer, halved for layers except the final one. We also use explicit depth loss $\mathcal{L}_d$ [26] to supervise the depth prediction. The total loss is:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {s s c}} + \lambda_ {2} \mathcal {L} _ {\text {a u g}} + \lambda_ {d} \mathcal {L} _ {d} \tag {11}
+$$
+
+In practice, we set the weights as: $\lambda_1 = 1$ , $\lambda_2 = 1$ , $\lambda_h = 5$ and $\lambda_d = 0.01$ .
+
+# 4. Experiments
+
+# 4.1. Dataset and Metric
+
+DISC is evaluated on two widely used datasets: SemanticKITTI [1] and SSCBench-KITTI-360 [24]. For evaluation metrics, we employ standard measures such as Intersection over Union (IoU) and mean IoU (mIoU) for voxelwise predictions. Additionally, we introduce instance mean
+
+| Method | IoU | InsM | ScnM | mIoU | road (5.30%) | sidewalk (11.19%) | parking (1.29%) | other-gmd. (0.56%) | building (4.19%) | car (0.92%) | truck (0.16%) | bicycle (0.03%) | motorcycle (0.03%) | other-veh. (0.20%) | vegetation (0.95%) | trunk (0.51%) | terrain (0.17%) | person (0.07%) | bicyclist (0.07%) | motorcyclist (0.05%) | fence (0.90%) | pole (0.29%) | traf-sign (0.08%) |
| Temporal Inputs Methods | |
| VoxFormer-T [25] | 43.21 | 4.79 | 22.97 | 13.41 | 54.10 | 26.90 | 25.10 | 7.30 | 23.50 | 21.70 | 3.60 | 1.90 | 1.60 | 4.10 | 24.40 | 8.10 | 24.20 | 1.60 | 1.10 | 0.00 | 13.10 | 6.60 | 5.70 |
| HASSC-T [39] | 42.87 | 5.27 | 24.51 | 14.38 | 55.30 | 29.60 | 25.90 | 11.30 | 23.10 | 23.00 | 2.90 | 1.90 | 1.50 | 4.90 | 24.80 | 9.80 | 26.50 | 1.40 | 3.00 | 0.00 | 14.30 | 7.00 | 7.10 |
| H2GFormer-T [41] | 43.52 | 5.37 | 25.06 | 14.60 | 57.90 | 30.40 | 30.00 | 6.90 | 24.00 | 23.70 | 5.20 | 0.60 | 1.20 | 5.00 | 25.20 | 10.70 | 25.80 | 1.10 | 0.10 | 0.00 | 14.60 | 7.50 | 9.30 |
| HTCL [18] | 44.23 | 6.48 | 28.86 | 17.09 | 64.40 | 34.80 | 33.80 | 12.40 | 25.90 | 27.30 | 5.70 | 1.80 | 2.20 | 5.40 | 25.30 | 10.80 | 31.20 | 1.10 | 3.10 | 0.90 | 21.10 | 9.00 | 8.30 |
| Single-frame Inputs Methods | |
| MonoScene* [2] | 34.16 | 3.59 | 19.4 | 11.08 | 54.70 | 27.10 | 24.80 | 5.70 | 14.40 | 18.80 | 3.30 | 0.50 | 0.70 | 4.40 | 14.90 | 2.40 | 19.50 | 1.00 | 1.40 | 0.40 | 11.10 | 3.30 | 2.10 |
| TPVFormer [12] | 34.25 | 3.49 | 19.88 | 11.26 | 55.10 | 27.20 | 27.40 | 6.50 | 14.80 | 19.20 | 3.70 | 1.00 | 0.50 | 2.30 | 13.90 | 2.60 | 20.40 | 1.10 | 2.40 | 0.30 | 11.00 | 2.90 | 1.50 |
| SurroundOcc [42] | 34.72 | 3.90 | 20.7 | 11.86 | 56.90 | 28.30 | 30.20 | 6.80 | 15.20 | 20.60 | 1.40 | 1.60 | 1.20 | 4.40 | 14.90 | 3.40 | 19.30 | 1.40 | 2.00 | 0.10 | 11.30 | 3.90 | 2.40 |
| OccFormer [52] | 34.53 | 4.02 | 21.53 | 12.32 | 55.90 | 30.30 | 31.50 | 6.50 | 15.70 | 21.60 | 1.20 | 1.50 | 1.70 | 3.20 | 16.80 | 3.90 | 21.30 | 2.20 | 1.10 | 0.20 | 11.90 | 3.80 | 3.70 |
| IAMSSC [43] | 43.74 | 4.50 | 21.12 | 12.37 | 54.00 | 25.50 | 24.70 | 6.90 | 19.20 | 21.30 | 3.80 | 1.10 | 0.60 | 3.90 | 22.70 | 5.80 | 19.40 | 1.50 | 2.90 | 0.50 | 11.90 | 5.30 | 4.10 |
| VoxFormer-S [25] | 42.95 | 4.39 | 20.89 | 12.20 | 53.90 | 25.30 | 21.10 | 5.60 | 19.80 | 20.80 | 3.50 | 1.00 | 0.70 | 3.70 | 22.40 | 7.50 | 21.30 | 1.40 | 2.60 | 0.20 | 11.10 | 5.10 | 4.90 |
| DepthSSC [46] | 44.58 | 4.87 | 22.26 | 13.11 | 55.64 | 27.25 | 25.72 | 5.78 | 20.46 | 21.94 | 3.74 | 1.35 | 0.98 | 4.17 | 23.37 | 7.64 | 21.56 | 1.34 | 2.79 | 0.28 | 12.94 | 5.87 | 6.23 |
| Symphonize [13] | 42.19 | 6.14 | 24.93 | 15.04 | 58.40 | 29.30 | 26.90 | 11.70 | 24.70 | 23.60 | 3.20 | 3.60 | 2.60 | 5.60 | 24.20 | 10.00 | 23.10 | 3.20 | 1.90 | 2.00 | 16.10 | 7.70 | 8.00 |
| HASSC-S [39] | 43.40 | 5.12 | 22.46 | 13.34 | 54.60 | 27.70 | 23.80 | 6.20 | 21.10 | 22.80 | 4.70 | 1.60 | 1.00 | 3.90 | 23.80 | 8.50 | 23.30 | 1.60 | 4.00 | 0.30 | 13.10 | 5.80 | 5.50 |
| StereoScene [17] | 43.34 | 5.73 | 26.04 | 15.36 | 61.90 | 31.20 | 30.70 | 10.70 | 24.20 | 22.80 | 2.80 | 3.40 | 2.40 | 6.10 | 23.80 | 8.40 | 27.00 | 2.90 | 2.20 | 0.50 | 16.50 | 7.00 | 7.20 |
| H2GFormer-S [41] | 44.20 | 5.05 | 23.33 | 13.72 | 56.40 | 28.60 | 26.50 | 4.90 | 22.80 | 23.40 | 4.80 | 0.80 | 0.90 | 4.10 | 24.60 | 9.10 | 23.80 | 1.20 | 2.50 | 0.10 | 13.30 | 6.40 | 6.30 |
| MonoOcc-S [53] | - | 5.36 | 23.14 | 13.80 | 55.20 | 27.80 | 25.10 | 9.70 | 21.40 | 23.20 | 5.20 | 2.20 | 1.50 | 5.40 | 24.00 | 8.70 | 23.00 | 1.70 | 2.00 | 0.20 | 13.40 | 5.80 | 6.40 |
| MonoOcc-L [53] | - | 6.95 | 25.29 | 15.63 | 59.10 | 30.90 | 27.10 | 9.80 | 22.90 | 23.90 | 7.20 | 4.50 | 2.40 | 7.70 | 25.00 | 9.80 | 26.10 | 2.80 | 4.70 | 0.60 | 16.90 | 7.30 | 8.40 |
| VPOcc [16] | 44.09 | 6.03 | 26.31 | 15.65 | 59.10 | 32.30 | 30.90 | 9.70 | 26.30 | 24.40 | 5.30 | 3.30 | 3.20 | 5.60 | 25.90 | 9.70 | 25.70 | 2.40 | 2.90 | 0.30 | 17.20 | 6.60 | 6.30 |
| CGFormer [50] | 44.41 | 6.15 | 28.24 | 16.63 | 64.30 | 34.20 | 34.10 | 12.10 | 25.80 | 26.10 | 4.30 | 3.70 | 1.30 | 2.70 | 24.50 | 11.20 | 29.30 | 1.70 | 3.60 | 0.40 | 18.70 | 8.70 | 9.30 |
| DISC(ours) | 45.32 | 7.25 | 28.56 | 17.35 | 63.10 | 34.70 | 34.60 | 12.60 | 26.60 | 26.70 | 5.50 | 4.00 | 4.70 | 8.10 | 26.50 | 10.30 | 29.30 | 2.80 | 2.50 | 1.10 | 19.30 | 8.40 | 8.70 |
+
+Table 1. Quantitative results on SemanticKITTI test. * represents the reproduced results from [12, 52]. Among all methods, the top three ranked approaches are marked as red, bold, and underlined. For single-frame methods, DISC achieves SOTA performance in mIoU, IoU, InsM, and ScnM. Notably, using only single-frame input, DISC surpasses even multi-frame SOTA methods in mIoU, IoU, and InsM.
+
+IoU (InsM) and scene mean IoU (ScnM) metrics to assess the model's perceptual capabilities across different categories. Further details regarding the datasets and metrics are provided in the supplementary materials.
+
+# 4.2. Implementation Details
+
+Following Symphonies [13], the ResNet-50 [9] backbone and image encoder are initialized with pre-trained MaskDINO [19] weights. Generally, categories such as car, bicycle, and traffic sign are classified as instances, while road, sidewalk, and building are categorized as scene. Detailed category definitions are provided in the supplementary materials. In our experiments, we observed that our network converges faster compared to previous works, allowing us to reduce the total training epochs to 20 which is shorter than most existing approaches. We use the AdamW [27] optimizer with an initial learning rate of 2e-4 and a weight decay of 1e-4. The learning rate is reduced by a factor of 0.1 at the 12th epoch.
+
+# 4.3. Comparison with state-of-the-art
+
+Tab. 1 presents our results on the SemanticKITTI hidden test set. DISC outperforms all competing methods in IoU, mIoU, InsM, and ScnM, achieving scores of 45.30, 17.35, 7.25, and 28.56, respectively. Notably, DISC shows sig-
+
+nificant progress in instance categories, surpassing the existing state-of-the-art (SOTA) method by $17.9\%$ , strongly validating the effectiveness of our instance-specific design. Additionally, DISC is the first single-frame-based method to outperform SOTA multi-frame fusion methods in IoU, mIoU, and InsM, while achieving a ScnM score only 0.30 lower, demonstrating its ability to fully exploit single-frame information. DISC achieves the best performance in most classes, such as sidewalk, parking, building, motorcycle, and other-vehicle.
+
+We also conducted experiments on SSCBench-KITTI-360. As shown in Tab. 2, DISC achieves excellent performance with an mIoU of 20.55, IoU of 47.35, InsM of 13.47, and ScnM of 28.88. Moreover, DISC outperforms all camera-based methods and LiDAR-based methods in mIoU and InsM. This analysis further confirms the effectiveness and outstanding performance of DISC.
+
+# 4.4. Ablation Studies
+
+Analysis of architecture. Tab. 3 analyzes different architectures. The baseline can be regarded as a simplified FlashOcc [49], which consists of a 2D backbone for extracting image features, a Coarse-to-fine BEV generation module for producing reliable BEV features, a BEV encoder for further processing, and a 3D global and local en
+
+| Method | IoU | InsM | ScnM | mIoU | car(2.85%) | bicycle(0.01%) | motorcycle(0.01%) | truck(0.16%) | other-veh.(5.75%) | person(0.02%) | road(4.98%) | parking(2.31%) | sidewalk(6.43%) | other-grd.(2.05%) | building(15.67%) | fence(0.96%) | vegetation(4.99%) | terrain(7.10%) | pole(0.22%) | traf.-sign(0.06%) | other-struct.(4.33%) | other-obj.(0.28%) |
| LiDAR-based methods | |
| SSCNet [36] | 53.58 | 4.96 | 28.88 | 16.95 | 31.95 | 0.00 | 0.17 | 10.29 | 0.00 | 0.07 | 65.70 | 17.33 | 41.24 | 3.22 | 44.41 | 6.77 | 43.72 | 28.87 | 0.78 | 0.75 | 8.69 | 0.67 |
| LMSCNet [31] | 47.35 | 2.42 | 24.96 | 13.65 | 20.91 | 0.00 | 0.00 | 0.26 | 0.58 | 0.00 | 62.95 | 13.51 | 33.51 | 0.20 | 43.67 | 0.33 | 40.01 | 26.80 | 0.00 | 0.00 | 3.63 | 0.00 |
| Camera-based methods | |
| MonoScene [2] | 37.87 | 5.22 | 19.41 | 12.31 | 19.34 | 0.43 | 0.58 | 8.02 | 2.03 | 0.86 | 48.35 | 11.38 | 28.13 | 3.32 | 32.89 | 3.53 | 26.15 | 16.75 | 6.92 | 5.67 | 4.20 | 3.09 |
| TPVFormer [12] | 40.22 | 5.89 | 21.39 | 13.64 | 21.56 | 1.09 | 1.37 | 8.06 | 2.57 | 2.38 | 52.99 | 11.99 | 31.07 | 3.78 | 34.83 | 4.80 | 30.08 | 17.52 | 7.46 | 5.86 | 5.48 | 2.70 |
| VoxFormer [25] | 38.76 | 4.89 | 18.93 | 11.81 | 17.84 | 1.16 | 0.89 | 4.56 | 2.06 | 1.63 | 47.01 | 9.67 | 27.21 | 2.89 | 31.18 | 4.97 | 28.99 | 14.69 | 6.51 | 6.92 | 3.79 | 2.43 |
| OccFormer [52] | 40.27 | 6.76 | 22.39 | 13.81 | 22.58 | 0.66 | 0.26 | 9.89 | 3.82 | 2.77 | 54.30 | 13.44 | 31.53 | 3.55 | 36.42 | 4.80 | 31.00 | 19.51 | 7.77 | 8.51 | 6.95 | 4.60 |
| DepthSSC [46] | 40.85 | 7.19 | 21.72 | 14.28 | 21.90 | 2.36 | 4.30 | 11.51 | 4.56 | 2.92 | 50.88 | 12.89 | 30.27 | 2.49 | 37.33 | 5.22 | 29.61 | 21.59 | 5.97 | 7.71 | 5.24 | 3.51 |
| Symphonies [13] | 44.12 | 13.11 | 24.05 | 18.58 | 30.02 | 1.85 | 5.90 | 25.07 | 12.06 | 8.20 | 54.94 | 13.83 | 32.76 | 6.93 | 35.11 | 8.58 | 38.33 | 11.52 | 14.01 | 9.57 | 14.44 | 11.28 |
| CGFormer [50] | 48.07 | 12.08 | 28.01 | 20.05 | 29.85 | 3.42 | 3.96 | 17.59 | 6.79 | 6.63 | 63.85 | 17.15 | 40.72 | 5.53 | 42.73 | 8.22 | 38.80 | 24.94 | 16.24 | 17.45 | 10.18 | 6.77 |
| DISC(ours) | 47.35 | 13.47 | 27.63 | 20.55 | 29.41 | 4.64 | 8.27 | 19.24 | 8.51 | 6.74 | 61.88 | 17.56 | 40.09 | 5.27 | 42.53 | 9.24 | 38.76 | 23.05 | 16.73 | 19.51 | 10.32 | 8.21 |
+
+Table 2. Quantitative results on SSCBench-KITTI360 test. The results for most counterparts are provided in [24]. Among all methods, the top three ranked approaches are marked as red, bold, and underlined. DISC achieves SOTA results in mIoU and InsM, while surpassing LiDAR-based methods across multiple category-specific metrics.
+
+| Method | IoU↑ | InsM↑ | ScnM↑ | mIoU↑ |
| Baseline | 20.05 | 6.06 | 19.14 | 12.69 |
| + Instance Stream | 45.12 | 9.79 | 24.73 | 16.86 |
| + Scene Stream | 45.85 | 8.55 | 25.80 | 16.73 |
| DISC(Ours) | 45.93 | 8.75 | 26.27 | 17.05 |
+
+Table 3. Ablation study on architecture of DISC. DISC achieves optimal comprehensive performance.
+
+| Method | InsM↑ | ScnM↑ | mIoU↑ |
| w/o C2FBEV | 8.56 | 25.74 | 16.70 |
| w/o Image-assisted strategy | 8.44 | 25.75 | 16.64 |
| Using a fixed threshold | 8.67 | 26.00 | 16.88 |
| DISC instance query | 8.75 | 26.27 | 17.05 |
+
+coder for handling 3D features, similar to CGFormer [50]. On top of the baseline, adding the instance stream and scene stream individually leads to significant improvements of 3.73 InsM and 6.66 ScnM for instance and scene, respectively. When integrating both the instance and scene streams, DISC achieves a balanced improvement in instance and scene metrics and delivers optimal IoU and mIoU scores, further validating the effectiveness of our methods.
+
+Analysis of discriminative query generator. Tab. 4 provide an ablation analysis of the Discriminative Query Generator (DQG). Tab. 4 shows that removing the Coarse-to-fine BEV generation module significantly reduces both InsM and ScnM. Additionally, eliminating the front-view-assisted candidate point localization strategy and replac
+
+Table 4. Ablation study on query generator. We evaluate diverse query generation strategies for optimal performance.
+
+| Ins. SA | Ins.-Img. CA | Ins.-Scn. CA | InsM | mIoU |
| × | × | × | 8.55 | 16.73 |
| ✓ | × | × | 8.62 | 16.69 |
| ✓ | ✓ | × | 8.73 | 16.98 |
| ✓ | × | ✓ | 8.69 | 16.86 |
| ✓ | ✓ | ✓ | 8.75 | 17.05 |
+
+Table 5. Ablation study on the Adaptive Instance Layer. Cross-attention with image plays a crucial role in instance performance.
+
+| Scn. SA | Scn.-Img. CA | ScnM | mIoU |
| × | × | 24.73 | 16.86 |
| ✓ | × | 25.99 | 17.01 |
| × | ✓ | 25.96 | 16.85 |
| ✓ | ✓ | 26.27 | 17.05 |
+
+Table 6. Ablation study on the Global Scene Layer. Self-attention proves critical for scene reconstruction.
+
+ing the grid-based candidate point selection strategy with a fixed threshold has a more pronounced impact on instance than on scene. Furthermore, we show that a patch size of 4 for scene query initialization yields the best mIoU and ScnM (see the appendix for details). These results highlight the effectiveness of the DQG in providing sufficient geometric and semantic priors for query initialization, leading to optimal network performance.
+
+Analysis of dual-attention class decoder. To analyze the flow of instance and scene queries within their respective decoder layers, we evaluate the interactions between various modules in Adaptive Instance Layer (AIL) and the Global Scene Layer (GSL). Tab. 5 shows that removing the instance-image cross-attention has the most significant im
+
+
+Figure 5. Qualitative visualization results on the SemanticKITTI [1] validation set. Compared to state-of-the-art (SOTA) methods, DISC produces more logical scene layouts and more accurate and detailed instance predictions.
+
+pact on performance, underscoring the importance of fusing instance queries with front-view features. Tab. 6 reveals that scene categories rely more on the self attention module to refine the global scene layout compared to instance categories, highlighting the distinct reconstruction challenges faced by each category.
+
+# 4.5. Visualizations
+
+Qualitative Results. Fig. 5 visualizes predicted results on the SemanticKITTI validation set from Symphonies [13], CGFormer [50], and our proposed DISC. We compare the performance differences between DISC and other SOTA methods on scene and instance categories. As highlighted by the yellow boxes, DISC predicts more logical scene layouts (e.g., roads do not intersect with terrain) and better geometric distributions (e.g., road structures are more complete and realistic), leveraging the scene features' global perception capabilities. For instances, DISC mitigates the impact of projection errors and occlusions, resulting in more accurate and detailed instance predictions. Additional qualitative results can be found in the Appendix.
+
+Attention Map Analysis. In Fig. 6, we visualize the interaction mechanisms of scene and instance queries within their respective layers. The patch-based scene queries expand their receptive field through multi-layer self-attention. Fig. 6 (b) shows the ground truth distribution of instance categories and the instance query candidate points generated by the Discriminative Query Generator, which are concentrated around the ground truth positions. Additionally, in instance self-attention, queries of the same category receive higher attention weights. These results highlight the effectiveness of our discriminative processing for scene and instance categories.
+
+
+(a) Visualization of self-attention in scene patch queries
+
+
+Layer2
+
+
+
+
+Instance BEV Segmentation
+
+
+
+
+(b) Visualization of self-attention in instance point queries
+Figure 6. Analysis of attention maps within DISC.
+
+# 5. Conclusion
+
+In this paper, we propose DISC, a dual-stream neural architecture that resolves semantic completion challenges through disentangled refinement of instance and scene representations on the BEV plane. The framework incorporates an efficient query generator (DQG) that fuses geometric-semantic features to enhance both instance and scene queries, complemented by a dual-attention class decoder (DACD) comprising a global-aware scene layer for contextual ambiguity reduction and an adaptive instance layer employing dynamic feature aggregation to address occlusion and projection errors. Experimental validation demonstrates that DISC achieves state-of-the-art performance on SemanticKITTI and SSCBench-KITTI-360 benchmarks while maintaining computational efficiency.
+
+# References
+
+[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9297-9307, 2019.
+[2] Anh-Quan Cao and Raoul De Charette. Monoscene: Monocular 3d semantic scene completion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3991–4001, 2022.
+[3] Li Chen, Chonghao Sima, Yang Li, Zehan Zheng, Jiajie Xu, Xiangwei Geng, Hongyang Li, Conghui He, Jianping Shi, Yu Qiao, et al. Persformer: 3d lane detection via perspective transformer and the openlane benchmark. In European Conference on Computer Vision, pages 550-567. Springer, 2022.
+[4] Sijia Chen, En Yu, Jinyang Li, and Wenbing Tao. Delving into the trajectory long-tail distribution for multi-object tracking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19341-19351, 2024.
+[5] Sijia Chen, En Yu, and Wenbing Tao. Cross-view referring multi-object tracking. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 2204-2211, 2025.
+[6] Ran Cheng, Christopher Agia, Yuan Ren, Xinhai Li, and Liu Bingbing. S3cnet: A sparse semantic scene completion network for lidar point clouds. In Conference on Robot Learning, pages 2148-2161. PMLR, 2021.
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+[8] Adam W Harley, Zhaoyuan Fang, Jie Li, Rares Ambrus, and Katerina Fragkiadaki. Simple-bev: What really matters for multi-sensor bev perception? In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 2759-2765. IEEE, 2023.
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+# Disrupting Model Merging: A Parameter-Level Defense Without Sacrificing Accuracy
+
+Wei Junhao*
+
+RIKEN AIP;
+
+Institute of Science Tokyo
+
+China
+
+wei.j.ac@m.titech.ac.jp
+
+Yu Zhe*
+
+RIKEN AIP
+
+China
+
+zhe.yu@riken.jp
+
+Jun Sakuma
+
+RIKEN AIP;
+
+Institute of Science Tokyo
+
+Japan
+
+sakuma@c.titech.ac.jp
+
+# Abstract
+
+Model merging is a technique that combines multiple finetuned models into a single model without additional training, allowing a free-rider to cheaply inherit specialized capabilities. This study investigates methodologies to suppress unwanted model merging by free-riders. Existing methods such as model watermarking or fingerprinting can only detect merging in hindsight. In contrast, we propose a first proactive defense against model merging. Specifically, our defense method modifies the model parameters so that the model is disrupted if the model is merged with any other model, while its functionality is kept unchanged if not merged with others. Our approach consists of two modules, rearranging MLP parameters and scaling attention heads, which push the model out of the shared basin in parameter space, causing the merging performance with other models to degrade significantly. We conduct extensive experiments on image classification, image generation, and text classification to demonstrate that our defense severely disrupts merging while retaining the functionality of the post-protect model. Our code is available on Github: https://github.com/ISCT-W/PaRaMS
+
+# 1. Introduction
+
+The pretrain–finetune paradigm trains models on large datasets before finetuning on smaller, task-specific ones, enabling efficient adaptation to specialized tasks. For instance, CNNs like ResNet [10] pretrained on ImageNet [7] extract rich visual features for downstream tasks. Platforms like Hugging Face have further popularized this approach, making it fundamental to language [3, 25], vision [8], and multimodal learning [20, 21].
+
+The success of this paradigm has led to model merging [31], a technique that integrates multiple fine-tuned models
+
+from the same pretrained source without additional training, often by linearly combining parameters. Specifically, consider two models: a digit classification model and an object classification model. The merged model is capable of handling both digit and object classification tasks. A basic model merging technique is parameter averaging, where the parameters of two fine-tuned models are combined using weight averaging [27]. More advanced methods, such as Task Arithmetic [14] and TIES-Merging [29], further refine the averaging approach. With nearly 30,000 merged models available on Hugging Face, model merging has become a practical and efficient approach for customizing models across diverse applications.
+
+Although model merging is convenient and low-cost, it introduces potential risks that have received relatively little attention. [6, 30] argue that a model's capabilities constitute valuable intellectual property (IP), and unwanted merging could lead to IP infringement. For example, suppose a company open-source finetuned models to showcase their technological advancements under certain license terms. Then, a free-rider could merge such models into their own finetuned versions at minimal cost by ignoring the license terms, which threatens IP rights. This infringement occurs because the merged model retains the specialized performance from the original finetuned models without requiring the same level of computational investment or expertise (Figure 1 top). Unlike traditional software, where direct code reuse is easily traceable, model merging blends parameter spaces in a way that makes it difficult to attribute contributions to specific sources. As a result, a merged model can inherit proprietary capabilities while obfuscating its origins, effectively allowing free-riders to bypass licensing restrictions and benefit from intellectual efforts they did not contribute to. This not only diminishes the commercial value of the original model but also raises concerns about fair attribution and ethical usage, as free-riders can publicly deploy the merged model under the guise of independent innova
+
+tion. Moreover, since merging does not inherently degrade performance and can even enhance it in some cases, it incentivizes free-riders to exploit this loophole, further exacerbating the risk of IP infringement.
+
+To address this, [6, 30] have proposed model watermarking or fingerprinting techniques that enable post-merging verification, allowing model owners to detect whether their models have been used without permission. Yet, these methods are inherently passive and do not prevent merging in the first place. This gap presents a critical security challenge, and there is an urgent need for proactive defenses that make model merging ineffective on protected models, preventing unwanted usage from the outset.
+
+In this study, to mitigate the IP infringement risk posed by model merging, we ask a fundamental research question: How can we proactively protect a finetuned model from unwanted merging while preserving its original capabilities? An illustration of proactive defense is shown in Figure 1 bottom. We consider that a proactive defense should meet two core requirements. First, before merging, the protected model must retain its original performance since releasing a degraded model would defeat the purpose of showcasing its strengths. Second, after merging, the model's performance should degrade significantly, thereby discouraging free-riders from exploiting it.
+
+To fulfill these pre-merging and post-merging requirements, we propose a proactive defense methods, termed PaRaMS, short for Parameter rearrangement & Random Multi-head Scaling, applied to two fundamental modules common across modern machine learning models: the Multi-Layer Perceptron (MLP) layers and attention modules of Transformer-based architectures. PaRaMS perturbs model parameters without altering the model's functionality, thereby preserving its original performance before merging. At the same time, these parameter modifications shift the protected model away from other finetuned models that share the same pretrained checkpoint, causing merged models to suffer poor performance. Thus, PaRaMS meets both requirements of retaining pre-merging capabilities and undermining post-merging utility. Moreover, since most model merging methods operate on MLP [27], Attention [24], or both [14, 29], our approach is generalizable to most merging techniques.
+
+We summarize our main contributions as follows:
+
+1. We are the first to propose a proactive solution against the free-rider threat in model merging, addressing the security gap where a free-rider can cheaply inherit a defender's finetuned capabilities.
+2. Our method preserves the pre-merging model's functionality while significantly decreasing the performance of post-merging models.
+3. Through experiments on multiple tasks and datasets, we show that our approach retains the model's performance
+
+yet severely undermines merging performance, and we provide in-depth analysis to explain why it succeeds in disrupting model merging.
+
+4. Considering the possibility of a free-rider attempting to bypass our defense, we comprehensively evaluated adaptive strategies to circumvent our method. In response to these adaptive approaches, we also proposed corresponding solutions, ensuring that the free rider either fails to bypass our method or incurs an excessively high cost to do so.
+
+# 2. Preliminaries
+
+Model Merging. Model merging techniques allow the merged model to inherit each model's task-specific performance without requiring additional training, relying instead on parameter-level operations. Formally, let $\theta$ be model parameters, with $\theta_{\mathrm{pre}}$ denoting pretrained parameters and $\theta_{i}$ finetuned parameters on dataset $\mathcal{D}_i$ . For $n$ task-specific models $\{\theta_1,\dots ,\theta_n\}$ derived from the same pretrained checkpoint $\theta_{\mathrm{pre}}$ , model merging can be written as
+
+$$
+\theta_ {\text {m e r g e}} = \mathcal {M} \left(\theta_ {\text {p r e}}, \theta_ {1}, \dots , \theta_ {n}\right),
+$$
+
+where $\mathcal{M}$ is a merging algorithm, often based on linear interpolation of parameters, as introduced later. Let $\mathcal{T}_i$ denote the data distribution (or test set) for the $i$ -th task, and $\mathrm{Perf}:\theta \times \mathcal{T}\to \mathbb{R}$ be a performance evaluation score of $\theta$ on samples from $\mathcal{T}_i$ (e.g. for classification task, this refers to accuracy). Under this notation, the goal of model merging is to find a merged model to retain each task's performance:
+
+$$
+\operatorname {P e r f} \left(\theta_ {\text {m e r g e}}, \mathcal {T} _ {i}\right) \approx \operatorname {P e r f} \left(\theta_ {i}, \mathcal {T} _ {i}\right) \quad \forall i \in \{1, \dots , n \}.
+$$
+
+In this paper, we focus on model merging methods that rely on parameter-level operations, which cover most mainstream approaches.
+
+Task Arithmetic. Task Arithmetic (TA) [14] is a classic model merging method, and many approaches [19, 29] are improvements on this method. Therefore, we will first introduce this method. In TA, they define a task vector as an element-wise difference: $\tau_{i} = \theta_{i} - \theta_{\mathrm{pre}}$ . It then merges these task vectors by a linear combination: $\theta_{\mathrm{merged}} = \theta_{\mathrm{pre}} + \lambda \Sigma_{i=1}^{n}\tau_{i}$ , where $\lambda$ is the scaling coefficient. By directly adding task vectors of different tasks to the pretrained parameters, a multi-task model can be constructed. This multi-task model is known to be able to achieve a similar performance [19, 31, 35] of each individual model on corresponding task.
+
+Other Merging Techniques. Several subsequent works have focused on improving TA, similarly rely on additive parameter operations and require a same pretrained model. However, they further refine the merging coefficients (e.g., AdaMerging [32]) or adjust parameter subspaces (e.g., TIES-Merging [29], DARE [33]). For more details, please see the appendix.
+
+
+Figure 1. Illustration of proactive defense against model merging
+
+# 3. Problem Formulation
+
+# 3.1. Threat Model
+
+Attack Scenario. We consider a common workflow where a defender starts with a large pretrained model and then finetunes it on specialized data to optimize performance for a particular domain or task. Once finetuning is complete, the defender open-sources this finetuned model, often to demonstrate its capabilities to the broader community. Meanwhile, a free-rider obtain this open-sourced model with the intent of merging it with a model under their control. We suppose the free-rider's model is also finetuned from the same pretrained checkpoint, enabling straightforward parameter combination. This assumption is reasonable because most finetuning workflows in deep learning begin with widely used pretrained models such as CLIP, Vision Transformers (ViTs), Diffusion models or Llama, which serve as standard initialization points across different applications. By merging the two models, the free-rider aims to inherit the defender's specialized performance with extremely low cost, and combine it with whatever capabilities already exist in their own model. To prevent such free-riders, the defender seeks to develop proactive defenses that maintain the model's original performance while making its performance significantly degraded when merged with any other models.
+
+Free-rider's capability. We assume the free-rider has limited computing resources, making expensive training approaches such as knowledge distillation or full re-training impractical. Instead, the free-rider relies on model merging as a low-cost alternative to acquire the defender's specialized capabilities. To enable effective merging, the free-rider possesses a finetuned model originating from the same pretrained checkpoint as the defender's model and has white-box access to the defender's open-source model. The success of the free-rider's attack is measured by whether the merged model achieves a similar performance as the defender's model without sacrificing the ability to deal with the free rider's task.
+
+Defender's capability. The defender has full control over their model's parameters and can apply modifications to protect it. These modifications must preserve the model's original performance while preventing effective merging. The defender does not have access to the free-rider's model but assumes, in line with common model merging practices, that it originates from the same pretrained checkpoint; otherwise, merging would inherently fail. The defender's success is defined by ensuring that their model remains fully functional for legitimate users, while any merged model suffers significant performance degradation on the defender's task.
+
+# 3.2. Problem Setup.
+
+Let $\theta_{\mathrm{def}}$ and $\theta_{\mathrm{fr}}$ be the defender's model and free-riders model derived from the same open-source pretrained model $\theta_{\mathrm{pre}}$ finetuned using data $\mathcal{D}_{\mathrm{def}}$ and $\mathcal{D}_{\mathrm{fr}}$ , respectively. The free-rider attempts to obtain $\theta_{\mathrm{merge}} = \mathcal{M}(\theta_{\mathrm{pre}}, \theta_{\mathrm{def}}, \theta_{\mathrm{fr}})$ which has comparable performance on both tasks,
+
+$$
+\operatorname {P e r f} \left(\theta_ {\text {m e r g e}}, \mathcal {T} _ {\text {d e f}}\right) \approx \operatorname {P e r f} \left(\theta_ {\text {d e f}}, \mathcal {T} _ {\text {d e f}}\right),
+$$
+
+$$
+\operatorname {P e r f} \left(\theta_ {\text {m e r g e}}, \mathcal {T} _ {\mathrm {f r}}\right) \approx \operatorname {P e r f} \left(\theta_ {\mathrm {f r}}, \mathcal {T} _ {\mathrm {f r}}\right).
+$$
+
+But for the defender, being merged by unknown free-rider is not wanted thus they employ a proactive defense for its model $\eta : \theta \to \theta$ to modify parameters without changing model architecture and publish the modified model $\hat{\theta}_{\mathrm{def}} = \eta(\theta_{\mathrm{def}})$ . $\hat{\theta}_{\mathrm{def}}$ is required to keep functional equivalence, i.e.,
+
+$$
+f (x, \theta_ {\mathrm {d e f}}) = f (x, \hat {\theta_ {\mathrm {d e f}}}) \quad \text {f o r a n y} x, \tag {1}
+$$
+
+therefore, $\operatorname{Perf}(\hat{\theta}_{\mathrm{def}},\mathcal{T}) = \operatorname{Perf}(\theta_{\mathrm{def}},\mathcal{T})$ holds for any dataset $\mathcal{T}$ . The free-rider may use model merging to get a merged model $\hat{\theta}_{\mathrm{merge}} = \mathcal{M}(\theta_{\mathrm{pre}},\hat{\theta}_{\mathrm{def}},\theta_{\mathrm{fr}})$ , and the defender wants that the performance of the merged model on $\mathcal{T}_{\mathrm{def}}$ is significantly low:
+
+$$
+\operatorname {P e r f} \left(\hat {\theta} _ {\text {m e r g e}}, \mathcal {T} _ {\text {d e f}}\right) \ll \operatorname {P e r f} \left(\theta_ {\text {m e r g e}}, \mathcal {T} _ {\text {d e f}}\right). \tag {2}
+$$
+
+In summary, our problem is to design a proactive defense $\eta$ that satisfies Eq. 2 (performance degradation after model
+
+
+Figure 2. Loss landscape before and after applying our proposal
+
+merging) under the condition Eq. 1 (functional equivalence before model merging).
+
+# 4. Method
+
+In this section, we introduce our defense, termed as PaRaMS, that satisfies the conditions defined in the Eq. 1 and 2. PaRaMS employs two distinct parameter transformations satisfying functional equivalence, tailored for two common modules, MLP and Attention modules. In the next subsection, we introduce the idea to disrupt the model with preserving functional invariance.
+
+# 4.1. Why Model Merging Works
+
+To disrupt model merging, we first ask why model merging works. In [35], they describe a basin in the loss landscape as a region where a model's parameters converge to a low-loss solution during optimization. They also found that, in the pretrain–finetune paradigm, finetuned models with the same pretrained model often end up in a shared or closely aligned basin (Figure 2, basin 1). They then conclude this is the reason why model merging works. Considering this observation from the opposite perspective, it also suggests that if the two model parameters located in different distant basins, model merge would disrupt even if the models were derived from the same checkpoint (Figure 2, basin 2). This can be experimentally confirmed in Section 5 empirically. Our proactive defense against model merge is designed based on this observation. More specifically, our idea is to use a model modification $\eta$ that satisfies the following two conditions: (1) The modified model $\eta(\theta)$ is functionally equivalent to the original model $\theta$ , and (2) $\eta(\theta)$ are largely distant from $\theta$ in the model parameter space.
+
+The first property guarantees that the performance of the model modified by our proactive defense is equivalent to that of the original model. In addition, even if model merging is performed, models modified by our proactive defense are expected to fail due to the second property. Figure 2 illustrates this idea.
+
+# 4.2. Our Proposal
+
+In this section, we propose two proactive defense methods that satisfy the two conditions introduced in the last subsection. The first is MLP parameter rearrangement, which is specifically designed for MLP architectures. The second is Random Multi-head Scaling, which is designed for multi-head attention blocks.
+
+MLP Parameter Rearrangement. In the following, we suppose the target model that consists of a 2-layer MLP for simplicity, but our method is applicable to any target model as long as it contains two or more consecutive MLP layers immediately. Concretely, consider a two-layer MLP of the following form:
+
+$$
+\operatorname {M L P} (X) = W _ {2} \sigma \left(W _ {1} X + b _ {1}\right) + b _ {2},
+$$
+
+where $\sigma$ is an element-wise nonlinear activation. We remark that element-wise nonlinear activations are commonly used for modern machine learning architectures (e.g., Sigmoid, ReLU [1], tanh, etc.).
+
+The idea is to randomly shuffle the weight matrices $W_{1}$ and $W_{2}$ of the MLP in an element-wise manner [2]. If the two shuffles are generated independently, this makes the behavior of the MLP completely different from the original model. In our construction, the shuffle provided for $W_{2}$ is set to restore the shuffle applied to $W_{1}$ . To realize this, we introduce a permutation matrix $P$ , which is a square binary matrix with exactly one "1" in each row and column and "0"s elsewhere. By multiplying this matrix with the MLP weight, we can reorder vector coordinates. Given such a matrix $P$ , $P^{-1} = P^{\top}$ and element-wise non-linear function $\sigma$ , we can find the following process does not change the MLP's output, as proved in [2].
+
+$$
+W _ {1} ^ {\prime} = P W _ {1}, \quad b _ {1} ^ {\prime} = P b _ {1}, \quad W _ {2} ^ {\prime} = W _ {2} P ^ {\mathsf {T}}.
+$$
+
+Here, $b_{1}$ refers to biases in the first layer of MLP, $W_{1}$ and $W_{2}$ are weights in the first/second layers of MLP.
+
+The functional equivalence is satisfied for any random $P$ that satisfies the constraint, but considering that our goal is to make the model merge disrupt, the optimal permutation matrix is one that makes the distance between the model parameters as large as possible before and after the permutation. Formally, considering the realistic situation that a model has $n$ MLPs, we can apply the permutation $P_{i}$ and $P_{i}^{\mathsf{T}}$ to every $\mathrm{MLP}_i$ $(i = 1,\dots,n)$ . We then summarize all the operations of $P_{i}$ and $P_{i}^{\mathsf{T}}$ into a function $\eta_{\mathrm{perm}}$ , and our optimization objective is shown below:
+
+$$
+\arg \max _ {\eta_ {\mathrm {p e r m}}} \left\| \theta_ {\mathrm {p r e}} ^ {\mathrm {M L P}} - \eta_ {\mathrm {p e r m}} \left(\theta_ {\mathrm {d e f}} ^ {\mathrm {M L P}}\right) \right\| ^ {2}.
+$$
+
+Here, $\theta_{\mathrm{pre}}^{\mathrm{MLP}}$ refers to all MLPs' parameters in the pretrained model. $\theta_{\mathrm{def}}^{\mathrm{MLP}}$ refers to all MLPs' parameters in the defender model. This optimization can be reformulated as a linear
+
+assignment problem, as proposed by [2] which attempts to optimize the permutation matrix to minimize two models' distance. We follow [2] to solve this optimization problem. More details about optimization are shown in the appendix.
+
+Random Multi-head Scaling. Next, we propose random multi-head scaling, which works as a proactive defense for attention block. An attention module with its corresponding output projection is defined as below:
+
+$$
+\text {A t t e n t i o n} = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d}}\right) V W _ {O},
+$$
+
+where $Q, K, V$ is the query, key and value matrix, $W_O$ is the projection matrix. We leverage the fact that $QK^{\top} = QA(KA^{-1})^{\top}$ when $A$ is real diagonal matrix. By introducing such random scaling with $A$ , we can change the model parameter values while keeping functional equivalence. This can be applied to $VW_O$ in the same manner. Similarly, for the value matrix $V$ and its associated output projection matrix $W_O$ , we can apply the same transformation by multiplying $V$ with a real diagonal matrix $B$ and compensating by multiplying $W_O$ with $B^{-1}$ , ensuring that the overall output of the attention module remains unchanged. Proof see the appendix.
+
+Specifically, for each attention head $i$ , we sample two diagonal matrices: $A_{i}, B_{i}$ , whose diagonal entries are drawn from a uniform distribution $\mathcal{U}(s_{\min}, s_{\max})$ and update:
+
+$$
+Q _ {i} ^ {\prime} = Q _ {i} A _ {i}, K _ {i} ^ {\prime} = K _ {i} A _ {i} ^ {- 1}
+$$
+
+$$
+V _ {i} ^ {\prime} = V _ {i} B _ {i}, W _ {O} ^ {\prime} [:, i ] = B _ {i} ^ {- 1} W _ {O} [:, i ],
+$$
+
+We summarize all the scalings into a function $\eta_{\mathrm{scaling}}$ . Our method $\eta = \eta_{\mathrm{perm}} \circ \eta_{\mathrm{scaling}}$ , which directly combines MLP parameter rearrangement and random multi-head scaling. The detailed algorithm is shown in the appendix.
+
+# 5. Experiment
+
+# 5.1. Experiment Setup
+
+Models. In our experiments, we considered three tasks: image classification, image generation, and text classification. For image classification, we use three ViT [8] models: ViT-B-16, ViT-B-32, and ViT-L-14. These ViT models have been pre-trained within the CLIP [20] framework. For the image generation task, we use Stable Diffusion 1.5 (SD1.5) [21]. For the text classification task, we use Llama2 [26]. All models listed here contain MLPs and attention blocks.
+
+Datasets. For image classification, we use seven datasets for the evaluations: Cars [15], RESISC45 [4], SVHN [18], GTSRB [23], MNIST [17], EuroSAT [11] and DTD [5]. Details about these datasets are shown in the appendix.
+
+Merging methods. To demonstrate the generality of our method, we tested its effectiveness across various model merging approaches as Task arithmetic (TA) [14], Weight
+
+Average (WA) [28], TIES-Merging [29] and AdaMerging (ADA) [32] along with a plug-in module DARE [33]. Details about these methods are shown in the appendix.
+
+Evaluation strategy. In our experiments, we evaluate the performance of four distinct types of models based on two key aspects: merge situation and protection mechanisms. The first aspect defines whether a model is unmerged (specialized for a single task) or merged (a multitask model capable of handling the free-rider model's task and the defender model's task). The second aspect defines whether a model is guarded with our protection or not. Specifically, we define the four models as follows: Unmerged Model without Protection (UMP-); Merged Model without Protection (MMP-); Unmerged Model with Protection (UMP+); and Merged Model with Protection (MMP+). For evaluation, unmerged models (UMP- and IMP+) are tested only on their designated tasks, while merged models (MMP- and MMP+) are assessed across all their supported tasks. Our preliminary goal is to ensure the performance of IMP+ are the same as UMP- and that the performance of MMP+ is much less than that of MMP-.
+
+# 5.2. Main Results
+
+# 5.2.1. Results on Image classification
+
+Comprehensive results on task arithmetic. In the first experiment, we trained both the defender's and free-rider's models on any two distinct datasets out of the seven, and measured the performance of protected and unprotected model before and after merge. We denote the task corresponding to the defender model as $\mathcal{T}_{\mathrm{def}}$ and the task corresponding to the free-rider model as $\mathcal{T}_{\mathrm{fr}}$ . Here, we employed ViT-B-32 for the models. Since ViT contains both MLP and multi-head attention, we applied MLP parameter rearrangement and random multi-head scaling for protection. We evaluated our proposal against TA because it serves as the foundation for many model merging methods.
+
+First, we measured the classification accuracy on $\mathcal{T}_{\mathrm{def}}$ for four models: UMP-, UMP+, MMP-, MMP+. Moreover, for MMP- and MMP+, we additionally measured the classification accuracy on $\mathcal{T}_{\mathrm{fr}}$ . If PaRaMS works, performance of $\mathrm{MMP+}$ on both tasks would be significantly degraded compared to MMP-. The results are summarized in Table 1. We observe a huge gap between performance of MMP- and $\mathrm{MMP+}$ on both $\mathcal{T}_{\mathrm{def}}$ and $\mathcal{T}_{\mathrm{fr}}$ , achieving at least gap of $65.16\%$ ( $67.82\% \rightarrow 2.66\%$ in GTSRB/DTD setting). Since our method does not alter the functionality of the defender model, UMP- and $\mathrm{UMP+}$ have the same performance.
+
+Evaluation on different model merging methods. Next, we evaluated the effectiveness of our method on other merging approaches. Specifically, we examined four merging methods: TA, TIES, WA, and ADA, along with a plugin in module DARE. Since DARE can be combined with each of the four merging methods to form a new merging ap
+
+Table 1. The classification accuracy of MMP-/MMP+ (merged by TA) on ${\mathcal{T}}_{\text{def }}$ and ${\mathcal{T}}_{\mathrm{{fr}}}$ on ViT-B-32 $\left( {\lambda = {0.8}}\right)$ .
+
+| MMP- Accuracy (%) on \( T_{\text{def}}/T_{\text{fr}} \) | \( T_{\text{fr}} \) |
| MMP+ Accuracy (%) on \( T_{\text{def}}/T_{\text{fr}} \) | Cars | RESISC45 | EuroSAT | SVHN | GTSRB | MNIST | DTD |
| \( T_{\text{def}} \) | Cars | NA | 70.29/94.240.51/2.13 | 72.23/99.760.50/12.78 | 67.53/97.230.47/12.62 | 67.99/98.560.63/2.84 | 67.93/99.700.53/8.92 | 70.61/77.070.62/2.13 |
| RESISC45 | 94.24/70.294.89/0.49 | NA | 83.27/99.193.76/18.44 | 90.56/96.812.86/9.63 | 90.46/97.964.92/1.23 | 90.62/99.602.10/10.10 | 93.21/72.182.49/2.18 |
| EuroSAT | 99.76/72.239.26/0.61 | 99.19/83.2713.54/2.90 | NA | 98.06/95.909.67/19.41 | 98.07/93.9710.33/2.14 | 96.89/99.469.26/9.58 | 99.74/70.649.54/1.86 |
| SVHN | 97.23/67.5310.53/0.55 | 96.81/90.569.16/2.52 | 95.90/98.0610.16/16.57 | NA | 94.60/94.2613.31/2.04 | 92.27/99.389.16/8.79 | 97.03/68.099.67/3.03 |
| GTSRB | 98.56/67.991.91/0.58 | 97.96/90.461.98/2.56 | 93.97/98.071.77/15.11 | 94.26/94.601.81/9.69 | NA | 91.58/99.381.26/9.82 | 98.20/67.821.93/2.66 |
| MNIST | 99.70/67.9211.39/0.44 | 99.60/90.6212.28/3.60 | 99.46/96.8911.35/9.24 | 99.38/92.2711.35/18.16 | 99.38/91.5811.47/2.24 | NA | 99.70/70.6911.26/2.29 |
| DTD | 77.07/70.612.13/0.52 | 72.18/93.212.07/2.17 | 70.64/99.742.23/14.33 | 68.09/97.031.97/18.30 | 67.82/98.201.91/2.15 | 70.69/99.702.07/10.09 | NA |
+
+proach, we tested a total of eight merging methods. Due to space limitations, we report the average results across all datasets based on each model in Figure 3. Full results are shown in the appendix.
+
+As shown in Figure 3, PaRaMS successfully degrades the classification accuracy across all eight merging methods on all three ViT models. Here, the blue bars represent the accuracy of MMP- which merged by TA, TIES, WA, and ADA respectively, The pink bars represent the accuracy of MMP- merged by TA plus DARE, TIES plus DARE, WA plus DARE, and ADA plus DARE, respectively. Similarly, the yellow and green bars indicate the accuracy of $\mathrm{MMP + }$ with or without DARE. A clear gap can be observed between the performance of MMP- and $\mathrm{MMP + }$ , demonstrating that our method effectively causes the merging to fail on different merge methods. Furthermore, in this experiment, the accuracy of UMP-/UMP+ (blue and pink dash lines) remains unchanged before and after applying our method. This shows that PaRaMS does not have a negative impact on model performance unless model merging is applied.
+
+Furthermore, the performance of model merging is affected by hyper-parameters such as the coefficient in TA. Additionally, model merging can involve merging more than two models. We also tested our method with different coefficients, different numbers of models to be merged and ablation. Our proposal successfully disrupted model merging in all these situations. Due to space limitations, we have included these results in the appendix.
+
+# 5.2.2. Results on Image Generation
+
+To demonstrate that our proposal is effective in other applications, we evaluated our proposal on a text-to-image generation task. Here, we downloaded finetuned Stable Diffusion 1.5 (SD) [21] trained on different image concepts from Hugging Face. By merging these SD by TA, the merged SD is able to generate images containing multiple concepts. For quality assessment, we present the images generated by the model before and after merging and its text-to-image align-
+
+Table 2. Average text-to-image alignment scores between prompts and 1000 generated images by UMP-, UMP+, free-rider, MMP- and MMP+
+
+ | UMP- | UMP+ | Free-rider | MMP- | MMP+ |
| Prompt1 | 0.3286 | 0.3306 | 0.3245 | 0.3416 | 0.1277 |
| Prompt2 | 0.3335 | 0.3428 | 0.2961 | 0.3386 | 0.0820 |
+
+ment. Following [9], text-to-image alignment was measured by the similarity between the prompt embedding and the generated images using a pretrained CLIP model. A higher similarity indicates better generation quality.
+
+In Figure 4, we show images generated by UMP-, UMP+, MMP-, and MMP+. We can observe that the images generated UMP+ are clear while images generated by MMP+ (the rightmost images) are almost noise images. Moreover, we synthesize 1000 generated images based on the prompts in the given cases of Figure 4, for UMP-, UMP+, MMP-, and MMP+, and measure their average text-to-image similarity. In Table 2, we observe that MMP+ has significantly lower text-to-image alignment scores compared to MMP-. And the text-to-image alignment scores of UMP- are closed to UMP+. This means PaRaMS decreases the merged SD model's text-to-image generation ability while keeping the unmerged model's text-to-image generation ability.
+
+# 5.2.3. Results on Text Classification
+
+We also evaluated our proposal on a different modality to show the wide applicability of PaRaMS other than image domain. In this experiment, we finetuned Llama2 [25] on the Emotion [22] and Twitter datasets [16], which are common text classification tasks, using parameter-efficient finetuning (PEFT) [13] and full-parameter finetuning. We then applied task arithmetic and PEM-based task arithmetic (PEM-TA) [34] to merge finetuned models with an Llama2 model finetuned on Alpaca. For TA with full parameter finetuning, we protect the defender's model using both
+
+
+Figure 3. The average classification accuracy of MMP-/MMP+ over all task combinations on three Vision Transformer architectures (ViT-B-16, ViT-B-32, and ViT-L-14). Here, we use different model merging techniques: TA, TIES, WA, and ADA with/without DARE. Dashed and dotted lines indicate baseline performances (UMP and UMP+, respectively).
+
+
+
+
+
+
+
+
+Figure 4. Generated images from UMP-, UMP+, MMP-, MMP+. Each row is related to one prompt set. More examples are in the appendix.
+
+Table 3. The classification accuracy of UMP-/UMP+ and MMP-/MMP+ on two classification task emotion and twitter. Here, the model is Llama2, and the merged methods are TA and PEM-TA
+
+| Dataset | UMP-/UMP+ | MMP-(TA) | MMP+(TA) | MMP-(PEM-TA) | MMP+(PEM-TA) |
| Emotion | 99.8 | 97.6 | 21.4 | 96.1 | 52.7 |
| Twitter | 99.7 | 95.3 | 35.8 | 95.2 | 61.2 |
+
+parameter scaling and rearrangement. In the PEFT setting, PEM-based TA only merges LoRA-adapted parameters. Since this part of the parameters can be viewed as the multiplication of two matrices, we applied the scaling method only. Table 3 shows that the MMP- has high classification performance, while $\mathrm{MMP + }$ performs poorly. For PEM-TA, since we only apply parameter scaling, the performance degradation after merge is relatively small compared to full parameter finetuning setting, but there is still significant performance degradation compared to MMP-. From these results, we can conclude that PaRaMS effectively suppress model merging in the NLP domain, too.
+
+# 5.3. Investigation based on Connectivity
+
+As discussed in Sec 4.1, our goal was to force the protected model far away from the basin shared by all finetuned
+
+
+Figure 5. Layer-wise similarity of MMP- and MMP+. The defender model was trained on RESISC45 and a free-rider model trained on Cars. The model architecture is ViT-L-14.
+
+models that trained from the same pretrain model. To verify whether we achieve this goal, we evaluated block-wise similarity between pre/post-protection models and the freerider's model. The layer-wise similarity evaluates whether interpolating two model parameters with task arithmetic will also result in feature interpolation [35]:
+
+$$
+\sin^ {(\ell)} = \operatorname {c o s i n e} \left[ \mathcal {M} _ {\mathrm {T A}} ^ {(\ell)} \left(\theta_ {\text {p r e}}, \theta_ {\text {d e f}}, \theta_ {\text {f r}}; x\right), \frac {1}{2} \theta_ {\text {d e f}} ^ {(\ell)} (x) + \frac {1}{2} \theta_ {\text {f r}} ^ {(\ell)} (x) \right].
+$$
+
+Here $\mathcal{M}_{\mathrm{TA}}^{(\ell)}(\theta_{\mathrm{pre}},\theta_{\mathrm{def}},\theta_{\mathrm{fr}})$ refers to the output of layer $\ell$ of the merged model (based on TA with a scaling factor $\lambda = 0.5$ ), $\theta^{(\ell)}$ refers to the output of a pre-merging model on layer $\ell$ . High similarity indicates two models reside in a shared basin [35]. Figure 5 shows that layer-wise similarity of MMP- is much higher than layer-wise similarity of $\mathrm{MMP+}$ . This confirms that our objective in Sec.4.1 is achieved.
+
+# 6. Possible Contermeasure
+
+In reality, a "determined free-rider" may attempt to bypass our proposal by utilizing countermeasures designed against our approach. In this section, we assume free riders who know the technical details of PaRaMS and understand that the published models are protected by PaRaMS. With this assumption, we consider how such an adaptive free-rider
+
+Table 4. Classification accuracy on merged models under different behavior of free-rider and defender. Here, the models are ViT-B-32 and are merged by TA with coefficient $= 0.3$ . The defender model was fine-tuned on SVHN (97.46% → 96.33% with/without dropout) and free-rider models covering six other tasks.
+
+| Defender | Free-rider | Merged models |
| No Defense | Non-adaptive | 84.13% |
| PaRaMS | Non-adaptive | 7.12% |
| PaRaMS+dropout | Non-adaptive | 7.01% |
| PaRaMS | Adaptive | 80.32% |
| PaRaMS+dropout | Adaptive | 64.35% |
| PaRaMS+dropout | knowledge distillation | 82.27% |
+
+would bypass PaRaMS, and then we discuss potential countermeasures and strategies to further defend against them.
+
+Adaptive attack. First, we consider an adaptive attack to bypass our defense for the MLP part. Recall that the defender's defense using permutation $\eta_{\mathrm{perm}}$ is designed to maximize the distance between the parameters of the MLP layer in pretrained model and those of the defender's model. Then, the free-rider might try to recover by finding an adaptive strategy using permutation $\eta_{\mathrm{perm}}'$ that minimizes the distance between the MLP layers in pretrained model and the MLP layers in defender's model:.
+
+$$
+\arg \min _ {\eta_ {\mathrm {p e r m}} ^ {\prime}} \left\| \theta_ {\mathrm {p r e}} ^ {\mathrm {M L P}} - \eta_ {\mathrm {p e r m}} ^ {\prime} \circ \eta_ {\mathrm {p e r m}} (\theta_ {\mathrm {d e f}} ^ {\mathrm {M L P}}) \right\| ^ {2}
+$$
+
+Here, $\eta_{\mathrm{perm}}^{\prime}$ refers to the MLP layer permutated by MLP parameter rearrangement. A similar adaptive attack works with the scaling module, too. We denote our protected attention module as $Q^{\prime}$ , $K^{\prime}$ , and $V^{\prime}$ . We assume that free-riders obtain the pretrained model's attention module $Q_{\mathrm{pre}}$ , $K_{\mathrm{pre}}$ , and $V_{\mathrm{pre}}$ . Then, the free-rider can reconvery our scaling strategy by $\min_{A^{\prime}}\left\| Q_{\mathrm{pre}} - A^{\prime}Q^{\prime}\right\|^{2}$ . Once $A^{\prime}$ is determined, the scaling factor for $K^{\prime}$ is set as $A^{\prime \mathsf{T}}$ immediately. A similar strategy can also be applied to $V^{\prime}$ .
+
+Experimental Results under Adaptive Free-riders. Table 4 shows the performance of the merged model under different combinations of the behaviors of the defender and free-rider. When the free-rider is not adaptive, the performance of the merged model is significantly degraded (7.12%, row 3) irrespective of the defender's strategy (rows 3-4). However, when the free-rider is adaptive, PaRaMS is bypassed, and the performance of the merged model is almost recovered (80.32%, row 5). This does not necessarily mean that PaRaMS is meaningless, as a free-rider needs to solve optimization problems and must have prior knowledge of our method. However, we need a defense strategy that can counter adaptive free-riders.
+
+Enhancing Robustness via Dropout-Based Pruning. To improve the robustness of PaRaMS to counter against adaptive attacks, we also propose an additional modification approach that applies dropout-based pruning after PaRaMS.
+
+Specifically, for the finetuned model, we set a dropout rate $(10\%)$ and randomly select that fraction of weights to set to zero. While this additional pruning means the model can no longer fully maintain its original functionality, its performance degradation due to dropout is minor empirically $(97.46\%$ to $96.33\%$ in SVHN). In exchange, the randomness of the dropout makes the recovery by the above adaptive strategy more challenging, gaining resistance against adaptive attacks; the accuracy drop after model merge is almost $20\%$ (84.13% to $64.35\%$ in SVHN, Table 4, row 6), indicating that even adaptive free-riders cannot restore performance close to the original model. Thus, this minor sacrifice in an unmerged model's accuracy significantly strengthens our defense against adaptive attacks.
+
+Evaluating an Ultimate Adaptive Attack. Finally, we consider an ultimate adaptive countermeasure. One of the major solutions to transfer a model's ability to other models is knowledge distillation (KD) [12]. Since KD does not require the assumption that the models have parameters that are close to each other, a free-rider could leverage models protected with PaRaMS + dropout by using KD. Specifically, they can prepare an unlabeled dataset that is sampled from the same distribution as the protected model's training data and use the protected unmerged model to infer labels. Then, they finetune the pretrained model using the labeled dataset to obtain a new model whose parameters have not been perturbed. Finally, the free-rider can merge the newly finetuned model. The last row of Table 4 shows the performance of the merged model through KD. This strategy is expected to bypass all possible proactive defense methods that maintain the performance of UMP. However, the cost is greater than fine-tuning a new model from a pretrained model. Furthermore, it requires additional data. Given these difficulties, reasonable free-riders have little motivation to bypass our method rather than simply train a new model. Hence, we can conclude that this ultimate adaptive attack is impractical. The time cost of KD compared with model merging and PaRaMS is proposed in the appendix.
+
+# 7. Conclusion
+
+In this paper, we presented a proactive defense, termed PaRaMS, against model merging, protecting a fine-tuned model's capabilities from being inherited by free-riders. PaRaMS maintains the pre-merging model's performance while largely reducing the post-merging model's performance. Extensive experiments on image classification, text-to-image generation, and text classification tasks indicate that our proposal is effective on different tasks and model structures. In future work, we plan to investigate owner-controlled merging method, where model owners can specify which models are allowed to be merged, enabling a more secure and customizable merging process.
+
+# 8. Acknowledgement
+
+This work is supported by Japan Science and Technology Agency under Grant No. JST JPMJNX25C2, JST JPMJKP24C3, JST JPMJCR23M4, and Japan Society for the Promotion of Science under Grant No. JSPS 23H00483, JSPS 120251002, and RIKEN FY2025 Incentive Research Projects.
+
+# References
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+# Dissecting Generalized Category Discovery: Multiplex Consensus under Self-Deconstruction
+
+Luyao Tang $^{1,2,5*}$ , Kunze Huang $^{1,2,*}$ , Chaoqi Chen $^{3,\dagger}$ , Yuxuan Yuan $^{1}$ , Chenxin Li $^{4}$ , Xiaotong Tu $^{1,2}$ , Xinghao Ding $^{1,2}$ and Yue Huang $^{1,2}$
+
+1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University 2 School of Informatics, Xiamen University 3 Shenzhen University 4 The Chinese University of Hong Kong 5 The University of Hong Kong {lytang, kzhuang}@stu.xmu.edu.cn, cqchen1994@gmail.com, yhuang2010@xmu.edu.cn
+
+# Abstract
+
+Human perceptual systems excel at inducing and recognizing objects across both known and novel categories, a capability far beyond current machine learning frameworks. While generalized category discovery (GCD) aims to bridge this gap, existing methods predominantly focus on optimizing objective functions. We present an orthogonal solution, inspired by the human cognitive process for novel object understanding: decomposing objects into visual primitives and establishing cross-knowledge comparisons. We propose ConGCD, which establishes primitive-oriented representations through high-level semantic reconstruction, binding intra-class shared attributes via deconstruction. Mirroring human preference diversity in visual processing, where distinct individuals leverage dominant or contextual cues, we implement dominant and contextual consensus units to capture class-discriminative patterns and inherent distributional invariants, respectively. A consensus scheduler dynamically optimizes activation pathways, with final predictions emerging through multiplex consensus integration. Extensive evaluations across coarse- and fine-grained benchmarks demonstrate ConGCD's effectiveness as a consensus-aware paradigm. Code is here.
+
+# 1. Introduction
+
+Generalizing inductive and recognition capabilities to unknown categories of objects is an innate ability of human vision [8], but it is incredibly challenging for machine learning models. Generalized Category Discovery (GCD) [39, 48, 52, 53, 57] is an advanced method to address this issue, which encourages models to cluster and
+
+
+Figure 1. Generalized category discovery inherently demands multiplex consensus via self-deconstruction, rejecting image-level processing in favor of attribute-aware compositional reasoning.
+
+recognize a subset of samples within the data that includes both unlabeled and unknown categories as well as known categories after training on partially labeled data.
+
+From the perspective of representation learning [44], current GCD paradigms including contrastive learning [10, 48], prototype classifiers [53], and sample selection [31, 39] share a fundamental oversight: they process images as atomic entities, neglecting the compositional nature of visual recognition. For instance, CMS [10] applies mean-shift to global embeddings, while SimGCD [53] distills category prototypes from holistic representations. Though effective for coarse discrimination, these methods fail to emulate the human capacity for attribute-level reasoning - the ability to decompose objects into semantic primitives and establish cross-category consensus through comparative analysis.
+
+Humans can transfer previously acquired knowledge when learning new concepts [22, 55]. If young children learn to distinguish between "cows" and "sheep" based on their shape, they can apply the same rule to differentiate between "pigs" and "horses". However, when it comes to telling "pandas" and "bears" apart, relying solely on shape can lead to confusion like Fig. 1; attention to additional
+
+visual primitives [16] such as stripes and ears is required. For instance, the Oxford Dictionary [13] defines a giraffe as “a tall animal with a very long neck, long legs, and dark marks on its coat”. This definition involves two shape primitives (long neck, long legs) and one texture-color attribute (dark marks). Unfortunately, shortcut learning [19] in deep networks typically activates a few primitives (such as the gray skin of an elephant [18]), causing confusion between categories with similar primitives, like rhinoceroses.
+
+In this work, we propose cognitive science-inspired CongCD, which attempts to address the above challenge by focusing on two aspects as shown in Fig. 2: the self-deconstruction of visual primitives and the formation of multiplex consensus. (1) For the decoupling of visual primitives, we define a set of primitive-oriented representations to bind intra-class shared visual primitives to spatial regions [8] in a construction manner. The competitive relationship among primitives-oriented representations ensures that each primitive mask focuses on a single visual attribute. Collectively, all primitive-oriented representations can be seen as a synthesis of the image's key visual primitives. (2) For the formation of multiplex consensus, unlike monolithic feature aggregation, we implement dominant and contextual consensus units: dominant units retain high-response neurons to capture class-discriminative patterns, while contextual units preserve weaker activations encoding distributional invariants. A dynamic consensus scheduler optimizes activation pathways between these units, with final predictions emerging through multiplex integration of their complementary perspectives. This process mimics how humans iteratively reconcile dominant cues (e.g., break shape for birds) with contextual invariants (e.g., flight posture) when categorizing novel exemplars [24, 25].
+
+Our main contributions can be summarized as follows:
+
+- A mechanism inducing visual primitives via competitive binding, enabling unsupervised discovery of primitive-discriminative attributes through topological competition.
+- A multiplex consensus framework: dominant units retain high-response neurons for class-related variables, while contextual units preserve weak activations for inherent distributions, coordinated by dynamic scheduling.
+- Extensive validation showing our paradigm's plug-and-play compatibility with GCD methods, achieving state-of-the-art performance across seven benchmarks.
+
+# 2. Related Works
+
+# 2.1. Generalized Category Discovery
+
+In Generalized Category Discovery (GCD) [48], the goal is to classify unlabeled samples into known and unknown classes using a limited labeled dataset from known classes, reflecting a realistic approach to real-world image recognition. Initially, GCD was formulated by [48], employing
+
+contrastive and semi-supervised learning methods that relied heavily on clustering during inference. Consequently, SimGCD, a robust baseline approach that replaces clustering with a classifier, is trained using a pseudo-labeling strategy that has shown remarkable effectiveness in SSL [53]. To address this limitation, subsequent works aim to improve feature representation by exploiting underlying cross-instance relationships [37]. An EM-like framework is proposed to alternate between contrastive learning and class number estimation [57]. Recent works have proposed using parametric classifiers to avoid prediction biases [14]. However, previous studies [31, 34] focused on class tokens for clustering, overlooking that similar visual attributes across samples can cause inter-class boundary confusion.
+
+# 2.2. Object-Centric Learning
+
+In the evolving landscape of Object-Centric Learning (OCL), Slot Attention established a significant milestone [30]. This mechanism enabled further research, like [14], which extended OCL to videos, using temporal consistency and dynamics within video sequences to better differentiate objects from backgrounds. Furthermore, to address the stability issue in single-view OCL, [21] introduces modules to guide slots away from background noise and towards consistent object representation. [2] explores self-supervision, offering the first unsupervised multi-object segmentation in real-world videos. And the challenge of adapting OCL to complex real-world settings was tackled by [41], bridging the gap between lab and real-world scenarios. OCL currently concentrates on object-level separation [28], and we extend it to a more fine-grained visual attribute discovery level, and let the model innately have the inductive ability for the semantics of visual attributes.
+
+# 3. Preliminaries
+
+# 3.1. Visual Primitives
+
+The generation process of an sample $\mathbf{x}$ is actually a combination process of a set of visual primitives $s^1, \dots, s^K$ ( $s^{1:K}$ ) with $s^i \in S$ , where $S$ is a finite set [16]. Considering the joint distribution of $\mathbf{x}$ and $s^{1:K}$ , due to biases in observation and annotation and deviation from the real-world distribution, the label of a sample can depend on one or more primitives. The data generation process can be expressed as
+
+$$
+\begin{array}{l} \mathbf {z} \sim p (\mathbf {z}), \quad s ^ {i} \sim p (s ^ {i} | \mathbf {z}), \quad \mathbf {x} \sim p (\mathbf {x} | \mathbf {z}), \\ p \left(s ^ {1: K}, \mathbf {x}\right) = p \left(s ^ {1: K}\right) \int p (\mathbf {x} | \mathbf {z}) p (\mathbf {z} | s ^ {1: K}) d \mathbf {z}, \tag {1} \\ \end{array}
+$$
+
+where $\mathbf{z}$ is a factor in the latent space. We believe that if different marginal distributions of given primitives exist but they share the same conditional generation process, there will be distribution shift between categories, that is
+
+
+Figure 2. Overview of the proposed ConGCD: (1) Visual primitives are discovered iteratively via competitive reconstruction; (2) Each visual primitive is processed by dominant consensus units with primitive mask, while the inherent distribution is processed by contextual consensus units scheduler with holistic representation. The weight of each unit is determined by the consensus scheduler.
+
+$p_{\mathrm{class - n}}(s^{1:K})\neq p_{\mathrm{class - n^{\prime}}}(s^{1:K})$ . However, due to the shared. generative model between distributions, certain primitives subset $\tilde{A}$ are highly similar across inter-class, we have $p_{\mathrm{class - n}}(\tilde{s}^{1:\tilde{K}},\mathbf{x}) = p_{\mathrm{class - n^{\prime}}}(\tilde{s}^{1:\tilde{K}})\int p(\mathbf{x}|\mathbf{z})p(\mathbf{z}|\tilde{s}^{1:\tilde{K}})d\mathbf{z},$ where $\tilde{s}^i\in \tilde{S}$ and $\tilde{S}\subseteq S$ . The similarity of inter-class primitives is disastrous for distinguishing between categories. Therefore, we aim to find a complementary set $S\setminus \tilde{S}$ , the discriminative visual primitives that maximize the distribution difference between categories, serving as the factors that contribute the most to inter-class separation.
+
+# 3.2. Problem Definition of GCD
+
+we consider a labeled subset for each dataset, denoted as $\mathcal{D}_l = \{(\mathbf{x}_i^l,y_i^l)\} \subset \mathcal{X}\times \mathcal{Y}_l$ . Additionally, there is an unlabeled subset $\mathcal{D}_u = \{(\mathbf{x}_i^u,y_i^u)\} \subset \mathcal{X}\times \mathcal{Y}_u$ . In $\mathcal{D}_l$ only known classes are present, i.e., $\mathcal{Y}_l = \mathcal{C}_{known}$ . On the other hand, $\mathcal{D}_u$ contains both known and novel classes, $\mathcal{Y}_u = \mathcal{C}_{known}\cup \mathcal{C}_{novel}$ . The task for models is to perform clustering on both the known and novel classes in $\mathcal{D}_u$ . The number of novel classes, represented as $N_{novel}$ , can be determined in advance [36, 48, 57]. The functions $f(\cdot)$ and $g(\cdot)$ act as the feature extractor and projection head respectively. Both the feature $\mathbf{h}_i = f(\mathbf{x}_i)$ and the projected embedding $\mathbf{z}_i = g(\mathbf{h}_i)$ are subjected to L-2 normalization.
+
+# 4. Methodology
+
+# 4.1. Self-Deconstruction of Visual Primitives
+
+Visual primitives Iterative Discovery. Referring to the process in which humans compare the visual features of an object with the existing knowledge in the brain and conduct cyclic searches after receiving visual signals [8], we define visual primitive discovery as an iterative process. It originates from slot-attention [30]. We predefine primitive-centric representations (learnable embeddings), $\mathbf{s} \sim \mathcal{N}(\mathbf{s}; \boldsymbol{\mu}, \boldsymbol{\sigma}) \in \mathbb{R}^{K \times D_s}$ . $K$ is the number of visual
+
+primitives, and $D_{s}$ is the number of dimensions.
+
+For the pre-trained encoder's output $\mathbf{z} = g(f(\mathbf{x}))\in$ $\mathbb{R}^{N\times D_z}$ , the attention mechanism of the human-like perception process [46] is implemented. Representing $\kappa_{\beta},\mathcal{Q}_{\gamma}$ and $\nu_{\phi}$ for $\mathbf{z}$ as the projection networks of key, query, and value with parameters $\beta ,\gamma$ ,and $\phi$ , respectively. The discovery process of visual primitives vpdis(·) and the attention function $\mathrm{attn}(\cdot)$ can be defined as
+
+$$
+\operatorname {v p d i s} (\boldsymbol {A}, \mathbf {v}) = \boldsymbol {A} ^ {T} \mathbf {v}, \quad A _ {i j} = \frac {\operatorname {a t t n} (\mathbf {q} , \mathbf {k}) _ {i j}}{\sum_ {l = 1} ^ {K} \operatorname {a t t n} (\mathbf {q} , \mathbf {k}) _ {l j}}, \tag {2}
+$$
+
+$$
+\mathrm {a t t n} (\mathbf {q}, \mathbf {k}) = \frac {e ^ {M _ {i j}}}{\sum_ {l = 1} ^ {N} e ^ {M _ {i l}}}, \quad M = \frac {\mathbf {k q} ^ {T}}{\sqrt {D _ {s}}},
+$$
+
+Where $\mathbf{A}$ is the attention matrix. The $\mathbf{k} = \mathcal{K}_{\beta}(\mathbf{z}) \in \mathbb{R}^{N \times D_s}$ and $\mathbf{v} = \mathcal{V}_{\phi}(\mathbf{z}) \in \mathbb{R}^{N \times D_s}$ are the key and value vectors, respectively. To ensure the binding of the attention relationship between visual primitives and feature embeddings, queries are a function of visual primitives s, and the formal expression is $\mathbf{q} = \mathcal{Q}_{\gamma}(\mathbf{s}) \in \mathbb{R}^{K \times D_s}$ .
+
+Similar to the process of thinking and reasoning [1], visual primitives are iteratively refined over $T$ attention iterations. Specifically, in iteration $t$ , the queries are given by $\hat{\mathbf{q}}^t = \mathcal{Q}_{\gamma}(\mathbf{s}^t)$ . The Gated Recurrent Unit (GRU) [11, 12] is applied, denoted as $\mathcal{G}_{\theta}$ . The visual primitives update process can be summarized as $\mathbf{s}^{t + 1} = \mathrm{vpdis}$ (attn $(\hat{\mathbf{q}}^t,\mathbf{k})$ ,v).
+
+Given $\mathbf{x}$ at $t = T$ iteration, the posterior distribution of the visual primitives is
+
+$$
+p \left(\mathbf {s} ^ {T} \mid \mathbf {x}\right) =
+$$
+
+$$
+\delta \left(\mathbf {s} ^ {T} - \prod_ {t = 1} ^ {T} \mathcal {G} _ {\theta} \left(\mathbf {s} ^ {t - 1}, \operatorname {v p d i s} \left(\operatorname {a t t n} \left(\hat {\mathbf {q}} ^ {t - 1}, \mathbf {k}\right), \mathbf {v}\right)\right)\right), \tag {3}
+$$
+
+where $\delta (\cdot)$ represents the Dirac delta distribution [4], we sample s from a Gaussian distribution [20], at $t = 0$ itera
+
+tion for initialization so that the distribution of $\mathbf{s}^0$ represents relatively uniform visual primitives, preventing biases in the visual primitive discovery process.
+
+Deconstruction via Competitive Reconstruction. $\hat{\mathbf{z}} = \Phi_d(\mathbf{s}_k)$ The discovery process of visual primitives is unsupervised, and we complete it through the surrogate task of reconstruction. After $\mathbf{s}^T$ goes through the above iterative discovery, it is sent in as a general lightweight multi-layer perceptron (MLP) as the decoder [42], denoted as $\Phi_d(\cdot)$ . $\Phi_d(\cdot)$ spatially broadcasts $K$ visual primitives to the same spatial dimension as $\hat{\mathbf{z}}_k = \Phi_d(\mathbf{s}_k) \in \mathbb{R}^{N \times (D_z + 1)}$ . The reconstructed $\hat{\mathbf{z}}_k$ is composed of $D_z + 1$ channels. After channel division, we obtain the reconstructed feature embeddings $\hat{\mathbf{z}}_k \in \mathbb{R}^{N \times D_s}$ and the activation region $\alpha_k \in \mathbb{R}^{N \times 1}$ . In order to bind the visual primitive embedding to the region with the same semantics in the image, we use softmax on $\alpha_k$ for normalization over $K$ visual primitives to introduce the competitive relationship between visual primitives, so that a certain primitive is associated with certain pixels
+
+$$
+\hat {\mathbf {z}} = \sum_ {k = 1} ^ {K} \hat {\mathbf {z}} _ {k} \odot \boldsymbol {m} _ {k}, \quad \boldsymbol {m} _ {k} = \operatorname {s o f t m a x} _ {k} (\alpha_ {k}). \tag {4}
+$$
+
+The optimization objective of the iterative discovery and decoupling process of visual primitives is simple
+
+$$
+\mathcal {L} _ {\text {r e c}} = \left\| \hat {\mathbf {z}} - \mathbf {z} \right\| ^ {2}, \quad \hat {\mathbf {z}} = \Phi_ {d} (\mathbf {s}). \tag {5}
+$$
+
+This self-supervised deconstruction establishes basic visual primitives through competitive binding, enabling machines to mirror human attribute-level perception. By disentangling objects into composable factors, we equip models with intrinsic interpretability for fine-grained comparisons while maintaining adaptability to novel category structures.
+
+# 4.2. Formation of Multiplex Consensus
+
+Models need to understand the visual primitives. However, exclusive reliance on dominant feature activations [18] creates self-reinforcing biases that degrade unknown-class generalization, as shown in Tab. 4, where strongly activated neurons encode class-agnostic structural primitives, while their weakly activated counterparts preserve cross-category contextual patterns [29].
+
+This duality (as visualized in Fig. 3) drives our consensus formation through two complementary pathways: (1) Dominant Consensus Units distill class-discriminative knowledge by routing high-activation visual primitives through neural competition layers, preventing primitive overcommitment to known categories. (2) Contextual Consensus Units continuously assimilate weakly activated embeddings to model class-transcendent relationships. The resultant multiplex architecture achieves self-stabilization through consensus scheduler, where primitive specificity and contextual generality co-evolve.
+
+
+Figure 3. Dominant and weak neurons capture the class-related variables and inherent distributions, respectively.
+
+Dominant Consensus Units. For the output $\mathbf{z}^i\in$ $\mathbb{R}^{N\times D_z^i}$ of the $i$ -th block in the network forward process, in order to be consistent with the pixel-level relationship of visual primitives, we selectively retain the top $r$ (\%) of neuron activation responses at the token-level from the spatial dimension. Specifically, we customize a sorting function sort(·) from large to small for neurons to generate $\mathbf{z}_{attr}^i$ after filtering neuron activation values. Furthermore, for each consensus units, their attention should be focused on a single visual primitive to ensure the expertise of the units (Analogous to human visual preferences, some people rely on the head to distinguish animals, and some people rely on the tail). We directly use $m_{k}$ to represent the activation of the visual primitive region to limit the input of $k$ -th unit. The forward process of each dominant consensus unit is
+
+$$
+\mathbf {z} _ {\text {D o m}} ^ {i k} := \left\{ \begin{array}{l} \mathbf {z} ^ {i} \odot \mathbf {m} _ {k}, \text {i f} \mathbf {z} ^ {i} [:,: ] \geq \operatorname {T o p - R} _ {k} (\operatorname {s o r t} (\mathbf {z} ^ {i} [:,: ])) \\ 0, \text {o t h e r w i s e ,} \end{array} \right. \tag {6}
+$$
+
+where $R_{k} = N \times r_{k}$ in $\mathrm{Top - R_k}(\cdot)$ , for visual primitive schedulers used to capture class-related variables, they need to perceive highly activated neurons and provide features conducive to separation between classes.
+
+Contextual Consensus Units. Due to the inherent distribution of the dataset, only maximizing the extraction of class-related visual primitives will cause difficulties for the model in recognizing novel classes. Therefore, we propose contextual consensus units based on weak neurons. It accepts the complete $\mathbf{z}^i$ as input and perceives all visual primitives of the object. We decompose the low-activation region in $\mathbf{z}^i$
+
+$$
+\mathbf {z} _ {\text {C o n}} ^ {i} := \left\{ \begin{array}{l} \mathbf {z} ^ {i}, \text {i f} \mathbf {z} ^ {i} [:,: ] \leq \operatorname {T o p - R} (\operatorname {s o r t} \left(\mathbf {z} ^ {i} [:,: ]\right)) \\ 0, \text {o t h e r w i s e ,} \end{array} \right. \tag {7}
+$$
+
+which is similarly to Eq. (6), but dominant consensus units on class-independent features activated in weak neurons, aiming to extract the information common to each sample from the feature embedding itself. This prevents the model
+
+ | Method | CUB-200 | FGVC-Aircraft | Stanford-Cars | Average |
| All | Known | Novel | All | Known | Novel | All | Known | Novel | All | Known | Novel |
| DINOv1 | GCD [48] | 51.3 | 56.6 | 48.7 | 45.0 | 41.1 | 46.9 | 39.0 | 57.6 | 29.9 | 45.1 | 51.8 | 41.8 |
| GPC [57] | 52.0 | 55.5 | 47.5 | 43.3 | 40.7 | 44.8 | 38.2 | 58.9 | 27.4 | 44.5 | 51.7 | 39.9 |
| XCon [15] | 52.1 | 54.3 | 51.0 | 47.7 | 44.4 | 49.4 | 40.5 | 58.8 | 31.7 | 46.8 | 52.5 | 44.0 |
| PromptCAL [56] | 62.9 | 64.4 | 62.1 | 52.2 | 52.2 | 52.3 | 50.2 | 70.1 | 40.6 | 55.1 | 62.2 | 51.7 |
| AMEND [3] | 64.9 | 75.6 | 59.6 | 52.8 | 61.8 | 48.3 | 56.4 | 73.3 | 48.2 | 58.0 | 70.2 | 52.0 |
| μGCD [49] | 65.7 | 68.0 | 64.6 | 53.8 | 55.4 | 53.0 | 56.5 | 68.1 | 50.9 | 58.7 | 63.8 | 56.2 |
| CMS [10] | 68.2 | 76.5 | 64.0 | 56.0 | 63.4 | 52.3 | 56.9 | 76.1 | 47.6 | 60.4 | 72.0 | 54.6 |
| InfoSieve [38] | 69.4 | 77.9 | 65.2 | 56.3 | 63.7 | 52.5 | 55.7 | 74.8 | 46.4 | 60.5 | 72.1 | 54.7 |
| SimGCD [53] | 60.3 | 65.6 | 57.7 | 54.2 | 59.1 | 51.8 | 53.8 | 71.9 | 45.0 | 56.1 | 65.5 | 51.5 |
| + ConGCD | 61.6 | 65.1 | 59.5 | 55.0 | 58.4 | 53.1 | 54.5 | 72.2 | 47.8 | 57.1 | 65.2 | 53.5 |
| LegoGCD [6] | 63.8 | 71.9 | 59.8 | 55.0 | 61.5 | 51.7 | 57.3 | 75.7 | 48.4 | 58.7 | 69.7 | 53.3 |
| + ConGCD | 65.3 | 72.6 | 61.7 | 55.6 | 61.2 | 54.0 | 58.1 | 75.9 | 49.5 | 59.7 | 69.9 | 55.1 |
| SPTNet [52] | 65.8 | 68.8 | 65.1 | 59.3 | 61.8 | 58.1 | 59.0 | 79.2 | 49.3 | 61.4 | 69.9 | 57.5 |
| + ConGCD | 68.1 | 68.5 | 67.8 | 59.7 | 61.3 | 59.2 | 59.1 | 79.0 | 49.8 | 62.3 | 69.6 | 58.9 |
| SelEx [39] | 78.7 | 81.3 | 77.5 | 60.9 | 70.3 | 56.2 | 57.0 | 77.4 | 47.2 | 65.5 | 76.3 | 60.3 |
| + ConGCD | 81.7 | 80.4 | 82.4 | 62.5 | 70.2 | 58.7 | 57.5 | 77.5 | 47.9 | 67.3 | 76.0 | 63.0 |
| Avg. △ | +2.03 | -0.25 | +2.83 | +0.85 | -0.40 | +1.80 | +0.53 | +0.10 | +1.28 | +1.18 | -0.18 | +1.98 |
| DINOv2 | GCD [48] | 71.9 | 71.2 | 72.3 | 55.4 | 47.9 | 59.2 | 65.7 | 67.8 | 64.7 | 64.3 | 62.3 | 65.4 |
| SimGCD[53] | 71.5 | 78.1 | 68.3 | 63.9 | 69.9 | 60.9 | 71.5 | 81.9 | 66.6 | 69.0 | 76.6 | 65.3 |
| μGCD [49] | 74.0 | 75.9 | 73.1 | 66.3 | 68.7 | 65.1 | 76.1 | 91.0 | 68.9 | 72.1 | 78.5 | 69.0 |
| SelEx[39] | 86.0 | 86.5 | 85.7 | 82.1 | 84.8 | 80.7 | 80.5 | 91.8 | 75.0 | 82.9 | 87.7 | 80.5 |
| + ConGCD | 86.3 | 87.4 | 85.8 | 81.7 | 83.3 | 81.0 | 79.8 | 93.1 | 73.3 | 82.6 | 87.9 | 80.1 |
+
+Table 1. Results on the fine-grained semantic shift benchmark. ConGCD offers excellent cross-scheme and cross-model compatibility.
+
+from overly focusing on the visual primitives of known classes and from effectively perceiving novel classes.
+
+Consensus Scheduler. The self-deconstruction process manifests in ViT blocks [7] through dual activation polarization: while multi-head self-attention (MHA) [46] captures cross-patch dependencies, the decomposed dominant/contextual consensus pathways exhibit complementary neuron activation patterns. We reformulate the FFN as parallel consensus units governed by activation separation:
+
+$$
+\begin{array}{l} f _ {\text {C o n G C D}} (\mathbf {z}) = \sum_ {k = 1} ^ {K + M} G (\mathbf {z}) _ {k} \cdot E _ {k} \left(\mathbf {z} _ {D o m} ^ {k} / \mathbf {z} _ {C o n}\right) \\ = \sum_ {k = 1} ^ {K + M} \operatorname {s o f t m a x} (\boldsymbol {W} \mathbf {z}) \cdot \boldsymbol {W} _ {\mathrm {F F N} _ {k}} ^ {2} \phi \left(\boldsymbol {W} _ {\mathrm {F F N} _ {k}} ^ {1} \mathbf {z} _ {D o m} ^ {k} / \mathbf {z} _ {C o n}\right), \tag {8} \\ \end{array}
+$$
+
+where $W$ and $W_{\mathrm{FFN}_k}^{1/2}$ are the learnable parameters. $\phi(\cdot)$ is a nonlinear activation function. The primitive scheduler operates densely for $K$ dominant units and $M$ contextual units and assigns a non-zero probability to each unit.
+
+Due to inconsistent preferences across units, determining the ratio $r_k$ (\%) for detecting dominant/contextual activation neurons becomes challenging. We address this via an Activation Separation Distributor (ASR) that dynamically generates unit-specific separation ratios from $\mathbf{z}$ , enabling adaptive boundary determination for activation decompo
+
+sition per sample. Scheduler adopt a new $R^{*}$ to screen neurons using $\mathrm{Top - R_k^*(\cdot)}$ ..
+
+$$
+R _ {k} ^ {*} = N \times \left(r _ {k} + \eta \cdot \operatorname {s o f t m a x} \left(\boldsymbol {W} _ {\mathrm {A S R}} \mathbf {z}\right) [ k ]\right), \tag {9}
+$$
+
+where $W_{\mathrm{ASR}}$ is learnable, $\eta$ controls scaling, and $N$ denotes patch count. This allows sample-aware adaptation to diverse visual primitives while maintaining activation balance between classes. In general, given $\mathbf{z}$ as the input, the update process is
+
+$$
+\mathbf {z} _ {\text {o u t}} = f _ {\text {C o n G C D}} (\mathrm {L N} (\mathbf {z})) + \mathbf {z}, \tag {10}
+$$
+
+where $\mathrm{LN}(\cdot)$ indicates layer normalization, and $\mathbf{z}_{\mathrm{out}}$ is the output and is sent to the next block. The multiplex consensus framework resolves fundamental tension in GCD through symbiotic coordination, dominant units sharpen categorical boundaries while contextual units maintain open-world continuity, mirroring human vision's dual processing of focal attributes and environmental context.
+
+# 5. Experiments
+
+Through comprehensive experimental verification and analysis, we aim to answer the following questions. (1) Can ConGCD improve the accuracy of GCD? (2) Can ConGCD be plugged and played in existing GCD schemes? (3) What is the source of the performance improvement of ConGCD? (4) Is ConGCD robust to changes in hyperparameters?
+
+ | Method | CIFAR-10 | CIFAR-100 | ImageNet-100 | Average |
| All | Known | Novel | All | Known | Novel | All | Known | Novel | All | Known | Novel |
| DINOv1 | ORCA [5] | 96.9 | 95.1 | 97.8 | 74.2 | 82.1 | 67.2 | 79.2 | 93.2 | 72.1 | 83.4 | 90.1 | 79.0 |
| GCD [48] | 91.5 | 97.9 | 88.2 | 73.0 | 76.2 | 66.5 | 74.1 | 89.8 | 66.3 | 79.5 | 88.0 | 73.7 |
| GPC [57] | 90.6 | 97.6 | 87.0 | 75.4 | 84.6 | 60.1 | 75.3 | 93.4 | 66.7 | 80.4 | 91.9 | 71.3 |
| XCon [15] | 96.0 | 97.3 | 95.4 | 74.2 | 81.2 | 60.3 | 77.6 | 93.5 | 69.7 | 82.6 | 90.7 | 75.1 |
| PIM [9] | 94.7 | 97.4 | 93.3 | 78.3 | 84.2 | 66.5 | 83.1 | 95.3 | 77.0 | 85.4 | 92.3 | 78.9 |
| PromptCAL [56] | 97.9 | 96.6 | 98.5 | 81.2 | 84.2 | 75.3 | 83.1 | 92.7 | 78.3 | 87.4 | 91.2 | 84.0 |
| DCCL [36] | 96.3 | 96.5 | 96.9 | 75.3 | 76.8 | 70.2 | 80.5 | 90.5 | 76.2 | 84.0 | 87.9 | 81.1 |
| InfoSieve [38] | 94.8 | 97.7 | 93.4 | 78.3 | 82.2 | 70.5 | 80.5 | 93.8 | 73.8 | 84.5 | 91.2 | 79.2 |
| SimGCD [53] | 97.1 | 95.1 | 98.1 | 80.1 | 81.2 | 77.8 | 83.0 | 93.1 | 77.9 | 86.7 | 89.8 | 84.6 |
| + ConGCD | 97.3 | 95.1 | 98.4 | 81.3 | 82.5 | 78.9 | 83.5 | 92.8 | 78.6 | 87.4 | 90.1 | 85.3 |
| LegoGCD [6] | 97.1 | 94.3 | 98.5 | 81.8 | 81.4 | 82.5 | 86.3 | 94.5 | 82.1 | 88.4 | 90.1 | 87.7 |
| + ConGCD | 97.2 | 94.8 | 97.9 | 82.2 | 82.1 | 82.3 | 85.8 | 94.4 | 81.7 | 88.4 | 90.4 | 87.3 |
| SPTNet [52] | 97.3 | 95.0 | 98.6 | 81.3 | 84.3 | 75.6 | 85.4 | 93.2 | 81.4 | 88.0 | 90.8 | 85.2 |
| + ConGCD | 97.4 | 95.2 | 98.5 | 82.5 | 85.9 | 77.3 | 85.9 | 93.4 | 82.5 | 88.6 | 91.5 | 86.1 |
| SelEx [39] | 94.1 | 97.7 | 92.2 | 80.0 | 84.8 | 70.4 | 82.3 | 93.9 | 76.5 | 85.4 | 92.1 | 79.7 |
| + ConGCD | 95.7 | 97.6 | 94.8 | 80.5 | 84.9 | 71.7 | 83.5 | 94.2 | 78.0 | 86.6 | 92.2 | 81.5 |
| Avg. △ | +0.50 | +0.15 | +0.55 | +0.83 | +0.93 | +0.98 | +0.43 | -0.03 | +0.73 | +0.63 | +0.35 | +0.75 |
+
+Table 2. Results on the coarse-grained classification benchmark. ConGCD offers excellent cross-scheme and cross-model compatibility.
+
+# 5.1. Setup
+
+**Benchmarks.** ConGCD is evaluated on a total of seven image recognition benchmarks, namely four fine-grained datasets, CUB-200-2011 [51], Stanford Cars [23], FGVC Aircraft [32], Herbarium19 [43], and three coarse-grained datasets, CIFAR10, CIFAR100 [26] and ImageNet100 [17]. When dealing with CUB, Stanford Cars, and FGVC Aircraft, to segregate target classes into sets of known and unknown, we follow the splits defined by the Semantic Shift Benchmark (SSB) [47]. For the remaining datasets, the splits from the previous study [48] are employed. Under the CIFAR100 benchmark, we designate $80\%$ of the classes as known. For the other benchmarks, the proportion of known classes is $50\%$ . Our labeled set, known as $\mathcal{D}_l$ , consists of $50\%$ images from the known classes for all benchmarks.
+
+Evaluation Protocols. Following existing research [39], we use Balanced Semi-Supervised K-means [50] to cluster the entire image collection $\mathcal{D}$ and calculate the model's recognition accuracy on the dataset $\mathcal{D}_u$ , which does not have access to ground truth labels. The Hungarian algorithm [54] is used to obtain the optimal mapping relationship between the unlabeled cluster set and the ground truth labels. Instances in the unlabeled set $\mathcal{D}_u$ are divided into Known and Novel categories based on their category primitives for clustering accuracy evaluation. In addition, the accuracy of All classes is reported, as it represents the comprehensive performance of the model.
+
+Implementation Details. We employ the pre-trained DINOv1 [7] on ImageNet-1K [27] as image encoder, and keep it frozen. Features from the 10-th block are utilized for the
+
+decoupling of visual primitives. We set number of visual primitives to 8. The Slot-Attention is trained with the Adam optimizer for 400 epochs with learning rate of 0.0005, batch size of 64. We construct the ConGCD for the last two blocks, following with the previous research [39, 48]. The $\lambda = 0.35$ , label smoothing coefficient $\alpha$ set to 0.5 in the fine-grained dataset and 0.1 in the coarse-grained dataset. Additionally, we conduct the above training on DINOv2 [33] pre-trained on ImageNet-22K [40]. All experiments are conducted on RTX-4090, and random number seeds are fixed at each stage to avoid data label leaks.
+
+# 5.2. Baselines
+
+In addition to the contrast-based method CMS [10] and the use of prototype classifiers in SimGCD [53], we also compare ConGCD with several other state-of-the-art existing methods. LegoGCD [6] [48] leverages a modular approach to discover novel categories in unlabelled datasets by combining different components. SPTNet [52] iteratively optimizes both model parameters and data parameters through spatial prompt tuning. SelEx [39] addresses GCD through self-expertise strategies for hierarchical pseudo-label.
+
+# 5.3. Results
+
+Quantitative Results. ConGCD demonstrates significant improvements in both fine-grained and coarse-grained classification tasks, particularly excelling in classifying new categories while maintaining performance on known categories. In fine-grained tasks (Tab 1), ConGCD enhances overall accuracy by an average of $1.18\%$ across four baselines, with accuracy on new categories increasing by $1.98\%$ .
+
+
+(a) $\log(\operatorname{rank}(\mathcal{A}))$
+
+
+of fine-grained datasets
+(b) $\hat{H} (\mathcal{A})$
+
+
+of fine-grained datasets
+(c) $\log(\operatorname{rank}(\mathcal{A}))$
+of coarse-grained datasets
+
+
+(d) $\hat{H} (\mathcal{A})$
+of coarse-grained datasets
+
+For coarse-grained tasks (Tab 2), ConGCD improves accuracy on new categories by $0.98\%$ on CIFAR-100, while accuracy on known categories remains stable or shows slight improvement. These results highlight ConGCD's ability to effectively classify new categories without compromising performance on known ones, demonstrating its effectiveness as a plug-and-play method with strong compatibility across diverse approaches.
+
+
+(a) CUB-200
+Figure 5. Visualization of visual primitives. In a dataset, primitives are bound to specific semantics in an unsupervised manner.
+
+
+
+
+
+
+(b) FGVC-Aircraft
+
+
+
+
+Figure 6. Visualisation of the embedding space with t-SNE [45].
+
+Qualitative Results. (1) Contextual consensus units capture inherent distributions, while dominant consensus units focus on class-related variables. As shown in Fig. 3, weak neurons activate in low-information areas like the background, whereas dominant neurons target high-semantic difference areas (e.g., wheels, headlights) to enhance GCD. (2) To highlight ConGCD's performance improvement, attention maps in Fig. 8 reveal that ConGCD emphasizes the main body of the object (foreground), unlike SelEx, which focuses more on the background and specific minor areas. This enables a more uniform extraction of task-related variables. (3) As shown in Fig. 5, it can be observed that within the same dataset, visual primitives possess a high degree of cross-sample consistency. A primitive focuses on a region that has similar semantics.
+
+# 5.4. Analysis
+
+Visual primitives increase von Neumann entropy. We analyze the sources of the effectiveness of ConGCD from the perspectives of representation learning and information quantification. We employ von Neumann entropy [35] as a measure of the amount of information in the representation. For the class token $\mathbf{z}$ used in GCD, its autocorrela
+
+
+Figure 4. Comparison between (a) $\log(\mathrm{rank}(\mathcal{A}))$ and (b) $\hat{H}(\mathcal{A})$ . The count of the largest eigenvalues necessary to account for $99\%$ of the total eigenvalue energy serves as a surrogate for the rank.
+(a) CIFAR-10 with SelEx
+
+
+(b) CIFAR-10 with ConGCD
+
+
+(c) CIFAR-100 with SelEx
+
+
+(d) CIFAR-100 with ConGCD
+
+tion matrix $\mathcal{A} \triangleq \sum_{i=1}^{N} \frac{1}{N} \mathbf{z}_i \mathbf{z}_i^\top$ . The von Neumann entropy (VNA) is expressed as $\hat{H}(\mathcal{A}) \triangleq -\sum_{j} \lambda_j \log \lambda_j$ , where $\lambda$ is the eigenvalues of $\mathcal{A}$ . As shown in Fig. 4d and Fig. 4a, compared with SelEx, the representation of ConGCD has a higher $\hat{H}(\mathcal{A})$ and a higher $\log(\mathrm{rank}(\mathcal{A}))$ , which means a larger amount of information. This indicates that ConGCD enables the GCD process to more discriminatively separate clusters by providing more discriminative features.
+
+The versatility of visual primitives. To verify the universality of ConGCD as a plug-and-play solution, we integrated ConGCD with existing GCD schemes, and the results are reported in Tab. 1 and Tab. 2. It is evident that ConGCD provides them with a consistent improvement in accuracy, which can be attributed to the unstructured decoupling of visual primitives from objects, enabling the model to possess a certain ability to model topological relationships. The model no longer solely relies on image-level embeddings from a single perspective and applies this category-independent topological relationship to the discovery of novel categories.
+
+ConGCD provides accurate distribution estimation. The core of GCD is to estimate category distributions as accurately as possible and separate different categories. We evaluate ConGCD's contribution to distribution estimation from two perspectives: clustering visualization and category number estimation. (1) We visualize embeddings using t-SNE [45], as shown in Fig. 6. Notably, ConGCD significantly enhances clustering quality without modifying the optimization objective. It reduces within-class distances, clarifying cluster boundaries. (2) As shown in ??,
+
+
+(a) CUB-200
+
+
+(b) FGVC-Aircraft
+
+
+(c) CIFAR-10
+
+
+(d) ImageNet-100
+Figure 7. The ablations of the number of visual primitives $K$ on (a, b) fine- and (c, d) coarse-grained benchmarks.
+
+| Method | CIFAR-100 | ImageNet-100 | CUB-200 | Stanford-Cars |
| |Yu| | Err(%) | |Yu| | Err(%) | |Yu| | Err(%) | |Yu| | Err(%) |
| Ground truth | 100 | - | 100 | - | 200 | - | 196 | - |
| GCD [48] | 100 | 0 | 109 | 9 | 231 | 15.5 | 230 | 17.3 |
| DCCL [36] | 146 | 46 | 129 | 29 | 172 | 9 | 192 | 0.02 |
| PIM [9] | 95 | 5 | 102 | 2 | 227 | 13.5 | 169 | 13.8 |
| GPC [57] | 100 | 0 | 103 | 3 | 212 | 6 | 201 | 0.03 |
| CMS [10] | 94 | 6 | 98 | 2 | 176 | 12 | 149 | 23.9 |
| ConGCD | 97 | 3 | 99 | 1 | 186 | 7 | 160 | 18.3 |
+
+
+Figure 8. Visualization on attention maps of SoTA and ConGCD.
+
+ConGCD combined with CMS [10] achieves the most accurate category number estimation $|\mathcal{V}_u|$ with the lowest error rate, demonstrating its superior ability to model data and partition the feature space, crucial for reaching GCD's upper bound.
+
+Table 3. Estimated number and error rate of $\left| {\mathcal{V}}_{u}\right|$ .
+
+| Components | CUB-200 | FGVC-Aircraft | CIFAR-10 | ImageNet-100 |
| All | Known | Novel | All | Known | Novel | All | Known | Novel | All | Known | Novel |
| conventional MoE | 78.2 | 79.1 | 77.3 | 59.4 | 78.1 | 53.6 | 93.6 | 97.1 | 91.8 | 80.4 | 92.5 | 74.9 |
| Ours w/o Dominant Consensus Units | 81.1 | 80.3 | 81.5 | 62.1 | 69.7 | 58.3 | 94.9 | 97.8 | 94.1 | 82.9 | 94.0 | 77.2 |
| Ours w/o Contextual Consensus Units | 80.4 | 79.7 | 81.0 | 61.3 | 70.6 | 57.1 | 94.2 | 97.6 | 92.3 | 81.5 | 93.5 | 75.4 |
| Ours w/o Consensus Scheduler | 79.8 | 79.5 | 80.0 | 60.9 | 70.1 | 56.7 | 94.4 | 97.7 | 92.7 | 81.4 | 92.7 | 77.0 |
+
+Table 4. Ablations on components of multiplex consensus.
+
+Ablations on the number of visual primitives. As a plug-and-play solution, ConGCD requires no hyperparameter tuning, which is an important prerequisite for its wide application. The only parameter that may potentially affect the performance is the number $K$ of visual primitives. We conducted ablation studies on it for both fine- and coarse-grained datasets, as shown in Fig. 7. It can be seen that in the open world, an appropriate $K$ is sufficient to handle
+
+multiple downstream tasks. When $K$ is in the range of 7 to 10, ConGCD achieves consistent and stable performance improvements, and $K$ is set to 8 for all dataset.
+
+Ablation Study on the Multiplex Consensus Mechanism. We conducted an ablation study on the key component of ConGCD in Sec. 4.2, with results summarized in Tab. 4. The mixture of experts (MoE) is the most comparable approach to our multiplex consensus mechanism, as it directly integrates with visual primitives. However, conventional MoE proves detrimental to the GCD task, as it only accepts image-level embeddings and overfits to labeled data from known classes. The experts merely memorize features of known classes, failing to generalize to novel categories. In contrast, our multiplex consensus mechanism offers three key advantages: (1) Dominant consensus units process diverse visual primitives, enabling primitive-level perception and improving classification accuracy for novel categories. (2) Contextual consensus units capture intrinsic distributions shared across known and unknown classes, ensuring balanced clustering and mitigating bias. (3) Consensus scheduler introduces a learnable threshold to refine the distinction between weak and dominant neurons, optimizing unit selection and weight distribution to enhance accuracy.
+
+# 6. Conclusion
+
+Current GCD approaches treat images as atomic entities, ignoring the human capacity for compositional reasoning. We propose ConGCD, a cognition-inspired paradigm bridging this gap with two key innovations: self-deconstruction decomposes objects into competing visual primitives via semantic reconstruction, while multiplex consensus dynamically integrates dual pathways, dominant consensus consensus units capturing class-specific attributes and contextual consensus units modeling distributional invariants. ConGCD achieves competitive performance on coarse- and fine-grained benchmarks, enhancing interpretability and generalization in open-world recognition.
+
+# Acknowledgement
+
+This work was supported in part by the National Natural Science Foundation of China under Grant 82172033, Grant U19B2031, Grant 61971369, Grant 52105126, Grant 82272071, and Grant 62271430; and in part by the Dreams Foundation of Jianghuai Advance Technology Center; and in part by the Open Fund of the National Key Laboratory of Infrared Detection Technologies.
+
+# References
+
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+# DistillDrive: End-to-End Multi-Mode Autonomous Driving Distillation by Isomorphic Hetero-Source Planning Model
+
+Rui Yu $^{1}$ Xianghang Zhang $^{2}$ Runkai Zhao $^{3}$ Huaicheng Yan $^{1\dagger}$ Meng Wang $^{1}$ $^{1}$ East China University of Science and Technology SenseAuto Research The University of Sydney y80220166@mail.ecust.edu.cn zhangxianghang@senseauto.com rzha9419@uni.sydney.edu.au hcyan@ecust.edu.cn mengwang@ecust.edu.cn † Corresponding author
+
+# Abstract
+
+End-to-end autonomous driving has been recently seen rapid development, exerting a profound influence on both industry and academia. However, the existing work places excessive focus on ego-vehicle status as their sole learning objectives and lacks of planning-oriented understanding, which limits the robustness of the overall decision-making process. In this work, we introduce DistillDrive, an end-to-end knowledge distillation-based autonomous driving model that leverages diversified instance imitation to enhance multi-mode motion feature learning. Specifically, we employ a planning model based on structured scene representations as the teacher model, leveraging its diversified planning instances as multi-objective learning targets for the end-to-end model. Moreover, we incorporate reinforcement learning to enhance the optimization of state-to-decision mappings, while utilizing generative modeling to construct planning-oriented instances, fostering intricate interactions within the latent space. We validate our model on the nuScenes and NAVSIM datasets, achieving a $50\%$ reduction in collision rate and a 3-point improvement in closed-loop performance compared to the baseline model. Code and model are publicly available at https://github.com/YuruiAI/DistillDrive
+
+# 1. Introduction
+
+End-to-end autonomous driving [15, 16, 21] has made significant progress in recent years, primarily driven by advancements in perception technologies [30, 31, 41] and imitation learning [19]. As show in Fig. 1 (b), it learns directly from complex sensor inputs to final planning and decision, eliminating the intermediate processes of data transfer and target characterization, thereby significantly reducing cascading errors [16]. However, in closed-loop experiments, the perceptually separated planning model in Fig. 1 (a) outperforms the end-to-end model, benefiting from contrastive
+
+
+(a) Perceptual Decoupled Learning-based Planning Paradigm
+
+
+(b) End-to-End Preception and Planning Paradigm
+
+
+(c) Distillation-based End-to-End Planning Paradigm
+Figure 1. Comparisons of different automatic driving planning paradigms. (a) Perceptual decoupled learning-based planning model [5, 46]. (b) End-to-end perception and planning model [16, 21]. (c) The proposed distillation-based drive model.
+
+learning [5] and simulation experiments [9]. Still, it faces a coupling barrier [20] between perception and planning.
+
+Unlike perceptual tasks with a unique solution, planning tasks have uncertain feasible solutions [4], and relying on a single expert trajectory can limit the model's ability to learn diverse representations. To address the issue of a limit planning goal, SparseDrive [37] incorporates unimodal planning features into multi-mode position embedding, enabling diverse planning. Meanwhile, VADV2 [4] abstracts planning tasks as a probabilistic action distribution, using the interaction between planning vocabulary and scenario tokens to sample a single action. DiffusionDrive [29] proposes a truncated diffusion policy with multi-mode anchors and the diffusion schedule, enabling the model to learn denoising from gaussian distribution. While the above approach offers some planning diversity, it still has several issues: (a) Single-mode Learning: Its target remains the expert trajectory from log playback, which lacks diverse supervision
+
+[27] for multi-mode features and motion properties. (b) Status Leakage: The model suffers from over-reliance on ego status [28] and lack of state-to-decision space optimization. (c) Motion-guidance Deprivation: The above approach lacks a planning-oriented feature modeling and fails to promote the instance interactions in a motion-guided manner.
+
+To address the above issues, we use a multi-mode decoupled planning model as a teacher to supervise motion-guided instance interaction in the end-to-end model through knowledge distillation, presented in Fig. 1 (c). Unlike existing methods [20, 27, 43] that focus on simulation environments and lack supervision of latent-space multi-mode features, we effectively implement multi-mode imitation. Meanwhile, we employ reinforcement learning to improve the comprehensive understanding of motion status and a generative model to boost interaction with motion distribution features from the expert's trajectory in latent space.
+
+To effectively improve the planning performance of the end-to-end model and tackle the challenge of imitation learning in capturing the complexity of the planning space, we propose DistillDrive, an end-to-end multi-mode autonomous driving framework based on the distillation of an isomorphic hetero-source planning model. Overall, we design a knowledge distillation architecture using decoupled planning models to efficiently supervise multi-mode planning learning in end-to-end models. To clarify the role of the ego status, we use inverse reinforcement learning and Q-learning to enhance the construction of state-to-decision relationships. Finally, motion-guided cross-domain feature interactions are enabled through generative modeling, enhancing the abstraction of instances to the planning space.
+
+The main contributions can be summarized as follows:
+
+- We propose a distillation architecture for multi-mode instance supervision in end-to-end planning, tackling single-target imitation learning limitations.
+- We introduce reinforcement learning-based state optimization to enhance state-to-decision space understanding and mitigate ego motion state leakage.
+- To address missing motion-guided attributes, we use a generative model for distribution-wise interaction between expert trajectories and instance features.
+- We conduct open- and closed-loop planning experiments on the nuScenes and NAVSIM datasets, achieving a $50\%$ reduction in collision rate and a 3-point increase in both EP and PDMS over the baseline.
+
+# 2. Related Work
+
+End-to-End Planning. Autonomous driving is rapidly advancing as end-to-end concepts [3, 38] gain popularity, with works [6, 15] achieving impressive results by using Transformers for spatial-temporal feature learning in planning models. Notably, UniAD [16] first integrates detection, tracking, and mapping using attention mechanisms, achiev-
+
+ing strong planning performance, while VAD [21] simplifies these steps, balancing accuracy and performance with vectorized representation. Unlike previous methods modeling planning as continuous trajectory learning, studies [4, 27] abstracted motion space into a probabilistic decision space. Meanwhile, Hu et al. [13] and Zheng et al. [45] enhance planning by modeling motion space as a gaussian distribution for capturing latent representations. While SparseDrive[37] propose a sparse query-centric paradigm for end-to-end autonomous driving, achieving strong performance. However, researches [28, 42] show that existing end-to-end planning models overly rely on ego status, lack of interaction with other agents. To address this, we design an end-to-end model that enhances distribution interaction and utilizes expert trajectories for supervised instance-wise representation, providing motion prior.
+
+Knowledge Distillation. Knowledge distillation (KD) allows a compact student model to mimic the behavior of a complex teacher model, inheriting its embedded knowledge [33, 47]. Hao et al. [12] proposes a cross-architecture method that aligns intermediate features into a logits space to distill knowledge from heterogeneous models. Simultaneously, approaches [26, 40, 44] enhance model expressiveness through multi-stage adaptive distillation and a dualpath mechanism. In autopilot planning, Roach [43] designed an RL-based expert to guide the IL agent in learning state space representations. In PlanKD [9], planning features are distilled, with trajectories and attention mechanisms extracting the feature center. While Hydra-MDP [27] supervises multimodal trajectory generation through a rule-based teacher. In contrast, our work tackles motion feature learning for cross-models via knowledge distillation, addressing the limitations of single-goal imitation learning.
+
+Reinforcement Learning in Planning. With the A3C agent [35] applied in CARLA [8] using reinforcement learning, more studies are emerging in the field of autonomous driving. Roach [43] trains a reinforcement learning expert to translate bird's-eye view images into continuous low-level actions, setting a performance benchmark in CARLA. RL methods have been applied to tasks like lane-keeping [22] and lane changing [39], enabling policies to learn from rewards through closed-loop training. Methods [10, 25] combine RL and IL to standardize Q-learning and prevent out-of-distribution value overestimation. Inverse reinforcement learning infers cost functions from expert demonstrations, eliminating manual specification. To better approximate the partition function, [17, 18] converts continuous behavioral modeling into a discrete setup, using a maximum entropy IRL architecture. In practice [32], actor goals are achieved by combining imitation learning and reinforcement learning, using the Soft Actor-Critic approach [11] to alternately train critics and actors. In our work, we combine Q-learning [25] and IRL [17] methods to
+
+
+Figure 2. The Overview of our proposed DistillDrive. Initially, we train a teacher model with scene-structured annotation data, integrating reinforcement and imitation learning to enhance multi-mode planning. Subsequently, we constructed an end-to-end student model and used a generative model to implement motion-oriented distribution interactions in latent space. Ultimately, multi-stage knowledge distillation and multi-mode supervision synergistically enhance the planning diversity and safety margins of autonomous driving models.
+
+improve the model's understanding of the state-to-decision space, enhancing both open- and closed-loop performance.
+
+# 3. Methodology
+
+# 3.1. Overview
+
+As illustrated in Fig. 2, we leverage a knowledge distillation-based planning model that improves multi-mode feature interaction through planning-based information. In Sec. 3.2, we present the teacher model's setup, including the encoder, planning decoder, IL-based head, and RL-based optimization. Following this, we explore end-to-end planning models that leverage generative models and sparse feature representations in Sec. 3.3. Afterward, in Sec. 3.4, we focus on our distillation scheme, integrating multi-mode instance distillation to enhance feature learning. Finally, we present the overall model training objectives in Sec. 3.5, combining knowledge distillation and reinforcement learning to overcome the limitations of single-mode representation in imitation learning for planning tasks.
+
+# 3.2. IRL-based Teacher Model
+
+The teacher model learns scene-to-planning relationships through an agent encoder, scene encoder, planning decoder, an imitation learning-based prediction head, and reinforcement learning-based state optimization.
+
+Agent Encoder. For a dynamic target agent, its state at each moment $t$ is characterized by the following information: position $p_i^t$ , orientation angle $\theta_i^t$ , velocity $v_i^t$ , dimen
+
+sions $b_{i}^{t}$ and binary mask information $m_{i}^{t}$ . To enhance the characterization of the target's motion properties, we vectorize the features to correlate information across successive frames, modeling the target's dynamic characteristics: $S_{i}^{t} = \{p_{i}^{t} - p_{i}^{t - 1},\theta_{i}^{t} - \theta_{i}^{t - 1},v_{i}^{t} - v_{i}^{t - 1},b_{i}^{t},m_{i}^{t}\}$ . Then, an MLP is applied to encode the $S\in \mathbb{R}^{N_A\times T\times 9}$ , resulting in $E_{A}\in \mathbb{R}^{N_{A}\times T\times D}$ , where $N_{A},T$ , and $D$ denote the number of agents, frames per agent, and dimension, respectively.
+
+$E_{A}$ incorporates the agent's temporal features, enhancing through position encoding $TE$ based on sequence positions. The global position embedding $PE_{A}$ is generated by encoding the position $p_i^{t_0}$ , providing rich spatial information and an encoder captures correlations among target temporal awareness via an attention mechanism:
+
+$$
+\boldsymbol {I} _ {\boldsymbol {A}} = A t t n (Q (\boldsymbol {E} _ {\boldsymbol {A}} + \boldsymbol {T E}), K (\boldsymbol {E} _ {\boldsymbol {A}} + \boldsymbol {T E})), V (\boldsymbol {E} _ {\boldsymbol {A}})). (1)
+$$
+
+Scene Encoder. Static targets (e.g., lane lines, road edges) help the model understand driving rules and areas, represented by a point set $M \in \mathbb{R}^{N_L \times N_P \times 2}$ , where $N_L$ is the number of lanes and $N_P$ is the number of points per lane. The lane center point $\mathbf{c}_{\mathrm{m}} \in \mathbb{R}^{N_L \times 2}$ serves as the position to encode $PE_M$ , representing lane distribution. The vectorized representation $\mathbf{v}_{\mathrm{m}}$ , the orientation $\theta_{\mathrm{m}}$ , and deviation $\mathbf{d}_{\mathrm{m}}$ are derived to refine the lane center encoding. Meanwhile, the labeling attribute $\mathbf{l}_{\mathrm{m}}$ for each lane is encoded through a weighting matrix $\omega_{\mathrm{m}}$ . Finally, the lane lines are encoded using the PointNet [36] polyline encoder, resulting in an effective representation $I_M \in \mathbb{R}^{N_L \times D}$ as follows:
+
+$$
+\boldsymbol {I} _ {M} = \operatorname {P o i n t N e t} \left(\operatorname {C o n c a t} \left\{\mathbf {v} _ {\mathbf {m}}, \theta_ {\mathbf {m}}, \mathbf {d} _ {\mathbf {m}} \right\}\right) + \mathbf {l} _ {\mathbf {m}} * \omega_ {\mathbf {m}}. \tag {2}
+$$
+
+Planning Decoder. As shown in Fig. 2, we derive $I_E, PE_E \in \mathbb{R}^{N_E \times D}$ from the planning vocabulary [4], obtained by clustering trajectories based on vectorization and end-points, where $N_E$ denotes the number of modes. These multi-mode instances, along with features from the agent encoder, achieve cross-temporal aggregation through the memory bank [37] to enhance multi-frame agent and ego instances $I_{A / E}'$ and position embeddings $PE_{A / E}'$ .
+
+To model the mutual interactions among Ego, Agent, and Map, we employ attention mechanism for representation learning across heterogeneous features, capturing their interactions. A temporal attention mechanism first captures associations between temporal features $I_{E / A}^{\prime}$ to comprehend the target's evolving dynamics, while a self-attention further captures Ego-Agent interactions and analyzes their behavioral patterns. Finally, cross-attention mechanism between the dynamic target $I_{E / A}$ and the static element $I_M$ enhances the agent's ability to abstract scenarios. Specific details are provided in the supplementary material.
+
+Imitation Learning-based Prediction Head. After obtaining the multi-mode ego instance $I_E$ , we use the MLP to predict trajectory regression $\tau \in \mathbb{R}^{N_E \times T \times 2}$ , classification $s \in \mathbb{R}^{N_E \times 1}$ , and ego-status $\xi \in \mathbb{R}^{N_E \times 10}$ within a multitask framework. Both the regressed trajectories and motion status are supervised using L1 loss, yielding $L_{\mathrm{reg}}$ and $L_{\mathrm{status}}$ , while the classification loss is enforced using KL divergence [4], resulting in $L_{\mathrm{cls}}$ for multi-mode planning. The details are provided in the appendix, where the imitation learning error $L_{IL}$ is the sum of the three losses.
+
+Reinforcement Learning-based Status Optimization. Ego status is learned from ego instances to prevent leakage and reduce state reliance [28]. The planning solution space is diverse due to motion complexity, while imitation learning [19]'s single objective limits model generality. Thus, integrating reinforcement learning principles to optimize the policy space across statuses and behaviors is key to enhancing the model's interaction and adaptability.
+
+First, based on the predicted trajectory $\hat{p}_{traj}$ and status $\hat{s}$ , the per-point error, collision rate, and speed limit are calculated relative to the expert trajectory $\bar{p}_{traj}$ and status $\bar{s}$ . The values are smoothed and normalized using a negative exponential function as the reward, with a learnable weight $\omega_{i}$ applied to each reward to optimize the planning reward: $r_t = \sum_{i=1}^{N_R} \omega_i e^{-x_i}$ , where $N_R$ is the number of rewards. Unlike maximum entropy inverse reinforcement learning [17], which maximizes rewards via entropy, we refine weight coefficients through learning and designed reward rules for more intuitive computation.
+
+Subsequently, Q-Learning [34] is applied to map state values $\hat{s}$ to the motion decision $\bar{a}$ , simplified to turn left, turn right, and go straight. The expert's motion state $\bar{s}$ is passed to the target network $Q_{T}$ to learn behavioral decisions, with the decisions $\bar{a}$ supervising the network, as shown in Eq. (4).
+
+Due to variability between $\hat{s}$ and $\bar{s}$ , we avoid the target network updating and use separate supervision to clarify the association between state space and decisions. We then compute the Q-value $y_{t}$ for the scene using the target network, where $\gamma$ is the reward decay coefficient:
+
+$$
+y _ {t} = r _ {t} + \gamma \max _ {\bar {a}} Q _ {T} (\bar {s}, \bar {a}). \tag {3}
+$$
+
+Finally, $L_{RL}$ is computed as the difference between the main network's prediction and the value $y_{t}$ , optimizing the model's state space representation for behavioral decisions:
+
+$$
+L _ {R L} = \sum_ {i = 1} ^ {\bar {a}} \| Q _ {T} (\bar {s}, \bar {a} _ {i}) - \bar {a} _ {i} \| + \| Q _ {M} (\hat {s}, \bar {a} _ {\max }) - y _ {t} \|. \tag {4}
+$$
+
+# 3.3. Motion-Guided Student Model
+
+Sparse Scene Representation. For the perceptual part of the model, we retain the SparseDrive [37] design, which uses fully sparse temporal representations. The instance $I_A, I_M$ remains the same structure as described in Sec. 3.2. Planning-oriented Interactions in Generative Models. To enhance the motion representation for Ego and Agent instances, we abstract $I_{E/A}$ and expert trajectories as Gaussian distributions, improving planning performance through distribution-wise interactions in the hidden space $\mathbb{Z}$ . As shown in Fig. 3, we map the expert trajectory $\bar{p}_{traj}$ to a Gaussian distribution in latent space $\mathbb{Z}$ via an encoder, learning $\mu_F, \sigma_F$ to model the distribution $d(\mathbb{Z}|\bar{p}_{traj}) = N(\mu_F, \sigma_F)$ , capturing the prior of expert trajectories.
+
+Similarly, for the instance $I_E, I_A$ of the Agent and Ego, we also use an encoder to map them to Gaussian space $\mathbb{Z}$ , obtaining $\mu_I$ and $\sigma_I$ to establish the distribution $d(\mathbb{Z} | I_E, I_A) = N(\mu_I, \sigma_I)$ for instance abstraction.
+
+The training process uses $N(\mu_F, \sigma_F)$ for the interaction of motion features and supervises $N(\mu_I, \sigma_I)$ , while the inference process utilizes $\mu_I, \sigma_I$ to generate motion-guided features $F_G = \mu_I + n \times e^{\zeta \times \sigma_I}$ . Here, $n$ denotes the Gaussian noise, $\zeta$ represents the coefficient. Then, $I_E, I_A$ are concatenated and transformed dimensionally to obtain the multi-level instance $I_G \in \mathbb{R}^{L \times (N_E + N_A) \times D'}$ , where $L$ represents the level number. Finally, the multi-scale instance $I_G$ serves as the hidden state, while the motion-guided feature $F_G$ is used as the input for distribution-level feature interaction via the GRU and MLP, as detailed in the appendix.
+
+$$
+\left(\boldsymbol {I} _ {\boldsymbol {E}}, \boldsymbol {I} _ {\boldsymbol {A}}\right) = M L P \left(G R U \left(\boldsymbol {F} _ {\boldsymbol {G}}, \boldsymbol {I} _ {\boldsymbol {G}}\right)\right). \tag {5}
+$$
+
+For the distribution $d(\mathbb{Z}|I_E, I_A)$ of the instance abstraction and the distribution $d(\mathbb{Z}|\bar{p}_{tra_j})$ of the expert trajectory, we supervise the distributions using KL divergence. The Ego distribution can be obtained directly, while the Agent target requires alignment using Hungarian algorithm [24].
+
+$$
+L _ {D S} = \frac {\sigma_ {I} - \sigma_ {F} - 0 . 5 + e ^ {2 \times \sigma_ {F}} + \left(\mu_ {F} - \mu_ {I}\right) ^ {2}}{2 \times e ^ {2 \times \sigma_ {I}}}. \tag {6}
+$$
+
+
+Figure 3. The Generative Models abstract expert trajectories, agent and ego feature as Gaussian distributions during training, using planning-oriented distribution to fuse instance tokens across multiple levels for distribution-wise interaction.
+
+Planning Decoders and Prediction Heads. As shown in Fig. 2, the student model's decoder and motion attributes learning layer are aligned with the teacher model, preventing heterogeneity in subsequent distillation tasks.
+
+# 3.4. Knowledge Distillation
+
+In this section, we design a distillation architecture that leverages the multi-mode teacher model to supervise the student model through diversified imitation learning.
+
+Instance Distillation of Encoders. First, we apply L2 loss to align the encoder features of the teacher and student, $F_{en}^{tc}$ and $F_{en}^{st}$ . This method effectively aligns the shallow features of both models, ensuring consistency in the latent space, with the encoder distillation loss $L_{en}^{KD}$ given by:
+
+$$
+L _ {e n} ^ {K D} = \sum_ {j = 1} ^ {N _ {E}} \left\| \boldsymbol {F} _ {e n} ^ {s t} - \boldsymbol {F} _ {e n} ^ {t c} \right\| _ {2}. \tag {7}
+$$
+
+Instance Distillation of Decoders. After the scene-wise and instance-wise decoders, we design a specialized adapter to accommodate the domain variability of the two models and address the heterogeneity between instances. The MLP adapter $\psi$ ensures isomorphism between the student and teacher decoder features, while the decoder distillation loss $L_{de}^{KD}$ is given as follows:
+
+$$
+L _ {d e} ^ {K D} = \sum_ {i = 1} ^ {N _ {E}} \left\| \psi \left(\boldsymbol {F} _ {\boldsymbol {d e}} ^ {\boldsymbol {s t}}\right) - \boldsymbol {F} _ {\boldsymbol {d e}} ^ {\boldsymbol {t c}} \right\| _ {2}. \tag {8}
+$$
+
+Motion Property Distillation. Ultimately, to capture its probabilities across modes, we also design multi-mode distillation. As shown below, we use KL divergence to supervise the multi-mode classifications $p_{cls}^{st}$ and $p_{cls}^{tc}$ , encouraging the student to learn a distribution closer to the teacher.
+
+$$
+L _ {c l s} ^ {K D} = \sum_ {i = 1} ^ {N _ {E}} p _ {c l s} ^ {t c} (i) \log \left(\frac {p _ {c l s} ^ {t c} (i)}{p _ {c l s} ^ {s t} (i)}\right). \tag {9}
+$$
+
+In summary, we design multi-stage distillation from the multi-mode teacher to the student model, addressing the challenge of a single learning objective. By supervising features and probabilities, we enrich the model's representation of agent interactions, thereby enhancing planning performance. The final multi-stage distillation loss is as follows:
+
+$$
+L _ {K D} = L _ {e n} ^ {K D} + L _ {d e} ^ {K D} + L _ {c l s} ^ {K D}. \tag {10}
+$$
+
+# 3.5. Training Object
+
+The learning objectives include the distillation loss $L_{KD}$ , distribution loss $L_{DS}$ , and reinforcement learning loss $L_{RL}$ . The imitation learning loss $L_{IL}$ follows Sec. 3.2, with total loss $L_{T}$ defined as follows, where $\lambda_1, \lambda_2, \lambda_3$ are the weight.
+
+$$
+L _ {T} = \lambda_ {1} \times L _ {K D} + \lambda_ {2} \times L _ {D S} + \lambda_ {3} \times L _ {R L} + L _ {I L}. \tag {11}
+$$
+
+# 4. Experiments
+
+# 4.1. Dataset and Metrics
+
+To evaluate the performances of the end-to-end planning model, we conducted comparison and ablation experiments on the nuScenes dataset [1]. It includes 1,000 driving scenes from Boston and Singapore, each lasting 20s, providing camera, LiDAR, and annotation at $2\mathrm{Hz}$ . However, most scenes involve uniform motion, and the dataset mainly targets perception tasks, using open-loop evaluations for planning, making it ideal for performance assessment.
+
+The NAVSIM dataset [7], streamlined from nuPlan [2], uses eight cameras for $360^{\circ}$ coverage and fuses LiDAR point clouds from five sensors for enhanced perception. The dataset provides high-quality annotations at $2\mathrm{Hz}$ , including HD maps and object bounding boxes, ensuring reliable data for autonomous planning tasks. Finally, the dataset focuses on challenging scenarios driven by dynamic changes in driving intentions, while excluding simpler cases like stationary or constant-speed driving, to better simulate autonomous planning in complex traffic environments.
+
+# 4.2. Experimental Settings
+
+To ensure a fair comparison, we use the same backbone and perception module as SparseDrive [37] on the nuScenes dataset, relying solely on panoramic images without additional LiDAR data. We trained on 8 NVIDIA A800 GPUs with a total batch size of 48, using the AdamW optimizer. The process involves training the teacher model for 30 epochs, followed by 100 epochs of perception pretraining. Then, the teacher and perception-pretrained models undergo 10 epochs of end-to-end distillation for the planning model. On the NAVSIM dataset, we use the baseline settings of Transfuser [6], with three cropped and scaled forward camera images $(1024\times 256)$ and rasterized BEV LiDAR as input, without temporal training to ensure a fair comparison. We trained using 8 NVIDIA A800 GPUs
+
+| Model | Input | L2(m)↓ | Collision(%)↓ | FPS ↑ |
| 1s | 2s | 3s | Avg. | 1s | 2s | 3s | Avg. |
| FF [14] | LiDAR | 0.55 | 1.20 | 2.54 | 1.43 | 0.06 | 0.17 | 1.07 | 0.43 | - |
| EO [23] | LiDAR | 0.67 | 1.36 | 2.78 | 1.60 | 0.04 | 0.09 | 0.88 | 0.33 | - |
| ST-P3 [15] | Camera | 1.33 | 2.11 | 2.90 | 2.11 | 0.23 | 0.63 | 1.27 | 0.71 | 1.6 |
| UniAD [16] | Camera | 0.45 | 0.70 | 1.04 | 0.73 | 0.62 | 0.58 | 0.63 | 0.61 | 1.8 |
| VAD [21] | Camera | 0.41 | 0.70 | 1.05 | 0.72 | 0.03 | 0.19 | 0.43 | 0.21 | 4.5 |
| SparseDrive [37] | Camera | 0.31 | 0.60 | 1.00 | 0.63 | 0.01 | 0.08 | 0.30 | 0.13 | 6.5 |
| DistillDrive (Teacher) | Annotation | 0.27 | 0.51 | 0.82 | 0.53 | 0.01 | 0.04 | 0.10 | 0.05 | 31.6 |
| DistillDrive (Student) | Camera | 0.28 | 0.54 | 0.83 | 0.57 | 0.00 | 0.03 | 0.17 | 0.06 | 6.0 |
+
+Table 1. Quantitative comparisons of planning performance using open-loop metrics on the nuScenes [1] val dataset. SparseDrive results are replicated under the same settings, and the teacher model, based on annotations, is excluded from the performance comparisons.
+
+| Model | Input | Backbone | NC↑ | DAC↑ | TTC | Comf.↑ | EP↑ | PDMS↑ |
| Const Velocity | - | - | 69.0 | 57.8 | 58.0 | 100 | 19.4 | 20.6 |
| Ego Status MLP | - | - | 93.0 | 77.3 | 83.6 | 100 | 62.8 | 65.6 |
| UniAD [16] | C | ResNet-34 | 97.8 | 91.9 | 92.2 | 100 | 78.8 | 83.4 |
| VADV2 [4] | C | ResNet-34 | 92.2 | 89.1 | 91.6 | 100 | 76.0 | 80.9 |
| Transfuser [6] | C & L | ResNet-34 | 97.8 | 92.3 | 92.9 | 100 | 78.6 | 83.5 |
| Hydra-MDP [27] | C & L | ResNet-34 | 97.9 | 91.7 | 92.9 | 100 | 77.6 | 83.0 |
| DistillDrive (Teacher) | GT | - | 97.5 | 96.0 | 92.8 | 100 | 81.0 | 86.5 |
| DistillDrive (Student) | C & L | ResNet-34 | 98.1 | 94.6 | 93.6 | 100 | 81.0 | 86.2 |
+
+and the AdamW optimizer (learning rate $1 \times 10^{-4}$ ) for 100 epochs. The process follows the same logic: first, the teacher model is trained separately, then used for end-to-end distillation of the student planning model. Where $\lambda_1, \lambda_2, \lambda_3, \gamma, \zeta$ are 0.5, 1, 1, 0.95, and 0.5.
+
+# 4.3. Results and Analysis
+
+Planning Performance on nuScenes Dataset. We validate the planning performance of the proposed DistillDrive on the nuScenes dataset, as shown in Tab. 1. The teacher model excels across all models, validating the effectiveness of reinforcement learning for state-space optimization, but it encounters coupling barriers [20] in real-world. Therefore, we propose a knowledge distillation scheme to enhance end-to-end multi-mode planning learning and validate our model's performance in the table. It outperforms both LiDAR-based [14, 23] and camera-based models [15, 16, 21], achieving a $50\%$ reduction in collision rate and a $10\%$ decrease in L2 error compared to SparseDrive. This demonstrates that diverse imitation learning effectively enhances the distinction between mode instances.
+
+Planning Performance on NAVSIM Dataset. Tab. 1 focuses on open-loop performance with assessment limitations, while Tab. 2 offers a comprehensive evaluation using NAVSIM's data-driven, non-reactive simulation. Results show the teacher model excels in performance, confirming
+
+Table 2. Quantitative comparison on planning-oriented NAVSIM [7] navest split with closed-loop metrics. "C" and "L" Denotes the use of camera and LiDAR sensor, While "GT" represents the use of ground truth annotations. Similarly, the teacher model is included only to demonstrate performance, not for actual performance comparison. The evaluation metrics are kept in default settings.
+
+| Model | NDS↑ | mAP↑ | mATE↓ | mASE↓ | mAOE↓ | mAVE↓ | mAAE↓ |
| UniAD | 49.8 | 0.38 | 0.684 | 0.277 | 0.383 | 0.381 | 0.192 |
| SparseDrive | 52.5 | 0.418 | 0.565 | 0.275 | 0.552 | 0.261 | 0.190 |
| DistillDrive | 53.0 | 0.420 | 0.568 | 0.275 | 0.539 | 0.265 | 0.1766 |
+
+Table 3. Quantitative Comparisons with end-to-end methods in detection performance on the nuScenes val dataset.
+
+| Model | AMOTA↑ | AMOTP↓ | Recall↓ | IDS↓ | APc↑ | APd↑ | APb↑ | mAP↑ |
| UniAD | 0.359 | 0.1320 | 04.67 | 906 | - | - | - | - |
| VAD | - | - | - | - | 40.6 | 51.5 | 50.6 | 47.6 |
| SparseDrive | 0.385 | 1.254 | 0.499 | 886 | 49.9 | 57.0 | 58.4 | 55.0 |
| DistillDrive | 0.371 | 1.252 | 0.500 | 767 | 49.5 | 57.3 | 58.3 | 55.0 |
+
+Table 4. Comparison of multi-target tracking and mapping performance on the nuScenes dataset. Here, $AP_{c}$ , $AP_{d}$ , and $AP_{b}$ represent the AP of crossing, divider, and boundary, respectively.
+
+the validity of its design. Through effective multi-mode instance imitation, our end-to-end student model outperforms the Transfuser [6] by $2.5\%$ on PDMS, with significant gains in DAC and EP. DistillDrive also surpass rule-based distillation [27] with significant performance gains. It even outperforms the teacher model on NC and TTC, demonstrating that multi-mode distillation not only transfers the teacher's knowledge but also enables significant breakthroughs.
+
+Perception Performance on nuScenes Dataset. To evaluate our planning model, Tab. 3 and Tab. 4 sequentially validate its detection, tracking, and mapping performance.
+
+
+Figure 4. Qualitative visualization with end-to-end methods in planning performance on the nuScenes val dataset. We conduct a comprehensive comparison with SparseDrive, focusing primarily on their planning performance in the bird's-eye view(BEV) space. The first and third rows show more diverse plans, while the second row exhibits better kinematic alignment under the same modality.
+
+
+
+
+Figure 5. Qualitative visualization of the planning performance on the NAVSIM navtest split, where the red line represents the predicted trajectory and the green line represents expert trajectory.
+
+Since no additional perception module was designed, the overall performance is similar to SparseDrive. However, we achieved improvements in metrics like IDS, thanks to the contribution of generative modeling.
+
+Qualitative Visualization. Fig. 4 visualizes the planning model's performance on the nuScenes dataset across three
+
+scenarios: right turn, left turn, and straight. The right-turn case shows greater trajectory diversity, highlighting the role of multi-mode instance distillation. In the left-turn case, our model produces smoother, more natural trajectories due to effective RL-based status optimization. The straight case shows a richer set of trajectory candidates, demonstrating enhanced planning capabilities. In Fig. 5, we validate the model's planning performance on NAVSIM dataset. In the first case, our model's trajectory closely matches the expert, demonstrating better completion. In the second case, while Transfuser fails due to braking, our model successfully overtakes, handling congestion effectively.
+
+To analyze the impact of multi-mode instance imitation on planning tokens, we use t-SNE to project tokens into two-dimensional space and compare SparseDrive, the teacher model, and DistillDrive in Fig. 6. DistillDrive compresses spatial representations while preserving the original model [37] distribution, learning intermediate representations through isomorphic model distillation, which demonstrates the feasibility of diverse instance imitation.
+
+# 4.4. Ablation Studies
+
+Effect of Reinforcement Learning Optimization. In Tab. 5, we apply reinforcement learning to refine the model, enhancing its comprehension of status and decision space. Comparing the second to fourth lines indicates that appropriate supervision and rewards enhance trajectory planning, while action selection in the fifth line refines performance. Finally, the proposed linear weighted reinforcement learn
+
+
+Figure 6. Visualization of multi-mode instances using t-SNE across SparseDrive, the teacher model, and DistillDrive.
+
+| \(L_{RL}\) | Reward | Select | IRL | Avg Collision(%) | Avg L2(m) |
| X | X | X | X | 0.066 | 0.5716 |
| ✓ | X | X | X | 0.057 | 0.5777 |
| ✓ | ✓ | X | X | 0.063 | 0.5653 |
| ✓ | ✓ | ✓ | X | 0.059 | 0.5522 |
| ✓ | ✓ | ✓ | ✓ | 0.053 -20% | 0.5364 -6% |
+
+ing dynamically integrates various reward values. This approach achieves a $20\%$ reduction in collision rate and a $6\%$ decrease in alignment L2 error, demonstrating its effectiveness in optimizing planning accuracy and safety.
+
+Ablation Study of DistillDrive Modules. To validate the design's effectiveness, we assess the core modules of the end-to-end planning model in Tab. 6. In rows second to fifth, individual evaluations reveal that Knowledge Distillation (KD) significantly enhances expressiveness via multimode supervision, while the generative model benefits from distribution-wise interaction for motion learning. However, Reinforcement Learning (RL) faces challenges due to limited state space representation. Meanwhile, result show that combining the components significantly improves model performance. KD as core elements, enhance multi-mode motion imitation, while RL, through state-to-decision supervision, boosts generalization to out-of-distribution data, improving decision stability and robustness. Further closed-loop experiment results are included in the appendix.
+
+Ablation Study on Generative Model. Analyzing Tab. 7 we observe that using Hungarian matching to align motion features encoded in the expert trajectory with those in the image decoding significantly improves planning and prediction performance. While adjusting the $\zeta$ parameter has a minor effect, setting $\zeta$ to 0.5 yields consistently high performance. Lastly, incorporating the autoregressive strategy negatively impacts performance by the difficulty of training. Effect of Knowledge Distillation. In Tab. 8, we validate our knowledge distillation approach and demonstrate that
+
+Table 5. Ablation study on reinforcement learning in the nuScenes val, where $L_{RL}$ , Reward, Select and IRL represent loss, reward, state-space allocation and inverse reinforcement learning.
+
+| RL | Distillation | Generative | Avg Collision(%) | Avg L2(m) |
| X | X | X | 0.132 | 0.6398 |
| ✓ | X | X | 0.137 | 0.6715 |
| X | ✓ | X | 0.092 | 0.5851 |
| X | X | ✓ | 0.107 | 0.5966 |
| ✓ | ✓ | X | 0.094 | 0.5915 |
| X | ✓ | ✓ | 0.101 | 0.5846 |
| ✓ | X | ✓ | 0.075 | 0.5968 |
| ✓ | ✓ | ✓ | 0.067 -50% | 0.5735 -10% |
+
+Table 6. Ablation study of designed modules on the nuScenes val.
+
+| ζ | HM | AR | Prediction | Planning |
| EPA | ADE | FDE | MR | Collision | ADE | FDE |
| 0.5 | × | × | 0.484 | 0.622 | 0.981 | 0.134 | 0.125 | 0.614 | 0.963 |
| 0.5 | ✓ | × | 0.539 | 0.422 | 0.538 | 0.045 | 0.093 | 0.583 | 0.914 |
| 1.0 | ✓ | × | 0.538 | 0.427 | 0.547 | 0.046 | 0.091 | 0.585 | 0.917 |
| 0.5 | ✓ | ✓ | 0.533 | 0.445 | 0.582 | 0.051 | 0.151 | 0.566 | 0.916 |
+
+Table 7. Ablation study of prediction and planning performance with generative model on the nuScenes val set, where HM and AR denote Hungarian Matching and autoregressive strategy.
+
+| \(L_{en}^{KD}\) | \(L_{de}^{KD}\) | \(L_{cls}^{KD}\) | Avg Collision(%) | Avg L2(m) |
| ✓ | ✘ | ✘ | 0.084 | 0.5884 |
| ✘ | ✓ | ✘ | 0.092 | 0.5851 |
| ✘ | ✘ | ✓ | 0.129 | 0.5857 |
| ✓ | ✘ | ✓ | 0.096 | 0.5918 |
| ✘ | ✓ | ✓ | 0.102 | 0.6010 |
| ✓ | ✓ | ✘ | 0.087 | 0.5769 |
+
+Table 8. Ablation study of distillation methods on nuScenes val.
+
+the gains from distillation are more pronounced in the encoders and decoders, thereby facilitating diverse instance imitation learning. The benefits of classification distillation are limited because the core planning functionality relies on regression heads, rendering classification supervision minimally impact on planning performance. Additional details on regression distillation are provided in the appendix
+
+# 5. Conclusion and Future Work
+
+To enhance the planning performance of End-to-end models, we implement a diversified instance imitation learning architecture to supervise the learning of multi-mode features. Reinforcement learning and generative modeling enhance motion-guided feature interactions, leading to significant improvements on the nuScenes and NAVSIM datasets.
+
+In future work, we aim to integrate world models with language models to enhance planning performance. More effective reinforcement learning methods will be employed to better understand the relationship between the semantic geometric space of the scene and the decision planning space, enhancing the model closed-loop performance.
+
+# References
+
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+
+# Acknowledgements
+
+This work is supported by National Natural Science Foundation of China (62333005), Shanghai International Science and Technology Cooperation Project (24510714000) and Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00105).
\ No newline at end of file
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+# Distilling Diffusion Models to Efficient 3D LiDAR Scene Completion
+
+Shengyuan Zhang1 An Zhao1 Ling Yang3 Zejian Li2,* Chenye Meng1
+
+Haoran Xu $^{4}$ Tianrun Chen $^{1}$ AnYang Wei $^{4}$ Perry Pengyun GU $^{4}$ Lingyun Sun $^{1}$
+
+$^{1}$ College of Computer Science and Technology, Zhejiang University $^{2}$ School of Software Technology, Zhejiang University
+
+3 Peking University 4 Zhejiang Green Zhixing Technology co., Ltd
+
+1,2{zhangshengyuan,zhaoan040113,zejianlee,mengcy,tianrun.chen,sunly}@zju.edu.cn
+
+$^{3}\{\text{yangling0818}\} @163$ com $^{4}\{$ Haoran.Xu5,weianyang,gupengyun $\} @$ geely.com *Corresponding author
+
+
+SemanticKITTI
+Input scan
+
+
+Ground Truth
+
+
+LiDiff (30.55s)
+
+
+ScoreLiDAR (5.37s)
+
+
+KITTI360
+Input scan
+(a)
+Figure 1. A demonstration of the LiDAR scene completion examples. Given a sparse LiDAR scan in (a), the model aims to recover the ground-truth dense scene as in (b). In these examples, scans are from SemanticKITTI [1] and KITTI360 [16] dataset. In both cases, LiDiff [23], a SOTA LiDAR scene completion method, requires about 30 seconds as in (c). In comparison, our proposed ScoreLiDAR takes only about 5 seconds in (d), achieving over 5x speedup with improved completion quality indicated by lower Chamfer Distance (CD).
+
+
+Ground Truth
+(b)
+
+
+LiDiff (29.43s)
+
+
+ScoreLiDAR (5.14s)
+(d)
+
+# Abstract
+
+Diffusion models have been applied to 3D LiDAR scene completion due to their strong training stability and high completion quality. However, the slow sampling speed limits the practical application of diffusion-based scene completion models since autonomous vehicles require an efficient perception of surrounding environments. This paper proposes a novel distillation method tailored for 3D LiDAR scene completion models, dubbed ScoreLiDAR, which achieves efficient yet high-quality scene completion. ScoreLiDAR enables the distilled model to sample in significantly fewer steps after distillation. To improve completion quality, we also introduce a novel Structural Loss, which encourages the distilled model to capture the geometric structure of the 3D LiDAR scene. The loss contains
+
+a scene-wise term constraining the holistic structure and a point-wise term constraining the key landmark points and their relative configuration. Extensive experiments demonstrate that ScoreLiDAR significantly accelerates the completion time from 30.55 to 5.37 seconds per frame $(>5\times)$ on SemanticKITTI and achieves superior performance compared to state-of-the-art 3D LiDAR scene completion models. Our model and code are publicly available on https://github.com/happyw1nd/ScoreLiDAR.
+
+# 1. Introduction
+
+Recognizing the surrounding environment accurately and efficiently using onboard sensors is crucial for the safe operation of autonomous vehicles [13, 14]. Among different types of sensors, 3D LiDAR has become one of the most
+
+
+Figure 2. A visualization of LiDAR scene completion performances with different models on SemanticKITTI [1] dataset. Generally, our proposed ScoreLiDAR achieves better scene completion performance and speed trade-off.
+
+widely adopted sensors due to its broader detection range and higher detection precision [21, 23]. However, driving scenarios are often complex, and the 3D point clouds collected by LiDAR are typically sparse, particularly in occluded areas [12, 31]. This sparsity causes a decline in the ability to understand 3D scenes [3, 23]. Thus, inferring and completing sparse 3D LiDAR scenes is necessary to provide a dense and more comprehensive scene representation.
+
+Due to the advantages of strong training stability and high-generation quality, existing works utilize diffusion models to complete the 3D LiDAR scenes and achieve outstanding results [22, 23]. However, the diffusion model often requires multiple network iterations to obtain a dense, complete, and high-quality LiDAR scene, which is time-consuming [10, 45]. Autonomous vehicles require fast and efficient perception and recognition of surrounding environments, so the slow sampling speed limits the practical application of diffusion models. Although existing works have proposed acceleration methods for diffusion models [18, 28, 30, 33, 41], due to the differences between 3D LiDAR scenes and image data—where LiDAR scenes often contain complex geometric structure information—these techniques have not been explored in the acceleration of diffusion-based LiDAR scene completion model.
+
+In this work, we propose ScoreLiDAR, a novel distillation method tailored for 3D LiDAR scene completion diffusion models, which enables efficient and high-quality scene completion (Fig. 1 and Fig. 2). ScoreLiDAR aims to tackle the unique 3D distribution alignment challenge in LiDAR scene completion. By exploiting a bidirectional gradient guidance mechanism, it allows the student model's com
+
+pletion results under sparse point cloud conditions to progressively approach the multi-step iterative reconstruction quality of the teacher model. Given a completed scene generated by the student model, the teacher model predicts the scene's score as a gradient to enhance realism, while a designed auxiliary model predicts the scene's another score as a gradient to suppress unrealistic completion. The student model is then updated according to the difference between these two gradients. This update drives the completion process toward more structurally coherent LiDAR scenes. Finally, we introduce a Structural Loss consisting of a scene-wise term and a point-wise term constraining the key landmark points and their relative configuration. Prior studies [15, 19, 34, 35] demonstrated that the bidirectional gradient guidance mechanism can effectively accelerate 3D rendering speed. In this work, we argue that a similar approach can be directly applied to the distillation of diffusion-based LiDAR scene completion models.
+
+Our contribution can be summarized as follows: (1) We propose ScoreLiDAR, a novel distillation method tailored for diffusion-based 3D LiDAR scene completion models, which achieves efficient scene completion. (2) We introduce a Structural Loss to effectively capture the geometric structure information of 3D point clouds during the distillation process, which ensures high-quality scene completion. (3) Extensive experiments show that ScoreLiDAR enables fast and efficient scene completion while achieving optimal generation quality compared to the existing models.
+
+# 2. Related work
+
+3D LiDAR Scene completion 3D LiDAR scene completion refers to recovering a complete scene from a sparse, incomplete LiDAR scan in applications such as autonomous driving [31, 38]. Current mainstream LiDAR scene completion methods include depth completion-based and Signed Distance Field (SDF)-based approaches. Depth completion-based methods aim to recover dense depth maps from sparse depth measurements [8, 36, 39]. These methods typically leverage deep learning techniques [4, 6] and can also incorporate guidance from RGB images to achieve higher-quality completion results [27, 42, 44]. SDF-based methods represent scenes as voxel grids, with the core idea of using signed distance fields to complete sparse LiDAR scenes [12, 31]. These methods are constrained by voxel resolution, making them prone to losing details within the scene [5, 23]. In addition, some methods introduce semantic information to enhance LiDAR scene completion [26, 37]. These methods can generate dense and complete scenes while providing semantic labels for each point, leading to broader application potential [32, 40].
+
+Diffusion-based 3D LiDAR scene completion Due to the strong training stability and high generation quality of
+
+diffusion models, many methods leverage diffusion models for LiDAR scene completion tasks [3, 11, 22-24]. The work of Lee et al. [11] is the first to apply diffusion models at the scene scale for LiDAR scene completion, enabling the generation of realistic scenes conditioned on partial observations from sparse point clouds. Similarly, R2DM [22] utilizes diffusion models based on distance and reflectance intensity image representations to generate various high-fidelity 3D LiDAR scenes. LiDiff [23] indicates that adding noise to point cloud data at the scene scale leads to a loss of detail. Therefore, LiDiff proposes operating directly on individual points and redefines the noise schedule and denoising processes to generate scenes with richer detail. Based on LiDiff, DiffSSC [3] further performs semantic scene completion tasks by implementing denoising and segmentation separately in both the point and semantic spaces. Moreover, LiDMs [24] constructs the pipeline from the perspectives of pattern realism, geometric realism, and object realism, achieving generation under different conditions.
+
+Due to the slow sampling inherent in diffusion models, diffusion-based 3D LiDAR scene completion suffers from slow inference, hindering its application in autonomous vehicles. Thus, this paper proposes a distillation method for diffusion-based 3D LiDAR scene completion models to achieve faster and higher-quality completion.
+
+# 3. Preliminary
+
+# 3.1. Brief introduction of diffusion models
+
+The diffusion models have two processes: forward diffusion and reverse denoising process [9, 29]. In the forward diffusion process, given the data $\pmb{x}^0 \sim q(\pmb{x})$ from the training distribution, the diffusion model adds different scales of noise to $\pmb{x}^0$ according to different timesteps $t \in [1, T]$ to obtain noisy data $\{\pmb{x}^1, \pmb{x}^2, \dots, \pmb{x}^T\}$ . When $T$ is large enough, $\pmb{x}^T$ approaches to standard Gaussian distribution, namely, $q(\pmb{x}^T) \approx \mathcal{N}(0, I)$ . This process is parameterized by a series of predefined noise factors $\beta^t$ . By defining $\alpha^t = 1 - \beta^t$ , the diffusion process is expressed as [9]:
+
+$$
+\boldsymbol {x} ^ {t} = \sqrt {\bar {\alpha} ^ {t}} \boldsymbol {x} ^ {0} + \sqrt {1 - \bar {\alpha} ^ {t}} \boldsymbol {\epsilon} ^ {t} \tag {1}
+$$
+
+Here $\bar{\alpha}^t = \prod_{t=1}^T \alpha^t$ , $p(\boldsymbol{x}^t \mid \boldsymbol{x}^0) = \mathcal{N}(\sqrt{\bar{\alpha}^t}, (1 - \bar{\alpha}^t)I)$ .
+
+During the training, the diffusion model tries to predict the added noise at different timesteps $t$ . Given the input $\pmb{x}^0$ and the condition $c$ (optional), the noisy data $\pmb{x}^t$ can be calculated by Eq. (1). The diffusion model $\epsilon_{\theta}$ predicts the noise according to $\pmb{x}^t$ , $c$ , $t$ and is then optimized by calculating the $\ell_2$ loss between the predicted and the real noise.
+
+$$
+\mathcal {L} _ {D M} = \mathbb {E} _ {t, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} \left(\boldsymbol {x} ^ {t}, c, t\right) \| ^ {2} \right] \tag {2}
+$$
+
+Here $\theta$ is the trainable parameter of $\epsilon_{\theta}$ .
+
+In the reverse denoising process, the diffusion model starts from the timestep $T$ and progressively removes the
+
+predicted noise to obtain a generated sample. The process of denoising $\pmb{x}^t$ to obtain $\pmb{x}^{t - 1}$ can be written as in [9]
+
+$$
+\boldsymbol {x} ^ {t - 1} = \frac {1}{\sqrt {\alpha^ {t}}} \left(\boldsymbol {x} ^ {t} - \frac {1 - \alpha^ {t}}{\sqrt {1 - \bar {\alpha} ^ {t}}} \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} ^ {t}, c, t\right)\right) + \sigma^ {t} \mathbf {z} \quad (3)
+$$
+
+Here $\mathbf{z} \sim \mathcal{N}(0, I)$ . In this process, the number of required inference steps varies depending on different sampling methods. For instance, DDPM [9] requires 1000 timesteps, while DDIM [29] and DPM solver [17] can reduce this to no more than 100 timesteps.
+
+# 3.2. 3D LiDAR scene completion diffusion models
+
+The 3D LiDAR scene completion diffusion models take the incomplete scan $\mathcal{P} = \{\pmb{p}_1, \pmb{p}_2, \dots, \pmb{p}_N\} (p_i \in \mathbb{R}^3)$ and try to generate the complete scene $\mathcal{G}^0 = \{\pmb{p}_1^0, \pmb{p}_2^0, \dots, \pmb{p}_M^0\}$ . Given the input LiDAR scan $\mathcal{P}$ and ground truth $\mathcal{G}$ , a diffusion model can be trained to perform 3D LiDAR scene completion. The noisy scene $\mathcal{G}^t$ at timestep $t$ is calculated from the ground truth $\mathcal{G}$ at point level [3, 23],
+
+$$
+\boldsymbol {p} _ {m} ^ {t} = \sqrt {\bar {\alpha} ^ {t}} \boldsymbol {p} _ {m} + \sqrt {1 - \bar {\alpha} ^ {t}} \boldsymbol {\epsilon} ^ {t}, \forall \boldsymbol {p} _ {m} \in \mathcal {G} \tag {4}
+$$
+
+Here $\mathcal{G}^t = \{\pmb {p}_1^t,\pmb {p}_2^t,\dots,\pmb {p}_M^t\}$ . Because the LiDAR point cloud is sparse, the noisy data retains very little information about the original data. To generate more realistic point cloud scenes, the LiDAR scan $\mathcal{P}$ can be used as a condition of the diffusion model [23]. In this case, the training loss of the diffusion model is given by:
+
+$$
+\mathcal {L} _ {D M} = \mathbb {E} _ {t, \epsilon} \left[ \left\| \epsilon - \epsilon_ {\theta} \left(\mathcal {G} ^ {t}, \mathcal {P}, t\right) \right\| ^ {2} \right] \tag {5}
+$$
+
+Then, as described in Sec. 3.1, the completed scene $\mathcal{G}^0$ can be generated by progressive denoising from $\mathcal{G}^T$ . Because the scale of the LiDAR scene is large and the data range is different across different point cloud axes, directly normalizing the entire scene compresses the data into a smaller range, which potentially leads to the loss of critical details [3, 23]. To solve this issue, LiDiff [23] modifies the diffusion process by adding a local noise offset to each point $\pmb{p}_m$ , gradually perturbing the point cloud at each timestep. For Eq. (1), $\pmb{x}^0$ is set to 0, and $\pmb{x}^t$ is added to each point $\pmb{p}_m$ ,
+
+$$
+\boldsymbol {p} _ {m} ^ {t} = \boldsymbol {p} _ {m} + \left(\sqrt {\bar {\alpha} ^ {t}} \mathbf {0} + \sqrt {1 - \bar {\alpha} ^ {t}} \boldsymbol {\epsilon} ^ {t}\right) = \boldsymbol {p} _ {m} + \sqrt {1 - \bar {\alpha} ^ {t}} \boldsymbol {\epsilon} ^ {t} \tag {6}
+$$
+
+Due to this special case, the initial noisy scene $\mathcal{G}^T$ cannot directly start from standard Gaussian noise in the sampling process. Instead, the LiDAR scan $\mathcal{P}$ is used to obtain $\mathcal{G}^T$ [23]. Firstly, given the initial incomplete scan $\mathcal{P}$ , the number of the point clouds is increased by duplicating the original points $K$ times and getting the pseudo dense scan $\mathcal{P}^* = \{\pmb{p}_1^*,\pmb{p}_2^*,\dots,\pmb{p}_M^*\}$ , where we assume $M = KN$ . Then, we calculate the noisy point cloud $\mathcal{P}^T$ by Eq. (6). As $\mathcal{P}^T$ is noisy enough, it can be regarded as $\mathcal{G}^T$ during the training. After that, a step-by-step denoising process is applied to obtain the completed scene $\mathcal{G}^0$ .
+
+
+Figure 3. The overall structure of ScoreLiDAR. (1) The student model generates the completed scene based on the sparse scan. (2) The sparse scan and noisy completed scene are input to $\epsilon_{\theta}$ and $\epsilon_{\phi}$ . (3) The predicted score of $\epsilon_{\theta}$ and $\epsilon_{\phi}$ are used to calculate the KL divergence. (4) Structural loss is calculated based on the completed scene and the ground truth. (5) The total loss is calculated with KL divergence and structural loss. (6) The student model is optimized according to the total loss. (7) The diffusion model $\epsilon_{\phi}$ is updated with the completed scene.
+
+# 4. Method
+
+Our goal is to distill a pre-trained 3D LiDAR scene completion diffusion model into a student model with significantly fewer sampling steps, enabling efficient and high-quality scene completion. Firstly, we introduce the distillation method tailored for 3D LiDAR scene completion diffusion models in Sec. 4.1. Then, we introduce the structural loss to improve the distillation process with both scene-wise loss and point-wise loss in Sec. 4.2. Finally, we describe the optimization procedure of ScoreLiDAR in Sec. 4.3. The overall structure of ScoreLiDAR is shown in Fig. 3.
+
+# 4.1. Distillation for 3D LiDAR scene completion
+
+Ideally, the final student model would achieve completion results comparable to those of the teacher model at a faster speed. In the 3D LiDAR scene completion scenario, let $q^0$ be the distribution of the ground truth $G$ , and $\epsilon_{\theta}$ be the pretrained scene completion diffusion model whose multi-step generated distribution approximates $q^0$ . Let $G_{stu}$ be the student model that can perform efficient LiDAR scene completion with the generated distribution $p_G^0$ . ScoreLiDAR aims to minimize the KL divergence between the distribution of the teacher model and the generated distribution of the student model [35, 43].
+
+$$
+\min _ {\eta} D _ {K L} \left(p _ {G} ^ {0} \left(\mathcal {G} ^ {0}; \eta\right) \| q ^ {0} \left(\mathcal {G} ^ {0}\right)\right) \tag {7}
+$$
+
+Here $\mathcal{G}^0$ is the completed scene generated by one-step sampling of $G_{stu}$ conditioned on $\mathcal{P}$ , for simplicity, we omit $\mathcal{P}$ when representing the distribution, $\eta$ is the trainable parameter of $G_{stu}$ . However, the high-density regions of $q^0$ are sparse in the data space, so it is hard to directly solve Eq. (7). According to Theorem 1 in [35], we expand the optimization problems in Eq. (7) by minimizing the KL divergence
+
+between two distributions at different noise levels as:
+
+$$
+\min _ {\eta} \mathcal {L} _ {K L} = \mathbb {E} _ {t, \epsilon} \left[ D _ {K L} \left(p _ {G} ^ {t} \left(\mathcal {G} ^ {t}\right) \| q ^ {t} \left(\mathcal {G} ^ {t}\right)\right) \right] \tag {8}
+$$
+
+Here $t$ is the timestep controlling the noise level, $\epsilon$ is random noise, and $\mathcal{G}^t = \{\pmb {p}_1^t,\pmb {p}_2^t,\dots ,\pmb {p}_M^t\}$ is the noisy version of the completed scene $\mathcal{G}^0$ at timestep $t$ . The gradient of $G_{stu}$ in Eq. (8) is approximated by
+
+$$
+\begin{array}{l} \nabla_ {\eta} D _ {\mathrm {K L}} \left(p _ {G} ^ {t} \left(\mathcal {G} ^ {t}\right) \| q ^ {t} \left(\mathcal {G} ^ {t}\right)\right) \\ = \mathbb {E} _ {t, \epsilon} \left[ \nabla_ {\mathcal {G} ^ {t}} \log p _ {G} ^ {t} (\mathcal {G} ^ {t}) - \nabla_ {\mathcal {G} ^ {t}} \log q ^ {t} (\mathcal {G} ^ {t}) \right] \frac {\partial \mathcal {G} ^ {t}}{\partial \eta} \tag {9} \\ \end{array}
+$$
+
+We use the pre-trained diffusion model $\epsilon_{\theta}$ to approximate $-\sqrt{1 - \bar{\alpha}^t}\nabla_{\mathcal{G}^t}\log q^t (\mathcal{G}^t)$ as discussed in Section 5 of Supplementary Materials (Sec S5). Similarly, $-\sqrt{1 - \bar{\alpha}^t}\nabla_{\mathcal{G}^t}\log p_G^t (\mathcal{G}^t)$ is approximated by an auxiliary diffusion model $\epsilon_{\phi}$ , which is independently trained with the denoising loss Eq. (5) on generated samples $\mathcal{G}^0$ . Then, with the simplification as in [9, 35], the $\mathcal{L}_{KL}$ is estimated by
+
+$$
+\mathcal {L} _ {K L} \approx \mathbb {E} _ {t, \epsilon} \left[ \| \epsilon_ {\theta} \left(\mathcal {G} ^ {t}, \mathcal {P}, t\right) - \epsilon_ {\phi} \left(\mathcal {G} ^ {t}, \mathcal {P}, t\right) \| _ {2} ^ {2} \right] \tag {10}
+$$
+
+Thus, the gradient in Eq. (9) is approximated by
+
+$$
+\begin{array}{l} \nabla_ {\eta} D _ {\mathrm {K L}} \left(p _ {G} ^ {t} \left(\mathcal {G} ^ {t}\right) \| q ^ {t} \left(\mathcal {G} ^ {t}\right)\right) \\ \approx \mathbb {E} _ {t, \epsilon} \left[ \epsilon_ {\theta} (\mathcal {G} ^ {t}, \mathcal {P}, t) - \epsilon_ {\phi} (\mathcal {G} ^ {t}, \mathcal {P}, t) \right] \frac {\partial \mathcal {G} ^ {t}}{\partial \eta} \tag {11} \\ \end{array}
+$$
+
+Intuitively, the orientation of $-\epsilon_{\theta}(\mathcal{G}^t,\mathcal{P},t)$ points to the pre-trained distribution, while that of $-\epsilon_{\phi}(\mathcal{G}^t,\mathcal{P},t)$ points to the student model's generative distribution. Thus, decenting along the bidirectional gradient $[\epsilon_{\theta}(\mathcal{G}^t,\mathcal{P},t) - \epsilon_{\phi}(\mathcal{G}^t,\mathcal{P},t)]$ updates the student model's generative distribution toward the pre-trained distribution, achieving a more accurate completion. Sec S2.1 discusses the efficiency of the distillation process.
+
+# 4.2. Structural loss
+
+Although the distillation process in Sec. 4.1 is effective in training models [18, 45], we found that directly applying it to LiDAR scene completion diffusion models leads to loss of local details and reduced realism. This is because the point cloud in LiDAR scenes includes complex geometric information that is not explicitly captured by diffusion models. Thus, we introduce a structural loss to further refine the distillation process and improve the completion quality. This structural loss includes scene-wise loss and point-wise loss and can help the student model effectively capture geometric structure information of the 3D point clouds.
+
+Scene-wise loss. In the distillation process mentioned in Sec. 4.1, the gradient $\nabla_{\eta}D_{\mathrm{KL}}$ in Eq. (11) is well-defined when $t\gg 0$ , i.e. the generated samples are totally disturbed by Gaussian noise. However, $\nabla_{\eta}D_{\mathrm{KL}}$ becomes unreliable when $t$ is small [43, 45]. This is because the student model often generates subpar results at the early stage due to the complexity of the point cloud data. It is easy for the noisy generated samples to lie outside the training distribution of the teacher model, causing the unreliable network prediction of the teacher model [43, 45].
+
+To solve this issue, we introduce the scene-wise loss, which minimizes the distance between the ground truth scene $\mathcal{G}$ and the completed scene $\mathcal{G}^0$ ,
+
+$$
+\mathcal {L} _ {\text {s c e n e}} = \frac {1}{| \mathcal {G} ^ {0} |} \sum_ {\boldsymbol {p} _ {i} ^ {0} \in \mathcal {G} ^ {0}} \min _ {\boldsymbol {p} \in \mathcal {G}} \| \boldsymbol {p} _ {i} ^ {0} - \boldsymbol {p} \| ^ {2} \tag {12}
+$$
+
+This loss calculates the mean squared error between each point $p_i^0$ in the generated scene $\mathcal{G}^0$ and its closest corresponding point $\pmb{p}$ in the ground truth $\mathcal{G}$ . It helps the student model capture the holistic structure, which prevents the optimization direction from deviating in the early stages and enhances training stability. The scene-wise loss enables the generated scenes to be closer to the ground truth globally, thereby enhancing the completion quality and fidelity.
+
+Point-wise loss. As seen in Eq. (11), the distillation process only constrains the overall distribution of the completed scene, ignoring the relative positions between different points. Directly using the gradient in Eq. (11) to optimize the student model may lead to loss of local details.
+
+Thus, we introduce the point-wise loss to capture the relative structural information between different points in the 3D LiDAR scene. The point-wise loss calculates the difference between the inter-point distance matrices of the completed scene and the ground truth. Due to the large number of points in the scene, calculating the distance matrix for all points is computationally intensive. Therefore, we select $n$ key points to compute the distance matrix with $n \ll M$ . Based on the local geometric features of each point, we
+
+choose key points that are critical for representing the structure of the 3D LiDAR scene. For each point $\pmb{p}_i^0$ in the completed scene $\mathcal{G}^0$ , we find its K-nearest neighbor, denoted as the set $\kappa_i$ . Then we select the key points by calculating their curvature $\kappa_i$ . The specific steps are as follows:
+
+Calculate the centroid $\bar{\pmb{p}}_i^0$ of the neighborhood $\kappa_{i}$
+
+$$
+\bar {\boldsymbol {p}} _ {i} ^ {0} = \frac {1}{K} \sum_ {\boldsymbol {p} _ {j} ^ {0} \in \mathcal {K} _ {i}} \boldsymbol {p} _ {j} ^ {0} \tag {13}
+$$
+
+Calculate the neighborhood covariance matrix $C_i$ for $\bar{\pmb{p}}_i^0$
+
+$$
+\mathcal {C} _ {i} = \frac {1}{K} \sum_ {\boldsymbol {p} _ {j} ^ {0} \in \mathcal {K} _ {i}} \left(\boldsymbol {p} _ {j} ^ {0} - \bar {\boldsymbol {p}} _ {i} ^ {0}\right) \left(\boldsymbol {p} _ {j} ^ {0} - \bar {\boldsymbol {p}} _ {i} ^ {0}\right) ^ {T} \tag {14}
+$$
+
+- Perform eigen-decomposition on the covariance matrix $\mathcal{C}_i$ to obtain the eigenvalues $\lambda_1 < \lambda_2 < \dots < \lambda_m$ .
+- Curvature $\kappa_{i}$ can be calculated using the eigenvalues
+
+$$
+\kappa_ {i} = \frac {\lambda_ {1}}{\sum_ {j = 1} ^ {m} \lambda_ {j}} \tag {15}
+$$
+
+A larger curvature $\kappa_{i}$ indicates greater local shape variation. Those points with great local variation are typically located at corners, edges, or endpoints, which tend to shape the main structure of the scene. Therefore, the top $n$ points with the highest curvature values are selected as key points.
+
+Given the ground truth $\mathcal{G} = \{\pmb{p}_1, \pmb{p}_2, \dots, \pmb{p}_M\}$ , we select $n$ key points ( $n \ll M$ ) from the point cloud to construct the $n \times n$ distance matrix $\mathcal{D}$ . The $d_{ij} \in \mathcal{D}$ represents the pairwise Euclidean Distance between points $i$ and $j$ . Then, for completed scene $\mathcal{G}^0$ , we select $n$ points that are closest to the key points in $\mathcal{G}$ as the corresponding key points to obtain the distance matrix $\mathcal{D}_G$ . Thus, the point-wise loss is calculated by
+
+$$
+\mathcal {L} _ {\text {p o i n t}} = \mathbb {E} _ {t, \epsilon} \left[ \| \mathcal {D} - \mathcal {D} _ {G} \| _ {2} ^ {2} \right] \tag {16}
+$$
+
+The point-wise loss can help the student model capture the relative configuration of key points and further enhance the geometric accuracy and detail retention of the completed scene. This ensures that key objects like cars, traffic cones, and walls are better completed, which is crucial for autonomous vehicles to recognize surroundings accurately.
+
+Structural loss. The final structural loss of $G_{stu}$ is
+
+$$
+\mathcal {L} _ {\text {s t r u c t u r a l}} = \lambda_ {\text {s c e n e}} \mathcal {L} _ {\text {s c e n e}} + \lambda_ {\text {p o i n t}} \mathcal {L} _ {\text {p o i n t}} \tag {17}
+$$
+
+Here $\lambda_{\text{scene}}$ and $\lambda_{\text{point}}$ are the weight of scene-wise loss and point-wise loss.
+
+| Model | CD ↓ | JSD ↓ | EMD ↓ | Times (s) ↓ |
| LMSCNet [25] | 0.641 | 0.431 | - | 0.40 |
| LODE [12] | 1.029 | 0.451 | - | 1.76 |
| MID [31] | 0.503 | 0.470 | - | 6.42 |
| PVD [46] | 1.256 | 0.498 | - | 262.54 |
| LiDiff [23] | 0.434 | 0.444 | 22.15 | 30.38 |
| LiDiff (Refined) [23] | 0.375 | 0.416 | 23.16 | 30.55 |
| ScoreLiDAR | 0.406 | 0.425 | 23.14 | 5.16 |
| ScoreLiDAR (Refined) | 0.342 | 0.399 | 23.26 | 5.37 |
+
+Table 1. The completion performance on the SemanticKITTI dataset. Colors denote the 1st, 2nd, and 3rd best-performing model. The sampling time is estimated based on the official code and the provided checkpoints.
+
+| Model | CD ↓ | JSD ↓ | EMD ↓ | Times (s) ↓ |
| LMSCNet [25] | 0.979 | 0.496 | - | 0.38 |
| LODE [12] | 1.565 | 0.483 | - | 1.64 |
| MID [31] | 0.637 | 0.476 | - | 6.23 |
| LiDiff [23] | 0.564 | 0.459 | 21.98 | 29.18 |
| LiDiff (Refined) [23] | 0.517 | 0.446 | 22.96 | 29.43 |
| ScoreLiDAR | 0.472 | 0.444 | 22.80 | 4.98 |
| ScoreLiDAR (Refined) | 0.452 | 0.437 | 23.02 | 5.14 |
+
+Table 2. The completion performance on the KITTI-360 dataset. The meaning of notations is the same as those in Tab. 1.
+
+| Model | SemanticKITTI | KITTI360 |
| CD↓ | JSD↓ | EMD↓ | CD↓ | JSD↓ | EMD↓ |
| ScoreLiDAR (Refined) | 0.342 | 0.399 | 23.26 | 0.452 | 0.437 | 23.02 |
| w/o Structural Loss (Refined) | 0.419 | 0.430 | 24.61 | 0.549 | 0.445 | 24.56 |
+
+# 4.3. Optimization procedure
+
+During the training, $G_{stu}$ and $\epsilon_{\phi}$ are initialized with the teacher model $\epsilon_{\theta}$ and optimized alternately. The auxiliary diffusion model $\epsilon_{\phi}$ is trained on the completed scene of the student model with Eq. (5). As for $G_{stu}$ , we follow the proposed method to select $\frac{1}{30}$ of the points from the entire point cloud as key points for calculating the point distance matrix. Then, $G_{stu}$ is optimized with the following objective
+
+$$
+\mathcal {L} _ {s t u} = \mathcal {L} _ {K L} + \mathcal {L} _ {\text {s t r u c t u r a l}} \tag {18}
+$$
+
+We set $\lambda_{\text{scene}} = 0.5$ and $\lambda_{\text{point}} = 0.01$ defaultly. The implementation details are provided in Sec S1.
+
+# 5. Experiment
+
+In this part, we conduct a series of experiments to evaluate the effectiveness of the proposed ScoreLiDAR. We compare ScoreLiDAR with advanced models including LMSC-Net [25], LODE [12], MID [31], PVD [46] and LiDiff [23]. We first evaluate the performance of ScoreLiDAR in scene
+
+Table 3. Ablation study of the structural loss.
+
+| Model | CD ↓ | JSD ↓ | EMD ↓ | Time (s) ↓ |
| LiDiff (50 steps) [23] | 0.434 | 0.444 | 22.15 | 30.38 |
| LiDiff (50 steps Refined) [23] | 0.375 | 0.416 | 23.16 | 30.55 |
| LiDiff (8 steps) [23] | 0.447 | 0.432 | 24.90 | 5.69 |
| LiDiff (8 steps Refined) [23] | 0.411 | 0.406 | 25.74 | 5.92 |
| ScoreLiDAR (8 Steps Refined) | 0.342 | 0.399 | 23.14 | 5.37 |
| ScoreLiDAR (4 Steps Refined) | 0.326 | 0.386 | 23.98 | 3.23 |
| ScoreLiDAR (2 Steps Refined) | 0.403 | 0.379 | - | 1.85 |
| ScoreLiDAR (1 Steps Refined) | 0.548 | 0.384 | - | 1.10 |
+
+Table 4. Ablation study of different sampling steps on the SemanticKITTI dataset.
+
+completion tasks (Sec. 5.1). Secondly, we present the results of ablation studies showing the effectiveness of the structural loss and the performances of ScoreLiDAR given different sampling steps (Sec. 5.2). Finally, we further evaluate ScoreLiDAR with the qualitative analysis (Sec. 5.3).
+
+# 5.1. Scene completion
+
+We validate ScoreLiDAR on SemanticKITTI [1] and KITTI-360 [16] datasets. The existing SOTA LiDAR scene completion model LiDiff [23] is chosen as the teacher model. The student model shares the network architecture with the teacher model and is initialized by the teacher model. Moreover, we also use the refinement network in LiDiff [23] to refine the completed scene generated by the student model. We calculate the Chamfer Distance (CD) [2], the Jensen-Shannon Divergence (JSD) [20] and the Earth Mover's Distance (EMD) [7] to evaluate the similarity between the completed scene and the ground truth. The smaller the value of these metrics, the closer the completed scene is to the ground truth.
+
+Tab. 1 shows that ScoreLiDAR achieves the optimal performance compared to the existing models in most cases on the SemanticeKITTI dataset. Compared to the SOTA method LiDiff [23] with refinement, which takes 30.55 seconds to complete a scene, ScoreLiDAR completes a scene in just 5.47 seconds (fivefold speedup) yet with $8\%$ improvement in CD, $4\%$ in JSD, and comparable results in EMD. The reason for the increase in EMD after refinement is the mismatch in the points numbers between $\mathcal{G}^0$ and $\mathcal{G}$ , leading to a higher matching cost. The refinement process optimizes local details but alters the global point cloud distribution, extending the overall transfer path. Although LMSCNet [25] and LODE [12] have faster completion speeds, their completion quality is significantly lower. The performance of ScoreLiDAR outperforms the teacher model LiDiff [23]. This is because ScoreLiDAR introduces a structural loss with scene-wise term and point-wise term, enabling the student model to effectively capture geometric structure information within LiDAR point cloud data during training. Results on KITTI-360 are shown in Tab. 2. ScoreLiDAR also achieves optimal performance in most cases and boasts
+
+
+
+
+(b)
+
+
+(a)
+(c)
+Figure 4. Qualitative results on KITTI-360. ScoreLiDAR achieves better completion than LiDiff [24] with fewer sampling steps.
+
+
+(d)
+
+a fivefold speedup with $12\%$ improvement in CD and $2\%$ in JSD compared to LiDiff [23].
+
+# 5.2. Ablation study
+
+In this part, we conduct the ablation study to verify the effectiveness of the structural loss in the training of the proposed ScoreLiDAR. We compared the scene completion performances of the proposed ScoreLiDAR with a variant that does not incorporate structural loss. The results are shown in Tab. 3. The results show that the variant without structural loss exhibits lower performance in scene completion on both datasets. However, after considering the structural loss, the performance of ScoreLiDAR improves significantly, which achieves better performance on all metrics. This supports our discussion in Sec. 4.3, incorporating structural loss enables the student model to capture the geometric structure feature of 3D point clouds, thereby facilitating the effective distillation of the student model.
+
+Furthermore, we compared the scene completion performance of ScoreLiDAR with different sampling steps, and the results are shown in Tab. 4. It can be observed that as the sampling steps decrease from 8 to 1, the time required for ScoreLiDAR to complete a scene also decreases, with single-step sampling allowing a scene to be completed in only 1.1 seconds. With 8-step and 4-step sampling, ScoreLiDAR performs better than LiDiff. All metrics decay at
+
+2-step and 1-step sampling, but in JSD ours still performs better than LiDiff. In summary, although the quality of scene completion decreases as the sampling steps are reduced, it still maintains performance comparable to or better than the existing model, achieving better performance and speed trade-off as in Fig. 2.
+
+In addition, we compared the ablation results about the terms of structural loss, different keypoint selection methods, varying numbers of keypoints, and different values of $\lambda_{\text{scene}}$ and $\lambda_{\text{point}}$ and so on, which are presented in Sec. S4.
+
+# 5.3. Qualitative analysis
+
+Fig. 4 shows the completed scenes by our proposed ScoreLiDAR and LiDiff [23] on KITTI-360. ScoreLiDAR achieves completion results with higher quality and greater fidelity in less time compared to LiDiff. For example, as shown in Fig. 4(c), in the left region, there should be two vehicles as in Fig. 4(b), but the scene completed by LiDiff only contains one. In contrast, the scene completed by ScoreLiDAR with only 8 steps in Fig. 4(d) completes two vehicles and has clearer and more complete vehicle structures, making it closer to the ground truth.
+
+To further demonstrate the effectiveness of ScoreLiDAR and the structural loss, we calculate the distance between the points in the completed scene and their corresponding points in the ground truth to evaluate the overall differ
+
+
+
+
+
+
+Figure 5. The qualitative analysis of structural loss. The bar chart shows the distribution of distances between corresponding points in the completed and ground truth scenes. A higher number of points with smaller distances demonstrates that the completed scene is closer to the ground truth. The heatmap represents the difference in distance matrices between the completed scene and the ground truth scene. Smaller values on the heatmap indicate that the completed scene is closer to the ground truth.
+
+
+
+
+
+
+
+ence. We display the calculated results in bar chat in Fig. 5. ScoreLiDAR has the highest number of points with smaller distances to their corresponding points in the ground truth. The results show that the scenes completed by ScoreLiDAR are closer to the ground truth overall, demonstrating higher fidelity. Moreover, we selected 36 corresponding key points from the ground truth and the completed scene using the method described in Sec. 4.2 and calculated the point distance matrices $\mathcal{D}$ and $\mathcal{D}_G$ . We then visualized the difference between $\mathcal{D}$ and $\mathcal{D}_G$ as a heatmap. As shown in Fig. 5, on both datasets, the difference of point distance matrix between the completed scene of LiDiff [23] and the ground truth is the largest, followed by the ScoreLiDAR variant without the structural loss and the smallest difference is achieved by ScoreLiDAR. This also indicates that the scene completed by ScoreLiDAR is closer to the ground truth.
+
+We also conduct a user study to evaluate the performance of ScoreLiDAR. We used ScoreLiDAR and LiDiff [23] to complete scenes based on the same input scans and asked users to choose the scene they believed was closer to the ground truth. ScoreLiDAR received a $65\%$ user preference over LiDiff [23]. This indicates that the detail and fidelity of the scenes completed by ScoreLiDAR more closely resemble the ground truth for most users. The details of the
+
+user study are shown in SM.
+
+# 6. Conclusion
+
+Summary. This paper proposes ScoreLiDAR, a novel distillation method tailored for 3D LiDAR scene completion diffusion models based on a bidirectional gradient guidance mechanism. By introducing the structural loss with scene-wise term and point-wise term, ScoreLiDAR trains the student model to effectively capture the holistic structure and the relative configuration of key points and achieve efficient and high-quality scene completion.
+
+Limitations. While ScoreLiDAR achieves efficient, high-quality LiDAR scene completion, its performance is constrained by the teacher model. As the performance of the teacher model improves, so does the capability of the student model. Although we conducted a preliminary experiment on the semantic scene completion in the Supplementary Material, a more comprehensive exploration is still required. Thus, further exploration is required to find a more effective method to improve the training process of ScoreLiDAR and avoid the limitations of the teacher model, achieving more efficient semantic LiDAR scene completion.
+
+# Acknowledgement
+
+This paper is supported by Provincial Key Research and Development Plan of Zhejiang Province under No. 2024C01250(SD2), National Natural Science Foundation of China (Grant No. 62006208) and Dream Set Off - Kunpeng & Ascend Seed Program.
+
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+# Distilling Parallel Gradients for Fast ODE Solvers of Diffusion Models
+
+Beier Zhu $^{1*}$ Ruoyu Wang $^{2*}$ Tong Zhao $^{2}$ Hanwang Zhang $^{1}$ Chi Zhang $^{2\dagger}$ $^{1}$ Nanyang Technological University, $^{2}$ Westlake University
+
+{beier.zhu, hanwangzhang}@ntu.edu.sg, {wangruoyu71, zhaotong68, chizhang}@westlake.edu.cn
+
+# Abstract
+
+Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face image quality degradation under a low-latency budget. In this paper, we propose the Ensemble Parallel Direction solver (dubbed as EPD-Solver), a novel ODE solver that mitigates truncation errors by incorporating multiple parallel gradient evaluations in each ODE step. Importantly, since the additional gradient computations are independent, they can be fully parallelized, preserving low-latency sampling. Our method optimizes a small set of learnable parameters in a distillation fashion, ensuring minimal training overhead. In addition, our method can serve as a plugin to improve existing ODE samplers. Extensive experiments on various image synthesis benchmarks demonstrate the effectiveness of our EPD-Solver in achieving high-quality and low-latency sampling. For example, at the same latency level of 5 NFE, EPD achieves an FID of 4.47 on CIFAR-10, 7.97 on FFHQ, 8.17 on ImageNet, and 8.26 on LSUN Bedroom, surpassing existing learning-based solvers by a significant margin. Codes are available in https://github.com/BeierZhu/EPD.
+
+# 1. Introduction
+
+Diffusion models (DMs) [7, 32, 39] have become a leading paradigm in generative modeling, achieving state-of-the-art performance across a diverse range of applications, including image synthesis [16, 32, 35], video generation [2, 8], speech synthesis [14], and 3D shape modeling [26]. These models operate by gradually refining a noisy input through a denoising process, producing high-fidelity outputs with impressive diversity and realism. However, the multi-step sequential denoising process introduces substantial latency, making sampling inefficient.
+
+In response to the challenge, recent efforts have focused on accelerating the sampling process of DMs. Notably,
+
+
+Figure 1. Comparison of various solvers on diffusion models. We compare the FID versus latency (ms) across different NFE settings on a NVIDIA 4090. Our proposed EPD-Solver shows superior image quality without increasing latency.
+
+these methods typically fall into three categories: solver-based methods, distillation-based methods, and parallelism-based methods, each with distinct advantages and limitations. Solver-based methods develop fast numerical solvers to reduce sampling steps [10, 12, 21, 23, 24, 40, 46, 50-52]. However, inherent truncation errors lead to significant quality degradation when the number of function evaluations (NFE) is low ( $e.g., < 5$ ). Distillation-based methods train a student DM to establish a bijective mapping between the data distribution and a predefined tractable noise distribution [1, 11, 22, 25, 27, 29, 36, 42, 53]. This process allows the distilled model to generate high-quality samples within a minimal number of NFEs, often as low as one. However, achieving this level of efficiency requires extensive training with carefully designed objectives, making the distillation process computationally expensive. Additionally, such methods struggle to leverage multi-NFE settings effectively, limiting their flexibility when a trade-off between speed and quality is desired. Parallelism-based methods accelerate diffusion models by trading computation for speed [4, 17, 19, 38]. While promising, this direction remains underexplored.
+
+To combine the advantages of these approaches, we investigate solver-based methods under low-latency constraints
+
+
+Figure 2. Computation graphs of various ODE solvers. (a) DDIM solver [40] (Euler's method) adopts the rectangle rule that uses the gradient at the start point: $\mathbf{d}_{t_{n + 1}} = \pmb{\epsilon}_{\theta}(\mathbf{x}_{t_{n + 1}}, t_{n + 1})$ . disclose EDM solver [10] (Heun's method) uses the trapezoidal rule that averages the gradients of both the start and the end timesteps, i.e., $\mathbf{d}_{t_{n + 1}} = \pmb{\epsilon}_{\theta}(\mathbf{x}_{t_{n + 1}}, t_{n + 1})$ and $\mathbf{d}_{t_n}' = \pmb{\epsilon}_{\theta}(\mathbf{x}_{t_n}', t_n)$ , where $\mathbf{x}_{t_n}'$ is the additional evaluation given by Euler's method. (c) AMED solver [52] optimizes a small network $g_{\phi}(\cdot)$ to output an intermediate timestep $s_n \in (t_n, t_{n + 1})$ to compute the gradient: $\mathbf{d}_{s_n} = \pmb{\epsilon}_{\theta}(\mathbf{x}_{s_n}, s_n)$ . Since AMED introduces a network in sequential computation, its latency is slightly higher than that of other solvers, as shown in Fig. 1. (d) Our EPD-Solver leverage $K$ parallel gradients to achieve more accurate integral approximation. We optimize $K$ intermediate timesteps $\tau_{n}^{1}, \ldots, \tau_{n}^{K}$ , compute their gradients $\mathbf{d}_{\tau_n^1}, \ldots, \mathbf{d}_{\tau_n^K}$ , and combine them via a simplex-weighted sum.
+
+and explore how additional computation can enhance image quality while maintaining minimal latency. We develop an Ensemble Parallel Direction (EPD) solver, which incorporates additional parallel gradient computations to mitigate truncation error in each ODE step. At a high level, various existing ODE solvers utilize gradients at different timesteps to approximate the ODE solution with varying accuracy. For instance, as shown in Fig. 2, EDM [10] (Fig. 2.b) and AMED (Fig. 2.c) improve image generation quality compared to DDIM (Fig. 2.a) by leveraging additional gradients evaluated at $t_n$ and $s_n \in (t_{n+1}, t_n)$ , respectively. Our EPD solver (Fig. 2.d) extends this idea by incorporating $K$ learned intermediate timesteps $(\tau_n^k \in (t_{n+1}, t_n), k \in [K])$ . Combining these additional gradients via simplex-weighted summation yields a more accurate integral estimate, reducing local truncation error and enhancing sampling fidelity. Furthermore, since the computations of these additional gradients are independent - each computed via a one-step Euler update from $\mathbf{x}_{t_{n+1}}$ - they can be efficiently parallelized, ensuring no increase in inference latency. In Fig. 1, we compare FID scores against latency for various ODE solvers on CIFAR-10 [15]. At each latency level, our EPD-Solver with $K = 2$ consistently achieves superior image quality.
+
+We optimize the learnable parameters (e.g., $\{\tau_n^k\}_{k=1}^K$ ) of our EPD-Solver in a distillation fashion. Since the parameter count is small (ranging from 6 to 45 in our experiments), the tuning overhead remains minimal. We further extend our method as a plugin to existing ODE samplers, termed EPD-Plugin. We evaluate EPD-Solver on a diverse set of image generation models, including CIFAR-10 [15], FFHQ [9], ImageNet [33], LSUN Bedroom [49], and Stable Diffusion [32]. At the same latency level of 5 NFE, EPD-Solver achieves an FID of 4.47 on CIFAR-10, 7.97 on FFHQ, 8.17 on ImageNet, and 8.26 on LSUN Bedroom.
+
+This performance outperforms other learning-based solvers by a significant margin; for example, AMED Solver [52] only achieves an FID of 13.20 on LSUN Bedroom. Our contributions can be summarized as follows:
+
+- We propose EPD-Solver, a novel ODE solver that leverages multiple parallel gradients to reduce truncation errors.
+- We propose EPD-Plugin, a plugin that extends parallel gradient estimation to existing ODE samplers.
+- With few learnable parameters, our solver is lightweight to train and does not increase inference latency.
+- EPD-Solver significantly outperforms existing ODE solvers in FID across multiple generation benchmarks.
+
+# 2. Related Work
+
+High latency in the sampling process is a major drawback of DMs compared to other generative models [6, 13]. Prior acceleration efforts mainly fall into three classes:
+
+Distillation-based methods. These methods accelerate diffusion models by re-training or fine-tuning the entire DM. One category is trajectory distillation, which trains a student model to imitate the teacher's trajectory with fewer steps [53]. This process can be achieved through offline distillation [22, 25], which requires constructing a dataset sampled from teacher models, or online distillation, which progressively reduces sampling steps in a multi-stage manner [1, 29, 36]. Another line of research is consistency distillation, where the denoising outputs along the sampling trajectory are enforced to remain consistent [11, 27, 42]. Apart from distilling noise-image pairs, distribution matching methods match real and reconstructed samples at the distribution level [31, 37, 45, 48]. Despite significantly enhancing quality, these approaches incur high training costs and require carefully designed training procedures.
+
+Solver-based methods. Beyond fine-tuning DMs, fast
+
+ODE solvers have been extensively studied. Training-free methods include Euler's method [40], Heun's method [10], Taylor expansion-based solvers (DPM-Solver [23], DPM-Solver++ [24]), multi-step methods (PNDM [21], iPNDM [50]), and predictor-corrector frameworks (UniPC [51]). Some solvers require additional training, e.g., AMED-Solver [52], D-ODE [12], and DDSS [46]. Recent work optimizes timestep schedules, with notable studies including LD3 [44], AYS [34], GITS [3], and DMN [47]. Though EPD-Solver falls into this category, we optimize solver parameters via distillation to achieve high-quality, low-latency generation through parallelism. With minimal learnable parameters, training remains highly efficient.
+
+Parallelism-based methods. While promising, parallelism remains an underexplored approach for accelerating diffusion models. ParaDiGMS [38] leverages Picard iteration for parallel sampling but struggles to maintain consistency with original outputs. Faster Diffusion [19] performs decoder computation in parallel by omitting encoder computation at some adjacent timesteps, but this compromises image quality. Distribision [17] divides high-resolution images into patches and performs parallel inference on each patch. AsyncDiff [4] implements model parallelism through asynchronous denoising. Unlike prior methods that focus on reducing latency, our EPD-Solver leverages parallel gradients to enhance image quality without incurring notable latency.
+
+# 3. Method
+
+# 3.1. Background
+
+Diffusion models gradually inject noise into data via a forward noising process and generate samples by learning a reversed denoising process, initialized with Gaussian noise. Let $\mathbf{x} \sim p_{\mathrm{data}}(\mathbf{x})$ denote the $d$ -dimensional data and $p(\mathbf{x}; \sigma)$ the data distribution with Gaussian noise of variance $\sigma^2$ injected. The forward process is controlled by a noise schedule defined by the time scaling $s(t)$ and the noise level $\sigma(t)$ at time $t$ . In particular, $\mathbf{x} = s(t) \hat{\mathbf{x}}_t$ , where $\hat{\mathbf{x}}_t \sim p(\mathbf{x}; \sigma(t))$ . Such forward process can be formulated by a SDE [10]:
+
+$$
+\mathrm {d} \mathbf {x} = \frac {\dot {s} (t)}{s (t)} \mathbf {x} + s (t) \sqrt {2 \sigma (t) \dot {\sigma} (t)} \mathrm {d} \mathbf {w} _ {t}, \tag {1}
+$$
+
+where $\mathbf{w} \in \mathbb{R}^d$ denotes Wiener process. In this paper, we adopt the framework of Karras et al. [10] by setting $\sigma(t) = t$ and $s(t) = 1$ . Generation is then performed with the reverse of Eq. (1). Notably, there exists the probability flow ODE:
+
+$$
+\mathrm {d} \mathbf {x} = - t \nabla_ {\mathbf {x}} \log p (\mathbf {x}; t) \mathrm {d} t \tag {2}
+$$
+
+We learn a parameterized network $\epsilon_{\theta}(\mathbf{x},t)$ to predict the Gaussian noise added to $\mathbf{x}$ at time $t$ . The network satisfies: $\epsilon_{\theta}(\mathbf{x},t) = -t\nabla_{\mathbf{x}}\log p(\mathbf{x};t)$ and Eq. (2) simplifies to:
+
+$$
+\mathrm {d} \mathbf {x} = \epsilon_ {\theta} (\mathbf {x}, t) \mathrm {d} t \tag {3}
+$$
+
+The noise-prediction model $\epsilon_{\theta}(\mathbf{x},t)$ is trained by minimizing the $\ell_2^2$ loss with a weighting function $\lambda (t)$ [10, 41]:
+
+$$
+\mathcal {L} _ {t} (\theta) = \lambda (t) \mathbb {E} _ {\mathbf {x} \sim p _ {\mathrm {d a t a}}, \epsilon \sim \mathcal {N} (0, \mathbf {I})} \| \epsilon_ {\theta} (\mathbf {x}, t) - \epsilon \| _ {2} ^ {2} \tag {4}
+$$
+
+Given a time schedule $\mathcal{T} = \{t_0 = t_{\mathrm{min}},\dots,t_N = t_{\mathrm{max}}\}$ , data generation involves starting from random noise $\mathbf{x}_{t_N}\sim \mathcal{N}(\mathbf{0},t_{\mathrm{max}}^2\mathbf{I})$ , then iteratively solving Eq. (3) to compute the sequence $\{\mathbf{x}_{t_{N - 1}},\dots,\mathbf{x}_{t_0}\}$ .
+
+# 3.2. The Proposed Solver
+
+Motivation. The solution of Eq. (3) at time $t_n$ can be exactly computed in the integral form:
+
+$$
+\mathbf {x} _ {t _ {n}} = \mathbf {x} _ {t _ {n + 1}} + \int_ {t _ {n + 1}} ^ {t _ {n}} \epsilon_ {\theta} (\mathbf {x} _ {t}, t) d t \tag {5}
+$$
+
+Various ODE solvers have been proposed to approximate the integral. At a high level, these solvers leverage one or several points to compute gradients, which are then used to estimate the integral. Let $I$ denote the integral $I = \int_{t_{n + 1}}^{t_n}\pmb {\epsilon}_\theta (\mathbf{x}_t,t)\mathrm{d}t$ and $h_n$ denote the step length $h_n = t_n - t_{n + 1}$ . For instance, DDIM [40] (Euler's method) adopts the rectangle rule that uses the gradient at the start point:
+
+$$
+I \approx h _ {n} \underbrace {\epsilon_ {\theta} \left(\mathbf {x} _ {t _ {n + 1}} , t _ {n + 1}\right)} _ {\text {s t a r t p o i n t g r a d .}}. \tag {6}
+$$
+
+EDM [10] considers the trapezoidal rule that averages the gradients of both the start and end points.
+
+$$
+I \approx \frac {1}{2} h _ {n} \left\{\underbrace {\boldsymbol {\epsilon} _ {\theta} \left(\mathbf {x} _ {t _ {n + 1}} , t _ {n + 1}\right)} _ {\text {s t a r t p o i n t g r a d .}} + \underbrace {\boldsymbol {\epsilon} _ {\theta} \left(\mathbf {x} _ {t _ {n}} ^ {\prime} , t _ {n}\right)} _ {\text {e n d p o i n t g r a d .}} \right\}, \tag {7}
+$$
+
+where $\mathbf{x}_{t_n}^{\prime}$ is the additional evaluation point given by Euler's method, i.e., $\mathbf{x}_{t_n}^{\prime} = \mathbf{x}_{t_{n + 1}} + h_n\epsilon_{\theta}(\mathbf{x}_{t_{n + 1}},t_{n + 1})$ . AMED-Solver [52] optimizes a small network to output an intermediate timestep $s_n\in (t_n,t_{n + 1})$ to compute the gradient:
+
+$$
+I \approx h _ {n} \underbrace {\epsilon_ {\theta} \left(\mathbf {x} _ {s _ {n}} , s _ {n}\right)} _ {\text {m i d p o i n t g r a d .}} \tag {8}
+$$
+
+where $\mathbf{x}_{s_n} = \mathbf{x}_{t_{n + 1}} + (s_n - t_{n + 1})\epsilon_\theta (\mathbf{x}_{t_{n + 1}},t_{n + 1})$ . The computational graphs of DDIM, EDM, and AMED-Solver, illustrating their respective integral approximation processes, are shown in Fig. 2.
+
+Compared to DDIM, EDM and AMED introduce an additional timestep for gradient computation ( $t_n$ and $s_n$ ), leading to improved integral estimation. The key motivation behind our method is to leverage multiple timesteps to reduce the truncation errors. Furthermore, since the computations of additional gradients are independent, they can be efficiently parallelized without increasing inference latency. In this work, we propose the Ensemble Parallel Direction (EPD)
+
+solver, which refines the integral estimation by incorporating multiple intermediate timesteps. Formally, the integral is approximated as:
+
+$$
+I \approx h _ {n} \underbrace {\sum_ {k = 1} ^ {K} \lambda_ {n} ^ {k} \epsilon_ {\theta} \left(\mathbf {x} _ {\tau_ {n} ^ {k}} , \tau_ {n} ^ {k}\right)} _ {\text {e n s e m b l e p a r a l l e l g r a d s .}}, \tag {9}
+$$
+
+where $\tau_{n}^{k}\in (t_{n},t_{n + 1})$ are the intermediate timesteps, and the weights form a simplex combination satisfying $\lambda_n^k\geq 0$ and $\sum_{k = 1}^{K}\lambda_{n}^{k} = 1$ . The state at each intermediate timestep $\tau_{n}^{k}$ is computed using Euler's method as: $\mathbf{x}_{\tau_n^k} = \mathbf{x}_{t_{n + 1}} + (\tau_k - t_{n + 1})\pmb {\epsilon}_\theta (\mathbf{x}_{t_{n + 1}},t_{n + 1})$ . Each gradient computation $\pmb{\epsilon}_{\theta}(\mathbf{x}_{\tau_n^k},\tau_n^k)$ is fully parallelizable, preserving efficiency without increasing inference latency. In fact, the use of gradients estimated at multiple timesteps for improved integral approximation can be theoretically justified by the following mean value theorem for vector-valued functions.
+
+Theorem 1 ([28]) When $f$ has values in an $n$ -dimensional vector space and is continuous on the closed interval $[a, b]$ and differentiable on the open interval $(a, b)$ , we have
+
+$$
+f (b) - f (a) = (b - a) \sum_ {k = 1} ^ {n} \lambda_ {k} f ^ {\prime} \left(c _ {k}\right), \tag {10}
+$$
+
+for some $c_{k}\in (a,b),\lambda_{k}\geq 0$ and $\sum_{k = 1}^{n}\lambda_{k} = 1$
+
+In the context of denoising process, the function outputs an $d$ -dimensional vector as $\mathbf{x} \in \mathbb{R}^d$ . According to Theorem 1, the exact integral of $\epsilon_{\theta}(\mathbf{x}_t, t)$ over the interval $[t_n, t_{n+1}]$ can be expressed as a simplex-weighted combination of gradients evaluated at $d$ intermediate points, scaled by the interval length $h_n = t_n - t_{n+1}$ , as formulated in Eq. (9).
+
+Parameters optimizing and inference. [18, 30] identify exposure bias—i.e., the mismatch between training and sampling inputs—as a key factor contributing to error accumulation and sampling drift. To mitigate this, they propose scaling the network output and shifting the timestep, respectively. Inspired by these insights, we introduce two learnable parameters, $o_n$ and $\delta_n^k$ , to perturb the scale of network output's and the timestep. Our EPD-Solver follows the update rule:
+
+$$
+\mathbf {x} _ {t _ {n}} = \mathbf {x} _ {t _ {n + 1}} + (1 + o _ {n}) h _ {n} \sum_ {k = 1} ^ {K} \lambda_ {n} ^ {k} \epsilon_ {\theta} \left(\mathbf {x} _ {\tau_ {n} ^ {k}}, \tau_ {n} ^ {k} + \delta_ {n} ^ {k}\right) \tag {11}
+$$
+
+We define the parameters at step $n$ as $\Theta_{n} = \{\tau_{n}^{k},\lambda_{n}^{k},\delta_{n}^{k},o_{n}\}_{k = 1}^{K}$ and denote the complete set of parameters for an $N$ -step sampling process as $\Theta_{1:N}$ . Consequently, the total number of parameters is given by $N(1 + 3K)$ .
+
+To determine $\Theta_{1:N}$ , we employ a distillation-based optimization process. Specifically, given a student time schedule with $N$ steps $\mathcal{T}_{\mathrm{stu}} = \{t_0 = t_{\min},\dots,t_N = t_{\max}\}$
+
+Algorithm 1 Optimizing $\Theta_{1:N}$
+1: Given: Time schedules $\mathcal{T}_{\mathrm{stu}}$ and $\mathcal{T}_{\mathrm{tea}}$ , teacher solver $\mathcal{S}$ .
+2: Return: $\Theta_{1:N}$ , where $\Theta_n = \{\tau_n^k, \lambda_n^k, \delta_n^k, o_n\}_{k=1}^K$
+3: repeat
+4: Initialize $\mathbf{x}_{t_N} = \mathbf{y}_{t_N} \sim \mathcal{N}(\mathbf{0}, t_N^2\mathbf{I})$
+5: Sample a teacher trajectory $\{\mathbf{y}_{t_n}\}_{n=1}^N$ via $\mathcal{S}$
+6: for $n = N - 1$ to 0 do
+7: Compute $\mathbf{x}_{t_n}$ using Eq. (11)
+8: Update $\Theta_{1:n}$ via min $\mathcal{L}_n(\Theta_{1:n})$ (Eq. (12))
+9: end for
+10: until converge
+
+Algorithm 2 EPD-Solver sampling
+1: Given: Time schedule $\mathcal{T}_{\mathrm{stu}}$ , learned parameters $\Theta_{1:N}$ .
+2: Return: $\mathbf{x}_{t_0}$
+3: Initialize $\mathbf{x}_{t_N} \sim \mathcal{N}(\mathbf{0}, t_N^2\mathbf{I})$
+4: for $n = N - 1$ to 0 do
+5: $I \gets (1 + o_n)h_n \sum_{k=1}^{K} \lambda_n^k \epsilon_\theta(\mathbf{x}_{\tau_n^k}, \tau_n^k + \delta_n^k)$ $\triangleright$ implement parallelism for accelerating
+6: $\mathbf{x}_{t_n} \gets \mathbf{x}_{t_{n+1}} + I$
+7: end for
+
+we insert $M$ intermediate steps between $t_n$ and $t_{n + 1}$ , i.e., $\mathcal{T}_{\mathrm{tea}} = \{t_0,\dots,t_n,t_n^1,\dots,t_n^M,t_{n + 1},\dots,t_N\}$ , to yield a more accurate teacher trajectories. The training process starts with generating teacher trajectories by any ODE solver (e.g., DPM-Solver) and store the reference states as $\{\mathbf{y}_{t_n}\}_{n = 0}^N$ . Afterward, we sample student trajectory with the same initial noise $\mathbf{y}_{t_N}$ , and optimize the parameters $\{\Theta_n\}_{n = 1}^N$ to obtain the student trajectory $\{\mathbf{x}_{t_n}\}_{n = 0}^N$ that aligns the teacher trajectory w.r.t some distance measurement $\mathrm{dist}(\cdot ,\cdot)$ . For noisy states $\{\mathbf{x}_{t_n}\}_{n = 1}^N$ , we use the squared $\ell_2$ distance as $\mathrm{dist}(\cdot ,\cdot)$ . For a generated sample $\mathbf{x}_{t_0}$ , we compute the squared $\ell_2$ distance in the feature space of the last layer of an ImageNet-pretrained Inception network [43]. In particular, to improve the alignment between $\mathbf{x}_{t_n}$ and $\mathbf{y}_{t_n}$ , since the value of $\mathbf{x}_{t_n}$ is dependent of the parameters $\Theta_{1}$ to $\Theta_{n}$ , we aim to optimize them by minimizing
+
+$$
+\mathcal {L} _ {n} \left(\Theta_ {1: n}\right) = \operatorname {d i s t} \left(\mathbf {x} _ {t _ {n}}, \mathbf {y} _ {t _ {n}}\right). \tag {12}
+$$
+
+In one training loop, we require $N$ backpropagation. The entire training algorithm is listed in Algorithm 1 and the inference procedure is provided in Algorithm 2. By default, we adopt the analytical first step (AFS) trick [5] in the first step to save one NFE by simply using $\mathbf{x}_{t_N}$ as direction.
+
+EPD-Plugin to existing solvers. EPD-Solver can be applied to existing solvers to further enhance diffusion sampling. The key idea is to replace their original gradient estimation with multiple parallel branches. As a representative case, we demonstrate this using the multi-step iPNDM sampler [21, 50]. We refer to the modified solver
+
+
+Figure 3. $\ell_2$ error between teacher and student trajectory w.r.t. $K$ .
+
+as EPD-Plugin. Due to space limitations, a detailed description is deferred to Suppl. A.2.
+
+# 3.3. Discussion
+
+Discussion with multi-step solvers. While multi-step solvers [21, 24, 50, 51] also use multiple gradients to approximate the integral, they typically rely on Taylor expansion or polynomial extrapolation to linearly combine historical gradients. In contrast, our method is grounded in the vector-valued mean value theorem and optimizes a convex combination of gradients evaluated within the current time interval. By focusing on in-interval gradients, our approach yields a more accurate and adaptive approximation of the integral.
+
+Discussion with AMED-Solver. AMED-Solver [52] estimates the direction using a single intermediate timestep per step. In contrast, our EPD-Solver method combines multiple intermediate gradients via a convex weighting scheme, without increasing inference latency. While a single direction may suffice when the trajectory is nearly one-dimensional, PCA analysis in [3] shows that the first principal component accounts for only $65\%$ of the variance, suggesting that multiple directions better capture the underlying geometry.
+
+To verify this, we conduct a controlled experiment with a 3-step schedule. As shown in Fig. 3, we compute the $\ell_2$ error between teacher and student trajectories over 1000 random samples, varying the number of intermediate gradients $K$ . The error drops significantly from $K = 1$ to $K = 2$ , but shows diminishing returns for $K > 2$ , indicating that two directions already capture most of the trajectory's structure.
+
+In addition, unlike AMED-Solver, which uses a neural network to predict sample-specific interpolation points, our EPD-Solver learns global sampling parameters in a plug-and-play fashion, without incurring extra runtime cost.
+
+# 4. Experiments
+
+This section is organized as follows:
+
+- Sec. 4.1 provides an overview of our experimental setup.
+- Sec. 4.2 compares our EPD-Solver and EPD-Plugin with state-of-the-art ODE samplers.
+- Sec. 4.3 analyzes the impact of the number of parallel directions $K$ on image quality and inference latency.
+- Sec. 4.4 ablates the main components of EPD-Solver.
+
+- Sec. 4.5 showcases qualitative visualizations of the sampling process and generated images.
+
+# 4.1. Setup
+
+Models. We test out ODE solvers on diffusion-based image generation models, covering both pixel-space [10] and latent-space models [32], across image resolutions ranging from 32 to 512. For pixel-space models, we evaluate the pretrained models on CIFAR $32 \times 32$ [15], FFHQ $64 \times 64$ [9], ImageNet $64 \times 64$ [33] from [10]. For latent-space models, we examine the pretrained models on LSUN Bedroom $256 \times 256$ [49] from [32] and Stable-Diffusion [32] at a resolution of 512.
+
+Baseline solvers. We compare against representative ODE solvers across three categories: (1) Single-step solvers: DDIM [40], EDM [10], DPM-Solver-2 [23], and AMED-Solver [52]; (2) Multi-step solvers: DPM-Solver++(3M)[24], UniPC[51], iPNDM [21, 50], and AMED-Plugin [52]; (3) Parallelism-based solver: ParaDiGMS [38]. For a fair comparison, we follow the recommended time schedules from their original papers [10, 24, 51]. Specifically, we use the logSNR schedule for DPM-Solver-2, DPM-Solver++(3M), and UniPC, the time-uniform schedule for AMED-Solver [52], while employing the polynomial time schedule with $\rho = 7$ for the remaining baselines. Please refer to Suppl. A.3 for implementation details of ParaDiGMS [38].
+
+Evaluation. We test our EPD-{Solver, Plugin} under low NFE budgets (NFE $\in$ {3,5,7,9}) where AFS [5] is applied. EPD-{Solver, Plugin} have the same NFE as the baselines when $K = 1$ . For $K > 1$ , each step involves $K - 1$ extra NFE. However, parallelism ensures that latency remains unchanged. We use the term Parallel NFE (Para. NFE) to denote the effective NFE under parallel execution. We assess sample quality using the Fréchet Inception Distance (FID) computed over 50k images. For Stable-Diffusion, we evaluate FID by generating 30k images using prompts sampled from the MS-COCO validation set [20].
+
+Implementation details. We optimize our parameters using the Adam optimizer on 10k images with a batch size of 32. To prevent overfitting, we constrain $o_n$ and $\delta_n^k$ using the sigmoid trick, ensuring they remain within $[-0.05, 0.05]$ . Since the parameter count is small (ranging from 6 to 45 in our experiments), training is highly efficient—taking $\sim 3$ minutes for CIFAR-10 on a single NVIDIA 4090 and $\sim 30$ minutes for LSUN Bedroom $256 \times 256$ on four NVIDIA A800 GPUs. To generate teacher trajectory, we employ DPM-Solver-2 solver with $M = 6$ intermediate time steps injected. Additional implementation details are available in Suppl. A.1.
+
+# 4.2. Main Results
+
+In Tab. 1, we compare the FID scores of images generated by our EPD-Solver with $K = 2$ against baseline solvers across the CIFAR-10, FFHQ, ImageNet, and LSUN Bedroom datasets. The results demonstrate consistent and sig
+
+ | Method | (Para.) NFE |
| 3 | 5 | 7 | 9 |
| Single-step | DDIM [40] | 93.36 | 49.66 | 27.93 | 18.43 |
| EDM [10] | 306.2 | 97.67 | 37.28 | 15.76 |
| DPM-Solver-2 [23] | 155.7 | 57.30 | 10.20 | 4.98 |
| AMED-Solver [52] | 18.49 | 7.59 | 4.36 | 3.67 |
| Multi-step | DPM-Solver++(3M) [24] | 110.0 | 24.97 | 6.74 | 3.42 |
| UniPC [51] | 109.6 | 23.98 | 5.83 | 3.21 |
| iPNDM [21, 50] | 47.98 | 13.59 | 5.08 | 3.17 |
| AMED-Plugin [52] | 10.81 | 6.61 | 3.65 | 2.63 |
| Parallel | ParaDiGMS [38] | 51.03 | 18.96 | 7.18 | 6.19 |
| EPD-Solver (ours) | 10.40 | 4.33 | 2.82 | 2.49 |
| EPD-Plugin (ours) | 10.54 | 4.47 | 3.27 | 2.42 |
+
+(a) Unconditional generation on CIFAR10 $32 \times 32$ [15]
+
+ | Method | (Para.) NFE |
| 3 | 5 | 7 | 9 |
| Single-step | DDIM [40] | 78.21 | 43.93 | 28.86 | 21.01 |
| EDM [10] | 356.5 | 116.7 | 54.51 | 28.86 |
| DPM-Solver-2 [23] | 266.0 | 87.10 | 22.59 | 9.26 |
| AMED-Solver [52] | 47.31 | 14.80 | 8.82 | 6.31 |
| Multi-step | DPM-Solver++(3M) [24] | 86.45 | 22.51 | 8.44 | 4.77 |
| UniPC [51] | 86.43 | 21.40 | 7.44 | 4.47 |
| iPNDM [21, 50] | 45.98 | 17.17 | 7.79 | 4.58 |
| AMED-Plugin [52] | 26.87 | 12.49 | 6.64 | 4.24 |
| Parallel | ParaDiGMS [38] | 43.64 | 20.92 | 16.39 | 8.81 |
| EPD-Solver (ours) | 21.74 | 7.84 | 4.81 | 3.82 |
| EPD-Plugin (ours) | 19.02 | 7.97 | 5.09 | 3.53 |
+
+(b) Unconditional generation on FFFQ $64\times 64$ [9]
+
+ | Method | (Para.) NFE |
| 3 | 5 | 7 | 9 |
| Single-step | DDIM [40] | 82.96 | 43.81 | 27.46 | 19.27 |
| EDM [10] | 249.4 | 89.63 | 37.65 | 16.76 |
| DPM-Solver-2 [23] | 140.2 | 42.41 | 12.03 | 6.64 |
| AMED-Solver [52] | 38.10 | 10.74 | 6.66 | 5.44 |
| Multi-step | DPM-Solver++(3M) [24] | 91.52 | 25.49 | 10.14 | 6.48 |
| UniPC [51] | 91.38 | 24.36 | 9.57 | 6.34 |
| iPNDM [21, 50] | 58.53 | 18.99 | 9.17 | 5.91 |
| AMED-Plugin [52] | 28.06 | 13.83 | 7.81 | 5.60 |
| Parallel | ParaDiGMS [38] | 41.11 | 17.27 | 13.67 | 6.38 |
| EPD-Solver (ours) | 18.28 | 6.35 | 5.26 | 4.27 |
| EPD-Plugin (ours) | 19.89 | 8.17 | 4.81 | 4.02 |
+
+(c) Conditional generation on ImageNet $64\times 64$ [33]
+
+ | Method | (Para.) NFE |
| 3 | 5 | 7 | 9 |
| Single-step | DDIM [40] | 86.13 | 34.34 | 19.50 | 13.26 |
| EDM [10] | 291.5 | 175.7 | 78.67 | 35.67 |
| DPM-Solver-2 [23] | 210.6 | 80.60 | 23.25 | 9.61 |
| AMED-Solver [52] | 58.21 | 13.20 | 7.10 | 5.65 |
| Multi-step | DPM-Solver++(3M) [24] | 111.9 | 23.15 | 8.87 | 6.45 |
| UniPC [51] | 112.3 | 23.34 | 8.73 | 6.61 |
| iPNDM [21, 50] | 80.99 | 26.65 | 13.80 | 8.38 |
| AMED-Plugin [52] | 101.5 | 25.68 | 8.63 | 7.82 |
| Parallel | ParaDiGMS [38] | 100.3 | 31.68 | 15.85 | 8.56 |
| EPD-Solver (ours) | 13.21 | 7.52 | 5.97 | 5.01 |
| EPD-Plugin (ours) | 14.12 | 8.26 | 5.24 | 4.51 |
+
+(d) Unconditional generation on LSUN Bedroom $256 \times 256$ [49]
+Table 1. Image generation results across four datasets: (a) CIFAR10, (b) FFHQ, (c) ImageNet, (d) LSUN Bedroom. We compared our EPD-Solver and EPD-Plugin with (1) Single-step solvers: DDIM, EDM, DPM-Solver-2 and AMED-Solver, (2) Multi-step solvers: DPM-Solver++(3M), UniPC, iPNDM and AMED-Plugin, (3) Parallelism-based solver: ParaDiGMS. The best results are in bold, the second best are underlined. See Suppl. B.1 for the value of the learned parameters of EPD-Solver and EPD-Plugin.
+
+| Method | (Para.) NFE |
| 8 | 12 | 16 | 20 |
| DPM-Solver++(2M) [24] | 21.33 | 15.99 | 14.84 | 14.58 |
| AMED-Plugin [52] | 18.92 | 14.84 | 13.96 | 13.24 |
| EPD-Solver (ours) | 16.46 | 13.14 | 12.52 | 12.17 |
+
+Table 2. FID results on Stable-Diffusion [32].
+
+nificant improvements from our learned directions across all datasets and NFE values. Specifically, with 9 (Para.) NFE, we achieve FID scores of 4.27 and 5.01 on the ImageNet and LSUN datasets, respectively, while the second-best baseline counterpart achieves 5.44 and 5.65, showing a notable improvement. Moreover, in the low NFE region, such as 3 NFE on LSUN Bedroom, our EPD-Solver achieves a remarkable 13.21 FID, significantly outperforming the second-best baseline solver (AMED-Solver), which achieves 58.21 FID. We further evaluate EPD-Plugin applied to the iPNDM solver, and observe that it outperforms EPD-Solver when
+
+$\mathrm{NFE} > 7$ , consistent with our expectation that iPNDM benefits from historical gradients only when the step is sufficiently large. With small NFE, this advantage is less pronounced.
+
+We evaluate our EPD-Solver method on Stable-Diffusion v1.5, setting the classifier-free guidance weight to 7.5, and report the FID score on the MS-COCO validation set in Tab. 2. Additionally, we compare the quality of samples generated by DPM-Solver(2M)++ (as recommended in the official implementation) and the AMED-Plugin Solver, a recent SoTA solver. The results demonstrate the consistent superiority of our proposed method.
+
+# 4.3. On the Number of Parallel Directions
+
+Image quality with different values of $K$ . In Fig. 4, we compare the quality of images generated using our EPD-Solver with different values of $K$ . As expected, increasing the number of intermediate points leads to improved FID scores. For example, on the FFHQ dataset with 3 Para. NFE, the FID score decreases from 26.0 to 22.7 when $K$
+
+
+(a) CIFAR-10 $32 \times 32$
+
+
+(b) FFHQ $64 \times 64$
+
+
+(c) ImageNet $64 \times 64$
+Figure 4. FID curves for different datasets and the number of parallel directions $(K)$ .
+
+
+(d) LSUN Bedroom $256 \times 256$
+
+ | K | Para. NFE |
| 3 | 5 | 7 | 9 |
| CIFAR | 1 | 28.1±0.84 | 47.2±0.88 | 63.5±0.71 | 80.5±0.73 |
| 2 | 27.6±0.78 | 45.3±0.77 | 62.7±0.76 | 79.8±0.81 |
| 3 | 27.7±0.85 | 45.7±0.80 | 63.5±0.86 | 82.0±0.94 |
| FFHQ | 1 | 34.4±0.79 | 56.1±0.78 | 77.4±0.96 | 100.4±0.74 |
| 2 | 34.4±0.85 | 56.4±0.83 | 79.6±0.92 | 98.6±0.83 |
| 3 | 34.1±0.92 | 56.0±0.88 | 78.0±0.89 | 99.8±0.94 |
+
+(a) CIFAR10 and FFHQ
+
+ | K | Para. NFE |
| 3 | 5 | 7 | 9 |
| N | 1 | 56.7±1.09 | 93.3±1.04 | 128.2±1.06 | 163.2±1.08 |
| 2 | 55.7±1.16 | 92.3±1.18 | 128.2±1.14 | 164.4±1.23 |
| 3 | 55.7±1.20 | 94.7±1.20 | 129.9±1.21 | 162.8±1.20 |
| L SUN | 1 | 57.5±1.26 | 78.8±1.02 | 104.3±1.15 | 131.1±1.03 |
| 2 | 56.6±1.16 | 82.6±1.12 | 109.6±1.10 | 138.9±1.23 |
| 3 | 57.9±1.15 | 86.2±1.16 | 117.8±1.10 | 147.8±1.19 |
+
+(b) ImageNet and LSUN Bedroom
+
+Table 3. Latency (ms) measured across different datasets, Para. NFE values, and the number of parallel directions $(K)$ . No noticeable latency increase was observed when $K$ increased to 2. The reported values include the $95\%$ confidence interval.
+
+increases from 1 to 2. Additionally, the results suggest that increasing the number of points beyond 2 yields diminishing returns. For instance, on ImageNet with 9 Para. NFE, the FID scores for $K = 2$ and $K = 3$ are 4.20 and 4.18, respectively, showing minimal improvement.
+
+Latency with different values of $K$ . Given that each intermediate gradient is fully parallelizable, we examine whether increasing $K$ noticeably impacts latency. Tab. 3 presents inference latency on a single NVIDIA 4090, evaluated over 1000 generated images with a batch size of 1. We report the average inference time along with the $95\%$ confidence interval. For CIFAR-10, FFHQ, and ImageNet, increasing $K$ to 3 does not noticeably impact latency. For LSUN Bedroom, we observe a slight increase in latency when $K = 3$ . However, earlier results show that $K = 2$ already yields significant quality improvements. Therefore, setting $K = 2$ provides an effective trade-off, achieving high-quality image generation while avoiding additional inference cost.
+
+# 4.4. Ablation Studies
+
+Effect of scaling factors. [18, 30] identify exposure bias—i.e., the input mismatch between training and sampling—as a key factor leading to error accumulation and sampling drift. To mitigate the bias, they propose scaling the gradient and shifting the timestep. Building on these insights, our EPD-Solver introduces two learnable parameters: $o_n$ and $\delta_n^k$ . We compare FID scores without these scaling factors to assess their impact. As shown in Tab. 4, omitting the scal
+
+ing factors noticeably reduces image quality. For instance, without $o_n$ , FID rises from 4.33 to 5.84 at Para. NFE = 5.
+
+Effect of time schedule. In Tab. 5, we present results on CIFAR-10 using commonly used time schedules: LogSNR, EDM, and Time-uniform. Our solver consistently performs better with the time-uniform schedule.
+
+Effect of teacher ODE solvers. We study the impact of different teacher ODE solvers in Tab. 6. The results show that using DPM-Solver-2 to generate teacher trajectories achieves the best performance. We hypothesize that this is because DPM-Solver-2 also estimates gradients using intermediate points, resulting in a smaller gap to our EPD-Solver.
+
+# 4.5. Qualitative Analyses
+
+Qualitative results on trajectory. Since visualizing the trajectories of high-dimensional data is challenging, we adopt the analysis framework in [21]. Specifically, as shown in Fig. 5, we randomly select two pixels from the images to perform local trajectory visualization, illustrating how their values evolve during the sampling process. Given the sampling $\mathbf{x}_{t_N},\mathbf{x}_{t_{N - 1}},\ldots ,\mathbf{x}_{t_0}$ , we track the corresponding values $v_{t}^{1}$ and $v_{t}^{2}$ at two randomly chosen positions $p_1$ and $p_2$ . We then represent $(v_{t}^{1},v_{t}^{2})$ as data points and visualize them in $\mathbb{R}^2$ . We can clearly observe that the pixel value trajectories of EPD-Solver (Para. NFE = 5, $K = 2$ ) are closer to the target trajectories compared to other samplers. This shows that our EPD-Solver can generate more accurate trajectory, significantly reducing errors in the sampling process.
+
+| Para. NFE | 3 | 5 | 7 | 9 |
| EPD-Solver | 10.40 | 4.33 | 2.82 | 2.49 |
| w.o. on | 13.25 | 5.84 | 3.59 | 2.79 |
| w.o. δnk | 13.02 | 5.47 | 3.23 | 2.69 |
| w.o. on & δnk | 16.01 | 6.62 | 4.24 | 3.24 |
+
+Table 4. Effect of scaling factors $\left( {{o}_{n},{\delta }_{n}^{k}}\right)$ .
+
+| Schedule | Para. NFE |
| 3 | 5 | 7 | 9 |
| LogSNR | 54.07 | 8.88 | 7.95 | 3.97 |
| EDM [10] | 11.10 | 8.89 | 4.50 | 3.72 |
| Time-uniform | 10.40 | 4.33 | 2.82 | 2.49 |
+
+Table 5. Effect of time schedules.
+
+| Teacher Solver | Para. NFE |
| 3 | 5 | 7 | 9 |
| Heun [10] | 15.91 | 6.65 | 4.61 | 3.57 |
| iPNDM [15, 21] | 13.69 | 6.64 | 4.59 | 3.59 |
| DPM-Solver-2 [23] | 10.40 | 4.33 | 2.82 | 2.49 |
+
+Table 6. Effect of teacher ODE solvers.
+
+
+Teacher DDIM
+
+
+DPM iPNDM
+
+
+EPD-Solver (ours)
+
+
+Start points
+End points
+
+
+Figure 5. Analysis on local sampling trajectory. The figure shows the generation path of two randomly selected pixels in the images. We employ the EPD (Para. NFE = 5, K = 2) sampler for sampling, using the trajectory of its teacher sampler as the target trajectory. We present the sampling trajectories with NFE = 5 of DDIM [40], DPM-Solver [23], and iPNDM [50] on CIFAR-10 [15].
+(a) FFHQ
+
+
+(b) ImageNet
+
+
+(c) LSUN Bedroom
+Figure 6. Comparison of generated samples among DPM-Solver-2 [23], iPNDM [50] and EPD-Solver. Compared to other samplers, EPD-Solver achieves high-quality results even at $\mathrm{NFE} = 3$ . Additional visualizations are provided in Suppl. B.3.
+
+Qualitative results on generated samples. In Fig. 6, we compare the generated images from DPM-Solver-2 [23], iPNDM [50], and EPD-Solver using the pretrained models on FFHQ, ImageNet and LSUN Bedroom. Under the same (Para.) NFE, our EPD-Solver consistently outperforms other samplers in terms of visual perception. This advantage is particularly pronounced in low-NFE settings $(\mathrm{NFE} = 3, 5)$ , where EPD-Solver is able to generate complete and clear images, while the outputs of other samplers appear highly blurred. These results highlight the superior performance of our method across different NFE settings. Additional visualizations are provided in Suppl. B.3.
+
+# 5. Conclusion
+
+In this paper, we propose Ensemble Parallel Direction (EPD), a novel ODE solver that improves diffusion model sam
+
+pling by leveraging multiple parallel gradient evaluations. Unlike conventional solver-based methods that suffer from truncation errors at low NFE, our approach significantly enhances integral approximation while maintaining low-latency inference. By optimizing a small set of learnable parameters in a distillation fashion, EPD-Solver achieves efficient training and seamless integration into existing diffusion models. We also generalize our EPD-Solver to EPD-Plugin, a plugin that can be extended to existing ODE samplers. Extensive experiments across CIFAR10, FFHQ, ImageNet, LSUN Bedroom, and Stable Diffusion demonstrate that EPD-Solver consistently outperforms state-of-the-art solvers in FID scores while maintaining computational efficiency. Our findings suggest that parallel gradient estimation is a powerful yet underexplored direction for accelerating diffusion models.
+
+# Acknowledgements
+
+This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL).
+
+# References
+
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\ No newline at end of file
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+# Dita: Scaling Diffusion Transformer for Generalist Vision-Language-Action Policy
+
+Zhi Hou $^{1*}$ Tianyi Zhang $^{2,1*}$ Yuwen Xiong $^{1}$ Haonan Duan $^{5}$ Hengjun Pu $^{3,1}$ Ronglei Tong $^{5}$ Chengyang Zhao $^{4,1}$ Xizhou Zhu $^{6,1}$ Yu Qiao $^{1}$ Jifeng Dai $^{6,1}$ Yuntao Chen $^{7\dagger}$ $^{1}$ Shanghai AI Lab $^{2}$ College of Computer Science and Technology, Zhejiang University
+ $^{3}$ MMLab, The Chinese University of Hong Kong $^{4}$ Peking University $^{5}$ SenseTime Research
+ $^{6}$ Tsinghua University $^{7}$ HKISI, CAS
+
+https://robodita.github.io
+
+
+Diffusion Transformer Pretraining
+
+
+
+
+
+
+
+
+10-Shot Multi-Task Finetuning on New Robot Setup
+Simulation Benchmark Evaluation
+
+Long-Horizon (close top drawer, open bottom drawer, put bowl into drawer, close bottom drawer)
+
+
+Background Variance (pick up the packet, and hit the ball into the goal)
+
+
+Figure 1. We introduce Dita, an open-source, simple yet effective policy for generalist robotic learning. Pretrained on large-scale cross-embediment datasets, Dita enables 10-shot adaptation to complex, multitask, long-horizon scenarios in novel robot setups. Particularly, Dita can complete intricate, extended-horizon tasks such as, "close the top drawer, then open the bottom drawer, subsequently place the bowl into the bottom drawer, and finally close the bottom drawer". Furthermore, Dita demonstrates remarkable robustness against complex object arrangements and even challenging lighting conditions in sophisticated 3D pick-and-rotation tasks. In this context, the long-horizon demonstration scene serves as the training environment for all tasks. Additionally, Dita seamlessly scales to a wide range of popular simulation benchmarks, achieving state-of-the-art performance across these tasks.
+
+Non-target Object Arrangements (pour the water from teapot into the left cup)
+
+
+Lighting Condition (pour coffee beans from bowl within the drawer into the outside bowl)
+
+
+
+# Abstract
+
+While recent vision-language-action models trained on diverse robot datasets exhibit promising generalization capabilities with limited in-domain data, their reliance on compact action heads to predict discretized or continuous actions constrains adaptability to heterogeneous ac
+
+tion spaces. We present Dita, a scalable framework that leverages Transformer architectures to directly denoise continuous action sequences through a unified multimodal diffusion process. Departing from prior methods that condition denoising on fused embeddings via shallow networks, Dita employs in-context conditioning—enabling fine-grained alignment between denoised actions and raw visual tokens from historical observations. This design explicitly models action deltas and environmental nuances.
+
+By scaling the diffusion action denoiser alongside the Transformer's scalability, Dita effectively integrates cross-embodiment datasets across diverse camera perspectives, observation scenes, tasks, and action spaces. Such synergy enhances robustness against various variances and facilitates the successful execution of long-horizon tasks. Evaluations across extensive benchmarks demonstrate state-of-the-art or comparative performance in simulation. Notably, Dita achieves robust real-world adaptation to environmental variances and complex long-horizon tasks through 10-shot finetuning, using only third-person camera inputs. The architecture establishes a versatile, lightweight and open-source baseline for generalist robot policy learning.
+
+# 1. Introduction
+
+Conventional robot learning paradigms typically depend on large-scale data collected for specific robots and tasks, yet the acquisition of data for generalized tasks remains both time-intensive and costly due to the inherent limitations of real-world robot hardware. Presently, foundational models in Natural Language Processing and Computer Vision [16, 41, 50-52, 62], pretrained on extensive, diverse, and task-agnostic datasets, have demonstrated remarkable efficacy in addressing downstream tasks either via zero-shot approaches or with minimal task-specific samples. This achievement implies that a universal robotic policy, pretrained on heterogeneous robotic data and finetuned with minimal supervision, could be instrumental in realizing true generalization in the development of vision-language-action (VLA) models. Nevertheless, training such policies across expansive cross-embediment datasets, encompassing diverse sensors, action spaces, tasks, camera views, and environments, remains an open challenge.
+
+In pursuit of a unified robotic policy, recent studies have directly mapped visual observations and language instructions to actions using expansive VLA models for navigation [65, 66] or manipulation [8, 9, 32, 72], thereby demonstrating zero-shot or few-shot generalization in novel environments. Robot Transformers [8, 9, 54] present policy frameworks based on Transformer architectures, achieving robust generalization by training on the extensive Open X-Embodiment (OXE) Dataset [54]. Furthermore, Octo [72] adopts an autoregressive Transformer design with a diffusion action head, while OpenVLA [32] discretizes the action space and leverages a pretrained visual-language model to construct a VLA model exposed to the OXE Dataset [54]. Nonetheless, despite the promising potential of these VLA models [32, 72] to learn robot policies from vast cross-embediment datasets [54], the intrinsic diversity of robot configurations within these datasets continues to constrain generalization.
+
+Diffusion policies [17, 30, 61, 83] have demonstrated
+
+
+Figure 2. Illustrations of different generalist robot policy architectures. Left head: the common robot Transformer architecture with discretization actions, e.g., Robot Transformer [8, 9] and OpenVLA [32]. Middle head: the Transformer architecture with diffusion action head which denoises the individual continuous action with a small network condition on each embedding from the causal Transformer, e.g., Octo [72] and $\pi_0$ [5]. Right head: the proposed Dita architecture that denoises actions inherently in an in-context conditioning style.
+
+reliable performance in robotic policy learning under the paradigm of single-task imitation learning. Specifically, [18, 72] introduces a generalist policy that denoises actions using a network (MLP/DiT) as diffusion head conditioned on a single embedding from an auto-regressive multimodal Transformer. However, the expansive robot space within large-scale cross-embodiment datasets, encompassing diverse camera views and action spaces, presents a substantial challenge for a tiny diffusion head to effectively denoise continuous actions. Other diffusion policies [30, 61, 72] attempt to integrate historical image observations and instructions into embeddings prior to the denoising process, which might limit the denoising learning. Action anticipation typically relies more on intuitive historical observations rather than on early-fused embeddings.
+
+In this paper, we introduce Dita, a Diffusion Transformer (DiT) Policy that capitalizes on the Transformer architecture, as demonstrated in prior work [8, 9, 32, 54, 72], thereby ensuring scalability across extensive cross-embediment datasets. The architecture integrates an incontext conditioning mechanism with causal transformer that intrinsically denoises action sequences, thereby enabling direct conditioning of action denoising on image tokens and empowering the model to discern subtle nuances, such as action deltas, within historical visual observations. Our objective is to provide a clean, lightweight (334M parameters), and open-source baseline model for generalist robot policy learning. The model is simple yet effective, achieving state-of-the-art or competitive results on extensive simulation benchmarks, and successfully generalizing to long-horizon tasks in novel environmental configurations—characterized by variations in background, non-target object arrangements, and lighting conditions through finetuning with a mere 10-shot set of real
+
+world samples. Remarkably, this promising performance is achieved exclusively with a single third-person camera input, while the model's inherent flexibility affords researchers the freedom to integrate additional input modalities (e.g., wrist-camera images, target image predictions, robot state, tactile feedback, etc.) for further investigation.
+
+# 2. Related Work
+
+Diffusion Policy Denoising diffusion models [11, 19, 25, 56, 63] have demonstrated remarkable proficiency in both image generation and multi-modal robotic action modeling [12, 14, 17, 30, 39, 42, 61, 74, 75, 77, 83]. Nevertheless, existing diffusion-based manipulation policies predominantly rely on U-Net architectures or shallow crossattention networks designed for single tasks, limiting their scalability to multi-modal applications. Recent generalist models [72, 76] employ VLM embeddings combined with compact MLP diffusers, while others, like RDT [42] and [18], utilize cross-attention Transformers or DiT decoders for bimanual manipulation. In contrast, we propose a scalable DiT with in-context conditioning, which directly processes historical observations through a causal Transformer architecture, thereby providing enhanced expressiveness and generalization capabilities for multi-modal action generation.
+
+Generalist Robot Policies Language-conditioned policies [15, 23, 44, 49, 60, 73, 84] have gained prominence for their adaptability in real-world applications, enabling robots to interpret and execute natural language instructions. Recent advancements in generalist robot policies leverage foundation multi-modal models across both navigation [6, 27, 65, 66, 71, 82] and manipulation [3, 7-9, 20, 21, 29, 32, 45, 46, 54, 55, 60, 64, 67, 68, 72, 79, 80], with scalable VLA models emerging as a dominant framework [1, 8, 9, 32, 54, 58, 72]. Some approaches incorporate large-scale video backbones trained on internet-scale data [13, 28, 34, 78] to improve temporal visual reasoning. While these methods enhance visual representation learning, our focus is on action generation, where diffusion-based models provide a more expressive alternative. Another crucial factor in generalist policies is the choice of pretrained VLM models for action generation. Unlike recent works [5, 38] that employ PaliGemma [2] to enhance vision-language understanding, we adopt a LLaMA-style causal Transformer for policy learning. This approach is both simple and highly scalable, demonstrating effectiveness across a wide range of benchmarks. Furthermore, by aligning robot actions with language instructions and visual observations in an in-context conditional manner, our method significantly enhances generalization across diverse robotic embodiments.
+
+# 3. Method
+
+In this section, we describe Dita in detail. We begin by detailing the architecture of the model, which is a scalable DiT with in-context conditioning. We then define the training objective for generating multi-modal actions. Finally, we present the data and implementation specifics for the pretraining of our model.
+
+# 3.1. Architecture
+
+Multi-modal Input Tokenization. Dita only takes language instructions and third-person camera images as input. The language instructions are tokenized using a frozen CLIP [59] model, while the image observations are first processed by DINOv2 [53] to extract image patch features. Notably, DINOv2 is trained on web data, which differs from robot-specific data. Thus, we jointly optimize the DINOv2 parameters alongside Dita in an end-to-end fashion. To mitigate computational costs, we incorporate a Q-Former [33] with FiLM [57] conditioning to select image features from the DINOv2 patch features based on the instruction context.
+
+Action Preprocess. We represent the end-effector action as a 7D vector, comprising 3 dimensions for the translation vector, 3 dimensions for the rotation vector, and 1 dimension for the gripper position. To align the dimensionality with the image and language tokens, we pad the continuous action vector with zeros to form the action representation. Noise is only introduced into the 7D action vector during the denoising diffusion optimization process.
+
+Model Design. Our core design is the DiT structure [56], which denoises the action chunk with multiple action tokens. This is achieved by conditioning directly on image observations and instruction tokens through an in-context conditioning approach using a causal Transformer. Specifically, we concatenate language tokens, image features, and timestep embeddings at the beginning of the sequence, treating the noisy action in conjunction with the instruction tokens, as illustrated in Figure 3. This design preserves the scalability of Transformer networks and enables denoising to be conditioned directly on image patches, thereby allowing the model to capture nuanced changes in action over historical observations. The model is supervised by the noise introduced into the continuous actions. In other words, we directly apply the diffusion objective in the action chunk space with a large Transformer model, in contrast to the diffusion action head approach [18, 61, 72]. Notably, our proposed Dita presents a versatile and scalable design, adaptable to diverse datasets for both pretraining and finetuning, while achieving promising performance. Furthermore, additional observation tokens and input can be seamlessly integrated into the Transformer architecture. Further details are provided in Appendix A.
+
+
+Figure 3. Our model employs a Transformer-based diffusion architecture, integrating a pretrained CLIP network to extract language instruction tokens. The DinoV2 [53] model encodes image observations, followed by a Q-Former that queries features for each image. The instruction tokens, image features, timestep embeddings, and noised action are concatenated to construct a token sequence, which is then fed into the network to denoise the raw actions.
+
+# 3.2. Training Objective
+
+The denoising network $\mathcal{E}_{\theta}(c_{lang}, c_{obs}, t, \boldsymbol{x}^t)$ is constructed upon a causal Transformer, where $c_{obs}$ represents the image observation, $c_{lang}$ denotes the language instruction, and $t \in 1, 2, \ldots, T_{train}$ is the timestep index within the total denoising steps $T_{train}$ . During training, a Gaussian noise vector $\boldsymbol{x}^t \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ is sampled at each timestep $t$ and added to the action $\boldsymbol{a}$ to form the noised action token $\hat{\boldsymbol{a}}$ . The network $\mathcal{E}_{\theta}$ is trained to predict the noise vector $\hat{\boldsymbol{x}}$ , with randomly sampled $t$ . The optimization objective of Dita is to minimize the mean squared error (MSE) loss between $\boldsymbol{x}^t$ and $\hat{\boldsymbol{x}}^t$ .
+
+The inference procedure is delineated as follows, $\alpha$ , $\gamma$ , and $\sigma$ constitute the noise scheduler [25]. The denoising process is iterated over $N_{eval}$ steps to yield a reliable action.
+
+$$
+\boldsymbol {x} ^ {t - 1} = \alpha (\boldsymbol {x} ^ {t} - \gamma \mathcal {E} _ {\theta} (c _ {l a n g}, c _ {o b s}, t, \boldsymbol {x} ^ {t}) + \mathcal {N} (\boldsymbol {0}, \sigma^ {2} \boldsymbol {I})). \tag {1}
+$$
+
+# 3.3. Pretraining Data
+
+To evaluate the proposed Dita policy, we select the OXE datasets [32, 54] for model pretraining. We primarily adhere to the method detailed in [32, 72] for dataset selection and weight assignment. Actions are normalized and filtered similar to [54].
+
+# 3.4. Pretraining Details
+
+We employ the DDPM diffusion objective [25] with $T_{train} = 1000$ timesteps for pretraining, while adopting DDIM [69] with $T_{eval} = 20$ timesteps during zero-shot evaluation to accelerate inference. Based on preliminary experiments reported in ManiSkill2 [22], we utilize 2-frame
+
+image observations to predict 16 action chunks. The network is optimized by AdamW [43] for 100,000 steps, with learning rates of $1e - 4$ for both the causal Transformer and Q-Former, and $1e - 5$ for DINOv2. Training is conducted with a batch size of 8192 across 32 NVIDIA A100 GPUs, allocating 256 samples per GPU. Additional pretraining configurations are detailed in Appendix A.
+
+# 4. Simulation Experiments
+
+We strive to develop a robust foundational VLA model that is both scalable across diverse simulation benchmarks and adaptive to new complex tasks in unseen robot environments with as few as 10 or even fewer samples. To assess the capabilities of the pretrained model, we conduct evaluations across four simulation benchmarks in this section: 1) SimplerEnv [37] (Google Robot) demonstrates the model's zero-shot adaptation to simulation environments; 2) LIBERO [40] assesses finetuning adaptability with a single-camera setup; 3) Calvin [47] evaluates long-horizon task performance in novel environments; and 4) ManiSkill2 [22] is re-rendered to illustrate generalization across unseen camera views. Across all four benchmarks, Dita pretrained on OXE datasets $\mathcal{E}_{\theta \sim OXE}$ is evaluated in a zero-shot manner on SimplerEnv, while it is finetuned on the remaining three benchmarks using their respective datasets.
+
+# 4.1. Baselines
+
+Diffusion Action Head The diffusion head for the action generation $\mathcal{E}_{\theta \sim s}^{Diff}$ [72] is also implemented. Specifically, we employ a three-layer MLP network as the denoising module, conditioned on each action token embedding out
+
+Table 1. Success rate comparison with RT-1-X [8], Octo-Base [72] and OpenVLA-7B [32] on SimplerEnv (both match and variant results of Google Robot [8]).
+
+| Method | coke_can | move_near | hunter |
| match | variant | match | variant | match | variant |
| RT-1-X [8] | 56.7% | 49.0% | 31.7% | 32.3% | 59.7% | 29.4% |
| Octo-Base [72] | 17.0% | 0.6% | 4.2% | 3.1% | 22.7% | 1.1% |
| OpenVLA-7B [32] | 16.3% | 54.5% | 46.2% | 47.7% | 35.6% | 17.7% |
| Dita (Ours) | 83.7% | 85.5% | 76.0% | 73.0% | 46.3% | 37.5% |
+
+puted by the same causal Transformer architecture (as Middle head illustrated in Figure 2). This approach introduces additional parameters (the extra MLP) compared to Dita.
+
+Octo & OpenVLA We also reproduce these two open-source VLA models using their released checkpoints, as they employ the same multimodal inputs (language instruction and third-person camera image) as our approach.
+
+# 4.2. SimplerEnv
+
+SimplerEnv [37] is a Real-to-Sim platform designed to evaluate policies learned from real robot data within a simulation environment. In this section, we compare our approach with leading generalist policies, including RT-1-X [8, 54], Octo [72], and OpenVLA [32], under both match and variant scenarios. For a fair comparison, we adhere to the evaluation protocol of SimplerEnv [37], which includes tasks "pick up coke can", "move an object near to others", "open drawer", "close drawer".
+
+Table 1 demonstrates that Dita achieves strong generalization performance under zero-shot evaluation across various types of variations, including background, texture, objects, spatial positions, and more. Leveraging the in-context conditioning design, Dita exhibits enhanced robustness, relying solely on third-person view images to detect subtle nuances and generate more reliable actions. The qualitative results are listed in Appendix B.1.
+
+# 4.3. LIBERO
+
+LIBERO [40] is a comprehensive benchmark for knowledge transfer in multitask and lifelong robot learning. It consists of four sub-datasets: LIBERO-SPATIAL, LIBERO-OBJECT, LIBERO-GOAL, and LIBERO-100. Notably, LIBERO-100 is further divided into LIBERO-90 and LIBERO-LONG, with the latter featuring 10 long-horizon tasks that encompass diverse object interactions and versatile motor skills. We employ the modified version of LIBERO from OpenVLA [32] as the data source for finetuning and evaluation.
+
+Comparisons. Table 2 demonstrates that Dita outperforms baseline methods on most LIBERO sub-datasets, achieving
+
+Table 2. Comparison with Diffusion Policy (denoted as DP*, training from scratch) [17], Octo [72], and OpenVLA [32] on LIBERO [40]. Except for Dita results, all other results are sourced from [32].
+
+| Method | SPATIAL OBJECT | GOAL LONG | Average |
| DP*[17] | 78.3% | 92.5% | 68.3% | 50.5% | 72.4% |
| Octo [72] | 78.9% | 85.7% | 84.6% | 51.1% | 75.1% |
| OpenVLA [32] | 84.9% | 88.4% | 79.2% | 53.7% | 76.5% |
| Dita (Ours) | 84.2% | 96.3% | 85.4% | 63.8% | 82.4% |
| Dita w/ wrist | 97.4% | 94.8% | 93.2% | 83.6% | 92.3% |
+
+an overall increase in average success rate by nearly $6\%$ . Notably, Dita exhibits a $10\%$ improvement on LIBERO- LONG, highlighting its strong potential for tackling long-horizon tasks.
+
+# 4.4.CALVIN
+
+CALVIN [47] is an open-source simulated benchmark designed for learning long-horizon, language-conditioned tasks. It consists of four distinct scenes (A, B, C, and D) and introduces the $\mathrm{ABC} \rightarrow \mathrm{D}$ evaluation protocol, where models are trained on environments A, B, and C and evaluated on environment D. The benchmark aims to solve up to 1,000 unique task sequences, each comprising five distinct subtasks. The primary evaluation metric is the success sequence length, which measures the ability to complete five consecutive subtasks within a sequence. To assess the long-horizon generalization of Dita, we adopt the $\mathrm{ABC} \rightarrow \mathrm{D}$ setting while only utilizing static RGB images as perception inputs. Additionally, we also implement a diffusion policy baseline $\mathcal{E}_{\theta \sim s}^{Diff}$ by introducing a three-layer MLP diffusion head, further demonstrating the effectiveness of Dita's in-context conditioning mechanism.
+
+Comparisons. Table 3 presents a comparative analysis of prior approaches and the proposed Dita on CALVIN. Without whistles and bells, the proposed Dita achieves comparable performance among methods relying solely on a single RGB camera for observation. Noticeably, only $1\%$ of the trajectories were labeled with text in Calvin [47]. The rest are unstructured play data collected by untrained users, with no information for downstream tasks. Dita does not utilize the play data which provides external trajectory data compared to the labeled data, while GR-MG uses it for training the policy. Remarkably, GHIL-Flue [4, 24], which builds upon SuSIE [4] with further finetuned generative models [10, 81], results in significantly larger models. Furthermore, Dita surpasses its non-pretrained variant by a margin of 1.23, underscoring its superior transferability. In contrast, employing diffusion head underperforms Dita by 0.45 points with similar pretrained weights, highlighting the
+
+Table 3. The comparisons with state-of-the-art approaches on Calvin (ABC→D) with the metrics of success rate and average success length. The abbreviations denote different input modalities: S-RGB for Static RGB, G-RGB for Gripper RGB, S-RGBD for Static RGB-D, G-RGBD for Gripper RGB-D, P for proprioceptive arm position, and Cam for camera parameters.
+
+| Method | Input | No. Instructions in a Row (1000 chains) |
| 1 | 2 | 3 | 4 | 5 | Avg.Len. |
| RoboFlamingo [36] | S-RGB,G-RGB | 82.4% | 61.9% | 46.6% | 33.1% | 23.5% | 2.47 |
| GR-1 [78] | S-RGB,G-RGB,P | 85.4% | 71.2% | 59.6% | 49.7% | 40.1% | 3.06 |
| 3D Diffuser [30] | S-RGBD,G-RGBD,P,Cam | 92.2% | 78.7% | 63.9% | 51.2% | 41.2% | 3.27 |
| GR-MG [34] | S-RGBD,G-RGBD,P | 96.8% | 89.3% | 81.5% | 72.7% | 64.4% | 4.04 |
| SuSIE [4] | S-RGB | 87.0% | 69.0% | 49.0% | 38.0% | 26.0% | 2.69 |
| GHIL-Glue [4, 24] | S-RGB | 95.2% | 88.5% | 73.2% | 62.5% | 49.8% | 3.69 |
| \(\mathcal{E}_{\theta \sim s}^{Diff}\)w/o Pretrain | S-RGB | 75.5% | 44.8% | 25.0% | 15.0% | 7.5% | 1.68 |
| \(\mathcal{E}_{\theta \sim s}^{Diff}\) | S-RGB | 94.3% | 77.5% | 62.0% | 48.3% | 34.0% | 3.16 |
| Ours w/o Pretrain | S-RGB | 89.5% | 63.3% | 39.8% | 27.3% | 18.5% | 2.38 |
| Ours | S-RGB | 94.5% | 82.5% | 72.8% | 61.3% | 50.0% | 3.61 |
+
+efficacy of Dita's in-context conditioning mechanism. The results illustrate that Dita excels at discerning subtle visual nuances in long-horizon tasks and generalizes proficiently across diverse environments, effectively transferring knowledge from extensive, real-world pretraining datasets to the CALVIN benchmark.
+
+# 4.5. ManiSkill2
+
+ManiSkill2 [22], the next generation of the SAPIEN ManiSkill benchmark [48], serves as a widely recognized platform for assessing the generalized manipulation capabilities of embodied models. It encompasses 20 distinct manipulation task families and over 4M demonstration frames across various configurations. Leveraging ManiSkill2, we establish a novel camera view generalization benchmark to evaluate the effectiveness of Dita.
+
+Setup. To construct the benchmark, we select 5 tasks (PickCube-v0, StackCube-v0, PickSingleYCB-v0, PickClutterYCB-v0, PickSingleEGAD-v0) from ManiSkill2 and create a camera pool comprising 300K random cameras. More details are provided in Appendix. We also implement RT-1 [8] style baseline model $\mathcal{E}_{\theta \sim s}^{Disc}$ with an architecture similar to ours for comparison. Unlikely, we discretize each action dimension into 256 bins [8] and utilize a Transformer network to predict the corresponding bin indices.
+
+Comparisons. Table 4 compares the proposed method with the discretization action head and the diffusion action head. The experiments demonstrate that Dita outperforms the $\mathcal{E}_{\theta \sim s}^{Disc}$ in large-scale, novel camera view scenarios. Additionally, Dita shows superior performance on more complex tasks and outperforms $\mathcal{E}_{\theta \sim s}^{Diff}$ by $20\%$ in the PickSingleYCB task and by $12\%$ in the PickClutterYCB task. The results highlight that Dita offers better scalability on large, diverse datasets, while also achieving enhanced camera view generalization.
+
+Table 4. Comparison of our model with two baseline methods (discretization and diffusion head) on ManiSkill2 success rate. The abbreviations denote the task names: S-YCB for PickSingleYCB, C-YCB for PickClutterYCB, EGAD for PickSingleEGAD.
+
+| Method | Avg. | PickC | StackC | S-YCB | C-YCB | EGAD |
| \( \mathcal{E}_{\theta \sim s}^{Disc} \) | 30.2% | 41.0% | 33.0% | 22.0% | 1.0% | 54.0% |
| \( \mathcal{E}_{\theta \sim s}^{Diff} \) | 58.6% | 86.0% | 76.0% | 37.0% | 24.0% | 70.0% |
| Dita (ours) | 65.8% | 79.0% | 80.0% | 62.0% | 36.0% | 72.0% |
+
+# 4.6. Ablation Study
+
+In this section, we conduct an ablation study on key factors in the model architecture design, including observation length, trajectory length, and denoising steps.
+
+Observation length. The length of historical observation images significantly impacts performance. As shown in Table 5, success rate drops sharply when the observation length is increased to 3. This could be due to the increased difficulty in model convergence, as the number of corresponding image tokens also rises. Additionally, we observe that using 2-frame observations enhances performance, particularly when the prediction horizon is extended. When the trajectory length is 32, Dita with 2-frame observations achieves superior performance. We argue that 2-frame observations strike an optimal balance, providing sufficient visual distinction between objects in the workspace and the robot states.
+
+Trajectory length. Trajectory length is the sum length of observation and action prediction chunks, which is also a critical factor influencing performance. Table 5 shows that performance improves as trajectory length increases. Notably, the performance of more complex tasks, such as Pick-ClutterYCB, increases substantially with longer trajectory lengths, while simpler tasks, like PickCube, maintain high
+
+Table 5. Ablation on ManiSkill2 about the observation length (# obs) and the trajectory length (# traj).
+
+| # obs | # traj | All | PickC | StackC | S-YCB | C-YCB | EGAD |
| 2 | 2 | 40.8% | 68.0% | 54.0% | 33.0% | 9.0% | 40.0% |
| 2 | 4 | 51.6% | 81.0% | 69.0% | 44.0% | 11.0% | 53.0% |
| 2 | 8 | 62.4% | 89.0% | 78.0% | 54.0% | 25.0% | 66.0% |
| 2 | 16 | 65.6% | 83.0% | 80.0% | 70.0% | 25.0% | 70.0% |
| 2 | 32 | 65.8% | 79.0% | 80.0% | 62.0% | 36.0% | 72.0% |
| 1 | 32 | 61.6% | 78.0% | 76.0% | 64.0% | 24.0% | 66.0% |
| 1 | 1 | 51.0% | 79.0% | 66.0% | 42.0% | 19.0% | 49.0% |
| 3 | 3 | 35.4% | 54.0% | 49.0% | 27.0% | 5.0% | 42.0% |
+
+
+Figure 4. The experimental platform consists of Franka Emika Panda robot arm, Robotiq 2F-85 gripper and RealSense D435i positioned in third-person view.
+
+performance once the trajectory length exceeds 4. Long trajectory length significantly boosts performance, as this optimization allows the model to better anticipate the target object's position and gain awareness of more future states.
+
+# 5. Real-Robot Experiments
+
+Few-shot real-world robot adaptation is a critical metric for evaluating the effectiveness of a generalist policy in practical applications. For real-robot experiments, We employ 10-shot finetuning to assess the model's adaptability in complex, long-horizon, multi-modal tasks within unseen robot environments.
+
+# 5.1. Real-Robot Task Finetuning
+
+Setup. To deploy the Dita model, as shown in Figure 4, the robot setup consists of a 7-DoF tabletop Franka Emika Panda robot arm and a Robotiq 2F-85 gripper. A RealSense D435i RGB-D camera, positioned approximately $1.5\mathrm{m}$ away from the robot in a third-person view, captures RGB scenes with cluttered background at each inference timestep. Robot control is managed from a desktop computer running ROS, communicating with the model-deploy
+
+server with 1 NVIDIA A100 GPU. The system is operating under control frequency of $3\mathrm{Hz}$ . Given the data domain gap between our robot platform and the pretrain dataset, we primarily evaluate Dita on 10-shot generalization for the following challenging tasks relevant to current VLA approaches:
+
+- Pick & Place. Two pick-and-place tasks with target object banana and kiwifruit are evaluated. 10 samples are collected for each task, with position variances introduced during evaluation to assess generalization performance.
+
+- Pour. We design two pouring tasks to evaluate the complex rotation finetuning: "pour the coffee beans into the bowl", and "pour the water from the teapot into the cup".
+
+- Stack. We design two stacking tasks for long-horizon pick-and-place: stacking three bowls and stacking three Russian dolls.
+
+- Pick & Rotation. These skills combine two tasks: "pick the banana and insert it into the small pen container" and "open the flip-top door box and then pick up the small cube".
+
+- Pull & Push. We design the task "open/close the drawer" to evaluate pull and push abilities of our models.
+
+- Long-Horizon Tasks. We further devise several long-horizon tasks (more than 3 steps), including "Pick up the bowl within the drawer and pour the coffee beans into the outside bowl", "pick up the ratchet and hit the ball into the goal", "open the top drawer, then pick the cube into the drawer, and finally close the drawer", "close the top drawer, then open the bottom drawer and put the bowl into the drawer, and finally close the drawer" and "open the box and move the green cube into the box then close the box", to demonstrate the long-horizon manipulation ability of Dita (detailed in demo videos in Supplementary Materials).
+
+The diffusion policy [17] has demonstrated strong capabilities in learning to mimic single tasks. Therefore, in addition to Octo and OpenVLA, we design a multimodal diffusion policy baseline based on a causal Transformer for comparison, which incorporates a similar diffusion head as described in Section 4.1.
+
+**Optimization.** We finetune the Dita on the aforementioned multiple manipulation tasks, with data collected on the same platform, using LoRA [26] for fair comparison and AdamW for 20,000 steps with image augmentations. The number of timesteps is set to 100 for DDPM [25], and the batch size of 512.
+
+10-shot Finetuning. We directly use the model pretrained on OXE datasets to evaluate 10-shot finetuning generalization for real-robot experiments. To ensure consistency with OpenVLA [32], we finetune the network with one observation and one-step prediction. We compare the proposed method with OpenVLA [32] and Octo-base [72] models. Overall, Dita achieves a $63.8\%$ success rate on two-step
+
+
+Figure 5. Quantitative results in real-robot experiments. Each task is manually divided into two sequential steps, except for the last two single-step tasks. In each stacked bar, the light-colored region represents the model's success rate in the first stage, while the dark-colored region indicates the contribution of second-stage success to the overall success rate. A larger proportion of the dark-colored region signifies a stronger capability of the model in completing long-horizon tasks. Since the open/close drawer tasks are single-step, they are excluded from the calculation of the average success rate.
+
+
+Figure 6. Qualitative comparison in real-robot experiments. Failures are highlighted with red circles. For a direct comparison, we initialize the layout consistently across all methods.
+
+tasks, with the second stage contributing nearly half, as shown in Figure 5. Dita consistently outperforms both Octo and OpenVLA, demonstrating superior performance on all complex tasks. For long-horizon tasks, OpenVLA effectively completes the first task but fails to handle the long-horizon task, such as completely misunderstanding the insert operation. In contrast, Octo performs better with rotation tasks and approaches the second step of the task more effectively. Supplementary materials provide extensive qualitative comparisons.
+
+Variance Robustness. To evaluate the robustness of Dita, we further validate its performance under different variances, including background changes, non-target object arrangements and lighting conditions. As illustrated in Figure 1, it is surprising to find that Dita not only excels in completing complex long-horizon tasks but also demonstrates resilience to a wide range of variations.
+
+# 5.2. Qualitative Comparison
+
+Figure 6 presents a comparison between Dita, diffusion head baseline, Octo [72], and OpenVLA [32] as evaluated in real-robot experiments under 10-shot finetuning setting. According to the visualized comparison, those baseline methods usually fail to grasp the correct position under the 10-shot setting, e.g., "fail to insert the gap of the box", "grasp when the gripper is not in the correct grasping position (the hand of cup or teapot)". Meanwhile, the baseline methods, e.g., the second raw (pouring water) in Figure 6, sometimes misunderstand the lifting action and get stuck after grasp. In contrast, Dita is able to effectively complete all the complex tasks with extreme 3D rotations.
+
+# 6. Conclusion
+
+We present Dita, an architecture for generalist robot learning that leverages a Transformer-based diffusion model to denoise continuous action sequences through an in-context conditioning mechanism. By harnessing the scalability of Transformers, Dita effectively models diverse robot behaviors across extensive cross-embodiment datasets, enabling robust generalization across multiple simulation benchmarks within a unified framework. Additionally, Dita demonstrates strong few-shot adaptation capabilities, successfully transferring to novel real-world robot setups and long-horizon tasks with minimal in-domain samples. Notably, the model is clean, lightweight, and open-source, and its promising performance—achieved exclusively with a single third-person camera input—underscores its potential as a scalable and flexible solution for generalist policies.
+
+# 7. Acknowledgment
+
+This work is supported by National Key RD Program of China (NO. 2022ZD0160201).
+
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+# Diversity-Enhanced Distribution Alignment for Dataset Distillation
+
+Hongcheng Li $^{1,2,3}$ Yucan Zhou $^{4*}$ Xiaoyan Gu $^{1,2,3\dagger}$ Bo Li $^{1,2,3}$ Weiping Wang $^{1}$
+
+$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
+ $^{2}$ School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
+ $^{3}$ State Key Laboratory of Cyberspace Security Defense, Beijing, China
+ $^{4}$ College of Intelligence and Computing, Tianjin University, Tianjin, China
+{lihongcheng,guxiaoyan,libo,wangweiping}@iie.ac.cn, zhouyucan@tju.edu.cn
+
+# Abstract
+
+Dataset distillation, which compresses large-scale datasets into compact synthetic representations (i.e., distilled datasets), has become crucial for the efficient training of modern deep learning architectures. While existing large-scale dataset distillation methods leverage a pre-trained model through batch normalization statistics alignment, they neglect the essential role of covariance matrices in preserving inter-feature correlations, resulting in reduced diversity in the distilled datasets. In this paper, we propose a simple yet effective approach, Diversity-Enhanced Distribution Alignment (DEDA), which enhances the diversity of distilled data by leveraging inter-feature relationships. Our method first establishes Gaussian distribution alignment by matching the means and covariances of each class in the original dataset with those of the distilled dataset in the feature space of a pre-trained model. Since features within the last layer of a pre-trained model are often highly similar within each class, aligning distributions in this layer cannot obtain diversified distilled data, resulting in gradient starvation during downstream training tasks. To overcome this limitation, we introduce a regularizer that constrains the covariance matrix of the distilled data in the last layer to maximize diagonal elements while minimizing non-diagonal elements. Extensive evaluations across CIFAR-10/100, TinyImageNet, and ImageNet-1K demonstrate state-of-the-art performance without additional computational overhead.
+
+# 1. Introduction
+
+The exponential growth of large-scale datasets has driven significant advancements in deep learning, enabling deep neural networks to achieve dramatic success across various tasks [7, 13, 18, 23, 38]. However, the increasing storage
+
+
+Figure 1. Visualization of the last layer feature distribution during CIFAR-100 model training. As training progresses, features become increasingly compact. In a well-trained model, samples within each class exhibit high cosine similarity (cosine distance $< 0.1$ ). This compact feature space can limit the diversity of distilled data when aligning with the original data features.
+
+requirements and extended training time due to the expanding dataset size present a fundamental challenge. Dataset distillation (or condensation) has emerged as a crucial solution, which compresses the large-scale datasets into significantly smaller and more representative ones (i.e., distilled datasets) [40, 44]. Such distilled datasets can accelerate model training in downstream tasks, while maintaining the training performance of the original dataset across a wide range of model architectures.
+
+Although many dataset distillation methods have shown strong performance on moderate-scale benchmarks, such as CIFAR-10/100 [11, 21, 25, 42], their scalability to large-scale datasets like ImageNet-1K remains inherently constrained. One primary bottleneck is the need to load the original data during each optimization step of the distilled data, resulting in significant memory and computational
+
+overhead. To address these challenges, SRe2L [43] introduces a novel decoupled framework for efficient large-scale dataset distillation. Instead of loading the original data repeatedly, this approach first trains a well-converged model on the original dataset. Then, the distilled samples are optimized by aligning their embeddings in the Batch Normalization (BN) layer with the statistics of the BN layer in the pre-trained well-converged model. While aligning global BN statistics effectively preserves the overall information of the original dataset, it will make all distilled samples capture highly similar information, leading to high inter-class similarity. To mitigate this issue, LPLD [41] proposes aligning intra-class BN statistics to enhance the class discriminability of the distilled data. However, we argue that simply aligning the mean and variance of the BN layer's multidimensional feature distributions is insufficient to capture the distribution of the original data.
+
+Notably, the covariance matrix is another critical statistic that captures intra-class feature variations, which contains more information than the variance with each non-diagonal element represents the relationship between two feature dimensions. An intuitive way is to align the distilled data with both the mean and covariance of the feature representations from the pre-trained model. However, samples in the last layer of a pre-trained well-converged model tend to be remarkably similar. As illustrated in Figure 1, the distribution of the original samples from the same category in the last-layer is gradually shrunk during the training process. It is evident that as the model converges, samples of a category in the last-layer become increasingly concentrated, with the cosine distance between individual samples and their class centers typically falling below 0.1. As a result, even if the distilled data is aligned with the distribution of the original sample in the last-layer of the pre-trained model, their diversity is still limited, leading to gradient starvation for the model training in downstream tasks.
+
+To enhance the diversity of distilled data, we propose a simple yet effective Diversity-Enhanced Distribution Alignment (DEDA) framework, which preserves the semantic richness of the original dataset through feature distribution alignment. Unlike the batch normalization-based alignment methods, our approach employs Gaussian distribution matching between the original and distilled data in the feature space. To obtain the Gaussian distribution of the original dataset, we design an Offline Gaussian Distribution Estimation, which extracts feature statistics with the pre-trained model by loading the original data once and stores the mean and covariance matrices in a memory bank. We then optimize the distilled data by aligning their feature distributions with the class-specific statistics of the original data in the memory bank to achieve efficient class-wise distillation. Furthermore, to address distribution compactness observed in the last-layer of the pre-trained model, we introduce a
+
+covariance regularization. This regularization simultaneously maximizes the diagonal elements to increase feature variance and minimizes the off-diagonal elements to eliminate redundant correlations. It effectively mitigates gradient starvation in downstream tasks caused by the limited samples' diversity in the abstract feature space. Experimental results on various datasets (e.g., CIFAR-10/100, TinyImageNet, and ImageNet-1K) demonstrate that our DEDA can effectively enhance semantic diversity and significantly improve the performance in downstream tasks. The main contributions of this work are as follows:
+
+- We propose a Diversity-Enhanced Distribution Alignment (DEDA) for dataset distillation. To the best of our knowledge, this is the first work to maintain the interfeature relationships in large-scale dataset distillation to enhance the diversity of the distilled data.
+- Due to the high similarity of samples from the same category in the last layer of a well-converged model, we propose a covariance regularization for distilled data to avoid gradient starvation in downstream tasks.
+- Our experiments demonstrate that the proposed DEDA achieves state-of-the-art results on multiple benchmarks while maintaining computational efficiency. Moreover, because of the high semantic diversity, our distilled data exhibits superior cross-architecture performance.
+
+# 2. Related Work
+
+Existing dataset distillation methods can be categorized into two principal paradigms: optimization process alignment and feature space alignment.
+
+Optimization Process Alignment. The optimization process alignment methods aim to incorporate the intermediate training dynamics of the original dataset into the distilled data synthesis process. The foundational framework involves gradient matching [16, 20, 47, 48], which minimizes the distance between the gradients generated by the original and distilled datasets during model parameter updates. Subsequently, trajectory alignment methods [3, 4, 8, 24] ensure consistency across entire optimization paths rather than at each individual optimization step. However, the information learned by the model from the original data at different training stages is inconsistent, and therefore, indiscriminate matching can lead to a loss of information in the distilled data. To address this, SeqMatch [9] and DATM [14] enhance the process by explicitly dividing the model into different training stages for alignment, thereby improving the diversity of the information captured in the distilled data. Moreover, DREAM [26] further improves the quality of the distilled data by dynamically selecting samples through clustering original data representatives. While these approaches achieve notable performance improvements, they are computationally expensive due to the iterative model updating and data synthesis processes.
+
+Feature Space Alignment. To reduce computational costs, this paradigm directly aligns the feature distributions between the original and distilled data, without requiring model updates [49]. CAFE [39] aligns the prototypes of intermediate features from deep networks. To reduce feature redundancy, DataDAM [31] utilizes spatial attention mechanisms to align key features. Additionally, M3D [46] reformulates prototype matching within Reproducing Kernel Hilbert Spaces (RKHS). However, these methods typically use randomly initialized models to extract features, which can lead to inaccurate embeddings. To enhance embedding accuracy, IDM [50] and DANCE [45] propose to use multiple pre-trained feature extractors for more robust feature extraction. While pre-trained models improve embedding accuracy, only matching class prototypes will limit the diversity of the distilled data. IID [6] and DSDM [22] address this limitation by aligning both the prototypes and covariance matrices of class features, thereby preserving semantic richness. However, the joint processing of original and distilled data introduces significant memory demands.
+
+Large-Scale Dataset Distillation. To achieve data distillation on large-scale datasets, some methods have introduced pre-trained generative models for data synthesis, where their performance relies heavily on the pretrained models [12, 35]. Orthogonal to the generation-base methods, recent advances address scalability bottlenecks through decoupled strategies [36, 42, 43]. The pioneering SRe2L framework [43] introduces a decoupled distillation paradigm that first trains a well-converged model on the original data and then optimizes the distilled data by aligning local batch statistics with the global Batch Normalization (BN) parameters of the pre-trained model. However, this global BN alignment mechanism enforces a uniform optimization objective across all synthetic samples, inherently limiting inter-class discrimination of the distilled data. LPLD [41] attempts to enhance class discriminability by aligning intra-class BN statistics. However, capturing a pre-trained model's BN statistics (mean and variance) is insufficient to guarantee the diversity of the distilled data. To address this limitation, alternative strategies have emerged with different alignment mechanisms. G-VBSM [33] matches multiple statistical characteristics of different network architectures. Meanwhile, DWA [10] introduces training perturbations and variance-weighted adjustments to enhance sample diversity. However, these methods incur extra computational overhead due to additional model training. Instead, we directly leverage the covariance matrix to capture inter-feature relationships, effectively enhancing the diversity without additional computational costs.
+
+# 3. Preliminary
+
+Background. In this paper, we denote the original large-scale dataset as $\mathcal{T} = \{(x_i,y_i)\}_{i = 1}^{|\mathcal{T}|}$ , where $y_{i}\in \mathcal{V} =$
+
+$\{0,1,\ldots ,C - 1\}$ represents the corresponding label. The distilled dataset is represented as $S = \{(s_i,y_i)\}_{i = 1}^{|S|}$ , with each class containing IPC (Images Per Class) samples. The total size of the distilled dataset is $|\mathcal{S}| = \mathrm{IPC}\times C\ll |\mathcal{T}|$ , ensuring that the distilled dataset is significantly smaller than the original dataset. The objective of dataset distillation is to compress a large-scale training dataset $\mathcal{T}$ into a much smaller distilled dataset $S$ while maintaining model performance. Specifically, a model $\mathcal{M}_{\theta_S}$ trained on the distilled dataset $S$ should achieve comparable performance to a model $\mathcal{M}_{\theta_{\mathcal{T}}}$ trained on the full dataset $\mathcal{T}$ when evaluated on a test set. This objective can be formally expressed as:
+
+$$
+\mathbb {E} _ {\boldsymbol {x} \sim \mathcal {D} _ {\text {t e s t}}} \left[ \ell \left(\boldsymbol {\mathcal {M}} _ {\boldsymbol {\theta} _ {T}}, \boldsymbol {x}\right) \right] \approx \mathbb {E} _ {\boldsymbol {x} \sim \mathcal {D} _ {\text {t e s t}}} \left[ \ell \left(\boldsymbol {\mathcal {M}} _ {\boldsymbol {\theta} _ {S}}, \boldsymbol {x}\right) \right], \tag {1}
+$$
+
+where $\ell (\cdot ,\pmb {x})$ denotes the loss function that measures the model's performance on a test sample $\pmb{x}$ , and $\mathcal{D}_{test}$ represents the test set.
+
+Large-Scale Dataset Distillation. Classical dataset distillation methods have demonstrated success in compressing information for medium-sized datasets [3, 31, 47], but they struggle to scale effectively to large-scale datasets. To overcome this limitation, SRe2L [43] introduces a decoupled learning paradigm, consisting of three key stages: Squeeze, Recover, and Relabel. In the Squeeze stage, a pretrained model $\theta_{\mathcal{T}}$ is first trained on the original dataset $\mathcal{T}$ , thereby compressing the feature of $\mathcal{T}$ into $\theta_{\mathcal{T}}$ . In the recover stage, the pre-trained model $\theta_{\mathcal{T}}$ is then used to optimize distilled data $S$ . The optimization objective is to align $S$ with the information encoded in $\theta_{\mathcal{T}}$ . Specifically, the goal is to minimize the following loss function:
+
+$$
+\arg \min _ {\mathcal {S}} \left[ \mathcal {L} _ {\mathrm {C E}} \left(\boldsymbol {\theta} _ {\mathcal {T}}, \mathcal {S}\right) + \mathcal {L} _ {\mathrm {B N}} \left(\boldsymbol {\theta} _ {\mathcal {T}}, \mathcal {S}\right) \right], \tag {2}
+$$
+
+where $\mathcal{L}_{\mathrm{CE}}$ is the standard cross-entropy loss function, and $\mathcal{L}_{\mathrm{BN}}$ is the batch normalization (BN) alignment loss. The BN loss $\mathcal{L}_{\mathrm{BN}}$ ensures that the mean and variance of the normalized feature distribution of $S$ are aligned with those stored in the batch normalization layer of $\theta_{\mathcal{T}}$ . Finally, in the Relabel stage, the downstream training task on $S$ is performed through soft label alignment, where soft labels are generated from the logits of $\theta_{\mathcal{T}}$ .
+
+# 4. Method
+
+We illustrate the framework of our proposed Diversity-Enhanced Distribution Alignment for Dataset Distillation in Figure 2. In the first stage, we estimate the Gaussian distribution for each class $c$ in the original dataset $\mathcal{T}$ using features extracted for the intermediate layer $l$ of the pretrained model $\theta_{\mathcal{T}}$ , i.e., $\mathcal{N}(\boldsymbol{\mu}_{\mathcal{T},c}^{l}, \boldsymbol{Cov}_{\mathcal{T},c}^{l})$ . These statistics of the Gaussian distribution in each layer are then stored in a memory bank. In the second stage, during the optimization process of the distilled data $\mathcal{S}_c$ , we retrieve the corresponding statistics from the memory bank and feed them
+
+
+
+
+Figure 2. Illustration of our proposed DEDA. Stage I: Offline Gaussian Distribution Estimate. Pre-trained model statistics (mean $\pmb{\mu}_{\mathcal{T},c}^{l}$ and covariance $Cov_{\mathcal{T},c}^{l}$ ) across network layers and stored in a memory bank $\mathcal{M}_c$ . Stage II: Distilled Data Optimization. DEDA (1) retrieves target statistics from $\mathcal{M}_c$ , (2) computes three objective components: Gaussian distribution alignment ( $\mathcal{L}_{\mathrm{GDA}}$ ), diversity-enriched regularizer ( $\mathcal{L}_{\mathrm{Var}}$ , $\mathcal{L}_{\mathrm{Cov}}$ ), and standard cross-entropy loss ( $\mathcal{L}_{\mathrm{CE}}$ ), and (3) updates distilled data through optimization iterations.
+
+to $\theta_{\mathcal{T}}$ . To ensure consistency across layers, we align the feature distribution $\mathcal{N}(\boldsymbol{\mu}_{\mathcal{S},c}^{l},\boldsymbol{Cov}_{\mathcal{S},c}^{l})$ of $S_{c}$ with the corresponding statistics from $\theta_{\mathcal{T}}$ . To address the issue of feature space compactness in the last layer of $\theta_{\mathcal{T}}$ , we introduce an explicit regularization term to constrain the covariance matrix of the distilled data $\boldsymbol{Cov}_{\mathcal{S},c}^{L}$ . Specifically, we maximize the diagonal elements (variance loss $\mathcal{L}_{\mathrm{Var}}$ ) and minimize the non-diagonal elements of the covariance matrix (covariance loss $\mathcal{L}_{\mathrm{Cov}}$ ), which encourages a maximally separable feature distribution for the distilled samples. The overall loss function is summarized in Section 4.3.
+
+# 4.1. Gaussian Distribution Alignment
+
+Although previous work [42, 43] that aligns the mean and variance of batch normalization (BN) layers in a pre-trained model using Eq. (2) has achieved promising results, we believe that these statistical measures are insufficient to fully capture the distribution of the original data. We argue that covariance is also a crucial statistical component, as it encapsulates the relationships between feature dimensions. Therefore, we propose an offline Gaussian distribution estimation to better describe the diversity of the original data.
+
+Specifically, for each class $c \in \{1, \dots, C\}$ , we model its sample distribution at layer $l$ as a Gaussian distribution. For the samples in class class $c$ , we extract their features
+
+by feeding them into the pre-trained model $\theta_{\mathcal{T}}$ , producing feature tensors $f^{l}(\boldsymbol{x})$ at each intermediate layer. Given the high dimensionality of the feature tensor (e.g., the first layer of ResNet-18 has a dimensionality of $64 \times 56 \times 56$ ), directly computing the covariance matrix is computationally expensive. To reduce this cost while preserving critical information, we apply an average pooling operation:
+
+$$
+\tilde {\boldsymbol {f}} ^ {l} (\boldsymbol {x}) = \operatorname {A v g P o o l 2 d} \left(\boldsymbol {f} ^ {l} (\boldsymbol {x})\right), \tag {3}
+$$
+
+where $\pmb{f}^{l}(\pmb{x}) \in \mathbb{R}^{D_{l} \times H_{l} \times W_{l}}$ , with $D_{l}$ indicating the number of channels in layer $l$ , and $H_{l}$ and $W_{l}$ denoting the height and width of the feature maps in layer $l$ , respectively. After average pooling, the feature dimension is reduced to $\tilde{\pmb{f}}^{l}(\pmb{x}) \in \mathbb{R}^{D_{l}}$ . Using the pooled features, we compute the feature statistics for each class $c$ , specifically the mean vector $\pmb{\mu}_{\mathcal{T},c}^{l}$ and the covariance matrix $Cov_{\mathcal{T},c}^{l}$ are:
+
+$$
+\boldsymbol {\mu} _ {\mathcal {T}, c} ^ {l} = \frac {1}{| \mathcal {T} _ {c} |} \sum_ {i = 1} ^ {| \mathcal {T} _ {c} |} \tilde {\boldsymbol {f}} ^ {l} (\boldsymbol {x} _ {i}), \tag {4}
+$$
+
+$$
+\boldsymbol {C o v} _ {\mathcal {T}, c} ^ {l} = \frac {1}{| \mathcal {T} _ {c} |} \sum_ {i = 1} ^ {| \mathcal {T} _ {c} |} (\tilde {\boldsymbol {f}} ^ {l} (\boldsymbol {x} _ {i}) - \boldsymbol {\mu} _ {\mathcal {T}, c} ^ {l}) (\tilde {\boldsymbol {f}} ^ {l} (\boldsymbol {x} _ {i}) - \boldsymbol {\mu} _ {\mathcal {T}, c} ^ {l}) ^ {\top}. \tag {5}
+$$
+
+where $\pmb{\mu}_{\mathcal{T},c}^{l}\in \mathbb{R}^{D_{l}}$ and $Cov_{\mathcal{T},c}^{l}\in \mathbb{R}^{D_{l}\times D_{l}}$ . To efficiently manage the Gaussian distribution of each class, we construct a memory bank to the mean and covariance of each
+
+Gaussian distribution. This memory bank allows for fast access during the optimization process, improving computational efficiency.
+
+During the optimization process of the distilled data, we sequentially optimize the distilled data for each class $c$ , denoted as $\mathcal{S}_c$ . Before optimizing $\mathcal{S}_c$ , we retrieve the mean and covariance of the Gaussian distribution statistics for class $c$ from the memory bank and assign them to $\theta_{\mathcal{T}}$ . Subsequently, following the same approach as in the original data modeling, we model the Gaussian distribution for $\mathcal{S}_c$ to obtain $\mathcal{N}(\boldsymbol{\mu}_{\mathcal{S},c}^l,\mathbf{Cov}_{\mathcal{S},c}^l)$ and align these statistics with those of the original data in $\theta_{\mathcal{T}}$ . Based on this, we define the Gaussian Distribution Alignment (GDA) loss for $L - 1$ layers (excluding the last layer) as follows:
+
+$$
+\mathcal {L} _ {\mathrm {G D A}} = \sum_ {l = 1} ^ {L - 1} \left(\| \boldsymbol {\mu} _ {\mathcal {S}, c} ^ {l} - \boldsymbol {\mu} _ {\mathcal {T}, c} ^ {l} \| _ {2} ^ {2} + \gamma \| \boldsymbol {C o v} _ {\mathcal {S}, c} ^ {l} - \boldsymbol {C o v} _ {\mathcal {T}, c} ^ {l} \| _ {2} ^ {2}\right), \tag {6}
+$$
+
+where $\gamma$ is a hyperparameter that balances the contributions of the mean and covariance alignment terms.
+
+# 4.2. Diversity-Enriched Regularizer
+
+While layer-wise Gaussian distribution alignment in a pretrained model effectively preserves the diversity of the original data, the excessively compact and homogeneous features in the last layer $L$ lead to a constrained matching space. Consequently, aligning with the last-layer features of the pre-trained model may result in insufficient diversity of the distilled data, leading to gradient starvation [1, 2, 29, 30] for model training in downstream tasks.
+
+To address this challenge, we propose an explicit covariance regularization for the last-layer features of the distilled data. For the covariance matrix of the distilled data's last layer, denoted as $\mathbf{Cov}_{S,c}^{L} \in \mathbb{R}^{D_{L} \times D_{L}}$ , we introduce two complementary properties to enhance feature representation: (1) Maximization of diagonal variances $\sigma = \mathrm{Diag}(\mathbf{Cov}_{S,c}^{L}) \in \mathbb{R}^{D_{L}}$ to ensure comprehensive utilization of each feature dimension, and (2) Minimization of non-diagonal covariances to promote feature independence and reduce redundancy. Therefore, our proposed regularizer consists of two components:
+
+$$
+\mathcal {L} _ {\text {V a r}} = \frac {1}{D _ {L}} \sum_ {i = 1} ^ {D _ {L}} \max (0, 1 - \sqrt {\sigma_ {i}}), \tag {7}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {C o v}} = \frac {1}{D _ {L} \left(D _ {L} - 1\right)} \sum_ {i \neq j} \left| \boldsymbol {C o v} _ {S, c} ^ {L} \right| _ {i, j} ^ {2}. \tag {8}
+$$
+
+The variance regularization term $\mathcal{L}_{\mathrm{Var}}$ employs a hinge-based formulation to enhance feature diversity, while the covariance term $\mathcal{L}_{\mathrm{Cov}}$ acts as a cross-correlation suppression regularizer aiming to improve representational efficiency. Further theoretical analysis is provided in Appendix 9.
+
+Algorithm 1: DEDA
+Input: T: Original training dataset; S: Distilled synthetic dataset; T: Number of training iterations; $\theta_{\mathcal{T}}$ : Pre-trained model; C: Number of classes; $\eta$ : Learning rate. 1 Initialize distilled dataset $S\gets \emptyset$
+2 Stage I: Offline Gaussian Distribution Estimate
+3 Group samples by class $c$ to form subset $\mathcal{T}_c\subseteq \mathcal{T}$
+4 Compute feature mean $\{\pmb {\mu}_{\mathcal{T},c}^{l}\}_{l = 1}^{l = L - 1}$ via Eq. (4).
+5 Compute covariance $\{Cov_{T,c}^{l}\}_{l = 1}^{l = L - 1}$ via Eq. (5).
+6 Store $\{\pmb {\mu}_{\mathcal{T},c}^{l}\}_{l = 1}^{l = L - 1}$ and $\{Cov_{T,c}^{l}\}_{l = 1}^{l = L - 1}$ in memory bank $\mathcal{M}_c$
+7 Stage II: Distilled Data Optimization
+8 for each class $c = 1$ to $C$ do
+9 Initialize the model parameters using the stored statistics from the memory bank $\mathcal{M}c$ .. $\theta_{\mathcal{T}}\gets \{\pmb{\mu}_{\mathcal{T},c}^{l}\}_{l = 1}^{l = L - 1},\{\pmb{Cov}_{\mathcal{T},c}^{l}\}_{l = 1}^{l = L - 1}.$
+10 for iteration $i = 1$ to $T$ do
+11 Compute $\mathcal{L}_{\mathrm{GDA}}$ via Eq.(6).
+12 Compute $\mathcal{L}_{\mathrm{Var}}$ via Eq.(7).
+13Compute $\mathcal{L}_{\mathrm{Cov}}$ via Eq.(8).
+14 Compute the total loss $\mathcal{L}$ via Eq.(9).
+15 Update $\mathcal{S}_c\gets \mathcal{S}_c - \eta \nabla_{\mathcal{S}_c}\mathcal{L}$
+Output: Distilled synthetic dataset $S$
+
+# 4.3. Overall Loss and Training Algorithm
+
+Following previous work [10, 41, 43], we preserve the cross-entropy loss $\mathcal{L}_{\mathrm{CE}}$ from Eq.(2) to maintain intra-class discriminability. In addition, our composite loss function comprises three key components: the Gaussian distribution alignment loss $\mathcal{L}_{\mathrm{GDA}}$ , variance regularization loss $\mathcal{L}_{\mathrm{Var}}$ , and covariance regularization loss $\mathcal{L}_{\mathrm{Cov}}$ . The overall loss function is formulated as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {C E}} + \mathcal {L} _ {\mathrm {G D A}} + \lambda_ {1} \mathcal {L} _ {\text {V a r}} + \lambda_ {2} \mathcal {L} _ {\text {C o v}}, \tag {9}
+$$
+
+where $\lambda_{1}$ and $\lambda_{2}$ are weighting coefficients. The training procedure is detailed in Algorithm 1.
+
+Computational Complexity. Traditional methods align feature maps across all BN layers by matching their means and variances, leading to a computational complexity of $O(2 \times D_l \times H_l \times W_l)$ . In contrast, our DEDA uses spatial average pooling to reduce spatial dimensions and aligns both the means and covariance matrices, lowering the computational complexity to $O(D_l^2 + D_l)$ .
+
+# 5. Experiment
+
+# 5.1. Experimental Setup
+
+Datasets. We evaluate our dataset distillation method on four widely-used image benchmarks: (1) Low-resolution
+
+Table 1. Comparison of different methods on CIFAR-10, CIFAR-100, and Tiny-ImageNet. For classical dataset distillation methods, ConvNet represents methods using ConvNet-128, with underlined results indicating their best performance. For modern large-scale dataset distillation methods, RN-18 represents methods using ResNet-18, where bold results highlight the overall best performance.
+
+ | Method | Venue | CIFAR-10 | CIFAR-100 | Tiny-ImageNet |
| IPC = 10 | IPC = 50 | IPC = 10 | IPC = 50 | IPC = 10 | IPC = 50 | IPC = 100 |
| ConvNet | Random | - | 26.0 ± 1.2 | 43.4 ± 1.0 | 14.6 ± 0.5 | 30.0 ± 0.4 | 5.0 ± 0.2 | 15.0 ± 0.4 | - |
| KIP [28] | ICLR21 | 62.7 ± 0.3 | 68.6 ± 0.2 | 28.3 ± 0.1 | - | - | - | - |
| DC [47] | ICLR21 | 44.9 ± 0.5 | 53.9 ± 0.5 | 32.3 ± 0.3 | 42.8 ± 0.4 | - | - | - |
| CAFE [39] | CVPR22 | 50.9 ± 0.5 | 62.3 ± 0.4 | 31.5 ± 0.2 | 42.9 ± 0.2 | - | - | - |
| DM [49] | WACV23 | 48.9 ± 0.6 | 63.0 ± 0.4 | 29.7 ± 0.3 | 43.6 ± 0.4 | 12.9 ± 0.4 | 24.1 ± 0.3 | - |
| MTT [3] | CVPR23 | 65.3 ± 0.7 | 71.6 ± 0.2 | 40.1 ± 0.4 | 47.7 ± 0.2 | 23.2 ± 0.2 | 28.0 ± 0.3 | - |
| DataDAM [31] | ICCV23 | 54.2 ± 0.8 | 67.0 ± 0.4 | 34.8 ± 0.5 | 49.4 ± 0.3 | 18.7 ± 0.3 | 28.7 ± 0.3 | - |
| RN-18 | SRe2L [43] | NeurIPS23 | 27.2 ± 0.4 | 47.5 ± 0.5 | 31.6 ± 0.5 | 52.2 ± 0.3 | 16.1 ± 0.2 | 41.1 ± 0.4 | 49.7 ± 0.3 |
| LPLD [41] | NeurIPS24 | - | - | - | - | - | 48.8 ± 0.4 | 53.6 ± 0.3 |
| DEDA | - | 38.2 ± 0.4 | 60.2 ± 0.5 | 43.6 ± 0.4 | 65.1 ± 0.4 | 44.5 ± 0.6 | 55.2 ± 0.3 | 59.3 ± 0.3 |
+
+Table 2. Comparison on ImageNet-1K using ResNet-{18, 50, 101}. Bold results indicate the best results. † denotes the reported results.
+
+| Method | ResNet-18 | ResNet-50 | ResNet-101 |
| IPC = 10 | IPC = 50 | IPC = 100 | IPC = 10 | IPC = 50 | IPC = 100 | IPC = 10 | IPC = 50 | IPC = 100 |
| SRe2L [43] | 21.3 ± 0.6 | 46.8 ± 0.2 | 52.8 ± 0.3 | 28.4 ± 0.1 | 55.6 ± 0.3 | 61.0 ± 0.4 | 30.9 ± 0.1 | 60.8 ± 0.5 | 62.8 ± 0.2 |
| LPLD [41] | 34.6 ± 0.9 | 55.4 ± 0.3 | 59.4 ± 0.2 | 41.7† | 62.2† | 65.7† | - | - | - |
| DEDA | 36.4 ± 0.7 | 56.3 ± 0.4 | 58.4 ± 0.3 | 42.5 ± 0.5 | 62.7 ± 0.4 | 65.4 ± 0.3 | 46.3 ± 0.5 | 62.4 ± 0.6 | 64.9 ± 0.3 |
+
+datasets: CIFAR-10/100 [17] ( $32 \times 32$ resolution, 60,000 images, 10/100 classes) and Tiny-ImageNet [19] ( $64 \times 64$ resolution, 100,000 images, 200 classes); (2) High-resolution dataset: ImageNet-1K [5] ( $224 \times 224$ resolution, 1.28 million images, 1,000 classes). These datasets vary in complexity, where ImageNet-1K is the most complex due to its high resolution and large image volume.
+
+Implementation Details. We implement our method following the experimental settings established in prior works [41, 43]. Specifically, we use ResNet-18 [15] as the default distillation architecture. We set the covariance matrix hyperparameter to $\gamma = 50$ by default to promote feature diversity while aligning Gaussian distributions. Our regularization strategy uses weighted coefficients of $\lambda_{1} = 0.2$ for variance regularization and $\lambda_{2} = 4.0$ for covariance regularization. More implementation details are in Section 8.
+
+Evaluation Metric. We evaluate the quality of the distilled data using the Top-1 test accuracy on the original dataset's test set. Following the evaluation strategy [41, 43], we use the soft labels generated by the pre-trained teacher model on the distilled data as the ground truth for training a model from scratch. These soft labels are dynamically updated by the teacher model at each validation epoch.
+
+Compared Methods. We evaluate our DEDA method against several state-of-the-art baselines. In addition to random sample selection, we compare with classical dataset distillation methods, including DC [47], KIP [28], DM [49],
+
+CAFE [39], MTT [3], and DataDAM [31]. For large-scale dataset distillation, we choose SRe2L [43] and LPLD [41] for comparison. Notably, G-VBSM [33] and DWA [10] are not compared, as they incorporate multiple model training.
+
+# 5.2. Main Results
+
+CIFAR-10/100 and Tiny-/ImageNet. Table 1 presents a comparative analysis of our DEDA framework against state-of-the-art methods on CIFAR-10, CIFAR-100, and TinyImageNet. Our findings highlight two key insights: (1) When utilizing larger pre-trained models (e.g., ResNet-18), DEDA achieves substantial performance gains, outperforming SRe2L by $12.7\%$ on CIFAR-10, $12.9\%$ on CIFAR-100, and $14.1\%$ on Tiny-/ImageNet with IPC = 50. These significant improvements validate the effectiveness of our Gaussian distribution matching mechanism in capturing essential features. (2) While conventional ConvNet-128-based methods, such as MTT [3], leverage bilevel optimization and are considered state-of-the-art for small-scale dataset distillation, they struggle to scale effectively to larger datasets. In contrast, DEDA consistently outperforms these approaches on more challenging benchmarks, demonstrating its superior ability to handle dataset expansion, particularly on CIFAR-100 and Tiny-/ImageNet.
+
+ImageNet-1K. Table 2 presents a comprehensive evaluation of our DEDA on ImageNet-1K using ResNet-18, ResNet-50, and ResNet-101 architectures. The results re
+
+
+(a) Effect of $\gamma$
+
+
+(b) Effect of $\lambda_{1}$ .
+
+
+(c) Effect of $\lambda_{2}$ .
+Figure 3. Hyperparameter ablation $(\gamma, \lambda_1, \lambda_2)$ on CIFAR-100 with IPC=50. $\gamma$ controls the covariance-to-mean ratio in $\mathcal{L}_{\mathrm{GDA}}$ , while $\lambda_1$ and $\lambda_2$ are the weights that are the variance maximization and off-diagonal covariance terms, respectively.
+
+Table 3. Cross-architecture performance of distilled dataset of CIFAR-100 using ResNet-18.
+
+| IPC | NetWorks | SRe2L | Ours |
| 10 | ResNet-50 | 22.4 ± 1.3 | 39.4 ± 0.9 |
| MobileNetV2 | 16.1 ± 0.5 | 30.1 ± 1.1 |
| EfficientNetB0 | 11.1 ± 0.3 | 24.6 ± 0.5 |
| ShuffleNetV2 | 11.8 ± 0.7 | 23.1 ± 0.8 |
| VGG-16 | 19.2 ± 0.2 | 29.7 ± 0.4 |
| 50 | ResNet-50 | 52.8 ± 0.7 | 63.7 ± 0.6 |
| MobileNetV2 | 43.2 ± 0.2 | 55.6 ± 0.6 |
| EfficientNetB0 | 24.9 ± 1.7 | 43.7 ± 1.2 |
| ShuffleNetV2 | 27.5 ± 1.1 | 45.1 ± 0.9 |
| VGG-16 | 40.4 ± 1.2 | 52.3 ± 0.8 |
+
+veal the following insights: (1) Both LPLD and our DEDA outperform SRe2L, highlighting the effectiveness of class-specific alignment in reducing inter-class similarity and enhancing class discriminability. (2) Our DEDA further surpasses LPLD, demonstrating that the introduction of covariance alignment and regularization significantly enhances the diversity of distilled data, ultimately leading to superior performance on downstream tasks.
+
+# 5.3. Cross-Architecture Evaluation
+
+A more critical evaluation metric for distilled data is its ability to generalize across different network architectures. As shown in Table 3, we comprehensively assess the cross-architecture generalization capability of our CIFAR-100 distilled dataset (trained on ResNet-18) by testing its performance on several unseen network architectures trained from scratch. The evaluation includes seven distinct architectures: ResNet-50 [15], MobileNetV2 [32], EfficientNetB0 [37], ShuffleNetV2 [27], and VGG-16 [34], showing that our method can achieve generalization without the need to optimize distilled data across multiple architectures.
+
+Table 4. Ablation study on CIFAR-100 with IPC=10/50.
+
+| Method | LGDA | DER | IPC |
| MA | CA | LVar | L Cov | 10 | 50 |
| SRe2L | - | - | - | - | 32.0 | 47.5 |
| Ours | ✓ | - | - | - | 39.8 | 63.1 |
| ✓ | ✓ | - | - | 41.6 | 63.8 |
| ✓ | ✓ | ✓ | - | 42.2 | 64.7 |
| ✓ | ✓ | - | ✓ | 42.1 | 64.2 |
| ✓ | ✓ | ✓ | ✓ | 43.6 | 65.1 |
+
+# 5.4. Analysis
+
+Ablation Study. To evaluate the effectiveness of each component in our DEDA, we conduct ablation experiments on CIFAR-100, considering two primary elements: Gaussian Distribution Alignment Loss $(\mathcal{L}_{\mathrm{GDA}})$ and Diversity-Enriched Regularizer (DER). As detailed in Table 4, our analysis reveals four key findings: (1) Our novel approach of storing complete Gaussian statistics (mean and covariance) from the pre-trained model demonstrates superior effectiveness compared to existing methods. The Mean Alignment (MA) component alone outperforms SRe2L's BN-layer alignment by $15.6\%$ , demonstrating the importance of class-specific alignment. (2) The Covariance Alignment (CA) component in $\mathcal{L}_{\mathrm{GDA}}$ provides an additional performance improvement when combined with MA. This demonstrates that preserving inter-feature relationships through covariance matching is crucial for maintaining the diversity of feature dimensions. (3) Our proposed Variance Maximization Regularization $(\mathcal{L}_{\mathrm{Var}})$ applied to last-layer features ensures sufficient diversity in semantic dimensions, yielding further accuracy gains of $0.6\%$ and $0.9\%$ . This validates our hypothesis that feature space expansion promotes better knowledge representation. (4) The Off-diagonal Covariance Minimization Regularization $(\mathcal{L}_{\mathrm{Cov}})$ effectively reduces inter-dimensional redundancy, achieving additional performance improvements of $1.4\%$
+
+
+Figure 4. Visualization of distilled data. (a) and (b) show distilled images from SRe2L and our DEDA, respectively. The first two rows display apples and aquarium fish from CIFAR-100, while the last two rows show ptarmigan birds and sorrel horses from ImageNet-1K. Compared to distilled images generated by SRe2L, those produced by our method exhibit significantly greater diversity.
+
+
+
+and $0.4\%$ . This confirms that promoting orthogonality in the last-layer feature dimensions effectively reduces the impact of feature redundancy.
+
+Effect of $\gamma$ . The hyperparameter $\gamma$ represents the ratio between covariance and mean alignment in our framework. Covariance matrices play a pivotal role as statistical descriptors that encode both intra-class variations and inter-dimensional correlations among feature dimensions. As demonstrated in Figure 3a for CIFAR-100 with IPC=50, we observe substantial performance gains when increasing $\gamma$ from 0 to 50. However, extending $\gamma$ beyond this optimal range (50 to 200) leads to performance degradation. This phenomenon stems from an inherent trade-off between covariance alignment and mean matching: excessive emphasis on preserving covariance structures may inadvertently weaken information on the inherent properties of each class.
+
+Effect of $\lambda_{1}$ and $\lambda_{2}$ . The regularization weights $\lambda_{1}$ (for variance minimization) and $\lambda_{2}$ (for off-diagonal covariance maximization) address distinct aspects of feature distribution. In the pre-trained model, last-layer features exhibit high concentration within classes while carrying high-level semantic information. $\lambda_{1}$ explicitly constrains feature diversity across distilled samples, whereas $\lambda_{2}$ encourages dimension decorrelation to enhance feature representational capacity. As shown in Figure 3b and 3c for CIFAR-100 with IPC=50, optimal performance is achieved with $\lambda_{1} = 0.2$ and $\lambda_{2} = 4$ . Notably, large $\lambda_{1}$ values may degrade performance due to excessive expansion of the feature space, which may compromise class discriminability. In contrast, performance remains relatively stable across variations in $\lambda_{2}$ , indicating lower sensitivity to this parameter.
+
+# 5.5. Visualization
+
+To assess whether our method preserves the feature diversity of the original dataset, we present visual comparisons between the distilled data from SRe2L and our DEDA on
+
+CIFAR-100 and ImageNet-1K in Figure 4. Our empirical observations yield two critical insights: (1) On low-resolution data like CIFAR-100, our DEDA demonstrates superior class discriminability compared to SRe2L, with distilled samples effectively preserving class-specific semantic information. This enhanced performance validates the effectiveness of our class-specific Gaussian distribution matching strategy in maintaining inter-class distinctions. (2) On high-resolution data like ImageNet-1K, our DEDA not only maintains class discriminability but also captures richer semantic diversity. For instance, the distilled images of the 'sorrel' class (red-brown horse) preserve various fine-grained attributes, including equine postures, anatomical features, and color variations. This underscores the robustness of our method across different data scales.
+
+# 6. Conclusion
+
+In this paper, we address two key limitations in modern dataset distillation: (1) the feature alignment of distilled data to original data overlooks crucial inter-feature correlations, and (2) the compact feature space of the pre-trained model's last layer leads to a lack of diversity in the distilled data. To overcome these challenges, we propose a novel Diversity-Enhanced Distribution Alignment (DEDA) method for dataset distillation. DEDA enhances diversity by aligning the distilled data with the Gaussian distribution of the original data and implementing a diversity-enriched regularizer at the last layer. Our experimental evaluation across multiple benchmarks demonstrates that DEDA consistently outperforms existing methods while maintaining computational efficiency. Although DEDA shows promising results on large-scale datasets, its performance declines as distilled samples increase (e.g., $\mathrm{IPC} = 100$ ), highlighting the need for further exploration to balance class-specific information retention and diversity enhancement.
+
+# 7. Acknowledgments
+
+This work was supported by the Chinese Academy of Sciences under grant No. XDB0690302.
+
+# References
+
+[1] Adrien Bardes, Jean Ponce, and Yann LeCun. Vicreg: Variance-invariance-covariance regularization for self-supervised learning. In ICLR, 2022. 5
+[2] Adrien Bardes, Jean Ponce, and Yann LeCun. Vicregl: Self-supervised learning of local visual features. Advances in Neural Information Processing Systems, 35:8799-8810, 2022. 5
+[3] George Cazenavette, Tongzhou Wang, Antonio Torralba, Alexei A. Efros, and Jun-Yan Zhu. Dataset distillation by matching training trajectories. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10718-10727, 2022. 2, 3, 6
+[4] Justin Cui, Ruochen Wang, Si Si, and Cho-Jui Hsieh. Scaling up dataset distillation toImagenet-1k with constant memory. In International Conference on Machine Learning, pages 6565–6590. PMLR, 2023. 2
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+# Divide-and-Conquer for Enhancing Unlabeled Learning, Stability, and Plasticity in Semi-supervised Continual Learning
+
+Yue Duan $^{1*}$ Taicai Chen $^{1*}$ Lei Qi $^{2}$ Yinghuan Shi $^{1\dagger}$ $^{1}$ Nanjing University $^{2}$ Southeast University
+
+{yueduan@smail., taicaichen@smail., syh@}nju.edu.cn, qilei@seu.edu.cn
+
+# Abstract
+
+Semi-supervised continual learning (SSCL) seeks to leverage both labeled and unlabeled data in a sequential learning setup, aiming to reduce annotation costs while managing continual data arrival. SSCL introduces complex challenges, including ensuring effective unlabeled learning (UL), while balancing memory stability (MS) and learning plasticity (LP). Previous SSCL efforts have typically focused on isolated aspects of the three, while this work presents USP, a divide-and-conquer framework designed to synergistically enhance these three aspects: (1) Feature Space Reservation (FSR) strategy for LP, which constructs reserved feature locations for future classes by shaping old classes into an equiangular tight frame; (2) Divide-and-Conquer Pseudo-labeling (DCP) approach for UL, which assigns reliable pseudo-labels across both high- and low-confidence unlabeled data; and (3) Class-mean-anchored Unlabeled Distillation (CUD) for MS, which reuses DCP's outputs to anchor unlabeled data to stable class means for distillation to prevent forgetting. Comprehensive evaluations show USP outperforms prior SSCL methods, with gains up to $5.94\%$ in the last accuracy, validating its effectiveness. The code is available at https://github.com/NJUyued/USP4SSCL.
+
+# 1. Introduction
+
+Recently, continual learning (CL) has emerged as a promising approach for handling such sequential data arrival scenarios [47, 50]. Yet, most existing CL methods rely heavily on fully labeled data, which is often impractical in real-world applications due to high annotation costs, privacy concerns, and limitations in adapting to real-time online scenarios. To address these challenges, researchers have turned to semi-supervised learning (SSL) [34, 53] frameworks, where only a subset of samples requires labeling.
+
+
+Figure 1. Illustration of the SSCL setting ( $E^t$ and $M^t$ indicate the exemplar set and model in task $t$ , respectively): in a dynamic data stream containing both labeled and unlabeled data, distinct tasks arrive sequentially with non-overlapping classes across tasks.
+
+Inspired by this paradigm, a new direction called semi-supervised continual learning (SSCL) [2, 46] has emerged, aiming to leverage SSL setups across all tasks within the CL setting, which is illustrated in Fig. 1.
+
+SSCL introduces distinct challenges due to the need to continuously learn from both labeled and unlabeled data. This setting demands careful management of the trade-off between learning plasticity—the model's ability to incorporate new knowledge, and memory stability—its capacity to retain past knowledge [24, 25, 61]. In SSCL, these dynamics become particularly complex as the model faces the risk of catastrophic forgetting of past tasks, while simultaneously being prone to overfitting on limited labeled samples [12, 17, 31]. Meanwhile, learning from a vast pool of unlabeled data is also challenging, as CL's anti-forgetting processes can disrupt learning under sparse supervision. Furthermore, standard CL techniques like experience replay face obstacles in SSCL: constrained replay buffers often prioritize labeled samples, limiting the use of valuable information from unlabeled data [5, 19, 39].
+
+We argue that addressing SSCL effectively requires a holistic approach that does not overlook any of these
+
+three aspects: unlabeled learning (UL), memory stability (MS), and learning plasticity (LP). Although previous approaches have made strides in SSCL, most of them primarily focus on just one or two of the three core challenges, often leaving the other aspects unaddressed. For examples, for UL, [39] employs pseudo-labeling technique used in SSL to utilize unlabeled data for training and [13] apply consistency loss to boost the robustness of unlabeled learning; For MS, [17] proposes dynamic sub-graph distillation (DSGD) to leverages semantic and structural information from unlabeled data, helping the model remain robust to distribution shifts. Motivated by this, we propose a divide-and-conquer approach with three interlinked modules: USP, each tailored to enhance one of these aspects while collectively improving the overall SSCL performance.
+
+The key to building a powerful SSCL lies in designing mechanisms that enable UL-, MS- and LP-components to complement and reinforce each other. With the established baseline SSCL learner, we first introduce a projection head to produce an additional feature branch, which serves as a unified feature output across all subsequent components aiming to strengthen their coupling for mutual enhancement. (1) For LP: We propose a simple yet effective Feature Space Reservation strategy (FSR). Leveraging the equiangular tight frame (ETF) for optimal feature geometry, we obtain anchor vectors that reserve space for future classes. A contrastive-like loss is proposed to align learned data features to these class-specific positions, laying a strong foundation for subsequent CL processes. (2) For UL: We propose a Divide-and-Conquer Pseudolabeling strategy (DCP) to handle high- and low-confidence unlabeled data separately, leveraging two complementary pseudo-labeling techniques. This approach ensures effective utilization of all data while maintaining pseudo-label accuracy, ultimately delivering a robust UL process—and even offering a "free lunch" benefit during testing phase. (3) For MS: We repurpose intermediate calculations from DCP to introduce the Class-mean-anchored Unlabeled Distillation (CUD). CUD aggregates the latent relationship between labeled and unlabeled data, enhancing model's resistance to catastrophic forgetting on unlabeled data, thus supporting stable and reliable representation retention in SSCL.
+
+Contribution. A divide-and-conquer framework, USP, is proposed that synergistically enhances unlabeled learning (UL), memory stability (MS), and learning plasticity (LP): (1) We introduce a novel pseudo-labeling scheme, which ensures high-quality pseudo-labels across confidence levels, fully utilizing all data to improve UL. (2) We propose a feature space reservation strategy and cross-labeled unlabeled distillation to jointly enhance LP and MS, helping the model resist forgetting. (3) Extensive evaluations across diverse SSCL settings demonstrate the performance benefits of USP, with up to a $4.10\%$ gain in average accuracy.
+
+# 2. Related Works
+
+# 2.1. Continual Learning
+
+Continual learning (CL) addresses catastrophic forgetting during incremental learning. As summarized in [61], mainstream approaches fall into three categories: replay-based, knowledge distillation-based, and dynamic network-based methods. Replay-based methods retain/rehearse past data through stored exemplars [3, 13, 57] or synthetic generation [18, 21, 37]. Knowledge distillation-based methods transfer knowledge from old to new models through distillation of logits [38, 40, 56], features [22, 30, 35], or relations [1, 29]. Dynamic network-based methods expand architectures via neuron [28], backbone [45, 52], or prompt [41, 49] growth.
+
+While CL methods are often categorized distinctly, their boundaries are fluid. Replay and distillation synergize as core anti-forgetting mechanisms across paradigms. Our method similarly harnesses their complementary strengths to combat catastrophic forgetting.
+
+# 2.2. Semi-supervised Learning
+
+Semi-supervised learning (SSL) aims to reduce the dependency of deep learning models on labeled data by leveraging abundant unlabeled data. Early SSL methods can be broadly categorized into pseudo-labeling and consistency regularization methods. Pseudo-labeling methods expand the training set by assigning predictions on unlabeled data as pseudo-labels [8, 16, 27, 51]. In contrast, consistency regularization methods enforce similar predictions across augmented versions of input samples, enhancing generalization boundaries through teacher-student interactions [43] or by applying diverse perturbations to inputs [15, 33, 42]. FixMatch [42] introduced a simple yet effective framework that integrates these two strategy: it applies weak and strong augmentations to unlabeled data and uses high-confidence predictions on weakly-augmented samples as pseudo-labels for the strongly-augmented counterparts, enforcing a strong-weak consistency regularization on unlabeled data. This approach demonstrated remarkable performance and has become a foundational benchmark in SSL, inspiring many subsequent methods that adjust pseudo-labeling strategies for unlabeled data [14, 58, 59] or modify confidence thresholding schemes [7, 9, 48].
+
+While FixMatch and similar methods have achieved significant success in SSL, current SSL methods still fall short in addressing learning scenarios where data distribution or class compositions may shift over time.
+
+# 2.3. Semi-supervised Continual Learning
+
+Existing continual learning methods generally rely on a fully supervised setup, whereas semi-supervised continual learning (SSCL) more realistically assumes that only a limited number of samples are labeled at each task. The core
+
+challenge in SSCL is effectively utilizing unlabeled data to mitigate catastrophic forgetting. CNNL [4] fine-tunes its incremental learner by generating pseudo-labels for the unlabeled data, enabling self-training. DistillMatch [39] employs knowledge distillation with prediction consistency on unlabeled data. It also optimizes an out-of-distribution detector to identify task-specific representations. Pseudogradient learner [31] introduces a gradient predictor using labeled data to estimate gradients for unlabeled data, thereby avoiding the potential risks of pseudo-labeling. ORDisCo [46] learns continuously from partially labeled data using a classifier-equipped conditional GAN and performs online data replay. MCSSL [5] extends ORDisCo into a meta-learning framework. DSGD [17] introduces a dynamic subgraph distillation method that leverages semantic and structural information for more stable knowledge distillation on unlabeled data.
+
+Unlike previous methods that focus on individual aspects of UL, MS, or LP, our proposed method integrates all three into a unified framework, aiming for a synergistic effect that amplifies their combined impact.
+
+# 3. Methods
+
+# 3.1. Baseline SSCL Learner
+
+Denoting the input space as $\mathcal{X}$ and the label space as $\mathcal{Y} = \{1,\dots,K\}$ over $K$ classes, we formally define the problem of continual learning (CL) as follows: Given training data that arrives sequentially as a sequence of $T$ tasks, each task $t$ is associated with a dataset $D^{t} \subseteq \mathcal{X}^{t} \times \mathcal{Y}^{t}$ , where $t \in \{1,\dots,T\}$ and $\mathcal{Y}^{1} \cap \mathcal{Y}^{2} \cap \dots \cap \mathcal{Y}^{T} = \emptyset$ . Same below, the superscript of $x^{t}$ is always used to indicate the variable $x$ at different task $t$ . The learning process is conducted task-by-task, and during the training of task $t$ , only the current dataset $D^{t}$ is accessible, while data from previous tasks is systematically discarded. Note that in actual continuous learning settings, a relatively small memory buffer is usually reserved to store past examples to help the model alleviate catastrophic forgetting, which is denoted as $E^{t}$ . $E^{t} = E^{t,(1)} \cup \dots \cup E^{t,(K)}$ and $E^{t,(i)}$ is the exemplar set of old class $i$ containing exemplars stored from the datasets in previous $t - 1$ tasks.
+
+In semi-supervised continual learning (SSCL), each dataset $D^{t}$ is partially labeled and can be divided into two subsets: $D^{t} = D_{l}^{t}\cup D_{u}^{t}$ , where $D_{l}^{t}\subseteq \mathcal{X}^{t}\times \mathcal{Y}^{t}$ denotes the labeled subset and $D_{u}^{t}\subseteq \mathcal{X}^{t}$ denotes the unlabeled subset, with $|D_l^t |\ll |D_u^t|$ . In breif, we can review SSCL as a optimization task on the model parameterized by $\theta$ :
+
+$$
+\min _ {\theta} \sum_ {t = 1} ^ {T} \mathcal {L} _ {\mathrm {s s l}} \left(D ^ {t}\right) + \mathcal {L} _ {\mathrm {c l}} \left(E ^ {t}\right), \tag {1}
+$$
+
+where $\mathcal{L}_{\mathrm{ss1}}$ is the semi-supervised learning (SSL) loss and $\mathcal{L}_{\mathrm{cl}}$ is the CL loss.
+
+
+Figure 2. Overview of USP. All losses of USP uniformly utilize the features output by a projection head $P^t$ to enhance synergy through coupling. (1) $\mathcal{L}_{\mathrm{fsr}}$ for LP (Sec. 3.2): Given the labeled and unlabeled data $(x_l^t, x_u^t)$ , a contrastive loss aligns their features with pre-computed ETF vectors that represent the optimal geometric structure for classification, preventing feature space conflicts between new and old classes during learning; (2) $\mathcal{L}_{\mathrm{uns}}'$ for UL (Sec. 3.3): For $x_u^t$ , we compute its class prediction $p_u^t$ and employ a confidence-based divide-and-conquer approach, which leverages complementary pseudo-labels based on classifier and NCM to provide a robust UL process; (3) $\mathcal{L}_{\mathrm{cod}}$ for MS (Sec. 3.4): Reusing intermediate results from DCP, we anchor the features of unlabeled data to class mean vectors enriched with information of labeled data, mitigating catastrophic forgetting in SSCL.
+
+We propose a divide and conquer approach to Unlabeled learning, Stability, and Plasticity (USP), which is shown in Fig. 2. Overall, we first set a feature extractor $F(\cdot)$ , a classifier $G(\cdot)$ and a projection head $P(\cdot)$ . Following [17], we build a basic SSCL learner using FixMatch [42] for $\mathcal{L}_{\mathrm{ss1}}$ and adopt iCaRL [38] or DER [52] for $\mathcal{L}_{c1}$ (DER's details are deferred to Sec. A.3 of supplementary).
+
+(1) $\mathcal{L}_{\mathrm{ssl}}$ . Given the labeled data $\{x_l^t,y_l^t\} \subset D_l^t$ and the unlabeled data $x_{u}^{t}\in D_{u}^{t}$ , following the most popular pseudo-labeling based SSL method FixMatch, the terms $\mathcal{L}_{\mathrm{ssl}}$ in Eq. (1) can be decomposed into two loss terms: $\mathcal{L}_{\mathrm{ssl}}(D^t) = \mathcal{L}_{\mathrm{sup}}(D_l^t) + \lambda_{\mathrm{uns}}\mathcal{L}_{\mathrm{uns}}(D_u^t)$ , where $\lambda_{\mathrm{uns}}$ is the loss weight. Denoting the model prediction of $x$ as $p_x^t = G^t (F^t (x))$ , we define the supervised loss as
+
+$$
+\mathcal {L} _ {\sup } \left(D _ {l} ^ {t}\right) = \mathbb {E} _ {\left(x _ {l} ^ {t}, y _ {l} ^ {t}\right) \sim D _ {l} ^ {t}} \left[ H \left(p _ {x _ {l} ^ {t}}, y _ {l} ^ {t}\right) \right], \tag {2}
+$$
+
+where $H(\cdot, \cdot)$ is the standard cross-entropy loss. Denoting $\tilde{x} = \max(x)$ and $\hat{x} = \arg \max(x)$ , the unsupervised loss is defined as
+
+$$
+\mathcal {L} _ {\mathrm {u n s}} \left(D _ {u} ^ {t}\right) = \mathbb {E} _ {x _ {u} ^ {t} \sim D _ {u} ^ {t}} \left[ \mathbb {1} \left(\tilde {p} _ {x _ {u} ^ {t}} ^ {t} \geq \tau\right) H \left(p _ {\alpha \left(x _ {u} ^ {t}\right)} ^ {t}, \hat {p} _ {x _ {u} ^ {t}} ^ {t}\right) \right], \tag {3}
+$$
+
+where $\mathbb{1}(\cdot)$ is the indicator function, $\hat{p}_{x_u^t}^t$ is the hard pseudolabel of $p_{x_u^t}^t$ and $\alpha (\cdot)$ represents a strong data augmentation function $^1$ and $\tau$ is a confidence threshold for $\tilde{p}_{x_t^t}$ (i.e., the maximum softmax probability) to select pseudo-labels that are more likely to be correct.
+
+(2) $\mathcal{L}_{\mathrm{cl}}$ . With the exemplar management of iCaRL [38] (see Sec. A.1 of supplementary for details), given $x_{e}^{t}\in E^{t}$ , we utilize the knowledge distillation loss for $\mathcal{L}_{\mathrm{cl}}$ in Eq. (1) by encouraging the current model to output the same prediction $p_e^t = G^t (F^t (x_e^t))$ as that of the old model:
+
+$$
+\mathcal {L} _ {\mathrm {c 1}} \left(E ^ {t}\right) = \mathbb {E} _ {x _ {e} ^ {t} \sim E ^ {t}} \left[ \mathrm {K L} \left(\frac {p _ {e} ^ {t}}{\beta} \parallel \frac {p _ {e} ^ {t - 1}}{\beta}\right) \right], \tag {4}
+$$
+
+where $\mathrm{KL}(\cdot \| \cdot)$ is the KL-divergence and $\beta$ is the temperature parameter.
+
+Note that from here on, all feature vectors extracted from an input $x$ mentioned in the following text are denoted as $f_{x}^{t}$ , which are output by the projection head $P(\cdot)$ and normalized using $L_{2}$ -normalization, i.e., $f_{x}^{t} = \frac{P^{t}(F^{t}(x))}{\|P^{t}(F^{t}(x))\|_{2}}$ (and after any operation on the features, they will be renormalized). All components of USP consistently leverage the output features from $P(\cdot)$ , aiming to strengthen the coupling of all components for mutual reinforcement.
+
+# 3.2. ETF-Based Feature Space Reservation
+
+We begin by enhancing the plasticity of USP. Inspired by [36, 54, 60], we aim to design a Feature Space Reservation (FSR) method for accommodating upcoming new classes without interfering with the feature patterns retained for previously learned classes.
+
+We aim to utilize a simple yet effective contrastive learning loss to align sample features of each class with a set of predefined class prototype features derived from a simplex equiangular tight frame (ETF) for the entire label space. The ETF is inspired by neural collapse phenomenon (more details and the calculation of ETF can be found in Sec. A.4 of supplementary), which indicates that the final-layer features of samples within the same class collapse to a single vertex. And the vertices of all classes align with class prototypes that form an ETF, which refers to a matrix $\mathcal{E} \in \mathbb{R}^{d \times k}$ ( $d$ is a predefined parameter, $k$ is the total number of classes). Crucially, the ETF structure pre-defines maximally separated prototype positions in the feature space,
+
+inherently reserving geometric capacity for future unseen classes while preserving semantic discrimination of learned ones. Each column vector $\mathcal{E}_{\cdot ,i}\in \mathbb{R}^d$ in ETF can be considered as the corresponding prototype for class $i$ . As the ETF corresponds to the optimal geometric structure for classification, anchoring the continually arriving class features to the different ETF-prototype-vectors as learning targets fundamentally enhances the plasticity of SSCL models. With obtained $\mathcal{E}_{\cdot ,i}$ , denoting the cosine similarity as $S(\cdot ,\cdot)$ , we define the following contrastive loss for feature alignment on both the labeled and unlabeled data:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathbf {f s r}} (D ^ {t}) = \mathbb {E} _ {(x _ {l} ^ {t}, y _ {l} ^ {t}) \sim D _ {l} ^ {t}} \left[ - \log \frac {\exp \left(\frac {S (\mathcal {E} _ {: , y _ {l} ^ {t}} , f _ {x _ {l} ^ {t}})}{\gamma}\right)}{\sum_ {i = 1} ^ {k} \exp \left(\frac {S (\mathcal {E} _ {: , i} , f _ {x _ {l} ^ {t}})}{\gamma}\right)} \right] \\ + \mathbb {E} _ {x _ {u} ^ {t} \sim D _ {u} ^ {t}} \left[ \mathbb {1} \left(\tilde {p} _ {x _ {u} ^ {t}} ^ {t} \geq \tau\right) - \log \frac {\exp \left(\frac {S \left(\mathcal {E} _ {: , \hat {p} _ {x _ {u} ^ {t}}} , f _ {x _ {u} ^ {t}} ^ {t}\right)}{\gamma}\right)}{\sum_ {i = 1} ^ {k} \exp \left(\frac {S \left(\mathcal {E} _ {: , i} , f _ {x _ {u} ^ {t}} ^ {t}\right)}{\gamma}\right)} \right], \tag {5} \\ \end{array}
+$$
+
+where $\gamma$ is the temperature parameter. We still use the confidence threshold to filter the pseudo-labels on unlabeled data to ensure the robustness of FSR as much as possible.
+
+# 3.3. Divide and Conquer Pseudo-Labeling
+
+For unlabeled learning, considering that we adopt a pseudolabeling framework similar to FixMatch for $\mathcal{L}_{\mathrm{uns}}$ , ensuring the accuracy of pseudo-labels is paramount. Thus, we propose Divide-and-Conquer Pseudo-labeling (DCP) that combines the two complementary classification methods to leverage their respective strengths in SSCL for $\mathcal{L}_{\mathrm{uns}}$ .
+
+# 3.3.1. Training Phase
+
+In FixMatch and its adaptation as a basic learner in [17] (Eq. (3)), pseudo-labeling involves assigning hard labels by applying a threshold to the softmax outputs of classifier logits on unlabeled data. However, this will result in low-confidence samples not participating in training and resulting in a waste of data. This is a drawback of classifier-classification, because the pseudo-labels of low-confidence samples are likely to be wrong and harm training. Thus, we consider another nearest class mean (NCM) classification method in CL [32], which classifies samples by matching them to prototype vectors—incrementally computed as the average features of observed examples, for pseudo-labeling on samples with low confidence.
+
+The work in [12] argues that NCM-like classification could maintain more stable performance in CL by measuring distances between test image features and class prototypes, which depend only on the parameters of the backbone model. In contrast, classifier-based predictions require feature input into an expanding fully connected layer, which is
+
+
+Figure 3. Kernel density estimation (KDE) of confidence distributions of pseudo-labels on 5-task CIFAR10-30 (see Sec. 4.1 for the experimental setting). We show the confidence of classifier-based pseudo-labels ("P-CLS"), divided into correct and incorrect parts, and the re-partitioning of these corresponding examples if the pseudo-labels are providing by NCM ("P-NCM"). The red dash lines indicate the confidence threshold $\tau$ in Eq. (3).
+
+updated only for the current session, often leading to classification instability in incremental tasks. In this work, as illustrated in Fig. 3, we observe that classifier-based pseudolabeling can yield highly reliable results at high-confidence levels but lack reliability for low-confidence predictions. NCM classification, on the other hand, maintains a relatively more robust accuracy across all confidence level of classifier predictions. Given discussed above, for high-confidence predictions, DCP apply hard pseudo-labels from the classifier outputs, while low-confidence predictions are assigned pseudo-labels using NCM classification.
+
+In our NCM classification, considering that the ground-truth of unlabeled data is unknown, the prototype vector is computed for each observed class by averaging the feature vectors of all exemplars selected from labeled data in that class. First, we separate the labeled data by class, where $C^{t,(i)}$ represents the labeled set of class $i$ . Then, we compute the feature mean of class $i$ by $\mu_{C^{t,(i)}} = \frac{\sum_{c\in C^{t,(i)}}f_c^t}{|C^{t,(i)}|}$ . Finally, the class label $q_{x_u^t}$ for an unlabeled sample $x_{u}^{t}$ is assigned based on $\mu_{C^{t,(i)}}$ with the highest similarity to the input's features, i.e.,
+
+$$
+q _ {x _ {u} ^ {t}} = \underset {i = 1, \dots , | \mathcal {Y} ^ {t} |} {\arg \max } S \left(f _ {x _ {u} ^ {t}} ^ {t}, \mu_ {C ^ {t, (i)}}\right). \tag {6}
+$$
+
+Hereafter, we can rewrite Eq. (3) as
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {u n s}} \left(D _ {u} ^ {t}\right) ^ {\prime} = \mathcal {L} _ {\mathrm {u n s}} \left(D _ {u} ^ {t}\right) + \\ \mathbb {E} _ {x _ {u} ^ {t} \sim D _ {u} ^ {t}} \left[ \mathbb {1} \left(\tilde {p} _ {x _ {u} ^ {t}} ^ {t} < \tau\right) H \left(p _ {\alpha (x _ {u} ^ {t})} ^ {t}, q _ {x _ {u} ^ {t}}\right) \right]. \tag {7} \\ \end{array}
+$$
+
+# 3.3.2. Testing Phase
+
+We can also treat the testing phase as a pseudo-labeling process, leveraging the benefits of DCP in this context. The key difference is that, for NCM classification of low-confidence samples, we rely on the full exemplar set $E^t$ rather than the labeled dataset of a specific task. Given a test sample $u^t$ , the predicted label $q_{u^t}$ is assigned by
+
+$$
+q _ {u ^ {t}} = \left\{ \begin{array}{l l} \hat {p} _ {u ^ {t}} ^ {t}, & \tilde {p} _ {u ^ {t}} ^ {t} \geq \tau \\ \underset {i = 1, \dots , k} {\arg \max } S \left(f _ {u ^ {t}} ^ {t}, \mu_ {E ^ {t, (i)}}\right), & \tilde {p} _ {u ^ {t}} ^ {t} < \tau \end{array} , \right. \tag {8}
+$$
+
+where $k$ is the number of class observed so far.
+
+# 3.4. Class-Mean-Anchored Unlabeled Distillation
+
+Finally, we enhance the stability of USP from a distillation perspective. Knowledge distillation (KD) is a common approach in CL that uses frozen models or stored features and probabilities from prior tasks as a "teacher" to guide the active "student" model on the new task. In traditional CL, KD typically focuses on independently distilling information from exemplars (e.g., Eq. (11)), often focusing on labeled samples alone. However, this is insufficient in the SSCL setting, where the forgetting of unlabeled data contributes significantly to catastrophic forgetting. Thus, we introduce Class-mean-anchored Unlabeled Distillation (CUD), which efficiently reuses the class mean features of labeled data computed in Sec. 3.3.1. Denoting the class
+
+mean feature matrix as $M = \begin{bmatrix} \mu_{C^{t,(1)}}\\ \vdots \\ \mu_{C^{t,(i)}} \end{bmatrix}$ , we define CUD loss as
+
+$$
+\mathcal {L} _ {\mathrm {c u d}} \left(D _ {u} ^ {t}\right) = \mathbb {E} _ {x _ {u} ^ {t} \sim D _ {u} ^ {t}} \left[ \mathrm {K L} \left(\frac {S \left(f _ {x _ {u} ^ {t}} ^ {t} , M\right)}{\xi} \| \frac {S \left(f _ {x _ {u} ^ {t}} ^ {t - 1} , M\right)}{\xi}\right) \right], \tag {9}
+$$
+
+where $\xi$ is the temperature parameter. CUD distills the combined relationships between labeled and unlabeled data by anchoring unlabeled samples to the stable class mean features derived from labeled data. This encourages the model to develop more reliable and robust representations, effectively enhancing the stability of USP.
+
+Finally, the total loss of USP can be presented as
+
+$$
+\mathcal {L} = \mathcal {L} _ {\sup } + \lambda_ {\text {u n s}} \mathcal {L} _ {\text {u n s}} ^ {\prime} + \lambda_ {\mathrm {c l}} \mathcal {L} _ {\mathrm {c l}} + \lambda_ {\text {f s r}} \mathcal {L} _ {\text {f s r}} + \lambda_ {\text {c u d}} \mathcal {L} _ {\text {c u d}}. \tag {10}
+$$
+
+# 4. Experiments
+
+# 4.1. Experimental setting
+
+Dataset. We conduct comparative experiments on CIFAR-10, CIFAR-100, and ImageNet-100 to evaluate our method. CIFAR-10 [26] is a dataset with 10 classes, containing 50,000 training images and 10,000 test images, with each image sized $32 \times 32$ . CIFAR-100 [26] is similar to CIFAR-10, but it contains 100 classes, with each class having 500 training images and 100 test images. ImageNet-100 [44] is a 100-class subset of the ImageNet-1k, with each class containing 1,300 training images and 500 test images. Additionally, we evaluate on a more challenging few-shot SSCL
+
+Table 1. Average and last accuracy on 5-task CIFAR10-X and 10-task CIFAR100-X with $X$ labels per class. We provide comparisons with multiple baseline methods reported in DSGD [17], which use the same baseline SSCL learner as ours. We mark out the best result.
+
+| Method | CIFAR10-30 | CIFAR10-150 | CIFAR100-20 | CIFAR100-25 | CIFAR100-80 | CIFAR100-125 |
| Avg | Last | Avg | Last | Avg | Last | Avg | Last | Avg | Last | Avg | Last |
| iCaRL [38] | 34.16 | 21.84 | 60.86 | 53.65 | 26.43 | 13.92 | 28.14 | 15.29 | 36.32 | 19.10 | 44.14 | 30.73 |
| DER [52] | 40.41 | 31.48 | 64.77 | 61.06 | 31.01 | 23.53 | 32.82 | 26.53 | 53.32 | 41.55 | 57.21 | 48.86 |
| CCIC [4] | - | 55.20 | - | 74.30 | - | - | - | 29.50 | - | - | - | 44.30 |
| ORDisCo [46] | - | - | 74.77 | 65.91 | - | - | - | - | - | - | - | - |
| NNCSL [23] | - | - | - | - | 55.19 | 43.53 | 57.45 | 46.00 | 67.27 | 55.35 | 67.58 | 56.40 |
| iCaRL&Fix [17] | 45.98 | 30.71 | 78.36 | 69.08 | 45.75 | 23.40 | 49.83 | 31.25 | 53.46 | 32.21 | 56.87 | 41.38 |
| + DSGD [17] | 77.33 | 76.41 | 84.14 | 79.69 | 52.80 | 35.47 | 53.42 | 35.95 | 57.92 | 37.81 | 58.08 | 43.14 |
| + USP (Ours) | 79.66 | 70.43 | 84.78 | 78.21 | 53.20 | 41.30 | 54.36 | 38.25 | 58.59 | 44.20 | 59.96 | 43.80 |
| DER&Fix [17] | 66.71 | 61.41 | 81.10 | 77.00 | 51.76 | 40.86 | 52.03 | 44.47 | 64.03 | 50.25 | 66.69 | 53.57 |
| + DSGD [17] | 75.04 | 72.59 | 83.08 | 79.39 | 55.63 | 44.63 | 57.94 | 46.68 | 65.48 | 55.40 | 69.14 | 58.50 |
| + USP (Ours) | 81.43 | 73.65 | 84.43 | 77.74 | 58.79 | 45.22 | 59.87 | 47.44 | 68.67 | 60.45 | 71.60 | 63.08 |
+
+task on the CUB [6] dataset, consisting of 200 bird species with 6,000 training images and 6,000 test images.
+
+Task Settings. For CIFAR-10, CIFAR-100 and ImageNet-100 datasets, we follow DSGD [17], where we sequentially train all 10, 100 and 100 classes in increments of 2, 10 and 10 classes per task, respectively. For CIFAR-10, we use two levels of supervision, with 30 and 150 labeled images per class. For CIFAR-100, we use four levels of supervision, with 20, 25, 80 and 125 labeled images per class. For ImageNet-100, we mainly use two levels of supervision, with 13 and 100 labeled images per class. To simplify notation, we denote the benchmark as Dataset-X (number of labeled samples per class). For example, CIFAR10-30 indicates CIFAR-10 with 30 labeled samples per class. For CUB, we follow UaD-CIE [12], a few-shot SSCL method, where the model trains on 100 classes under full supervision in the first task, and each subsequent task trains 10 classes with SSL settings, including 5 labeled images per class.
+
+Metrics. We adopt the average incremental top-1 accuracy as our primary evaluation metric: $A_{Avg} = \frac{1}{T}\sum_{t=1}^{t}A_{t}$ , where $A_{t}$ is incremental accuracy for task $t$ , defined as $A_{t} = \frac{1}{t}\sum_{t=1}^{t}a_{t,i}$ and $a_{t,i}$ is the accuracy on test set of $i^{th}$ task after learning the $t^{th}$ task. Additionally, we report the final model accuracy $A_{Last}$ in the last task as a reference.
+
+Implementation Details. We use ResNet-32 [20] as the feature extractor $F$ for the CIFAR-10 and CIFAR-100 and ResNet-18 [20] for the ImageNet-100 and CUB. For unlabeled data, we apply the data augmentation approach from FixMatch [42]. The projection head $P$ is a simple linear layer outputting 512-dimension features (i.e., $d = 512$ ), which is consistent with the dimension of the generated ETF vectors across all datasets. All loss weights $\lambda_{\mathrm{uns}}, \lambda_{\mathrm{cl}}, \lambda_{\mathrm{fsr}}$ and $\lambda_{\mathrm{cud}}$ are set to 1, and all temperature parameters $\beta, \gamma$ and $\xi$ are set to 0.1. Following [42], the confidence threshold $\tau$ is set to 0.95. We utilize the SGD optimizer with a momentum of 0.9 and the weight decay is set to $10^{-5}$ . For SSCL tasks, we use a memory buffer of size 5120, set the batch size to 64, and use a learning rate of 0.03. We train for
+
+Table 2. Comparisons on 10-task ImageNet-100. We re-run NNCSL under our setting for a direct comparison. See supplementary Sec. B.1.1 for results under the original NNCSL protocol.
+
+| Method | ImageNet100-13 | ImageNet100-100 |
| Avg | Last | Avg | Last |
| iCaRL [38] | 19.89 | 12.88 | 30.78 | 16.68 |
| NNCSL [23] | 42.19 | 33.64 | 56.78 | 53.84 |
| iCaRL&Fix [17] | 26.37 | 15.58 | 37.49 | 21.02 |
| + DSGD [17] | 28.35 | 19.14 | 50.53 | 32.10 |
| + USP (Ours) | 43.91 | 35.40 | 56.84 | 50.36 |
| DER&Fix [17] | 35.40 | 29.22 | 61.96 | 52.91 |
| + DSGD [17] | 35.73 | 31.53 | 62.27 | 52.82 |
| + USP (Ours) | 46.09 | 39.58 | 62.29 | 55.01 |
+
+200 epochs with a 10-epoch warm-up followed by a cosine scheduler to reduce the learning rate. For few-shot SSCL, we follow the settings of UaD-CIE [12] for the training parameters (see Sec. A.2 of supplementary for details).
+
+Baselines. For SSCL tasks, we primarily consider published SSCL methods, including the previous SOTA methods: DSGD [17] and NNCSL [23], as well as classic methods like CCIC [4] and ORDisCo [46]. Our main competitors is DSGD [17]. For a fair comparison, we adopt the same base SSCL learners (i.e., iCaRL&FixMatch and DER&FixMatch). Additionally, we consider converting traditional fully-supervised CL methods to SSCL setting for reference. Specifically, this adaptation involves using only labeled data during training and discarding all unlabeled data. We apply this approach to classic methods like iCaRL [38] and DER [52]. For few-shot SSCL task, we primarily compare against the previous SOTA method, UaD-CIE [12], and include several baselines used in its original paper.
+
+# 4.2. Main Results
+
+CIFAR-10 and CIFAR-100. We first report the results of different methods on CIFAR-10 and CIFAR-100 in Tab. 1. USP achieves the best performance across nearly all settings, showing even more pronounced advantages on the more challenging CIFAR-100. Both USP and DSGD are
+
+Table 3. Performance comparisons on 11-task CUB. We provide the test accuracy on different tasks and average accuracy. We replace UaD-CIE's uncertainty-based distillation with CUD and incorporate FSR and CUP into its training pipeline. For fairness, we use the official code of UaD-CIE to build USP on top of it and report the results based on our re-run of UaD-CIE.
+
+| Method | Task ID | Avg |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| SS-iCaRL [10] | 69.89 | 61.24 | 55.81 | 50.99 | 48.18 | 46.91 | 43.99 | 39.78 | 37.50 | 34.54 | 31.33 | 47.29 |
| SS-NCM [10] | 69.89 | 61.91 | 55.51 | 51.71 | 49.68 | 46.11 | 42.19 | 39.03 | 37.50 | 34.54 | 31.33 | 47.33 |
| SS-NCM-CNN [10] | 69.89 | 64.87 | 59.82 | 55.14 | 52.48 | 49.60 | 47.87 | 45.10 | 40.47 | 38.10 | 35.25 | 50.78 |
| Semi-SPPR [62] | 68.44 | 61.66 | 57.11 | 53.41 | 50.15 | 46.68 | 44.93 | 43.21 | 40.61 | 39.21 | 37.43 | 49.34 |
| Semi-CEC [55] | 75.82 | 71.91 | 68.52 | 63.53 | 62.45 | 58.27 | 57.62 | 55.81 | 54.85 | 53.52 | 52.26 | 61.32 |
| Us-KD [11] | 74.69 | 71.71 | 69.04 | 65.08 | 63.60 | 60.96 | 59.06 | 58.68 | 57.01 | 56.41 | 55.54 | 62.89 |
| UaD-CIE [12] | 75.87 | 73.05 | 69.50 | 65.61 | 64.37 | 61.84 | 61.49 | 58.93 | 56.95 | 56.21 | 55.66 | 64.33 |
| + USP (Ours) | 78.21 | 74.48 | 71.81 | 68.16 | 67.58 | 64.77 | 62.87 | 62.27 | 59.97 | 60.10 | 60.55 | 66.43 |
+
+Table 4. Base and novel classes accuracy on 11-task CUB. Base classes refer to the classes used for fully supervised training on the first task, while novel classes refer to non-base classes trained on in subsequent tasks.
+
+| Method | Classes | Task ID | Avg |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| SS-iCaRL [10] | Base | 69.89 | 62.32 | 60.62 | 58.99 | 58.59 | 57.77 | 59.88 | 56.21 | 54.46 | 50.54 | 46.11 | 57.76 |
| Novel | - | 53.22 | 32.38 | 24.07 | 22.76 | 23.34 | 17.58 | 16.40 | 16.39 | 16.13 | 16.32 | 23.86 |
| SS-NCM-CNN [10] | Base | 69.89 | 65.80 | 64.97 | 63.79 | 63.81 | 61.08 | 65.24 | 63.73 | 58.77 | 55.74 | 51.88 | 62.24 |
| Novel | - | 56.37 | 34.70 | 26.03 | 24.04 | 24.68 | 19.14 | 18.60 | 17.70 | 17.79 | 18.36 | 25.74 |
| UaD-CIE [12] | Base | 75.87 | 74.58 | 74.09 | 73.46 | 72.24 | 71.68 | 71.33 | 70.50 | 70.15 | 69.27 | 69.13 | 72.03 |
| Novel | - | 57.35 | 46.29 | 39.58 | 45.02 | 42.54 | 45.37 | 42.75 | 40.82 | 41.98 | 42.49 | 44.42 |
| +USP (Ours) | Base | 78.21 | 75.00 | 74.13 | 73.36 | 72.42 | 70.74 | 68.99 | 68.44 | 67.25 | 66.62 | 66.66 | 71.07 |
| Novel | - | 69.18 | 60.07 | 50.93 | 55.67 | 53.08 | 52.86 | 53.64 | 51.07 | 53.00 | 54.57 | 55.41 |
+
+based on distillation, but on CIFAR-10/-100, USP achieves an approximately $1 - 6\%$ higher $A_{Avg}$ and $A_{Last}$ than DSGD using the same SSCL learner. These results indicate that USP is overall more robust than DSGD, specifically demonstrating a significant advantage in stability.
+
+ImageNet-100. The results on ImageNet-100 are shown in Tab. 2, where it can be seen that USP significantly outperforms DSGD in both average accuracy and final task accuracy. As with the results on CIFAR, USP demonstrates a more pronounced advantage when the amount of labeled data is smaller, indicating higher efficiency in utilizing unlabeled data. Notably, compared to DSGD, USP shows a smaller difference between the average and the final accuracy under the same task settings, suggesting that USP achieves more stable performance across different training task and is better at mitigating forgetting than DSGD.
+
+CUB. The results on CUB are shown in Tab. 3. We conduct experiments on CUB following few-shot SSCL setting, comparing USP with the sota method UaD-CIE. USP can effectively improve the performance of UaD-CIE. To further illustrate USP's effectiveness, we report base class and novel class accuracies across different training task, in Tab. 4. We observe that our method shows only a slight drop in base class accuracy compared to UaD-CIE (0.96%), yet achieves a substantial improvement in novel class accuracy (10.99%). UaD-CIE mitigates forgetting in base classes by applying uncertainty-based loss weighting to corresponding
+
+
+(a) Training phase
+
+
+(b) Testing phase
+Figure 4. Ablation studies on the main components of USP. The experiments are conducted on CIFAR-10 with 30 labels per class.
+
+labeled samples. In contrast, USP leverages unlabeled samples and employs CUD distillation strategy to support old class learning. This effective distillation allows us to further enhance novel class learning through our DCP.
+
+In addition to the standard settings, more realistic SSCL settings are provided in Sec. B.1 of supplementary.
+
+# 4.3. Ablation Analysis and Discussions
+
+We perform extensive ablation studies on the components and training strategies of USP. By default, our experiments are all based on iCaRL&Fix. More ablations on distillation methods (Sec. B.2.2), hyper-parameters (Sec. B.2.3), backbones/pre-training (Sec. B.2.4) and different memory buffer sizes (Sec. B.3) can be found in the supplementary.
+
+
+Figure 5. Pseudo-label accuracy of different pseudo-labeling strategies on CIFAR100-20. The y-axis represents the pseudo-label accuracy, and the x-axis represents the number of training epochs. We present the results for different training tasks.
+
+Ablation on Method Components. We conduct ablation experiments on the main components of USP. With the basic SSCL learner training objective, USP incorporates the ETF-based feature space reservation (FSR) loss $\mathcal{L}_{\mathrm{fsr}}$ , the unsupervised training loss $\mathcal{L}_{\mathrm{uns}}^{\prime}$ with our divide and conquer pseudo-labeling (DCP) strategy, and the class-mean-anchored unlabeled distillation (CUD) loss $\mathcal{L}_{\mathrm{cud}}$ . To examine the effects of these modules, we ablate these losses, which is denoted as "wo. $\mathcal{L}_{\mathrm{fsr}}$ ", "wo. $\mathcal{L}_{\mathrm{uns}}^{\prime}$ " and "wo. $\mathcal{L}_{\mathrm{cud}}$ ", respectively. As shown in Fig. 4a, each component of USP contributes to improved model performance, with the DCP strategy having the most substantial impact on USP performance. To further investigate this, we conduct additional experiments by replacing DCP with alternative approaches: a classifier-based pseudo-labeling strategy ("P-CLS"), an NCM-based pseudo-labeling strategy ("P-NCM"), and a hybrid strategy where high-confidence samples use NCM pseudo-labels while low-confidence samples use classifier pseudo-labels ("P-R"). All these replacements lead to varying degrees of performance degradation, with P-R showing the most substantial decline, further underscoring the rationale behind our DCP. In Fig. 5, we further experiment to illustrate the reasons for its effectiveness. Additionally, we perform an ablation study on DCP used in testing phase. Fig. 4b presents results for classifier-only inference ("T-CLS") and NCM-only inference ("T-NCM") in isolation. Our DCP again achieves the best performance. While the improvement over NCM alone is not substantial, our strategy is a "free lunch" benefit.
+
+Effect of Pseudo-Labeling Strategy. To demonstrate the effectiveness of DCP, we present the pseudo-label accuracy across different tasks on CIFAR100-20 in Fig. 5, comparing DCP with the traditional classifier pseudo-labeling strategy. Considering DCP fully utilizes unlabeled data, for a direct comparison of pseudo-label quality, we do not apply a confidence threshold to the classifier pseudo-labeling approach (see Tab. 7 of supplementary for more comparison with thresholded pseudo-labeling). In the first task, our accuracy is comparable to the classifier's. However, as training progresses, DCP significantly outperforms the classifier, with an increasing advantage in later tasks.
+
+
+Figure 6. Average accuracy on CIFAR10-30 with different values of each loss weight (i.e., $\lambda_{\mathrm{fsr}}$ , $\lambda_{\mathrm{uns}}$ and $\lambda_{\mathrm{cod}}$ ).
+
+During incremental training, the classifier faces stability-plasticity trade-offs, resulting in performance degradation. In contrast, the NCM classifier, leveraging feature similarity, is less affected by incremental training and achieves higher accuracy on low-confidence samples. DCP effectively combines the strengths of both methods, enhancing overall pseudo-label accuracy. To illustrate this, we report the pseudo-label accuracy of both approaches on low-confidence samples (confidence $< \tau$ ), where the NCM's higher accuracy affirms the rationale behind DCP.
+
+Loss Weights. We traverse the values of $\{0.1, 0.5, 1, 1.5, 2\}$ to separately set the each weights (i.e., $\lambda_{\mathrm{fsr}}$ , $\lambda_{\mathrm{uns}}$ , and $\lambda_{\mathrm{cod}}$ ) while keeping the other two weights fixed at 1.0. We report the average incremental accuracy of the model on CIFAR10-30 under different weight coefficients, as shown in Fig. 6. The model achieves the best performance when the weights are set to 1.0, and we observe that the model's final performance fluctuates within $2\%$ across different weight coefficients, indicating that our method is not sensitive to the choice of weight coefficients.
+
+# 5. Conclusion
+
+We propose a divide-and-conquer SSCL framework called USP, comprising three main components: (1) ETF-based feature space reservation (FSR) strategy for learning plasticity; (2) divide-and-conquer pseudo-labeling (DCP) approach for unlabeled learning; and (3) class-mean-anchored unlabeled distillation (CUD) for memory stability, which are designed to synergistically enhance the SSCL model. In future work, we plan to adapt our USP into more SSCL paradigms to further contribute to the community.
+
+# Acknowledgments
+
+Yue Duan, Taicai Chen and Yinghuan Shi are with the National Key Laboratory for Novel Software Technology and the National Institute of Healthcare Data Science, Nanjing University. Lei Qi is with the School of Computer Science and Engineering, Southeast University. This work is supported by NSFC Project (624B2063, 62222604, 62206052), China Postdoctoral Science Foundation (2024M750424), Fundamental Research Funds for the Central Universities (020214380120, 020214380128), State Key Laboratory Fund (ZZKT2024A14, ZZKT2025B05), Postdoctoral Fellowship Program of CPSF (GZC20240252), Jiangsu Funding Program for Excellent Postdoctoral Talent (2024ZB242) and Jiangsu Science and Technology Major Project (BG2024031).
+
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+# Diving into the Fusion of Monocular Priors for Generalized Stereo Matching
+
+Chengtang Yao $^{1,2}$ , Lidong Yu $^{3}$ , Zhidan Liu $^{1,2}$ , Jiaxi Zeng $^{1,2}$ , Yuwei Wu $^{1,2*}$ , Yunde Jia $^{2,1*}$ $^{1}$ Beijing Key Laboratory of Intelligent Information Technology, School of Computer Science & Technology, Beijing Institute of Technology, China
+ $^{2}$ Guangdong Laboratory of Machine Perception and Intelligent Computing, Shenzhen MSU-BIT University, China
+ $^{3}$ NVIDIA
+
+{zdliu, wuyuwei, jiayunde}@bit.edu.cn
+{yao.c.t.adam, yvlidong, jiaxizeng.jx}@gmail.com
+
+
+
+HuggingFace
+
+
+
+GitHub Repo
+
+
+
+Model Weights
+
+Download
+
+# Abstract
+
+The matching formulation makes it naturally hard for the stereo matching to handle ill-posed regions like occlusions and non-Lambertian surfaces. Fusing monocular priors has been proven helpful for ill-posed matching, but the biased monocular prior learned from small stereo datasets constrains the generalization. Recently, stereo matching has progressed by leveraging the unbiased monocular prior from the vision foundation model (VFM) to improve the generalization in ill-posed regions. We dive into the fusion process and observe three main problems limiting the fusion of the VFM monocular prior. The first problem is the misalignment between affine-invariant relative monocular depth and absolute depth of disparity. Besides, when we use the monocular feature in an iterative update structure, the over-confidence in the disparity update leads to local optima results. A direct fusion of a monocular depth map could alleviate the local optima problem, but noisy disparity results computed at the first several iterations will misguide the fusion. In this paper, we propose a binary local ordering map to guide the fusion, which converts the depth map into a binary relative format, unifying the relative and absolute depth representation. The computed local ordering map is also used to re-weight the initial disparity update, resolving the local optima and noisy problem. In addition, we formulate the final direct fusion of monocular depth to the disparity as a registration problem, where a pixel-wise linear regression module can globally and adaptively align them. Our method fully exploits the monocular prior to support stereo matching results effectively and efficiently. We significantly improve the performance from the experiments when generalizing from SceneFlow to Middlebury and Booster datasets while barely reducing the efficiency.
+
+# 1. Introduction
+
+Stereo matching provides dense depth for various downstream applications, such as autonomous driving, robotics, AR/MR, etc. These applications require stereo matching to generalize across different scenes from wild worlds. However, the generalization of stereo matching becomes poor in ill-posed regions due to occlusion, texture-less, and non-Lambertian surfaces (e.g., reflective or transparent surfaces). Fusion of monocular priors is proven to help correct the ill-posed binocular matching results [9, 15, 18, 22, 23, 33, 47, 54]. But the monocular prior trained on the limited data distribution of stereo datasets is susceptible to domain bias and can only capture significantly biased monocular features for certain scenes [13, 30].
+
+Taking advantage of large-scale scenes and the easily collected ground truth of monocular depth, the vision foundation model can provide an unbiased monocular prior [16, 48, 49]. Recently, some methods have made great progress in fusing the unbiased monocular prior into the stereo matching to improve the generalization in ill-posed regions [3, 8, 46]. In this paper, we dive into the fusion mechanism and find three main problems limiting a full exploration of the unbiased monocular prior. The first problem lies in the natural gap between the affine-invariant relative depth from monocular depth and absolute depth from disparity. Although we can forcibly align the two kinds of depth with a complex mutual refinement, these alignments could involve heavy computation and greatly harm the efficiency [8, 46]. The other problem exists in the fusion with monocular feature maps in an iterative refinement structure [7, 43, 47]. The implicit feature fusion makes the fusion more biased to the binocular information due to the iterative update training scheme, where the over-confidence of the disparity update causes local optima, as shown in Figure 1. An additional fusion of monocular depth could alleviate
+
+
+Figure 1. The visualization of different ill-posed regions in the Booster dataset. Our method achieves an overwhelming advantage in all kinds of regions.
+
+local optima, but direct fusion of the depth is easily affected by noisy depth results. Even with unbiased, smooth monocular depths from the VFM, noisy disparity in the first several iterations slows down good fusion.
+
+In this paper, we present a new depth representation called the local binary ordering map that indicates whether two pixels are farther or closer. It converts the depth into a binary relative depth representation, unifying the monocular depth and binocular disparity. The local binary order map also guides fusion in an explicit manner, which restricts the influence of the large noise from outliers. Furthermore, we formulate the binocular disparity map as a noisy version of monocular depth registered by specific pixel-wise scale and shift. Therefore, the alignment between monocular depth and binocular disparity can be deemed a noisy linear regression problem about the registration parameters. The registration formulation globally and adaptively aligns the two kinds of depth in an efficient manner.
+
+Our network can be divided into three modules. The monocular encoder extracts unbiased monocular priors, including monocular depth and context features, using a large pre-trained monocular network like [48-50]. Then, the fusion can be realized by an iterative local fusion module and a global fusion module to fully exploit the usage of the monocular priors with matching information. The iterative local fusion module uses a two-stream architecture to update the disparity iteratively. The first stream computes two binary ordering maps from monocular depth and binocular disparity through a series of LBP-like convolution blocks.
+
+Then, we compute the differences between the two binary ordering maps to form a local guidance for fusion. At the same time, the second stream predicts an initial disparity update result through a multi-level GRU using cost volume and monocular context features. The local guidance is used to re-weight the initial disparity update result, resolving the local optima. After local fusion, the global fusion module realizes the optimization of the disparity map by registering to monocular depth. We first compute two parameters to register the relative depth to the absolute depth globally. It solves the noisy linear regression problem between optimized disparity and monocular depth through a series of convolutions. Then, we compute a confidence map using the cost volume, the hidden state of GRU, and the local guidance from the last iteration. The confidence map guides the fusion of the optimized binocular disparity and the registered monocular depth as the final prediction.
+
+We compare our model with SOTA methods under the standard setting: training on SceneFlow and testing on five real-world datasets (KITTI 2012&2015, Middlebury, ETH3D, and Booster) with various ill-posed regions. Results demonstrate our method significantly boosts SOTA performance, as shown in Figure 1. Our method achieves a 10-point improvement in the bad2 metric for transparent regions on Booster and reduces errors by over $50\%$ on Middlebury and ETH3D, without using extra stereo data or specific augmentation. Despite involving a VTF model, it barely increases the time cost due to the elegant designs.
+
+# 2. Related Work
+
+# 2.1. Generalized Stereo Matching
+
+Generalized stereo matching aims to produce a reliable dense disparity map when the target domain (e.g., real-world data) differs from the source domain (e.g., synthetic data). Some methods focus on learning domain-invariant features [4, 9, 17, 22, 33, 40, 54]. MS-PSMNet [4] replaces learning-based features with hand-crafted ones to force the stereo network to focus on the matching space. Although it achieves significant improvement, its hand-crafted features limit the performance. Thus, many methods improve training via transfer learning [22], meta-learning [17, 40], contrastive learning [33, 54], and Fisher information [9].
+
+The above feature-based methods significantly improve stereo matching generalization. However, due to real-world complexity, they struggle to eliminate domain gaps. Some researchers integrate other modalities to enrich RGB features [42, 52], achieving strong performance but requiring extra devices. Others instead generate more and better training data [3, 5, 39, 41, 46]. AdaStereo [39] and HVT-RAFT [5] augment data in color space to enrich domain distribution. While effective, rendered images remain unrealistic. Thus, NerfStereo [41] reconstructs real scenes via NeRF and re-renders stereo images to improve training quality.
+
+Beyond improving generalization through features and data, some methods focus on architecture design leveraging stereo-specific knowledge [7, 12, 14, 20, 43, 47, 53]. DSMNet [53] uses long-range matching in cost aggregation to correct mismatches. While effective, its 3D operations are time-consuming. Many later methods incorporate global information in cost volume construction. STTR [20] and CSTR [14] apply transformers to capture long-range dependencies. Others [7, 43, 47] build auxiliary volumes to enhance the original cost volume. Some approaches also improve generalization via uncertainty learning [15, 23].
+
+The aforementioned approaches have achieved great performance but still rely on biased monocular priors. Our method introduces unbiased monocular priors from a pretrained large model and uses effective fusion mechanisms to fuse them, achieving impressive generalization ability.
+
+# 2.2. Fusing Monocular and Stereo Estimation
+
+Inspired by the human visual system fusing binocular disparity and monocular cues [3, 8, 10, 34, 44-46], researchers have explored similar fusion mechanisms in machine vision. Traditional methods [35] use MRF optimization based on disparity and monocular cues. Deep learning methods mainly adopt volume or depth map fusion [3, 8, 46]. Volume fusion injects monocular priors into cost volumes [3, 8, 19, 46, 51], but relies on fixed disparity ranges and domain-biased priors. In contrast, our method removes disparity range limits and uses unbiased priors from
+
+a large pre-trained model. Depth map fusion methods [1, 2, 6, 24, 55] combine monocular and binocular results in post-processing, but often suffer from misalignment and noise due to affine-invariant monocular predictions. Instead, we employ local ordering maps for better compatibility, reducing noise during matching. The final monocular depth is globally aligned to the optimized disparity by learning two parameters to address scale ambiguity.
+
+# 3. Method
+
+Our network structure is illustrated in Figure 2. First, we extract features from the left and right images to construct a cost volume. Meanwhile, the monocular encoder module extracts initial hidden states, context features, and monocular depth from the left image using a pre-trained large monocular model [49]. Then, the local fusion module iteratively optimizes the disparity estimation with monocular priors using the local binary ordering map. Finally, the global fusion module registers the optimized disparity with the monocular depth as the final result.
+
+# 3.1. Monocular Encoder
+
+The monocular priors learned by the stereo-matching model are heavily biased due to the scarcity of wild-world stereo data [13, 30]. This paper uses the widely used DepthAnything v2[49] to extract unbiased monocular priors to mitigate the domain gap, including monocular context features and depth. However, it is flexible to use other VTFs as long as the monocular prior is not biased to specific scenarios.
+
+As shown in Figure 2, given an image with a resolution of $H \times W$ , we pre-process the image as DepthAnything v2 [49] by resizing the longest side of the image to 512 pixels. The resized image is then fed into a frozen DepthAnything v2 to extract intermediate features before the DPTHead [32] and monocular depth after the DPTHead. These intermediate features and monocular depth are subsequently resized to a $H/4 \times W/4$ resolution using a bilinear function to interact with the stereo-matching pipeline. We build a two-stream convolution module to generate the initial hidden state and monocular context features from the intermediate features. Although both the prediction and supervision of DepthAnything v2 are in the form of inverse depth, which is disparity under some unknown camera parameters and baseline, we still refer to it as monocular depth here to maintain consistency with the terminology used in DepthAnything v2.
+
+# 3.2. Iterative Local Fusion
+
+The iterative local fusion module leverages the binary local ordering map to update disparity with monocular priors iteratively. The binary ordering map $M_O$ encodes the relative ordering of depth $D$ between a center pixel and its neigh-
+
+
+Figure 2. The pipeline of our method. $\widehat{\mathbb{W}}$ represents the warping operation when constructing the cost volume. $①$ is look up operation used to sample cost volume. $\text{已}$ represents concatenation. $\oplus$ represents add operation, while $\otimes$ represents multiplication.
+
+bors:
+
+$$
+M _ {O} (u, v) = \left\{\sigma \left(D \left(u ^ {\prime}, v ^ {\prime}\right) - D (u, v)\right) \right\}, \tag {1}
+$$
+
+where $(u', v') \in \mathcal{N}_{(u, v)}$ , $\sigma$ is the sigmoid function and $\mathcal{N}$ is the neighborhood. The binary local ordering map helps mitigate the impact of outlier noises by converting absolute values into ordering relationships, which is much more robust than the pixel-wise depth value. Besides, it also unifies the affine-invariant depth and absolute disparity to be compatible with the order relationship.
+
+To compute the binary local ordering map, we use a series of LBP-like operations [28, 29] with varying window sizes to extract local ordering features. Each LBP-like operation consists of a convolution with fixed weights followed by a sigmoid function, which measures the relative depth relationships between the center pixel of the window and its neighboring pixels, indicating which pixels are closer
+
+or farther. To employ the binary local ordering map into the iterative refinement structure, we use the LBP-like encoder to extract local ordering maps from both monocular depth and binocular disparity in the previous iteration, as shown in Figure 2. These two kinds of local ordering maps are concatenated to predict the monocular guidance. The guidance $G$ is modeled by a Beta distribution with parameters $\{\alpha, \beta\}$ predicted via convolutions. During training, $G$ is sampled via reparameterization: $G = g_1 / (g_1 + g_2)$ , $g_1 \sim \mathrm{Gamma}(\alpha, 1)$ , $g_2 \sim \mathrm{Gamma}(\beta, 1)$ . At test time, $G = \alpha / (\alpha + \beta)$ . The guidance $G$ is then used to re-weight the initial disparity update $\Delta_d$ to avoid local optima.
+
+As we mentioned, the first several disparity predictions are noisy, especially during training. The local ordering map may still have many wrong relative depth values, leading to wrong guidance and slow training convergence. Therefore, we propose to gradually release the influence of
+
+guidance to the initial disparity update results as
+
+$$
+\tilde {\Delta} _ {d} = \Delta_ {d} (1 + G \cdot r \cdot t / T). \qquad (2)
+$$
+
+Here, $r$ is the manually specified amplitude parameter that controls the influence of the guidance. $t$ represents the current iteration number, and $T$ is the total number of iterations. The initial disparity update $\Delta_d$ is predicted by a multi-level GRU followed by a convolution block. Finally, the disparity is updated by adding the re-weighted disparity update to the disparity from the previous iteration:
+
+$$
+D _ {d} ^ {t} = D _ {d} ^ {t - 1} + \tilde {\Delta} _ {d}. \tag {3}
+$$
+
+# 3.3. Global Fusion
+
+After all iterations of disparity update, we use a global fusion module to incorporate fine-grained 3D shape priors from the monocular depth map into the disparity map, as shown in Figure 2. Here, we formulate the optimized binocular disparity as a registered version of monocular depth with minor noise by specific intrinsic parameters. Therefore, monocular depth can be globally registered to binocular disparity. The registration can be deemed a linear regression problem with noise between monocular depth and binocular disparity. To this end, we first align the monocular depth $D_{m}$ with the optimized disparity $D_{d}$ by estimating two registration parameters, $a, b$ by
+
+$$
+\tilde {D} _ {m} = a \cdot D _ {m} + b, \tag {4}
+$$
+
+$$
+a, b = \mathcal {F} (D _ {m}, D _ {d} ^ {T}),
+$$
+
+where $\mathcal{F}$ represents a network with a series of convolution layers and ReLU activation, which take the concatenation of the monocular depth $D_{m}$ and the optimized disparity $D_d^T$ as input. Simultaneously, we use the sampled cost volume, hidden state, and weights from the previous iteration to predict a confidence map. This confidence, $c$ , is then used to fuse the aligned monocular depth $\tilde{D}_m$ and the optimized disparity $D_{d}$ as follows
+
+$$
+D _ {f} = c \cdot D _ {d} ^ {T} + (1 - c) \cdot \tilde {D} _ {m}. \qquad (5)
+$$
+
+$D_{f}$ is the final disparity prediction.
+
+# 3.4. Loss
+
+We use $L_{1}$ loss to supervised the learning of each updated disparity $D_{d}^{t}$ , registered monocular depth $\tilde{D}_{m}$ , and the final output of our method $D_{f}$ :
+
+$$
+\begin{array}{l} \mathcal {L} = \sum_ {t = 1} ^ {T} \gamma^ {T + 2 - t} \left| \left| D _ {d} ^ {t} - D _ {G} \right| \right| _ {1} \tag {6} \\ + \gamma | | \tilde {D} _ {m} - D _ {G} | | _ {1} + | | D _ {f} - D _ {G} | | _ {1}. \\ \end{array}
+$$
+
+$D_G$ is the ground-truth disparity. $\gamma$ is the balancing scalar.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+For the stereo part, our pipeline is built on the classical iterative structure of RAFT-Stereo [21], which is widely used and flexible to deploy without stacking network tricks to raise the computation burden. As for the monocular part, we use DepthAnything V2 [48, 49] to extract unbiased monocular priors. Still, it is flexible to use other VTFs as long as the monocular prior is generalizable to practical scenarios. We set parameters as $r = 1$ and $\gamma = 0.9$ . The window sizes for the LBP-like operations are configured to 5, 3. The training was conducted on 4 NVIDIA A40 GPUs using the AdamW optimizer with a one-cycle learning rate schedule. During training, the DepthAnything V2 module remains frozen. Specifically, we first train the model without the global fusion module on the SceneFlow dataset, using a maximum learning rate of 0.0002, a batch size of 8, and for 100k steps, maintaining the consistency of matching parts with the total data used in RAFT-Stereo. Then, we train the monocular registration of the global fusion module while keeping the other modules frozen, using a maximum learning rate of 0.0005 and a batch size of 32 for 100k steps on the SceneFlow dataset. Finally, we train the entire global fusion module while keeping the other modules frozen, using a maximum learning rate of 0.0005, a batch size of 32, and 100k steps on the SceneFlow dataset. Our results are not sensitive to the hyperparameters of the training process.
+
+# 4.2. Evaluation
+
+Datasets. Domain generalized stereo matching is typically trained on the SceneFlow dataset [25] and evaluated on the training sets of various real-world datasets. We select five real-world datasets, each containing different ill-posed regions, to evaluate the in-the-wild generalization ability of the models, including KITTI 2012 [11], KITTI 2015 [26, 27], Middlebury [36], ETH3D [37], and Booster [31].
+
+Metrics. (1) We use two metrics: EPE, which measures the mean absolute disparity error in pixels, and Bad $x$ , which represents the percentage of pixels where the predicted disparity deviates from the ground truth by at least $x$ pixels. (2) It is important to note that many recent methods report their results with some implicit assumptions, such as evaluating only pixels with ground truth disparity less than 192 or only evaluating non-occluded regions. In our experiments, unless otherwise specified, both ours and the compared methods consider all regions as the classical metric does without limitations. For the Middlebury dataset, we evaluate both all regions and non-occluded regions. For the Booster dataset, we evaluate all regions, as well as transparent and non-transparent regions. (3) Additionally, we observe fluctuations in model performance when trained with different numbers of steps. To fully analyze the improvement con
+
+| Method | Year | Additional Data/Aug | KITTI 2015 | KITTI 2012 | Middlebury (H) | ETH3D | |
| EPE | bad 3.0 | EPE | bad 3.0 | All EPE | bad 2.0 | NonOcc EPE | bad 2.0 | Occ EPE | bad 1.0 | | |
| FC-PSMNet [54] | 2022 | | 1.58 | 7.50 | 1.42 | 7 | 4.14 | 18.3 | - | - | - | 1.25 | 12.8 | |
| ITSA-PSMNet [9] | 2022 | | 1.39 | 5.80 | 1.09 | 5.2 | 3.25 | 12.7 | - | - | - | 0.94 | 9.8 | |
| Graft-PSMNet [22] | 2022 | | 1.32 | 5.30 | 1.09 | 5 | 2.34 | 10.9 | - | - | - | 1.16 | 10.7 | |
| Mask-CFNet [33] | 2023 | | - | 5.80 | - | 4.8 | - | 13.7 | - | - | - | - | 5.7 | |
| STTR* [20] | 2021 | | 2.14 | 9.5 | 2.51 | 9.62 | 9.13 | 21.76 | 5.03 | 13.49 | 35.98 | 78.84 | - | |
| PCWNet [38] | 2022 | | - | 5.60 | - | 4.2 | - | 15.8 | - | 15.8 | - | 3.8 | 14.4 | |
| RAFTStereo* [21] | 2021 | | 1.13 | 5.69 | 0.9 | 4.35 | 1.92 | 12.6 | 1.09 | 8.65 | 3.31 | 26.39 | 0.36 | 3.3 |
| IGEV* [47] | 2023 | | 1.21 | 6.03 | 1.03 | 5.13 | 2.63 | 11.93 | 2.27 | 9.49 | 5.02 | 26.04 | 0.33 | 4 |
| ELFNet* [23] | 2023 | | 2.31 | 7.68 | 1.36 | 5.85 | 5.16 | 17.5 | 2.16 | 10.14 | - | - | - | - |
| Mocha-Stereo* [7] | 2024 | | 1.29 | 5.97 | 1.02 | 4.83 | 2.66 | 10.18 | 2.49 | 7.96 | 3.84 | 24.16 | 0.28 | 3.47 |
| NMRF* [12] | 2024 | | 1.17 | 5.31 | 0.92 | 4.63 | 2.91 | 13.36 | 2.73 | 10.90 | - | - | 0.31 | 3.8 |
| Selective-RAFT* [43] | 2024 | | 1.27 | 6.68 | 1.08 | 5.19 | 2.34 | 12.04 | 2.05 | 9.45 | 4.17 | 27.4 | 0.34 | 4.36 |
| Selective-IGEV* [43] | 2024 | | 1.25 | 6.06 | 1.08 | 5.64 | 2.59 | 11.79 | 2.31 | 9.22 | 4.35 | 28.10 | 0.33 | 4.05 |
| HVT-RAFT [5] | 2023 | ✓ | 1.12 | 5.20 | 0.87 | 3.7 | 1.37 | 10.40 | - | - | - | - | 0.29 | 3.00 |
| NerfStereo* [41] | 2023 | ✓ | 1.14 | 5.41 | 0.84 | 3.6 | 1.42 | 9.67 | 0.91 | 6.39 | 4.09 | 29.89 | 0.29 | 2.94 |
| RAFT-Stereo + ME Ours | | | 1.18 | 6.18 | 0.87 | 4.19 | 1.42 | 9.73 | 1.11 | 7.00 | 3.06 | 26.50 | 0.26 | 2.31 |
| | 1.12 | 5.60 | 0.87 | 4.10 | 1.15 | 8.39 | 0.85 | 5.67 | 2.89 | 26.50 | 0.25 | 1.88 |
+
+Table 1. Generalization from SceneFlow dataset to KITTI2015, KITTI 2012, Middlebury (H), and ETH3D dataset. 'ME' represents our monocular encoder module. * represents the results evaluated in our metrics and settings using official models and weights. 'All', 'NonOcc', and 'Occ' represent all regions, non-occluded regions, and occluded regions, respectively.
+
+| Method | Additional Data/Aug | Booster (Q) |
| ALL | Trans | NonTrans |
| EPE | bad 2.0 | bad 3.0 | bad 5.0 | EPE | bad 2.0 | bad 3.0 | bad 5.0 | EPE | bad 2.0 | bad 3.0 | bad 5.0 |
| Mocha-Stereo [7] | | 3.88 | 16.82 | 14.31 | 11.84 | 9.45 | 66.44 | 57.96 | 45.73 | 2.89 | 12.31 | 10.19 | 8.38 |
| ELFNet [23] | | 6.05 | 24.51 | 20.43 | 16.40 | 9.03 | 72.07 | 62.73 | 49.82 | 5.33 | 20.85 | 17.18 | 13.84 |
| Selective-RAFT [43] | | 4.14 | 19.52 | 16.69 | 13.63 | 10.34 | 69.84 | 61.64 | 49.55 | 2.99 | 14.99 | 12.44 | 10.00 |
| Selective-IGEV [43] | | 4.62 | 19.28 | 16.58 | 13.92 | 9.50 | 66.85 | 58.9 | 47.15 | 3.60 | 14.74 | 12.34 | 10.27 |
| IGEV [47] | | 4.26 | 17.58 | 15.21 | 12.89 | 10.00 | 68.96 | 61.14 | 49.51 | 3.25 | 12.99 | 10.94 | 9.24 |
| NMRF [12] | | 5.05 | 26.22 | 21.31 | 16.58 | 10.36 | 70.92 | 60.93 | 47.16 | 4.00 | 22.43 | 17.77 | 13.50 |
| NerfStereo [41] | ✓ | 3.48 | 13.40 | 11.13 | 9.22 | 8.88 | 62.67 | 53.35 | 41.79 | 2.49 | 9.06 | 7.19 | 5.89 |
| RAFTstereo [21] | | 4.18 | 17.64 | 14.92 | 12.23 | 9.79 | 67.69 | 59.31 | 47.40 | 3.23 | 13.13 | 10.75 | 8.70 |
| RAFT-Stereo + ME Ours | | 2.40 | 11.44 | 9.17 | 7.30 | 8.97 | 64.84 | 56.05 | 43.95 | 1.45 | 6.96 | 5.08 | 3.89 |
| 2.26 | 11.02 | 8.59 | 6.6 | 7.93 | 59.83 | 50.36 | 38.44 | 1.52 | 6.98 | 4.97 | 3.64 |
+
+tributed by each model component, we calculate the mean and standard deviation (std) of results from the last 100k, 90k, and 80k training steps. We use mean $\pm$ std to measure the accuracy and robustness of our model.
+
+# 4.3. In-the-wild Generalization Ability
+
+Table 2. Generalization from SceneFlow dataset to Booster dataset in quarter resolution and balanced set. 'ME' represents our monocular encoder module. 'All', 'Trans', and 'NonTrans' represent all regions, transparent regions, and nontransparent regions, respectively.
+
+| Method | Additional Data/Aug | DrivingStereo |
| Sunny | Cloudy | Rainy | Foggy |
| RAFTStereo [21] | | 1.01 | 0.97 | 1.8 | 0.95 |
| IGEV [47] | | 1.11 | 1.11 | 2.32 | 1.14 |
| MoCha-Stereo [7] | | 1.01 | 0.99 | 1.35 | 0.98 |
| Selective-IGEV [43] | | 1.18 | 1.13 | 2.22 | 1.12 |
| NerfStereo [41] | ✓ | 0.90 | 0.91 | 1.46 | 1.01 |
| Ours | | 0.93 | 0.92 | 1.29 | 0.93 |
+
+Table 3. Generalization from SceneFlow to DrivingStereo. EPE is used as the evaluation metric.
+
+As shown in Table 1, our method achieves state-of-the-art results across all datasets, with particularly strong performance on Middlebury and ETH3D. Compared to other methods that do not use additional data or augmentation, we almost double their performance. Even when compared to methods incorporating additional data or augmentation, our approach leverages limited stereo data to achieve superior results. Furthermore, as presented in Table 2, our method demonstrates substantial improvements in the Booster dataset. Compared to methods without additional data or augmentation, we nearly double the improvement on EPE and Bad 5.0 across all regions, achieve more than a 10-point improvement on Bad x.0 in transparent regions, and show double or even triple the improvement in nontransparent regions. For more detailed quantitative results and analysis, please refer to our supplementary materials.
+
+We also provide visualization results on the Booster
+
+| Method | All | NonOcc | Occ |
| EPE ↓ | bad 2.0 ↓ | EPE ↓ | bad 2.0 ↓ | EPE ↓ | bad 2.0 ↓ |
| DA V2 - M | 205.04 | 99.99 | 207.51 | 99.99 | 196.96 | 99.98 |
| DA V2 - GA | 5.83 | 69.28 | 5.61 | 69.16 | 6.95 | 69.34 |
| Metric3D | 33.14 | 97.18 | 33.05 | 97.06 | 34.54 | 98.09 |
| Ours | 1.15 | 8.39 | 0.85 | 5.67 | 2.89 | 26.50 |
+
+(a) Metric disparity space
+
+| Method | All | NonOcc | Occ |
| δ1↑ | RMS ↓ | δ1↑ | RMS ↓ | δ1↑ | RMS ↓ |
| DA V2 - M | 0.022 | 6.356 | 0.024 | 6.171 | 0.008 | 7.189 |
| DA V2 - GA | 0.923 | 1.487 | 0.934 | 1.342 | 0.852 | 2.022 |
| Metric3D | 0.288 | 4.097 | 0.298 | 4.014 | 0.223 | 4.588 |
| Ours | 0.985 | 0.677 | 0.991 | 0.492 | 0.948 | 1.282 |
+
+(b) Metric depth space
+Table 4. Comparison to DepthAnything V2 and Metric3D on Middlebury (H). M: the fine-tuned metric version. GA: alignment to GT scale using identical registration parameters computed from GT for all pixels.
+
+| Exp | Middlebury (H) |
| epe | bad 2.0 |
| Baseline | 2.11±0.16 | 14.12±0.64 |
| Baseline w/o mono feature | 1.83±0.11 | 12.45±0.86 |
| Baseline + ME | 1.42±0.01 | 9.81±0.18 |
| Baseline + ME + IDF | 1.41±0.04 | 10.34±0.19 |
| Baseline + ME + PF | 1.41±0.00 | 9.71±0.00 |
| Baseline + ME + ILF | 1.20±0.08 | 9.06±0.70 |
| Baseline + ME + ILF + GF | 1.15±0.01 | 8.35±0.04 |
+
+
+Monocular
+
+
+t=1
+
+
+t=2
+
+
+t=4
+
+
+t=7
+
+
+t=12
+Figure 3. The visualization of local ordering map. The monocular represents the results from monocular depth. $t = x$ represents the results from binocular disparity.
+
+dataset to show the zero-shot generalization ability of our method in the wild world. As illustrated in Figure 1, our method significantly improves performance in various challenging regions, such as areas with occlusion, textureless surfaces, reflections, and transparent regions. Due to space limitations, additional visualization results are available in the supplementary materials.
+
+# 4.4. Ablation Study and Analysis
+
+We conduct comprehensive ablation studies to analyze the impact of each module and illustrate the construction pro
+
+Table 5. The effectiveness of each module. The baseline is RAFT-Stereo. w/o mono feature: removing the context features from RAFTStereo. ME: our monocular encoder, DF: iterative direct fusion, ILF: iterative local fusion, PF: post-fusion, GF: global fusion.
+
+| Exp | LBP
+Kernel | S | OP | r | Middlebury (H) |
| epe | bad 2.0 |
| L(1) | 1 | | L | 1 | 1.38±0.06 | 10.20±0.53 |
| L(2) | 3 | | L | 1 | 1.36±0.04 | 10.10±0.25 |
| L(3) | 3 | ✓ | L | 1 | 1.44±0.06 | 9.65±0.26 |
| L(4) | 5,3 | ✓ | L | 1 | 1.20±0.08 | 9.06±0.70 |
| L(5) | 9,7,5,3 | ✓ | L | 1 | 1.32±0.07 | 9.57±0.62 |
| L(6) | | ✓ | C | 1 | 1.32±0.14 | 9.53±1.03 |
| L(7) | | ✓ | DC | 1 | 1.39±0.03 | 9.71±0.29 |
| L(8) | 13,11,9,7,5,3 | ✓ | L | 1 | 1.31±0.02 | 9.89±0.04 |
| L(9) | 5,3, | ✓ | L | 2 | 1.32±0.03 | 9.45±0.14 |
| L(10) | 5,3 | ✓ | L | 3 | 1.26±0.09 | 9.42±0.42 |
+
+Table 6. Ablation study on iterative local fusion. S: an LBP-like operation with or without a sigmoid function. OP: the type of operation, L: the LBP-like operation, C: the convolution, DC: a deeper convolution, r: the amplitude parameter.
+
+| Exp | Reg | Confidence | Middlebury (H) |
| epe | bad 2.0 |
| G(1) | | Cost | 1.23±0.03 | 9.69±0.38 |
| MonoDepth | ✓ | | 1.19±0.02 | 8.72±0.20 |
| G(2) | ✓ | Cost | 1.18±0.02 | 8.77±0.07 |
| G(3) | ✓ | Hybrid | 1.15±0.01 | 8.35±0.04 |
+
+Table 7. Ablation study on the global fusion. Reg: registration for monocular depth. Cost: estimating the confidence from the sampled cost volume. Hybrid: estimating the confidence from the concatenation of sampled cost volume, hidden state, and guidance from the last iteration. MonoDepth: evaluation of the registered monocular depth.
+
+cess of our model. It is important to note that each ablation study involves training the model from scratch rather than removing a component from an already well-trained model. The Effectiveness of Each Module. As shown in Table 5, the baseline model performs better without context features, indicating that monocular priors are susceptible to domain bias when data is limited. By incorporating less-biased monocular priors from a pre-trained large monocular network in the monocular encoder (ME), generalization performance is significantly improved, highlighting the importance of robust monocular priors in the wild world. Comparing the Baseline + ME with Baseline in Table 1, its performance becomes worse than Raft-Stereo, showing that it is easy to suffer from over-confidence when simply fusing monocular features with disparities during iterative disparity update. The iterative direct fusion method (IDF) fuses monocular depth and binocular disparity through direct concatenation and convolution at each iteration. Compared to this approach, our iterative local fusion (ILF) is more robust to noise in binocular disparity, resulting in superior performance. The post-fusion method (PF) fuses monocular depth with the optimized binocular disparity from the previous iteration without registration. Compared to this approach, our global fusion (GF) achieves better compatibility between monocular depth and binocular disparity, mitigat
+
+
+
+
+
+
+
+
+Left Image
+
+
+GT Disparity
+
+
+Left Image
+
+
+Error Map
+Scale $a$
+
+
+Ours
+Shift $b$
+Figure 4. The visualization of registration parameters, scale $a$ and shift $b$ .
+
+
+Error Map
+Scale $a$
+
+
+GT Disparity
+
+
+Left Image
+
+
+GT Disparity
+
+
+Ours
+
+
+
+
+Ours
+
+
+Shift $b$
+
+
+Error Map
+Scale $a$
+
+
+Shift $b$
+
+ing the noise caused by scale ambiguity during fusion. Our iterative local fusion and global fusion modules further enhance performance and improve model robustness with the monocular encoder. It is also noted that the Baseline time cost is 0.32s, while our model's is 0.4s. Though it involves a VTF model, thanks to the elegant and controllable design, our model barely raises the time cost.
+
+The Analysis of Iterative Local Fusion. We also analyze the specific configurations of iterative local fusion. As shown in Table 6, the fixed weights in the LBP-like operation have a slight impact on performance, with a kernel size of 3,5 providing optimal results. We also try to use convolutions with learnable weights to replace LBP-like convolutions. Comparing L(4), L(9-10) with L(6-7), we find that fixed-weight convolutions are more robust than learnable convolutions, and deeper learnable convolutions produce worse results. This is because limited data makes monocular-related learning unreliable for generalization, whereas manually designed convolutions incorporate prior knowledge and are less affected by data bias. Using a sigmoid function after LBP-like convolutions further improves overall performance. The amplitude parameter does not show a significant influence. We also visualize the local ordering map in Figure 3. The local ordering maps of predicted disparity gradually become similar to the result of monocular depth as the iteration increases. For more visualizations, please refer to our supplemental materials.
+
+The Analysis of Components in Global Fusion. We analyze the specific configurations of global fusion, as shown in Table 7. Comparing G(1) with G(2), global fusion achieves nearly a 1-point improvement in the Bad 2.0 metric after registration. Comparing G(2) with G(3), learning confidence with more information enhances overall performance. Comparing MonoDepth and G(3), the fused results are more robust to monocular depth. We also visualize the registration parameters $\{a,b\}$ in Figure 4. $\{a,b\}$ are
+
+changed in different areas but remain inconsistent for every pixel. Due to page limitations, please refer to our supplementary materials for additional failure case analysis and future work discussion.
+
+# 5. Conclusion
+
+In this paper, we dived into the fusion of monocular priors from VTF stereo matching and found three main problems limiting the fusion process. We proposed a binary local ordering map to unify the relative monocular depth and absolute disparity map. It also guided the fusion between monocular and binocular depth information in an explicit and controllable manner. Besides, we formulated the optimization of the disparity map as a registration process to monocular depth, which can adaptively and globally align the two kinds of depth maps. We designed a network to extract the unbiased monocular priors from the VFM and and leveraged the above two modules to fully exploit the unbiased monocular prior to the stereo matching pipeline to improve generalization in the ill-posed regions. Benefiting from the explicit design, our method barely increased the computation cost. Experimental results demonstrated the effectiveness of our method, with a significant improvement of 10 points on Booster and an error reduction of more than half on Middlebury and ETH3D, without using additional stereo data or data augmentation.
+
+Acknowledgement This work was supported by the Shenzhen Science and Technology Program under Grant No. JCYJ20241202130548062, the Natural Science Foundation of Shenzhen under Grant No. JCYJ20230807142703006, the Natural Science Foundation of China (NSFC) under Grants No. 62176021 and No. 6217204, and the Key Research Platforms and Projects of the Guangdong Provincial Department of Education under Grant No.2023ZDZX1034.
+
+# References
+
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+# Do It Yourself: Learning Semantic Correspondence from Pseudo-Labels
+
+Olaf Dülkel1, Thomas Wimmer1,2, Christian Theobalt1,4, Christian Rupprecht3, Adam Kortylewski1,5
+
+$^{1}$ Max Planck Institute for Informatics, Saarland Informatics Campus $^{2}$ ETH Zurich $^{3}$ University of Oxford
+
+$^{4}$ Saarbrücken Research Center for Visual Computing, Interaction and AI $^{5}$ University of Freiburg
+
+https://genintel.github.io/DIY-SC
+
+# Abstract
+
+Finding correspondences between semantically similar points across images and object instances is one of the everlasting challenges in computer vision. While large pretrained vision models have recently been demonstrated as effective priors for semantic matching, they still suffer from ambiguities for symmetric objects or repeated object parts. We propose improving semantic correspondence estimation through 3D-aware pseudo-labeling. Specifically, we train an adapter to refine off-the-shelf features using pseudolabels obtained via 3D-aware chaining, filtering wrong labels through relaxed cyclic consistency, and 3D spherical prototype mapping constraints. While reducing the need for dataset-specific annotations compared to prior work, we establish a new state-of-the-art on SPair-71k, achieving an absolute gain of over $4\%$ and of over $7\%$ compared to methods with similar supervision requirements. The generality of our proposed approach simplifies the extension of training to other data sources, which we demonstrate in our experiments.
+
+# 1. Introduction
+
+Finding correspondences between images remains a fundamental task in computer vision, having various applications in tracking [8, 10, 20], mapping and localization [24, 37], affordance understanding [25], pose estimation [58], analysis of characteristic object parts [16, 50], image and video generation or editing [12, 39, 53], 3D representation learning [31, 46, 56], or style transfer [23]. One remaining challenge in the correspondence estimation field is the task of finding matches across different instances of similar objects, i.e., finding semantic correspondences. This is a highly semantic task with a certain amount of ambiguity, especially for man-made objects.
+
+Recently, foundation model features have demonstrated surprisingly high zero-shot performance for this task [49, 62, 63]. However, these features still have various weaknesses for finding correspondences, such as ambiguities for
+
+
+
+
+
+
+Figure 1. Our method, DIY-SC, is able to find semantic correspondences even for extreme appearance and shape changes. All matches are computed from the keypoints in the top-left image.
+
+
+
+
+
+
+
+similar object parts [35] or symmetric objects [63]. In addition, supervised methods [63] indicate that there are more effective strategies to combine foundational features for solving semantic correspondence than simple concatenation [62] or weighted averaging [35]. Recent works [33, 59, 63] train models in a supervised manner using manual keypoint annotations and achieve strong performance when evaluated on the same dataset. However, as the required manual annotations are scarce and difficult to obtain, this strategy is not scalable to larger, more diverse datasets. It thus remains an open challenge to determine the best way to extract and enhance knowledge encoded in foundation models for finding semantic correspondences without relying on labor-intensive keypoint supervision.
+
+Recent works reduce the necessary level of supervision for learning semantic correspondences by regularizing with
+
+3D information [35] or injecting information about label definitions [9, 63]. However, they either require careful tuning of weighting factors [35] or rely on access to dataset-specific labeling conventions [63].
+
+We address both limitations in our work by learning features that significantly outperform the previous SOTA without requiring manual keypoint label definitions: Our work demonstrates that training with self-generated labels, i.e., pseudo-labels, where label quality is improved through weak 3D-aware supervision, is surprisingly effective for improving the semantic correspondence performance, also generalizing to heavy appearance changes (Fig. 1). To achieve this, we train a lightweight adapter supervised by the pseudo-labels, which effectively refines the foundation model's features, as shown in Fig. 2. Specifically, we pursue a zero-shot approach [62] for generating pseudo-labels for image pairs exhibiting moderate viewpoint variation, a strategy that has been demonstrated to be effective in such contexts but fails for larger viewpoint variations [63]. We compose these labels over multiple image pairs to acquire higher label quality for harder correspondence pairs, i.e., with larger viewpoint variance. We then employ a spherical prototype as a weak geometric prior [35] to reject wrong matches, which addresses the inherent challenge of matchability and reduces feature ambiguity.
+
+In contrast to previous weakly supervised methods [9, 63], our approach does not rely on dataset-specific keypoint definitions, reducing the barriers to applying it to other datasets. To demonstrate this, we also train a model on the recent ImageNet-3D dataset [34]. Pre-training on this larger dataset notably also improves the performance on SPair71k [36], demonstrating the effectiveness of our more generalizable approach.
+
+To summarize our contributions:
+
+- We show that pseudo-labeling is effective for learning better semantic correspondence features, and we demonstrate that the quality of pseudo-labels can be improved through 3D-aware chaining, relaxed cyclic-consistency constraints, and the integration of a weak geometric prior.
+- We show that our strategy is scalable to a larger dataset, further improving the model's performance.
+- Finally, we set a new SOTA on SPair-71k with weak supervision, outperforming the previous best model by 4.5 absolute points.
+
+# 2. Related Work
+
+Semantic correspondence. Semantic matching, i.e., finding correspondences between different instances of the same object class, is more challenging than geometric matching due to potential variations in appearance and shape. The scarcity and ambiguity of manually annotated data pose an extra challenge to learning-based methods for this task [51, 65].
+
+
+Figure 2. Self-training using pseudo-labels. Using foundational features, we generate pseudo-labels, which are subsequently filtered and used as supervision signals to train a light-weight adapter that refines the features for semantic matching.
+
+While early works relied on hand-crafted descriptors [30, 32], deep learning enabled learning better-suited feature extractors [22, 38, 44, 60] and direct semantic correspondence detection networks [14, 23, 43]. Due to the limited ground truth data, techniques emerged that rely on weak supervision [6, 26, 52, 64], leverage warp supervision and cycle consistency losses [51, 52, 66], or rely on increasing label supervision with pseudo-labels [18, 21, 28].
+
+With the advent of so-called foundation models, the semantic matching literature has come full circle: Recent studies demonstrated that features obtained from such models can be utilized for detecting semantic correspondences in a zero-shot manner [1, 2, 7, 15, 49, 62]. More specifically, DINO features [5, 40] have been shown to exhibit strong coarse semantic awareness useful for handling larger, cross-instance variations [2, 9, 48, 59, 62, 63], while features from diffusion models [45, 47] can complement them, resulting in better performance [9, 15, 29, 35, 49, 59, 62, 63].
+
+While a simple nearest-neighbor search in feature space proves to be a powerful zero-shot method for correspondence estimation, prior work also uncovered systematic problems of this approach, e.g., in the disambiguation of symmetric object parts [29, 33, 35, 46, 55, 63]. Therefore, several works have proposed appending adapter modules that are fine-tuned using supervision with ground-truth correspondences [59, 63]. While reducing the labeling requirements, methods that build a joint atlas for objects in multiple images usually require larger quantities of input images and perform test-time optimization [11, 39]. Zhang et al. [63] use keypoint-specific information to disambiguate left-right symmetries at test time. While their strategy is simple, not all symmetries can be solved by image transformations, e.g., flipping, and the required keypoint-specific information is generally not available. Fundel et al. [9]
+
+proposed fine-tuning distilled foundational features for geometric matching using 3D ground truth data. This approach is, however, inherently limited to the same object instance, resulting in suboptimal results for cross-instance matching. Mariotti et al. [35] proposed learning a map from features to the surface of a sphere using 3D pose information as a weak supervision signal. While this method successfully resolves most symmetries for simple objects, such as cars, a spherical prior does not accurately capture objects with more complex topologies.
+
+Our work also aims to improve the performance of semantic matching by refining foundational features. In contrast to Zhang et al. [63], we do not require dataset-specific keypoint definitions since our work only relies on weak supervision that is available at scale. Similar to Mariotti et al. [35], we leverage 3D information to reduce ambiguities. However, our work does not suffer from performance drops for objects with more complex topology and thus does not require tuning of weighting factors
+
+Pseudo-labeling. Lee et al. [27] proposed pseudolabeling, also referred to as self-training, as a technique for semi-supervised training of neural networks, where a small initial set of labels is propagated to a larger set of unlabeled instances. Various methods have been developed based on this concept, demonstrating the generality and scalability of this approach [3-5, 13, 20, 57], sometimes in conjunction with knowledge distillation from other pre-trained models. Previous works have expanded manual keypoint annotations and demonstrated improved semantic correspondence performance [18, 21, 28]. In our work, we propose to extract pseudo-labels using off-the-shelf foundational features (at training time), which we use to fine-tune a light-weight adapter for the task of semantic correspondence estimation.
+
+# 3. Method
+
+Foundational features show strong semantic awareness for zero-shot matching across instances. However, while the high feature similarity of similar object parts is reasonable from a semantic perspective, distinguishing them is crucial for accurate semantic correspondences. The performance gap between supervised and unsupervised semantic matching methods [63] shows that a learned combination and refinement of features outperforms a simple concatenation or averaging of multiple foundational features. As we aim to supervise a refinement stage without relying on human annotations, we draw on the effectiveness of pseudo-labeling for other tasks [4, 19, 20] and hypothesize its potential for improving features for semantic correspondence.
+
+In this section, we first formalize the semantic correspondence task (Sec. 3.1). Then, we introduce our two-stage method: First, pseudo-labels are generated via a zero-shot matching strategy and subsequently filtered (Sec. 3.2). These pseudo-labels are then used to supervise the training
+
+of a light-weight adapter $f_{p}$ (Sec. 3.3). Finally, we detail how our method can be scaled to a larger dataset in Sec. 3.4.
+
+# 3.1. Problem Definition
+
+The problem of finding semantic correspondences is defined as follows: Given a source image $I^s$ , a target image $I^t$ , and a query point $p_i^s \in \mathbb{R}^2$ on the object in the source image, the task is to find the target point $p_i^t \in \mathbb{R}^2$ on the target image that localizes the object part that semantically corresponds to the queried object part. One strategy to solve this task is to find the nearest neighbor in feature space via the cosine similarity $\mathrm{sim}(\cdot)$ of the feature maps $\mathcal{F}^s$ and $\mathcal{F}^t$ :
+
+$$
+p _ {i} ^ {t} = \mathrm {N N} ^ {s \rightarrow t} \left(p _ {i} ^ {s}\right) = \arg \max _ {q _ {i} ^ {t} \in I ^ {t}} \sin \left(\mathcal {F} ^ {s} \left(p _ {i} ^ {s}\right), \mathcal {F} ^ {t} \left(q _ {i} ^ {t}\right)\right). \tag {1}
+$$
+
+However, in contrast to zero-shot strategies that solely apply pre-trained feature extractors [62], we aim to improve the features such that the refined features are better suited for finding semantic correspondences. Since the features $\mathcal{F}^{\mathrm{DINO}}$ [40] and $\mathcal{F}^{\mathrm{SD}}$ [45] generalize well due to their large training corpus, we learn a light-weight adapter $\mathcal{F} = f_{\mathrm{P}}(\tilde{\mathcal{F}})$ on top of the concatenated features $\tilde{\mathcal{F}} = [\mathcal{F}^{\mathrm{DINO}},\mathcal{F}^{\mathrm{SD}}]$ , as proposed by Zhang et al. [63].
+
+# 3.2. Generation of High-Quality Pseudo-Labels
+
+Given a pair of images $(I^s, I^t)$ with their feature maps $(\mathcal{F}^s, \mathcal{F}^t)$ and the instance masks $(\mathcal{M}^s, \mathcal{M}^t)$ , the goal is to find matches $(p_i^s, p_i^t)$ that can be used as pseudo-labels for supervising the training of the adapter $f_p(\cdot)$ . A naive strategy would apply the nearest-neighbor (NN) computation (Eq. (1)) of all points on the mask:
+
+$$
+p _ {i} ^ {t} = \mathrm {N N} ^ {s \rightarrow t} \left(p _ {i} ^ {s}\right) \tag {2}
+$$
+
+with $p_i^s \in \mathcal{M}^s$ and $p_i^t \in \mathcal{M}^t$ . However, due to viewpoint variations, topological variations, or occlusions, not all points on the mask $\mathcal{M}^s$ can be mapped to the target image. This challenge is commonly referred to as the matchability or visibility problem [51]. We show that training an adapter with these naively obtained pseudo-labels already improves results (see 5). However, as self-training heavily relies on the quality of the pseudo-labels, we aim to improve their quality by rejecting wrong matches. Pseudo-labels should be removed if no matching is possible (matchability) or if points are matched wrongly because of erroneous zero-shot correspondences, e.g., because of feature ambiguity of object parts with a similar appearance.
+
+Our work addresses the challenge of removing wrong labels in the following ways: (1) We perform 3D-aware sampling of image pairs along a chain $(I^s, I^t)$ where image pairs have similar viewpoints and more accurate pseudolabels are expected. (2) We enforce cyclic consistency for the pseudo-labels along the chain to reduce the number of spurious matches. (3) We reject wrong pseudo-labels by integrating a canonicalized spherical 3D prior.
+
+
+
+
+Figure 3. Method overview. We use azimuth information to sample image pairs for which higher zero-shot performance can be expected (1). We then chain the pairwise predictions to get correspondences for larger viewpoint changes, where we reject matches that do not fulfill a relaxed cyclic consistency constraint (2). We further filter pseudo-labels by rejecting pairs that can not be mapped to a similar location on a 3D spherical prototype (3). Finally, we use the resulting pseudo-labels to train an adapter $f_{p}$ in a supervised manner (4).
+
+
+
+
+
+| Δv | [0°,45°) | (0°,90°) | (45°,135°) | (90°,180°) | (135°,225°) |
| PCK@0.1 | 75.9 | 68.1 | 57.2 | 54.0 | 52.6 |
+
+Table 1. Zero-shot performance (SD+DINO) degrades for larger viewpoint changes. The SPair-71k dataset has 8 azimuth bins with an equidistant size of $45^{\circ}$ . We compute the ratio of correctly corresponded keypoints (PCK@0.1 per.img) for increasing viewpoint changes averaged over all categories.
+
+(1) 3D-aware image pair sampling. The zero-shot approach, which utilizes features from Stable Diffusion [45] and DINOv2 [40], performs well for objects that do not undergo significant changes in their topology and appearance, and are presented from a similar viewpoint. However, the performance clearly degrades for larger viewpoint changes, as studied by Zhang et al. [63]. We study the sensitivity of the semantic correspondence performance for varying viewpoint differences using the azimuth angle annotations of the object-centric semantic correspondence dataset SPair-71k [36] in Tab. 1. We find that the zero-shot performance decreases for larger viewpoint changes, i.e., if the viewpoint's azimuth angle $\phi$ varies by more than $45^{\circ}$ .
+
+This observation motivates the generation of pseudolabels for image pairs with a similar viewpoint. However, more challenging image pairs where the viewpoint heavily deviates are also required to learn a strong point matcher.
+
+To account for this, we propose propagating matches through a $K$ -tuple $(I_1,\dots,I_K)$ , where each pair $(I_k,I_{k + 1})$ represents an image pair of the same category with a small but non-zero viewpoint variation (Fig. 3, (1)), such that $d_{\mathrm{circ}}(\phi_k,\phi_{k + 1}) < 90^\circ$ with the spherical distance $d_{\mathrm{circ}}(\cdot)$ which is equivalent to one azimuth bin in the SPair-71K
+
+dataset. The matches $\mathcal{K}^k = \{(p_i^k, p_i^{k+1}) : p_i^k \in \mathcal{P}^k \subseteq \mathcal{M}^k, p_i^{k+1} \in \mathcal{P}^{k+1} \subseteq \mathcal{M}^{k+1}\}$ are propagated via recursive application of the NN operator for the subsequent pairs:
+
+$$
+\begin{array}{l} \mathcal {P} ^ {k + 1} = \mathrm {N N} ^ {k \rightarrow k + 1} (\mathcal {P} ^ {k}) \tag {3} \\ = \mathrm {N N} ^ {k \rightarrow k + 1} \left(\mathrm {N N} ^ {k - 1 \rightarrow k} \left(\mathcal {P} ^ {k - 1}\right)\right) = \dots \\ \end{array}
+$$
+
+$$
+\mathcal {P} ^ {1} = \mathcal {M} ^ {1}. \tag {4}
+$$
+
+Through this strategy, each considered image pair is expected to have a higher pseudo-label quality than the naïve strategy, where pseudo-labels are generated for tuples with potentially very different poses $(I_1, I_k)$ .
+
+(2) Cyclic consistency of propagated pseudo-labels. While the aforementioned strategy can improve the quality of matches, it does not necessarily prevent spurious matches that can occur due to feature ambiguities, e.g., because of similar appearance. In order to reduce such spurious matches or matching of incompatible regions, we apply a cyclic consistency constraint for the matched points, as proposed by Aberman et al. [1]. A match $(p_i^s,p_i^t)$ is cyclic consistent if the following holds:
+
+$$
+\mathrm {N N} ^ {s \rightarrow t} \left(p _ {i} ^ {s}\right) = p _ {i} ^ {t} \quad \text {a n d} \quad \mathrm {N N} ^ {t \rightarrow s} \left(p _ {i} ^ {t}\right) = p _ {i} ^ {s}, \tag {5}
+$$
+
+with the nearest neighbor operator NN in feature space, as introduced in Eq. (1).
+
+We observe that this cyclic consistency constraint rejects many keypoint tuples $(p_i^s, p_i^t)$ , as the zero-shot matching approach has difficulties mapping back to the exact location of $p_i^s$ . For this reason, we relax the cyclic consistency constraint, where we do not enforce exact consistency but allow
+
+a small deviation from the source point:
+
+$$
+\begin{array}{l} p _ {i} ^ {t} = \mathrm {N N} ^ {s \rightarrow t} \left(p _ {i} ^ {s}\right), \quad \hat {p} _ {i} ^ {s} = \mathrm {N N} ^ {t \rightarrow s} \left(p _ {i} ^ {t}\right), \tag {6} \\ \text {a n d} \quad \| \hat {p} _ {i} ^ {s} - p _ {i} ^ {s} \| _ {2} < r _ {\max } \\ \end{array}
+$$
+
+with the rejection radius $r_{max}$ , see Fig. 3 (2). We iteratively apply this relaxed cyclic consistency constraint to all matches $\mathcal{K}^k$ , which filters out incompatible pairs and keeps matches capturing concepts that could be propagated through the set of $K$ images. We choose $K = 4$ in our experiments since this considers the full range of viewpoint variations of $180^\circ = 4 \cdot 45^\circ$ , given that the azimuth annotations for SPair-71k are only coarse bins of $45^\circ$ .
+
+(3) Rejection of wrong pseudo-labels with a canonicalized spherical 3D prior. Although our chaining strategy removes spurious matches, wrong matches might still occur, in particular for cases of left-/right-ambiguity and repeated object parts, as, e.g., illustrated in Fig. 3, where simple nearest-neighbor search on foundational features fails.
+
+Therefore, we aim to specifically remove such wrong matches by leveraging a canonicalized object-centric spherical 3D prior that captures objects in an aligned coordinate system. Mariotti et al. [35] propose a spherical mapper that maps DINOv2 feature patches $\mathbf{x}_i^{\mathrm{DINO}} = \mathcal{F}^{\mathrm{DINO}}(p_i)$ to points $\psi_{i}\in S^{2}$ on a canonicalized sphere $\psi_{i} = f_{s}(\mathbf{x}_{i}^{\mathrm{DINO}})$ by using only coarse view point information and instance masks during training. The key advantage of this strategy is that it naturally assigns object parts to regions on a spherical prototype across different instances and categories, which allows rejecting wrong samples in case they are in different areas of the sphere, e.g., when considering visually similar wheels on the left or the right side of a car.
+
+Mariotti et al. [35] demonstrate that this approach significantly improves the performance on SPair-71k when combining their spherical features with the concatenated features of SD and DINO via a weighted average. However, as this approach modulates the original feature similarity, the performance deteriorates for categories that are not well represented by a sphere, e.g., non-rigid categories. In contrast, our approach uses the spherical mapper only for removing potentially wrong pseudo-labels. That filter should have a high true positive rate while still keeping a sufficiently high true negative rate: Supervising with few correct matches is more desirable than supervising with many matches that are partially systematically wrong, as we show in our experiments. For this purpose, we compute the spherical points $\mathcal{P}^s$ and $\mathcal{P}^t$ for all matches:
+
+$$
+\Psi^ {s} = f _ {s} \left(\mathcal {F} ^ {\text {D I N O}} \left(\mathcal {P} ^ {s}\right)\right) \quad \text {a n d} \quad \Psi^ {t} = f _ {s} \left(\mathcal {F} ^ {\text {D I N O}} \left(\mathcal {P} ^ {t}\right)\right). \tag {7}
+$$
+
+Then, we reject all matches $(p_i^s,p_i^t)$ where
+
+$$
+\operatorname {s i m} \left(\psi_ {i} ^ {s}, \psi_ {i} ^ {t}\right) < \theta_ {\text {t h}}
+$$
+
+with the threshold $\theta_{\mathrm{th}} < 0.15 \cdot \pi$ that is selected to allow disambiguating left and right and potentially repeated object parts, such as the wheels of a car. While this thresholding may also remove correct matches for classes that are not well-represented by a rigid object prototype, we observe that the number of matches is still sufficiently large to serve as a dense supervision signal. Most importantly, only removing pseudo-labels does not modulate the original zero-shot matches. This is in contrast to regularizing with spherical mapper features, which deteriorates the localization accuracy of the original foundational features [35].
+
+# 3.3. Supervised Training with Pseudo-Labels
+
+After having generated the pseudo-labels, we train the adapter $f_{p}(\cdot)$ using supervised training with the following two losses: First, we train a CLIP [41]-inspired sparse contrastive loss as proposed by Luo et al. [33]:
+
+$$
+\mathcal {L} _ {\text {s p a r s e}} = C L \left(\mathcal {F} ^ {s} \left(\mathcal {P} ^ {s}\right), \mathcal {F} ^ {t} \left(\mathcal {P} ^ {t}\right)\right). \tag {8}
+$$
+
+This loss maximizes feature similarity for corresponding points while minimizing similarity to non-matching points. Second, we also supervise with the dense loss
+
+$$
+\mathcal {L} _ {\text {d e n s e}} = \sum \left\| \hat {p} _ {i} ^ {t} - \left(p _ {i} ^ {t} + \epsilon\right) \right\| _ {2} \quad \text {w i t h} \tag {9}
+$$
+
+$$
+\hat {p} _ {i} ^ {t} = \operatorname {W i n d o w S o f t A r g m a x} \left(\mathcal {F} ^ {s} \left(p _ {i} ^ {s}\right) ^ {\top} \mathcal {F} ^ {t}\right),
+$$
+
+with a window soft-argmax [23, 63] and Gaussian noise samples $\epsilon$ . The dense loss is particularly important for us since it propagates the gradient also to areas in the feature map without labels, i.e., unmatched areas. This learned combination and refinement of foundational features is a decisive improvement over previously proposed simple concatenation [62, 63] or weighted averaging of feature similarities of a weak geometric regularizer [35].
+
+# 3.4. Scaling to a Larger Dataset
+
+The comparatively small size of the SPair-71k dataset, with only 18 categories and 1,800 images in total, motivates scaling to a larger dataset with more diverse classes and a greater number of images. The spherical mapper [35] is potentially applicable to larger object-centric datasets with 3D annotations, but the simple geometric prior limits the improvement when applied via weighted average, as proposed by Mariotti et al. [35]. The geometric-aware flipping used by the current SOTA methods [9, 63] is not applicable to other datasets since it requires access to the keypoint label definitions, only presented in correspondence datasets.
+
+In contrast, our work relies solely on categories, masks, and 3D object poses as a weak supervision signal, which are available on a larger scale. Therefore, our method can be scaled to larger datasets, leading to generalizable semantic correspondence matching by training on objects that are
+
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| ASIC | [11] | 57.9 | 25.2 | 68.1 | 24.7 | 35.4 | 28.4 | 30.9 | 54.8 | 21.6 | 45.0 | 47.2 | 39.9 | 26.2 | 48.8 | 14.5 | 24.5 | 49.0 | 21.6 | 45.0 | 47.2 | 39.9 | 26.2 | 48.8 | 14.5 | 24.5 | 49.0 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.9 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.6 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.6 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.7 | 36.8 | 25.8 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.7 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.8 | 24.8 | 36.8 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.8 | 24.7 | 36.7 | 25.8 | 24.8 | 36.7 | 25.8 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.8 | 25.7 | 24.8 | 36.7 | 25.7 | 24.8 |
+
+not present in the SPair-71k dataset. We demonstrate this by training our whole pipeline on the recently proposed ImageNet-3D [34] dataset, which has around 86k images. We train the spherical mapper similarly to Mariotti et al. [35], where we use masks acquired from SAM [42]. As more accurate 3D pose labels are present in the ImageNet-3D dataset, we do not supervise the viewpoint direction only using the bin of the azimuth angle, as proposed by Mariotti et al. [35] for the SPair-71k dataset. Instead, we extend their formulation by computing the correlation coefficient on the two-sphere $S^2$ with the pose annotation:
+
+$$
+\mathcal {L} _ {\mathcal {S} ^ {2}} = \sum_ {\mathbf {I}, \mathbf {I} ^ {\prime}} \| \psi_ {\mathbf {I}} \cdot \psi_ {\mathbf {I} ^ {\prime}} - \mu \left(f _ {S} (\mathbf {I})\right) \cdot \mu \left(f _ {S} \left(\mathbf {I} ^ {\prime}\right)\right) \| ^ {2}, \tag {10}
+$$
+
+with $\psi_{\mathbf{I}} \in S^2$ and $\psi_{\mathbf{I}'} \in S^2$ computed from the 3D pose annotations of the objects in the two images. This not only supervises the azimuth viewpoint information (yaw) but also the pitch of an object and, therefore, improves canonicalization. We provide more details in the supplementary.
+
+This strategy enables us to scale our proposed method to more classes and images from a significantly larger dataset, ultimately leading to improved generalization.
+
+# 4. Experiments
+
+Details on pseudo-label generation. Using our sampling strategy, we generate $30\mathrm{k}$ pseudo-labeled image pairs per category from SPair-71k. We use a maximum of 50 randomly sampled keypoints for supervised training for each image pair. Following Zhang et al. [62], we resize the input images to $960^2$ and $840^2$ to extract the SD and DINOv2 features, resulting in feature maps of resolution $60 \times 60$ . We choose the rejection radius $r_{\max}$ for the relaxed bicyclic consistency constraint such that a deviation of one feature patch is allowed.
+
+Details on adapter training. Similar to Zhang et al. [63], we use four bottleneck layers with 5M parameters for the adapter. The model is trained using the AdamW optimizer
+
+Table 2. Per-category PCK@0.1 scores (per-keypoint) on SPair-71k. Best and second best are highlighted. When pre-training on ImageNet3D [34], results are improved. ${}^{ \dagger }$ SphMap avg is slightly higher than in the original paper where they used macro averaging. We trained using their code. *DistillDIFT was evaluated using their trained checkpoints. SphMap and DIY-SC require 3D pose annotations.
+
+| Models | | SPair-71k | AP-10k (PCK@0.1) |
| 0.1 | 0.05 | 0.01 | I.S | C.S. | C.F. |
| SD + DINOv2 | [62] | 59.9 | 44.7 | 7.9 | 62.9 | 59.3 | 48.3 |
| DistillDIFT* (U.S.) | [9] | 60.8 | 45.4 | 8.0 | - | - | - |
| SphMap† | [35] | 64.4 | 48.2 | 8.4 | 65.4 | 63.1 | 51.0 |
| TLR | [63] | 65.4 | 49.1 | 9.9 | 68.7 | 64.6 | 52.7 |
| DistillDIFT* (W.S.) | [9] | 65.3 | 49.8 | 8.9 | - | - | - |
| Ours | | 71.6 | 53.8 | 10.1 | 70.6 | 69.1 | 57.8 |
| Ours (DINOv2) | | 70.6 | 51.1 | 9.0 | 71.2 | 69.8 | 58.3 |
| TLR (sup) | [63] | 82.9 | 72.6 | 21.6 | 70.1 | 68.3 | 58.4 |
+
+Table 3. Results for different PCK levels (per-image) on the SPair-71k and the AP-10k dataset. Reproduced supervised results for the model [63] solely trained on SPair-71k. Results for AP-10K are intra-species (I.S.), cross-species (C.S.), and cross-family (C.F.), as introduced in [63]. $\dagger$ and $*$ as in Tab. 2. DINOv2: Only application and refinement of DINOv2 features.
+
+with a weight decay rate 0.001, a learning rate of $5 \cdot 10^{-3}$ and the one-cycle scheduler for 200k steps.
+
+Datasets. Recent works [35, 49, 62, 63] find SPair-71k [36] to be the most challenging and informative semantic matching benchmark due to its larger size and more challenging matches, containing images from 18 different categories with 600 to 900 image pairs per category. We also evaluate the methods on the recently proposed AP-10k [61] semantic correspondence dataset [63] without training on it.
+
+Metrics. We follow the standard settings [11, 17, 35, 36, 59, 63] and evaluate the semantic correspondence performance via the Percentage of Correct Keypoints (PCK). It is defined by computing the ratio of correctly predicted matched keypoints that lie within a radius of $R = \alpha \cdot \max(h, w)$ around the correct ground truth match, where we report the bbox variant with $h$ and $w$ referring to the height and width of the bounding box of the considered object, respectively. Since various prior works report it differently, we report both the PCK when averaged over keypoints (per kpt) and when averaged over images (per img).
+
+
+(a) Appearance change, repeated object parts.
+
+
+(c) Viewpoint change, feature ambiguity in background.
+
+
+(b) Appearance change, repeated object parts, viewpoint change.
+
+
+(d) Left-right ambiguity, semantically similar categories.
+Figure 4. Qualitative results for challenging examples. We present four challenging examples of the SPair-71K test dataset where current SOTA models mostly fail. Correct matches that lie within the $\mathrm{PCK}_{\mathrm{bbox}}@0.1$ radius of the ground-truth label are color-coded in green, while incorrectly matched keypoints are depicted in red.
+
+Prior work. We compare our method with recent zero-shot and weakly-supervised strategies. DIFT [49], DINo2 [40], and $SD +$ DINo2 [62] extract features from foundation models and perform nearest-neighbor matching in feature space. DistillDIFT (U.S.) [9] is further fine-tuned for correspondence detection on 3D data. ASIC [11] uses DINO features to establish coarse correspondences and refines them at test-time. Spherical mapper (SphMap) [35] uses class labels, object masks, and 3D pose information as weak supervision signals during training, similar to us. We note, however, that we do not use any of this information at test time. Telling Left from Right (TLR) [63] and DistillDIFT (W.S.) [9] make use of the keypoint label definitions to flip images at test time. We compare to zero-shot approaches and the spherical mapper [35] trained on ImageNet-3D with our extended 2-sphere configuration.
+
+# 4.1. Experimental Results
+
+Quantitative results on SPair-71k. The category-specific results in Tab. 2 show that our model achieves strong gains across nearly all categories, setting a new SOTA on SPair-71k and demonstrating the effectiveness of our pseudo-labeling strategy. Improvements are especially large for categories that are symmetric or contain repeated object parts, e.g., $+15.7\%$ for bus or $+14.0\%$ for car. While Mariotti et al. [35] already improved performance for such cases, our approach outperforms theirs by effectively combining SD and DINOv2 features through pseudo-label supervision. Unlike their method, we retain original features and simply reject matches that strongly deviate from a spherical prototype.
+
+All in all, we clearly outperform all previous methods on all PCK-levels (Tab. 2 and Tab. 3), including methods that use the same weak supervision as we do [35] and methods that include dataset-specific information about the definition of the keypoint labels [9, 63]. Surprisingly, training an adapter only on top of DINOv2 features with the same pseudo-labels results in competitive semantic correspondence performance compared to the adapter on top
+
+| Models | SPair-71k | AP-10k (PCK@0.1) |
| 0.1 | 0.05 | 0.01 | I.S | C.S. | C.F. |
| Ours (SPair) | 71.6 | 53.8 | 10.1 | 70.6 | 69.1 | 57.8 |
| SphMap-S2 (IN3D) | 58.5 | 44.0 | 7.7 | 56.6 | 53.2 | 38.9 |
| Ours (IN3D) | 68.0 | 51.1 | 9.8 | 67.8 | 65.8 | 53.3 |
| Ours (IN3D → SPair) | 72.2 | 54.6 | 10.6 | 71.1 | 69.4 | 58.1 |
+
+Table 4. Effect of pre-training on ImageNet-3D (PCK per img). SphMap- $S^2$ represents the weighted application of our 2-sphere-based spherical mapper, evaluated following Mariotti et al. [35].
+
+of SD+DINOv2 features, even outperforming this strategy for the animal AP-10K dataset. This demonstrates that DINOv2 features achieve competitive semantic correspondence performance if refined effectively.
+
+Evaluation on AP-10k. Additionally, we also evaluate on the AP-10k dataset and report the results in Tab. 3. We find that, despite not being trained on this dataset and only having a few animal categories in the SPair-71k training dataset, we outperform the current SOTA, the geometry-aware approach by Zhang et al. [63], showcasing the generalization capabilities of our method. We additionally compare to a fully-supervised model [63] trained on SPair-71k. We observe a severe performance drop of this model $(-17.4\%)$ PCK@0.1 for I.S.) compared to fully-supervised training on AP-10k [63, Tab.3]. On the other hand, our approach does not suffer such a performance drop and, thus, achieves comparable results to a model trained with manual annotations. We hypothesize that this is due to the denser and more diverse pseudo-labels compared to the fixed set of manually annotated keypoints that are being overfitted in supervised training.
+
+Scaling to a larger dataset. Our weakly-supervised training strategy allows scaling the training to larger object-centric datasets that do not include keypoint annotations. While pre-training improves the model performance on SPair-71k and AP-10k (Tab. 3 and Tab. 4), we surprisingly even outperform the previous SOTA on SPair-71k despite not having trained on the SPair-71k dataset, showcasing strong generalization capabilities. This is in contrast to the
+
+naive weighted application of the ImageNet-3D spherical mapper, where the results significantly deteriorate, potentially explained by the fact that this model does not generalize well to the unseen categories in SPair-71k. We also study the impact of automatically acquired 3D pose labels in the supplementary.
+
+Qualitative results. We present qualitative results in Fig. 4 comparing our model to current SOTA models on four challenging examples of the SPair-71k test dataset. While the spherical mapper effectively addresses cases of symmetries and repeated object parts for rigid objects, it comes with the inherent challenge of finding the correct weighting factor for interpolating between foundational and processed spherical feature similarities, where the optimal weight depends on the considered category and sample. For example, while the weighting is too low in (a), the weighting is too large in (d) since the ill-defined background features of SphMap result in a match with an object in the background. Additionally, its effectiveness is limited to categories that are well represented by a spherical prototype, e.g., a potential reason for the motorbike failure case in (c). TLR and DistillDIFT both suffer from the fact that simply flipping an object does not resolve all ambiguities, such as for categories with repeated object parts (a,b), rotated objects (b), or cases with left-/right ambiguities (d). DistillDIFT is less prone to incorrect matches caused by background clutter (c), whereas TLR and SphMap suffer from the fact that they rely on the potentially noisy nearest neighbor of SD and DINOv2 features. However, DistillDIFT still fails to disambiguate the human and the horse in (d), and it suffers from left-right ambiguity if the flipping is not effective (d). Furthermore, as visible in (b), DistillDIFT's performance deteriorates for pairs with heavy appearance change, which may be attributed to the multi-view fine-tuning on 3D instances, which does not generalize well to cross-instance correspondences. In contrast, our method identifies high-quality semantic correspondences for these challenging examples, as it successfully resolves feature ambiguities and does not rely on the weighting of two similarity terms.
+
+# 4.2. Ablations
+
+We thoroughly ablate all components of our method and present the main results in Tab. 5. First, supervision with naively generated pseudo-labels already outperforms the zero-shot approach. This is due to the fact that learning the light-weight adapter naturally stabilizes feature maps for semantic correspondence estimation by merging the complementary information captured by SD and DINOv2 features. Constraining pseudo-labels to the mask of an object further enhances the performance. We also observe that the relaxed cyclic consistency constraint outperforms both unfiltered pseudo-labels and exact cyclic consistency filtering. The performance further increases when employing our chain-
+
+| pseudo | cyc. cons. | relaxed c.c. | chaining | sph. rej. | PCK@0.1 |
| | | | | 65.0 |
| ✓ | | | | | 67.2 |
| ✓ | ✓ | | | | 66.9 |
| ✓ | | ✓ | | | 68.4 |
| ✓ | | ✓ | ✓ | | 70.0 |
| ✓ | | | | ✓ | 72.9 |
| ✓ | | ✓ | ✓ | ✓ | 74.4 |
+
+Table 5. Ablations on SPair-71k. All introduced components bring a significant improvement. The baseline is evaluated using the SD+DINO zero-shot approach with window soft argmax.
+
+ing strategy that improves the pseudo-label quality because (1) NN matching is only performed for easier image pairs, i.e., a similar object pose, and (2) the bicyclic consistency constraint reduces spurious matches. Adding the sphere-based rejection strategy substantially improves all model instantiations by reducing wrong matches for objects with symmetries and repeated object parts that make up a significant ratio of the SPair-71k dataset. This rejection also clearly enhances the naive pseudo-labeling strategy, combining all modules to achieve the best performance.
+
+Failure Cases. While our method outperforms previous methods, it still fails for some challenging cases of SPair-71K, such as images containing objects that are upside-down. We show visual examples and discuss failure cases of our method in the supplementary.
+
+# 5. Conclusion
+
+We presented DIY-SC, a method for finding semantic correspondences with weak supervision. We demonstrated the effectiveness of training with pseudo-labels for semantic correspondence: By generating labels using a zero-shot approach with foundational features and carefully designing methods for rejecting wrong matches, we provide a strong supervision signal that can be used to train an adapter that refines foundational features. Our experiments showed improvements of $+4.5\%$ and $+6.8\%$ over the previous SOTA for PCK@0.1 on SPair-71k, measured per-keypoint and per-image, respectively. Our ablation studies have shown that the proposed chaining and filtering steps, as a means of enhancing the quality of pseudo-labels, improve the corresponding performance significantly.
+
+Limitations and future work. Although our weak supervision strategy scales to larger datasets, reducing the supervision requirements is of importance to further scale the approach. See the supplementary for a preliminary feasibility analysis. Furthermore, while the match rejection with the spherical mapper shows significant improvements, it is less effective for objects that are not represented well by a sphere, which motivates extending this strategy. We hope that the proposed improved correspondence features can enhance tasks that rely on semantic features.
+
+# Acknowledgments
+
+Adam Kortylewski acknowledges support via his Emmy Noether Research Group funded by the German Research Foundation (DFG) under Grant No. 468670075. Thomas Wimmer is supported through the Max Planck ETH Center for Learning Systems.
+
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\ No newline at end of file
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+# DocThinker: Explainable Multimodal Large Language Models with Rule-based Reinforcement Learning for Document Understanding
+
+Wenwen Yu $^{1}$ , Zhibo Yang $^{2}$ , Yuliang Liu $^{1}$ , Xiang Bai $^{1\boxtimes}$
+
+1Huazhong University of Science and Technology, 2Alibaba Group
+
+{wenwenyu,ylliu,xbai}@hust.edu.cn, yangzhibo450@gmail.com
+
+# Abstract
+
+Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in document understanding. However, their reasoning processes remain largely black-box, making it difficult to ensure reliability and trustworthiness, especially in high-stakes domains such as legal, financial, and medical document analysis. Existing methods use fixed Chain-of-Thought (CoT) reasoning with supervised fine-tuning (SFT) but suffer from catastrophic forgetting, poor adaptability, and limited generalization across domain tasks. In this paper, we propose DocThinker, a rule-based Reinforcement Learning (RL) framework for dynamic inference-time reasoning. Instead of relying on static CoT templates, DocThinker autonomously refines reasoning strategies via policy learning, generating explainable intermediate results, including structured reasoning processes, rephrased questions, regions of interest (RoI) supporting the answer, and the final answer. By integrating multi-objective rule-based rewards and KL-constrained optimization, our method mitigates catastrophic forgetting and enhances both adaptability and transparency. Extensive experiments on multiple benchmarks demonstrate that DocThinker significantly improves generalization while producing more explainable and human-understandable reasoning steps. Our findings highlight RL as a powerful alternative for enhancing explainability and adaptability in MLLM-based document understanding. Code will be available at https://github.com/wenwenyu/DocThinker.
+
+# 1. Introduction
+
+Multimodal Large Language Models (MLLMs) [29-31] have significantly advanced document understanding, yet their reasoning mechanisms remain largely opaque. This lack of explainability [10, 39] limits their application in high-stakes domains such as legal, financial, and medical document analysis, where transparency is critical for en
+
+
+Figure 1. Comparison of different approaches for improving model's explainability and transparency in MLLM-based document understanding. Traditional methods, including Chain-of-Thought (CoT), Visualization-of-Thought (VoT), and Multimodal Visualization-of-Thought (MVoT) rely on static reasoning templates, predefined heuristics, or external agents and tools, limiting their adaptability and generalization. In contrast, the proposed DocThinker leverages rule-based reinforcement learning to explore diverse reasoning paths and generate explainable intermediate steps, including reasoning traces, rephrased questions, regions of interest (RoI) supporting the answer, and the final answer, enabling more adaptive and explainable document understanding.
+
+suring trustworthiness. Unlike human reasoning, which involves structured and multi-step inference, MLLMs typically operate as black-box systems, making it difficult to validate their decision-making process [4]. While Chain-of-Thought (CoT) [43] prompting has been widely adopted to enhance explainability, existing approaches heavily rely on static reasoning templates, which struggle to generalize across diverse complex scenarios and tasks.
+
+To address this, recent research has explored multimodal CoT reasoning techniques, as shown in Fig. 1. ReFocus [8] presents a visual-editing-based CoT framework, allowing models to selectively highlight and modify key regions via
+
+invoking external tools and agents in structured document images, improving comprehension of charts and tables. Visual CoT [35] introduces multi-turn processing pipelines that dynamically focus on key regions in visual images, enabling more explainable intermediate reasoning steps. Similarly, Multimodal Visualization-of-Thought (MVoT) [17] extends CoT reasoning by generating interleaved visual and textual reasoning traces, aiming to improve transparency. The Mind's Eye of LLMs [44] further proposes Visualization-of-Thought (VoT), a technique that elicits spatial reasoning by generating visual representations of thought processes. But this method applies in navigation-based applications, and its adaptability to document understanding remains limited. Besides, these approaches still depend on predefined heuristics and static reasoning paths, making them inherently inflexible and susceptible to catastrophic forgetting and poor generalization across varied document types and tasks.
+
+Another emerging direction is reinforcement learning (RL)-based [40] reasoning, which has shown promise in overcoming the rigidity of fixed CoT methods. DeepSeek-R1 [5] framework demonstrates that pure RL training can incentivize emergent reasoning behaviors without relying on extensive supervised fine-tuning (SFT), achieving state-of-the-art performance in complex reasoning tasks. Inspired by this, MedVLM-R1 [32] applies RL techniques to medical vision-language models, proving its effectiveness in enhancing transparency and generalization in medical image understanding. Visual-RFT [24] introduces Visual Reinforcement Fine-Tuning, a reward-driven optimization framework designed to enhance the reasoning capabilities of vision-language models. Unlike conventional supervised fine-tuning, which relies on large annotated datasets, Visual-RFT employs verifiable reward functions to guide learning, significantly improving data efficiency. Experimental results indicate that reinforcement fine-tuning improves performance in open-vocabulary detection, few-shot object recognition, and reasoning grounding tasks, demonstrating its ability to generalize across diverse visual domains. While these methods primarily focus on general visual tasks, their success highlights the potential of RL in optimizing reasoning strategies for MLLMs. However, RL-based approaches for document understanding remain underexplored, particularly in designing effective reward functions that optimize both reasoning adaptability and explainability.
+
+While humans naturally employ structured, multi-step reasoning when interpreting documents, integrating inference-time reasoning into MLLM-based document understanding is still an open challenge. Inspired by recent advancements, we propose DocThinker, a novel rule-based Reinforcement Learning (RL) framework designed for inference-time reasoning in document understanding. Unlike fixed CoT or VoT-style methods, DocThinker explores diverse reasoning paths and get explainable intermediate steps, including
+
+explicit reasoning traces, rephrased questions, regions of interest (RoI) supporting the answer, and the final answer, highlighting its ability to produce more flexible and varied outputs compared to traditional CoT. Instead of following fixed reasoning templates, DocThinker autonomously refines its reasoning process through policy learning based on the Group Relative Policy Optimization (GRPO) algorithm [36], mitigating catastrophic forgetting and improving adaptability. The model is trained using reinforcement learning with a proposed multi-objective reward function, enabling it to self-adapt to diverse document structures while preserving explainability. Although VoT-like methods generate grounded thought, they lack revision ability. Our RL enables self-reflection and correction that is complementary to VoT-like methods. Additionally, KL-constrained optimization is employed to ensure stable policy updates, preventing reward exploitation and preserving reasoning coherence.
+
+Our main contributions are summarized as follows:
+
+- We introduce DocThinker, to the best of our knowledge, the first RL-based framework for document understanding, enabling adaptive inference-time reasoning without relying on fixed CoT templates.
+- We propose a set of multi-objective reward functions that incentivize the model to generate human-understandable reasoning steps, while ensuring robust generalization across diverse document types and tasks.
+- We conduct extensive experiments on multiple benchmark datasets, demonstrating that DocThinker significantly improves generalization and explainability compared to existing CoT-based and SFT-based methods. Our findings highlight the potential of RL as a key enabler for more explainable, adaptable, and reliable MLLM-based document understanding systems.
+
+# 2. Related Work
+
+# 2.1. MLLMs for Document Understanding
+
+Multimodal Large Language Models (MLLMs) have shown strong potential in document understanding by integrating textual and visual elements. Existing approaches enhance comprehension through layout-awareness, high-resolution processing, and specialized encoding techniques. DocLLM [41], LLaVAR [53], and mPLUG-DocOwl [46] improve text-centric document reasoning via instruction tuning, while methods like DocPedia [7] and Vary [42] refine image processing for structured text extraction. Other models, such as UReader [47] and InternVL1.5 [2], incorporate OCR and adaptive resolution techniques to enhance text recognition. To further optimize efficiency, models like TextMonkey [23] and Fox [19] introduce token compression and unified encoding for multi-page document analysis. Additional improvements, including compression strategies in DocKylin [52] and multi-scale integration in StrucTexTv3 [26], enhance
+
+structure-aware reasoning. Despite these advancements, explainability remains a critical limitation. While step-wise reasoning frameworks [51] and visual editing-based approaches like ReFocus [8] improve transparency, they rely on static reasoning strategies that hinder adaptability. Most models depend on supervised fine-tuning (SFT), which improves task performance but often leads to overfitting and weak generalization across diverse document types. This highlights the need for adaptive learning frameworks capable of dynamic reasoning refinement while preserving explainability across varied document scenarios.
+
+# 2.2. RL for Explainability and Reasoning
+
+Explainability is crucial for deploying MLLMs in sensitive domains, ensuring transparency and trust in model decisions [4, 39]. Reinforcement Learning (RL) has emerged as a promising alternative to supervised fine-tuning (SFT) [3], addressing overfitting and limited generalization by allowing models to self-improve reasoning strategies through interaction with an environment. Unlike static Chain-of-Thought (CoT) approaches, RL enhances adaptability, explainability, and generalization in complex reasoning tasks. Recent advancements demonstrate RL's effectiveness in language and vision-language models. The OpenAI o1 model [13] applies RL to enhance reasoning capabilities, while DeepSeek-R1-Zero [5] achieves better reasoning and thinking process ability by training entirely with RL, incentivizing emergent reasoning via its Group Relative Policy Optimization (GRPO) framework without relying on SFT. MedVLM-R1 [32] extends this to medical image analysis, showing improved explainability and transparency. In multimodal learning, Visual-RFT [24] introduces verifiable reward functions, improving data efficiency and reasoning adaptability in open-vocabulary detection, few-shot recognition, and grounding tasks. RLHF-V [49] further aligns MLLMs with human trustworthiness through fine-grained RL-based feedback. Despite RL's success in vision-language tasks, its application in document understanding remains largely unexplored. Existing RL-based approaches fail to jointly process text, layout, and visual elements while maintaining explainability. Furthermore, designing effective reward functions that balance reasoning adaptability and explainability remains an open challenge. To bridge this gap, we propose DocThinker, a rule-based RL framework optimized with Group Relative Policy Optimization (GRPO) [36], incorporating verifiable multi-objective rewards to enable inference-time reasoning for complex document understanding.
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+Group Relative Policy Optimization (GRPO). The GRPO algorithm, first introduced in DeepSeekMath [36],
+
+is a reinforcement learning framework designed to improve reasoning without the need for a separate critic model, a key limitation of existing methods such as Proximal Policy Optimization (PPO)[34]. Traditional RL approaches like PPO rely on a value network to estimate the quality of model predictions, which can introduce instability and additional computational costs. In contrast, GRPO directly compares a group of generated responses, making it a more efficient alternative for large-scale language model training.
+
+In GRPO, given a question $q$ , the old policy model $\pi_{\theta_{\mathrm{old}}}$ first generates a group of different candidate response outputs $\{o_1, o_2, \dots, o_G\}$ with size of $G$ . These response outputs are then evaluated through a rule-based reward function $R(q, o)$ to obtain $G$ rewards denoted as $\{r_1, r_2, \dots, r_G\}$ correspondingly, which is defined as follows:
+
+$$
+r _ {i} = R \left(q, o _ {i}\right) = \left\{ \begin{array}{l l} 1, & \text {i f} o _ {i} = \text {g r o u n d t r u t h}, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {1}
+$$
+
+where $R(\cdot, \cdot)$ is the rule-based verifiable reward function. $R$ takes the question and output pair $(q, o_i)$ as inputs, and checks whether the prediction $o_i$ is correct compared to ground truth under predefined rules. In our works, we proposed multi-objective reward functions tailored for document understanding, which will be detailed in Sec. 3.2.2, to incentivize the model to generate human-understandable reasoning steps, while ensuring robust generalization across diverse document types and tasks.
+
+Instead of computing absolute values for each response, GRPO normalizes the rewards within the group, ensuring that the model learns from relative advantages. Specifically, the advantage is computed by taking the difference between each reward and the mean of the group, normalized by the standard deviation std, formulated as follows:
+
+$$
+A _ {i} = \frac {r _ {i} - \operatorname {m e a n} \left(\left\{r _ {1} , \dots , r _ {G} \right\}\right)}{\operatorname {s t d} \left(\left\{r _ {1} , \dots , r _ {G} \right\}\right)}, \tag {2}
+$$
+
+where $A_{i}$ represents the advantage of $i$ -th output $o_{i}$ , meaning the relative quality of the $i$ -th responses. The advantage $A_{i}$ is sequence-level normalized reward, and we set the advantage $A_{i,t}$ of $t$ -th auto-regressive decoding time step token in the output $o_{i}$ as the sequence-level advantage $A_{i}$ . This process eliminates the need for a critic network, making policy updates computationally efficient and stable. The intuition behind GRPO objective is to maximize the advantage of the generated responses, while ensuring that the model remains close to the reference policy model $\pi_{ref}$ . Consequently, the GRPO loss $\mathcal{L}_{\mathrm{GRPO}}$ is defined as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {G R P O}} (\theta) = - \frac {1}{G} \sum_ {i = 1} ^ {G} \frac {1}{| o _ {i} |} \sum_ {t = 1} ^ {| o _ {i} |} \left[ \frac {\pi_ {\theta} (o _ {i , t} \mid q , o _ {i , < t})}{\varphi [ \pi_ {\theta} (o _ {i , t} \mid q , o _ {i , < t}) ]} A _ {i, t} \right. \\ \left. - \beta \mathbb {D} _ {\mathrm {K L}} \left(\pi_ {\theta} \| \pi_ {\text {r e f}}\right) \right], \tag {3} \\ \end{array}
+$$
+
+
+Figure 2. Schematic illustration of the proposed DocThinker framework. Given an input image $I$ and question $q$ , we first sample $G$ candidate outputs $\{o_i\}_{i=1}^G$ from the old policy model $\pi_{\theta_{old}}$ . The $i$ -th output $o_i$ has explainable and human-understandable intermediate results, including reasoning processes, rephrased question, regions of interest (RoI) supporting the answer, and final answer. Then we compute a reward $r_i$ for each output $o_i$ using our proposed multi-objective reward functions, which will be detailed in Sec. 3.2.2, including XML format reward, rephrased question reward, RoI IoU reward, and final answer accuracy reward. Subsequently, each reward $r_i$ is normalized by subtracting the group average mean and dividing by the group standard deviation std to get a group relative advantage $A_i$ . Finally, we optimize the current policy model $\pi_\theta$ where $\theta$ is trainable parameters by maximizing the advantage $A_i$ while ensuring that the model remains close to the reference policy model $\pi_{ref}$ , via KL divergence between $\pi_\theta$ and $\pi_{ref}$ .
+
+where the first term represents the scaled advantage and the second term is regularization to penalize deviations from the reference policy $\pi_{ref}$ through Kullback-Leibler (KL) divergence $\mathbb{D}_{\mathrm{KL}}(\pi_{\theta} \parallel \pi_{\mathrm{ref}})$ , helping prevent catastrophic forgetting. $\varphi[\cdot]$ represents stop gradient operation. $\theta$ is the trainable parameter of the current policy model $\pi_{\theta}$ . $\beta \in \mathbb{R} \geq 0$ is a hyper-parameter and controls the regularization strengths. For more introduction of the general version of GRPO, please refer to appendix.
+
+# 3.2. DocThinker
+
+As illustrated in Fig. 2, we introduce DocThinker, a reinforcement learning (RL)-based framework designed for inference-time reasoning in multimodal document understanding. Unlike conventional supervised fine-tuning (SFT), which is often prone to overfitting and limited generalization, DocThinker refines its reasoning strategies by leveraging rule-based reward signals, enabling greater robustness across diverse document types.
+
+Built on Group Relative Policy Optimization (GRPO), DocThinker optimizes for explainability, adaptability, and accuracy, allowing the model to iteratively improve its decision-making process. While the original GRPO algorithm has been primarily applied to text-only question-answering tasks, DocThinker extends its application to multimodal settings, where both document images and textual queries serve as inputs. Given a document image $I$ and a question $q$ , DocThinker generates a response $o_i$ that includes explainable intermediate reasoning results, such as explicit reasoning traces, rephrased questions for improved clarity, identified Regions of Interest (RoI) supporting the answer, and the final predicted response. Through a multi-objective reward system, DocThinker continuously refines its reasoning strat
+
+egy via the GRPO algorithm, ensuring stable learning and enhanced adaptability across a wide range of document scenarios. The following sections discuss the choice of base model and prompt template in Sec. 3.2.1, and the design of verifiable multi-objective rewards for document understanding tasks in Sec. 3.2.2.
+
+# 3.2.1. Base Model and Prompt Template
+
+For our base model, we adopt the state-of-the-art multimodal large language model Qwen2.5-VL 3B and 7B [1], denoted as $\pi_{\theta}$ , where $\theta$ are the trainable parameters. Given a training dataset $X$ , each sample $x$ consists of a document image $I$ and a text prompt $p$ , which includes the user's question $q$ alongside a fixed template message. The prompt template is designed to instruct the MLLM to produce structured output $o$ , which includes both a reasoning trace and a final output encoded in designated XML-like tags ( $<\text{think}>\ldots\text{think}>$ and $<\text{answer}>\ldots\text{answer}>)$ . The reasoning trace enclosed in $<\text{think}>\ldots\text{think}>$ serves as a key component in the model's self-improvement and optimization process during reinforcement fine-tuning. The answer enclosed in $<\text{answer}>\ldots\text{answer}>$ is formatted in JSON, containing three critical fields: "rephrase_question", "bbox_2d", and "final_answer". The "rephrase_question" represents an improved, more descriptive version of the original query. This refinement reduces ambiguity, helping users better understand how the model processes the question and formulates an inference. By enhancing question clarity, this component significantly contributes to the model's overall explainability. The "bbox_2d" encodes the 2D bounding box coordinates corresponding to the regions of the document image that the model deems highly relevant to answering the question. This visual cue serves as an explainability aid, providing insights
+
+into which parts of the document influence the model's reasoning. The "final_answer" contains the model's predicted response to the given question $q$ , ensuring that all intermediate reasoning steps contribute to a well-supported final decision. By incorporating both textual and visual reasoning elements, DocThinker enhances explainability across two modalities. The "rephrase_question" field refines the linguistic aspect of reasoning, while the "bbox_2d" field introduces a visual grounding mechanism, making the model's decision-making process more transparent. For further details of the prompt template, please refer to appendix.
+
+Optimization. We adopt the GRPO-based RL objective formulated in Eq. (3) to optimize $\pi_{\theta}$ , ensuring that the generated answers are accurate, well-structured, and transparently reasoned. The reasoning trace, enclosed within ..., serves as a crucial component for self-learning, allowing the model to iteratively refine its reasoning process. Meanwhile, the reward signal, derived from the correctness of the final answer, guides policy optimization, reinforcing high-quality responses. Through this structured reinforcement learning framework, DocThinker achieves greater explainability and generalization in multimodal document understanding.
+
+# 3.2.2. Multi-objective Reward Functions
+
+The reward model plays a crucial role in reinforcement learning (RL) by aligning the model's predictions with predefined correctness criteria. While traditional RL approaches often rely on human preference-based reward models[20, 50], recent advancements, such as DeepSeek-R1 [5], have demonstrated that verifiable reward functions can significantly enhance a model's reasoning ability. Inspired by this success, we extend Reinforcement Learning with Verifiable Rewards (RLVR) to the visual document understanding domain by designing a rule-based multi-objective reward function that evaluates both textual reasoning and visual comprehension. This ensures that the model not only produces accurate answers but also generates explainable intermediate steps, improving both generalization and transparency. Our framework evaluates model outputs based on four core criteria: format compliance, final answer accuracy, region of interest (RoI) consistency, and rephrased question quality.
+
+Format Reward. The format reward ensures that the model's output adheres to a structured XML-style schema, enforcing consistency for explainable and machine-parsable outputs. It verifies that the reasoning trace is enclosed in ...tags and that the final response in ...is valid JSON with required key-value pairs. Outputs deviating from this format are penalized to maintain structured and systematic reasoning. Given a model
+
+output $o$ , the format reward is defined as:
+
+$$
+R _ {\text {f o r m a t}} = \left\{ \begin{array}{l l} 1, & \text {i f o f o l l o w s t h e X M L - s t y l e s c h e m a a n d} \\ & \text {J S O N s t r u c t u r e w i t h v a l i d k e y - v a l u e p a i r s}, \\ 0, & \text {o t h e r w i s e}. \end{array} \right.
+$$
+
+Accuracy Reward. The final answer accuracy reward measures whether the model's generated response "final_answer" aligns with the ground truth answer. Unlike traditional RLHF, where correctness is determined through human preference rankings, we leverage a direct verification function that compares the model's final answer against predefined ground truth values. For a given question $q$ and model-generated answer "final_answer", the reward function is defined as:
+
+$$
+R _ {\text {a c c u r a c y}} = \left\{ \begin{array}{l l} 1, & \text {i f}" \text {f i n a l \_ a n s w e r}" = \text {t h e g r o u n d t r u t h}, \\ 0, & \text {o t h e r w i s e}. \end{array} \right.
+$$
+
+RoI IoU Reward. The RoI IoU reward evaluates how accurately the model identifies key visual regions in a document. For a given predicted bounding box $B_{\mathrm{pred}} =$ "bbox_2d" and ground truth bounding box $B_{\mathrm{gt}}$ , the corresponding reward function is defined as:
+
+$$
+R _ {\mathrm {R o I}} = \left\{ \begin{array}{l l} 1, & \text {i f I o U (B _ {\mathrm {p r e d}} , B _ {\mathrm {g t}}) \geq 0 . 5}, \\ 0, & \text {o t h e r w i s e}. \end{array} \right.
+$$
+
+This reward encourages precise localization of relevant document regions, ensuring extracted information directly supports the model's final answer.
+
+Rephrase Question Reward. To enhance explainability, we introduce a rephrase question reward, which evaluates how effectively the model reframes the original query for improved clarity. Since document-based questions are often ambiguous or underspecified, an ideal model should generate a well-structured and informative rephrased question that provides additional context without altering the intent.
+
+The quality of the rephrased question is assessed based on two criteria: semantic similarity to the original query and word diversity. Given the original question $q_{\mathrm{orig}} = q$ and the rephrased version $q_{\mathrm{rephrase}} =$ "rephrase_question", we compute the soft reward, including cosine similarity $s$ and the ratio $r$ of new words compared to the original question:
+
+$$
+R _ {\text {r e p h r a s e}} = \left\{ \begin{array}{l l} s + r, & \text {i f} R _ {\text {a c c u r a c y}} = 1, \\ 0, & \text {o t h e r w i s e}, \end{array} \right.
+$$
+
+where $R_{\mathrm{rephrase}}$ is normalized to [0, 1]. This reward encourages the model to generate refined queries that clarify ambiguous input while preserving the original meaning, ultimately improving transparency in its reasoning process.
+
+| MLLM | Res. | Data | Str. | Document-oriented Understanding | General Multimodal Understanding |
| Doc/Text | Chart | General VQA | Relation Reasoning |
| DocVQA | TextCaps | TextVQA | DUDE | SROIE | InfoQA | F30k | V7W | GQA | OI | VSR |
| LLaVA-1.5-7B [22] | \( 336^2 \) | - | SFT | 0.244 | 0.597 | 0.588 | 0.290 | 0.136 | 0.400 | 0.581 | 0.575 | 0.534 | 0.412 | 0.572 |
| LLaVA-1.5-13B [22] | \( 336^2 \) | - | SFT | 0.268 | 0.615 | 0.617 | 0.287 | 0.164 | 0.426 | 0.620 | 0.580 | 0.571 | 0.413 | 0.590 |
| SPHINX-13B [18] | \( 224^2 \) | - | SFT | 0.198 | 0.551 | 0.532 | 0.000 | 0.071 | 0.352 | 0.607 | 0.558 | 0.584 | 0.467 | 0.613 |
| VisCoT-7B [35] | \( 224^2 \) | 438k | SFT | 0.355 | 0.610 | 0.719 | 0.279 | 0.341 | 0.356 | 0.671 | 0.580 | 0.616 | 0.833 | 0.682 |
| VisCoT-7B [35] | \( 336^2 \) | 438k | SFT | 0.476 | 0.675 | 0.775 | 0.386 | 0.470 | 0.324 | 0.668 | 0.558 | 0.631 | 0.822 | 0.614 |
| Qwen2.5VL-7B†[1] | \( 336^2 \) | - | - | 0.350 | 0.642 | 0.735 | 0.202 | 0.472 | 0.325 | 0.603 | 0.556 | 0.455 | 0.347 | 0.616 |
| Qwen2.5VL-7B†[1] | \( 1536^2 \) | - | - | 0.773 | 0.710 | 0.792 | 0.492 | 0.708 | 0.663 | 0.685 | 0.604 | 0.457 | 0.371 | 0.603 |
| Qwen2.5VL-7B* [1] | \( 336^2 \) | 4k | SFT | 0.355 | 0.658 | 0.740 | 0.215 | 0.489 | 0.334 | 0.624 | 0.563 | 0.467 | 0.405 | 0.619 |
| Qwen2.5VL-7B* [1] | \( 1536^2 \) | 4k | SFT | 0.784 | 0.725 | 0.801 | 0.498 | 0.714 | 0.674 | 0.680 | 0.609 | 0.472 | 0.427 | 0.624 |
| DocThinker-3B | \( 336^2 \) | 4k | RL | 0.460 | 0.663 | 0.746 | 0.213 | 0.486 | 0.335 | 0.664 | 0.572 | 0.486 | 0.485 | 0.625 |
| DocThinker-3B | \( 1536^2 \) | 4k | RL | 0.751 | 0.691 | 0.762 | 0.469 | 0.735 | 0.566 | 0.682 | 0.583 | 0.490 | 0.517 | 0.637 |
| DocThinker-7B | \( 336^2 \) | 4k | RL | 0.579 | 0.682 | 0.802 | 0.408 | 0.495 | 0.347 | 0.674 | 0.580 | 0.546 | 0.542 | 0.656 |
| DocThinker-7B | \( 1536^2 \) | 4k | RL | 0.795 | 0.738 | 0.827 | 0.515 | 0.806 | 0.689 | 0.701 | 0.625 | 0.694 | 0.686 | 0.721 |
| DocThinker-7B | \( 1536^2 \) | 8k | RL | 0.802 | 0.757 | 0.836 | 0.568 | 0.814 | 0.697 | 0.734 | 0.641 | 0.737 | 0.784 | 0.768 |
+
+Table 1. Performance on the Visual CoT benchmark. Grey results indicate zero-shot performance. The final row uses 8k data including F30k, GQA, OI, and VSR; only DUDE, SROIE, V7W are zero-shot. Res. and Str. short for resolution and strategy. InfoQA, F30k, V7W, and OI short for InfographicsVQA, Flickr30k, Visual7W, and Open Images, respectively. † indicate evaluating the model using the official checkpoint. * means trained it on 4data4k setting via supervised fine-tuning. DocThinker and Qwen2.5VL* differ only in training strategy.
+
+Final Reward Function. The total reward combines four rewards to optimize both accuracy and explainability:
+
+$$
+R _ {\text {t o t a l}} = \lambda_ {1} R _ {\text {f o r m a t}} + \lambda_ {2} R _ {\text {a c c u r a c y}} + \lambda_ {3} R _ {\text {R o I}} + \lambda_ {4} R _ {\text {r e p h r a s e}},
+$$
+
+where hyperparameters $\lambda_{i} = 1$ balance reward contributions and avoid reward hacking. This joint optimization ensures the model generates structured, explainable, and verifiable reasoning outputs for document understanding.
+
+# 4. Experiments
+
+Datasets. We utilize the Visual CoT dataset [35] as training data, which contains 438k question-answer pairs annotated with intermediate bounding boxes that highlight key regions essential for answering questions. These bounding box annotations facilitate the computation of the RoI IoU reward during reinforcement learning, improving the model's ability to focus on relevant areas within document images. The dataset spans five domains, including text/document understanding, fine-grained understanding, charts, general visual question answering (VQA), and relational reasoning.
+
+We establish two training configurations to examine the model's adaptability to different levels of data diversity. The 4data4k setup focuses on document understanding, selecting 1,000 samples each from DocVQA [27], InfographicsVQA [28], TextCaps [37], and TextVQA [38] of Visual CoT dataset, totaling 4,000 instances. The 8data8k configuration extends training data to general VQA and relational reasoning by adding Flickr30k [33], GQA [12], Open Images [15], and VSR [21], with 1,000 samples per dataset, totaling 8,000 instances. This comparison examines how broader domain coverage impacts generalization. Unless specified, we adopt 4data4k configuration as default setting.
+
+Implementation Details. Our base model is Qwen2.5-VL
+
+3B and 7B [1], a state-of-the-art MLLM pretrained on curated web pages, open-source datasets, and synthetic data. To adapt it for document understanding tasks, we train it using the GRPO reinforcement learning framework, as described in Sec. 3. The model is trained for two epochs on eight NVIDIA A100 80GB GPUs, with a batch size of 2. The number of generated candidate responses for GRPO is set to $G = 6$ . We employ the AdamW optimizer [25], using a learning rate of $1e - 6$ . KL coefficient $\beta$ set to 0.04.
+
+Evaluation. We adopt Visual CoT Benchmark [35], a comprehensive multimodal data, to measure performance across a broad range of document reasoning tasks. Following Visual CoT evaluation protocol, we also assess model's zero-shot ability using SROIE [11], DUDE [16], and Visual7W [54] datasets, evaluating its capacity to generalize beyond its training distribution. We leverage the standard metrics provided by Visual CoT Benchmark [35] to evaluate the model.
+
+# 4.1. Main Results
+
+Tab. 1 presents the results of our model DocThinker compared to several state-of-the-art MLLMs on the Visual CoT benchmark. The evaluation spans both document-oriented understanding tasks (including text-based document comprehension and chart analysis) and general multimodal understanding (covering general VQA and relational reasoning). Our model demonstrates significant improvements over baseline models, particularly in document understanding tasks, and achieves strong generalization across multiple reasoning domains. Across document-oriented tasks, DocThinker-7B $(1536^{2},8\mathrm{k})$ achieves the highest overall scores, outperforming prior methods, including VisCoT-7B, Qwen2.5VL, and LLaVA variants. The document understanding improvements are largely attributed to the GRPO-based RL strategy with the multi-objective rewards, which enhances the
+
+model's ability to focus on task-relevant regions within documents. In chart understanding (InfoQA), DocThinker-7B $(1536^{2}, 4k)$ achieves 0.689, surpassing both VisCoT-7B $(336^{2}, 438k,$ row 5) and Qwen2.5VL-7B $(1536^{2},$ row 9), which score 0.324 and 0.674, respectively. This suggests that RL enables better multimodal reasoning, allowing the model to extract and interpret structured information from chart data representations.
+
+Zero Shot Capabilities. As shown in Tab. 1, highlighted results in gray indicate zero-shot generalization performance, where training data splits were not included in the training phase. Our model achieves competitive zero-shot results, particularly in DUDE and SROIE requiring fine-grained text recognition and layout-aware reasoning. Compared to Qwen2.5VL-7B (1536², row 7), which achieves 0.492 on DUDE and 0.708 on SROIE, our model reaches 0.568 on DUDE and 0.814 on SROIE. DocThinker outperforms all non-RL-based models, demonstrating that RL with verifiable rewards substantially improves performance in text-heavy, document-based tasks. The performance gap stems from training scale (4k vs. 438k) and zero-shot tasks compared to VisCoT. Still, DocThinker-7B (336²) outperforms VisCoT-7B (336²) on all non-zero-shot tasks using only 4k samples and same input. For general multimodal understanding, including VQA and relational reasoning, DocThinker (row 13) continues to achieve competitive performance compared to baselines on Flickr30k (0.701), Visual7W (0.625), GQA (0.694), and VSR (0.721). Particularly in relational reasoning tasks, which require understanding object interactions and contextual relationships, our RL framework enables superior performance. The zero-shot improvements suggest that RL enhances adaptability and generalization, allowing the model to generalize beyond its training distribution and reason effectively in previously unseen scenarios.
+
+RL vs. SFT. A direct comparison between supervised fine-tuning (SFT) and RL-based models demonstrates the clear advantage of reinforcement learning. Comparing Qwen2.5VL-7B (SFT, $336^{2}$ , 4k, row 8) with DocThinker-7B (RL, $336^{2}$ , 4k, row 12), we observe substantial gains across multiple tasks. For example, in DocQA, our model improves from 0.355 to 0.579, and in TextQA, it rises from 0.740 to 0.802. Similarly, in Visual7W, our RL model achieves 0.580 compared to 0.563 with SFT, and in GQA, it improves from 0.467 to 0.546. These improvements highlight that GRPO-based RL training enhances model reasoning and decision-making, enabling it to produce more explainable, structured, and accurate outputs. The multi-objective reward functions, particularly those focused on RoI IoU and rephrased question quality, contribute significantly to the model's ability to focus on relevant document regions and generate clearer reasoning traces.
+
+Explainability Ability. A key advantage of DocThinker
+
+over existing MLLMs for document understanding is its ability to generate explicit, explainable reasoning steps, rather than merely providing direct answers. Through our reinforcement learning framework, the model systematically breaks down its thought process into structured intermediate steps, with detailed reasoning enclosed in tags and the final response presented within tags. This structured output enhances transparency, making it easier to analyze how the model arrives at its conclusions. As qualitative performance is shown in Fig. 3, by incorporating structured reasoning rewards, including rephrased question clarity and RoI localization accuracy, our approach significantly enhances explainability over traditional SFT-based MLLMs, ensuring that responses are not only accurate but also more explainable and systematically derived.
+
+Visual Grounding. We further evaluate DocThinker on the TextREC dataset [9], which requires locating objects based on text-conditioned referring expressions. By leveraging RoI IoU reward, DocThinker effectively aligns textual and visual information, improving grounding accuracy. As shown in Tab. 2, DocThinker-7B achieves $82.4\%$ Precision@1, surpassing specialized models like TAMN $(80.8\%)$ and MDETR $(63.3\%)$ . The improvement highlights the impact of reinforcement learning with verifiable rewards, which enhances the model's ability to precisely localize objects tied to scene text. These results demonstrate that DocThinker extends beyond document understanding, excelling in spatial reasoning and multimodal grounding.
+
+| Model | Template1 | Template2 |
| Specialist Models |
| TransVG [6] | 50.1 | 54.0 |
| MAttNet [48] | 52.3 | 60.5 |
| QRNet [45] | 52.7 | 59.1 |
| MDETR [14] | 54.4 | 63.3 |
| TAMN [9] | 77.8 | 80.8 |
| DocThinker-7B | 82.4 |
+
+Table 2. Performance on the TextREC dataset. Precision@1 (%) is reported. Template1 and Template2 represent using two different ways to construct referring expressions proposed in [9]. Template1 is "The object with on it", and Template2 is "The with on it".
+
+# 4.2. Ablation Study
+
+Ablating Reward Functions. To assess the impact of reward functions, we ablate RoI IoU (RI) and Rephrase Question (RQ) rewards, analyzing their effect across four datasets, as provided in Tab. 3. Removing RoI IoU reduces performance, particularly on InfoQA and TextCaps, indicating its role in document understanding tasks requiring precise visual grounding. Eliminating Rephrase Question leads to notable
+
+Question: What is the number written in the clock?
+
+# Explainable Output:
+
+#
+
+The original question is quite vague and lacks context. However, since the image is about COVID-19, I will assume the question is about a specific number in the image. The number 24 is prominently displayed in the "What To Do" section, possibly related to a clock or a timer. I will rephrase the question to be more specific and then provide the answer.
+
+#
+
+#
+
+{“rephrase question”:"What is the number displayed on the clock in the 'What To Do' section of the image?", "bbox_2d":[822,480,842,515], "final_answer":"24"}
+
+#
+
+
+Figure 3. Qualitative results of DocThinker. The thinking process significantly improves the reasoning ability and explainability.
+
+Question: What is the name of the road mentioned in this letter?
+
+# Explainable Output:
+
+ The original question is straightforward but lacks context. To improve it, we need to specify the document and the part of the text that mentions the road. The image is a contract letter, which typically contains specific details such as addresses and locations. The road mentioned is part of the address for the recipient of the letter. The improved question should focus on the road in the recipient's address.
+
+#
+
+{ "rephrase question"; "What is the name of the road mentioned in the address of the recipient in this letter?"; "bbox_2d"; [255, 767, 519, 812],
+
+"final answer": "Pension Road"
+
+#
+
+EPP Contract
+
+January 19, 1999
+
+Contract No. 9104-00-00
+
+t R. J. Reynolds Tobacco Company
+
+Mr. Vincent Napp
+Cape Town, South Africa
+
+230 Pension Road
+P.O. Box 165
+San Francisco, CA
+
+EnglishroomNJ-07-16
+
+Attention: Mr. Napp
+
+
+
+When signed by you, this letter will constitute the Agreement between Old Bridge Tobacco Company and the United States Tobacco Association (the "TSA") and the United Nations Tobacco Enterprises, including its client, R. J. Reynolds Tobacco Company (both hereinafter referred to as SME), concerning advertising displays and promotional materials of the brand's brand name. The TSA's agreement on the termination of the mutual promises contained herein, the parties agree as follows:
+
+1. Rights Granted to SME
+
+During the term of this Agreement, Track grants to SME the following lignia:
+a. Signaee and Advertising
+
+SME shall have the right to use, erect or cause to be erected signage at Track as described in and conforming to all of the specifications in paragraph 1.2.1. The signs shall be used only for the purpose of including the right to display advertising copy on said signage during the construction of the building; otherwise provided herein, all signage shall be the property of Track.
+
+Question: At what time will the Birmingham Bowl match be broadcast?
+
+# Explainable Output:
+
+ The image provides details about the SEC Bowl and Alabama Bowl Games in 2014, including the times and dates for each game. The Birmingham Bowl match is scheduled for January 3rd at 11 am CT on ESPN. The question asks for the broadcast time of the Birmingham Bowl match, which is clearly stated in the image.
+
+#
+
+{"bbox_2d":[448,850,876,889],"final_answer":“11 am CT”,"rephrase question": "At what time will the Birmingham Bowl match, featuring East Carolina vs. Florida, be broadcast
+
+#
+
+
+
+drops in TextVQA and DocVQA, highlighting its importance for clarifying ambiguous queries to help the model generate more accurate and explainable responses. The most severe degradation occurs when both are removed, confirming their complementary contributions. This confirms that reinforcement learning with multi-objective rewards is crucial for enhancing both accuracy and reasoning quality in multimodal document understanding.
+
+| Method | DocVQA | TextCaps | TextVQA | InfoQA |
| DocThinker-7B | 0.795 | 0.738 | 0.827 | 0.689 |
| w/o RoI IoU | 0.775 | 0.693 | 0.803 | 0.637 |
| w/o Rephrase Question | 0.763 | 0.716 | 0.772 | 0.658 |
| w/o RI & RQ | 0.741 | 0.662 | 0.758 | 0.602 |
+
+Ablating KL Divergence. To evaluate the impact of KL divergence regularization, we analyze different values of the coefficient $\beta$ and its effect on performance across four document-oriented datasets. As shown in Tab. 4, when KL regularization is entirely removed ( $\beta = 0$ ), the model exhibits a decline in performance across all datasets, particularly in TextVQA and DocVQA, indicating that KL regularization plays a key role in stabilizing training and preventing catastrophic forgetting during reinforcement learning. Introducing a small KL weight ( $\beta = 0.001$ ) improves performance slightly but does not fully match the stability
+
+compared to setting $\beta = 0.04$ . The results suggest that an appropriate KL divergence coefficient is crucial for maintaining balance between exploration and stability, ensuring robust performance across datasets.
+
+Table 3. Ablation study of reward functions. The DocThinker uses $1536^{2}$ input size with 4data4k training data setting. RI and RQ short for RoI IoU and rephrase question reward, respectively.
+
+| Method | DocVQA | TextCaps | TextVQA | InfoQA |
| DocThinker-7B (β = 0.04) | 0.795 | 0.738 | 0.827 | 0.689 |
| w/o KL (β = 0) | 0.780 | 0.719 | 0.803 | 0.676 |
| β = 0.001 | 0.785 | 0.726 | 0.812 | 0.682 |
+
+Table 4. Ablation study of the effect of KL Divergence. The DocThinker uses $1536^{2}$ input size with 4data4k training data setting.
+
+# 5. Conclusions and Future Works
+
+In this work, we introduced DocThinker, a reinforcement learning-based framework designed to enhance explainability, adaptability, and reasoning ability in multimodal document understanding. By leveraging Group Relative Policy Optimization and a multi-objective reward system, our approach dynamically refines reasoning strategies at inference time, overcoming the limitations of static Chain-of-Thought reasoning and supervised fine-tuning. DocThinker achieves state-of-the-art or highly competitive performance on standard benchmarks compared with previous SFT-based methods across multiple document understanding tasks. Expanding DocThinker to larger multimodal models and broader reasoning tasks and scenarios, such as scientific and legal document analysis, could further improve adaptability.
+
+Acknowledgements. This work was supported by the NSFC (62225603, 62206104), and Alibaba AIR program.
+
+# References
+
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+# Does Your Vision-Language Model Get Lost in the Long Video Sampling Dilemma?
+
+Tianyuan $\mathrm{Qu}^{1*}$ Longxiang Tang $^{2*}$ , Bohao Peng $^{1}$ , Senqiao Yang $^{1}$ , Bei Yu $^{1}$ , Jiaya Jia $^{2}$ $^{1}$ CUHK ${ }^{2}$ HKUST
+
+
+Figure 1. Illustration of the Sampling Dilemma in Long Video Analysis: (Left) In Q1, identifying a camera wearer's visited locations requires analyzing the entire video. However, key frames are sparse, so sampling one frame per minute often provides enough information. In contrast, Q2 examines the packing order during checkout, requiring high-resolution sampling to capture rapid actions. (Right) Sampling Dilemma emerges in tasks like Q2: a low sampling density fails to provide sufficient visual cues for accurate answers, while a high sampling density results in redundant frames, significantly slowing inference speed. This challenge underscores the need for adaptive sampling strategies, especially for tasks with high necessary sampling density.
+
+
+
+
+
+# Abstract
+
+The rise of Large Vision-Language Models (LVLMs) has significantly advanced video understanding. However, efficiently processing long videos remains a challenge due to the "Sampling Dilemma": low-density sampling risks missing critical information, while high-density sampling introduces redundancy. To address this issue, we introduce LDBench, the first benchmark designed to evaluate LVLMs on long-video tasks by constructing high Necessary Sampling Density (NSD) questions—where NSD represents the minimum sampling density required to accurately answer a given question. LDBench focuses on dense, short-duration actions to rigorously assess the sampling strate
+
+gies employed by LVLMs. To tackle the challenges posed by high-NSD questions, we propose a novel Reasoning-Driven Hierarchical Sampling (RHS) framework, which combines global localization of question-relevant cues with local dense sampling for precise inference. Additionally, we develop a lightweight Semantic-Guided Frame Selector to prioritize informative frames, enabling RHS to achieve comparable or superior performance with significantly fewer sampled frames. Together, our LSDBench and RHS framework address the unique challenges of high-NSD long-video tasks, setting a new standard for evaluating and improving LVLMs in this domain. Our benchmark and evaluation codes has been released at: https://github.com/dvlabresearch/LSDBench
+
+# 1. Introduction
+
+With the emergence of large vision-language models (LVLMs) [2, 4, 8, 14, 16, 19, 22, 24, 34, 43, 49], research on video understanding [4, 7, 19, 21, 27, 32, 40, 46, 48] has advanced significantly; however, tasks involving the understanding of long videos [9, 28, 41, 50] remain in an exploratory stage. For LVLMs, learning from real-world recordings is vital to grasp the complexities of the physical world. This capability is particularly critical for downstream applications such as embodied intelligence [12, 13, 36, 42], wearable devices [38, 39], and security surveillance [29, 51], where the ability to process long videos efficiently and accurately is a fundamental requirement.
+
+To complete video tasks effectively, it is necessary to acquire a sufficient amount of visual cues relevant to the given question. Existing video LVLMs [4, 17, 34, 40] typically utilize a global uniform sampling strategy to collect such visual cues. While this approach works well when videos are short or the required visual cues persist over a long segment, it encounters significant challenges when the critical visual cues are concentrated within a small portion of a long video. In such cases, increasing the sampling density may appear to be a solution. However, this introduces the "Sampling Dilemma", which arises from the following trade-offs:
+
+- With low sampling rates risk overlooking critical information in essential segments, leading to task failure.
+- Conversely, with high sampling rates, numerous redundant frames from irrelevant segments are included, which wastes valuable context length, increases computational overhead, and potentially introduces noise, thereby reducing accuracy.
+
+For example, consider Question 2 in Figure 1, which asks about the details of packing items at a cashier counter. The relevant actions occur within a brief segment of a one-hour video, with each step lasting about one second. Answering this question using global uniform sampling would require a high rate—around 1 frame per second—to capture sufficient cues. However, this approach leads to an overwhelming number of irrelevant and redundant frames, significantly increasing computational costs and often exceeding the input context length of VLMs. This trade-off between sampling density and efficiency is a core challenge for long-video tasks.
+
+To emphasize the sampling dilemma in long video tasks, we first define the concept of Necessary Sampling Density (NSD): the minimum sampling density required, under uniform sampling, to extract sufficient information from a video to answer a question. Building upon this, we introduce the Long-video Sampling Dilemma Benchmark (LSDBench), which consists of a set of questions characterized by high NSD requirements and videos lasting for hour. In our benchmark, we construct questions about action sequences within short segment of long videos [10], such as
+
+Question 2 in Figure 1. These sequences involve densely distributed, short-duration actions, ensuring a high NSD for each question. Meanwhile, we incorporate temporal referring in the question phrasing to explicitly direct attention to the target segment. This design—featuring local segments with high NSD and a high proportion of question-irrelevant content across the whole video—provides a more intuitive and rigorous way to evaluate the effectiveness of different sampling strategies.
+
+To efficiently construct such a dataset, we developed a fully automated pipeline for question generation and filtering. Central to this process is a temporal structuring strategy, designed to effectively organize video content for question generation. To guarantee the quality of the generated questions, we introduced a two-round filtering mechanism, which successfully eliminated over $90\%$ of low-quality questions. Furthermore, we incorporated an adversarial iteration strategy to enhance the distractor options in multiple-choice questions. This approach minimizes the possibility of models correctly answering questions based solely on the text of the question and options, particularly in scenarios where the sampled visual cues are limited.
+
+With LSDBench, we can investigate sampling dilemma quantitatively. A straightforward method to tackle it is to allow the model to perform dense sampling only in important regions. Based on this, we propose a two-stage Reasoning-Driven Hierarchical Sampling (RHS) framework: in the first stage, the video is sparsely sampled, and the VLM locate visual cues relevant to the question via reasoning. In the second stage, the segments corresponding to these key frames are densely sampled to provide sufficient information for the model to infer the final answer. Considering the potential missing of necessary information during sparse sampling, we further introduce a light-weighted Semantic-guided Frame Selector (SGFS), extracting an optimal frame set with maximum visual information. Using this approach, our method enables existing models to achieve better performance than uniform global sampling, even with a significantly reduced number of sampled frames.
+
+Our contributions can be summarized as following:
+
+- LSDBench: We propose LSDBench, a benchmark that focuses on the sampling dilemma in long-video tasks. Through well-designed tasks, it evaluates the sampling efficiency of long-video VLMs. We also provide a fully automated data generation and filtering pipeline, which can easily construct high-quality multiple-choice QA pairs for very long video.
+- Reasoning-Driven Hierarchical Sampling: We propose a two-stage, training-free framework that improves long-video processing efficiency by focusing VLM on important segments. This provides a sampling-efficient solution for handling long video tasks.
+
+- Semantic-Guided Frame Selector: We introduce a module that selects frames with higher visual information content without any question prior. Combined with RHS, this approach achieves comparable or even better accuracy on LDBench with significantly fewer total sampled frames.
+
+# 2. Related Work
+
+Long Video Benchmarks. In recent years, benchmarks for evaluating long-video processing capabilities [6, 7, 9, 28, 37, 50] have gained attention. EgoSchema [28] and ActivityNet-QA [45] introduced high-quality datasets focusing on actions within long videos. EgoSchema proposed the concept of temporal certificates to measure the inherent difficulty of video-related tasks. LongVideoBench [41], Video-MMLU [33] and Video-MMMU [11] designed reasoning tasks, such as referring reasoning, to test models' ability to handle long videos, with a primary focus on segment retrieval. However, like other benchmarks such as VideoMME [9] and CinePine [31], many of their question relies heavily on audio modality. In contrast, our work emphasizes understanding long videos purely in the visual modality. Additionally, works like LongVA [48], MLVU [50], and LongVila [7] introduced the Visual Needle-In-A-Haystack (V-NIAH) experiment to evaluate models' ability to locate and retrieve visual information within long contexts. However, these experiments insert probes after sampling, ignoring the sampling challenges inherent to long video analysis, a critical issue for long-video processing. Our LSDBench specifically addresses the sampling problem by designing tasks on long videos with high necessary sampling density, aiming to evaluate the effectiveness of sampling strategies employed by video VLMs.
+
+Long-form Video Understanding. In the domain of long-form video understanding, end-to-end models such as Qwen2VL [4], Qwen2.5VL [4], LongVila [48], LLaVA-OV [19], and Gemini [34] have demonstrated remarkable performance. However, these approaches still encounter notable challenges when it comes to sampling strategies. For instance, Qwen2.5VL introduced a dynamic sampling strategy aimed at balancing efficiency and performance, yet this approach operates at the global video level, overlooking redundancy in video segments. To adress this, some recent works try to reduce the redundancy from a token level. To tackle this issue, some recent works [5, 20, 23, 25, 44, 49] attempt to reduce redundancy at the token level by leveraging visual token compression strategies. Additionally, some other methods [3, 26, 47] leverage the Retrieval-Augmented Generation (RAG) [15, 18] paradigm by segmenting long videos into smaller chunks, pre-processing them, and building an index to facilitate the quick retrieval of question-
+
+relevant details during inference, thus enabling accurate responses. While this approach effectively avoids the tradeoff between sampling density and inference speed, it inherently makes RAG-based methods unsuitable for real-time scenarios.
+
+# 3. Dataset
+
+In this section, we first introduce our definition of necessary sampling density (NSD) and explain how this concept serves as the foundation for designing our task. Next, we detail the automated pipeline we developed for question-answer generation. Finally, we provide statistical information about the LSDBench dataset.
+
+# 3.1. Necessary Sampling Density
+
+We define the necessary sampling density (NSD) of a question as the minimum sampling density required, under uniform sampling, to extract sufficient information from a video to answer a question, assuming no prior knowledge of the video.
+
+Consider the question shown in Figure 1, "What is the journey of the camera wearer in the video?" To answer this question, we need to watch the entire video, identify all locations visited, and determine their chronological order. Although the video is nearly an hour long and the task seems challenging, the camera wearer usually stays at each location for several minutes to tens of minutes, making the process more manageable. As a result, even if we employ a sparse sampling strategy—capturing only a single frame every few minutes—it is highly likely that a sampled frame will contain sufficient visual cues to identify the location. This suggests that even with such sparse sampling density, there is a significant chance of gathering enough visual cues to answer the question.
+
+Furthermore, when the question is presented in a multiple-choice format and the distractors are not well-designed, the model can often guess the correct answer by leveraging the provided options, even if some critical cues are missed. The idea that "sampling just one frame per minute can allow us to answer a question about an hour-long video" may seem counterintuitive and unreliable. However, this type of low NSD problem fails to truly reveal the challenges of designing sampling strategies for long-video tasks since high NSD problem is more important and common.
+
+# 3.2. Task Design
+
+We aim to design a task for hour-long videos that has a sufficient NSD to emphasize the importance of sampling in long video tasks. Specifically, we construct questions about action sequences within short segments of long videos, such as Question 2 in Figure 1. Since the intervals between actions and the duration of each action are only a few seconds, this ensures that the questions have a sufficiently high
+
+
+Figure 2. Pipeline of our four-stage data annotation pipeline. We first segment the video into one-minute intervals and generate captions for each segment. These captions are then hierarchically clustered: the first layer clusters by scenes, while the second layer clusters by actions or events. Once the hierarchical tree structure is established, we utilize GPT-4o to generate questions, which are subsequently filtered and optimized through a two-round refinement process. For generating free-form answers to the questions, we leverage Gemini 2.0 Flash combined with narration-based annotations as auxiliary input. Finally, we construct multiple-choice options iteratively in an adversarial manner using GPT-4o.
+
+NSD. Meanwhile, temporal references are integrated into the question formulation to explicitly direct attention to the target segment, thereby reinforcing the necessity of understanding the video's overall temporal structure. This design—featuring local segments with high NSD and a high proportion of redundant content across the video—makes our LSDBench more effective in evaluating the performance of VLMs in handling long videos and assessing the quality of their sampling strategies.
+
+# 3.3. Annotation Pipeline
+
+We have meticulously designed a four-stage pipeline for fully automated QA generation. These four stages include (1) video hierarchical structuring, (2) question generation, (3) answer generation, and (4) multiple-choice question construction, as illustrated in Figure 2. We utilized the subset of long videos1 and corresponding action narrations annotated by human provided by EGO4D [10] for our data construction.
+
+Video Hierarchical Structuring. Due to the extreme length of long videos, directly inputting the entire video and its annotations into an LLM for question generation is not
+
+feasible [6]. Excessively long context inputs significantly degrade the instruction-following capabilities of LLMs and the quality of generated questions. Moreover, it becomes difficult to control the necessary sampling density and temporal certificate length for the questions.
+
+To address this, we propose a hierarchical structuring of the video. First, we use the caption generated by GPT-4o for each individual minute of the video. These captions are then clustered hierarchically: high-level clustering is performed at the scene level, and low-level clustering is based on activities/events within each scene. A summary is simultaneously generated for each cluster. This process produces a tree-structured temporal hierarchy of the video, facilitating targeted questioning for specific segments of the video.
+
+Question Generation. We select nodes in the hierarchical structure with a duration of less than 5 minutes and use their summaries for question generation. We observed that directly providing narrations to LLM along with generating answers leads to reduced question diversity. To address this, we decouple question and answer generation into two independent stages. At this stage, LLM [1, 14] generates questions solely based on the summaries of the clustered segments. This approach largely enhances the diversity of
+
+
+(a) Option length (words)
+
+
+(b) Word cloud
+
+
+(c) Target segment duration (min)
+Figure 3. Dataset statistics visualization.
+
+
+(d) Video duration (min)
+
+the questions.
+
+We also stipulate that the generated questions must include a referring expression that explicitly points to the relevant video segment to avoid ambiguity.
+
+Next, we perform a two-round filtering process to refine the generated questions:
+
+- First round of filtering: We remove questions with unclear or ambiguous referring expressions. By providing LLM with only the question statement and the hierarchical structure, we validate whether the question clearly targets a specific segment. Questions leading to ambiguity or targeting segments too long are discarded.
+- Second round of filtering: Since all previous stages rely on LLM-generated content, factual inaccuracies may arise. In this stage, we incorporate narrations from the corresponding time segment along with an additional 2 minutes of context on either side (before and after the segment) to verify the question. Questions totally unrelated to the narrations are removed, and the time boundaries of the target segment are adjusted based on the narrations.
+
+Answer Generation. We use large multi-modal modal (LMM, here we use Gemini-2.0-Flash [34], which supports long video inputs) to generate answers. The input to the model consists of all narrations within the target segment, the question, and corresponding video clip. LMM organizes and generates the answer based on these inputs.
+
+Multiple-Choice Question Construction. We leverage LLM to transform free-form answers into multiple-choice questions. To prevent scenarios where the correct answer can be easily guessed based on the question and options alone, we incorporate an adversarial option optimization process. Specifically, we simulate the process of guessing the correct answer by reasoning solely based on the question and options, without any visual information. The reasoning process is collected and used to iteratively refine the design of the options.
+
+# 3.4. Dataset Statistics
+
+The dataset comprises 1304 QA pairs derived from 400 videos, with an average option length of 20.7 words. The
+
+
+Figure 4. Overview of our Reasoning-Driven Hierarchical Sampling (RHS) framework.
+
+target segments have an average duration of 3 minutes, with the majority falling within the 2-4 minute range, and very few exceeding 5 minutes. The analyzed videos have an average duration of 45.39 minutes, with lengths ranging from 20.32 to 115.32 minutes. A QA generation pipeline was applied to 400 videos, initially producing 11,342 questions. However, through a rigorous multi-stage filtering process, this number was reduced to 1304 finalized QA pairs, representing a retention rate of $11.6\%$ , ensuring high data quality.
+
+# 4. Method
+
+# 4.1. Reasoning-Driven Hierarchical Sampling
+
+To address the challenge of high necessary sampling density in long videos efficiently, we propose Reasoning-Driven Hierarchical Sampling (RHS), a two-stage framework tailored for long video tasks.
+
+Our core idea is to leverage large model's reasoning capability to exploit the temporal structure of the video in a top-down manner. Specifically, we aim to infer the approximate locations of short-term temporal information by reasoning over the sparse sampled keyframes. For example, we can reason about event progression, temporal order, or scene transitions. Since short-term temporal information is largely derived from motion, and adjacent frames tend to be spatially similar, we can identify regions where dense sampling is necessary by reasoning over the spatial semantics of sparsely sampled keyframes. This demand-driven sampling approach not only significantly reduces the computational overhead caused by processing redundant segments but also preserves the ability to capture highly fine-grained temporal details.
+
+As shown in Figure 4, our method comprises two stages: ① Reasoning-driven Visual Cues Localization, and ② Dense-Sampling Inference. In the first stage, we perform Sparse Sampling to select keyframes. The video is then partitioned into segments, with midpoints between keyframes as boundaries. These keyframes and their indices are fed into VLM, which reasons over the question and spatiotemporal context (e.g., chronological order, causal logic,
+
+co-occurrence of objects) to identify segments that has visual cues relevant to the question. In the second stage, the selected segments are densely sampled to gather finer-grained temporal details. The sampled frames are concatenated and input into the VLM for question answering.
+
+This framework focuses dense sampling only on key segments, significantly reducing redundant inputs while handling high NSD tasks. However, sparse sampling in first stage may occasionally miss critical information, motivating us to explore more effective sampling strategies.
+
+# 4.2. Semantic-Guided Frame Selector
+
+Our primary objective is to ensure that the sparsely sampled keyframe set captures as much essential information as possible. Each keyframe should effectively represent a distinct temporal segment of the video, facilitating more accurate reasoning by the VLM during the first stage.
+
+To achieve this, we propose the efficient, plug-and-play Semantic-Guided Frame Selector (SGFS) that selects a subset of frames containing the richest information from the initial larger frame set.
+
+Specifically, we begin by uniformly sampling $n$ frames without any prior knowledge. Our objective is to select a subset of keyframes with target size $k$ such that the sum of similarities between any two adjacent frames in the subset is minimized, thereby maximizing the diversity of the selected frames and the overall information captured. Using a lightweight visual encoder (e.g. SigLIP2 [30, 35]), we extract embeddings for these frames. Formally, for a frame $F_{i}$ , we compute its embedding vector $e_{i}$ as: $e_{i} = \operatorname{Encoder}(F_{i})$ , $i \in \{1, 2, \dots, n\}$ , where $e_{i} \in \mathbb{R}^{d}$ and $d$ is the dimension of the embedding space. Next, we compute pairwise cosine similarity between frames to form a similarity matrix $S$ . For two frames with indices $i$ and $j$ , the similarity is given by:
+
+$$
+S _ {i j} = \frac {e _ {i} \cdot e _ {j}}{\left\| e _ {i} \right\| \cdot \left\| e _ {j} \right\|}. \tag {1}
+$$
+
+To improve robustness and prevent the selected subset from being overly concentrated in some period, we introduce distance penalty for the temporal proximity of adjacent frames. For two frames with indices $i$ and $j$ :
+
+$$
+P _ {i j} = - \lambda * \left| \frac {i}{n} - \frac {j}{n} \right| ^ {\beta}, \tag {2}
+$$
+
+where $P_{ij}$ denotes the distance penalty between these two frames, $\lambda$ and $\beta$ are hyperparameters. This results in a final weight matrix $W$ where:
+
+$$
+W _ {i j} = S _ {i j} + P _ {i j}. \tag {3}
+$$
+
+Formally, the optimal subset of keyframes can be selected by minimizing the sum of pairwise weights between
+
+consecutive frames in the subset. Let the selected set of keyframe indices be denoted as $\mathcal{K} = \{K_1, K_2, \ldots, K_k\}$ , where $K_1 < K_2 < \dots < K_k$ . The selection objective can be written as:
+
+$$
+\mathcal {K} = \underset {\mathcal {K} \subseteq \{1, 2, \dots , n \}, | \mathcal {K} | = k} {\arg \min } \sum_ {i = 1} ^ {k - 1} W _ {K _ {i}, K _ {i + 1}}. \tag {4}
+$$
+
+We use a dynamic programming algorithm as shown in Algorithm 1 to compute the optimal subset of keyframes efficiently.
+
+Algorithm 1: Frame Sampling Algorithm
+Input: $n$ frames, target count $k$ , weight matrix $W$
+Output: Selected frame indices
+1 dp[0..n, 0..k] $\leftarrow \infty$ , trace[0..n, 0..k] $\leftarrow -1$ , dp[0, 0] $\leftarrow 0$ ;
+2 for $j = 1$ to $k$ do
+3 for $i = j$ to $n$ do
+4 for $p = j - 1$ to $i - 1$ do
+5 if dp[p, j - 1] + W[p, i] < dp[i, j] then
+6 dp[i, j] $\leftarrow dp[p, j - 1] + W[p, i]$ ;
+7 trace[i, j] $\leftarrow p$ ;
+8 sel $\leftarrow \emptyset$ , $i \leftarrow n$ , $j \leftarrow k$ ;
+9 while $j > 0$ do
+10 sel $\leftarrow$ sel $\cup \{i\}$ , $i \leftarrow$ trace[i, j], $j \leftarrow j - 1$ ;
+11 return reverse(sel);
+
+# 5. Experiments
+
+In this section, we present the results of state-of-the-art long-video VLMs, as well as our proposed 2-stage method on our benchmark. We also conduct ablation studies on RHS and the SGFS.
+
+# 5.1. Experiment Setting
+
+To comprehensively evaluate the performance of long-video VLMs on our task, we selected the following models: Gemini-2.0-Flash [34], Qwen-2.5VL [4], Qwen-2VL [4], LongVA [48], LongVila [7], InternVideo2.5 [8]
+
+We experimented with different sampling strategies and frame count settings for these models to explore the relationship between sampling configurations and model performance on the task. The specific configurations are detailed in the table provided. It is worth noting that under the 1-FPS sampling density setting, the number of sampled frames exceeded the context length limitation of most models. Therefore, for models that could not support a sampling rate of 1-FPS, we adopted a fixed sampling frame count setting for evaluation. To ensure fairness, all other generation configurations followed their original settings.
+
+Additionally, we report the performance of our 2-stage method applied on Qwen2.5-VL. In our approach, we use Siglip2 [35] as the encoder for the sampling module. The initial sampling rate is set to 4 frames per minute, and the
+
+| Method | Sampling | Frames | SD (f/s) | Acc (%) |
| Only Text |
| Gemini-2.0-Flash | - | - | - | 29.1 |
| Qwen2-VL | - | - | - | 30.5 |
| LongVila | - | - | - | 36.9 |
| Qwen2.5-VL | - | - | - | 30.2 |
| InternVideo2.5 | - | - | - | 36.1 |
| Oracle (avarage 3 min) |
| Gemini-2.0-Flash Oracle | 1-FPS | 180 | 1 | 64.8 |
| LongVila Oracle | Fixed | 64 | 0.35 | 54.2 |
| 128 | 0.7 | 52.0 |
| 256 | 1.4 | 51.9 |
| InternVideo2.5 Oracle | Fixed | 64 | 0.35 | 58.3 |
| 128 | 0.7 | 58.9 |
| 256 | 1.4 | 59.1 |
| Qwen2.5-VL Oracle | 0.1-FPS | 18 | 0.1 | 49.6 |
| 0.2-FPS | 36 | 0.2 | 52.1 |
| 0.25-FPS | 45 | 0.25 | 53.2 |
| 0.5-FPS | 90 | 0.5 | 54.9 |
| 1-FPS | 180 | 1 | 56.4 |
| Full Video (average 45 min) |
| LongVA | Fixed | 256 | 0.1 | 31.3 |
| 512 | 0.2 | 33.0 |
| 1024 | 0.4 | 32.5 |
| Qwen2-VL | Fixed | 256 | 0.1 | 48.0 |
| Qwen2.5-VL | Fixed | 256 | 0.1 | 50.1 |
| 768 | 0.3 | 52.5 |
| LongVila | Fixed | 256 | 0.1 | 49.8 |
| InternVideo2.5 | Fixed | 256 | 0.1 | 50.1 |
| Qwen2.5-VL (Ours) | RHS | 225 | 1 | 52.2 |
| Gemini-2.0-Flash | 1-FPS | 2700 | 1.00 | 56.2 |
+
+frame retention ratio for the sampling module is set to 0.25. The length penalty $\lambda$ is 10.0 and $\beta$ is 0.3.
+
+# 5.2. Results On Benchmark
+
+We conducted the Oracle experiment by exclusively using the annotated target segments of the videos as input. This setup was designed to evaluate the upper-bound performance achievable under ideal sampling conditions, where sufficient visual information is guaranteed, given a fixed total number of sampled frames. Comparatively, the results obtained from global uniform sampling of the full video input reveal a striking contrast. Even with several times more
+
+Table 1. Performance comparison of different models and sampling strategies. We present three testing settings in total: Only Text, Oracle, and Full Video. In the Only Text setting, the model is provided with no visual information whatsoever. The Oracle setting involves using the annotated target segment as the video input, while the Full Video setting provides the complete long video as input. The "Sampling" column lists the sampling strategies used: FPS represents sampling at fixed time intervals, fixed denotes uniform sampling with a fixed number of frames, and 2stage refers to the method we propose. Under each sampling strategy, the average number of sampled frames during evaluation on the LSD-Bench dataset is reported in the "Frames" column, along with the corresponding sampling density (SD).
+
+| Gemini-2.0-Flash | Qwen2.5-VL | Qwen2.5-VL (Oracle) |
| LongVA | InternVideo2.5 | InternVideo2.5 (Oracle) |
| Qwen2-VL | Gemini-2.0-Flash (Oracle) | Qwen2.5-VL (Ours) |
| LongVila | LongVila (Oracle) | |
+
+
+Figure 5. The line graph illustrates the relationship between the number of sampled frames (x-axis) and accuracy on LSD-Bench (y-axis). Solid lines represent results under the Full Video setting, while dashed lines with inverted triangles correspond to the Oracle setting. The gap between the Oracle and global uniform sampling highlights the potential for improved sampling strategies in long-video VLMs.
+
+sampled frames under uniform sampling, the performance remains significantly below that of the Oracle setup.
+
+As illustrated in Table 1, the benefits of increasing the number of sampled frames diminish progressively under global uniform sampling. For example, when increasing the sampled frames from 128 to 256, many models even exhibit a decline in accuracy. Additionally, further increasing the sampling density often results in input lengths exceeding the maximum context length supported by the models. While Gemini-2.0-Flash is capable of handling an ultralong context length of up to 1 million tokens, even at a 1 fps sampling rate, its global uniform sampling results lag by $8.6\%$ compared to the Oracle setup. These findings underscore the inefficiency of global uniform sampling in utilizing the sampled frames. The redundant inputs not only fail to enhance performance but also introduce noise, negatively impacting the model's ability to realize its full potential. The gap between Oracle performance and global uniform sampling highlights a substantial opportunity for improvement in sampling strategies for long-video VLM.
+
+Our proposed RHS demonstrates significant efficiency gains. For instance, on Qwen2.5-VL, it achieves an accuracy of $52.2\%$ using just 225 sampled frames, which is comparable to the global uniform sampling result achieved with the model's maximum setting of 768 frames. Moreover, it surpasses the result obtained with 256 globally uniformly sampled frames by $2.1\%$ . Notably, our method achieves these results without requiring any additional training of the model. This demonstrates that improving the sampling strategy can lead to better performance with substantially fewer sampled frames, validating the effectiveness of our approach.
+
+| Sampling | Frames | Acc (%) |
| 1 Stage Methods |
| Fixed 32 | 32 | 45.2 |
| Fixed 128→32 | 32 | 48.3 (+3.1) |
| Fixed 64 | 64 | 48.3 |
| Fixed 128→64 | 64 | 47.3 (-1.0) |
| Fixed 256→64 | 64 | 48.7 (+0.4) |
| Fixed 128 | 128 | 51 |
| Fixed 256→128 | 128 | 51.3 (+0.3) |
| Fixed 512→128 | 128 | 51.8 (+0.8) |
| Fixed 256 | 256 | 50.1 |
| Fixed 512→256 | 256 | 49.6 (-0.5) |
| Fixed 1024→256 | 256 | 51.0 (+0.9) |
| Fixed 768 | 768 | 52.5 |
| 0.1-FPS | 262 | 50.2 |
| 0.2-FPS | 523 | 51.6 |
| 0.25-FPS | Out of context length | - |
| 0.3-FPS | Out of context length | - |
+
+2 Stage Methods
+
+| Sparse Sampling | Dense Sampling | Frames | Acc (%) |
| Oracle | 0.25-FPS | 45 | 53.2 |
| 1-FPM | 0.25-FPS | 90 | 49.4 |
| 4-FPM→1-FPM | 0.25-FPS | 90 | 49.9 (+0.5) |
| Oracle | 0.5-FPS | 90 | 54.9 |
| 1-FPM | 0.5-FPS | 135 | 49.4 |
| 4-FPM→1-FPM | 0.5-FPS | 135 | 50.2 (+0.8) |
| Oracle | 1-FPS | 180 | 56.4 |
| 1-FPM | 1-FPS | 225 | 51.0 |
| 4-FPM→1-FPM | 1-FPS | 225 | 52.2 (+1.2) |
+
+Table 2. Comparison with different sampling strategies and ablation studies on SGFS. We conducted experiments on Qwen2.5-VL. The "Frames" column shows the average total sampled frames for different settings on LSBench. In the 1-stage section, we compare global uniform sampling with direct SGFS results. In the 2-stage section, we present results for the Oracle and RHS methods. FPM denotes sampling one frame per minute. The arrow $(\rightarrow)$ indicates the initial uniform sample count on the left and the retained frames after SGFS filtering, along with the average sampling density, on the right.
+
+# 5.3. Ablation Study
+
+As shown in the Table 2, we conducted an ablation study to evaluate our proposed method. For the experiments, we selected Qwen2.5-VL as the VLM. Initially, we tested global sampling approach, where we fixed the number of sampled frames passed into the VLM. When the initial sampled frames reached 4 times the target frame count, our sampling module was able to improve the accuracy of the VLM to varying extents, even though our module only considers semantic information. We provide additional visualizations of the frames sampled with using SGFS in Appendix for reference. Notably, our sampling module is lightweight, when compared to the computational cost of the VLM processing the video, the overhead introduced by the sampling process is almost negligible.
+
+When employing the complete RHS method, where the sampling module is used during the initial sparse sampling phase, the results demonstrate significant improve
+
+
+Figure 6. Correlation between overall accuracy (y-axis) and the coverage rate of the first-stage predictions on the ground truth target segments (x-axis).
+
+
+
+ments over direct uniform sampling. For instance, in the first stage, we set the initial sampling rate to 4 frames per minute, with the sampling module retaining 1 in 4 frames. In the second stage, we adopted a 1-FPS sampling rate. This configuration achieved an accuracy of $52.2\%$ , with the total number of sampled frames averaging around 225. In contrast, using a global uniform sampling method at 0.1 FPS resulted in an accuracy of only $50.23\%$ , despite averaging 263 sampled frames. These findings highlight the efficiency advantage of our method in terms of sampling density.
+
+Additionally, as illustrated in Figure 6, we plotted the correlation between overall accuracy and the coverage rate of the first-stage predictions on the ground truth target segments. It is evident that with the inclusion of our SGFS, the correlation line exhibits a steeper slope compared to uniform sparse sampling. Furthermore, under the same coverage rate, our approach achieves higher accuracy. This highlights that the frame set selected by our sampling module retains more valuable information, allowing the VLM to better localize and reason about visual cues. Further ablation studies on hyperparameters are provided in the Appendix.
+
+# 6. Conclusion
+
+In this work, we present LSDBench, the first benchmark designed to emphasize Necessary Sampling Density (NSD) in long-video tasks. LSDBench evaluates LVLMs in high-NSD scenarios with densely packed actions and temporally structured questions. To tackle the sampling challenge, we propose a Reasoning-Driven Hierarchical Sampling framework and a Semantic-Guided Frame Selector (SGFS), improving efficiency and accuracy by focusing on key segments and informative frames. AAdditionally, the SGFS can be applied to various video tasks while taking only a small amount of additional computational overhead. Our contributions set a new standard for advancing long-video understanding in high-NSD tasks.
+
+# References
+
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+
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+
+# Acknowledgement
+
+This work was supported in part by the Research Grants Council under the Areas of Excellence scheme grant AoE/E-601/22-R.
\ No newline at end of file
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+# Domain Generalizable Portrait Style Transfer
+
+Xinbo Wang $^{1\dagger}$
+
+Wenju $\mathbf{X}\mathbf{u}^{2\dagger}$
+
+Qing Zhang $^{1,3*}$
+
+Wei-Shi Zheng $^{1,3}$
+
+$^{1}$ School of Computer Science and Engineering, Sun Yat-sen University, China $^{2}$ AMAZON
+ $^{3}$ Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China
+
+wangxb29@mail12.sysu.edu.cn xuwenju123@gmail.com
+
+zhangq93@mail.sysu.edu.cn wszheng@ieee.org
+
+
+
+
+Figure 1. Domain generalizable portrait style transfer. By training on the CelebAMask-HQ dataset with only 30K portrait photos, our method allows for high-quality semantic-aware style transfer between any two portraits from a wide variety of domains including photo, cartoon, sketch, animation, etc.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+# Abstract
+
+This paper presents a portrait style transfer method that generalizes well to various different domains while enabling high-quality semantic-aligned stylization on regions including hair, eyes, eyelashes, skins, lips, and background. To this end, we propose to establish dense semantic correspondence between the given input and reference portraits based on a pre-trained model and a semantic adapter, with which we obtain a warped reference semantically aligned with the input. To ensure effective yet controllable style transfer, we devise an AdaIN-Wavelet transform to balance content preservation and stylization by blending low-frequency information of the warped reference with high-frequency information of the input in the latent space. A style adapter is also designed to provide style guidance from the warped reference. With the stylized latent from AdaIN-Wavelet transform, we employ a dual-conditional diffusion model
+
+that integrates a ControlNet recording high-frequency information and the style guidance to generate the final result. Extensive experiments demonstrate the superiority of our method. Our code and trained model are available at https://github.com/wangxb29/DGPST.
+
+# 1. Introduction
+
+Portrait style transfer has gained popularity as an advanced image editing technique, providing an automated way to apply the visual style of a reference portrait to an input portrait. This task is particularly challenging as it requires precise local tone adjustments across different facial regions, such as the skin, lips, eyes, hair, and background, to faithfully replicate the reference style while preserving the portrait identity and facial structure details. As illustrated in Figure 1, this technique is expected to enable a wide range of transformations, such as converting a human portrait into various artistic styles, modernizing old photographs, and adding color to sketch images, allowing casual photographers to effortlessly transform their photos into stunning
+
+masterpieces inspired by their favorite artworks.
+
+To enhance the efficiency of portrait style transfer, several prior works [1, 7, 28, 29, 32, 34, 38, 41, 48] have demonstrated compelling results. However, these methods are not easily adaptable for generating portraits across multiple domains. More recently, diffusion models have been leveraged for various applications, including semantic matching [15, 33, 43] and style transfer [2, 3, 5, 10, 35, 36, 39, 47]. While techniques such as those proposed in [1, 16, 28, 29] aim to achieve stylization by aligning semantic regions, they are effective only when the structural differences between the input and reference portraits are minimal. When applied to portraits with significant structural variations, these methods struggle to transfer style effectively between corresponding semantic regions.
+
+In this paper, we propose a novel domain-generalizable diffusion model for portrait style transfer. Our approach first warps the reference portrait using correspondences learned from diffusion models, producing a high-quality warped style reference. To generate realistic and visually coherent portrait, our framework is designed to integrate a dual-conditional diffusion model, leveraging ControlNet to extract high-frequency details from the input image for structural guidance, while an image adapter utilizes the warped reference to provide style guidance.
+
+Unlike previous diffusion-based methods [2, 3, 5, 36, 47], our approach establishes dense semantic-aligned correspondences to enhance the quality of style transfer. Specifically, we introduce a semantic adapter, comprising a frozen diffusion U-Net and a CLIP encoder to extract image features from both the content and style reference images. As naively using these extracted features for correspondence estimation can result in incomplete semantic regions due to misalignment, we introduce mask warping loss and cyclic warping consistency loss for optimizing the semantic adapter to encourage semantic consistency in the extracted features. With this refined representation, our method enables accurate semantic-aware style transfer while ensuring the visual coherence in the generated portraits.
+
+Color tone plays a crucial role in defining artistic style during portrait style transfer. If the generation process starts from the latent representation of the input image, the resulting portrait tends to retain its original color tone, limiting the effectiveness of style transfer. To better integrate structure and style, we propose a novel AdaIN-Wavelet Transform for latent initialization. Specifically, we first compute the latent representation of the warped reference image using DDIM inversion, as initializing from this latent naturally enhances color transfer effect. However, since the warped reference image may lose some fine-scale content details, directly using its latent representation may result in blurred portrait. To mitigate this, we blend the low-frequency information of the warped reference latent with
+
+the high-frequency information of the input latent, achieving a balance between stylization and content preservation.
+
+With the aforementioned designs—learning domain-agnostic semantic correspondences for portraits and the AdaIN-Wavelet latent initialization—our model enables effective portrait style transfer across various different domains. Through extensive experiments, we demonstrate the effectiveness of our approach in various artistic styles, modernizing old photographs, and colorizing sketch images. Our key contributions can be summarized as follows:
+
+- We present a portrait style transfer framework that can robustly process portraits from various different domains by training on a small-scale real-world portrait dataset.
+- We propose to utilize pre-trained diffusion model and also a semantic adapter for robust dense correspondence extraction. In addition, we develop a AdaIN-Wavelet transform to balance stylization and content preservation.
+- Extensive experiments show that our method significantly outperforms previous methods in both visual quality and quantitative metrics.
+
+# 2. Related Work
+
+Diffusion-based Style Transfer. Diffusion models have been explored for style transfer, with a common approach leveraging cross-attention layers in text-to-image diffusion models. These methods can be broadly categorized into three groups: (i) directly using text prompts [37], (ii) mapping the reference image into textual embeddings [46, 47], and (iii) incorporating an additional cross-attention mechanism with image prompts [24, 35, 42]. Beyond these approaches, training-free methods have also been developed based on pre-trained text-to-image diffusion models. These methods inject features into self-attention layers [3, 5, 17] during the generation process to guide stylization. Additionally, StyleDiffusion [39] fine-tunes a diffusion model for a given reference image using a CLIP-based style disentanglement loss. However, most existing diffusion-based methods are designed for artistic style transfer that does not need to consider semantic correspondence, and thus basically struggle to deal with portrait style transfer involving strong semantic relevance, especially when the portraits are from different domains.
+
+**Portrait Style Transfer.** Significant progress has recently been made in this field. Shih et al. [28] pioneered photorealistic portrait style transfer by first warping the reference portrait to align with the input portrait, followed by a multiscale local contrast transfer. Concurrently, Shu et al. [29] redefined portrait relighting as a mass transport problem and proposed an algorithm to address it. With the advent of CNN-based neural style transfer [6, 21], specialized methods for portrait style transfer emerged, including pho
+
+
+Figure 2. Framework overview. (Left) Illustration of the proposed portrait style transfer method. We first feed the input and reference portraits into Stable Diffusion and the Semantic Adapter. Next, we extract diffusion features and compute a correlation matrix, which is used to warp the reference portrait. During sampling, we provide structure guidance by extracting the high-frequency information of the input portrait using Discrete Wavelet Transform and feed it into ControlNet. For style guidance, the warped reference is input into the style adapter. To obtain the initial latent, we perform DDIM inversion on both the warped reference and input portraits, followed by applying AdaIN between them. The final initial latent is obtained by combining the low-frequency information of the warped reference latent with the high-frequency information from the input latent after AdaIN.
+
+
+
+torealistic [8] and artistic styles [27]. Among them, Guo and Jiang [8] enhanced spatial transformations by maximizing the cross-correlation of features within segmented regions between the input and reference images. GAN-based methods have also gained popularity in face stylization due to their ability to generate high-quality, highly detailed images [1, 7, 34]. Notably, some approaches leverage semantic masks to enable style transfer for specific facial regions [7, 34]. Moreover, StyleGAN [11, 12], known for its impressive high-resolution face synthesis and hierarchical style control, has served as a foundation for several recent artistic portrait style transfer methods [30, 40, 41, 48]. However, these methods are unsuitable for our task, as they inevitably alter portrait identity.
+
+# 3. Preliminary
+
+Diffusion model is a class of generative models consisting of a $T$ -step forward process and a $T$ -step reverse process. Here, $T$ represents the total number of steps in the forward process. At each timestep $t$ , the forward process adds Gaussian noise to the input according to a predetermined noise
+
+schedule $\alpha_{t}$
+
+$$
+z _ {t} = \sqrt {\alpha_ {t}} \cdot z _ {0} + \sqrt {1 - \alpha_ {t}} \cdot \epsilon , \epsilon \sim \mathcal {N} (0, I). \tag {1}
+$$
+
+A corresponding reverse process involves predicting the added noise $\epsilon$ using a network $\epsilon_{\theta}$ , which takes $z_{t}$ and timestep $t$ as input, and then samples $z_{t-1}$ from $z_{t}$ using a formula, such as DDPM [9] and DDIM [31]. The $\epsilon_{\theta}$ is usually parameterized as a U-Net for image generation. The added noise is progressively removed, ultimately resulting in a clean image. In this paper, we implement our method using Stable Diffusion (SD) [26], a large-scale pre-trained text-to-image model. The training objective of SD is defined as:
+
+$$
+\mathcal {L} = \mathbb {E} _ {z _ {t}, t, y, \epsilon \sim \mathcal {N} (0, 1)} \left[ \| \epsilon - \epsilon_ {\theta} (z _ {t}, t, y) \| _ {2} ^ {2} \right], \tag {2}
+$$
+
+where $y$ is the embedding of text prompts generated by a pre-trained CLIP [25] text encoder.
+
+# 4. Method
+
+Our method aims to achieve semantically aligned portrait style transfer while preserving content details. Since our
+
+
+Figure 3. Qualitative comparison with SOTA portrait style transfer methods.
+
+focus is on detailing the proposed method within the diffusion process, we denote the content image as $z_0^c$ and the style image as $z_0^s$ . As illustrated in Figure 2, our approach first warps the portrait style image using the correspondence learned from diffusion models to obtain a high-quality warped style reference $z_0^{s - w}$ (Section 4.1). To generate a realistic portrait, our framework incorporates a dual-conditional diffusion model (Section 4.2). This model utilizes the ControlNet $\epsilon_{\theta}$ , which extracts high-frequency information from the content image $z_0^c$ to provide content guidance, while an image adapter leverages the warped reference $z_0^{s - w}$ to offer style guidance. Additionally, we introduce a latent initialization strategy (Section 4.3) to achieve a better balance between stylization and content preservation.
+
+# 4.1. Semantic-Aware Style Alignment
+
+Different from previous diffusion-based methods [33, 43] for correspondence extraction, our approach focuses on establishing dense correspondence across portraits to achieve high-quality portrait style transfer. By ensuring style transfer between semantically aligned regions, we enhance both accuracy and visual coherence. This section details our method for constructing robust semantic correspondence to enable precise and effective style alignment.
+
+Correspondence Extraction. We first utilize a semantic adapter and a pre-trained CLIP image encoder to extract image features. Specifically, we obtain features from the penultimate layer of the encoder, which consists of a total of $16 \times 16 + 1 = 256$ tokens with one class token and 256 tokens corresponding to individual image patches. These tokens are then processed through a projection network and fed into Stable Diffusion U-Net for decoupled cross-attention [42]. Next, we feed $z_0^c$ and $z_0^s$ into the Stable Diffusion U-Net and extract features from the third upsampling block of the U-Net, represented as $F_0^c \in \mathbb{R}^{HW \times C}$ and $F_0^s \in \mathbb{R}^{HW \times C}$ for images $z_0^c$ and $z_0^s$ (H and W represent the feature spatial sizes, while C is the number of channels), respectively. Then, the element of $i_{th}$ row and $j_{th}$ column in the correlation matrix is computed as:
+
+$$
+\mathcal {M} (i, j) = \frac {\left(F _ {0} ^ {c} (i) - \mu_ {F _ {0} ^ {c} (i)}\right) \cdot \left(F _ {0} ^ {s} (j) - \mu_ {F _ {0} ^ {s} (j)}\right)}{\| F _ {0} ^ {c} (i) - \mu_ {F _ {0} ^ {c} (i)} \| _ {2} \| F _ {0} ^ {s} (j) - \mu_ {F _ {0} ^ {s} (j)} \| _ {2}}, \tag {3}
+$$
+
+where $\mu_{F_0^c} \in \mathbb{R}^{HW}$ and $\mu_{F_0^s} \in \mathbb{R}^{HW}$ are mean vectors of $F_0^c$ and $F_0^s$ along the channel dimension.
+
+Semantic-Aware Image Warping. With the semantic correspondence, we perform a differentiable warping of the reference portrait $z_0^s$ toward the input $z_0^c$ , resulting in $z_0^{s - w}$ .
+
+Each pixel of $z_0^{s - w}$ is computed as a weighted average of $z_0^s$ :
+
+$$
+z _ {0} ^ {s - w} (i) = \sum_ {j} \operatorname {s o f t m a x} _ {j} (\mathcal {M} (i, j) / \tau) \cdot z _ {0} ^ {s} (j), \tag {4}
+$$
+
+where $\tau$ is set to 0.01 to make the softmax curve sharper. To further enhance the accuracy of semantic correspondence, we introduce a mask warping loss during training, defined as:
+
+$$
+\mathcal {L} _ {\text {m a s k}} = \left\| M ^ {c} - M ^ {s - w} \right\| _ {1}, \tag {5}
+$$
+
+where $M^c$ represents the semantic mask of $z_0^c$ , and $M^{s - w}$ is obtained by warping the mask $M^s$ of $z_0^s$ following Equation 4. Besides, we introduce a cyclic warping consistency loss to reinforce style preservation during the warping process:
+
+$$
+\mathcal {L} _ {c w c} = \mathcal {L} _ {L P I P S} \left(z _ {0} ^ {s}, z ^ {s ^ {\prime} - w}\right), \tag {6}
+$$
+
+where $z^{s' - w}$ is obtained by warping $z^{s - w}$ using the transposed correlation matrix $\mathcal{M}^\top$ . By incorporating these two losses, the dense correspondence learned from diffusion models is further refined and enhanced. Figure 4 compares the effect of replacing the correspondence in our method with two alternatives [33]. As shown in the warped reference, output, and visualized correspondence map, the correspondence in our method is more accurate. This accuracy enables our method to generate portrait images that faithfully replicate the reference style while preserving the portrait's identity and facial structure details.
+
+# 4.2. Dual Conditional Diffusion Model
+
+The proposed dual-conditional diffusion model leverages both structure guidance and style guidance to generate realistic portrait images. This novel architectural design enables the integration of high-frequency structures and semantically aligned style references, enhancing the quality and coherence of the generated images.
+
+Structure Guidance. Unlike the previous method [36], our model utilizes the high-frequency information from the content image $z_0^c$ through ControlNet to provide style-independent structural guidance. To achieve this, we apply the Haar Discrete Wavelet Transform (DWT) to extract the high-frequency components of the content image. Specifically, the Haar wavelet transform performs a depth-wise convolution with four kernels, $\{ \mathrm{LL}^\top \mathrm{LH}^\top \mathrm{HL}^\top \mathrm{HH}^\top \}$ , where $\mathrm{L} = \frac{1}{\sqrt{2}} [1 - 1]^\top$ , $\mathrm{H} = \frac{1}{\sqrt{2}} [-1 - 1]^\top$ . Among these, $\mathrm{LL}^\top$ acts as a low-pass filter, while $\mathrm{LH}^\top$ , $\mathrm{HL}^\top$ , and $\mathrm{HH}^\top$ serve as high-pass filters that capture high-frequency information in the horizontal, vertical, and diagonal directions, respectively. We use the outputs from the three high-pass filters $\mathrm{LH}^\top$ , $\mathrm{HL}^\top$ and $\mathrm{HH}^\top$ as the corresponding input to ControlNet, which can be formulated as:
+
+$$
+\begin{array}{l} c ^ {c n t} = \left[ z _ {L H} ^ {c}, z _ {H L} ^ {c}, z _ {H H} ^ {c} \right] (7) \\ = \operatorname {C o n v} \left(\left[ \mathrm {L H} ^ {\top}, \mathrm {H L} ^ {\top}, \mathrm {H H} ^ {\top} \right], z _ {0} ^ {c}\right). (8) \\ \end{array}
+$$
+
+
+Figure 4. Effect of our semantic correspondence. For a query point (yellow point in input), the first row shows the similarity map computed by different methods. The second row displays the warped references. The third row shows the outputs generated using these different warped references. As seen, our correspondence achieves higher similarity in the semantic region of the reference, demonstrating its superior accuracy.
+
+Note that the original spatial size of $c^{cnt}$ is half that of $z_0^c$ . Therefore, we upsample $c^{cnt}$ using bilinear interpolation and use the upsampled $c^{cnt}$ as input to the ControlNet.
+
+Style Guidance. We employ a style adapter consisting of a text encoder and an image encoder [42], integrated into the cross-attention layers for style guidance extraction and injection. The text prompt is fixed as "a photo of a portrait," while image features is extracted from the penultimate layer of CLIP. The extracted latent representation is then passed through a projection layer to obtain the style guidance $c^{sty} = [c^t, c^i]$ , where $c^t$ represents the text feature and $c^i$ represents the image feature. These features are then fused with the main Denoising U-Net. Specifically, we perform decoupled cross-attention operations on both text and image features, injecting them into the corresponding layers of the Denoising U-Net. The decoupled cross-attention mechanism can be illustrated as:
+
+$$
+Z ^ {n e w} = \operatorname {s o f t m a x} \left(\frac {Q K ^ {t}}{\sqrt {d}}\right) V ^ {t} + \lambda \cdot \operatorname {s o f t m a x} \left(\frac {Q K ^ {i}}{\sqrt {d}}\right) V ^ {i}, \tag {9}
+$$
+
+where $\lambda$ is a weight that balances the contributions of text and image prompts. $Q$ , $K^t$ , $V^t$ represent the query, key, and value matrices for text cross-attention, while $K^i$ and $V^i$ correspond to image cross-attention. Given the query features $Z$ from the main denoising UNet, we define $Q =$
+
+$ZW_{q}$ , $K^{i} = c^{i}W_{k}^{i}$ , $V^{i} = c^{i}W_{v}^{i}$ , $K^{t} = c^{t}W_{k}^{t}$ and $V^{t} = c^{t}W_{v}^{t}$ , where only $W_{k}^{i}$ and $W_{v}^{i}$ are trainable weights.
+
+# 4.3. Initial Latent AdaIN-Wavelet Transform
+
+In portrait style transfer, color tone plays a crucial role in conveying style information. If sampling begins from the latent $z_{T}^{c}$ of the content image, the generated image will largely retain its original color tone. To achieve an initial latent representation that preserves the structural details of the input image while enhancing local color style transfer, we propose a novel AdaIN-Wavelet transform for latent initialization. First, we compute the latent representation of the warped reference image $z_{0}^{s - w}$ using DDIM inversion, denoted as $z_{T}^{s - w}$ . Since initiating the denoising process from $z_{T}^{s - w}$ strongly enhances color transfer, directly using it may result in a blurred output. To address this, we propose blending the low-frequency components of $z_{T}^{s - w}$ with the high-frequency components of the content latent, striking a balance between effective stylization and content detail preservation. We first apply AdaIN between $z_{T}^{s - w}$ and $z_{T}^{c}$ , formulated as:
+
+$$
+z _ {T} ^ {c s ^ {\prime}} = \sigma \left(z _ {T} ^ {s _ {-} w}\right) \left(\frac {z _ {T} ^ {c} - \mu \left(z _ {T} ^ {c}\right)}{\sigma \left(z _ {T} ^ {c}\right)}\right) + \mu \left(z _ {T} ^ {s _ {-} w}\right), \tag {10}
+$$
+
+where $\sigma ()$ and $\mu ()$ denote channel-wise mean and standard deviation, respectively. We then apply the wavelet transform to integrate the high-frequency information from $z_T^{cs'}$ and the low-frequency informatoin from $z_T^{s,w}$ , which is obtained as:
+
+$$
+z _ {T} ^ {c s} = \mathrm {I D W T} \left(z _ {T, L L} ^ {s - w}, z _ {T, L H} ^ {c s ^ {\prime}}, z _ {T, H L} ^ {c s ^ {\prime}}, z _ {T, H H} ^ {c s ^ {\prime}}\right), \tag {11}
+$$
+
+where IDWT denotes the inverse wavelet transform.
+
+To control the strength of stylization, we introduce a parameter $\gamma$ . Since stylization is influenced by both the latent initialization and the style adapter, $\gamma$ is applied in two key areas. First, we interpolate between the input latent $z_{T}^{c}$ and stylized latent $z_{T}^{cs}$ :
+
+$$
+z _ {T} ^ {c s} = \gamma \times z _ {T} ^ {c s} + (1 - \gamma) \times z _ {T} ^ {c}. \tag {12}
+$$
+
+Similarly, $\gamma$ is used in style adapter to interpolate between the feature embeddings of the warped reference image and the input image. In this paper, we set $\gamma = 1.0$ by default for best stylization effects.
+
+# 4.4. Training and Implementation Details
+
+We implement our method using Stable Diffusion 1.5 and follow a two-stage training strategy. In the first stage, we train the semantic adapter while freezing the other parameters of the pre-trained diffusion model. To ensure the features encode meaningful information, we incorporate a noise prediction loss during this stage:
+
+$$
+\mathcal {L} _ {s e m} = \mathbb {E} _ {z _ {t}, t, I ^ {x}, \epsilon \sim \mathcal {N} (0, I)} \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, I ^ {x}\right) \| _ {2} ^ {2}, \tag {13}
+$$
+
+| Method | Gram loss↓ | LPIPS↓ | ID↓ |
| Shih et al. [28] | 0.376 | 0.187 | 0.093 |
| Chen et al. [1] | 0.287 | 0.156 | 0.344 |
| Zhou et al. [48] | 0.688 | 0.393 | 0.657 |
| Wang et al. [38] | 0.208 | 0.181 | 0.106 |
| IP-A[42] + C.N.[44] | 2.835 | 0.245 | 0.774 |
| Deng et al. [5] | 1.745 | 0.162 | 0.393 |
| StyleID[3] | 0.505 | 0.198 | 0.222 |
| InstantStyle + [36] | 0.557 | 0.294 | 0.272 |
| Ours | 0.274 | 0.116 | 0.057 |
| Ours (w/o ControlNet) | 0.236 | 0.333 | 0.450 |
| Ours (w/o style adapter) | 0.548 | 0.145 | 0.086 |
| Ours (w/ Init AdaIN) | 1.196 | 0.151 | 0.062 |
+
+Table 1. Quantitative comparison on CelebAMask-HQ.
+
+| Method | Gram loss↓ | LPIPS↓ | ID↓ |
| Shih et al. [28] | 0.802 | 0.156 | 0.105 |
| Chen et al. [1] | 0.926 | 0.169 | 0.316 |
| Zhou et al. [48] | 0.827 | 0.423 | 0.669 |
| Wang et al. [38] | 1.488 | 0.119 | 0.096 |
| IP-A[42] + C.N.[44] | 4.211 | 0.375 | 0.763 |
| Deng et al. [5] | 1.493 | 0.178 | 0.331 |
| StyleID[3] | 1.343 | 0.149 | 0.165 |
| InstantStyle+ [36] | 0.723 | 0.192 | 0.203 |
| Ours | 0.657 | 0.083 | 0.087 |
+
+Table 2. Quantitative comparison on a mixed dataset with portraits from multiple domains.
+
+where $I^x$ represent an arbitrary input image. The total loss at this stage is:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {s e m}} + \lambda_ {c} \mathcal {L} _ {\text {c y c}} + \lambda_ {m} \mathcal {L} _ {\text {m a s k}}, \tag {14}
+$$
+
+where $\lambda_{c}$ and $\lambda_{m}$ are set to 1 and 10, respectively.
+
+In the second training stage, we train the ControlNet and style adapter. Due to the absence of paired training data for our tasks, we train the model to reconstruct images conditioned on both the style and content inputs. The loss function at this stage can be formulated as follows:
+
+$$
+\mathcal {L} _ {r e c} = \mathbb {E} _ {z _ {t}, t, c ^ {c n t}, c ^ {s t y}, \epsilon \sim \mathcal {N} (0, I)} \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, c ^ {c n t}, c ^ {s t y}\right) \| _ {2} ^ {2}, \tag {15}
+$$
+
+where $c^{cnt}$ and $c^{sty}$ are both extracted from a single input image.
+
+Our method is implemented in PyTorch [23]. We utilize 2 Nvidia RTX 4090 GPUs with a batch size of 1 per GPU for training. The AdamW [20] optimizer is employed, with a learning rate of 1e-5. The first stage of training runs for 500K iterations, while the second stage is trained for 300K iterations. The training process requires approximately 24GB of memory, and testing necessitates 16GB of
+
+
+Reference
+
+
+Input
+
+
+w/o Cont.
+
+
+Canny Cont.
+
+
+Input Cont.
+
+
+w/o style adapter
+
+
+IP-A.(4 tokens)
+
+
+Ours
+
+
+Reference
+
+
+Input
+
+
+A.N. $(t = 699)$
+
+
+Figure 5. Effect of the ControlNet and style adapter.
+A.N. $(t = T)$
+
+
+Input latent $(z_T^c)$
+
+
+w.r. latent $(z_{T}^{s - w})$
+
+
+AdaIN $(z_T^{cs'})$
+
+
+Ours $(z_T^{cS})$
+
+
+Figure 6. Effect of the initialization of latent noise. "A.N." means initializing latent by adding noise of level $t$ to input. "w.r." stands for warped reference.
+Reference
+
+
+Input
+
+
+Hair
+
+
+face
+
+
+lips
+
+
+Figure 7. Controllable region-specific style transfer.
+
+
+Reference
+
+
+
+
+Input
+Figure 8. Style interpolation.
+
+
+
+
+$\gamma = 0.25$
+
+
+
+
+$\gamma = 0.50$
+
+
+
+
+$\gamma = 0.75$
+
+
+
+
+$\gamma = 1.0$
+
+memory for images with a resolution of $512 \times 512$ . For testing, we use the DDIM sampler [18] with 10 timesteps for inversion and 30 timesteps for sampling.
+
+# 5. Experiments
+
+# 5.1. Datasets and Evaluation Metrics
+
+Datasets. We evaluate our method on CelebAMask-HQ [13], FFHQ [11], and AAHQ [19]. CelebAMask-HQ contains 30K high-resolution portrait images, each paired with a facial segmentation mask covering 19 facial semantic categories. FFHQ consists of 70K high-quality images depicting a wide range of human faces. AAHQ includes approximately 25K high-quality artistic images with varied painting styles, color tones, and face attributes. To demonstrate the generalization ability of our method, we train it solely on the 28K training images from the CelebAMask-HQ dataset [38].
+
+Metrics. To evaluate the stylization effects for semantically
+
+corresponding regions, we follow Wang et al. [38] to compute the Gram loss between the input image and the warped reference. Additionally, we use LPIPS [45] to measure content preservation performance and adopt the Identity Distance (ID) [4], as used in [14, 22], to quantitatively assess identity preservation.
+
+# 5.2. Comparison with State-of-the-art Methods
+
+Baselines. We compare our method with two types of state-of-the-art style transfer methods: (i) conventional portrait style transfer methods, including Shih et al.[28], Chen et al. [1], Zhou et al. [48], and Wang et al. [38], and (ii) diffusion-based style transfer methods, including IP-Adapter (IP-A) [42] + ControlNet (C.N.) [44], Deng et al. [5], StyleID [3], and InstantStyle-Plus (InstantStyle+) [36]. For learning-based methods, we retrain them on CelebAMask-HQ using the publicly available training code provided by the authors, with the recommended parameter settings. For methods with pre-trained models only, we fine-tune their models on CelebAMask-HQ.
+
+Quantitative Evaluation. Tables 1 and 2 present the quantitative comparison results on the CelebAMask-HQ dataset and a mixed dataset from multiple domains, including portraits from CelebAMask-HQ, FFHQ, and AAHQ for a more comprehensive evaluation. As shown, on CelebAMask-HQ, the Gram loss of our method is comparable to the state-of-the-art method [38], while our LPIPS and ID scores are significantly better, demonstrating superior content and identity preservation. On the mixed dataset, our method achieves the lowest Gram loss. Furthermore, our method outperforms other style transfer techniques in both LPIPS and ID, highlighting its strong domain generalizability.
+
+Qualitative Evaluation. Figure 3 compares our results with those of previous style transfer methods [3, 5, 38, 42, 44]. Our method achieves more faithful stylization
+
+
+Input
+
+
+Output
+
+
+Input
+
+
+Output
+
+
+Input
+
+
+Output
+
+
+Figure 9. Results of adding color to grayscale and sketch portraits.
+Input
+
+
+Output
+
+
+Input
+
+
+Output
+
+
+Input
+
+
+Output
+
+
+
+
+Figure 10. Results of modernizing old photographs.
+
+
+
+
+
+
+Reference
+Figure 11. Results of transferring real portraits to sketch style.
+
+
+Output 1
+
+
+Output 2
+
+
+Output 3
+
+effects by effectively transferring styles across semantically aligned regions, such as skin, lips, hair, and background. Additionally, our method demonstrates superior performance in content preservation, unlike artistic methods [5, 42, 44], which often alter facial identity. Please see the supplementary material for more visual results.
+
+# 5.3. More Analysis
+
+Ablation Studies. Figure 5 investigates the effects of ControlNet and the style adapter. Our high-frequency ControlNet preserves content details more effectively than using a canny edge detection map or the input image. Moreover, with the style adapter, the accuracy of stylization is further enhanced, surpassing the performance of the common IP-Adapter with 4 tokens. Figure 6 compares results using different initializations of latent noise. Initializing latent by adding noise of different levels to input, or using the inversion input latent as the initial tend to preserve the original color style. Performing AdaIN between the input and reference latents [3] improves overall stylization effects but doesn't ensure local style similarity. Using the latent of the warped reference yields strong stylization effects, but the output becomes blurry. In comparison, our AdaIN-Wavelet initialization strikes a better balance between stylization and content detail preservation. Quantitative results in Table 1
+
+| Metric | Deng et al. | StyleID | InstantStyle+ | Ours |
| Time ↓ (sec) | 24.18 | 9.12 | 67.40 | 6.97 |
+
+Table 3. Comparison on inference time.
+
+further support this conclusion. More results can be found in the supplementary material.
+
+Controllable Region-specific Style Transfer. As shown in Figure 7, our method generates natural results by transferring the style of specific semantic regions, such as hair, face, or lips. Given the mask of a specific region, we achieve this by simply replacing the corresponding regions in the warped reference with those from the input portrait.
+
+Style interpolation. Figure 8 demonstrates that our method supports continuous style interpolation, allowing for control over the stylization strength by adjusting the parameter $\gamma$ as described in Section 4.3.
+
+- Portrait Style Transfer across Different Domains. Figure 9 demonstrates that our method can colorize grayscale and sketch portraits using reference portraits from different domains. Figure 10 showcases the ability of our method to restore the color of old photos. Finally, Figure 11 illustrates that our method can replicate a sketch style. Note, by adjusting the ControlNet conditioning scale, our method allows for controlling the level of detail preservation for better stylization effects. Please see the supplementary material for more visual results.
+
+Inference time. Our model processes images at a resolution of $512 \times 512$ in approximately 6.97 seconds on an NVIDIA RTX 4090 GPU, making it more efficient than other diffusion-based methods, as shown in Table 3. The efficiency comes from two factors: (i) our AdaIN-Wavelet module is robust to the number of DDIM inversion steps—only 10 steps are needed to achieve high-quality results; (2) our content guidance is delivered via ControlNet, which helps remove the necessity for intermediate feature extraction [3, 5]. These advantages collectively contribute to the accelerated inference.
+
+# 6. Conclusion
+
+We have presented a portrait style transfer framework that excels in domain generalization and produces high-quality results. By leveraging pre-trained diffusion models and a semantic adapter, we get reliable dense correspondence between portraits, enabling semantically aligned stylization. Besides, we develop an AdaIN-Wavelet transform to balance stylization and content preservation, and also introduce a style adapter as well as a ControlNet to offer style and content guidance. Extensive experiments demonstrate that our method outperforms existing approaches.
+
+Acknowledgement. This work was supported by the National Key Research and Development Program of China (2023YFA1008503), the National Natural Science Foundation of China (62471499), and the Guangdong Basic and Applied Basic Research Foundation (2023A1515030002).
+
+# References
+
+[1] Shu-Yu Chen, Feng-Lin Liu, Yu-Kun Lai, Paul L Rosin, Chunpeng Li, Hongbo Fu, and Lin Gao. Deepfaceediting: deep face generation and editing with disentangled geometry and appearance control. ACM Transactions on Graphics (TOG), 40(4):1-15, 2021. 2, 3, 6, 7
+[2] Hansam Cho, Jonghyun Lee, Seunggyu Chang, and Yonghyun Jeong. One-shot structure-aware stylized image synthesis. In CVPR, pages 8302-8311, 2024. 2
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\ No newline at end of file
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+# Domain-aware Category-level Geometry Learning Segmentation for 3D Point Clouds
+
+Pei He, Lingling Li*, Licheng Jiao*, Ronghua Shang, Fang Liu, Shuang Wang, Xu Liu, Wenping Ma Xidian University, China
+
+hepei@stu.xidian.edu.cn, llli@xidian.edu.cn, lchjiao@mail.xidian.edu.cn
+
+# Abstract
+
+Domain generalization in 3D segmentation is a critical challenge in deploying models to unseen environments. Current methods mitigate the domain shift by augmenting the data distribution of point clouds. However, the model learns global geometric patterns in point clouds while ignoring the category-level distribution and alignment. In this paper, a category-level geometry learning framework is proposed to explore the domain-invariant geometric features for domain generalized 3D semantic segmentation. Specifically, Category-level Geometry Embedding (CGE) is proposed to perceive the fine-grained geometric properties of point cloud features, which constructs the geometric properties of each class and couples geometric embedding to semantic learning. Secondly, Geometric Consistent Learning (GCL) is proposed to simulate the latent 3D distribution and align the category-level geometric embeddings, allowing the model to focus on the geometric invariant information to improve generalization. Experimental results verify the effectiveness of the proposed method, which has very competitive segmentation accuracy compared with the state-of-the-art domain generalized point cloud methods. The code will be available at https://github.com/ChicalH/DCGL.
+
+# 1. Introduction
+
+Point clouds segmentation is widely used in autonomous driving [21, 34], medical analysis [22, 37], and robot navigation [4, 7, 45]. The point cloud data captured by Li-DAR can be used to understand the three-dimensional scene through semantic segmentation, which assigns the category to each point cloud [14, 18, 40]. Although deep learning-based segmentation models have made significant progress, existing methods usually assume that training data and test data have the same distribution [13, 23, 29]. In real scenes, complex data collection conditions, different sensors, and
+
+environmental changes will affect the generalization and robustness of point cloud semantic segmentation [2, 16, 35]. Currently, unsupervised domain adaptation (UDA) methods [11, 39] can adapt the source domain (training data) to a specific target domain. Although UDA shows promising performance on predefined target domains, its effectiveness decreases when applied to unseen domains.
+
+Domain generalization aims to improve the generalization of unknown domain. Data augmentation that simulates the target domain has been shown to be an effective approach [10, 25, 35, 43]. PointDR [35] is a pioneering work in this field that proposes a benchmark dataset and a domain randomization technique to improve generalization in the wild. DGUIL [10] improves data diversity by simulating point uncertainty in domain shift. And some methods consider synthesizing data patterns under adverse weather[25, 43]. UniMix [43] proposes a general method to simulate adverse weather data and mix in the source domain. LiDARWeather [25] identifies the key factors of severe weather and proposes a jittering strategy to enhance point cloud data.
+
+However, point clouds are presented in 3D physical space, and how to deal with complex geometric information to improve cross-domain generalization has been ignored. The geometric relations of point clouds generally show cross-domain stability. However, two issues need to be considered when exploring domain-invariant geometric information in point clouds. On the one hand, the model learns global geometric patterns while ignoring the category-level distribution. Geometric information is important for representing 3D point clouds. Although data augmentation brings some geometric perturbations that allow the model to automatically learn geometric patterns in point clouds, this focuses on the global distribution of the domain while the perturbations make the model ignore the geometric patterns within the class. On the other hand, the alignment of geometric features before and after the perturbation is ignored. Although augmented data methods are conducive to model learning diverse features, they lack special attention to the domain-invariant information in geometric features.
+
+In this work, we propose category-level geometry learning to explore the domain-invariant geometric features for generalized 3D point clouds. For the first problem, Category-level Geometry Embedding (CGE) is proposed to embed the source features of each category into geometric space and learn correlation parameters to couple the geometric embedding to semantic learning. CGE constructs the embedding of each class separately, enabling the model to perceive the fine-grained geometric properties of categories. To solve the second problem, Geometric Consistent Learning (GCL) is proposed to learn a domain-invariant geometric representation. GCL randomly simulates the potential 3D scene with matter accumulation and fuzzy recognition, and aligns the category-level geometric embeddings, which encourages the model to focus on generalized geometric features. The framework provides a geometric perspective on point cloud features, which encourages the model to focus on the geometric invariant information within classes and improves generalization.
+
+Our contributions can be summarized as follows:
+
+- Category-level Geometry Learning framework is proposed to exploit the domain-invariant geometric features of 3D point clouds to improve domain generalization in unknown domains.
+- Category-level Geometry Embedding (CGE) is proposed to perceive the categoric geometric properties of point cloud features, which constructs the geometric properties of each class and couples geometric embedding to semantic learning.
+- Geometric Consistent Learning (GCL) is proposed to simulate the latent 3D distribution and align the category-level geometric embeddings, allowing the model to focus on the geometric invariant information to improve generalization.
+- Extensive experiments on multiple benchmarks demonstrate the superior performance of the proposed method over the state-of-the-art domain generalized point cloud segmentation.
+
+# 2. Related work
+
+# 2.1. 3D Semantic Segmentation
+
+3D semantic segmentation aims to classify each point in point cloud data with semantic label [28]. The challenge lies in the disorder and sparsity of point cloud data, which is different from 2D image segmentation [9, 20] that operates on a structured pixel grid. Therefore, point cloud segmentation focuses on how to effectively represent 3D information for unstructured data processing.
+
+Existing 3D point cloud segmentation methods can be divided into three categories according to data processing [7, 21, 34]. Point-based methods [26, 27] use variant networks such as PointNet to directly process 3D points. How-
+
+ever, due to the complexity of processing large-scale point clouds, these methods usually suffer from huge computational costs. Projection-based methods [17, 36] convert 3D point clouds into 2D representations and use mature image segmentation models. However, the projection process has inevitable information loss, which limits the performance. Voxel-based methods [3, 24] discretize 3D point clouds into voxel grids for calculation, achieving a balance between efficiency and segmentation performance, and becoming a practical choice for a wide range of applications.
+
+Despite substantial progress in 3D segmentation, existing approaches still face challenges in handling domain shifts, particularly in autonomous driving scenarios where adverse weather conditions can degrade performance. This highlights the necessity of developing domain generalization techniques to improve the robustness of 3D point cloud segmentation in real-world applications.
+
+# 2.2. Domain Generalization for Point Cloud
+
+Domain generalization (DG) [31, 44] aims to enhance the robustness of model learning so that they can generalize well to unseen target domains without access to target data during training [12, 42]. Unlike domain adaptation [6, 41] which accesses the target distribution for transfer, DG focuses on learning domain-invariant representations that can generalize across diverse data distributions such as different environments and sensors.
+
+Data augmentation improves domain generalization by increasing sample diversity, and has been shown to be effective on images [31, 44]. Some point cloud segmentation methods improve model generalization through explicit or implicit data augmentations[10, 25, 35, 43]. PointDR [35] proposes a domain randomization technique to enhance point cloud data. DGUIL [10] proposed domain generalization-aware uncertainty introspective learning to deal with the point uncertainty in domain shift. UniMix [43] generates data of different weather conditions and mixes them into the source domain distribution. LiDARWeather [25] proposes random jitter and learnable point drop strategies to augment point cloud data.
+
+Although these methods have made significant progress, geometric invariance in 3D point cloud segmentation remains underexplored. The geometric relations of point clouds show the tendency for cross-domain stability: Although the domain shift can significantly affect the distribution of point clouds, the underlying geometric relations of points remain consistent under different acquisition conditions. This paper takes a closer look at the geometric features in point clouds, considering category-level geometric distribution and alignment, which improves the domain generalization of point cloud segmentation by learning domain-invariant geometric representations.
+
+
+Figure 1. Overview of the proposed category-level geometry learning framework. Category-level Geometry Embedding constructs the geometric properties of each class and couples geometric embedding to semantic learning. Geometric Consistent Learning simulates the latent 3D distribution and aligns the geometric embeddings of original and simulated features through consistent learning.
+
+# 3. Category-level Geometry Learning
+
+# 3.1. Problem Definition and Framework
+
+Given a source domain dataset $\mathcal{S} = \{(X,Y)\}_{i=1}^{K}$ , where $X \in \mathbb{R}^{N \times 4}$ represents a point cloud with $N$ points, each point contains three-dimensional coordinates and intensity information. $Y \in \{1,\dots,C\}^{N}$ represents the semantic label of each point with $C$ categories. The goal of domain generalization is to learn a segmentation model $\Theta : \mathbb{R}^{N \times 4} \rightarrow \{1,\dots,C\}^{N}$ , which can achieve high-accuracy point-level classification on any unseen target domain $\mathcal{T}$ , using only source domain data $S$ for training:
+
+$$
+\Theta^ {*} = \arg \min _ {\Theta} \mathbb {E} _ {(X, Y) \sim \mathcal {S}} \mathcal {L} _ {S E G} (\Theta (X), Y), \tag {1}
+$$
+
+where $\mathcal{L}_{SEG}$ is the cross entropy loss for the segmentation. The target domain $\mathcal{T}$ cannot be accessed during training. And the target distribution $P_{\mathcal{T}}(X,Y)$ is inconsistent with the source: $P_{\mathcal{T}}(X,Y)\neq P_{\mathcal{S}}(X,Y)$ . Therefore, the model $\Theta$ needs to be robust to the potential domain shift.
+
+To improve generalization, we introduce category-level geometry learning as shown in Figure 1. The source domain point cloud $X$ obtains the original features through the feature extractor, which can be used for classifier $h_\Theta$ to predict results. Category-level Geometry Embedding is proposed to map the original features to category-level geometry embedding, which gives the model feedback on the geometric perspective and encourages the model to pay more attention to category-level geometric attributes to predict the results. In addition, Geometric Consistent Learning is proposed to
+
+randomly augment the source domain point cloud $X$ and align the category-level geometry embeddings of the original and simulated feature, thereby learning to bridge the domain shift through feedback. This framework focuses on the learning of domain-invariant point cloud geometric features of each category to improve generalization.
+
+# 3.2. Category-level Geometry Embedding
+
+To achieve category-level geometry embedding, we first construct geometric properties in each class. Then, the geometric embedding is coupled to the model learning process, which enables the model to learn fine-grained geometric representations.
+
+# 3.2.1. Category-level Geometry Construction
+
+Assume that the point cloud is passed through the feature extractor to obtain feature $F \in \mathbb{R}^{N \times D}$ , where $N$ represents the number of points, and $D$ is the dimension of point features. We expected a mapping $U^0: F \mapsto G$ that can map $F$ with the underlying geometric structure of the point cloud. And it is expected that the mapping is category-unbiased, that is, it contains the geometric properties of all categories. Therefore, the mapping can be represented as $G^0 = U^0(F, G): \mathbb{R}^{N \times D} \to \mathbb{R}^{N \times C \times M}$ , where $C$ is the number of categories and $M$ is the geometric property.
+
+The geometric properties of the feature can be represented in Wasserstein spaces [5], which are larger than Euclidean spaces to represent metric structures. Therefore, the embedding feature $G^0 \in \mathbb{R}^{N \times C \times M}$ is expected to fit the
+
+geometric properties of each category in Wasserstein space $W$ . In one batch iteration, the number of points in the $c$ -th class is set to $N_{c}$ . Therefore, for the $c$ -th class, it is expected that $G_{(c,N_c)}^0$ and $W_{(c,N_c)}^0$ are similar, that is, minimize the distance: $\min \langle G_{(c,N_c)}^0, W_{(c,N_c)}^0 \rangle$ with the constraint that each point has only one unique correspondence and is uniformly distributed in space. This process can be viewed as an instance of the optimal transportation problem [15] and solved using the Sinkhorn divergence [5] as:
+
+$$
+W _ {(c, N _ {c})} ^ {*} = \Delta (u) e x p \left(- \frac {G _ {(c , N _ {c})} ^ {0}}{\sigma}\right) \Delta (v), \tag {2}
+$$
+
+where $\Delta(u)$ and $\Delta(v)$ are diagonal vectors of scaling coefficients, $\sigma$ is the regularization parameter. The optimal geometric feature $W_{(c,N_c)}^* \in \mathbb{R}^{N_c \times M}$ includes underlying geometry awareness [15], that can take into account some underlying geometric properties of the $c$ -th class.
+
+Therefore, for the point feature $F_{(c,N_c)}$ , the mapping from $F_{(c,N_c)}$ to $W_{(c,N_c)}^*$ can be expressed as $U^{*}(F_{(c,N_{c})},W_{(c,N_{c})}^{*}): \mathbb{R}^{N_{c}\times D}\to \mathbb{R}^{N_{c}\times M}$ . Assume that this mapping can be expressed as a matrix $A_{c}\in \mathbb{R}^{D\times M}$ , so $U^{*}(F_{(c,N_{c})},W_{(c,N_{c})}^{*}) = F_{(c,N_{c})}A_{c}$ and the matrix can be derived by:
+
+$$
+A _ {c} = \left(F _ {\left(c, N _ {c}\right)}\right) ^ {\top} W _ {\left(c, N _ {c}\right)} ^ {*}. \tag {3}
+$$
+
+Concatenating the matrices of all classes to obtain the geometry embedding matrix $A$ :
+
+$$
+A = C O N _ {c = 1} ^ {C} \left(\left(F _ {\left(c, N _ {c}\right)}\right) ^ {\top} W _ {\left(c, N _ {c}\right)} ^ {*}\right), \tag {4}
+$$
+
+where $A \in \mathbb{R}^{D \times C \times M}$ . Therefore, for all points, the category-level geometry embedding can be presented as
+
+$$
+U (F, G) _ {\mathbb {R} ^ {N \times D} \rightarrow \mathbb {R} ^ {N \times C \times M}} = F A. \tag {5}
+$$
+
+# 3.2.2. Coupling the Geometry Embedding
+
+The category-level geometry embedding needs to be learned by the model to perceive the geometric property. However, this mapping lacks feedback to the model. Therefore, a loss function is required to guide model learning with the correct category semantic information.
+
+For the embedding feature $G = FA$ , where $G \in \mathbb{R}^{N \times C \times M}$ , each class has $M$ geometric attributes. However, these geometric attributes may not all have a positive effect on point cloud classification. Therefore, adaptive geometric attribute learning can be performed by learning a correlation parameter $Q$ . In addition, the semantic information of the category can be learned by supervision of source label $Y$ . Therefore, through backpropagation, the model learns reliable geometric features through the geometry property learning (GPL) loss:
+
+$$
+\mathcal {L} _ {G P L} = - \frac {1}{N} \sum_ {n = 1} ^ {N} \sum_ {c = 1} ^ {C} Y _ {n c} \log \left(\left| \left| G Q \right| \right| _ {c}\right) _ {n c}, \tag {6}
+$$
+
+where $Q \in \mathbb{R}^{CM \times C}$ represents the relationship matrix between geometric properties and categories, which learns the correlation between geometric embedding and category semantics through adaptive learning. $\| \cdot \|_c$ represents normalization within the category channel, which normalizes all point features to a consistent scale. $\mathcal{L}_{GPL}$ gives the model feedback on the geometric perspective and encourages the model to pay more attention to category-level geometric attributes to predict the results.
+
+Besides, the backpropagation gradient of each iteration should be stable. However, the geometric embedding matrix $A$ is calculated from a batch of data, which is not stable in global training. Therefore, in each iteration, $A$ can be accumulated through momentum update:
+
+$$
+A = \epsilon A + (1 - \epsilon) C O N _ {c = 1} ^ {C} \left(\left(\left\| \dot {A} _ {c} \right\| _ {2}\right)\right), \tag {7}
+$$
+
+where $\epsilon$ is the momentum coefficient, $||\cdot ||_2$ represents the L2 normalized of the embedding matrix. $\dot{A}_c$ further considers enhancing training stability by accumulating only reliable points $\dot{N}_c$ in each iteration, which filters true positive points by label and prediction in each category. Then, $\dot{A}_c$ can be calculated by $\dot{A}_c = ((F_{(c,\dot{N}_c)})^\top W_{(c,\dot{N}_c)}^*)$
+
+The proposed CGE first constructs category-level geometric embeddings. Then, the geometric embedding is coupled to the learning process, which enables the model to learn category-aware geometric representations.
+
+# 3.3. Geometric Consistent Learning
+
+Categorical geometric features are perceived by the network for segmenting point clouds. However, how to further align the category distribution needs to be considered to improve generalization. Therefore, there are two issues to consider. 1. What kind of distribution to align? Because the target domain is unknown in domain generalization, the potential 3D domain shift needs to be effectively simulated. 2. How to align the different domains in a fine-grained manner. For the first issue, we propose a random 3D distribution simulation for the potential domain. For the second issue, we design category-level geometry alignment to align the potential domain with the original domain by consistent learning.
+
+# 3.3.1. Physics-inspired Adverse Geometry Simulation
+
+We first simulate the potential domain shift in 3D scenes. This takes into account that 3D scenes need to conform to more real-world physical regular patterns, which are more complex than flat images. Matter accumulation and confusion recognition need to be taken care of.
+
+In addition, the change of domain is random, so we design a compound random scheme. For the point cloud $X\in \mathbb{R}^{N\times 4}$ , each point $X_{n}$ contains information on three-dimensional coordinates $(x,y,z)$ and reflection intensity $I$ . The corresponding label $Y\in \mathbb{R}^N$ represents the semantic
+
+category of the point cloud. We design a random 3D simulation to obtain the augmented sample pair $(X^{\psi}, Y^{\psi})$ by processing the information of the original sample:
+
+$$
+\left(X ^ {\psi}, Y ^ {\psi}\right) = \sum_ {i} \eta_ {i} \Psi_ {i} (X, Y), \text {s . t .} \eta_ {i} \sim B \left(\beta_ {i}\right), \tag {8}
+$$
+
+where $B$ represents Bernoulli distribution, $\eta_{i}\in \{0,1\} \sim B(\beta_{i})$ means that $\eta_{i}$ gets 1 with a probability of $\beta_{i},\sum_{i}$ means that in one iteration, the simulation $\Psi_{i}$ are randomly adopted.
+
+$\Psi_{1}$ : Simulated Matter Accumulation. Universal gravitation states that every particle in the universe attracts every other particle with a force, which creates four seasons and scene changes. Typical changes occur when matter in the air accumulates downward, and this accumulation causes changes in the surface of objects. In more specific scenes such as snow and rain, it is not just snowflakes that appear randomly in the air, but more importantly, the accumulation of snow and rain changes the reflective properties of the surface, destroying the inherent characteristics. If there are key surface features for model to recognize covered object, and those features are obscured by external elements, recognition will be hindered. For example, the ground categories such as roads, sidewalks, and terrain, are easily covered, making the boundaries on the ground blurred. For vertically distributed objects such as vegetation and trunks, snow accumulation can change the 3D shape or point cloud features.
+
+Therefore, $\Psi_{1}$ is designed to simulate this matter accumulation. Set the coverage rate to $\rho$ , whose physical meaning is the cumulative duration of snowfall or rainfall. For the point cloud with a cumulative surface, randomly select $\rho |X|$ object points, where each point has information $(x,y,z,I)$ . For the height information $z$ , a random accumulation height can be added by $zI = z + h$ , s.t. $h\sim U(h_1,h_2)$ , where $h$ is a random variable uniformly sampled between $(h_1,h_2)$ . Meanwhile, due to the influence of the LiDAR reflection signal, the reflection intensity of the point needs to be randomly adjusted by $I / = I\cdot \gamma$ , s.t. $\gamma \sim U(\gamma_1,\gamma_2)$ , where $\gamma$ is a random variable uniformly sampled between $(\gamma_{1},\gamma_{2})$ . Therefore, the simulated point can be expressed as $(x,y,z,I)$ .
+
+$\Psi_{2}$ : Simulated Fuzzy Recognition. LiDAR signals are affected by water droplets and aerosol particles in the air during propagation [8, 43]. Some signals are scattered, causing the returned signal intensity to attenuate. Others are reflected back to the sensor, forming additional backscattering noise. This leads to missing points at long distances and enhancement of false points. Although the transition from clear weather to foggy weather can be achieved by simulating light scattering in a real foggy environment, the generation mode is limited. Inspired by the fuzzy processing in the human brain, people perform contextual reasoning
+
+and automatic completion of the absence when their sight is blocked.
+
+Therefore, we design a simple simulation to allow the model to perceive this missing and automatically learn reliable features. We first estimate the echo intensity affected by light scattering [8]. When light scattering makes the echo intensity too low, indicating that the fog is too thick, we set the corresponding label to an unknown category. This slight masking perturbation not only provides a distribution hypothesis, but also allows the model to automatically learn contextual reasoning by more attention to geometric features.
+
+# 3.3.2. Category-level Geometry Alignment
+
+The enhanced point cloud $X^{\psi}$ , together with the original point cloud, is put into the model $\Theta(X^{\psi})$ to obtain the simulated feature $F^{\psi} \in \mathbb{R}^{N \times D}$ . Then we use the category-level geometry matrix $A$ obtained from the original distribution to embed $F^{\psi}$ into the geometric space, that is, embedded the enhanced feature into the geometry distribution of the original feature and obtain $G^{\psi} = F^{\psi} A$ . Therefore, $G^{\psi} \in \mathbb{R}^{N \times C \times M}$ represents the consistent embedding, including $M$ geometric properties for each category.
+
+In addition, consistent learning helps the model learn both the original distribution and the enhanced distribution. Therefore, the correlation parameter $Q$ is also used to learn the relationship between the consistent embedding $G^{\psi}$ and the semantics of the corresponding category $Y^{\psi}$ . This can be achieved by calculating the geometric consistency learning (GCL) loss:
+
+$$
+\mathcal {L} _ {G C L} = - \frac {1}{N} \sum_ {n = 1} ^ {N} \sum_ {c = 1} ^ {C} Y _ {n c} ^ {\psi} \log \left(\left| \left| G ^ {\psi} Q \right| \right| _ {c}\right) _ {n c}. \tag {9}
+$$
+
+The model performs a backpropagation by accumulating the gradients of $\mathcal{L}_{GCL}$ and $\mathcal{L}_{GPL}$ , which are calculated from the original features and the simulated features, respectively. Therefore, the model automatically learns to align the representations of the source domain and the latent domain. The proposed method utilizes category-level geometric learning to push the segmentation model to focus on and learn reliable geometric features to improve generalization.
+
+# 4. Experiments and Analysis
+
+# 4.1. Datasets Description
+
+Three point cloud semantic segmentation datasets are used to compare the methods. SemanticKITTI [1] consists of LiDAR point clouds captured in urban environments under normal weather conditions. The point is annotated with 19 semantic categories, of which the training set serves as the source domain. The validation group is set as the additional target domain. SynLiDAR [33] is a synthetic LiDAR
+
+Table 1. Quantitative comparison between the proposed method and existing generalized point cloud segmentation methods. Top three results are highlighted as best, second and third, respectively. All models use the MinkUNet18 backbone.
+
+| Methods | car | bi.cle | mt.cle | truck | oth-v. | pers. | bi.clst | mt.clst | road | parki. | sidew. | oth-g. | build. | fence | veget. | trunk | terra. | pole | traf. | mIoU | D-fog | L-fog | Rain | Snow | Mean | |
| SemanticKITTI → SemanticSTF |
| PCL [38] | 65.9 | 0.0 | 0.0 | 17.7 | 0.4 | 8.4 | 0.0 | 0.0 | 59.6 | 12.0 | 35.0 | 1.6 | 74.0 | 47.5 | 60.7 | 15.8 | 48.9 | 26.1 | 27.5 | 26.4 | 28.9 | 27.6 | 30.1 | 24.6 | 27.8 | |
| MMD [19] | 63.6 | 0.0 | 2.6 | 0.1 | 11.4 | 28.1 | 0.0 | 0.0 | 67.0 | 14.1 | 37.9 | 0.3 | 67.3 | 41.2 | 57.1 | 27.4 | 47.9 | 28.2 | 16.2 | 26.9 | 30.4 | 28.1 | 32.8 | 25.2 | 29.1 | |
| PointDR [35] | 67.3 | 0.0 | 4.5 | 19.6 | 9.0 | 18.8 | 2.7 | 0.0 | 62.6 | 12.9 | 38.1 | 0.6 | 73.3 | 43.8 | 56.4 | 32.2 | 45.7 | 28.7 | 27.4 | 28.6 | 31.3 | 29.7 | 31.9 | 26.2 | 29.8 | |
| UniMix [43] | 82.7 | 6.6 | 8.6 | 4.5 | 15.1 | 35.5 | 15.5 | 37.7 | 55.8 | 10.2 | 36.2 | 1.3 | 72.8 | 40.1 | 49.1 | 33.4 | 34.9 | 23.5 | 33.5 | 31.4 | 34.8 | 30.2 | 34.9 | 30.9 | 32.7 | |
| DGLSS [16] | 72.6 | 0.1 | 11.7 | 29.4 | 13.7 | 48.3 | 0.5 | 21.2 | 65.0 | 20.2 | 38.3 | 3.8 | 78.9 | 51.8 | 57.0 | 36.4 | 47.0 | 26.9 | 34.9 | 34.6 | 34.2 | 34.8 | 36.2 | 32.1 | 34.3 | |
| DGUIL [10] | 77.9 | 10.6 | 19.1 | 26.0 | 9.7 | 46.3 | 6.0 | 9.3 | 69.1 | 18.0 | 38.6 | 9.4 | 73.3 | 51.2 | 60.8 | 30.9 | 50.8 | 31.8 | 22.3 | 35.5 | 36.3 | 34.5 | 35.5 | 33.3 | 34.8 | |
| LiDARWeather [25] | 86.1 | 4.8 | 13.8 | 39.7 | 26.6 | 55.4 | 8.5 | 50.4 | 63.7 | 14.9 | 37.9 | 5.5 | 75.2 | 52.7 | 60.4 | 39.7 | 44.9 | 30.1 | 40.8 | 39.5 | 36.0 | 37.5 | 37.6 | 33.1 | 36.1 | |
| Ours | 84.0 | 3.5 | 32.8 | 37.8 | 13.7 | 43.9 | 5.0 | 61.8 | 66.8 | 11.0 | 41.1 | 8.7 | 73.9 | 46.6 | 61.6 | 33.8 | 50.1 | 31.5 | 34.9 | 39.1 | 39.9 | 37.1 | 39.5 | 33.7 | 37.5 | |
| SynLiDAR → SemanticSTF |
| MMD [19] | 25.5 | 2.3 | 2.1 | 13.2 | 0.7 | 22.1 | 1.4 | 7.5 | 30.8 | 0.4 | 17.6 | 0.2 | 30.9 | 19.7 | 37.6 | 19.3 | 43.5 | 9.9 | 2.6 | 15.1 | 17.3 | 16.3 | 20.0 | 12.7 | 16.6 | |
| PolarMix [32] | 39.2 | 1.1 | 1.2 | 8.3 | 1.5 | 17.8 | 0.8 | 0.7 | 23.3 | 1.3 | 17.5 | 0.4 | 45.2 | 24.8 | 46.2 | 20.1 | 38.7 | 7.6 | 1.9 | 15.7 | 16.1 | 15.5 | 19.2 | 15.6 | 16.6 | |
| PCL [38] | 30.9 | 0.8 | 1.4 | 10.0 | 0.4 | 23.3 | 4.0 | 7.9 | 28.5 | 1.3 | 17.7 | 1.2 | 39.4 | 18.5 | 40.0 | 16.0 | 38.6 | 12.1 | 2.3 | 15.5 | 17.8 | 16.7 | 19.3 | 14.1 | 17.0 | |
| PointDR [35] | 37.8 | 2.5 | 2.4 | 23.6 | 0.1 | 26.3 | 2.2 | 3.3 | 27.9 | 7.7 | 17.5 | 0.5 | 47.6 | 25.3 | 45.7 | 21.0 | 37.5 | 17.9 | 5.5 | 18.5 | 19.5 | 19.9 | 21.1 | 16.9 | 19.4 | |
| LiDARWeather [25] | 42.1 | 2.8 | 2.7 | 19.2 | 0.7 | 29.2 | 1.9 | 4.8 | 42.3 | 8.7 | 21.1 | 1.6 | 48.2 | 26.0 | 47.2 | 22.1 | 32.8 | 21.7 | 6.5 | 20.1 | 19.1 | 20.7 | 22.0 | 17.3 | 19.8 | |
| DGUIL [10] | 43.3 | 2.8 | 2.6 | 23.2 | 3.2 | 31.3 | 2.5 | 4.4 | 34.3 | 9.2 | 17.9 | 0.3 | 57.1 | 27.6 | 50.0 | 24.2 | 41.5 | 19.0 | 6.1 | 21.1 | 22.3 | 21.9 | 26.0 | 19.8 | 22.5 | |
| UniMix [43] | 65.4 | 0.1 | 3.9 | 16.9 | 5.3 | 32.3 | 2.0 | 19.3 | 52.1 | 5.0 | 27.3 | 3.0 | 49.4 | 20.3 | 58.5 | 22.7 | 23.2 | 26.9 | 10.4 | 23.4 | 24.3 | 22.9 | 26.1 | 20.9 | 23.6 | |
| Ours | 54.4 | 2.6 | 1.7 | 28.0 | 5.9 | 30.9 | 5.6 | 23.0 | 46.1 | 8.0 | 21.7 | 0.5 | 60.3 | 29.4 | 52.6 | 27.5 | 40.7 | 28.8 | 11.0 | 25.2 | 27.9 | 25.1 | 28.7 | 23.2 | 26.3 | |
+
+Table 2. Comparison of domain generalization on SynLiDAR $\rightarrow$ SemanticKITTI. All models use the MinkUNet18 backbone.
+
+| Model | car | bi.cl | mt.cl | tru. | oth-v. | pers. | bi.cls | mt.cls | road | park. | sidew. | oth-g. | build. | fen. | vege. | tru. | terr. | pole | traf. | mIoU |
| PointDR [35] | 62.0 | 6.9 | 19.1 | 1.8 | 6.3 | 20.7 | 37.4 | 4.3 | 49.2 | 5.3 | 36.5 | 0.1 | 36.3 | 12.0 | 65.5 | 27.9 | 45.5 | 31.9 | 5.5 | 24.9 |
| DGLSS [16] | 62.7 | 6.4 | 20.4 | 1.0 | 7.1 | 25.4 | 39.2 | 4.9 | 33.7 | 7.7 | 35.6 | 0.0 | 44.7 | 25.4 | 68.0 | 35.5 | 44.5 | 38.3 | 10.2 | 26.8 |
| DGUIL [10] | 61.0 | 8.6 | 20.5 | 0.9 | 8.3 | 29.9 | 43.3 | 5.0 | 44.1 | 7.6 | 37.5 | 0.0 | 56.7 | 31.8 | 70.1 | 36.5 | 38.3 | 39.0 | 14.6 | 29.1 |
| Ours | 74.3 | 13.2 | 25.8 | 1.2 | 7.5 | 26.9 | 58.1 | 5.2 | 65.2 | 6.1 | 40.3 | 0.0 | 56.3 | 11.9 | 70.5 | 38.0 | 33.2 | 43.7 | 17.8 | 31.3 |
+
+Table 3. Domain generalization comparison on MinkUNet34 backbone with SemanticKITTI as source and SemanticSTF as target domain.
+
+| Model | car | bi.cl | mt.cl | tru. | oth-v. | pers. | bi.cls | mt.cls | road | park. | sidew. | oth-g. | build. | fen. | vege. | tru. | terr. | pole | traf. | mIoU |
| PointDR [35] | 72.5 | 0.8 | 24.5 | 28.1 | 14.4 | 48.6 | 4.6 | 34.2 | 57.4 | 16.4 | 31.7 | 5.2 | 72.9 | 48.6 | 53.9 | 35.2 | 46.3 | 31.2 | 24.0 | 34.3 |
| DGLSS [16] | 69.6 | 0.8 | 42.8 | 34.4 | 8.9 | 41.9 | 12.8 | 44.5 | 52.0 | 14.5 | 30.8 | 6.0 | 77.8 | 51.1 | 57.6 | 38.9 | 43.2 | 29.7 | 30.6 | 36.2 |
| DGUIL [10] | 78.2 | 2.5 | 33.0 | 29.7 | 6.1 | 49.8 | 0.8 | 40.9 | 67.3 | 7.2 | 38.0 | 2.2 | 79.8 | 54.4 | 64.1 | 36.8 | 52.3 | 31.0 | 40.0 | 37.6 |
| Ours | 79.5 | 0.6 | 62.3 | 31.4 | 4.9 | 35.0 | 4.8 | 63.1 | 65.7 | 15.8 | 39.7 | 8.7 | 78.6 | 52.5 | 60.3 | 32.0 | 50.2 | 28.8 | 35.4 | 39.4 |
+
+dataset generated from diverse virtual environments, such as downtown, suburban towns, neighborhoods, etc. The training set labeled with 19 categories serves as the source domain. SemanticSTF [35] comprises LiDAR point clouds of urban scenes collected under adverse weather conditions, such as light fog, dense fog, snow, and rain. SemanticSTF serves as the target domain.
+
+# 4.2. Implementation Details
+
+The framework is built upon PyTorch with an NVIDIA GeForce RTX 3090. For a fair comparison, we follow the previous settings [10, 35, 43] that adopt MinkowskiNet [3] as the segmentation backbone. Stochastic gradient descent (SGD) with 0.9 momentum is utilized for optimization. The batch size is 4, and the initialized learning rate is 0.24 with weight decay regularization of 1e-4. The training pipeline incorporates multiple random augmentation strategies like previous methods [35], such as affine transformations (full rotation range, scaling in [0.95, 1.05]), horizontal and vertical flipping, jittering, noise injection, and dropout with 0.2
+
+rates, to prevent overfitting of the source domain. The coverage rate $\rho$ is set to 0.3, and $\sigma$ is set to 0.05.
+
+# 4.3. Compared with the State-of-the-arts
+
+We compare the proposal with the state-of-the-art methods on multiple benchmarks, as shown in Tables 1, 2, and 3, illustrating that our method achieves superior performance on all benchmarks.
+
+SemanticKITTI $\rightarrow$ SemanticSTF represents the domain generalization comparison of typical real-world scenarios from normal weather (SemanticKITTI) to adverse weather scenarios (SemanticSTF). The upper part of Table 1 shows the performance comparison from normal to adverse weather, which includes four conditions (Dense fog, Light fog, Rain, and Snow). It can be seen that the proposed method shows stable generalization performance and is superior in most adverse weather conditions, with an average performance of $37.5\%$ higher than the state-of-the-art method [25] by $1.4\%$ . It should be noted that generalization in dense fog scenes is advantageous and reaches $39.9\%$
+
+
+Figure 2. Qualitative results of PointDR [35], DGUIL [10], and our approach from normal conditions (SemanticKITTI) to adverse weather.
+
+mIoU, which is $3.9\%$ higher than LiDARWeather [25]. This is because the model perceives geometric information and can rely on contextual prediction in a noisy environment. In addition, Figure 2 provides an intuitive comparison of the results. Our method shows superior domain generalization capabilities in different target distributions.
+
+SynLiDAR $\rightarrow$ SemanticSTF is the domain generalization from virtual scenes (SynLiDAR) to real adverse weather scenes (SemanticSTF). The lower part of Table 1 shows the comparison results of the proposed method with the outstanding methods. On this benchmark, UniMix [43] has an advantageous performance of $23.6\%$ under four realistic adverse weather conditions. The proposed method performs outstandingly, achieving an average performance of $26.3\%$ . Compared with the state-of-the-art method [43], the mIoU in dense fog, light fog, rain, and snow increases by $3.6\%$ , $2.2\%$ , $2.6\%$ , and $2.3\%$ , respectively. This demonstrates that the proposed geometric learning has a significant advantage in generalization.
+
+SynLiDAR $\rightarrow$ SemanticKITTI represents the generalization from virtual scenes (SynLiDAR) to general realworld scenes (SemanticKITTI). Table 2 shows the results of the proposed method and the current state-of-the-art methods in each category. DGUIL [10] achieves an advantageous performance with a mIoU of $29.1\%$ . The proposed method achieves mIoU of $31.3\%$ , which is $2.2\%$ higher than the state-of-the-art method.
+
+Besides, to demonstrate the integration of the proposed
+
+method, the comparison is carried out on another backbone MinkUNet34 [16], as shown in Table 3. The current most advantageous mIoU performance is $37.6\%$ , while our method achieves $39.4\%$ . The experiments show that the proposal also has advantages on another backbone.
+
+# 4.4. Ablation Studies
+
+To verify the effectiveness of the proposed modules, we conducted extensive ablation experiments on SemanticKITTI $\rightarrow$ SemanticSTF, as shown in Table 4. We add the proposed modules one by one to the baseline model, which is trained only with segmentation loss. CGC maps the original features of each category to the geometric space, which can improve mIoU to $32.8\%$ and increase by $1.4\%$ . Coupling the category geometry with $\mathcal{L}_{GPL}$ further improves mIoU to $33.0\%$ . The proposed CGE improves mIoU by $1.6\%$ , which shows the potential of category-level geometry embedding to improve generalization. GCL significantly boosts the mIoU, among which PAGS reaches $35.3\%$ mIoU and $\mathcal{L}_{GCL}$ reaches $37.5\%$ . PAGS simulates snow accumulation on object surface and fog recognition, so the generalization is effective in adverse weather. Furthermore, the more fundamental key is the domain-invariant geometry promotes generalization. We verify the impact of removing PAGS on the generalization from virtual to general real world, as shown in Table 5. The competitive performance further shows that the domain-invariant geometry promotes generalization. The performance improvement of GCL is based on the model's perception of geometry, focus-
+
+Table 4. Ablation studies of the modules on SemanticKITTI $\rightarrow$ SemanticSTF. CGE: Category-level Geometry Embedding. CGC: Category-level Geometry Construction. GPL: Geometry Property Learning. GCL: Geometric Consistent Learning. PAGS: Physics-inspired Adverse Geometry Simulation. TTA: Test Time Augmentation.
+
+| Method | CGE | GCL | mIoU | Δ |
| CGC | \( \mathcal{L}_{GPL} \) | PAGS | \( \mathcal{L}_{GCL} \) |
| Baseline | - | - | - | - | 31.4 | - |
| +CGC | ✓ | - | - | - | 32.8 | +1.4 |
| \( \mathcal{L}_{GPL} \) | ✓ | ✓ | - | - | 33.0 | +1.6 |
| +PAGS | ✓ | ✓ | ✓ | - | 35.3 | +4.1 |
| \( \mathcal{L}_{GCL} \) | ✓ | ✓ | ✓ | ✓ | 37.5 | +6.1 |
| +TTA | ✓ | ✓ | ✓ | ✓ | 39.1 | +7.7 |
+
+Table 5. Ablations on SynLiDAR $\rightarrow$ SemanticKITTI.
+
+| Method | Baseline | Ours | Ours*(w/o PAGS) |
| mIoU | 25.1 | 31.3 | 30.1 |
+
+Table 6. Ablation studies of geometric awareness and alignment.
+
+| Method | D-fog | L-fog | rain | snow | Mean |
| Ours | 39.9 | 37.1 | 39.5 | 33.7 | 37.5 |
| w/o geo. | 38.9 | 32.6 | 37.4 | 31.9 | 35.2 |
| w/o ali. | 37.8 | 33.2 | 33.7 | 27.6 | 33.1 |
+
+ing on the geometrically invariant information of each class, thereby improving generalization ability. Besides, considering the rotation invariance of point cloud data, TTA is utilized to rotate and scale the point cloud and integrate the prediction results. The results in Table 4 show that TTA can further improve mIoU to $39.1\%$ based on the proposed modules, which means that the proposal expands the representation space by introducing geometry awareness, giving the prediction a potential advantage.
+
+In addition, to verify the impact of geometric awareness and alignment for adverse weather, additional ablation verification is shown in Table 6. Removing the geometry awareness, i.e., features are not represented in Wasserstein space but in Euclidean space, reduces the performance in all adverse weather conditions. This result illustrates the necessity of geometric feature embedding. Besides, removing the alignment reduces the performance of all conditions, which illustrates the necessity of embedding alignment for stable generalization.
+
+# 4.5. Feature Visualization
+
+In order to intuitively compare the category distribution, we visualized the features using t-SNE [30], as shown in Figure 3. It can be seen that our method focuses on the distribution of all categories, and the clusters of different categories are slightly separated, which is conducive to better generalization. Besides, Figure 4 visualizes the local details of the simulation $\Psi_{1}$ . Intuitively, the ground points have random height enhancement to simulate the accumulated noise.
+
+# 4.6. Parameter Studies
+
+In this experiment, we first study the effect of the enhancement ratio of the two simulation methods, as shown in
+
+
+(a) Ours
+
+
+(b) Baseline
+
+
+Figure 3. Features visualization by t-SNE. The colors and categories have the same corresponding relationship as the results.
+(a) Original point cloud
+Figure 4. Visualization of simulation $\Psi_{1}$ .
+
+
+(b) Simulated point cloud
+
+Table 7. The effect of ${\beta }_{1}$ and ${\beta }_{2}$ on results.
+
+| β1 | 0.5 | 0.3 | 0.3 | 0.3 | 0.1 |
| β2 | 0.5 | 0.5 | 0.3 | 0.7 | 0.5 |
| mIoU | 38.1 | 39.1 | 37.4 | 36.8 | 36.5 |
+
+Table 8. The effect of different $\epsilon$ on the results.
+
+| ε | 0.9 | 0.99 | 0.999 | 0.9999 | 0.99999 |
| mIoU | 34.4 | 36.9 | 39.1 | 39.4 | 37.0 |
+
+Table 9. Hyperparameter ablations of $\rho ,{h}_{1},{h}_{2},{\gamma }_{1},{\gamma }_{2}$ .
+
+| ρ | 0.1 | 0.2 | 0.3 | 0.5 |
| mIoU | 38.7 | 38.9 | 39.1 | 38.6 |
| (h1,h2) | (0.05,0.1) | (0.05,0.3) | (0,0.3) | (0,0.5) |
| mIoU | 38.4 | 39.1 | 38.7 | 38.0 |
| (γ1,γ2) | (0.1,1.0) | (0.3,1.0) | (0.5,0.8) | (0.6,0.7) |
| mIoU | 39.4 | 39.6 | 39.1 | 38.0 |
+
+Table 7. The best results are obtained when probability $\beta_{1}$ is 0.3 and $\beta_{2}$ is 0.5. Secondly, we study the effect of the momentum parameter $\epsilon$ of the matrix A, as shown in Table 8. The most favorable performance of $39.4\%$ is achieved when $\epsilon$ is 0.9999, which also shows that is necessary for stable generalization with slow updates. Table 9 provides ablation experiments on hyperparameters $\rho$ , $h_{1}$ , $h_{2}$ , $\gamma_{1}$ , $\gamma_{2}$ . The best miou of $39.6\%$ can be achieved when $\rho = 0.3$ , $h_{1} = 0.05$ , $h_{2} = 0.3$ , $\gamma_{1} = 0.3$ , $\gamma_{2} = 1.0$ .
+
+# 5. Conclusions
+
+In this paper, a category-level geometry learning framework is proposed to explore the domain-invariant geometric features for domain-generalized 3D point cloud semantic segmentation. Category-level Geometry Embedding (CGE) is proposed to construct the geometric properties of each class and couple geometric embedding to category semantics. Geometric Consistent Learning (GCL) is proposed to simulate the latent 3D distribution and learn domain-invariant geometric representations. Extensive experiments demonstrate that the proposed method achieves state-of-the-art performance on multiple benchmarks. This work bridges a critical research gap in generalized point cloud segmentation. We hope this will inspire future work.
+
+Acknowledgments. This work was supported in part by the Joint Funds of the National Natural Science Foundation of China (U22B2054), the National Natural Science Foundation of China (62076192, 62276199, 62431020 and 62276201), the 111 Project, the Program for Cheung Kong Scholars and Innovative Research Team in University (IRT 15R53), the Science and Technology Innovation Project from the Chinese Ministry of Education, the National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Xi'an Jiaotong University (HMHAI-202404and HMHAI-202405), the Natural Science Basic Research Program of Shaanxi (Program No.2025JC-YBQN-827).
+
+# References
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+# Doodle Your Keypoints: Sketch-Based Few-Shot Keypoint Detection
+
+Subhajit Maity1* Ayan Kumar Bhunia2 Subhadeep Koley2 Pinaki Nath Chowdhury2
+Aneeshan Sain2 Yi-Zhe Song2
+
+$^{1}$ Department of Computer Science, University of Central Florida, United States. $^{2}$ SketchX, CVSSP, University of Surrey, United Kingdom.
+
+Subhajit@ucf.edu; {a.bhunia, s.koley, p.chowdhury, a.sain, y-song}@surrey.ac.uk https://subhajitmaity.me/DYKp
+
+
+Figure 1. Keypoint detection [17], usually approached in a supervised setting [29], along with cross-domain adaptation [15], can be set up in a few-shot paradigm [123] by typically learning to localize novel keypoints from limited annotated photos [41], also adapting to novel classes [67]. Unlike the existing works, we approach the problem in a cross-modal setup. (right) The proposed few-shot framework adapts to localize novel keypoints on photos of unseen classes given a few annotated sketches.
+
+# Abstract
+
+Keypoint detection, integral to modern machine perception, faces challenges in few-shot learning, particularly when source data from the same distribution as the query is unavailable. This gap is addressed by leveraging sketches, a popular form of human expression, providing a source-free alternative. However, challenges arise in mastering cross-modal embeddings and handling user-specific sketch styles. Our proposed framework overcomes these hurdles with a prototypical setup, combined with a grid-based locator and prototypical domain adaptation. We also demonstrate success in few-shot convergence across novel keypoints and classes through extensive experiments.
+
+# 1. Introduction
+
+Keypoint detection, a fundamental component in modern machine perception and visual understanding, has been integral to computer vision tasks since its inception [15, 17, 113, 133]. Initially harnessed as distinctive features [4, 38, 66], keypoints have evolved from handcrafted designs to play crucial roles in contemporary pose estimation [17, 61] and landmark detection [116, 123]. Their sig-
+
+nificance extends to applications such as localizing landmarks in faces [113, 116] and joints [36], contributing to pose [17, 19, 29, 135] and action [64] understanding.
+
+While existing approaches predominantly rely on heatmap regression or direct regression methods dependent on large annotated datasets [17, 18, 29, 78, 117, 135], few-shot keypoint learning remains a challenge. Current strategies, often repurposed from unsupervised or semi-supervised techniques, are constrained to specific image domains, limiting their applicability to novel keypoints on unseen objects [67]. The scarcity of research addressing the challenge of unavailable source modality in few-shot keypoint learning, particularly for novel keypoints, highlights a significant gap in the current landscape.
+
+Why choose sketches? Sketches [42] serve as a popular form of human expression and offer a viable alternative when the source data is limited in a few-shot setting. Unlike real images, human sketches, easily annotated, provide a practical solution for localizing novel keypoints in unseen classes. While generalized few-shot keypoint detection [67] must handle domain shifts and necessitates a few annotated examples, sketches present the opportunity to create a source-free pipeline for practical implementations.
+
+In the pursuit of utilizing sketches as an alternative sup
+
+port modality for a source-free few-shot keypoint detection approach, several distinct challenges emerge. First, mastering cross-modal keypoint embeddings proves formidable due to inherent disparities between these embeddings and joint sketch-photo embedding as per conventional cross-modal learning. Second, encoding images within this joint feature space may lack direct correspondence for specific keypoint embeddings, adding intricacy to the task. Third, the untested nature of few-shot capability within this cross-modal feature space introduces additional complexity. Simultaneously, sketches, as expressive forms of human representation rather than precise depictions of photorealism, introduce variability through user-specific styles, necessitating effective generalization across diverse styles to facilitate efficient keypoint learning.
+
+To tackle these challenges, we adopt a prototypical setup [108], constructing keypoint prototypes by pooling embeddings from encoded support feature maps. These prototypes are then correlated with query feature maps, generating rich keypoint descriptors. The subsequent use of the Grid Based Locator (GBL) [67] allows for the localization of keypoints from the rich descriptor through direct regression. To bridge the sketch-photo domain gap at the keypoint level, we introduce prototypical domain adaptation [115], which addresses the disparity between support prototypes and query keypoint embeddings pooled from query feature maps. Managing user style diversity is deemed crucial, and therefore, we maximize the similarity between corresponding keypoint embeddings extracted from different sketch versions. Each version represents a single object-level photo and exhibits varying styles.
+
+Our contributions include (a) the introduction of a sketch-based prototypical keypoint detection framework, (b) the pioneering exploration of source-free few-shot keypoint detection, and (c) extensive experimentation and analysis establishing the proposed method as a successful solution for few-shot convergence on novel keypoints in novel classes within a source-free cross-modal setup.
+
+# 2. Related Works
+
+Sketch for Visual Understanding: Having a surprisingly similar interpretation as real objects for human perception [42], sketch [22] and line drawings [56, 60, 109] have been a popular mode of expression, driving applications of hand-drawn sketches in multiple tasks including retrieval [7, 8, 20, 102, 103, 142], generation [34, 50], inpainting [128], segmentation [44], 3D modeling [143], and augmented reality [132]. In particular, sketch-based image retrieval [24, 28, 100, 101, 107, 138] involving various deep networks [7, 24, 96] to learn a cross-modal embedding space has been immensely popular among recent research directions due to its significant commercial importance. Due to the popularity of sketch as a barrier-free
+
+mode of human interaction across ethnic and social diversity, it has been used to guide object detection [21], saliency exploration [10], video synthesis [59], editing [134], and other computer vision problems [23, 131]. Attributing to the cognitive and creative potential [32] of humane intelligence, sketch has been used for Pictionary-styled gaming [6]. With all these diverse directions, the research community has explored the exploitation of both representative [119] and discriminative [9, 21] properties of sketch images. A more detailed exploration of sketches for various visual understanding tasks and their comparative analysis with several future directions are given in [5]. In this work, we particularly explore the representative property of the sketch in a localized context at a cross-modal latent for learning distinct keypoints in real photos.
+
+Few-Shot Learning: Few-shot learning [121] relates to meta-learning [139] closely, delving into strategies promoting faster convergence with fewer training samples and is approached by a learning-to-learn [51] approach. From an early age meta-learning [124] usually involved models [90], either specifically designed to use external memory buffers [35, 105, 125] and fast weights [76], or strategies [99, 145] designed to imitate and manipulate optimization [74, 88, 91, 136] and gradients [30, 80]. Irrespective of strategies like context adaptation [148], cross-modal setup [85, 106, 130], Bayesian [140], Low-shot [31, 37, 86, 122], or the recent metric learning approaches [2, 12, 62, 82, 141], modern few-shot learning uses a support set of a few unseen examples to maximize task-level performance on the query set. Among metric-based approaches [49, 114, 118], the prototypical network [108] and improvements [53, 58] became popular recently. Few-shot strategies, primarily curated for classification to distinguish class-specific semantics, cannot directly cater to keypoint detection due to significantly different task spaces. In this context, prototypes [108], carrying rich representative features from semantically distinct keypoints, are suitable for the few-shot keypoint learning regimes [67].
+
+Keypoint Detection: Ever since its inception [4, 38, 66], keypoint detection has been one of the major research trends in computer vision. The advent of deep learning [16, 113] has propelled the strategies and the usefulness of keypoint detection. Although being motivated by object detection [13, 95] and semantic segmentation [40] research, keypoint detection has advanced object detection by rethinking it from keypoints [52, 146, 147]. However, it has been traditionally used for identifying landmarks in the face [113, 116] and joints [36], specifically to understand the skeletal structure or pose [17, 61] of both living [15] and non-living objects [133]. Keypoint detection is typically solved either by employing a heat-based localization strategy [11, 29, 78, 113, 135], or using direct regression [18, 117]. The heatmap-based strategies, specif
+
+
+Figure 2. Overview of the proposed few-shot key-point detection framework that processes sketches or edgemaps in the support set and photos in the query set. It employs an encoder to extract deep feature maps followed by the derivation of keypoint embeddings through Gaussian Pooling. Support keypoint prototypes are constructed by averaging keypoint embeddings after disentangling style information through the de-stylization network. Support-query correlation is performed by a point-to-point multiplication of prototype and a query feature map, and subsequently a descriptor network formulates a query descriptor, which is used for localization by the GBL module.
+
+ically the ones for pose estimation, can be further classified into top-down approaches [29, 111] and bottom-up approaches [17, 19, 72, 78]. Keypoint detection research towards cross-domain adaptation [15], shape deformation aware pose translation [57], self-supervision [47, 81], contrastive learning [3], semi-supervision [27, 43, 73, 75, 87] and unsupervised pipelines [46, 65, 116] were also seen. The initial few-shot approaches [11, 137] explored semi-supervised or few-shot adaptation [123] following self-supervised pre-training, without leaving any room for cross-modal adaptation. While some strategies [33, 68, 69, 112] adapt to novel keypoints, exploiting shape-level [41, 126] or location-level [67] uncertainty, and additional textual guidance [70], they inherently cannot address the domain gap between sketches to learn from and photos to localize on.
+
+Sketch as an Alternate to Photos: Multi-modal learning [120] has been a recent trend to boost performance [63] and perform semi-supervision [8], and cross-modal [54, 144] adaptations. In this regard, sketch [104, 142] became a popular choice for cross-modal [7, 100] counterparts of object detection [21], saliency recognition [10] etc. Despite multimodal [45, 83, 130] approaches for few-shot learning included sketch [9], keypoints regime remained unexplored. Sketch [42] being easy to achieve using a few strokes remains a potential alternative for photos in particular scenarios, e.g. when the photo collection is hazardous or the subject is a rare species of bird or animal, or when the photo cannot be used due privacy and ethical constraints or, particularly when variability in object pose and perspective becomes a big challenge by occluding keypoints.
+
+# 3. Methodology
+
+Overview: In the context of few-shot keypoint detection, we have access to relevant dataset $\mathcal{D} = \{x_i^{\mathrm{P}},y_i\}$ with keypoint annotations of multiple species or objects where $x_{i}^{\mathrm{P}}\in \mathcal{I}^{3\times H\times W}$ is a standard RGB image and the annotation $y_{i} = \{\mathbf{u}_{n},\mathbf{v}_{n}\}_{n = 1}^{N}$ where $\mathbf{u}\in \mathbb{R}^2$ denotes coordi
+
+nate location $\mathbf{x}, \mathbf{y} \in [-1, 1]$ of a keypoint, and visibility $\mathbf{v} \in \{0, 1\}$ specifies if the keypoint is visible in the photo $x_{i}^{\mathrm{P}}$ , for each of the $N$ pre-defined keypoints. Due to the lack of a sketch-photo dataset with keypoint-level annotation, we use off-the-shelf edge detectors [14, 110, 129] to generate multiple versions of edgemaps from each photo $x_{i}^{\mathrm{P}}$ , considering them as equivalent to sketch data. In particular, we consider PiDiNet [110] as the primary edge detector to generate $x_{i}^{\mathrm{S}}$ , and HED [129] and Canny [14] as additional detectors providing style diversity, respectively producing $x_{i}^{\mathrm{S}_{1}}$ and $x_{i}^{\mathrm{S}_{2}}$ against any real photo $x_{i}^{\mathrm{P}}$ . All the edgemaps are standard RGB images $\mathcal{I}^{3 \times H \times W}$ . Thus, it is formulated as an N-way K-shot learning problem to detect $N$ keypoints on query photos using $K$ annotated sketches. The support set $S = \{x_{k}, y_{k}\}_{k=1}^{K}$ and query set $Q = \{x_{m}, y_{m}\}_{m=1}^{M}$ contains $K$ and $M$ distinct samples $\{x_{i}, y_{i}\}$ respectively from $D$ where $x_{k} = x_{k}^{\mathrm{S}}$ and $x_{m} = x_{m}^{\mathrm{P}}$ .
+
+# 3.1. Few-Shot Framework
+
+The proposed few-shot framework closely follows Lu et al. [67] by building prototypes [108] for all $N$ keypoints from support set $S$ , satisfying the requirements of keypoint localization, which is achieved by direct regression using a Grid-based Locator (GBL) [67] catering it towards sketch data (Sec. 3.1.2). The proposed architecture (Fig. 2) uses an image encoder $F$ to extract feature maps from the support edgemaps and the query photo. Subsequently, given the support keypoint locations, a keypoint extractor $\mathcal{P}$ extracts keypoint embeddings from support features, followed by computing support prototypes, which correlate to the query features using a feature modulator $\mathcal{M}$ . Feature descriptors are obtained from correlated feature maps through a descriptor network [67] $D$ and lastly, the GBL modules (grid classifier $G^{C}$ and regressor $G^{R}$ ) operating in multi-scale localizes the keypoints. The system is trained with keypoints loss $\mathcal{L}_{\mathrm{KP}}$ . Additionally, a domain adaptation strategy [115] optimizes a domain loss $\mathcal{L}_{\mathrm{DA}}$ discussed in Sec. 3.2 and a novel de-stylization network $Z$ utilizing an attention mechanism [25] maximizes information across diverse edgemap
+
+styles using $\mathcal{L}_{\mathrm{style}}$ as elaborated in Sec. 3.3. Moreover, auxiliary keypoints and tasks improve performance using auxiliary losses $\mathcal{L}_{\mathrm{KP - aux}}$ , $\mathcal{L}_{\mathrm{DA - aux}}$ , and $\mathcal{L}_{\mathrm{style - aux}}$ as given in Sec. 3.4. The total loss is in Eq. (1) where $\lambda_{\mathrm{KP}}$ , $\lambda_{\mathrm{DA}}$ and $\lambda_{\mathrm{style}}$ are corresponding loss scaling factors.
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {\mathrm {K P}} \left(\mathcal {L} _ {\mathrm {K P}} + \mathcal {L} _ {\mathrm {K P - a u x}}\right) + \lambda_ {\mathrm {D A}} \left(\mathcal {L} _ {\mathrm {D A}} + \mathcal {L} _ {\mathrm {D A - a u x}}\right) \tag {1} \\ + \lambda_ {\text {s t y l e}} \left(\mathcal {L} _ {\text {s t y l e}} + \mathcal {L} _ {\text {s t y l e - a u x}}\right) \\ \end{array}
+$$
+
+# 3.1.1. Support Prototypes & Query Correlation
+
+Image Encoder: The image encoder $F: \mathcal{I}^{3 \times H \times W} \to \mathbb{R}^{c \times h \times w}$ is an essential component of the framework that takes an input $x_{i}$ , i.e. either a support sketch or edgemap $x_{k}^{\mathrm{S}}$ or a query photo $x_{m}^{\mathrm{P}}$ , and encodes it to convolutional feature map $f_{i}$ . Meaning, for each of the $K$ edgemaps $x_{k} \in S$ and for each of the $M$ photos $x_{m} \in Q$ , the encoder $F$ generates support feature $f_{k}$ and query feature $f_{m}$ respectively.
+
+Support Prototypes: The keypoint detection task inherently demands the learning of keypoint embeddings $\Phi_{k,n} \in \mathbb{R}^c$ . So, we use $\mathcal{P}$ operator for extracting embedding $\Phi_{k,n} = \mathcal{P}(f_k, \mathbf{u}_{k,n})$ for keypoint $n$ in $x_k \in S$ . $\mathcal{P}$ is realized by Gaussian pooling [67] in Eq. (2) to encode sufficiently discriminative local context without any hard local boundary at the corresponding ground-truth location $\mathbf{u}_{k,n} \in y_k$ , where $f_k[\mathbf{x}]$ refers to the $\mathbb{R}^c$ vector from $f_k$ indexed at location $\mathbf{x}$ .
+
+$$
+\mathcal {P} \left(f _ {k}, \mathbf {u} _ {k, n}\right) = \sum_ {\mathbf {x}} \exp \left(\frac {- \| \mathbf {x} - \mathbf {u} _ {k , n} \| _ {2} ^ {2}}{2 \xi^ {2}}\right) \cdot f _ {k} [ \mathbf {x} ] \tag {2}
+$$
+
+Each $\Phi_{k,n}$ from support $x_{k}$ is mapped to a style-agnostic embedding $\delta_{k,n} \in \mathbb{R}^{c}$ enriched with mutual information across styles (Sec. 3.3) using de-stylization network $Z$ .
+
+Following the standard prototypical network [108], we compute each support keypoint prototype $\mu_{n} : n = 1, \ldots, N$ as a mean of the visible de-stylized support keypoint embeddings $\delta_{k,n}$ across the support set $S$ as per Eq. (3). The visibility of the prototype $\mu_{n}$ is true if $\mathbf{v}_{k,n} = 1$ for at least one $x_{k} \in S$ . The loss uses it to not penalize the model for predicting keypoints absent in $S$ .
+
+$$
+\mu_ {n} = \frac {1}{K} \sum_ {k = 1} ^ {K} \delta_ {k, n} \tag {3}
+$$
+
+Support-Query Correlation: While the original prototypical network [108] used a distance metric to assign class probabilities for the classification task, the keypoint localization is inherently different from it and requires local-level feature correspondence for each keypoint. Hence, support prototypes $\mu_{n}: n = 1, \ldots, N$ for all the keypoints are separately correlated with query feature $f_{m}$ encoded from query photo $x_{m} \in \mathcal{Q}$ with a feature modulator [67] $\mathcal{M}$ .
+
+$$
+\mathcal {A} _ {m, n} = \mathcal {M} \left(f _ {m}, \mu_ {n}\right) \quad \mathcal {A} _ {m, n} [ \mathbf {x} ] = f _ {m} [ \mathbf {x} ] \odot \mu_ {n} \tag {4}
+$$
+
+$\mathcal{M}$ is defined by elementwise multiplication of prototype $\mu_{n}$ and query feature $f_{m}$ at every location index $\mathbf{x}$ of $f_{m}$ for each of the $N$ keypoints, as in Eq. (4) and generates correlated feature $\mathcal{A}_{m,n} \in \mathbb{R}^{c \times h \times w}$ corresponding to $x_{m}$ .
+
+Following, Lu et al. [67] a descriptor network $D: \mathcal{A}_{m,n} \to \Psi_{m,n}$ refines and encodes the positional information in the query photo $x_m$ from the correlated feature maps $\mathcal{A}_{m,n}$ to descriptors $\Psi_{m,n} \in \mathbb{R}^d$ for all $N$ keypoints.
+
+# 3.1.2. Keypoints Localization
+
+Overview: Grids [77, 94, 98], being used for more than a decade for detection [92-94] tasks, were extended to keypoint localization [67] using a grid regression by modeling keypoint uncertainty. Inspired by the same, we use a direct regression in our GBL without any notion of uncertainty, as it becomes daunting due to the sparse nature of sketches.
+
+We dismantle the localization task of GBL into two subproblems, grid classification and local grid offset regression, to restrict the error margin to a small patch. To be precise, to localize keypoint $n$ in a query photo $x_{m}$ in multi-scale, a set of $S$ grid-scales $L = \{L_1,\dots ,L_S\}$ is considered and each grid-scale $L_{i}\in L$ is used to divide $x_{m}$ into $L_{i}\times L_{i}$ patches across height and width, of size $3\times \frac{H}{L_i}\times \frac{W}{L_i}$ each. The patches are labelled as the set $l_{i} = \{0,1,2,\ldots ,(L_{i}^{2} - 1)\}$ in left-to-right and top-to-bottom order. The ground-truth $\mathbf{u}_n$ in the corresponding $y_{m}$ , in the range $[-1,1]$ , is converted to the grid map label $\mathbf{u}_n^C$ and offset $\mathbf{u}_n^R$ as per Eq. (5). Formally, $\mathbf{t}$ denotes the ground-truth coordinates $\mathrm{x},\mathrm{y}\in \mathbf{u}_n$ normalized in $[0,L_i]$ , and $\mathbf{z}$ refers to the $\mathbf{x},\mathbf{y}$ indexing of the grids $l_{i}$ . Next, the grid index $\mathbf{z} = \{\mathbf{z}_{\mathbf{x}},\mathbf{z}_{\mathbf{y}}\}$ is converted to actual grid label $\mathbf{u}_n^C\in l_i$ and the grid offset $\mathbf{u}_n^R$ is the deviation from the center, i.e. location inside the grid $\mathbf{u}_n^C$ normalized in $[-1,1]$ .
+
+$$
+\begin{array}{l} \mathbf {t} = \left(\mathbf {u} _ {n} / 2 + 0. 5\right) * L _ {i} \quad \mathbf {z} = \lfloor \max (0, \min (\mathbf {t}, 1)) \rfloor \\ \mathbf {u} _ {n} ^ {C} = \mathbf {z} _ {\mathrm {y}} \cdot L _ {i} + \mathbf {z} _ {\mathrm {x}} \quad \mathbf {u} _ {n} ^ {R} = 2 (\mathbf {t} - \mathbf {z} - 0. 5) \tag {5} \\ \end{array}
+$$
+
+The submodules of our version of GBL, the grid classifier $G^{C}$ and the grid regressor $G^{R}$ try to predict $\mathbf{u}_n^C$ and $\mathbf{u}_n^R$ respectively for localizing keypoints. The total loss is given $\mathcal{L}_{\mathrm{KP}} = \mathcal{L}_{\mathrm{cls}} + \mathcal{L}_{\mathrm{dev}}$ which optimizes a completely different objective compared to Lu et al. [67]. All the loss calculations and predictions for keypoint $n$ are considered only if it is visible in $x_{m}$ and has a visible support prototype $\mu_{n}$ .
+
+Grid Classifier: The grid classifier $G^{C}$ learns to estimate the probability distribution $\hat{\mathbf{u}}_n^C = p(l|\Psi_{m,n})$ of keypoint $n$ being located in patch $l\in l_i$ from the query keypoint descriptor $\Psi_{m,n}$ using softmax on a linear layer as described in Eq. (6), with an output space $\mathbb{R}^{L_i^2}$ for each keypoint $n$ . This specifically resolves the dependency of grid regressor by providing it with a smaller scope to localize.
+
+$$
+p (l | \Psi_ {m, n}) = \frac {\exp \left(G ^ {C} \left(\Psi_ {m , n}\right) _ {l}\right)}{\sum_ {l ^ {\prime} \in l _ {i}} \exp \left(G ^ {C} \left(\Psi_ {m , n}\right) _ {l ^ {\prime}}\right)} \tag {6}
+$$
+
+While Lu et al. [67] considers grid-level uncertainty using log-likelihood, we opted to train $G^{C}$ with the much simpler cross-entropy loss $\mathcal{L}_{\mathrm{cls}}$ , as given in Eq. (7), leveraging the one-hot encoded ground-truth $\mathbb{1}(\mathbf{u}_n^C)$ .
+
+$$
+\mathcal {L} _ {\mathrm {c l s}} = - \sum \log \left(\hat {\mathbf {u}} _ {n} ^ {C}\right) \odot \mathbb {1} \left(\mathbf {u} _ {n} ^ {C}\right) (7) \quad \mathcal {L} _ {\mathrm {d e v}} = \| \hat {\mathbf {u}} _ {n} ^ {R} - \mathbf {u} _ {n} ^ {R} \| _ {1} \tag {8}
+$$
+
+Grid Regressor: The grid regressor $G^{R}$ tries to predict the offset values $\hat{\mathbf{u}}_n^R = G^R (\Psi_{m,n})$ against the relevant grid
+
+$l$ (from ground-truth $\mathbf{u}_n^C$ during training, and from grid classifier prediction $\max (\hat{\mathbf{u}_n^C})$ during inference) for keypoint $n$ from the corresponding query keypoint descriptor $\Psi_{m,n}$ using a linear layer with output space $\mathbb{R}^2$ . Unlike modeling the offset as a sample of multivariate Gaussian distribution in Lu et al. [67], our $G^{R}$ uses an $l_{1}$ loss $\mathcal{L}_{\mathrm{dev}}$ as in Eq. (8).
+
+Prediction: The final prediction for keypoint $n$ in query $x_{m}$ is computed from the predicted grid label probability $\hat{\mathbf{u}}_n^C$ and grid offset $\hat{\mathbf{u}}_n^R$ . Considering the predicted grid label as $\max(\hat{\mathbf{u}}_n^C)$ , for any grid scale, the prediction is computed by adding $\hat{\mathbf{u}}_n^R$ to its center. The final prediction is given as a mean across all $S$ grids in $L$ .
+
+# 3.2. Optimizing Sketch-Photo Domain Gap
+
+From the problem definition, the sketch-photo domain gap remains the biggest challenge as no sketch $x_{k} \in S$ has content-level pairing with any of the photo $x_{m} \in \mathcal{Q}$ . Considering this, we seek guidance from modern domain adaptation [115] that particularly implements a prototypical framework [108] to optimize transport loss pulling source prototypes and target samples closer. However, as keypoint detection differs significantly from the classification at the task level, the transport loss [115] cannot be used naively. Moreover, the unsupervised setting [115] practically ignores the keypoint-level class information available.
+
+Bi-directional transport loss [115] uses source and target data along with a common prototype in an unsupervised setting. As the cross-modal task space needs domain adaptation at the keypoint-level instead of feature-level, we consider support keypoint embeddings $\phi_{k,n}$ and extract similar keypoint embeddings $\hat{\Phi}_{m,n}$ from query photo $x_{m}$ .
+
+Transport loss [115] uses a point-to-point cost $\mathbf{C}(\mu_n,\hat{\Phi}_{m,n}) = \|\mu_n - \hat{\Phi}_{m,n}\|_2$ between prototypes and query keypoints which is realized by $l_2$ distance. It also relies on a cosine similarity score between $\mu_n$ and $\hat{\Phi}_{m,n}$ as an unnormalized class likelihood measure to adjust the cost $\mathbf{C}$ , which is adapted to a normalized distance-based similarity measure $\mathbf{Sim}(\mu_n,\hat{\Phi}_{m,n}) = \exp\left(-\|\mu_n - \hat{\Phi}_{m,n}\|_2^2\right)$ signifying the likelihood of a query keypoints embedding $\hat{\Phi}_{m,n}$ relating to corresponding support keypoints prototype $\mu_n$ , to encourage transport guided by keypoints-level representative information instead of discriminative class information. See §Suppl.
+
+$$
+p \left(\hat {\mu} _ {n}\right) = \exp \left(- \| \hat {\mu} _ {n} - \mu_ {n} \| _ {2} ^ {2}\right) \quad \hat {\mu} _ {n} = \frac {1}{M} \sum_ {m = 1} ^ {M} \hat {\Phi} _ {m, n} \tag {9}
+$$
+
+While iteratively updating the target distribution $p(\hat{\mu}_n)$ was necessary for an unsupervised setting, we have access to the information of query keypoint correspondence to the prototypes and thus, we convert this domain adaptation [115] paradigm to a supervised one using Eq. (9). As the class-level probability distribution to relate the prototype $\mu_n$ to query embedding $\hat{\Phi}_{m,n}$ is not coherent with our task, we ignore the softmax operation from both the transport losses,
+
+
+Figure 3. The design of the de-stylization network $Z$ to disentangle the styles fusing global context to local keypoint embeddings.
+
+resulting in reduction of two transport losses [115] to one:
+
+$$
+\mathcal {L} _ {\mathrm {D A}} = \sum p (\hat {\mu} _ {n}) \mathbf {C} \left(\mu_ {n}, \hat {\Phi} _ {m, n}\right) \mathbf {S i m} \left(\mu_ {n}, \hat {\Phi} _ {m, n}\right) \tag {10}
+$$
+
+# 3.3. Learning Style-Agnostic Keypoints
+
+Sketch largely depends on the user's expressive intent and imagination as opposed to photorealism and has significant user-specific variance in terms of sparsity, information content, and style [100]. This style diversity impacts performance as the framework eventually learns dense information at the keypoint level, irrespective of sketch sparsity. So, we design a de-stylization network $Z$ that de-stylizes any support keypoint embedding $\Phi_{k,n}$ extracted from support edgemap $x_{k}$ to $\delta_{k,n} \in \mathbb{R}^{c}$ . The off-the-shelf edge detectors [14, 110, 129] generate different instances of edgemap $x_{k}^{\mathrm{S}}, x_{k}^{\mathrm{S}_{1}}$ and $x_{k}^{\mathrm{S}_{2}}$ for the same photo $x_{k}^{\mathrm{P}} \in S$ not only providing the style diversity but also aiding the encoder to learn dense features to tackle inherent sparsity of the sketch data. The design of the de-stylization network $Z$ illustrated in Fig. 3 is inspired by the multi-scale channel attention module [25] that aggregates local and global context. (Design detailed in §Suppl.) The disentanglement being targeted at the keypoint embeddings with the local context, $Z$ is devised to take the encoded feature $f_{k}^{\mathrm{S}}, f_{k}^{\mathrm{S}_{1}}$ and $f_{k}^{\mathrm{S}_{2}}$ respectively, providing the notion of sparsity in a global scale along with keypoint embeddings $\Phi_{k,n}^{\mathrm{S}}, \Phi_{k,n}^{\mathrm{S}_{1}}$ and $\Phi_{k,n}^{\mathrm{S}_{2}}$ for mapping to $\delta_{k,n}^{\mathrm{S}}, \delta_{k,n}^{\mathrm{S}_{1}}$ and $\delta_{k,n}^{\mathrm{S}_{2}}$ respectively using an attention mechanism [25]. Considering all the versions of edgemap $x_{k}^{\mathrm{S}}, x_{k}^{\mathrm{S}_{1}}$ and $x_{k}^{\mathrm{S}_{2}}$ as supplements to various user styles with different levels of abstraction and information content, $Z$ ideally should disentangle the same and map any keypoint similar to each other. Taking $x_{k}^{\mathrm{S}}$ as primary sketch equivalent for training, we have $f_{k} = f_{k}^{\mathrm{S}}, \Phi_{k,n} = \Phi_{k,n}^{\mathrm{S}}$ and $\delta_{k,n} = \delta_{k,n}^{\mathrm{S}}$ . Thus $\mathcal{L}_{\mathrm{style}}$ is derived as:
+
+$$
+\mathcal {L} _ {\text {s t y l e}} = \sum_ {n} \left(\left\| \delta_ {k, n} - \delta_ {k, n} ^ {\mathrm {S} _ {1}} \right\| _ {2} + \left\| \delta_ {k, n} - \delta_ {k, n} ^ {\mathrm {S} _ {2}} \right\| _ {2} + \left\| \delta_ {k, n} ^ {\mathrm {S} _ {1}} - \delta_ {k, n} ^ {\mathrm {S} _ {2}} \right\| _ {2}\right)
+$$
+
+# 3.4. Auxiliary Keypoints Improve Performance
+
+(11)
+
+Along with the main keypoints given by the annotations, we strategically interpolate auxiliary keypoints [67] for the episodic training of our framework. Precisely, given two visible annotated main keypoints $n_1$ and $n_2$ , and a relative position $t \in (0,1)$ , interpolation $\mathcal{T}(t,(\mathbf{u}_{n_1},\mathbf{u}_{n_2}))$ obtains an auxiliary keypoint at $t$ times the length on the line running from $n_1$ to $n_2$ . Simply, auxiliary keypoints [67] are considered on the line interpolating a particular keypoint to another when both are visible. An off-the-shelf saliency detector [127] is used to see if an auxiliary keypoint is inside the saliency region of the object, determining its visibility.
+
+While the generation strategy $\mathcal{T}$ is inspired by Lu et al. [67], our auxiliary keypoints serve a completely different set of objectives. Unlike using auxiliary keypoints, particularly to aid the uncertainty learning, we do not model any interaction between main and auxiliary keypoints. Instead, we use these additional keypoints to provide additional augmented data for the components in our framework. To this end, we extend the existing objectives of localization, domain adaptation, and de-stylization to $T$ auxiliary keypoints by creating an auxiliary task of $T$ way keypoint learning and calculating $\mathcal{L}_{\mathrm{KP - aux}}$ , $\mathcal{L}_{\mathrm{DA - aux}}$ , and $\mathcal{L}_{\mathrm{style - aux}}$ accordingly.
+
+# 4. Experiments
+
+Dataset: For the experiments, we have used the Animal Pose dataset [15] consisting of 5 different species of animals (cat, cow, dog, horse, sheep) with a total of 4,666 images and 6,117 instances. The annotations contain 20 keypoints for each species, from which we used 17 (11 as base for training and 6 as novel for evaluation). All the ablation experiments are also done on this dataset.
+
+Additionally, we consider Animal Kingdom dataset [79] with 33,099 photos of 850 different species of broadly 5 superclasses (mammal, amphibian, reptile, bird, fish), which we treat as image classes for our purpose. It contains 23 keypoint annotations for each photo, and keeping similarity, we use only 11 base keypoints and 7 novel keypoints.
+
+Implementation Details: The entire framework is implemented in Python with PyTorch [84] and is trained on a 6GB Nvidia RTX 3060 mobile GPU. The encoder $F$ uses aImagenet [26] pre-trained ResNet50 [39] backbone. The descriptor network $D$ uses 3 convolution layers with ReLU [1] in sequence. The de-stylization network $Z$ follows Fig. 3. The GBL components, $G^{C}$ and $G^{R}$ use a linear layer each, with an additional softmax for $G^{C}$ .
+
+We set $K = 1$ shot and $M = 5$ with $N = 11$ base keypoints for training and $N = 6$ novel keypoints for evaluation. The ablations also use the same setup unless otherwise specified. The input images $x_{i}$ , for both sketch or edgemap $x_{k}$ and photo $x_{m}$ are resized to the height and width $H = W = 384$ and thus the resulting feature map $f_{i}$ has height and width $h = w = 12$ . According to the encoder $F$ configuration, the feature map $f_{i}$ has $c = 2048$ channels and the descriptor network $D$ allows it to produce query keypoint descriptors of dimension $d = 4096$ . The auxiliary keypoints use 6 pre-defined pairs from 11 base keypoints and set $t = \{0.25, 0.5, 0.75\}$ as interpolation points; meaning a maximum of 18 auxiliary keypoints can possibly exist for any $x_{i}$ during training. The multi-scale aspect of GBL is realized using 3 grid scales, $L = \{8, 12, 16\}$ . The empirically determined hyper-parameters are $\xi = 14$ , $\lambda_{\mathrm{KP}} = 0.5$ , $\lambda_{\mathrm{DA}} = 0.001$ and $\lambda_{\mathrm{style}} = 0.001$ . The entire setup is trained for 80,000 iterations of episodes with Adam [48] optimizer with a learning rate of 0.0001.
+
+
+Figure 4. Sample support $(S)$ and query $(\mathcal{Q})$ for training $(top)$ and evaluation (bottom) for all evaluation settings.
+
+Evaluation Protocol: We use percentage correct keypoints (PCK) [81] with a margin $\tau = 0.1$ as metric. The prediction is correct if within a range $\tau$ times the larger side of the object bounding box. We consider four different settings (see Fig. 4) to analyze the performance of our framework. From the definition of few-shot keypoint detection, we evaluate performance with novel keypoints along with the base keypoints used in training for the base classes it is trained on, as well as never-before-seen classes. All the ablation studies are done for novel keypoints on unseen classes of Animal Pose [15] dataset unless otherwise specified. For the evaluation of a novel class, we trained the framework with episodes with data from the rest of the classes, and for seen classes, we used a random $7:3$ train-test split.
+
+Competitors: Due to the lack of existing works on cross-modal few-shot keypoint learning, we repurposed the next best alternative FSKD [67] to use edgemaps [110] as support and photos as query, providing a comparable strategy, thanks to its robustness in detecting novel keypoints across significant differences in object classes.
+
+We establish a vanilla baseline B-Vanilla using only the base framework (Sec. 3.1). For B-Vanilla, $Z$ is replaced by an identity function such that we have $\Phi_{k,n} = \delta_{k,n}$ and the additional edgemaps $x_{k}^{\mathbb{S}_{1}}$ and $x_{k}^{\mathbb{S}_{2}}$ are not used, setting $\mathcal{L}_{\mathrm{style}} = 0$ . We further establish a few incremental baselines. B-DA represents the usage of sketch-photo domain adaptation [115] on top of B-Vanilla. B-Style uses only style-agnostic keypoint learning presented in Sec. 3.3 on B-Vanilla. As B-Full uses both domain adaptation (Sec. 3.2) and de-stylization (Sec. 3.3), it provides the proposed model when used with auxiliary keypoints (Sec. 3.4).
+
+| Class | Keypoints | Methods | PCK@0.1 on Animal Pose Dataset [15] | PCK@0.1 on Animal Kingdom Dataset [79] |
| Cat | Cow | Dog | Horse | Sheep | Mean | Mammal | Amphibian | Reptile | Bird | Fish | Mean |
| Seen | Base | B-Vanilla | 54.12 | 39.27 | 44.65 | 45.58 | 37.17 | 44.16 | 22.32 | 21.07 | 18.94 | 21.77 | 18.19 | 20.46 |
| FSKD [67] | 58.95 | 44.61 | 49.53 | 50.21 | 40.47 | 48.75 | 25.52 | 24.42 | 21.81 | 25.73 | 22.24 | 23.94 |
| Proposed | 67.34 | 49.89 | 56.28 | 56.35 | 45.65 | 55.10 | 31.31 | 29.93 | 28.41 | 30.88 | 27.87 | 29.68 |
| Novel | B-Vanilla | 24.70 | 15.62 | 19.08 | 12.45 | 18.44 | 18.06 | 9.67 | 7.24 | 6.55 | 8.41 | 4.96 | 7.37 |
| FSKD [67] | 47.70 | 35.44 | 39.81 | 35.42 | 31.59 | 37.99 | 18.89 | 17.39 | 16.72 | 19.23 | 15.94 | 17.63 |
| Proposed | 55.69 | 43.09 | 46.58 | 43.94 | 36.39 | 45.14 | 25.05 | 23.27 | 22.56 | 24.04 | 21.78 | 23.34 |
| Unseen | Base | B-Vanilla | 43.03 | 40.31 | 36.28 | 44.72 | 38.03 | 40.47 | 12.83 | 14.12 | 12.57 | 13.68 | 12.41 | 13.12 |
| FSKD [67] | 41.54 | 38.10 | 33.72 | 41.02 | 36.30 | 38.14 | 14.86 | 14.28 | 13.79 | 15.65 | 12.16 | 14.15 |
| Proposed | 47.36 | 42.97 | 38.30 | 46.17 | 41.03 | 43.17 | 21.98 | 20.15 | 18.96 | 21.52 | 17.19 | 19.96 |
| Novel | B-Vanilla | 22.71 | 15.56 | 16.92 | 13.58 | 18.18 | 17.39 | 7.26 | 5.12 | 3.93 | 5.69 | 4.08 | 5.22 |
| FSKD [67] | 36.75 | 35.76 | 32.84 | 32.66 | 31.58 | 33.92 | 10.96 | 9.34 | 9.68 | 11.45 | 8.86 | 10.06 |
| Proposed | 44.42 | 40.13 | 36.91 | 37.77 | 35.77 | 39.00 | 16.48 | 14.62 | 13.76 | 15.91 | 11.33 | 14.42 |
+
+Table 1. A quantitative comparison of the baseline and state-of-the-art strategies with the proposed framework in $K = 1$ shot setting delineating the superiority of the proposed method in overall performance on Animal Pose [15] and Animal Kingdom [79] datasets.
+
+
+Figure 5. Visualising detection $(\star)$ and ground-truth $(\bullet)$ for novel keypoints for base classes (top) and unseen classes (bottom).
+
+# 4.1. Performance Analysis
+
+A detailed performance comparison of the naive baseline B-Vanilla and FSKD [67] (repurposed for the cross-modal paradigm) with the proposed framework is presented in Tab. 1. We evaluate in four aforementioned settings for both datasets [15, 79], and our findings are: (a) B-Vanilla performs poorly in the majority of the settings as it lacks robustness in keypoint learning due to the sketch-photo domain gap, and absence of auxiliary keypoints. The significant performance gap comes from the lack of auxiliary keypoints during training, discussed further in Sec. 4.4. (b) FSKD [67] performs much better than the baseline due to its clever use of localization uncertainty. The huge margin over B-Vanilla can be attributed to uncertainty modeling with main and auxiliary keypoints. However, it falls short of the proposed model due to the sketch-photo domain gap. (c) The proposed framework significantly outperforms all its counterparts for all evaluation settings and datasets [15, 79]. This is due to the careful consideration of the sketch-photo domain gap and information maximization across diverse styles. (d) All methods have the poorest performance on novel keypoints for unseen classes, which is expected due to the two levels of domain shift defined by the evaluation protocol. However, our work accounts for the third domain gap between sketches or edemaps and photos. (e) Our method outperforms FSKD [67] by $\approx 5$ and $\approx 4$ PCK in Animal Pose [15] and Animal Kingdom [79], respectively, for novel keypoints on unseen classes. A few sample predictions with
+
+
+Figure 6. Inference $(\mathbf{x})$ with ground-truth $(\bullet)$ for base $(top)$ and novel (bottom) keypoints with annotated sketch prompts.
+
+ground truth from Animal Pose [15] are presented in Fig. 5. It also has superior performance over FSKD [67], maintaining a margin of $\approx 4 - 8$ in all evaluation settings. (f) B-Vanilla performs significantly lower for novel keypoints than base keypoints, showing its poor few-shot capability.
+
+# 4.2. Generalization on Free-Hand Sketches
+
+The proposed framework is trained on synthetic sketches or edgemaps [110] of the photos in the Animal Pose dataset [15]. Thus, we curate a small subset of real sketches of the same classes from the Sketchy database [104] to evaluate how well the model generalizes on real free-hand sketches. The evaluation is performed on query photos in the training dataset [15] using a total of 30 real sketches [104] with manual keypoint prompts in $K = 1$ shot setting. The PCK@0.1 values reported for base and novel keypoints are $42.40\% (\downarrow 0.77)$ and $38.49\% (\downarrow 0.51)$ for unseen classes, and $53.29\% (\downarrow 1.81)$ and $44.99\% (\downarrow 0.15)$ for seen classes respectively, showing the trained model easily adapting to free-hand sketches [104]. See §Suppl. (Tab. 5). The inference on a few samples is shown
+
+| Method | N(only Main) | N + T(+ Auxiliary) |
| B-Vanilla | 17.39 | 29.98 |
| B-DA | 18.31 | 31.76 |
| B-Style | 18.97 | 32.51 |
| B-Full | 19.03 | 39.00 |
+
+Table 2. Performances of incremental baselines.
+
+
+Figure 7. Performance with varying shots.
+
+
+Figure 8. Impact of varying main keypoints.
+
+
+Figure 9. Impact of varying auxiliary keypoints.
+
+in Fig. 6. The framework, designed for few-shot settings, possesses a high capability for adapting to novel data distributions, which helps it generalize well on real sketches. Sketches are contour-level depiction [42] of real photos and are represented closely to edgemaps due to de-stylization (Sec. 3.3), facilitating easy adaptation.
+
+# 4.3. Experiments on Multi-modality
+
+Considering novel keypoints on unseen classes, our framework establishes its superiority with a PCK@0.1 of $39.00\%$ ( $\uparrow$ 5.08) (Tab. 1) compared to FSKD [67] ( $33.92\%$ ). While it is impeccable with sketches, we experiment to see how it fares when being trained with photos instead. FSKD [67] being a state-of-the-art on photos with $44.75\%$ PCK@0.1, our model proves to be robust enough to achieve $43.72\%$ ( $\downarrow$ 1.03) when trained with photos. However, jointly training our model with sketch and photo results in $46.54\%$ outperforming FSKD [67] by 1.79. Evidently, mutual information from both modalities helps in having a more generalized keypoint understanding. Details of the multi-modal training and results are in $\S \mathrm{Suppl}$ .
+
+# 4.4. Ablation Study
+
+Number of Shots: Typically, increasing the number of shots in a few-shot setting boosts performance [67]. We present the empirical data in Fig. 7 that shows performance increase with increasing $K$ , although the rate of increment gradually diminishes, denoting information saturation.
+
+Significance of Loss Objectives: Justifying the independent contribution of the loss objectives, we present a strip-down-styled performance analysis of the incremental baselines at $K = 1$ shot in Tab. 2. B-Vanilla is a naive baseline with the poorest performance. B-DA uses domain adaptation [115], B-Style accounts for style diversity, improving $\approx 1 - 1.5$ over B-Vanilla. B-Full devises both modules (Secs. 3.2 and 3.3), has superior performance. Evidently, auxiliary keypoints [67] (Sec. 3.4) significantly boost performance by enhancing the capability of other modules.
+
+Number of Keypoints: Increasing the number of keypoints manifests better keypoint diversity, resulting in better generalization with improved performance (Figs. 8 and 9). This is also coherent with auxiliary keypoints that, being synthetic in nature, provide robustness to the keypoints learning regime in a semi-supervised setup. Unlike Lu et al. [67], we augment keypoints for the enhancement of
+
+the sub-module performances, resulting in improvements of $\approx 12 - 20$ for all the baselines (Tab. 2). Clearly, better-performing baselines improve more than others.
+
+Viability of Edgemaps: As we have used edgemaps as synthetic sketch data to train our framework, to justify the choice of edge detectors, i.e. PiDiNet [110], HED [129], and Canny [14], we experimented with a large number of algorithms, and this particular combination proved to have the best performance. Moreover, our framework is flexible to incorporate superior algorithms from future research.
+
+Further Insights: (a) Albeit the support keypoint representations $\Phi_{k,n}$ are disentangled to $\delta_{k,n}$ by $Z$ , the query keypoints $\hat{\Phi}_{m,n}$ from photos do not have style or sparsity associated and thus do not require de-stylization. Alongside learning robust support keypoint representations $\delta_{k,n}$ , this implicitly poses a support-query embedding alignment restricting $\mathcal{L}_{\mathrm{DA}}$ from collapsing. (b) Computation of $\hat{\mu}_n$ for domain adaptation [115] (Sec. 3.2) is detached from the computation graph to prevent a collapse caused by simultaneous gradients through the query and support prototypes. (c) The architecture of the de-stylization network (Sec. 3.3) $Z$ is non-trivial as complex models lead to unstable training, and simpler ones are incapable of style disentanglement. (See §Suppl.) (d) The additional edgemaps $x_i^{\mathrm{S}_1}$ and $x_i^{\mathrm{S}_2}$ are only used in de-stylization loss $\mathcal{L}_{\mathrm{style}}$ , but not in localization loss $\mathcal{L}_{\mathrm{KP}}$ due to significant performance degradation.
+
+# 5. Conclusion
+
+The few-shot approach to keypoint localization being fairly new in the research community, we explore the scope of cross-modal few-shot keypoint detection, adapting quickly to novel keypoints as well as unknown image classes. To this end, we propose a framework to detect novel keypoints on query photos from a few annotated sketches, achieving a source-free setup in this paradigm. Particularly, we carefully address the sketch-photo domain gap using domain adaptation, besides catering to the style and abstraction diversity of sketches. Despite being trained on synthetic sketch-like data, our method proves to be adapting well for free-hand sketches. Furthermore, we show that multi-modal training helps generalize better on query photos. To the best of our knowledge, this is amongst the first of the works on cross-modal few-shot keypoint learning, and we hope our work inspires future research in this context.
+
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+# DoppDrive: Doppler-Driven Temporal Aggregation for Improved Radar Object Detection
+
+Yuval Haitman* and Oded Bialer*
+
+General Motors, Technical Center Israel
+
+haitman@post.bgu.ac.il, oded.bialer8@gmail.com
+
+# Abstract
+
+Radar-based object detection is essential for autonomous driving due to radar's long detection range. However, the sparsity of radar point clouds, especially at long range, poses challenges for accurate detection. Existing methods increase point density through temporal aggregation with ego-motion compensation, but this approach introduces scatter from dynamic objects, degrading detection performance. We propose DoppDrive, a novel Doppler-Driven temporal aggregation method that enhances radar point cloud density while minimizing scatter. Points from previous frames are shifted radially according to their dynamic Doppler component to eliminate radial scatter, with each point assigned a unique aggregation duration based on its Doppler and angle to minimize tangential scatter. DoppDrive is a point cloud density enhancement step applied before detection, compatible with any detector, and we demonstrate that it significantly improves object detection performance across various detectors and datasets. Our project page: https://yuvalhg.github.io/DoppDrive/
+
+# 1. Introduction
+
+Radar plays an important role in autonomous driving and active safety systems due to its capability to provide detection at long range [17, 24, 43]. While some approaches use neural networks to detect objects directly from the radar's reflection intensity tensor spectrum [11, 16, 19, 44, 45], spanning spatial and Doppler domains, this low-level data is not always accessible. When available, it requires substantial communication bandwidth, memory, and computational resources to process. A more efficient alternative is object detection from radar point cloud data [14, 22, 27-29, 31, 38], where the point cloud is generated by filtering high-probability reflection points from the intensity ten
+
+
+1) No Aggregation
+2) Ego-Motion Compensation Aggregation
+
+
+3)DoppDrive
+
+
+Figure 1. Object detection with different input point clouds. (1) single frame, highly sparse point cloud, (2) temporally aggregated with ego-motion compensation—scattered points from dynamic objects, (3) Doppler-driven aggregation—dense points with minimal scatter, enhancing object detection.
+
+sor spectrum [32]. This paper focuses on object detection using radar point clouds, a method conceptually similar to LIDAR-based detection but with critical distinctions.
+
+One key difference between radar and LIDAR point clouds is radar's much lower density, due to its lower angular resolution and longer wavelength [15]. This sparsity increases with distance, resulting in only a few reflections from distant objects, making it challenging to distinguish true objects from noise and accurately detect their shape, orientation, and size. As objects' reflection points vary with changes in the relative position between objects and the radar, a common approach to increasing point cloud density and improving object detection is to aggregate point clouds from multiple frames over a short duration (about 0.5 seconds), applying ego-motion compensation and adding a timestamp to each point [22, 28, 29, 33, 38, 42]. While this method aligns reflections from static objects, the unknown velocities of dynamic objects cause significant scatter in the
+
+
+
+
+
+
+
+
+GT Bbox
+
+
+Dete
+on - Radar Dynamic Points
+
+
+- Radar Static Points
+Figure 2. Qualitative examples demonstrating DoppDrive in two scenarios: the upper row (a) from the aiMotive dataset [25] and the lower row (b) from LRR-Sim (Sec. 5). Columns show: (left) Sparse point cloud without aggregation, leading to missed detections; (center) Aggregation with ego-motion compensation, causing scattered points around dynamic objects and inaccuracies in object size and position; (right) DoppDrive enhances density around dynamic objects (blue points) with minimal scatter, improving detection accuracy. Detections are obtained using SMF [22].
+
+aggregated data, limiting performance.
+
+Developing methods to increase radar point cloud density without introducing scatter could greatly improve object detection, especially for long-range radar, which must detect objects at distances of up to $300m$ for high-speed autonomous driving [1, 2, 5, 23, 34, 36, 48]. However, current automotive radar datasets are limited to $175m$ , primarily due to the difficulty of obtaining accurate annotations at greater distances. At these ranges, radar points become very sparse, and the LIDAR and camera sensors typically used for annotation struggle to detect objects accurately. A dataset extending beyond $175m$ with precise annotations could significantly advance research in long-range radar detection.
+
+Another key distinction between radar and LIDAR is radar's Doppler measurement, which captures the radial velocity of each reflection point relative to the radar. The Doppler measurement consists of two components: the ego-speed Doppler component (due to ego-vehicle motion) and the dynamic Doppler component (due to object motion). The ego-speed component can be calculated from the ego-vehicle's velocity [38], which is either obtained from auxiliary sensors like GPS-INS or odometers [3, 9, 13, 35] or can be estimated from the radar's point cloud Doppler in
+
+formation [4, 18, 30, 38]. Previous work on radar-based object detection incorporates Doppler information as an additional input feature for each point, using object detection networks originally designed for LIDAR point clouds with the added Doppler feature [22, 28, 29, 38]. Removing the ego-speed Doppler component from the Doppler measurement has been shown to aid object detection [28, 38], as it enables the residual Doppler to indicate whether a point reflects a static (zero residual Doppler) or dynamic (non-zero residual Doppler) object, helping the neural network learn distinct features for detection. However, exploring additional ways to leverage the dynamic Doppler component information to enhance object detection yet remains a valuable and important direction for research.
+
+This paper introduces DoppDrive, a Doppler-driven temporal aggregation method that uses Doppler information in a novel way to enhance radar point cloud prior to object detection. DoppDrive increases point cloud density while minimizing scatter in reflections from dynamic objects. By aligning points from previous frames to the current frame along the radial direction based on dynamic Doppler velocity, DoppDrive eliminates range scatter. Additionally, it mitigates tangential spread by setting each point's aggregation duration based on its specific Doppler and angle, result
+
+ing in dynamic aggregation durations per point rather than a fixed duration for all.
+
+Fig. 1 shows the high-level concept of DoppDrive compared to standard aggregation with ego-vehicle motion compensation and no aggregation. Fig. 2 presents qualitative examples of these point clouds, demonstrating DoppDrive's increased density with minimal dispersion. As we will show, this enhancement improves object detection performance. DoppDrive is compatible with any point cloud detection network, and we validate its performance improvements across four detectors and three datasets.
+
+To address the shortage of datasets for testing methods on sparse radar point clouds beyond $200m$ , we introduce a new dataset, LRR-Sim, as part of this work. LRR-Sim simulates a long-range automotive radar in highway scenarios, providing annotated point clouds up to $300m$ . We use it to evaluate our method alongside reference approaches at extended detection ranges. The dataset is publicly released to support future research in long-range radar perception.
+
+The main contributions of the paper are as follows:
+
+1. A novel Doppler-driven temporal aggregation method that increases the density of radar point clouds while minimizing spatial scattering of points from dynamic objects, thereby enhancing object detection performance.
+2. The release of LRR-Sim, a long-range automotive radar dataset with sparse point clouds from extended detection ranges and precise annotations up to $300m$ . It is generated by radar simulation to address the challenge of obtaining accurate long-distance annotations. The dataset is publicly available and serves as a valuable resource for advancing radar-based long-range detection.
+
+# 2. Related Work
+
+# 2.1. Object Detection From Radar Point Cloud
+
+Various methods exist for radar point cloud object detection. Several methods leverage PointPillars [20] for radar detection [22, 28, 38, 40, 47], while NVRadarNet [29] uses 2D convolution with a Feature Pyramid Network [21] in bird's-eye view, and K-Radar [27] applies 3D sparse convolution. RADIal [31] utilizes FIXOR [41], and Radar-transformer [6] employs a transformer architecture for radar detection. Additional approaches include graph convolution [14, 37] and hybrid of point-based and grid-based networks [39]. All radar point cloud detection networks face challenges due to point cloud sparsity, which limits performance. Increasing point cloud density can enhance their effectiveness, which is the focus of our work.
+
+# 2.2. Radar Datasets
+
+Radar point cloud datasets are characterized by detection range and angular resolution, where higher resolution results in a denser point cloud, while a longer detection range
+
+reduces point density.
+
+Publicly available low-resolution radar datasets with object annotations include nuScenes [8], covering urban, residential, and industrial areas; PixSet [10], focused on high-density urban environments, both limited to object ranges below $80m$ ; and aiMotive [25], which extends detection up to $175m$ in urban and highway environments. High-resolution radar datasets with object annotations include K-Radar [27], which has limited Doppler speed measurements; View-of-Delft [28], with a maximum detection range of $50m$ ; Astyx [26], which is relatively small; TJ4DRadSet [46], with a detection range up to $90m$ ; and RADial [31], which has a $103m$ range and captures data from highway, country-side and city driving.
+
+In this paper, we evaluate our method performance on the aiMotive and RADIal datasets, representing low- and high-resolution radars with relatively long detection ranges. Additionally, we introduce a new dataset for long-range radar detection, with point clouds and objects up to $300m$ , significantly extending the range of existing datasets (see Sec. 5).
+
+# 2.3. Ego-Vehicle Velocity
+
+Ego-vehicle velocity is typically obtained from a GPS-INS sensor or vehicle odometers [3, 9, 13, 35]. Alternatively, it can be estimated from radar point clouds by identifying static objects (e.g., guardrails, buildings, poles, ground) via Doppler clustering. The Doppler of each static point represents a different radial component of the vehicle's velocity. Thus, Doppler measurements from static reflections can be expressed as a function of point angles and ego-vehicle velocity, allowing the velocity to be resolved [4, 18, 30, 38].
+
+# 3. Background: Doppler Components
+
+This section provides background material used in deriving our method in Sec. 4. In automotive scenarios, the variation in height over short aggregation durations is relatively small. Thus, throughout this paper, we assume zero vertical velocity and focus only on longitudinal and lateral velocity. Fig. 3 shows a reflection point in top view relative to the radar, where the point's angle to the radar is $\theta$ and its heading angle is $\alpha$ with speed $s$ (blue arrow). The radial and tangential velocity components are $v$ and $u$ (green and red arrows), respectively, and are given by:
+
+$$
+v = s \cos (\theta + \alpha), \tag {1}
+$$
+
+$$
+u = s \sin (\theta + \alpha). \tag {2}
+$$
+
+Solving for $s$ in Eq. (1) and substituting into Eq. (2), we obtain:
+
+$$
+u = v \tan (\theta + \alpha). \tag {3}
+$$
+
+
+Figure 3. Scenario with a dynamic reflection point and a moving radar. The reflection point's radial and tangential velocity components are $v$ and $u$ , respectively. The Doppler measurement is the sum of the radial velocity $v$ of the dynamic object (dynamic Doppler component) and the radial velocity due to ego-vehicle motion $h$ (ego-speed Doppler component).
+
+In Fig. 3, the radar-equipped host vehicle moves along the black arrow with speed vector $\pmb{c} = [c_x, c_y]$ . The projection of $\pmb{c}$ onto the reflection point's direction is denoted by $h$ , and calculated by:
+
+$$
+h = c _ {x} \sin (\theta) + c _ {y} \cos (\theta). \tag {4}
+$$
+
+The radar measures Doppler frequency, which is converted to velocity units. The point's Doppler measurement, denoted by $d$ , is the relative radial velocity between the radar and the point, accounting for both the point and ego-vehicle motions: $d = v + h$ , where $v$ is the dynamic Doppler component (point's radial velocity) and $h$ is the ego-speed Doppler component.
+
+The speed of the ego vehicle $c$ can be obtained from a GPS-INS sensor or estimated from the radar point cloud (see Sec. 2.3). Given $c$ , we calculate $h$ for each point from Eq. (4) and obtain its dynamic Doppler component as $v = d - h$ . In Sec. 4, we represent the reflection point's velocity vector using the radial component $v$ (dynamic Doppler component) and the tangential component from Eq. (3).
+
+# 4. Doppler-Driven Temporal Aggregation
+
+Our point cloud aggregation algorithm enhances reflection point density to improve object detection by combining radar point clouds from previous frames with those of the current frame, as shown in Fig. 1. This aggregation adjusts for both the ego-vehicle's motion and the movement of dynamic objects between frames, using Doppler information from the radar point clouds.
+
+Fig. 4 illustrates the proposed Doppler-Driven aggregation method. In the bird's-eye-view scenario in Fig. 4(a), the radar-equipped host vehicle (bottom) and an oncoming
+
+
+(a) Doppler based shifting
+(c) Our Aggregation Result
+Figure 4. Overview of the Doppler-driven temporal aggregation method. (a) Top view of the scenario with the radar-equipped host vehicle and a dynamic vehicle moving toward each other. Points from previous frames $T_{-1}$ and $T_{-K}$ are aggregated with the current frame $T_0$ , compensating for the dynamic vehicle's motion by shifting points along the radial direction based on their dynamic Doppler measurement. (b) Zoom-in on (a), showing the accurate shift $\pmb{q}_k^i$ vs. the approximated shift $\tilde{\pmb{q}}_k^i$ , with resulting offset distance $\epsilon_k^i$ . (c) Result of our aggregation method, showing denser reflection points with minimal disparity where the aggregation duration of $\tilde{\pmb{q}}_{-K}^{i}$ yields an expected offset beyond the tolerated limit, so it is discarded. (d) Result of standard aggregation, showing significant scatter in the aggregated points.
+
+
+(b) Zoom in on vehicles
+(d) Standard Aggregation Result
+
+
+
+
+
+
+
+Legend:
+
+- $\mathbf{p}_k^i$ point position at $T_{k}$
+
+Time color code: $0, -1, -N$
+
+$\tilde{\pmb{q}}_k^i$ radial shift of $\pmb {p}_k^i$ from $T_{k}$ to $T_{0}$
+
+$\mathbf{x}\pmb{q}_k^i$ accurate shift of $\pmb{p}_k^i$ from $T_{k}$ to $T_0$
+
+$\epsilon_{k}^{i}$ offset between $\pmb{q}_{k}^{i}$ and $\widetilde{\pmb{q}}_k^i$
+
+dynamic vehicle approach each other. Frame times are denoted by $T_{k}$ , where $k = 0$ is the current frame and negative $k$ values indicate earlier frames. The figure shows both vehicles at three frames: the current frame $T_{0}$ , one prior frame $T_{-1}$ , and $K$ frames back at $T_{-K}$ . Let $\pmb{p}_{k}^{i}$ represent the 3D position $(x, y, z)$ of the $i$ -th reflection point at frame $T_{k}$ . In this example, a single reflection point from the approaching vehicle appears in each frame, represented as $\pmb{p}_{-K}^{i}$ , $\pmb{p}_{-1}^{i}$ , and $\pmb{p}_{0}^{i}$ , shown in top view as solid circles in purple, green, and blue, respectively, in Fig. 4. Throughout this section, all point positions are referenced to a unified coordinate system, such as the radar's coordinate system at $T_{0}$ . This is achieved by transforming all points to $T_{0}$ coordinates, using ego-vehicle motion data from external sensors or estimating it from the radar point cloud (see Sec. 2.3).
+
+The radial direction between each reflection point, $\pmb{p}_k^i$ , and the radar position at frame time $T_{k}$ is shown as dashed
+
+lines in Fig. 4(a). Our key idea is to compensate for the shift in reflection points from previous frames to the current frame caused by the dynamic vehicle's motion, using the dynamic Doppler measurement, which represents the dynamic vehicle's radial velocity. Each previous point is shifted along its radial direction according to its dynamic Doppler measurement, as illustrated by solid arrows in Fig. 4(a), with arrow colors matching the points. The adjusted positions, marked by hollow circles in corresponding colors, correct for radial motion but still leave a tangential offset. To mitigate this, we limit each point's aggregation duration, as explained further below.
+
+To further explain our aggregation method, we refer to Fig. 4(b), which provides a zoomed-in view of Fig. 4(a). Let $\pmb{q}_k^i$ be the position of $\pmb{p}_k^i$ after shifting it accurately to the current time frame $T_0$ based on the dynamic object's precise velocity. These shifted points are marked with an 'x' in Fig. 4(b), with colors matching their original positions. We neglect any slight motion in height during the short integration interval and approximate zero velocity in this dimension. Thus, the velocity vector that accurately shifts $\pmb{p}_k^i$ has only radial and tangential components, $v_k^i$ and $u_k^i$ , respectively, so that:
+
+$$
+\boldsymbol {q} _ {k} ^ {i} = \boldsymbol {p} _ {k} ^ {i} + v _ {k} ^ {i} \hat {\boldsymbol {v}} _ {k} ^ {i} \left(T _ {0} - T _ {k}\right) + u _ {k} ^ {i} \hat {\boldsymbol {u}} _ {k} ^ {i} \left(T _ {0} - T _ {k}\right), \tag {5}
+$$
+
+where $\hat{\pmb{v}}_k^i$ and $\hat{\pmb{u}}_k^i$ are 3D unit vectors in the radial and tangential directions on a plane (zero in height), as indicated by dashed arrows in Fig. 4(b) (with further explanation in Sec. 3). In Eq. (5), the radial velocity $v_{k}^{i}$ is known from the dynamic Doppler measurement, while the tangential velocity $u_{k}^{i}$ is unknown. Therefore, we approximate the shifted position $\pmb{q}_k^i$ by only compensating for the radial shift. This approximation, $\tilde{\pmb{q}}_k^i$ , is given by:
+
+$$
+\boldsymbol {q} _ {k} ^ {i} \approx \tilde {\boldsymbol {q}} _ {k} ^ {i} = \boldsymbol {p} _ {k} ^ {i} + v _ {k} ^ {i} \hat {\boldsymbol {v}} _ {k} ^ {i} \left(T _ {0} - T _ {k}\right). \tag {6}
+$$
+
+The shifted points, $\tilde{\pmb{q}}_{-K}^{i}$ and $\tilde{\pmb{q}}_{-1}^{j}$ , from times $T_{-K}$ and $T_{-1}$ , are shown in Fig. 4(b), with green and purple hollow circles, respectively. The distance offset between the accurate and approximated positions is given by:
+
+$$
+\epsilon_ {k} ^ {i} = \left\| \boldsymbol {q} _ {k} ^ {i} - \tilde {\boldsymbol {q}} _ {k} ^ {i} \right\| = \left| u _ {k} ^ {i} \right| \left(T _ {0} - T _ {k}\right). \tag {7}
+$$
+
+By substituting Eq. (3) into Eq. (7) we have that
+
+$$
+\epsilon_ {k} ^ {i} = \left| v _ {k} ^ {i} \right| \left(T _ {0} - T _ {k}\right) \tan \left(\theta_ {k} ^ {i} + \alpha_ {k} ^ {i}\right), \tag {8}
+$$
+
+where $\theta_{k}^{i}$ , and $\alpha_{k}^{i}$ , are the $i^{th}$ reflection point angle and heading direction at frame time $T_{k}$ . The offsets $\epsilon_{-K}^{i}$ and $\epsilon_{-1}^{i}$ for points $\tilde{\pmb{q}}_{-K}^{i}$ and $\tilde{\pmb{q}}_{-1}^{i}$ are indicated by dotted lines in Fig. 4(b) with purple and green colors, respectively.
+
+The average offset is obtained by taking the expectation of Eq. (8) with respect to $\alpha_{k}^{i}$ . We set a pre-defined limit to the tolerated average offset, denoted by $\mathcal{D}$ , such that
+
+$$
+\mathbb {E} _ {\alpha_ {k} ^ {i}} \left[ \epsilon_ {k} ^ {i} \right] = \left| v _ {k} ^ {i} \right| \left(T _ {0} - T _ {k}\right) g \left(\theta_ {k} ^ {i}\right) \leq \mathcal {D} \tag {9}
+$$
+
+where
+
+$$
+g \left(\theta_ {k} ^ {i}\right) = \mathbb {E} _ {\alpha_ {k} ^ {i}} \left[ \tan \left(\theta_ {k} ^ {i} + \alpha_ {k} ^ {i}\right) \right] = \int_ {- \pi / 2} ^ {\pi / 2} \tan \left(\theta_ {k} ^ {i} + \alpha\right) f _ {\alpha_ {k} ^ {i}} (\alpha) d \alpha \tag {10}
+$$
+
+and $f_{\alpha_k^i}(\alpha)$ is the distribution of the dynamic vehicle orientation angle $\alpha$ (shown in Fig. 3), which can be empirically derived from an annotated dataset or approximated by a Laplace distribution. For further details on calculating of $g(\theta_k^i)$ , please refer to the Supplementary Material.
+
+By rearranging terms in Eq. (9) we can express a limit on the aggregation duration per each point, depending on its Doppler and angle, that will ensure the average shift offset will be below the predefined tolerance $\mathcal{D}$ as follows:
+
+$$
+T _ {0} - T _ {k} \leq \frac {\mathcal {D}}{\left| v _ {k} ^ {i} \right| g \left(\theta_ {k} ^ {i}\right)}. \tag {11}
+$$
+
+In aggregating points from previous frames to the current time, we include only those with an aggregation duration $(T_0 - T_k)$ that satisfy Eq. (11), ensuring the average shift offset remains within the specified tolerance $\mathcal{D}$ . Note that as a result, each point has a specific aggregation duration, which differs from conventional methods that use a fixed aggregation duration to all points.
+
+In the illustrated example of Fig. 4(b), the aggregation duration $T_0 - T_{-1}$ results in an offset $\epsilon_{-1}^i$ for $\tilde{q}_{-1}^i$ that is below $\mathcal{D}$ , so it is included in the aggregation at $T_0$ . In contrast, $\epsilon_{-K}^i$ for $\tilde{q}_{-K}^i$ exceeds $\mathcal{D}$ , hence this point is excluded. The final aggregated result is shown in Fig. 4(c), this includes the current frame point and the previous frame point with low disparity. For comparison, Fig. 4(d) shows conventional aggregation without dynamic motion compensation, resulting in point spread along both radial and tangential directions. In contrast, our method increases the points density with minimal tangential spread and no radial spread.
+
+While Fig. 4 illustrates a single reflection point from one dynamic object per time instance, the method applies to multiple reflection points from objects with varying velocities, including static ones. Each point is independently shifted along its radial direction to the ego-vehicle based on its dynamic Doppler measurement, with static points (zero dynamic Doppler) remaining unchanged. Fig. 2 demonstrates DoppDrive's effectiveness in complex scenarios with multiple vehicles at different speeds. The pseudocode for the proposed Doppler-Driven aggregation algorithm is provided in Algorithm 1.
+
+# 4.1. Object Detection
+
+The DoppDrive point cloud aggregation, as described in Algorithm 1, operates frame by frame. For each new frame, a set of aggregated points, $\mathcal{Q}$ , is computed in a sliding window fashion, combining points from the current frame and previous frames. For object detection, each point in $\mathcal{Q}$ is
+
+Algorithm 1 Doppler-Driven Aggregation (DoppDrive)
+1: Setting: Tolerated aggregation shift error, $\mathcal{D}$
+2: Input:
+ - Set of points $p_k^i$ , with their dynamic Doppler velocity $v_k^i$ , radial unit vector $\hat{\boldsymbol{v}}_k^i$ , angle $\theta_k^i$ , and frame time $T_k$
+ - Indices: $i \in \{0, 1, \dots, N\}$ (points), $k \in \{0, -1, \dots, -K\}$ (frame times)
+3: Output: Aggregated set of shifted points $\mathcal{Q}$ across frame times $T_0, T_{-1}, \dots, T_{-K}$
+4: Initialize: Aggregation set $\mathcal{Q} \gets \emptyset$
+5: for $k = -K$ to 0 do
+6: for $i = 0$ to $N$ do
+7: Calculate $g(\theta_k^i)$ from Eq. (10)
+8: if $T_0 - T_k \leq \frac{\mathcal{D}}{|v_k^i| g(\theta_k^i)}$ then
+9: Shift point: $\tilde{\boldsymbol{q}}_k^i = \boldsymbol{p}_k^i + v_k^i \hat{\boldsymbol{v}}_k^i (T_0 - T_k)$
+10: Append $\tilde{\boldsymbol{q}}_k^i$ to aggregation set $\mathcal{Q}$
+11: else
+12: Discard point $p_k^i$
+13: end if
+14: end for
+15: end for
+16: return Aggregated set of points $\mathcal{Q}$
+
+represented by six features: its 3D position $(x,y,z)$ in the radars coordinate system of the current frame time $T_{0}$ , the dynamic Doppler component, reflection intensity, and the time frame index $k$ when the point was originally received. Any object detection network designed for point clouds can then be used to detect objects from the aggregated points of each frame, utilizing these input features.
+
+# 5. Long Range Radar Dataset - LRR-Sim
+
+Our Doppler-Driven aggregation method addresses the increasing sparsity of radar point clouds at long ranges, therefore we are particularly interested in evaluating its performance at long distances. Existing radar point cloud datasets cover short and medium range distances, reaching up to $175m$ [25]. However, there is a gap in datasets for long-range automotive radar [1, 2, 5, 34], which can detect up to $300m$ , a range critical for autonomous driving on highways and at high speeds [23, 36, 48]. Obtaining accurate annotations beyond $175m$ is challenging, as the radar's point cloud becomes very sparse at these distances, and typical LIDAR and camera sensors used for annotations lack this range. To address this, we introduce a long-range radar dataset with point clouds up to $300m$ and accurate annotations generated via radar simulation, building on prior work that demonstrates the realism and reliability of simulated radar data [7].
+
+The simulation models a high-end, long-range radar in highway scenarios. Automotive scenarios were generated in CARLA [12] using CARLA highway environment maps,
+
+and converted to radar point clouds using a physical model of a 77GHz MIMO radar with 12 transmit and 16 receive antennas. The radar's received signal was computed via ray tracing between the radar antennas and objects in the scene, followed by range-Doppler 2D FFT and azimuth-elevation beamforming to obtain the reflection intensity spectrum. Point clouds were then extracted from this spectrum using the CFAR algorithm [32]. Additional implementation details are provided in the Supplementary Material.
+
+We refer to the long-range radar simulation dataset as LRR-Sim. It includes 42 training and 8 testing highway scenarios, each lasting approximately 30 seconds at 20 frames per second, resulting in 18,172 training frames and 3,363 testing frames. Vehicle types include cars, trucks, and vans, with an average of 7.3 vehicles per frame and a total of $\sim 160K$ vehicle instances with $\sim 28K$ beyond $175m$ . The point cloud extends up to $300m$ with a field of view of $\pm 55^{\circ}$ in azimuth, and $\pm 20^{\circ}$ in elevation. All vehicles within this range and field of view are accurately annotated with 3D bounding boxes. For more details on LRR-Sim and example demonstrations, please refer to our GitHub1. We hope this dataset serves as a valuable resource for advancing radar research, including applications beyond the scope of this paper.
+
+# 6. Results
+
+We evaluate the performance improvement of object detection when using DoppDrive as a preprocessing step with four radar-based detection networks across three datasets, covering diverse conditions and settings. The radar detection networks include Radar PillarNet (RPNet) [47], based on PointPillars [20]; SMURF (SMF) [22], which enhances PointPillars with kernel density estimation; Nvradarnet (NVR) [29], a 2D convolutional Feature Pyramid Network in bird's-eye view; and K-Radar (KRD) [27], which utilizes 3D sparse convolution. Implementation details are provided in the Supplementary Material.
+
+We selected datasets with large detection ranges to highlight the role of aggregation in addressing long-range sparsity, and with varying point cloud densities due to differences in radar resolution. Tab. 2 compares the datasets used in our evaluation. aiMotive has the lower angular resolution and sparsest point cloud compared to RADial and LRR-Sim; all are sparser than LiDAR. Detection ranges reach up to $175m$ for aiMotive, $103m$ for RADial, and $300m$ for LRR-Sim, meeting the requirements for long-range automotive radar [1, 2, 5, 23, 34, 36, 48]. Velocity sources also differ: aiMotive uses INS-GPS, RADial lacks accurate INS and uses radar-based estimation, and LRR-Sim provides ground-truth from simulation. The datasets span diverse
+
+scenarios: RADial includes city, countryside, and highway scenes; aiMotive covers urban and highway; and LRR-Sim focuses on highways.
+
+In all tests, we set the tolerance disparity distance to $\mathcal{D} = 2m$ to limit the aggregation duration in DoppDrive. This value was empirically found to give the best results, as detailed in Sec. 6.3. We compare DoppDrive with two reference methods: (1) standard aggregation, which combines points from frames up to $0.7s$ in the past with ego-vehicle motion compensation, an empirically optimized duration for best performance; and (2) no aggregation. In both references, unless specified otherwise, the ego-speed Doppler component is removed from the point cloud Doppler measurements. This aids object detection by distinguishing reflections from static objects (near-zero Doppler) and dynamic objects (non-near-zero Doppler).
+
+We evaluated object detection performance using average precision (AP), the integral of the precision-recall curve, for the 'vehicle' class, which includes cars, trucks, vans, and buses. Detection accuracy is measured by 2D bounding box IOU in birds-eye-view between detections and ground truth, using a 0.1 threshold. While aiMotive and LRR-Sim provide bounding box annotations, RADial offers only a single point on the object's front-facing contour. To enable consistent evaluation, we assigned a fixed-size bounding box—based on average vehicle dimensions—so that its front edge aligns with the provided point, assuming zero heading angle.
+
+# 6.1. Object Detection Performance Gain
+
+Tab. 1 compares the performance of the four selected object detection methods across three datasets, all detailed in Sec. 6. The evaluation uses three types of point cloud inputs: (1) single-frame reflection points without aggregation, (2) standard aggregation with ego-motion compensation, and (3) our Doppler-driven aggregation method, DoppDrive. For all methods, ego-speed Doppler components were removed from the Doppler measurements, and the input features of each point included the $x,y,z$ coordinates, Doppler, reflection intensity, and time index for aggregated inputs. The results show that both aggregation methods outperform single-frame detection, with Doppler-driven aggregation achieving a greater improvements over standard aggregation across all detectors and datasets. The largest performance gain is observed on the aiMotive dataset, likely due to its radar's lower angular resolution and sparser point cloud compared to the other datasets. Because the point cloud is more sparse, it benefits more from DoppDrive's aggregation, which increases its density with minimal scatter. Notably, the performance improvement is evident not only when precise ego-vehicle velocity is provided by GPS-INS (aiMotive) or simulation (LRR-Sim) but also when the velocity is estimated directly from the radar point cloud (RA
+
+Dial). Among the four detectors compared, SMF [22] and KRD [27] achieve the highest performance, both with and without aggregation. Qualitative examples demonstrating DoppDrive's effectiveness appear in Fig. 2 and in the Supplementary Material.
+
+To analyze the performance gains, we present an ablation study in Tab. 3 using the aiMotive dataset and SMF [22] detector, assessing the contributions of each component in DoppDrive as outlined in the table columns: (1) Ego-vehicle velocity compensation in aggregation (Ego. agg.), (2) GPS-INS ego-vehicle velocity measurement or radar-based estimation (GPS-INS Vel.), (3) Ego-speed Doppler component removal (Ego-Dopp.), (4) radial motion compensation using Eq. (6) (Radial Comp.), and (5) tangential spread mitigation by limiting aggregation duration based on Eq. (11) (Non-fix Duration).
+
+The ablation test shows that both radial compensation and variable aggregation durations per point contribute to DoppDrive's performance gains (rows 6 vs. 5, and 8 vs. 6, respectively). It also shows that using the ego-vehicle velocity estimated from the radar point cloud, instead of the GPS-INS velocity measurement, results in a relatively small performance degradation for DoppDrive (row 7 vs. 8).
+
+# 6.2. Long Range Detection Performance
+
+In this section, we evaluate DoppDrive at long ranges (175m-300m), where the point cloud is highly sparse. Detecting objects at these distances is crucial for high-speed autonomous driving. Since datasets like aiMotive and RA-Dial are limited to 175m, we use LRR-Sim (Sec. 5), which provides simulated long-range radar data with accurate annotations up to 300m.
+
+Tab. 4 shows detection performance on LRR-Sim for objects within $175m - 300m$ using four object detectors from Sec. 6. We compare three input types: DoppDrive, standard aggregation with ego-motion compensation, and no aggregation, with the ego-speed Doppler component removed in all cases. Compared to the full-range results in Tab. 1, accuracy drops significantly at longer distances, but DoppDrive retains and even enhances its advantage. This improvement at longer ranges is due to the sparser point cloud, where increased density from temporal aggregation with minimal scatter proves even more beneficial.
+
+# 6.3. Optimization of the Dispersion Tolerance $\mathcal{D}$
+
+We perform an ablation study on DoppDrive's hyperparameter $\mathcal{D}$ , which defines the tolerated average position offset during aggregation and controls the aggregation duration for each point. Tab. 5 shows the average precision performance of the SMF [22] object detection network with the LRR-Sim dataset for different values of $\mathcal{D}$ . The results indicate that the best performance was achieved with $\mathcal{D} = 2m$ , which was used for all tests presented in the paper.
+
+| Method | aiMotive | Radial | LRR-Sim |
| SMF | KRD | RPNet | NVR | SMF | KRD | RPNet | NVR | SMF | KRD | RPNet | NVR |
| No Agg. | 74.6 | 75.0 | 73.4 | 70.9 | 91.3 | 91.4 | 91.0 | 89.3 | 89.2 | 88.7 | 88.7 | 86.6 |
| Standard Agg. | 81.7 | 82.3 | 80.2 | 75.2 | 92.5 | 92.1 | 92.3 | 91.2 | 91.1 | 89.9 | 90.8 | 90.1 |
| DoppDrive | 89.1 | 89.4 | 87.8 | 81.8 | 95.8 | 95.5 | 95.7 | 94.1 | 93.3 | 93.1 | 92.9 | 92.7 |
+
+Table 1. Average Precision (AP) of four detectors: SMURF (SMF) [22], K-Radar (KRD) [27], Radar PillarNet (RPNet) [47], and Nvradar-net (NVR) [29]. Results are evaluated across three datasets (aiMotive, Radial, LRR-Sim) with no aggregation, standard aggregation with ego-vehicle motion compensation, and DoppDrive.
+
+ | aiMotive | RADIal | LRR-Sim |
| Resolution | Low | High | High |
| Range | 175m | 103m | 300m |
| FOV | ±16° | ±90° | ±55° |
| Ego-vel | INS-GPS | Radar | Simulation |
| FPS | 18 | 5 | 20 |
| # Train | 21402 | 5450 | 18172 |
| # Test | 5181 | 1873 | 3363 |
| # 3D Boxes | 427K | 9.5K | 160K |
+
+Table 2. Comparison of the three tested datasets by angular resolution (Resolution), point cloud maximal range (Range), azimuth field-of-view (FOV), ego-vehicle velocity source (Ego-vel), frame rate (FPS), the number of frames in the training (# Train) and test (# Test) sets, and number of objects (# 3D Boxes).
+
+| ID | Ego. agg. | GPS-INS Vel. | Ego-Dopp. | Radial Comp. | Non-fix Duration | AP |
| 1 | X | - | X | X | X | 66.3 |
| 2 | X | X | ✓ | X | X | 73.1 |
| 3 | X | ✓ | ✓ | X | X | 74.8 |
| 4 | ✓ | ✓ | X | X | X | 76.1 |
| 5 | ✓ | ✓ | ✓ | X | X | 81.4 |
| 6 | ✓ | ✓ | ✓ | ✓ | X | 85.2 |
| 7 | ✓ | X | ✓ | ✓ | ✓ | 87.7 |
| 8 | ✓ | ✓ | ✓ | ✓ | ✓ | 89.1 |
+
+Table 3. Ablation study of DoppDrive components: Average Precision (AP) on aiMotive dataset with SMF detector [22].
+
+| Method | SMF | KRD | RPNet | NVR |
| No Agg. | 61.2 | 61.5 | 61.8 | 60.7 |
| Standard Agg. | 63.1 | 64.1 | 62.7 | 61.3 |
| DoppDrive | 69.2 | 68.9 | 68.6 | 66.9 |
+
+# 6.4. Point Elimination Evaluation
+
+DoppDrive shortens integration duration to filter out points with high tangential dispersion, resulting in point elimina
+
+Table 4. Average Precision at range $> {175m}$ on the LRR-Sim dataset with four detectors: SMF [22], K-Radar (KRD) [27], RP-Net [47], and Nvradarnet (NVR) [29].
+
+| D[m] | 1 | 2 | 3 | 4 | 5 |
| AP | 91.2 | 93.3 | 92.5 | 92.3 | 89.6 |
+
+
+Table 5. Average precision (AP) of SMF [22] on the LRR-Sim dataset as a function of the aggregation displacement tolerance $\mathcal{D}$ .
+Figure 5. Point elimination in urban and highway (aiMotive)
+
+tion compared to fixed-duration aggregation. Fig. 5 shows that DoppDrive removes an average of $11\%$ of dynamic points per frame, relative to fixed-duration aggregation, in aiMotive's urban and highway scenes, with most frames exhibiting less than $20\%$ elimination. This yields a 3.9-point AP gain (rows 8 vs. 6 in Tab. 3), demonstrating that even modest elimination improves performance. A detailed breakdown of point elimination is provided in the supplementary material.
+
+# 7. Conclusion
+
+In this paper, we present DoppDrive, a novel method to enhance radar point cloud density before object detection with minimal scatter by leveraging Doppler information in temporal aggregation. DoppDrive reduces scatter from dynamic objects by adjusting previous frames' points in the radial direction based on their dynamic Doppler components and by limiting each point's aggregation duration according to its specific parameters. An ablation study validated the contribution of both elements, while complexity analysis showed minimal computational overhead. DoppDrive's enhanced point cloud improves object detection performance, as demonstrated across four detectors and three datasets.
+
+Additionally, we introduce LRR-Sim, a long-range radar simulation dataset with sparse point clouds resulting from extended detection ranges, and precise annotations up to $300m$ , significantly beyond existing datasets. The dataset is publicly available to support advancements in long-range radar detection, which is essential for high-speed autonomous driving.
+
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+# Doppler-Aware LiDAR-RADAR Fusion for Weather-Robust 3D Detection
+
+Yujeong Chae, Heejun Park, Hyeonseong Kim, and Kuk-Jin Yoon
+Korea Advanced Institute of Science and Technology
+
+{yujeong, parkheeticket,brian617,kjyoon}@kaist.ac.kr
+
+# Abstract
+
+Robust 3D object detection across diverse weather conditions is crucial for safe autonomous driving, and RADAR is increasingly leveraged for its resilience in adverse weather. Recent advancements have explored 4D RADAR and LiDAR-RADAR fusion to enhance 3D perception capabilities, specifically targeting weather robustness. However, existing methods often handle Doppler in ways that are not well-suited for multi-modal settings or lack tailored encoding strategies, hindering effective feature fusion and performance. To address these shortcomings, we propose a novel Doppler-aware LiDAR-4D RADAR fusion (DLRFusion) framework for robust 3D object detection. We introduce a multi-path iterative interaction module that integrates LiDAR, RADAR power, and Doppler, enabling a structured feature fusion process. Doppler highlights dynamic regions, refining RADAR power and enhancing LiDAR features across multiple stages, improving detection confidence. Extensive experiments on the K-RADAR dataset demonstrate that our approach effectively exploits Doppler information, achieving state-of-the-art performance in both normal and adverse weather conditions.
+
+# 1. Introduction
+
+3D object detection is a crucial technology for autonomous driving, and its robustness under adverse weather conditions is essential for real-world applications. Unlike cameras and LiDAR, RADAR operates at longer wavelengths, making it inherently resilient to challenging weather conditions. Consequently, RADAR has been actively utilized for weather-robust perception tasks [3, 13, 43, 44, 50, 74]. Recent advancements in 3D object detection have explored 4D RADAR, which extends traditional 3D RADAR (range, azimuth, Doppler) by incorporating elevation data [10, 27, 37, 39, 44]. Additionally, multi-modal approaches fuse LiDAR's precise 3D scanning capabilities with RADAR's weather resilience, improving object classification and re
+
+RADAR Point Cloud RADAR Point Cloud Range-Doppler
+
+
+(a) Various RADAR Representations
+
+
+(b) Our Framework using LiDAR, Power, and Doppler
+Figure 1. RADAR has been widely used for multi-modal weather-insensitive perception, yet existing methods either rely solely on power or combine power and Doppler, failing to fully leverage their distinct cues. While range-Doppler maps enhance RADAR-only perception, they are less suited for multi-sensor configurations for autonomous driving. In contrast, our framework independently encodes the unique information from RADAR power and Doppler through separate branches, while enabling effective multi-modal interaction between LiDAR and RADAR, ensuring robust detection in adverse weather.
+
+gression across various environmental conditions [5, 6, 62].
+
+However, existing methods often fail to fully leverage Doppler information. Many approaches either neglect Doppler entirely or encode it alongside RADAR power or LiDAR intensity without considering its distinct characteristics, thus limiting its potential for motion-aware perception. Some studies employ RD (Range-Doppler) or RAD (Range-Azimuth-Doppler) map representations to independently utilize Doppler [36, 38], but these representations are not naturally aligned with the 3D coordinate systems of other sensors, making them less compatible for multi-modal
+
+integration. To address these limitations, a more structured approach is needed to effectively incorporate Doppler into multi-modal frameworks while preserving its unique motion-related properties to enhance object perception.
+
+In this paper, we propose a Doppler-aware LiDAR-4D RADAR fusion (DLRFusion) framework that effectively integrates Doppler into 3D object detection. Our approach begins with the 4D RADAR data, where we apply a CFAR method to create a RADAR point cloud containing both RADAR power and Doppler values, which is then subjected to RADAR preprocessing. This method implements a simple Doppler range-based compensation strategy, ensuring the framework is universally applicable, even in situations where absolute velocity cannot be computed. To better capture the distinct characteristics of RADAR power and Doppler, we treat them as separate sparse tensors, as empirically validated by the experiments in Table 3, which show improved effectiveness. These two RADAR features, along with a single LiDAR feature, serve as three distinct inputs to our method. These inputs are processed through a multi-path iterative interaction module, which refines and fuses the features in a structured manner. The compensated Doppler emphasizes dynamic elements in the scene, while RADAR power provides objectness cues. An attention mechanism between these two features ensures that Doppler updates RADAR power, shifting the focus toward relevant objects rather than static structures. Subsequently, the updated RADAR power is used to refine LiDAR features through a KNN-based voxel attention mechanism, which enhances degraded LiDAR data in adverse weather conditions. This refinement is not one-directional; Doppler also updates LiDAR features via the same voxel attention approach. This multi-path interaction between the three features continues through several blocks, progressively utilizing the unique advantages of each modality to update and refine the others, ultimately improving detection performance. We evaluate the detection performance of DLRFusion on the K-RADAR dataset, which provides LiDAR and 4D RADAR data under various weather conditions. The experiments demonstrate that our Doppler-aware fusion approach successfully increases robustness and enhances performance across various weather scenarios.
+
+Our key contributions are as follows: (I) We propose a robust Doppler-based multi-modal 3D object detection framework for diverse weather conditions. (II) We introduce a multi-path iterative interaction mechanism that leverages the distinct advantages of Doppler, RADAR power, and LiDAR modalities through multi-directional refinement and fusion, progressively enhancing robustness against weather-induced degradation. (III) Extensive experiments conducted on the K-RADAR dataset demonstrate the effectiveness of our Doppler-aware approach in improving both robustness and performance.
+
+# 2. Related Works
+
+# 2.1. LiDAR and RADAR for 3D Object Detection
+
+LiDAR is a sensor that measures precise 3D spatial structures of a scene through laser reflection. Consequently, extensive research has been conducted on LiDAR-based 3D object detection, achieving remarkable performance [28, 52, 53, 65, 70, 76]. These methods typically encode LiDAR point clouds in a point-wise manner [40, 52, 64, 68, 75] or utilize voxel-wise [9, 11, 65, 70, 76] and pillar-wise [28, 51] representations to handle large-scale driving environments. Hybrid approaches [42, 53, 54, 69] combining these representations have also been explored. Object detection is then performed using 3D sparse convolutions [8, 15, 65, 72] or transformer-based architectures [14, 64, 75, 77].
+
+RADAR, on the other hand, detects environmental structures using radio waves, typically producing measurements in the range-azimuth-Doppler (R-A-D) space. Detection methods either transform RADAR signals into RD, RAD or heatmaps for BEV detection [36, 38] or apply CFAR to extract 2D points [49]. The recent introduction of 4D RADAR, which includes an additional elevation axis, enables the generation of 3D point clouds for object detection [27, 34, 44, 59]. Despite these advancements, RADAR-only methods still underperform compared to LiDAR-based approaches, encouraging research into sensor fusion to enhance detection performance.
+
+LiDAR-RADAR fusion for 3D object detection often encodes both sensors' data in a uniform format, applying grid-based self- or cross-attention mechanisms without fully considering their distinct characteristics [41, 61, 62, 66]. Recent studies have explored more effective fusion strategies by addressing the misalignment of RADAR measurements compared to LiDAR. Methods incorporating deformable attention [7, 16] and other adaptive mechanisms [55, 63] have been developed to better exploit RADAR data. Additionally, leveraging RADAR's robustness to adverse weather, methods incorporating neighbor search have been proposed to improve multi-modal fusion under diverse conditions [5, 6]. While some [18] have used Doppler in a RADAR feature, its characteristics differ significantly from LiDAR intensity or RADAR power. As a result, an effective feature fusion strategy that fully utilizes Doppler remains underdeveloped, limiting the performance gains of LiDAR-RADAR-based 3D object detection.
+
+# 2.2. Doppler-based Perception
+
+Doppler has been leveraged for various perception tasks, broadly categorized into pre-CFAR and post-CFAR methods. In pre-CFAR, where the entire RADAR signal is utilized, ADC data has been explored for image reconstruction [56, 67], while tasks such as object detection [36, 71], denoising [12, 60], action recognition [1, 2], gesture recog
+
+nition [24] and super-resolution [17, 48] commonly rely on RD or RAD maps. These maps are also transformed from polar to Cartesian coordinates for use in 3D or 4D RADAR tensors [36]. Most methods treat Doppler as a single value [4], while some architectures attempt to utilize it more effectively in feature extraction [36, 43, 71]. However, pre-CFAR representations, such as ADC, RD, and RAD maps, are highly specialized for RADAR, making multi-modal fusion challenging. Additionally, 3D RADAR data lacks height information, while 4D RADAR tensors have excessively large data sizes (e.g., 250MB per sample in the K-RADAR dataset), limiting real-world deployment.
+
+The post-CFAR approach applies the CFAR technique to extract key RADAR signals from pre-CFAR data, generating a RADAR point cloud. This representation retains rich information (R, A, D, power, elevation) while offering compatibility with multi-modal applications. RADAR point clouds can be directly used or processed through techniques such as pillar-based or voxel-based encoding for downstream tasks like 3D object detection [39, 47, 58], motion estimation [21, 22], velocity estimation [20] and tracking [19, 23, 47]. In multi-modal settings, RADAR point clouds have demonstrated their effectiveness by enhancing 3D object detection when fused with camera data [33] or LiDAR [63]. This fusion ultimately improves both performance and robustness. However, most post-CFAR methods still treat Doppler as either unused or simply as a sub-dimension, failing to explicitly leverage its relationship with other RADAR features such as power. Developing more structured approaches to encode Doppler and power remains an open challenge, which could further enhance the robustness of multi-modal 3D object detection.
+
+# 2.3. 3D Object Detection in Adverse Weather
+
+In LiDAR-based 3D object detection, techniques like data-driven noise filtering [31, 45] and domain gap reduction using simulated data [26] have been developed to address the impact of noisy LiDAR points in adverse weather. In contrast, RADAR's robustness in harsh conditions has been exploited in multi-modal models to improve 3D object detection reliability. However, most of these methods focus on camera-RADAR [25, 57, 73] or LiDAR-RADAR fusion [29, 30, 46], demonstrating effectiveness on limited adverse weather samples without specifically targeting extreme conditions. A few studies have concentrated on adverse weather, with one introducing voxel attention with LiDAR and RADAR, combined with weather-based gating to enhance feature representation [6]. Other approach utilizes RADAR prompting for LiDAR models to generate weather-insensitive features [5]. While these studies do not use Doppler, incorporating it in adverse weather for 3D object detection with radar and LiDAR can enhance robustness by capturing motion cues.
+
+# 3. Methods
+
+# 3.1. Framework Overview
+
+Before introducing the model architecture, we first define the input representation and notation. For LiDAR, we directly use the raw LiDAR point cloud $L = \{(x_{l}^{i},y_{l}^{i},z_{l}^{i},i_{l}^{i})\}_{i = 1}^{M}$ . For RADAR, we preprocess the RADAR signal through multiple FFT operations and a polar-to-Cartesian transformation to obtain a 4D RADAR tensor. We then apply CFAR based on power values, retaining only the top $10\%$ of RADAR points. Each RADAR point includes power and Doppler values, forming $R = \{(x_r^i,y_r^i,z_r^i,p_r^i,\mathbf{d}_r^i)\}_{i = 1}^N$ . Then, a simple Doppler-based motion compensation is applied, and two separate RADAR representations, $\hat{R}^p$ and $\hat{R}^d$ , are created, containing power and Doppler information, respectively (see Sec. 3.1.1).
+
+As shown in Fig. 2, the DLRFusion framework consists of three encoder branches for LiDAR, RADAR power, and Doppler. These are followed by Multi-path Iterative Interaction (MPII) blocks, BEV encoders for each MPII block, and a detection head. The inputs $L$ , $\hat{R}^p$ and $\hat{R}^d$ are first converted into 3D sparse tensors and passed through an initial 3D convolution to generate LiDAR feature $L_0 \in \mathbb{R}^{M_0 \times C_0}$ , RADAR power feature $R_0^p \in \mathbb{R}^{N_0 \times C_0}$ and RADAR Doppler feature $R_0^d \in \mathbb{R}^{N_0 \times C_0}$ respectively. Each modality is then processed independently, generating $L_b \in \mathbb{R}^{M_b \times C_b}$ , $R_b^p \in \mathbb{R}^{N_b \times C_b}$ , and $R_b^d \in \mathbb{R}^{N_b \times C_b}$ at the $b$ -th stage, where $b \in \{1, 2, 3\}$ , before entering the corresponding MPII block. Within the $b$ -th MPII block, Doppler feature $R_b^d$ first updates RADAR power feature $R_b^p$ , producing $\tilde{R}_b^p$ . This refined RADAR power feature then enhances the LiDAR feature $L_b$ , generating $\tilde{L}_b^p$ , while Doppler feature $R_b^d$ also independently updates $L_b$ to yield $\tilde{L}_b^d$ (see Sec. 3.2). The refined features $\tilde{L}_b^d$ , $\tilde{R}_b^p$ , and $R_b^d$ serves as inputs to the next MPII block, ensuring continuous refinement across iterations. Parallel to the MPII updates, BEV encoding is applied to $L_b$ , $\tilde{L}_b^p$ , and $\tilde{L}_b^d$ , followed by concatenation to form the classification map $A_{cls}$ and the regression map $A_{reg}$ , which are used for final detection results (see Sec 3.3).
+
+# 3.1.1. RADAR Preprocessing
+
+Rather than constructing a single voxel feature from the RADAR point cloud $R = \{(x_r^i, y_r^i, z_r^i, p_r^i, \mathbf{d}_r^i)\}_{i=1}^N$ , we separate RADAR power $p_r^i$ and Doppler $\mathbf{d}_r^i$ values to better preserve their characteristics. Since the current Doppler values are derived through Doppler FFT, they provide a naive relative velocity estimation. Computing absolute velocity requires the knowledge of the RADAR sensor's bandwidth, which is unavailable. As a result, we employ a simple motion compensation strategy to adjust the Doppler values.
+
+To estimate the approximate ego-velocity, we partition the Doppler values into fixed-size bins with interval $\Delta \mathbf{d}$ . The bin with the highest frequency is selected, and its mean
+
+
+Figure 2. The illustration of DLRFusion framework. DLRFusion first takes LiDAR, preprocessed 4D RADAR power and 4D RADAR Doppler point clouds as input. After these inputs are encoded through the input layer and sparse encoder, the three features interact via multiple paths, leveraging their distinct characteristics and strengths. This fusion process is performed iteratively, progressively enhancing multi-modal feature representations. Each BEV encoder for individual features at multiple stages contributes to the final detection results.
+
+value $\bar{\mathbf{d}}$ is subtracted from all Doppler measurements:
+
+$$
+\hat {\mathbf {d}} _ {r} ^ {i} = \mathbf {d} _ {r} ^ {i} - \bar {\mathbf {d}}, \quad \forall i \tag {1}
+$$
+
+This approach provides a robust estimation, minimizing noise sensitivity and enhancing generalization. For the RADAR power, we apply a logarithmic transformation to scale the values, resulting in $\hat{R}^p = \{(x_r^i,y_r^i,z_r^i,10\cdot \log (p_r^i))\}_{i = 1}^{N_0}$ . Meanwhile, the Doppler values are adjusted and represented as $\hat{R}^d = \{(x_r^i,y_r^i,z_r^i,\hat{\mathbf{d}}_r^i)\}_{i = 1}^{N_0}$ .
+
+# 3.2. Multi-path Iterative Interaction
+
+In our framework, Doppler and RADAR power are treated as distinct sparse tensors, each carrying different types of valuable information for 3D object detection. To effectively combine these features, we propose a novel structured interaction mechanism that systemically models the relationships between Doppler and RADAR power, LiDAR and RADAR power, and LiDAR and Doppler. Each interaction is modeled as follows.
+
+Doppler-Power Interaction. Doppler features $R_{b}^{d}$ captures dynamic, motion-related cues, while RADAR power features $R_{b}^{p}$ encode signal strength and objectness. Instead of directly fusing them, we refine RADAR power using Doppler as a guide to preserve their distinct characteristics. This approach enhances the emphasis on moving objects while mitigating static clutter, ensuring each modality retains its unique properties.
+
+To achieve this, Doppler and RADAR power features are first projected into a shared latent space using learnable linear transformations:
+
+$$
+\dot {P} _ {b} = W _ {b} ^ {p} R _ {b} ^ {p} + \beta_ {b} ^ {p}, \dot {D} _ {b} = W _ {b} ^ {d} R _ {b} ^ {d} + \beta_ {b} ^ {d}. \tag {2}
+$$
+
+Then, their similarity is measured via the Euclidean distance for each RADAR point:
+
+$$
+\left\{\Delta_ {b} \right\} _ {i} ^ {p d} = | | \left\{\dot {P} _ {b} \right\} _ {i} - \left\{\dot {D} _ {b} \right\} _ {i} | | _ {2}. \tag {3}
+$$
+
+To effectively capture the interaction between these two distinct modalities, we employ a kernelized attention mechanism that combines two specialized kernels. The first, the motion emphasis kernel, enhances Doppler's influence by assigning higher importance to similar feature pairs, ensuring smooth integration:
+
+$$
+\mathcal {F} _ {e m p h.} \left(\dot {P} _ {b}, \dot {D} _ {b}\right) = e x p \left(- \frac {\left(\left\{\Delta_ {b} \right\} _ {i} ^ {p d}\right) ^ {2}}{2 \sigma^ {2}}\right). \tag {4}
+$$
+
+This mechanism smooths the interaction between Doppler and RADAR power, reinforcing motion-related information while preventing the propagation of noisy or irrelevant variations. The second, the feature separation kernel, reinforces substantial differences by multiplying the motion emphasis score with the feature distance $\{\Delta_b\}_i^{pd}$ . While the motion emphasis kernel highlights similar feature pairs, this modulation ensures that only sufficiently distinct interactions influence the refinement, preventing feature collapse and preserving discriminative motion cues.
+
+By taking the element-wise product of these two kernels, we obtain a final attention score $\mathcal{F}_b$ that balances the smooth, similarity-based weighting with the need to emphasize notable differences.
+
+$$
+\mathcal {F} _ {b} = \mathcal {F} _ {e m p h.} (\acute {P} _ {b}, \acute {D} _ {b}) \cdot \mathcal {F} _ {s e p.} (\acute {P} _ {b}, \acute {D} _ {b}). \qquad (5)
+$$
+
+This score is then used to refine RADAR power, dynamically adjusting its response based on Doppler information:
+
+$$
+\tilde {R} _ {b} ^ {p} = \mathcal {F} _ {b} \cdot R _ {b} ^ {p}. \tag {6}
+$$
+
+The resulting RADAR power features retain their original objectness properties while benefiting from motion-aware refinements, ultimately enhancing the model's ability to detect dynamic objects under various conditions.
+
+Power-LiDAR Interaction. Modeling the interaction between RADAR power and LiDAR features requires careful consideration of their differing voxel distributions and densities. Inspired by [6], we adopt a modified voxel attention mechanism tailored to our setting, enabling LiDAR to attend to neighboring RADAR voxels and ensuring robust feature adaptation across varying weather conditions. In [6], LiDAR features were enhanced using RADAR power alone, ignoring Doppler cues. We instead utilize the Doppler-aware refined power feature, $\tilde{R}_b^p$ . This modification allows LiDAR to dynamically adapt based on both RADAR signal strength and motion cues, yielding more robust feature fusion especially under adverse weather conditions where LiDAR-only representations may falter.
+
+Formally, given LiDAR feature $L_{b}$ and Doppler-aware refined RADAR power feature $\tilde{R}_b^p$ , we compute the voxel attention score by attending to the neighboring RADAR voxels for each LiDAR voxel. For each LiDAR voxel $i$ , the attention weight is defined as:
+
+$$
+\left(\alpha_ {b} ^ {p}\right) _ {i j} = \sum_ {j \in \mathcal {N} (i)} \frac {\exp \left(\left(L _ {b}\right) _ {i} \cdot \left(\tilde {R} _ {b , j} ^ {p}\right) ^ {\top}\right)}{\sum_ {k \in \mathcal {N} (i)} \exp \left(\left(L _ {b}\right) _ {i} ^ {\top} \cdot \left(\tilde {R} _ {b , k} ^ {p}\right) ^ {\top}\right)}, \tag {7}
+$$
+
+where $\mathcal{N}(i)$ denotes the set of RADAR voxels neighboring LiDAR voxel $i$ . The updated LiDAR feature is then obtained as a weighted sum of attended RADAR power features, with a learnable feature transformation $\psi(\cdot)$ applied:
+
+$$
+\left(\tilde {L} _ {b} ^ {p}\right) _ {i} = \left(L _ {b}\right) _ {i} + \sum_ {j \in \mathcal {N} (i)} \left(\alpha_ {b} ^ {p}\right) _ {i j} \cdot \psi \left(\tilde {R} _ {b, j} ^ {p}\right). \tag {8}
+$$
+
+This voxel attention mechanism enables LiDAR to dynamically incorporate refined RADAR power information, making the representation more resilient under challenging conditions. By leveraging Doppler-power interaction into Power-LiDAR interaction, our approach captures motion-induced variations while maintaining the structural integrity of LiDAR features.
+
+Doppler-LiDAR Interaction. While the Doppler-based power update followed by the power-based LiDAR update hierarchically enhances feature robustness, relying solely on these interactions has limitations. Specifically, this approach may not fully capture the complementary dynamics between Doppler and LiDAR, potentially resulting in suboptimal integration of motion and spatial cues while overlooking subtle interactions.
+
+To overcome this shortcoming, we establish a direct interaction between Doppler and LiDAR features. This multiple-path interaction ensures that all three feature modalities—Doppler, refined RADAR power, and LiDAR—are effectively fused, further enhancing overall robustness. The direct Doppler-LiDAR interaction is implemented in a similar manner to the previous power-LiDAR interaction, with the key difference being that it utilizes Doppler features instead of refined power, leading to the formation of $\tilde{L}_b^d$ . While the same formulation is used, the weights are not shared between these two interactions, allowing each path to specialize in capturing unique aspects of the multi-modal data.
+
+Each of these interactions is iteratively refined through the Multi-path Iterative Interaction (MPII) blocks, progressively enhancing feature representations at multiple scales. The resulting refined features $\tilde{L}_b^d$ , $\tilde{L}_b^p$ , and $L_{b}$ are then passed through the BEV encoder and detection head to produce robust 3D object detection results. The refined features $\tilde{L}_b^d$ , $\tilde{R}_b^p$ , and $R_b^d$ are then fed into the subsequent MPII block, enabling continuous refinement throughout the process.
+
+# 3.3. Detection Head and Losses
+
+After the features from the previous MPII blocks, $L_{b}$ , $\tilde{L}_{b}^{d}$ and $\tilde{L}_{b}^{p}$ pass through the individual BEV encoder, the denified sparse features are encoded to generate BEV features of the same size. They are transformed into three BEV features: $B_{b}$ , $B_{b}^{p}$ , and $B_{b}^{d}$ . These three BEV features from each block are then concatenated and passed to the classification and regression heads to form the classification map $A_{cls}$ and regression map $A_{reg}$ . The classification map is learned using focal loss [32], and the regression map is learned using smooth L1 loss. The total loss is the sum of both classification and regression losses:
+
+$$
+L = L _ {f o c a l} (A _ {c l s}, A _ {c l s} ^ {G T}) + L _ {s m o o t h \_ L 1} (A _ {r e g}, A _ {r e g} ^ {G T}). (9)
+$$
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Dataset and Metrics. The K-RADAR dataset is a large-scale autonomous driving dataset focused on 4D RADAR, and includes additional sensors such as camera, LiDAR, and GPS. It is primarily used for 3D object detection research and is the only dataset including 4D RADAR along with
+
+Table 1. Quantitative detection results of ${AP}_{BEV}/{AP}_{3D}$ at IoU=0.5 of LiDAR and 4D RADAR-based 3D object detection methods on K-RADAR dataset [44] under various weather conditions (L: LiDAR, 4DR: 4D RADAR). Best in bold, second in underline.
+
+| Methods | Modality | Normal | Overcast | Fog | Rain | Sleet | Light Snow | Heavy Snow | Total |
| RTNH [44] | 4DR | 44.6 / 15.5 | 61.1 / 27.5 | 51.6 / 21.7 | 47.1 / 9.21 | 28.8 / 6.17 | 53.8 / 28.4 | 42.5 / 10.6 | 44.4 / 14.1 |
| \( RTNH^† \) [44] | L | 69.4 / 39.8 | 86.8 / 41.4 | 82.1 / 58.5 | 72.9 / 28.2 | 42.3 / 24.5 | 78.0 / 50.4 | 42.3 / 21.2 | 65.8 / 37.2 |
| PointPillars [28] | L | 54.3 / 26.4 | 60.6 / 32.4 | 43.5 / 29.6 | 60.1 / 25.7 | 18.5 / 5.97 | 43.3 / 28.3 | 28.6 / 7.50 | 47.8 / 21.5 |
| VoxelNext [9] | L | 70.6 / 29.8 | 87.2 / 35.9 | 80.3 / 34.7 | 79.0 / 33.8 | 37.4 / 9.98 | 82.1 / 54.9 | 48.0 / 20.4 | 70.5 / 32.7 |
| InterFusion [62] | 4DR+L | 56.4 / 20.4 | 83.4 / 30.8 | 68.7 / 33.6 | 65.3 / 20.8 | 27.5 / 10.6 | 77.6 / 53.6 | 51.7 / 19.8 | 59.3 / 22.4 |
| \( BEVFusion^† \) [35] | 4DR+L | 70.7 / 30.1 | 88.8 / 38.7 | 80.7 / 40.1 | 82.1 / 32.2 | 42.6 / 9.20 | 84.0 / 50.9 | 52.2 / 25.3 | 71.6 / 29.0 |
| LOD_PDR [5] | 4DR+L | 72.1 / 40.3 | 87.3 / 43.3 | 83.9 / 63.4 | 75.2 / 31.6 | 45.1 / 27.9 | 79.1 / 51.6 | 48.1 / 24.9 | 71.3 / 40.4 |
| DLRFusion | 4DR+L | 72.3 / 45.0 | 86.8 / 55.6 | 86.7 / 45.4 | 81.6 / 46.1 | 43.3 / 26.3 | 84.0 / 61.0 | 54.5 / 30.6 | 73.2 / 45.7 |
+
+Table 2. Quantitative detection results of ${AP}_{BEV}/{AP}_{3D}$ at IoU=0.3 of LiDAR and 4D RADAR-based 3D object detection methods on K-RADAR dataset [44] under various weather conditions (L: LiDAR, 4DR: 4D RADAR). Best in bold, second in underline.
+
+| Methods | Modality | Normal | Overcast | Fog | Rain | Sleet | Light Snow | Heavy Snow | Total |
| RTNH [44] | 4DR | 60.1 / 50.3 | 67.3 / 57.8 | 68.7 / 50.3 | 58.0 / 41.3 | 50.8 / 33.7 | 61.1 / 57.5 | 58.2 / 48.5 | 59.1 / 47.5 |
| \( RTNH^† \) [44] | L | 81.5 / 72.9 | 88.1 / 76.4 | 85.4 / 83.0 | 83.4 / 68.9 | 49.1 / 43.2 | 87.3 / 85.1 | 55.7 / 50.3 | 80.5 / 70.6 |
| PointPillars [28] | L | 58.4 / 52.7 | 61.4 / 58.2 | 43.6 / 34.4 | 61.2 / 49.1 | 19.6 / 13.9 | 44.4 / 42.1 | 29.6 / 29.5 | 50.6 / 45.7 |
| VoxelNext [9] | L | 80.8 / 69.9 | 92.9 / 74.5 | 82.6 / 71.8 | 82.7 / 66.3 | 44.0 / 37.2 | 86.5 / 83.3 | 57.1 / 52.6 | 78.4 / 67.7 |
| InterFusion [62] | 4DR+L | 71.9 / 58.0 | 85.8 / 73.5 | 69.8 / 62.2 | 76.1 / 61.5 | 31.6 / 28.1 | 79.0 / 76.7 | 55.6 / 53.6 | 71.9 / 59.2 |
| \( BEVFusion^† \) [35] | 4DR+L | 81.7 / 69.9 | 95.3 / 77.4 | 87.3 / 66.8 | 84.9 / 70.5 | 55.3 / 43.2 | 88.4 / 85.2 | 67.8 / 61.6 | 81.5 / 69.4 |
| LOD_PDR [5] | 4DR+L | 83.9 / 74.4 | 88.3 / 76.9 | 87.7 / 85.5 | 84.4 / 70.3 | 52.4 / 45.9 | 89.1 / 87.8 | 59.6 / 54.4 | 82.1 / 73.2 |
| DLRFusion | 4DR+L | 83.7 / 79.8 | 93.5 / 84.4 | 88.7 / 84.5 | 84.6 / 75.1 | 54.6 / 44.2 | 88.1 / 86.8 | 62.7 / 61.1 | 82.9 / 74.8 |
+
+seven different weather conditions, enabling a detailed evaluation of model performance across various weather scenarios. Following the 3D detection model developed in the official paper, we also computed $AP_{3D}$ and $AP_{BEV}$ for different weather conditions, using the detection performance of the Sedan class as the metric at IoU=0.3 and IoU=0.5.
+
+Implementation Details. Following the official paper of K-RADAR dataset, point clouds within the driving corridor were used for the experiment, with the x-axis range (0, 72m), y-axis range (-6.4, 6.4m), and z-axis range (-2, 6m). The voxel size was set to $0.4 \times 0.4 \times 0.4\mathrm{m}$ , and the preprocessing bin size with $\Delta d$ was set to 0.2. The number of MPII and stages was set to $b = 3$ . Training was conducted with a batch size of 4 using the Adam optimizer until performance convergence. More details are in Suppl. Material.
+
+# 4.2. Main Results
+
+Table 1 and 2 show the quantitative comparison of 3D object detection results in K-RADAR dataset [44]. We compared various state-of-the-art 4D RADAR, LiDAR, and 4D RADAR-LiDAR-based 3d object detection methods, providing detection results under different weather conditions. Specifically, we experimented with voxel-based RTNH [44] for RADAR-based model. For LiDAR-based methods, we tested $\mathrm{RTNH}^{\dagger}$ , which modifies the input modalities from 4D RADAR to LiDAR, as well as pillar-based PointPillars [28] and voxel-based VoxelNext [9]. For 4D RADAR-LiDAR fusion methods, we explored pillar-based fusion (InterFusion [62]) and BEV-based fusion (BEVFusion† [35]), by
+
+changing the input modality from camera and LiDAR to 4D RADAR and LiDAR, documenting the performance.
+
+From Table 1, it is evident that our DLRFusion significantly outperforms other RADAR, LiDAR, and fusion methods with $AP_{BEV}$ and $AP_{3D}$ at IoU=0.5. Especially in terms of $AP_{3D}$ , our method shows a $13\%$ improvement over the second-best method, LOD_PDR, demonstrating that our Doppler-aware approach enables effective interaction of different modalities in 3D space. Moreover, the performance across both AP metrics consistently outperforms others under various weather conditions, indicating that our method maintains robustness across environments, ranging from normal to weather-degraded conditions. At IoU=0.3, our method similarly demonstrates superior performance, consistently surpassing other approaches.
+
+Qualitative results are also provided in Fig. 3. We compare our method against the top-2 single-modal baselines (RTNH and $\mathrm{RTNH}^{\dagger}$ ) and the top-2 multi-modal baselines (VoxelNext and BEVFusion $^{\dagger}$ ), all of which have publicly available implementations. Additional qualitative comparisons including other single- and multi-modal methods are provided in the Suppl. Material. Consistent with the quantitative results, our DLRFusion demonstrates the highest precision in object detection, both in BEV and in 3D space. While RADAR-based method suffers from false positives, LiDAR-based methods experience missed detections in adverse weather, and RADAR-LiDAR fusion methods struggle with ineffective fusion. In contrast, our results demonstrate robust object detection across various weather condi
+
+
+
+
+
+
+
+
+(a)
+
+(b)
+(c)
+(d)
+(e)
+Figure 3. Visual comparison of (a) RTNH, (b) $\mathrm{RTNH}^{\dagger}$ , (c) VoxelNext, (d) BEVFusion $^{\dagger}$ , and (e) DLRFusion (ours) on K-RADAR dataset. Each column shows a sample from normal, overcast, rain, and heavy snow conditions. (a) $\sim$ (e) depict LiDAR and RADAR in BEV, while (f) shows our 3D results in range view with camera and LiDAR. The red represents the ground truth (GT), while the black represents the prediction. More results under various weather conditions can be found in Suppl. Material.
+
+
+
+
+
+
+
+
+(f)
+
+tions. This highlights the thoughtful design of how to effectively leverage LiDAR, RADAR power, and Doppler, thus validating our approach.
+
+# 4.3. Model Analysis
+
+Effect of Doppler. We conducted experiments to explore how to fully exploit the 3D coordinates, power, and Doppler information in RADAR data, as shown in Table 3. In (a) and (b), the 3D information and power/Doppler are encoded in 4 dimensions, and it is observed that power alone outperforms Doppler alone. As shown in (d), encoding in 5 dimensions leads to better performance due to the increased amount of information. In (c) and (e), we applied RADAR preprocessing to compensate for the naive relative velocity of Doppler, and performance improves compared to (b) and (d), especially in terms of $AP_{3D}$ . Furthermore, when power and Doppler are encoded with separate branches, the performance improves even further. This demonstrates
+
+that to fully exploit the distinct characteristics of power and Doppler, RADAR preprocessing, separate encoding, and effective fusion are more beneficial than combining them into a single tensor. Based on these experimental results, we designed the RADAR preprocessing and DLRFusion.
+
+Component Analysis. To demonstrate that the three interactions in our MPII block play a key role in modality information transfer, we conducted a component analysis in Table 4, evaluating how each interaction contributes to the overall performance. First, the power-LiDAR interaction [6] in (a) shows decent performance with effective RADAR-LiDAR updates in adverse weather. Then, as seen in (b), when the Doppler-LiDAR interaction is added, there is a slight performance improvement, but it is not substantial. However, in (c), when the power-Doppler interaction is additionally introduced, a significant performance boost is observed across all metrics. This significant improvement, achieved without any additional information, suggests that
+
+Table 3. Experiment results for encoding Doppler in a RADAR-only model, evaluating strategies for incorporating Doppler information into the 3D object detection framework. Pw., Dop., PP., Sep. indicate power, Doppler, preprocessing in Sec. 3.1.1, and separate encoding of power and Doppler, respectively.
+
+ | Pw. | Dop. | PP. | Sep. | IoU=0.3 | IoU=0.5 |
| APBEV | AP3D | APBEV | AP3D |
| (a) | ✓ | | | | 59.1 | 47.5 | 44.4 | 14.1 |
| (b) | | ✓ | | | 57.9 | 46.1 | 42.3 | 14.6 |
| (c) | | ✓ | ✓ | | 57.7 | 47.5 | 42.1 | 18.7 |
| (d) | ✓ | ✓ | | | 59.7 | 48.5 | 46.2 | 15.7 |
| (e) | ✓ | ✓ | ✓ | | 61.1 | 49.5 | 45.4 | 16.3 |
| (f) | ✓ | ✓ | ✓ | ✓ | 61.6 | 52.1 | 49.9 | 19.9 |
+
+Table 4. Detection results based on the interaction components of MPII. P-L, D-L, and P-D represent power-LiDAR, Doppler-LiDAR, and power-Doppler interactions, respectively.
+
+ | P-L | D-L | P-D | IoU=0.3 | IoU=0.5 |
| APBEV | AP3D | APBEV | AP3D |
| (a) | ✓ | | | 81.7 | 73.4 | 71.6 | 37.9 |
| (b) | ✓ | ✓ | | 81.9 | 72.7 | 71.2 | 37.9 |
| (c) | ✓ | ✓ | ✓ | 82.9 | 74.8 | 73.2 | 45.7 |
+
+we have effectively designed the interaction by leveraging the distinct characteristics of each modality. The multi-path Doppler to Power to LiDAR update ensures that only valuable information is passed through, and the iterative process progressively strengthens the features, enhancing the overall performance. This confirms that the power-Doppler interaction is an extremely effective fusion method for 4D RADAR-LiDAR systems, alongside the power-LiDAR and Doppler-LiDAR interactions.
+
+Fusion Comparison. We conducted various Doppler-based variant methods to explore the performance of different Doppler interaction strategies in 3D object detection, and the results are reported in Table 5. All methods separately encode LiDAR, RADAR power, and Doppler for a fair comparison. The concatenation model in (a) encodes the three modalities with individual encoders, concatenating the features before they enter the detection head. The voxel attention model in (b) applies voxel attention between power and LiDAR, as well as Doppler and LiDAR. The BEVFusion model in (c) was further modified to separately encode the three types of data and fuse them in the BEV space. As shown in (a), even though RADAR separate encoding might perform well, if LiDAR data is also encoded separately and fused only at the detection head, there is minimal information exchange, which leads to decent but not high performance. In (b), there is more information exchange between feature encodings, resulting in better performance than concatenation. In (c), the individual encodings and fusion in
+
+Table 5. Detection results of various Doppler-based variant methods, comparing the performance of different Doppler interaction strategies in 3D object detection.
+
+ | Doppler-based Methods | IoU=0.3 | IoU=0.5 |
| APBEV | AP3D | APBEV | AP3D |
| (a) | Concatenation | 81.4 | 73.2 | 71.4 | 36.9 |
| (b) | Voxel Attention | 81.9 | 72.7 | 71.2 | 37.9 |
| (c) | BEVFusion† | 81.5 | 69.1 | 72.0 | 31.0 |
| (d) | DLRFusion | 82.9 | 74.8 | 73.2 | 45.7 |
+
+the BEV space lead to decent performance as well. However, our DLRFusion outperforms these variants. Unlike methods that fuse at the detection head, at specific layers, or only once in a one-way manner (or those that fuse and never separate), our multi-path approach allows for better performance. It effectively refines data-specific information through each encoding branch and iterative fusion, proving that this design is more effective.
+
+# 4.4. Limitation
+
+Due to limited RADAR sensor information in the dataset and a restricted Doppler measurement range, we were unable to accurately estimate the absolute velocity of surrounding objects. Therefore, we use a simple Doppler-based motion compensation technique. Our method demonstrates strong detection performance within a single frame, but under conditions where absolute velocity estimation is possible, we expect even better performance. If these limitations are addressed, multi-frame detection or tracking could be achieved by exploiting temporal relations, which we propose as a direction for future work.
+
+# 5. Conclusion
+
+We propose a Doppler-aware LiDAR-4D RADAR fusion (DLRFusion) framework that enhances 3D object detection under diverse weather conditions. By treating RADAR power and Doppler as separate sparse tensors, our multipath iterative interaction module refines both LiDAR and RADAR power using Doppler, ensuring motion cues contribute effectively to objectness estimation and improving detection in degraded environments. Experiments on the K-RADAR dataset demonstrate that our approach effectively integrates Doppler into multi-modal fusion, leading to improved detection performance across varying conditions.
+
+Acknowledgement. This work was supported by the Technology Innovation Program (1415187329,20024355, Development of autonomous driving connectivity technology based on sensor-infrastructure cooperation) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF2022R1A2B5B03002636).
+
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+# Draw Your Mind: Personalized Generation via Condition-Level Modeling in Text-to-Image Diffusion Models
+
+Hyungjin Kim, Seokho Ahn, Young-Duk Seo*
+Department of Electrical and Computer Engineering, Inha University
+
+flslzk@inha.edu, sukho0514@inha.edu, mysid88@inha.ac.kr
+
+*Corresponding author https://github.com/Burf/DrUM
+
+
+(a)
+
+
+Figure 1. DrUM personalizes synthesis results on popular foundation T2I models without fine-tuning by incorporating open-source text encoders. It integrates key preference information such as style, texture within the latent space, effectively satisfying individual demands. (a) Conceptual illustration of our methodology. (b) Personalized results using multiple prompts on Stable Diffusion V3.
+
+
+
+
+(b)
+
+
+
+
+
+# Abstract
+
+Personalized generation in T2I diffusion models aims to naturally incorporate individual user preferences into the generation process with minimal user intervention. However, existing studies primarily rely on prompt-level modeling with large-scale models, often leading to inaccurate personalization due to the limited input token capacity of T2I diffusion models. To address these limitations, we propose DrUM, a novel method that integrates user profiling with a transformer-based adapter to enable personalized generation through condition-level modeling in the latent space. DrUM demonstrates strong performance on large-scale datasets and seamlessly integrates with open-source text encoders, making it compatible with widely used foundation T2I models without requiring additional fine-tuning.
+
+# 1. Introduction
+
+Recently, various techniques in text-to-image (T2I) diffusion models, such as fine-tuning, additional conditioning, editing, and guidance, have been developed. These approaches enable users to exert more direct control over the generation process beyond prompt engineering, allowing for greater alignment with their intended outcomes [9]. However, they often require substantial computational resources and iterative refinements before achieving results that accurately reflect user preferences [22, 28].
+
+Personalized generation presents a promising solution to these limitations by directly integrating individual preferences into the generation process [4, 22, 25, 28, 31]. In this context, many studies have employed large language models (LLMs) and multimodal models to generate person-
+
+alized inputs for T2I models [4, 22, 25, 31]. However, these approaches primarily rely on prompt-level modeling, which is restricted by the limited input length and the constrained references imposed by the token capacity of text encoders. Furthermore, the dependence on large-scale models results in significant computational costs. To enable personalized generation with minimal user intervention while effectively addressing individual needs, the following challenges must be addressed: (i) accurately identifying individual preferences, (ii) overcoming the constraints of prompt-level modeling, and (iii) precisely incorporating user preferences into the generation process.
+
+To address these challenges, we propose DrUM (Draw Your Mind), a novel approach to achieve all the core requirements for personalized generation. The DrUM first constructs a user profile by applying coreset sampling (Section 4.2) to extract key information from the user's history. It then employs a transformer-based adapter for condition-level modeling (Section 4.3), enabling the integration of diverse user preferences into a personalized T2I model input within the latent space. Additionally, DrUM leverages a guidance mechanism (Section 4.4) within the adapter to precisely capture detailed user profiles while maintaining minimal structural complexity, offering flexible control over preference intensity and personalization degree. Notably, it seamlessly incorporates with open-source text encoders, such as OpenCLIP [5] and Google T5 [17], making it compatible with widely used foundation T2I models, including Stable Diffusion V1/V2/XL/V3 [7, 16, 19] and FLUX, without requiring additional fine-tuning.
+
+The main contributions of this study are as follows:
+
+- We introduce DrUM, the first de facto approach to personalized generation via condition-level modeling in T2I diffusion models.
+- DrUM effectively integrates individual preferences into high-quality personalized synthesis results by considering both preference intensity and personalization degree, overcoming the limitations of prompt-level modeling.
+- DrUM achieves superior performance while preserving creativity and diversity across various foundation T2I models, all without requiring additional fine-tuning.
+
+# 2. Related works
+
+We review existing studies on T2I diffusion models and personalized generation.
+
+# 2.1. Text-to-image diffusion models
+
+T2I diffusion models primarily generate realistic images by using text prompts as input. GLIDE [14] was the first study to produce high-dimensional pixel-level images from text by employing classifier-free guidance [8]. DALL-E 2 [18] adopted the OpenCLIP text encoder to generate images that accurately reflect user inputs. Imagen [21] uti
+
+lized a hierarchical structure and the Google T5 encoder to create high-quality images that fully capture textual semantics. Stable Diffusion [19] introduced the latent diffusion model (LDM), a standard T2I architecture that leverages the OpenCLIP text encoder to perform diffusion in a lower-dimensional latent space. The most widely adopted T2I diffusion architectures are based on LDM with open-source text encoders to achieve precise generative capabilities. These models have significantly enhanced users' creative activities, and various methods have been explored to meet the increasing and diverse demands of users.
+
+Fine-tuning methods like DreamBooth [20] effectively reflect input images as a special token within personalized diffusion models. However, they still require substantial resources for additional training and rely on well-designed prompts to achieve satisfactory results. Additional condition methods like ControlNet [34] allows users to directly control desired composition through additional inputs, but they struggle to fully capture semantic information such as style and texture. Editing methods like InstructPix2Pix [2] enable precise edits but often demand additional inputs or manual adjustments to produce the desired outcomes. Guidance methods like StyleDiffusion [29] generate results emphasizing specific attributes but require expert user intervention for fine adjustments. In general, when users aim for precise results with T2I diffusion models, a higher level of expertise and significant time investment are required. Moreover, the process may require additional input data or high-performance hardware [9].
+
+# 2.2. Personalized generation
+
+Personalized generation aims to naturally incorporate individual user preferences into the generative process, providing highly satisfactory results with minimal user intervention. This approach has demonstrated its effectiveness across various domains, including fashion [30, 33], music [6, 15], modeling [3, 13], and advertising [27, 32], and recent attempts have extended to diffusion models.
+
+Fabric [28] utilizes attention-level guidance during the self-attention process of Stable Diffusion V1/V2 to reflect key image-level features, but it can only consider a single positive/negative image pair. Tailored Visions (TV) [4] uses ChatGPT 3.5 to rewrite prompts by retrieving three historical prompts similar to the input using OpenCLIP ViT-L. However, considering more than three prompts degrades generation quality, and necessitates additional resources for API calls and retrieval. ViPer [22] employs the multi-modal model IDEFICS2-8b [12] to construct a single like/dislike prompt pair for virtual users' visual preferences and uses simple contrastive guidance to transform this prompt pair into personalized input on Stable Diffusion V1/XL. However, it relies only on a single pair within a limited input length and requires at least 8–20 images with detailed com
+
+ments for user profiling. PMG [25] employs LLaMA2-7B [26] to reconstruct inputs using keywords extracted from users' preferred products, but it integrates only limited preference information and is restricted to specific domains such as movie posters and stickers. Additionally, it introduces soft preference embedding to complement keyword modeling, but this focuses on considering the next preferred product rather than reflecting the user's overall preferences. Pigeon [31] fine-tunes the multi-modal generative model LaVIT [10] for personalized generation using both historical prompts and images. However, it relies on LaVIT's built-in LDM and remains limited to specific domains such as movie posters and stickers. Additionally, it requires reference images for personalized generation, but maintaining large amounts of these images incurs significant costs, making scalability a challenge.
+
+# 3. Preliminaries
+
+This section describes preliminaries on T2I conditioning and personalized generation in T2I diffusion models.
+
+# 3.1. Text encoder-based T2I conditioning
+
+T2I conditioning is the process that text encoders transform prompts into conditions for T2I generation [9]. Recent trends have shifted the focus from smaller encoders like OpenCLIP ViT-L to more powerful architectures such as OpenCLIP ViT-bigG and Google T5. These larger-scale encoders with optimized combinations have been shown to enhance the quality of T2I conditioning, leading to more semantically accurate outputs [7, 16].
+
+Notably, the T2I condition $y$ directly influences the variation in generated results, as modeled in the reverse diffusion process with the following formula:
+
+$$
+p _ {\theta} \left(x _ {t - 1} \mid x _ {t}, y\right) = \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, t, y\right), \Sigma_ {\theta} \left(x _ {t}, t, y\right)\right) \tag {1}
+$$
+
+Here, the conditional probability $p_{\theta}(x_{t - 1}|x_t,y)$ models the transition from the current state $x_{t}$ to the previous state $x_{t - 1}$ under the T2I condition $y$ , with mean $\mu_{\theta}$ and covariance $\Sigma_{\theta}$ parameterizing the Gaussian distribution to guide denoising for semantically faithful image generation.
+
+Despite the effectiveness of this approach, the unique combinations of various text encoders in each T2I model make it challenging to establish a unified method for consistently improving all models.
+
+# 3.2. Personalized generation in T2I diffusion models
+
+As introduced in the previous section, personalized generation identifies user preferences as a profile and integrates this profile into the generation process to provide personalized content. However, existing studies on three key steps of personalized generation have several limitations:
+
+- **User profiling:** Identifying individual preferences is a crucial step in personalized generation [22], but it only leverages a limited number of historical entries [4, 25, 31] or relies on detailed user feedback [22, 28].
+- Personalized T2I input: Existing methods primarily model T2I inputs at the prompt-level, which limits expressiveness due to restricted input token length [4, 22, 25]. Additionally, incorporating more preference information often degrades performance [4, 25].
+- Integrating user preference: Precise personalization requires fine-grained user profile integration during the generation process. However, most studies rely only on large-scale models, even for detailed information (i.e., preference intensity and personalization degree) [4, 22, 25, 31].
+
+In summary, achieving personalized generation that accurately reflects individual preferences with minimal user intervention is crucial. This requires a design that ensures both creativity and diversity for a wide range of users while addressing these limitations.
+
+# 4. Methodology
+
+This section introduces DrUM, a method designed to sample key user preferences and generate precise synthesis results accordingly.
+
+# 4.1. Overview
+
+Figure 2 illustrates the overall structure of DrUM for personalized generation in T2I diffusion models. DrUM customizes the T2I conditioning process using a transformer-based adapter to integrate historical prompts and the target prompt, enabling the synthesis of personalized outputs.
+
+First, we identify the user profile from historical prompts and preference intensities (e.g., ratings) using a coreset sampling method (Section 4.2). This method effectively captures user preferences while reducing the number of references required for personalized conditioning. Next, to combine diverse user preferences into a personalized condition for T2I generation, we propose the Personalized Conditioning Adapter (PeCA), a transformer composed of only a few cross-attention layers for condition-level modeling (Section 4.3). PeCA effectively integrates rich preference information with the target prompt in the latent space, overcoming constraints imposed by prompt-level limitations. Finally, we introduce a guidance mechanism (Section 4.4), which enables fine-grained control over preference intensity and personalization degree, ensuring highly refined personalized synthesis results.
+
+These components are designed as adapter modules for open-source text encoders, making them applicable to popular foundation T2I models. Detailed explanations of these components are provided in the following sections.
+
+
+Figure 2. Overview of methodology. || denotes concatenation.
+
+# 4.2. Coreset sampling
+
+To effectively identify user profile, we sample key information from historical prompts. However, simple methods like random sampling may lead to information loss, and make it difficult to effectively utilize details such as preference intensity. Therefore, we employ the coreset sampling to exclude unnecessary references, reducing computational overhead while enhancing personalization.
+
+Coreset sampling is a technique that selects a subset that effectively approximates the entire set [1]. We perform sampling by measuring the CLIP similarity between historical prompts using the minimum enclosing ball technique. However, since precisely measuring distances between samples is NP-Hard [11], we adopt an iterative greedy approximation [23] to reduce computational cost.
+
+Our user profiling is summarized in Algorithm 1. Initially, we randomly select $k$ from $N$ samples to approximate the average score across entire embeddings $E = (\mathbf{e}_i)_{i=1}^N$ to reduce computational complexity. Subsequently, we sample core prompts incorporating the CLIP similarity $\mathrm{Sim}_{\mathrm{CLIP}}(*)$ (See Equation (3)) and preference intensities $P = (p_i)_{i=1}^N$ to enable more refined user profiling.
+
+# Algorithm 1 Coreset sampling
+
+1: Input: CLIP embeddings $E$ , preference intensities $P$ , sample size $n$ , approximate size $k$
+2: Output: Coreset indices $\mathcal{I}$
+3: Initialize $\mathcal{I} \gets \emptyset$
+4: Select subset $E_{k} \subseteq E$ where $|E_{k}| = k$
+5: Define operator $\operatorname{Sim}(\mathbf{e}, E) = (\operatorname{Sim}_{\mathrm{CLIP}}(\mathbf{e}, \mathbf{e}_i, p_i))_{i=1}^N$
+6: Distances $D\gets \frac{1}{k}\sum_{\mathbf{e}\in E_k}\operatorname {Sim}(\mathbf{e},E)$
+7: repeat
+8: $s\gets \arg \max_{i}D$
+9: $\mathcal{I}\gets \mathcal{I}\cup \{s\}$
+10: $D\gets \min \left(D,\operatorname {Sim}(\mathbf{e}_s,E)\right)$
+11: $D_{s}\gets -\infty$
+12: until $|\mathcal{I}| = n$
+
+# 4.3. Condition-level modeling
+
+This section proposes a condition-level modeling approach that effectively integrates sufficient reference prompts in the latent space to overcome prompt-level limitations. However, it presents several challenges that must be addressed. First, there is no standard dataset or training method for constructing personalization based on condition embeddings. In T2I diffusion models, mapping users' historical data to the corresponding personalized data for training is a complex task. Moreover, personalized conditions must preserve the original embedding distribution to prevent performance degradation of foundation T2I models. Second, the positions and distributions of special or valid tokens can vary depending on the prompts. This difference affects class embeddings in text encoders like OpenCLIP, making token-level modeling more difficult. Finally, a generalizable solution is required, as different T2I models integrate text encoders into T2I conditioning in varying ways.
+
+To achieve this, we propose PeCA, a transformer-based adapter attached with text encoders such as OpenCLIP and Google T5. PeCA generates personalized conditions by refining them using conditions tailored to each T2I model. PeCA is trained to reconstruct the target condition $y$ , which helps the model learn reproducibility from the given conditions. This enables PeCA to effectively capture meaningful information at the token-level and reproduce it using cross-attention layers, where $y$ serves as both the key and value. We use cosine similarity as a training objective to keep the distribution of the reconstructed condition similar to that of the original text encoder while maintaining generative capability. From a technical perspective, $y$ is obtained from the embeddings before applying normalization; and PeCA on Google T5 add a single linear layer both before and after the adapter to handle the large embedding dimension.
+
+# 4.4. Conditioning guidance
+
+PeCA effectively combines input conditions by concatenating them at the condition-level. However, since softmax is applied only once along the token axis, this limits its abl-
+
+| T2I Models | Text Encoders |
| OpenCLIP | Google |
| ViT-L | ViT-H | ViT-bigG | T5 |
| Stable Diffusion V1 | ✓ | | | |
| Stable Diffusion V2 | | ✓ | | |
| Stable Diffusion XL | ✓ | | ✓ | |
| Stable Diffusion V3 | ✓ | | ✓ | ✓ |
| Flux | ✓ | | | ✓ |
+
+Table 1. Text encoders used in popular foundation T2I models.
+
+ity to capture individual preferences precisely. Therefore, DrUM employs a guidance mechanism that enables detailed control over both preference intensity and personalization. This ensures that the generated outputs reflect user profiles accurately. To achieve this, the computation of attention scores for multiple reference conditions $\{y_{i}\}_{i = 1}^{n}$ and the target condition $y_{n + 1}$ is decoupled within the multi-head cross-attention module. Next, softmax is applied independently to each condition, and then overall personalization is modulated by a weighting parameter $\alpha$ . Formally, the guidance formula is as follows:
+
+$$
+w _ {i} = \left\{ \begin{array}{l l} (1 - \alpha) \cdot \operatorname {S o f t m a x} \left(s _ {i}\right), & \text {i f} i \in \text {t a r g e t}, \\ \alpha \cdot \frac {\operatorname {S o f t m a x} \left(s _ {i}\right) \cdot p _ {i}}{\sum_ {j} \operatorname {S o f t m a x} \left(s _ {j}\right) \cdot p _ {j}}, & \text {i f} i \in \text {r e f e r e n c e s}. \end{array} \right. \tag {2}
+$$
+
+Here, $w_{i}$ is the final attention weight for the index $i$ , and $s_{i}$ is calculated from the scaled dot product of the query and the key embeddings. Note that this mechanism also effectively accommodates cases that require separate class embedding (e.g., OpenCLIP).
+
+Additionally, inspired by classifier-free guidance [8], our method uses unconditional text embeddings as a input query to establish the central distribution of text encoders. This approach ensures consistent and precise personalization by applying weight-based adjustments to each condition.
+
+# 5. Experiments
+
+This section describes the training settings for DrUM, outlines the evaluation setup and the baselines, and demonstrates effectiveness through various observations.
+
+# 5.1. Training
+
+We train DrUM using the Conceptual Captions 3M (CC3M) dataset [24]. CC3M consists of 3.3 million images with captions covering diverse concepts (e.g., nature, animals, and objects). Since our personalized generation does not require images, we utilize only the set of prompts from CC3M.
+
+We also focused on four encoders associated with popular foundation T2I models, as listed in Table 1, despite DrUM's ability to integrate with most open-source text encoders. Using the same text encoders in the T2I models allows DrUM to scale seamlessly without training costs.
+
+For training DrUM, we use 10 cross-attention layers on a single Nvidia RTX 6000 Ada GPU with a batch size of 256, initialized the learning rate at $5 \times 10^{-4}$ , and employed the AdamW optimizer with a cosine annealing schedule over approximately 23K steps. For Google T5, we applied an encoding ratio of 4 to a linear layer both before and after PeCA. Note that we deliberately excluded the preference intensities $P$ and personalization degree $\alpha$ , encouraging DrUM to precisely reconstruct the target condition while aligning with the original text encoder distribution.
+
+# 5.2. Evaluation setup
+
+We conduct both quantitative and qualitative evaluations on two datasets introduced in previous studies [4, 25]: (i) Personalized Image Prompt1 (PIP): A large-scale dataset containing 3,115 users, each having 18 to $\sim 4,700$ historical prompts, along with images generated by Stable Diffusion V1. (ii) MovieLens Latest Small2 (ML): A dataset containing movie-watching records from 610 users, each having 20 to $\sim 2,600$ interactions/ratings. We convert each movie information (e.g., title, genre, keyword, and description) into prompts using TMDB3 API. Notably, we use only the prompts for our evaluation, as the dataset images are not directly associated with the results generated by various T2I models from the given prompts. Additionally, we select the two most recent historical entries for each user, following the process in [4].
+
+For quantitative evaluation, we measure the CLIP score and text alignment (Text align) between the personalized results and prompts by using the CLIP similarity $\mathrm{Sim}_{\mathrm{CLIP}}(*)$ :
+
+$$
+\operatorname {S i m} _ {\mathrm {C L I P}} \left(\mathbf {e}, \mathbf {r} _ {i}, p _ {i}\right) = \frac {\mathbf {e} \cdot \mathbf {r} _ {i}}{\| \mathbf {e} \| \| \mathbf {r} _ {i} \|} \cdot p _ {i} \tag {3}
+$$
+
+where $\mathbf{e}$ is a CLIP embedding, $\mathbf{r}_i$ is the CLIP embedding for index $i$ , and $p_i$ is the corresponding preference intensity. The CLIP score and Text align are set by defining $\mathbf{e}$ as a personalized generated image and a personalized T2I condition, respectively. Both metrics are averaged over target and historical text prompts $\{\mathbf{r}_i\}$ .
+
+For foundation T2I models, we use Stable Diffusion V1/V2/XL/V3 for quantitative evaluation, while qualitative case studies are conducted with Stable Diffusion V3 and FLUX. In terms of Text align, we employ only OpenCLIP text encoders ViT-L/H/bigG as they contain class tokens. Notably, the sampling ratio for user profiles was set to $10\%$ . The personalization degree $\alpha$ was set to 0.3 in PIP and 0.1 in ML for ensuring the target's originality, and the preference intensities (ratings) in ML were only applied as weights in the guidance mechanism and metrics.
+
+| CLIP score ↑ | PIP | ML |
| Target | History | Imp | Target | History | Imp |
| Stable Diffusion V1 | - | 20.52 | 10.89 | - | 31.27 | 12.27 | - |
| FABRIC | 24.33 | 15.85 | +32.04% | 30.80 | 12.13 | -1.35% |
| TV | 22.62 | 14.65 | +22.40% | 30.02 | 11.95 | -3.31% |
| PMG | - | - | - | 27.03 | 12.21 | -7.03% |
| DrUM | 25.13 | 16.03 | +34.83% | 29.49 | 13.07 | +0.38% |
| Stable Diffusion V2 | - | 21.20 | 11.71 | - | 33.32 | 11.30 | - |
| FABRIC | 23.67 | 16.33 | +25.61% | 25.64 | 10.27 | -16.05% |
| TV | 23.38 | 15.50 | +21.34% | 31.58 | 11.28 | -2.68% |
| PMG | - | - | - | 27.81 | 11.15 | -8.93% |
| DrUM | 25.82 | 17.27 | +34.68% | 32.25 | 11.96 | +1.34% |
| Stable Diffusion XL | - | 23.26 | 13.64 | - | 33.89 | 8.92 | - |
| FABRIC | - | - | - | - | - | - |
| TV | 25.44 | 17.19 | +17.71% | 32.04 | 8.69 | -3.97% |
| PMG | - | - | - | 28.63 | 9.24 | -5.95% |
| DrUM | 26.77 | 18.16 | +24.13% | 29.12 | 10.93 | +4.26% |
| Stable Diffusion V3 | - | 22.60 | 12.75 | - | 37.69 | 9.76 | - |
| FABRIC | - | - | - | - | - | - |
| TV | 23.85 | 15.42 | +13.24% | 35.83 | 9.37 | -4.47% |
| PMG | - | - | - | 32.48 | 9.67 | -7.39% |
| DrUM | 25.14 | 15.87 | +17.86% | 30.17 | 10.61 | -5.60% |
+
+(a) CLIP score
+
+| Text align ↑ | PIP | ML |
| Target | History | Imp | Target | History | Imp |
| OpenCLIP ViT-L | - | 100.00 | 52.60 | - | 100.00 | 34.16 | - |
| TV | 68.50 | 44.65 | -23.32% | 86.14 | 30.41 | -12.42% |
| PMG | - | - | - | 67.75 | 29.00 | -23.67% |
| DrUM | 96.42 | 61.24 | +6.42% | 99.48 | 36.48 | +3.13% |
| OpenCLIP ViT-H | - | 100.00 | 42.10 | - | 100.00 | 36.05 | - |
| TV | 64.79 | 37.86 | -22.63% | 85.88 | 33.93 | -10.01% |
| PMG | - | - | - | 64.72 | 29.94 | -26.12% |
| DrUM | 95.91 | 50.81 | +8.30% | 99.56 | 38.21 | +2.77% |
| OpenCLIP ViT-bigG | - | 100.00 | 47.56 | - | 100.00 | 32.90 | - |
| TV | 68.03 | 41.69 | -22.15% | 86.82 | 30.21 | -10.68% |
| PMG | - | - | - | 69.66 | 29.07 | -21.00% |
| DrUM | 96.41 | 55.85 | +6.92% | 99.58 | 34.91 | +2.84% |
+
+# 5.3. Baselines
+
+As mentioned in Section 2.2 and 3.2, personalized generation should effectively consider individual preferences to provide both creativity and diversity with minimal user intervention. However, ViPer [22] requires detailed user comments, while Pigeon [31] relies on LaViT's built-in LDM with reference images, complicating its general evaluation on PIP and ML. Therefore, we selected FABRIC [28], TV [4], and PMG [25] as baselines for evaluating various foundation T2I models. FABRIC's reference pairs were determined based on preference intensity, when unavailable, the latest image was used as a positive. TV implemented ChatGPT 4o instead of 3.5 due to version issue to rewrite prompts with more advanced insight.
+
+
+Figure 3. Sampling performance of personalization on Text align for different methods using OpenCLIP ViT-L. Random selects randomly and uniform choices evenly.
+
+
+
+
+
+
+
+(b) Text align
+Table 2. Overall performance of DrUM compared to baselines. Imp means the average performance improvement rate compared to original models, and bold indicates the highest performance.
+
+| CLIP score ↑ | PIP | ML |
| Target | History | Imp | Target | History | Imp |
| - | 20.52 | 10.89 | - | 31.27 | 12.27 | - |
| DrUM | 25.13 | 16.03 | +34.83% | 29.49 | 13.07 | +0.38% |
| w/o S | 25.49 | 15.85 | +34.88% | 29.56 | 13.06 | +0.46% |
| w/o G | 19.04 | 17.46 | +26.55% | 22.74 | 14.49 | -4.64% |
| w/o S & G | 18.13 | 18.85 | +30.71% | 21.23 | 15.44 | -3.15% |
+
+Table 3. Ablation study on the effect of removing sampling $S$ and guidance mechanism $G$ on CLIP score using Stable Diffusion V1 and OpenCLIP ViT-L.
+
+# 5.4. Quantitative analysis
+
+Effectiveness comparison. Table 2 presents the personalized generation performance across various T2I models compared to baselines. In particular, ML consists of complex and diverse product information, leading to lower performance compared to PIP. Overall, DrUM demonstrates superior performance. However, with Stable Diffusion V3 on ML, the CLIP score and Text align intersect. This can be semantically attributed to the accumulation of complex product information within the limited canvas of the image, as text alignment increases with enhanced generative capability. Moreover, since the ML dataset contains diverse movie information, even small adjustments can significantly impact the target performance across all baselines. Notably, the enhanced Text align indicates that DrUM effectively generates content that aligns with both the target and historical preferences, even when the CLIP score is similar.
+
+Impact of sampling method. Figure 3 represents how different sampling methods affect personalization performance as the sampling ratio changes. Coreset sampling consistently achieves excellent performance across all ratios. At a $10\%$ sampling ratio, it shows superior overall performance, so we select it for user profiling. As a result, our coreset sampling method effectively and efficiently integrates more of each user's history into their profile.
+
+Ablation study. Table 3 presents an ablation study on the effect of removing modules from DrUM. When only
+
+
+Figure 4. Qualitative comparison using multiple prompts with baselines. Key keywords extracted from historical user prompts.
+
+
+Figure 5. Prompt-based style transfer using a single style prompt on Stable Diffusion V3. User's interest illustrates the results from single style prompts.
+
+$G$ is removed, a significant drop in the target score is observed, highlighting the essential role of guidance mechanism in balancing between target and history. When both $S$ and $G$ are removed, DrUM shows a convergence of performance between target and history. This is likely due to an overabundance of historical information, which causing the results to lose a clear separation. Although removing only $S$ leads to slight performance changes, sampling is crucial in reducing computational costs and prioritizing the most relevant user information. Thus, DrUM not only enhances efficiency but also better preserves the balance between personalization and target fidelity.
+
+# 5.5. Case study
+
+Qualitative comparison. Figure 4 compares personalized content on Stable Diffusion V3 and Flux with the baselines. TV is a general approach but struggles to incorporate user preferences, and often distorts original content in ML. PMG captures key user preferences better than TV, but relies on keyword-centered modeling in ML, which lacks detail. In contrast, DrUM effectively preserves the originality while precisely reflecting user preferences. As shown in the quantitative results, it is visually demonstrated that higher Text align provides more effective personalization, even when the CLIP score is similar. Furthermore, for user 71263, Flux fails to generate 'clothes', whereas DrUM successfully satisfies this requirement while aligning with user preferences. This indicates that personalized generation not only reflects individual preferences but also enhances originality.
+
+Real-world scenarios. We introduce two additional scenarios for real-world users. Figure 5 shows prompt-based style transfer. Rather than constraining users to write detailed prompts within a limited token length, we recommend separating prompts into target and visual attributes. This approach enables a more comprehensive representation of target prompts without requiring detailed information such as style, texture. Figure 6 illustrates prompt-based multi-subject transfer. DrUM effectively captures both single and multiple subjects, while preserving their characteristics. Similar to the previous scenario, this is easily achieved by separating subject attributes in the prompt.
+
+Personalization degree. DrUM enables flexible adjustment of personalization degree at the latent-level. Figure 7 shows how personalized results change between two different prompts on the given degree. In Figure 7(a), the background and season are semantically interpolated, while in Figure 7(b), the occupation and age are blended. Even simple adjustments yield effective personalized results.
+
+# 5.6. Discussion
+
+In our experiments, DrUM showed a slight decrease in ML, likely due to the complexity of product information. Overincorporating rich details can inadvertently compromise the
+
+
+Figure 6. Prompt-based subject transfer using multiple prompts on Flux.
+
+
+Figure 7. Impact of personalization degree $\alpha$ on different prompts.
+
+output. In contrast, as shown in PIP, DrUM achieves very high performance with natural prompts commonly used by real-world users. This indicates that personalization should be applied cautiously to products or similarly complex descriptions. We also note that adjusting the number of references or refining token-level information may be beneficial, though this remains to be explored further.
+
+On the other hand, our architecture employs only a small number of cross-attention layers, which may not fully capture all patterns. Our objective was to showcase the potential of direct modeling without relying on large-scale models and to assess the reproducibility of the embeddings derived through transformers. While our approach provides promising results, a more in-depth exploration with deeper architectures remains a subject for future research.
+
+# 6. Conclusion
+
+We propose DrUM, a novel method for personalized generation via condition-level modeling to precisely integrate individual user preferences into T2I diffusion models. Experiments demonstrate that DrUM's modules effectively generate high-quality personalized synthesis results, while ensuring creativity and diversity across various foundation T2I models, without additional fine-tuning. Future work will explore more optimized architectures and modeling approaches for complex inputs like product information.
+
+# Acknowledgements
+
+This work was supported in part by Institute of Information & communications Technology Planning & Evaluation (IITP) grants funded by the Korea government (MSIT) (No. 2022-0-00448/RS-2022-II220448, Deep Total Recall: Continual Learning for Human-Like Recall of Artificial Neural Networks, and No. RS-2022-00155915, Artificial Intelligence Convergence Innovation Human Resources Development (Inha University)), and in part by INHA UNIVERSITY Research Grant.
+
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+# Drawing Developmental Trajectory from Cortical Surface Reconstruction
+
+Wenxuan Wu $^{1,2}$ Ruowen Qu $^{1}$ Zhongliang Liu $^{1}$ Zhuoyan Dai $^{1}$ Dongzi Shi $^{1}$ Sijin Yu $^{1}$ Tong Xiong $^{1}$ Shiping Liu $^{2}$ Xiangmin Xu $^{1,3}$ Xiaofen Xing $^{1,*}$ Xin Zhang $^{1,*}$ $^{1}$ South China University of Technology $^{2}$ BGI Research, Hangzhou $^{3}$ Foshan University $\{\mathbf{x} \mathbf{f} \mathbf{x} \mathbf{i} \mathbf{g},$ eexinzhang}@scut.edu.cn
+
+# Abstract
+
+Diffeomorphic transformation-based cortical surface reconstruction typically involves a series of deformation processes to extract the cerebral cortex from brain magnetic resonance images (MRI). While most methods are designed for adult brains using Neural Ordinary Differential Equations (NODE) with fixed step sizes, the neonatal brain, which exhibits dramatic changes in cortical folding patterns early in life, requires a more adaptive approach. To address this, we develop a dual-task framework to directly characterize the brain development trajectory through processes of cortical surface reconstruction. For white matter (inner surfaces), we employ an Age-Conditioned ODE with adaptive step sizes. It is initially trained on a limited set of longitudinal paired data to establish a coarse trajectory, which is then refined through sample training of single-point data and knowledge distillation. For the pial surfaces (outer surfaces), we position the midthickness surfaces as intermediates and employ a cycle-consistent semi-supervised training strategy to depict a coherent brain development trajectory between the inner and outer surfaces. Our approach achieves precise developmental prediction directly on triangular meshes. Furthermore, by enhancing interpretability at each stage of the deformation process, this approach improves the applicability of diffeomorphic transformation-based methods. The proposed method has demonstrated state-of-the-art performance in modeling developmental trajectories and cortical surface reconstruction within the developing Human Connectome Project dataset (dHCP). The Code will be available at https://github.com/SCUT-Xinlab/DDT-from-CSR.
+
+# 1. Introduction
+
+In the early stages of fetal or neonatal life, the cerebral cortex undergoes significant morphological changes. With advancements in medical imaging technologies such as Magnetic Resonance Imaging (MRI), non-invasive methods can be used clinically to collect more early-life data, aiding in
+
+
+Figure 1. Comparison of our ACDE and traditional ODE
+
+the elucidation of the fundamental mechanisms and patterns of brain development. The highly folded nature of the cerebral cortex makes it challenging to accurately represent this complex structure at the voxel level. Therefore, cortical surface reconstruction is commonly employed to extract the inner (white matter) and outer (pial) surfaces, representing the cerebral cortex in a precise 3D triangular mesh structure.
+
+Typically, the cortical surfaces are generated through the neuroimaging processing pipeline [6, 7, 11, 12, 26, 30] involving skull stripping, tissue segmentation, hemisphere separation, topology correction, and surface reconstruction. This multi-step procedure is frequently time-consuming, thereby posing challenges in processing substantial volumes of clinical data. With the rapid advancement of deep learning [8, 13, 17, 19, 29], numerous studies [1, 2, 5, 14, 20, 33] have integrated deep neural networks, enabling precise reconstruction of cortical surfaces within a few seconds. The diffeomorphic transformation-based method [18, 21, 22, 25, 34] [18, 22, 25] breaks the traditional two-stage pipeline of segmentation followed by reconstruction. It generates a velocity field from brain MRI scans to directly
+
+drive an initial template mesh to smoothly deform into the final surfaces. Due to the complex folding pattern of the cerebral cortex, this process is typically modeled by Neural Ordinary Differential Equations (NODE) and solved using fixed multiple steps to reduce self-intersections. While these diffeomorphic transformation-based approaches have demonstrated superior performance on several public adult datasets[16, 28], two main issues persist in modeling the developmental trajectory of the cerebral cortex.
+
+Since cerebral cortex varies smoothly among adults with different age, a fixed step integration scheme is sufficient to cover all age groups. However, in the first few postnatal periods, the cortex undergoes rapid development with significant growth in terms of many morphology measurements such as sulcal depth [9, 10, 24, 27]. This leads to evident structural differences among newborns at different post-menstrual ages (PMA). Therefore, existing methods utilizing a fixed step deformation is unable to capture these structure difference in newborns. Furthermore, frequent neonatal head movements significantly increase the challenge of acquiring high-quality brain MRI. Additionally, due to the high costs of scanning and the complexities of follow-up, weekly longitudinal tracking scans are difficult to sustain. As a result, current neonatal brain imaging datasets are limited in sample size, with most data collected at a single time point. Even for longitudinal tracking data, there are typically only two time points available. Given the rapid weekly changes in the neonatal cerebral cortex, accurately analyzing the longitudinal changes remains challenging, even with fast and precise reconstruction algorithms.
+
+Given these two issues, we rethink the diffeomorphic transformation-based cortical surface reconstruction (as shown in Figure 1). The ODE models a deformation function across an independent variable $t \in [0,T]$ , where $t = 0$ represents a smooth initial template that progressively transforms into $t = T$ , the final reconstructed surface with a complex folded structure. Similar to this process, brain development progresses with age, transitioning from a smooth surface to exhibit a complex folding pattern. However, in contrast to the fixed-step deformation process in reconstruction where surfaces at intermediate times lack substantial significance, each point along the developmental trajectory holds genuine importance.
+
+Inspired by this, we propose a two-stage framework from white matter to pial surface, drawing brain development trajectory from cortical surface reconstruction. In the first stage, we propose an Age-conditioned ODE (ACDE) with adaptive step to relax the constraint of fixed step in the diffeomorphic transformation-based approach. It models individual-level neonatal brain development, enabling the extraction of cerebral cortex at multiple time points from a single brain MRI scan. Furthermore, to address the challenge of limited longitudinal data in effectively establish
+
+ing developmental trajectories, we propose a Progressive Curriculum Incremental Learning (PCIL) strategy. This approach gradually integrates single-time-point data into ACDE training, enabling continuous refinement of surface representation while maintaining a balanced focus on developmental modelling. Concurrently, we propose a self-knowledge distillation framework employs cyclic iterations to further refine this dual task. In the second stage, we propose a parameter-efficient architecture that takes constructed white matter surfaces as inputs and progressively generates midthickness and pial surfaces at multiple time points through two simple MLPs and a lightweight 3D U-Net. To better exploit a large volume of unlabeled data, we propose a semi-supervised cyclic consistency training framework that enhances prediction and reconstruction accuracy without additional training costs. In summary, we have redefined the ODE process in diffeomorphic transformation-based cortical surface reconstruction to model neonatal brain development, providing an interpretable deformation process and being the first to achieve surface-level development prediction.
+
+# 2. Method
+
+As shown in Figure 2, we propose a two-stage framework that simultaneously reconstructs cortical surfaces and generates developmental trajectories from neonatal brain MRI. The first stage achieves this dual task for the white matter surfaces, while the second stage extends the reconstruction and trajectory modeling to the pial surfaces.
+
+# 2.1. Stage 1: Modeling Development Trajectory for the White Matter Surface
+
+# 2.1.1. Age-conditioned ODE.
+
+The cortical surface reconstruction process based on diffeomorphic transformation is typically modeled by an ODE. Through predefined iteration steps, numerical solutions gradually deform the initial smooth cortical template into the reconstructed surface. Inspired by the similarity between this process and brain development, we propose an ACDE with adaptive iteration steps to directly model white matter surface development while simultaneously achieving surface reconstruction. Considering the formation period of cortical folding patterns and the distribution of PMA in the dHCP dataset, the ACDE is employed for model development across PMA values ranging from 29 to 45 weeks. The independent variable $t \in [0,T]$ in ACDE represents the temporal axis of the developmental trajectory, while the solution $S_{t}^{w} \in \mathbb{R}^{N \times 3}$ represents the white matter surface geometry at time $t$ .
+
+In practical applications, we characterize the developmental trajectory of the white matter surface in weekly increments. Given a PMA $a \in \mathcal{A} = \{29, 30, \ldots, 45\} \subseteq \mathbb{Z}$
+
+
+a) Stage 1: White Matter Surface Reconstruction
+Figure 2. The architecture of the proposed framework.
+
+spanning 17 discrete weeks), we first uniformly select $M = 17$ discrete time points $\{t_a\}_{a=29}^{45} \in [0, T]$ . To ensure strict temporal ordering, these points are generated by partitioning $[0, T]$ into $M + 1$ equal subintervals, such that:
+
+$$
+t _ {a} = \frac {(a - 2 8) T}{1 8}, \quad \forall a \in \{2 9, 3 0, \dots , 4 5 \}, \tag {1}
+$$
+
+which guarantees $0 < t_{29} < t_{30} < \dots < t_{45} < T$ . Subsequently, the mapping $f: \mathcal{A} \to \{t_a\}$ is implicitly constructed through the subscript notation $t_a$ , establishing a natural one-to-one correspondence between each biological PMA value $a$ in developmental trajectory and its associated normalized time variable $t_a$ in the ACDE.
+
+Given a smooth template $S_0$ as the initial state for brain development and a neonatal brain MRI with PMA at $a$ week $I_{a} \in \mathbb{R}^{H \times W \times D}$ as the condition, the solution of ACDE is computed as follows:
+
+$$
+\frac {d \phi}{d t} = V \left(F _ {1}, t, a\right), \quad \phi_ {0} = S _ {0}, \quad F _ {1} = \mathcal {U} _ {1} \left(I _ {a}\right) \tag {2}
+$$
+
+$$
+\hat {S} _ {t} ^ {w} = S _ {0} + \int_ {0} ^ {t} V \left(F _ {1}, s, a\right) \mathrm {d} s, \quad t \in [ 0, t _ {a} ] \tag {3}
+$$
+
+where $\phi$ signifies the surface-level developmental trajectory, $\mathcal{U}_1$ is a 3D U-Net that converts the input MRI $I_{a}$ into a diffeomorphic velocity field $F_{1}$ , which drives white matter surface deformation through the time- and age-dependent velocity field $V(F_{1},t,a)$ . The solution set $\hat{\boldsymbol{S}}^{w} = \{\hat{S}_{t_k}^w\}_{k = 1}^a$ encapsulates: 1) the terminal state $\hat{S}_{t_a}^w$ representing the reconstructed white matter surface associated with $\pmb{I}_{a}$ , and 2) intermediate states $\{\hat{S}_{t_k}^w\}_{k = 1}^{a - 1}$ constituting the developmental trajectory. Here, $t_a$ denotes the temporal endpoint of the numerical solution process, corresponding to the biological age at week $a$ .
+
+We numerically solve the ACDE using the Euler method, where the state evolves as $S_{n + 1} = S_n + h\Delta S_n$ for discrete time steps $n \in [0,N]$ . Here, $n$ represents a discretization of continuous time $t$ , defined by $t = nh$ with step size $h = T / N$ . Each instance $t_a$ maps to a discrete step $n_a = \lfloor t_a / h \rfloor$ , where $S_{n_a}$ corresponds to the white matter surface PMA at $a$ week. The $\Delta S_n$ representing time-varying velocity field [22] is computed through a two-stage process: First, the input $I_a$ is transformed by $\mathcal{U}_1$ into a multi-static velocity field $F_1 \in \mathbb{R}^{K \times H \times W \times D \times 3}$ , where $K$ represents the number of components. Second, an MLP
+
+generates an attention weight vector $w \in \mathbb{R}^{K \times 1}$ by taking as input the concatenation of the PMA value $a$ and the current step $n$ , enabling dynamic aggregation of the velocity field via $w^{\top} F_1 \in \mathbb{R}^{H \times W \times D \times 3}$ . Finally, the aggregated velocity field is transformed into $\Delta S_n \in \mathbb{R}^{N \times 3}$ via linear interpolation based on the coordinates of $S_n$ .
+
+# 2.1.2. Training Strategy.
+
+The ACDE accommodates flexible training with multi-time point and single time point data. For training on single time point data, let $\hat{S}_{t_a}^w$ denote the reconstructed white matter surface at PMA $a$ week, and $S_{t_a}^w$ be the corresponding ground-truth. The surface-level loss $\mathcal{L}_s$ is defined as:
+
+$$
+\mathcal {L} _ {s} = \mathcal {L} _ {c} \left(\hat {S} _ {t _ {a}} ^ {w}, S _ {t _ {a}} ^ {w}\right) + \alpha \mathcal {L} _ {\text {l a p}} \left(\hat {S} _ {t _ {a}} ^ {w}\right) + \beta \mathcal {L} _ {n} \left(\hat {S} _ {t _ {a}} ^ {w}, S _ {t _ {a}} ^ {w}\right), \tag {4}
+$$
+
+where $\mathcal{L}_c$ , $\mathcal{L}_{\mathrm{lap}}$ , and $\mathcal{L}_n$ represent Chamfer Distance, Laplacian Smoothness, and Normal Consistency, respectively, and $\alpha$ and $\beta$ balance geometric accuracy and topological regularity. For paired data at time points $\{t_{a_1}, t_{a_2}\}$ , where $t_{a_1} < t_{a_2}$ , the ACDE conditions on the brain MRI $I_{a_2}$ scanned at week $a_2$ to reconstruct $\hat{S}_{t_{a_2}}$ and generate $\hat{S}_{t_{a_1}}$ along the developmental trajectory via numerical solution. This process yields the composite training objective:
+
+$$
+\min _ {\theta} \mathcal {L} _ {s} \left(\hat {S} _ {t _ {a _ {2}}} ^ {w}, S _ {t _ {a _ {2}}} ^ {w}\right) + \mathcal {L} _ {s} \left(\hat {S} _ {t _ {a _ {1}}} ^ {w}, S _ {t _ {a _ {1}}} ^ {w}\right). \tag {5}
+$$
+
+However, in the neonatal brain MRI dataset, the longitudinal subset $\mathcal{D}_L$ and the single-timepoint subset $\mathcal{D}_S$ exhibit severe data imbalance, with $N_S \gg N_L$ . Such imbalance may bias the model toward prioritizing cortical surface reconstruction rather than simultaneously achieving the dual task of brain development modeling and reconstruction when jointly trained on single and multi-timepoint data. To address this, we propose Progressive Curriculum Incremental Learning (PCIL), which implements a phased curriculum that gradually introduces single-timepoint data $\mathcal{D}_S$ at ratios $\gamma_k \in \{0, 0.25, 0.5, 0.75, 1\}$ into the longitudinal subset $\mathcal{D}_L$ , formalized as $\mathcal{D}_{\mathrm{train}}^{(k)} = \mathcal{D}_L \cup \gamma_k \mathcal{D}_S$ . The ratio $N_S / N_L$ in $\mathcal{D}_{\mathrm{train}}^{(k)}$ reflects the difficulty of brain development learning for the ACDE. Each stage is trained to convergence before progressing, ensuring robust learning of developmental dynamics from $\mathcal{D}_L$ while incrementally enhancing surface-level representation capabilities from $\mathcal{D}_S$ . This strategy preserves trajectory consistency through persistent longitudinal constraints and improves surface reconstruction precision, ultimately enabling the ACDE to synthesize biologically plausible growth trajectories from sparse heterogeneous data.
+
+# 2.1.3. Knowledge Distillation.
+
+Although our training strategy mitigates data imbalance, the multi-stage learning paradigm risks overfitting in developmental trajectory modeling, which may compromise surface representation. To further address data imbalance, we
+
+additionally propose a self-knowledge distillation framework alongside PCIL. In this framework, a teacher model $M_{t}$ trained via PCIL, generates developmental trajectories for each single timepoint data $S_{t_a}^w \in \mathcal{D}_S$ , thereby constructing an augmented pseudo-longitudinal subset $\mathcal{D}_L^{\mathrm{syn}}$ . The composite training set $\mathcal{D}_{\mathrm{train}} = \mathcal{D}_L \cup \mathcal{D}_L^{\mathrm{syn}}$ is used to guide an untrained student model $M_{s}$ (which shares the same architecture as $M_{t}$ ) toward enhanced performance. Specifically, given an observation time point $t_{a_2}$ , we first randomly select a time point $t_{a_1}$ (where $a_1 < a_2$ ) and use $M_{t}$ to generate the corresponding white matter surface $S_{a_1}^w$ along the developmental trajectory. The knowledge distillation loss for training $M_{s}$ integrates multi-time supervision:
+
+$$
+\mathcal {L} _ {\mathrm {k d}} = \mathcal {L} _ {r} (\hat {S} _ {t _ {a _ {1}}} ^ {w}, S _ {t _ {a _ {1}}} ^ {w}) + \mathcal {L} _ {r} (\hat {S} _ {t _ {a _ {2}}} ^ {w}, S _ {t _ {a _ {2}}} ^ {w}), \tag {6}
+$$
+
+where $\hat{S}_{t_{a_2}}^w$ denotes surfaces reconstructed by $M_s$ , $\hat{S}_{t_{a_1}}^w$ represents surfaces generated by $M_s$ , and $S_{t_{a_2}}^w$ corresponds to the ground truth. Notably, since the majority of single-timepoint data correspond to term newborns (PMA $>37$ weeks), we impose the temporal constraint $a_1 < \min(37, a_2)$ . This ensures that the generated early-timepoint surfaces $S_{a_1}^w$ precede the term period, thereby maintaining a balanced distribution of surfaces across different age groups in the training set.
+
+To further enhance pseudo-trajectory accuracy, the teacher model undergoes progressive refinement via exponential moving averaging (EMA) of student parameters. Let $\theta_t^{(k)}$ and $\theta_s^{(k)}$ denote the teacher and student parameters at update step $k$ , respectively. The EMA operation is defined as:
+
+$$
+\theta_ {t} ^ {(k + 1)} \leftarrow \alpha_ {\mathrm {e m a}} \theta_ {t} ^ {(k)} + (1 - \alpha_ {\mathrm {e m a}}) \theta_ {s} ^ {(k)}, \tag {7}
+$$
+
+where $\alpha_{\mathrm{ema}}$ serves as a hyperparameter to control the update rate of teacher model.
+
+# 2.2. Stage 2: Extension from White Matter to Pial Developmental Trajectory
+
+In this section, we deform ACDE-generated white matter surfaces $\{S_{t_k}^w\}_{k = 1}^a$ into pial surfaces $\{S_{t_k}^p\}_{k = 1}^a$ , achieving the final cortical surface reconstruction and development trajectory modeling. We achieve this process through two cascaded fully-connected networks $\mathrm{FC}_1$ and $\mathrm{FC}_2$ . Given the predicted white matter surface $\hat{S}_{t_{a_1}}^w$ and a neonatal brain MRI $I_{a_2}$ (where $t_{a_1} \leq t_{a_2}$ ), $\mathrm{FC}_1$ firstly generates the mid-thickness surface $\hat{S}_{t_{a_1}}^m$ . Subsequently, $\mathrm{FC}_2$ leverages $\hat{S}_{t_{a_1}}^m$ and the same brain MRI $I_{a_2}$ to synthesis the pial surface $\hat{S}_{t_{a_1}}^p$ . Notably, the midthickness surface represents the midpoint of white matter and pial surfaces.
+
+Due to the similarity between the two stages $\mathrm{FC}_1$ and $\mathrm{FC}_2$ , we exemplify the computational workflow using $\mathrm{FC}_1$ as an example. $\mathrm{FC}_1$ synthesizes the mid-thickness surface $\hat{S}_{t_{a_1}}^m$ by processing concatenated features
+
+$$
+\left[ \hat {S} _ {t _ {a _ {1}}} ^ {w}, \mathbf {n} _ {t _ {a _ {1}}} ^ {w}, \mathbf {F} _ {t _ {a _ {1}}} \right] \in \mathbb {R} ^ {N \times 9} \tag {8}
+$$
+
+where $\mathbf{n}_{t_{a_1}}^w\in \mathbb{R}^{N\times 3}$ denotes vertex normals and $\mathbf{F}_{t_{a_1}}\in \mathbb{R}^{N\times 3}$ represents the time-varying velocity field derived in the same manner as ACDE.
+
+During the white-to-pial surface transformation stage, the issue of data imbalance persists. However, instead of employing the PCIL and Knowledge Distillation framework, we introduce a more elegant consistency loss $\mathcal{L}_c$ , which enables direct model training using the white matter surfaces generated by ACDE. Specifically, given a brain MRI $I_{a_2}$ , the input white matter surface $\hat{S}_{t_{a_1}}^w$ , the output mid-thickness surface $\hat{S}_{t_{a_1}}^m$ , and the pial surface $\hat{S}_{t_{a_1}}^p$ , the definition of $\mathcal{L}_c$ is as follows:
+
+$$
+\mathcal {L} _ {c} = \mathcal {L} _ {s} \left(\hat {S} _ {t _ {a _ {1}}} ^ {m}, \frac {1}{2} \left(\hat {S} _ {t _ {a _ {1}}} ^ {w} + \hat {S} _ {t _ {a _ {1}}} ^ {p}\right)\right). \tag {9}
+$$
+
+The $\mathcal{L}_c$ implements a self-supervised training strategy, enabling model optimization by constraining the outputs of $\mathrm{FC_1}$ and $\mathrm{FC_2}$ to align with the white matter surface in the absence of ground-truth data for developmental trajectories. This approach facilitates the inclusion of more early timepoint data in training, thereby balancing the dual tasks of cortical surface reconstruction and developmental trajectory modeling.
+
+Finally, a global loss $\mathcal{L}_g$ is proposed to constrain the average cortical thickness between the predicted surface and the ground truth (GT) surface, enabling rapid identification of the inflation range and facilitating more precise extension from white matter surface to pial surface.
+
+# 3. Experiments and Results
+
+# 3.1. Datasets and Pre-processing
+
+In our study, we utilized 877 T2-weighted brain MRI images from the third release of the developing Human Connectome Project (dHCP) [3, 15, 23]. These scans are acquired from newborns with a PMA ranging from 29 to 45 weeks. In the dHCP dataset, most of the cases are full-term infants (PMA $>37$ weeks), scanned only once at birth. A small number of preterm infants undergo two or more scans, with one at birth and another when they reach full-term status. All the brain images are processed using the dHCP structural processing pipeline to extract the corresponding cortical surfaces and features for downstream analysis.
+
+The deformation process of our model is in the MNI spacing, which all the input brain images and pseudo ground-truth cortical surfaces are aligned to the MNI152-1mm template. In paired data, we used preterm surface as pseudo ground-truth at early time point for the brain image scanned in term. Therefore, these preterm surfaces are first registered with the intra-subject surfaces at term and subsequently transformed to the MNI spacing.
+
+The dataset was divided into training $(60\%)$ , validation $(10\%)$ , and test $(20\%)$ sets. It is worth noting that most of
+
+cases are single time point data, with a few cases are paired data (less than $20\%$ for each set).
+
+# 3.2. Developmental Trajectory Generation
+
+# 3.2.1. Experiment Setup and Evaluation Metrics.
+
+The developmental trajectory generation experiment comprises two parts: direct and indirect validation. For direct validation, paired data are utilized to assess the alignment between the predicted trajectory surface and the ground-truth (GT) surface. Since existing methods [4, 31, 32] model cerebral cortex developmental trajectories at the feature level, morphological features of the predicted and GT cortical surfaces are extracted using FreeSurfer [7] and mapped onto a standardized spherical space for fair comparison. Sulcal depth and cortical thickness serve as proxies for the white matter and pial surfaces, respectively. The developmental relevance of the generated surfaces is assessed using the Pearson Correlation Coefficient (PCC), Mean Absolute Error (MAE), and Cosine Similarity (COS).
+
+For the large cohort of single-time-point subjects lacking GT developmental trajectory data, the experiment indirectly validates model performance at both population and individual levels. For population-level evaluation, a neonatal PMA prediction model [4] is employed to ascertain the age segment of each generated surface. The MAE between the predicted PMA and the PMA on the developmental trajectory is calculated to assess the longitudinal consistency. For individual-level evaluation, we postulate that the same brain should exhibit consistent brain regions across different time points. Accordingly, we employed a neonatal brain parcellation model [4] to both the generated surface along the developmental trajectory and the corresponding ground-truth surface at the final time point. The Dice Similarity Coefficient (DSC) was calculated to evaluate the anatomical consistency between the surface on the developmental trajectory and the reconstructed surface.
+
+# 3.2.2. Comparative Results.
+
+In this section, the proposed method is compared with three brain development prediction approaches: S-UNet [4], S-Transformer [32], and DITSAA [31]. These methods can predict longitudinal cortical features for infants aged 0-2 years, such as sulcal depth, on a monthly basis. To adapt these methods for a neonatal dataset, age information is incorporated in weeks to generate the development trajectory. Table 1 displays the results on the test set paired data, with the proposed method achieving a $17\%$ improvement in MAE, $1.47\%$ improvements in PCC and $1.15\%$ improvements for COS, compared to the second-best method. Despite not directly performing feature-level longitudinal prediction, the proposed method demonstrates exceptional performance. The sulcal depth computed from the white matter surface generated by our method reveals richer and more re
+
+Table 1. Results of morphological features of the cerebral cortex estimation.
+
+| Method | Sulcal Depth | Cortical Thickness |
| PCC ↑ | MAE ↓ | COS ↑ | PCC ↑ | MAE ↓ | COS ↑ |
| S-UNet | 0.951 ± 0.061 | 0.532 ± 0.224 | 0.952 ± 0.060 | 0.858 ± 0.035 | 0.196 ± 0.022 | 0.976 ± 0.006 |
| S-Trans | 0.946 ± 0.063 | 0.565 ± 0.170 | 0.947 ± 0.062 | 0.851 ± 0.041 | 0.199 ± 0.078 | 0.976 ± 0.006 |
| DITSAA | 0.952 ± 0.047 | 0.578 ± 0.319 | 0.956 ± 0.047 | 0.854 ± 0.037 | 0.192 ± 0.020 | 0.977 ± 0.004 |
| Proposed | 0.965 ± 0.026 | 0.451 ± 0.075 | 0.963 ± 0.025 | 0.866 ± 0.027 | 0.173 ± 0.029 | 0.987 ± 0.003 |
+
+
+Figure 3. Visualization of generated white matter surfaces and corresponding ground-truth.
+
+Table 2. The results of PMA estimation and brain pracellation.
+
+| PMA | MAE ↓ | Dice ↑ |
| 29w | 0.949 ± 0.723 | 0.852 ± 0.022 |
| 30w | 0.877 ± 0.682 | 0.880 ± 0.015 |
| 31w | 0.796 ± 0.596 | 0.889 ± 0.013 |
| 32w | 0.702 ± 0.541 | 0.911 ± 0.012 |
| 33w | 0.739 ± 0.714 | 0.910 ± 0.011 |
| 34w | 0.937 ± 0.899 | 0.917 ± 0.010 |
| 35w | 1.094 ± 0.942 | 0.924 ± 0.010 |
| 36w | 1.159 ± 0.891 | 0.932 ± 0.009 |
| 37w | 1.078 ± 0.858 | 0.942 ± 0.009 |
| 38w | 0.896 ± 0.857 | 0.956 ± 0.010 |
| 39w | 0.908 ± 0.738 | 0.975 ± 0.008 |
| 40w | 1.187 ± 0.552 | 0.976 ± 0.007 |
+
+alistic details compared to SU-Net, demonstrating both the enhanced developmental modeling capability and superior
+
+surface representation of our approach. Figure 4 presents the visualization of sulcal depth generated by SU-Net, the proposed method, and the corresponding GT. Furthermore, while all these methods predict changes at a single time point, the ODE-based approach of this study generates predictions for multiple time points within one deformation process, offering a more elegant solution.
+
+It is noteworthy that the cortical folding pattern is largely established at full-term birth, making SUNet-based methods appear reasonable for directly predicting morphological features for infant cortical analysis. However, in neonates and fetuses, the cortical folding pattern undergoes significant changes early in development, which cortical features may not sufficiently represent. Figure. 3 demonstrates the predicted surfaces at multiple time points, demonstrating that our mesh-based development trajectory generation effectively captures these changes.
+
+# 3.2.3. Results of Indirect Validation.
+
+In this section, we validate the generated brain development trajectory at both population and individual levels. The
+
+Table 3. Comparative results of neonatal cortical surface reconstruction on dHCP.
+
+| Method | White Matter Surface | Pial Surface |
| ASSD (mm) ↓ | HD (mm) ↓ | SIF (%) ↓ | ASSD (mm) ↓ | HD (mm) ↓ | SIF (%) ↓ |
| Corticalflow | 0.137 ± 0.022 | 0.286 ± 0.059 | 0.007 ± 0.002 | 0.149 ± 0.041 | 0.331 ± 0.174 | 0.097 ± 0.029 |
| CFPP | 0.142 ± 0.023 | 0.298 ± 0.062 | 0.002 ± 0.003 | 0.132 ± 0.024 | 0.287 ± 0.056 | 0.024 ± 0.010 |
| CoTAN | 0.112 ± 0.017 | 0.227 ± 0.042 | 0.001 ± 0.004 | 0.124 ± 0.123 | 0.269 ± 0.123 | 0.001 ± 0.004 |
| Proposed | 0.109 ± 0.023 | 0.221 ± 0.076 | 0.001 ± 0.003 | 0.121 ± 0.023 | 0.263 ± 0.058 | 0.064 ± 0.017 |
+
+Table 4. Ablation study on the effectiveness of each component in the proposed method. ACDE: Age-conditioned ODE. ST: Single-time-point training. MT: Multi-time-point training. KD: Knowledge distillation.
+
+| Components | Sulcal Depth | White Matter Surface |
| ACDE | ST | MT | Training Strategy | PCC ↑ | MAE ↓ | ASSD (mm) ↓ | CD (mm) ↓ |
| ✘ | ✓ | ✓ | ✘ | - | - | 0.112 ± 0.017 | 0.227 ± 0.042 |
| ✓ | ✓ | ✘ | ✘ | - | - | 0.115 ± 0.025 | 0.240 ± 0.087 |
| ✓ | ✘ | ✓ | ✘ | 0.905 ± 0.048 | 0.720 ± 0.098 | 0.338 ± 0.230 | 0.946 ± 0.785 |
| ✓ | ✓ | ✓ | Resampling | 0.921 ± 0.065 | 0.782 ± 0.103 | 0.191 ± 0.042 | 0.426 ± 0.123 |
| ✓ | ✓ | ✓ | PCIL | 0.955 ± 0.029 | 0.502 ± 0.095 | 0.137 ± 0.029 | 0.291 ± 0.086 |
| ✓ | ✓ | ✓ | PICL + KD | 0.962 ± 0.026 | 0.451 ± 0.075 | 0.109 ± 0.023 | 0.263 ± 0.058 |
+
+
+Figure 4. Visualization of sulcal depth comparison: (top) ground truth, (middle) sulcal depth generated by SU-Net, and (bottom) sulcal depth extracted by the proposed method.
+
+cerebral cortex generated at discrete time points between 29-40 weeks is utilized for experimentation. As shown in Table 2, the difference between the predicted PMA and the PMA in the developmental trajectory is approximately one week. This indicates that the generated surfaces are positioned at the correct time points, exhibiting high consistency at the population level. Furthermore, surfaces at any time point show high overlap with the reconstructed surface (surface at the final time point), with all Dice exceeding 0.9. This suggests that the generated cortical surfaces belong to the same subject, demonstrating consistency at the individual level. Figure. 5 presents the generated brain development trajectory for a single subject, illustrating that the
+
+Table 5. Ablation study of the impact of different loss functions on generated cortical thickness. $\mathcal{L}_g$ : Global Thickness Loss. $\mathcal{L}_c$ : Consistency Loss.
+
+| Method | Cortical Thickness |
| PCC ↑ | MAE ↓ |
| Baseline | 0.568 ± 0.106 | 0.482 ± 0.089 |
| Baseline+Lg | 0.672 ± 0.086 | 0.327 ± 0.078 |
| Baseline+Lc | 0.819 ± 0.056 | 0.199 ± 0.047 |
| Baseline+Lg+Lc | 0.866 ± 0.027 | 0.173 ± 0.029 |
+
+generated surfaces maintain accurate and consistent brain partitioning results, reflecting true anatomical significance and offering expanded possibilities for surface analysis.
+
+# 3.3. Cortical Surface Reconstruction
+
+Following previous work, geometric accuracy of reconstructed surfaces is assessed using Chamfer Distance (CD), average symmetric surface distance (ASSD), and Hausdorff Distance (HD) as evaluation metrics. Furthermore, the ratio of self-intersecting (SIF) faces is employed as a metric for assessing the geometric quality of the mesh. These distances are calculated on point clouds, each containing 150k uniformly sampled points from both the predicted and pseudo ground-truth surfaces. Surface quality is evaluated by calculating self-intersection using Pymeshlab.
+
+To assess the efficacy of the proposed method, we conducted a comparative analysis with existing diffeomorphic
+
+
+Figure 5. Visualization of generated surface-level developmental trajectory for a single subject.
+
+transformation-based cortical surface reconstruction models, including Corticalflow [18], CFPP [25], and CoTAN [22]. Given the absence of these methods being evaluated on the dHCP dataset or providing a dataset partitioning scheme, we retrained and evaluated each model using the optimal hyperparameter settings. As depicted in Table 3, the proposed method surpasses all existing methods in geometric accuracy and demonstrates the minimal standard deviation. These results underscore the accurate and robust performance of our proposed model.
+
+# 3.4. Ablation Study
+
+In this section, the effectiveness of each component in the proposed method is validated. For the development trajectory generation and cortical surface reconstruction on the white matter surface, a fixed-step diffeomorphic transformation-based method is set as the baseline. First, the introduction of the ACDE adds developmental significance to the deformation process, transforming the single-task surface reconstruction into a dual-task framework with the addition of longitudinal prediction. Without increasing computational load, the geometric accuracy of the reconstructed white matter surface shows significant improvement. The ACDE enables flexible training for both single time-point (ST) and multi-time-point (MT) scenarios. As shown in Table 4, using only ST, surface reconstruction maintains high performance, but the model struggles to construct accurate development trajectories. With MT training using paired data, while good longitudinal predictions are achieved, accurate cortical surface reconstruction is compromised.
+
+In the next step, we compare different training strategies under both ST and MT settings. While Resampling-based training achieves performance enhancement on both tasks, the proposed PCIL strategy addresses data distribution challenges, significantly improving surface reconstruction and developmental modeling compared to Resampling, with improvements of $35.8\%$ in MAE for developmental modeling and $28.2\%$ in ASSD for surface reconstruction. Furthermore, due to the sparsity of longitudinal data, overemphasizing final developmental trajectory generation during training may slightly compromise reconstruction performance. To address this, KD is applied after PCIL, refining the model to achieve performance that surpasses or matches
+
+state-of-the-art methods in both tasks. Therefore, the proposed ACDE provides a flexible framework that effectively leverages both individual-level and population-level data, enabling accurate developmental trajectory prediction and cortical reconstruction within a single deformation process.
+
+For the dual-task on the pial surface, the effects of global thickness loss $\mathcal{L}_g$ and consistency loss $\mathcal{L}_c$ are explored. $\mathcal{L}_c$ more effectively utilizes unlabeled data along the developmental trajectory. As shown in Table 5, this semi-supervised training framework balances surface reconstruction and thickness prediction, yielding strong results in both. $\mathcal{L}_g$ by considering the global average cortical thickness, enables the model to quickly learn the expansion from white matter to gray matter. Table 5 shows that this improves longitudinal prediction without compromising geometric accuracy. These results demonstrate that the proposed method can capture a consistent developmental trajectory across both white and pial surfaces while maintaining high geometric accuracy.
+
+# 4. Conclusion
+
+In this paper, we introduce a dual-task framework for cortical surface reconstruction and development trajectory generation, extracting multi-temporal cerebral cortex data from single-time-point brain MRI. The proposed method pioneers direct longitudinal prediction based on triangular mesh. Inspired by brain development, the proposed ACDE achieves precise reconstruction and developmental prediction in a single ODE iteration, maintaining high computational efficiency. Knowledge distillation addresses the issue of long-tail distributions, effectively balancing the two tasks. A semi-supervised training approach based on internal and external consistency extends the development trajectory from white matter surface to gray matter, ensuring accurate cortical thickness. Despite limited longitudinal brain imaging data, the proposed method achieves superior or competitive results in both tasks.
+
+# Acknowledgements
+
+This work is supported by General Program of the National Natural Science Foundation of China (NSFC-62471185), Key-Area Research and Development Program of Guangdong Province (2023B0303040001), Guangdong Basic and
+
+Applied Basic Research Foundation (2024A1515010180), and the Guangdong Provincial Key Laboratory of Human Digital Twin (2022B1212010004).
+
+# References
+
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+[24] E Orasanu, A Melbourne, MJ Cardoso, H Lomabert, GS Kendall, NJ Robertson, N Marlow, and S Ourselin. Cortical folding of the preterm brain: a longitudinal analysis of extremely preterm born neonates using spectral matching. brain behav 6, e00488, 2016.
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\ No newline at end of file
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+# Dream-to-Recon: Monocular 3D Reconstruction with Diffusion-Depth Distillation from Single Images
+
+Philipp Wulff1
+
+Felix Wimbauer $^{1,2}$
+
+Dominik Muhle $^{1,2,3}$
+
+Daniel Cremers1,2
+
+$^{1}$ Technical University of Munich $^{2}$ MCML $^{3}$ SE3 Labs
+
+philippwulff.github.io/dream-to-recon
+
+
+Figure 1. Dream-to-Recon. We leverage fine-tuned diffusion models for inpainting and a pre-trained depth predictor to generate high-quality scene geometry from a single image, as seen on the right side. Afterwards, we distill a feed-forward scene reconstruction model, which performs on par with reconstruction methods trained with multi-view supervision. The color in the plots indicates the up-coordinate.
+
+# Abstract
+
+Volumetric scene reconstruction from a single image is crucial for a broad range of applications like autonomous driving and robotics. Recent volumetric reconstruction methods achieve impressive results, but generally require expensive 3D ground truth or multi-view supervision. We propose to leverage pre-trained 2D diffusion models and depth prediction models to generate synthetic scene geometry from a single image. This can then be used to distill a feed-forward scene reconstruction model. Our experiments on the challenging KITTI-360 and Waymo datasets demonstrate that our method matches or outperforms state-of-the-art baselines that use multi-view supervision, and offers unique advantages, for example regarding dynamic scenes. For more details and code, please check out our project page.
+
+# 1. Introduction
+
+Understanding the 3D geometry of a scene from a single image is fundamental for a wide range of applications, in particular for autonomous driving and robotics. A dense reconstruction of the environment enables machines to react to their surroundings and to reason about further actions such as path planning.
+
+Traditionally, this task has been mainly approached via monocular depth estimation (MDE), where a network predicts per-pixel distance values for a given single image. Through architectural improvements, scaled-up datasets with high-quality ground-truth, and cross-dataset training, these methods have achieved strong generalization capabilities and can be used in an off-the-shelf way [1, 38, 44, 65]. In particular, MDE methods are now even able to predict metric-scale depth maps. While MDE is already useful for many applications, it has a severe limitation: Depth maps are only a 2D projection of the 3D scene, and do not capture the scene's full 3D structure. Consequently, it is not possible to infer information about areas that are beyond the parts visible in the input image. This limitation makes pure MDE unsuitable for many 3D understanding tasks, e.g. planning the path of a vehicle into a parking spot that was only partially observed.
+
+To address this shortcoming, a new line of work aims to infer a volumetric 3D reconstruction of the scene from a single image [4, 27, 28, 37, 53, 60]. Here, the 3D geometry is either represented as a discrete voxel grid [4, 28, 53] or as a continuous density field [27, 37, 60]. Many approaches are trained in a fully-supervised way using dense 3D annotations. However, such 3D ground truth is difficult and expensive to obtain, e.g. by accumulating Lidar scans from a
+
+moving vehicle over time. Even then, dynamic scenes with many moving objects pose a significant challenge, as accumulation over time can lead to trailing artifacts and inconsistencies. Recent works propose to avoid the need for explicit 3D ground-truth from Lidar by using a self-supervised loss based on multi-view consistency and volume rendering [22, 27, 37, 60]. Notably, Behind the Scenes (BTS) [60] demonstrates accurate volumetric reconstruction, even in occluded areas, by relying on multi-view image data captured from a moving car. Despite its impressive performance, BTS still requires a special multi-camera setup and accumulation of views over time to have sufficient observations of the scene. Furthermore, this training scheme is still not robust towards dynamic objects.
+
+Recently, there has also been impressive progress in the field of scene generation, enabled by the success of image diffusion models. Several works combine image diffusion models with pre-trained depth predictors to generate novel views of a scene using the render-refine-repeat framework [7, 17, 29]. Starting from an input image, they first warp the pixels into a virtual novel view using the depth predictor. Then, they inpaint and refine the warped image using an image diffusion model, which is conditioned on the warped pixels. By repeating this process multiple times, it is possible to generate several consistent views of a 3D environment and subsequently optimize a 3D representation such as 3D Gaussian Splatting. So far, these methods have focused on generating high-fidelity novel views of constrained scenes. However, the generated geometry, which is important for many downstream tasks, is still lacking in quality. Furthermore, these approaches are very compute-intensive and not (yet) suitable for real-time applications.
+
+In this work, we propose a specialized approach based on the render-refine-repeat framework to generate high-quality geometry reconstructions of a scene from a single image. Given a color image and its predicted depth, we render novel views, jointly remove artifacts and inpaint occluded regions. Subsequently, we fuse all views into a 3D occupancy field. These generated scene geometries are then distilled into a robust feed-forward model for single-image volumetric 3D reconstruction. The distillation involves both 3D volumetric supervision and 2D rendering supervision from virtual novel views. To deal with inherent ambiguities in occluded regions, our model also predicts 3D uncertainty. During both scene generation and distillation, we exclusively rely on single image and do not require multiview data or 3D supervision.
+
+Experiments on the challenging KITTI-360 [31] and Waymo [54] datasets show that our distilled model is competitive with state-of-the-art methods for monocular 3D reconstruction using multi-view supervision. Furthermore, we show that our method has unique advantages when it comes to dynamic scenes. Through extensive ablation stud
+
+ies, we validate the effectiveness of our design choices both for scene generation and distillation. Our contributions are:
+
+- A specialized view completion model that inpaints and refines synthetic novel views and which can be trained using only a single image per scene.
+- A synthetic occupancy field formulation to construct dense scene geometry from multiple synthetic views.
+- A single-view scene reconstruction model, which is trained from the synthesized data and is competitive with reconstruction methods trained on multi-view data.
+
+# 2. Related Work
+
+# 2.1. Monocular depth prediction
+
+The task of inferring depth information from a single image is a fundamental challenge in computer vision. Early works trained neural networks in a supervised way to directly regress relative depth for specific domains, e.g. autonomous driving [8, 9, 11, 15, 26, 33, 57]. Some works avoided the need for explicit supervision and relied on self-supervised loss formulations based on multi-view consistency [13, 14]. As one of the first, Midas [44] proposed a training formulation that allows effective training on many diverse datasets at the same time, shifting the focus to build more general-purpose monocular relative depth prediction networks. A number of follow-up approaches have since improved different parts of the pipeline [1, 45, 62-64]. Most recently, several works [2, 20, 38, 65], notably Metric3D [20] and UniDepth [38], proposed methods for general-purpose metric depth prediction. As monocular depth prediction methods have matured over the years, many applications now use such models in an off-the-shelf fashion.
+
+# 2.2. Scene as occupancy
+
+While depth predictions are useful, they only capture 2.5D information about the scene and do not provide details in e.g. occluded regions. Recently, a new line of work started training neural networks to directly infer a volumetric reconstruction from a single image [4, 5, 60]. Volumetric reconstructions allow to determine binary occupancy values for any point in the observed camera frustum. In general, the scene is either represented as a dense voxel grid [4, 28, 30, 35, 53], a continuous density field [5, 16, 27, 37, 60], or hybrid approaches like tri-planes [21, 22]. To obtain ground truth data for supervision, many works accumulate Lidar scans from a moving sensor over time [21, 28, 30, 35, 53]. Other approaches use losses on multi-view supervision and photometric consistency and can thus avoid the need for explicit 3D data [5, 16, 22, 27, 37, 60].
+
+In general, methods for volumetric reconstruction from a single image require complex sensor setups to generate training data. This limits the scale of these datasets and
+
+makes generalization challenging. Furthermore, they struggle with dynamic objects which violate the static scene assumption. Many approaches either ignore [60] or filter out [37] dynamic objects at training time. In contrast, our approach can be trained using single images and can deal with dynamic objects by design. It only requires an off-the-shelf diffusion model and depth prediction model.
+
+# 2.3. 3D scene generation
+
+Following the recent success of diffusion models for image generation [6, 39, 43, 47, 48], researchers also aimed to create powerful 3D generative models. However, similar to 3D reconstruction, the amount of training data available for 3D generation is limited. Consequently, models that directly generate 3D are restricted to object-centric content [19, 59].
+
+Several lines of work propose to leverage 2D image generation models to improve 3D generation. Inspired by DreamBooth [40], some works [41, 50, 58] apply score distillation sampling (SDS) to generate 3D objects. However, such models are not stable and are thus still limited to object-centric 3D generation. Another promising direction [12, 18, 24, 34, 52, 55, 56, 59, 61] finetunes or retransits 2D diffusion models to generate multiple, 3D consistent views of a scene from different viewing directions. The generated views then enable 3D reconstruction in a second step. While these approaches often benefit from the generalization capabilities of pretrained 2D diffusion models, they are inherently limited. Besides requiring multi-view training data, the views that the models can generate are predefined and usually arranged in a circular pattern around an object in the center. Therefore, this line of work also struggles with unbounded in-the-wild scenes. Finally, a number of methods [7, 10, 17, 29, 32, 49, 51, 68] follow an iterative paradigm called render-refine-repeat. Every iteration is made up of two steps: 1) The current scene is rendered into an unobserved, virtual view, 2) the virtual view is refined (inpainted) using a 2D generative model and then lifted back into the scene using a pretrained depth prediction model. Earlier works like Infinite Nature [32] and Text2Room [17] represent the scene as 3D meshes, while more recent approaches use NeRFs [66] or Gaussian Splitting [7, 51]. Unlike this work, most approaches in that domain focus on novel-view-synthesis, which does not require perfect geometry.
+
+# 3. Method
+
+In the following, we first introduce our view completion model (VCM), which completes occlusions and removes artifacts in warped images. We then present how we apply the VCM in combination with a depth prediction network to iteratively synthesize 3D scene geometry in the form of a synthetic occupancy field (SOF) from just a single image. Finally, we describe how we distill these synthesized scenes into a lightweight feed-forward scene reconstruction model.
+
+Fig. 2 provides a comprehensive overview.
+
+# 3.1. Preliminaries
+
+For a given scene, our method receives as input a single image $\mathbf{I}_{\mathrm{in}} \in ([0,1]^3)^\Omega$ , where $\Omega = \{1,\dots,H\} \times \{1,\dots,W\}$ denotes the grid of pixels. Through an off-the-shelf monocular depth prediction network, we can additionally obtain per-pixel depths $\mathbf{D_I} \in \mathbb{R}_+^\Omega$ . For a synthetic novel view $\hat{\mathbf{I}}_i$ , let $\mathbf{P}_i \in \mathrm{SE3}$ be the camera pose and let $\mathbf{P}_{i\rightarrow j}$ denote a relative camera pose between views $i$ and $j$ . For all views, we assume the same projection $\pi (\mathbf{x}): \mathbb{R}^3 \to \mathbb{R}^2$ and unprojection $\pi^{-1}(\mathbf{p},d): (\mathbb{R}^2, \mathbb{R}_+) \to \mathbb{R}^3$ function, which map from 3D points $\mathbf{x} \in \mathbb{R}^3$ to pixels $\mathbf{p} \in \mathbb{R}^2$ with depth $d_{\mathbf{p}} \in \mathbb{R}_+$ and vice-versa. By combining $\pi$ and $\mathbf{P}$ , we can map a pixel from the input view into another view:
+
+$$
+\mathbf {p} _ {i} = \pi \left(\mathbf {P} _ {\mathrm {i n} \rightarrow i} \pi^ {- 1} \left(\mathbf {p} _ {\mathrm {i n}}, d _ {\mathbf {p} _ {\mathrm {i n}}}\right)\right) \tag {1}
+$$
+
+# 3.2. Training the View Completion Model
+
+A single image only provides a partial observation of the 3D scene. We aim to use the ability of 2D generative models to inpaint realistic content given some context. Concretely, we follow the render-refine-repeat framework. First, the known scene content (e.g. the input image) is warped into a virtual novel view, where unknown regions remain empty. Then, a generative model fills in the empty or occluded regions conditioned on the known context and ideally removes artifacts. The now completed and refined view can be lifted into 3D again to refine the scene. However, naively applying an inpainting diffusion model like StableDiffusion-2.1 yields insufficient inpainting quality. This is because the views found in e.g. autonomous driving differ significantly from the ones the model was originally trained on, which tend to be casual photos. Therefore, we rely on a specialized view completion model (VCM).
+
+The VCM is implemented as a ControlNet [67] for a pretrained StableDiffusion-2.1-unCLIP diffusion model. Rich conditioning and the correct parameterization are very important for effective view completion. Thus, the VCM receives as input the warped RGB, the (incomplete) depth representing the current scene geometry, and an inpainting mask. We mask out areas for inpainting with random noise in all inputs and apply morphological closing to the mask. Additionally, we provide the model with the CLIP [42] embedding of the input image. From this input, the VCM produces an inpainted and refined image.
+
+The VCM needs to be trained using ground-truth pairs of conditioning and target image. Since we have only a single image per scene available, we take inspiration from [3] and design a training scheme based on forward-backward warping. Given an input image $\mathbf{I}_{\mathrm{in}}$ and predicted depth $\mathbf{D}_{\mathbf{I}_{\mathrm{in}}}$ , we first warp the pixels into a virtual novel view with a random camera pose. Then, the virtual view is warped back into
+
+
+
+
+Figure 2. Method overview. a) We train a view completion model (VCM) that inpaints occluded areas and refines warped views. Training uses only a single view per scene and leverages forward-backward warping for data generation. b) The VCM is applied iteratively alongside a depth prediction network to synthesize virtual novel views, enabling progressive refinement of the 3D geometry. c) The synthesized scene geometries are then used to distill a feed-forward scene reconstruction model by supervising occupancy and virtual depth.
+
+
+
+
+
+the input camera pose. For areas of the input image, which would be occluded in the novel view, the backward warped image will be corrupted. We can find these occluded regions by doing a per-pixel comparison of the back-projected depth with the original depth. If the reprojected depth is lower for a pixel, then that pixel is occluded. Through this process, we create realistic occlusions and rendering artifacts to train the VCM. The warping uses the same rendering formulation as for synthesizing a new scene which is described in the following.
+
+# 3.3. Synthesizing Scene Geometry
+
+Within the render-refine-repeat framework, we generate several synthetic novel views, complete them using the VCM, predict corresponding depth maps, and update the scene geometry. To this end, we require a way to model scene geometry from the predicted depth maps, render novel views, and determine occlusions. Let $\mathbb{V} = \left\{(\mathbf{I}_{\mathrm{in}},\mathbf{D}_{\mathrm{in}},\mathbf{P}_{\mathrm{in}}),(\hat{\mathbf{I}}_i,\hat{\mathbf{D}}_i,\hat{\mathbf{P}}_i),\ldots \right\}$ be the set of currently active view-depth-pose triplets. Initially, $\mathbb{V}$ contains only the input view and is then extended via render-refine-repeat.
+
+Modeling scene geometry. Throughout our approach, we consider a continuous synthetic occupancy field $\Theta_{\mathbb{V}}(\mathbf{x}) : \mathbb{R}^3 \to \{0,1\}$ , which maps every point $\mathbf{x} \in \mathbb{R}^3$ in the scene to a binary occupancy value and which depends on $\mathbb{V}$ . Intuitively, a point $\mathbf{x}$ is regarded as not occupied if it lies in front of the predicted depth of any active view, for which it is in the camera frustum. Conversely, if it lies behind the predicted depth for all views, it is considered occupied. Let $\mathbf{x}_i = \mathbf{P}_i\mathbf{x}$ be the point transformed into the coordinate system of view $i$ , $\mathbf{p}_i = \pi (\mathbf{x}_i)$ the corresponding pixel after
+
+projection to the image plane, and $d_{\mathbf{p}_i}$ the predicted depth at that pixel. We determine the occupancy of $\mathbf{x}$ through the following logical formula:
+
+$$
+\theta_ {i} ^ {\text {i n s i d e - f r u s t u m}} (\mathbf {x}) = \left[ \mathbf {p} _ {i} \in \Omega \right] \tag {2}
+$$
+
+$$
+\theta_ {i} ^ {\text {b e h i n d - d e p t h}} (\mathbf {x}) = \left[ \mathbf {x} _ {i} ^ {z} > d _ {\mathbf {p} _ {i}} \right] \tag {3}
+$$
+
+$$
+\theta_ {i} ^ {\text {o c c}} (\mathbf {x}) = \theta_ {i} ^ {\text {i n s i d e - f r u s t u m}} (\mathbf {x}) \wedge \theta_ {i} ^ {\text {b e h i n d - d e p t h}} (\mathbf {x}) \tag {4}
+$$
+
+$$
+\Theta_ {\mathbb {V}} (\mathbf {x}) = \bigwedge_ {i \in \mathbb {V}} \theta_ {i} ^ {\text {o c c}} (\mathbf {x}) \tag {5}
+$$
+
+**Rendering novel views.** We rely on the established volume rendering formulation [23], popularized in recent years by NeRF [36]. Here, an image is rendered by casting a ray for every pixel from the camera into 3D space. The ray is evaluated at discrete steps $\mathbf{x}$ for density $\sigma(\mathbf{x})$ and color $c(\mathbf{x})$ . The final pixel color is determined by integrating over the density along the ray.
+
+In our case, we can directly use our binary occupancy as density: $\sigma (\mathbf{x}) = \Theta_{\mathbb{V}}(\mathbf{x})$ . Because color information is not defined in 3D space, we sample it from the 2D views. When projecting $\mathbf{x}$ into view $i$ and obtaining pixel location $\mathbf{p}_i$ , let $\mathbf{c}_i$ be the corresponding pixel color. However, not all $\mathbf{c}_i$ are valid, as the 3D point could be occluded or in empty space in the image. To aggregate the sampled color values, we use a heuristic: If $\mathbf{x}$ is closer than a threshold $\tau_{s}$ to a surface in view $i$ , then it is likely valid. The final color is obtained by averaging all valid color values:
+
+$$
+\theta_ {i} ^ {\text {s u r f a c e}} (\mathbf {x}) = \left[ \left| \mathbf {x} _ {i} ^ {z} - d _ {\mathbf {p} _ {i}} \right| < \tau_ {s} \right] \wedge \theta_ {i} ^ {\text {i n s i d e - f r u s t u m}} (\mathbf {x}) \tag {6}
+$$
+
+$$
+c (\mathbf {x}) = \frac {\sum_ {i \in \mathbb {V}} \mathbf {c} _ {i} \cdot \theta_ {i} ^ {\text {s u r f a c e}} (\mathbf {x})}{\sum_ {i \in \mathbb {V}} \theta_ {i} ^ {\text {s u r f a c e}} (\mathbf {x})} \tag {7}
+$$
+
+Let $\tilde{\mathbf{I}}_{\mathrm{nv}}$ denote the rendered view, which can contain invalid regions (due to occlusions) and sampling artifacts. By computing the expected ray termination depth (which in our case corresponds to where a ray hits occupancy for the first time), we can also render a depth map $\tilde{\mathbf{D}}_{\mathrm{nv}}$ .
+
+Detecting occlusions in novel views. When warping one view into another and the viewpoint change is limited, then sharp changes in the reference depth map serve as a good proxy for which regions will introduce occlusions. We leverage this aspect and compute a depth gradient map using Sobel filters on the inverse depth map, which highlights regions with significant depth changes. Subsequently, a threshold $\tau_{d}$ is applied to binarize the map.
+
+$$
+\mathbf {O} _ {i} = \sqrt {\left(\frac {\partial}{\partial x} \mathbf {D} _ {i}\right) ^ {2} + \left(\frac {\partial}{\partial y} \mathbf {D} _ {i}\right) ^ {2}} > \tau_ {d} \tag {8}
+$$
+
+We finally render it alongside the RGB color channels into the novel view to obtain $\tilde{\mathbf{O}}_{\mathrm{nv}}$ . In a post-processing step, we apply morphological opening to remove isolated noise followed by morphological closing join neighboring patches.
+
+Sampling and completing novel views. By adding more views to the set of active views $\mathbb{V}$ , we refine the scene geometry represented by the synthetic occupancy field. The better the views cover different areas of the scene, the better the resulting geometry will be. Therefore, we predefine a set $\mathbb{P} = \{\mathbf{P}_1,\dots ,\mathbf{P}_{n_{\mathrm{synth}}}\}$ of camera poses for synthetic novel views. For every view $j\in \mathbb{P}$ , we render the RGB $\tilde{\mathbf{I}}_j$ , depth $\tilde{\mathbf{D}}_j$ , and occlusions $\tilde{\mathbf{O}}_j$ . From this conditioning, the VCM then inpaints and refines the incomplete view, resulting in the synthetic novel view $\hat{\mathbf{I}}_j$ . Finally, we apply the depth predictor to obtain the completed depth map $\hat{\mathbf{D}}_j$ and we can update $\mathbb{V}$ with the triplet $(\hat{\mathbf{I}}_j,\hat{\mathbf{D}}_j,\hat{\mathbf{P}}_j)$ .
+
+# 3.4. Distilling into a Scene Reconstruction Model
+
+While we can synthesize high-quality scene geometry using the view completion model, the process is expensive and not suitable for real-time applications. Furthermore, the pipeline involves several independent components, which makes it prone to artifacts. To address these limitations, we generate scene geometry for all images of a dataset and distill a feed-forward scene reconstruction model. Given a single image as input, it predicts a discretized occupancy field $\Theta_{\mathrm{SRM}} \in [0,1]^{Z \times H \times W}$ . However, there is an inherent ambiguity when generating or reconstructing scenes from a single image. Therefore, we also predict an uncertainty field $\omega \in \mathbb{R}_{+}^{Z \times H \times W}$ .
+
+The training involves two loss terms. First, we directly supervise the predicted occupancy. Concretely, we rely on an uncertainty-based loss formulation inspired by [25],
+
+which is self-calibrating.
+
+$$
+\mathcal {L} _ {\mathrm {o c c}} \left(\Theta_ {\mathrm {S R M}}, \Theta\right) = \sum_ {\mathbf {x}} \frac {\left(\Theta (\mathbf {x}) - \Theta_ {\mathrm {S R M}} (\mathbf {x})\right) ^ {2}}{\omega (\mathbf {x})} + \log \omega (\mathbf {x}) \tag {9}
+$$
+
+Additionally, we render depth maps $\tilde{\mathbf{D}}_i$ using our $\Theta_{\mathrm{SRM}}$ from the same camera poses as the synthetic views in $\mathbb{V}$ . We then directly supervise them via the depth predictions $\mathbf{D}_i$ from $\mathbb{V}$ using a Gaussian Negative Log-Likelihood (GNLL) loss, as proposed in [46]. The loss term provides training signals to the surface areas of the predicted density field, which are particularly hard to learn.
+
+$$
+\mathcal {L} _ {\text {d e p t h}} = \sum_ {i \in \mathbb {V}} \operatorname {G N L L} \left(\tilde {\mathbf {D}} _ {i}, \mathbf {D} _ {i}\right) \tag {10}
+$$
+
+The final loss is then a weighted sum:
+
+$$
+\mathcal {L} = \lambda_ {\text {o c c}} \mathcal {L} _ {\text {o c c}} + \lambda_ {\text {d e p t h}} \mathcal {L} _ {\text {d e p t h}}. \tag {11}
+$$
+
+# 4. Experiments
+
+To demonstrate the capabilities of our approach, we conduct extensive experiments regarding volumetric scene reconstruction both for the synthesized scenes and the distilled reconstruction model. Furthermore, we carefully validate our design choices for the view completion model, scene synthesis, and distillation procedure.
+
+# 4.1. Setup
+
+Data. We test our method on the challenging KITTI-360 [31] and Waymo [54] self-driving datasets. Both datasets contain scenes with complex layouts and possibly dynamic objects. While they provide multi-view data, we use only a single view per scene both for training and testing. For KITTI-360, we load images at $384 \times 1280$ resolution during View Completion Model training and at $192 \times 640$ resolution otherwise. On Waymo, we use images at a resolution of $320 \times 480$ .
+
+Implementation details. For the depth predictor, we rely on Metric3D [65]. The scene reconstruction model adopts the ResNet50-based U-Net backbone from [60]. We add batch-normalization layers to the backbone's decoder to stabilize mixed-precision training. The predicted occupancy field has a resolution $Z = 64$ , inversely spaced between $3m$ and $50m$ . The training takes approximately 2 days for the View Completion Model and 3 days for the reconstruction model on 4 Nvidia A100 GPUs. For more details regarding data setup and training, please refer to the supplementary material.
+
+| Method | Learns occlusions | No multi-view data | KITTI-360 [31] | Waymo [54] |
| Oacc↑ | IEacc↑ | IREc↑ | Oacc↑ | IEacc↑ | IREc↑ |
| UniDepth* [38] | X | ✓ | 0.89 | - | - | 0.96 | - | - |
| Metric3D-ViT-Large* [65] | X | ✓ | 0.91 | - | - | 0.97 | - | - |
| BTS* [60] | ✓ | X | 0.92 | 0.69 | 0.64 | 0.95 | 0.63 | 0.94 |
| BTS + depth supervision | ✓ | X | 0.92 | 0.70 | 0.66 | 0.95 | 0.61 | 0.96 |
| KYN† [27] | ✓ | X | 0.92 | 0.70 | 0.72 | - | - | - |
| Ours | ✓ | ✓ | 0.93 | 0.72 | 0.75 | 0.97 | 0.73 | 0.96 |
| Ours (Distilled) | ✓ | ✓ | 0.90 | 0.71 | 0.71 | 0.96 | 0.72 | 0.93 |
+
+Table 1. Quantitative scene reconstruction. We report cene geometry estimation results using ground-truth derived from accumulated LiDAR scans and semantic annotations on KITTI-360 and Waymo. Both the synthesized scenes and the distilled model match or surpass baselines, despite not requiring multi-view training data. Legend: $\star$ : official checkpoint, $\dagger$ : results as reported in the reference.
+
+Evaluation procedure. We use 2D reconstruction metrics to evaluate image synthesis results in the input camera's viewpoint, where ground truth is available. Here, PSNR measures reconstruction quality of RGB images, and absolute relative error (Abs Rel) is used for depth. When evaluating novel view quality, we apply refinement in the novel view and then re-project the refined views into the input view to compute the metrics w.r.t. the input image (masking out invalid pixels).
+
+Furthermore, we rely on the established occupancy evaluation strategy using LiDAR GT from [27, 60] to evaluate 3D consistency of novel views and the quality of the 3D reconstruction in an area of dimension $x = [-4m, 4m]$ , $y = [-1m, 0m]$ , $z = [4m, 20m]$ . On Waymo, we augment the LiDAR GT with occupancy from object bounding boxes to keep dynamic objects. We evaluate the overall accuracy of the reconstruction $\mathrm{O}_{\mathrm{acc}}$ , as well as the accuracy and recall of the reconstruction in invisible and empty regions (i.e. behind the visible surface in the input image).
+
+# 4.2. Scene Reconstruction
+
+We first test our method's ability to generate accurate volumetric geometry from a single image in complex scenes. Here, the state-of-the-art volumetric reconstruction methods Behind the Scenes (BTS) [60] and Know Your Neighbor (KYN) [27] serve as baselines. Both use multi-view supervision from all cameras and multiple time steps. Because our approach uses an off-the-shelf depth predictor to synthesize geometry, we also train a second BTS baseline that uses depth prediction in addition to multi-view supervision. This ensures similar priors and a fair comparison. Furthermore, we test the recent MDE models UniDepth [38] and Metric3D [20]. Since depth prediction cannot reason about occluded areas, we do not report the $\mathrm{IE}_{\mathrm{acc}}$ and $\mathrm{IE}_{\mathrm{rec}}$ metrics.
+
+As shown in Tab. 1, compared to previous methods, our reconstructed synthetic occupancy field achieve the best overall reconstruction $(\mathrm{O_{acc}})$ and the best reconstruction of invisible and empty regions $(\mathrm{IE_{acc}}$ and $\mathrm{IE_{rec}}$ ). Our distilled scene reconstruction model matches the performance
+
+of KYN and surpasses BTS [60], despite using only single images. Even with depth supervision, BTS performance still lags behind. We hypothesize that this lack of improvement stems from the strong depth cues already inherent in multi-view data. In fact, inconsistent depth predictions with slightly varying scales may even harm BTS training.
+
+We visualize the scene geometry by discretizing the occupancy into a voxel grid. As illustrated in Fig. 3, both the synthesized scenes and the geometry predicted by the scene reconstruction model exhibit high overall quality. However, the synthesized scenes occasionally display artifacts caused by poor view completion or depth prediction. The distilled scene reconstruction model does not exhibit these issues, as it is trained on a diverse dataset. We contend that, despite being slightly outperformed in quantitative metrics by the directly synthesized geometry, the distilled model is more reliable and significantly faster. As shown in the 3rd and 4th columns, both BTS variants fail to reconstruct the dynamic object. This failure stems from their use of multi-view data across multiple timesteps, which introduces inconsistency when the object is in motion. In contrast, our synthesized scenes naturally handle such scenarios.
+
+# 4.3. Scene Synthesis using the VCM
+
+The process of synthesizing scene geometry – by generating novel views and fusing depth maps – relies on multiple components that significantly influence the final result's quality. To this end, we rigorously validate our design choices through a series of ablation studies.
+
+# 4.3.1. Conditioning of the VCM
+
+Our VCM receives a range of conditioning inputs. To assess the impact of conditioning, we compare our full VCM model against a simplified variant, denoted as $\mathrm{VCM}^{\mathrm{simple}}$ . This simplified configuration receives only the RGB input, where the region to be inpainted is masked with zeros instead of noise. We evaluate both configurations on the KITTI-360 dataset $(\mathrm{VCM}^{\mathrm{K}})$ , and further examine the effect of finetuning on Waymo $(\mathrm{VCM}^{\mathrm{K}\rightarrow \mathrm{W}})$ .
+
+
+Figure 3. Qualitative scene reconstruction. We present scene reconstructions from several models on KITTI-360 [31] (left) and Waymo [54] (right). The geometry is discretized into a voxel grid with dimensions $x = [-9m, 9m]$ , $y = [-0.25m, 4m]$ , $z = [4m, 25m]$ . The color in the plots indicates the y-coordinate (up-axis). Despite being trained on single images only, our method achieves accurate reconstructions overall. In addition, it reliably reconstructs dynamic objects, and the distilled model effectively avoids artifacts.
+
+| Method | Input View | Novel View |
| PSNR ↑ | Abs Rel ↓ | PSNR ↑ | Abs Rel ↓ |
| KITTI-360 VCM®simple | 20.197 | 0.174 | 21.323 | 0.154 |
| VCMK | 23.908 | 0.161 | 23.394 | 0.135 |
| Waymo VCMK | 26.963 | 0.286 | 21.432 | 0.177 |
| VCMK→W | 28.781 | 0.260 | 22.603 | 0.135 |
+
+Table 2. Effect of VCM conditioning. We evaluate different model configurations and training setups. $\mathrm{VCM}^{\mathrm{simple}}$ receives only masked RGB input. $\mathrm{VCM}^{\mathrm{K}}$ and $\mathrm{VCM}^{\mathrm{K}\rightarrow \mathrm{W}}$ denote the full model trained on KITTI-360 and finetuned on Waymo, respectively.
+
+As shown in Tab. 2, the full model consistently outperforms the baseline in both color and depth reconstruction metrics on KITTI-360. On Waymo, finetuning clearly enhances reconstruction quality even further.
+
+
+Figure 4. Effect of VCM conditioning. See Tab. 2.
+
+# 4.3.2. Occlusion detection in novel views
+
+The accuracy and robustness of our occlusion detection strategy directly influence the effectiveness of refining incomplete novel views using VCM. We compare our depth-gradient-based method against an alternative approach that
+
+
+Figure 5. Effect of occlusion detection strategies. We compare gradient-based (ours) to optical-flow based occlusion detection, and a combination of both. Occlusions are shown in yellow.
+
+| Pose sampling | ||P|| | Oacc↑ | IEacc↑ | IErec↑ |
| Random orbit | 4 | 0.923 | 0.674 | 0.596 |
| Random shift | 4 | 0.927 | 0.692 | 0.636 |
| Rig | 4 | 0.930 | 0.708 | 0.687 |
| Rig | 8 | 0.932 | 0.720 | 0.729 |
+
+leverages two-way optical flow between the input and novel views to identify regions visible only in the latter, as well as a conservative fusion of both techniques. As shown in Fig. 5, the depth gradient method robustly captures occlusions without requiring extensive post-filtering. In contrast, the optical flow approach introduces numerous false positives in the presence of large warps, necessitating aggressive filtering that subsequently reduces true positive detections. Moreover, it incorrectly classifies all pixels outside the input view's field of view as occluded. The fused strategy mitigates some of the false positives compared to optical flow alone but still inherits many of its limitations.
+
+# 4.3.3.Viewpoint sampling
+
+The selection of poses for novel views has a substantial impact on 3D scene geometry reconstruction, especially in occluded regions. We evaluate several pose sampling strategies using our occupancy reconstruction benchmark. As shown in Tab. 3, translating the camera along the input baseline by $[-3m, 3m]$ yields better results than orbiting it by $[-10^{\circ}, 10^{\circ}]$ around a vertical axis at a depth of $5m$ . Camera rigs outperform random warp sampling strategies, as their cameras are already defined in sensible poses.
+
+# 4.4. Distillation into a Feed-Forward Model
+
+The loss configuration used to distill synthetic data into the scene reconstruction model is critical to its performance. We assess the contribution of individual loss terms by evaluating occupancy reconstruction metrics in Tab. 4 and providing qualitative comparisons in Fig. 6. Compared to ab
+
+Table 3. Pose sampling strategies. We evaluate the quality of generated geometry under various pose sampling strategies. A camera rig with eight predefined poses and random rotations achieves the best performance.
+
+| Method | Oacc↑ | IEacc↑ | IErec↑ |
| Full | 0.902 | 0.705 | 0.706 |
| w/o Ldepth | 0.857 | 0.656 | 0.443 |
| w/o Locc | 0.907 | 0.699 | 0.757 |
| w/o uncertainty | 0.907 | 0.697 | 0.701 |
+
+Table 4. Quantitative effect of different loss terms. We show reconstructions produced by models with different loss terms turned off. Overall, the full model produces the most convincing results.
+
+
+Figure 6. Qualitative effect of different loss terms. See Tab. 4.
+
+lated variants, our full loss setup achieves competitive $\mathrm{O_{acc}}$ and the highest $\mathrm{IE_{acc}}$ . While removing $\mathcal{L}_{\mathrm{occ}}$ increases the invisible and empty region recall ( $\mathrm{IE_{rec}}$ ), it lowers $\mathrm{IE_{acc}}$ - indicating that the model over-predicts free space, which may not be correct. Moreover, the predicted uncertainty is needed to balance the depth and volumetric loss w.r.t. each other. As illustrated in Fig. 6, omitting $\mathcal{L}_{\mathrm{depth}}$ leads to less accurate reconstruction of invisible and empty regions. Eliminating $\mathcal{L}_{\mathrm{occ}}$ worsens the reconstruction of invisible but non-empty space, an effect not reflected in $\mathrm{IE_{rec}}$ . Finally, the predicted uncertainty is essential for balancing the depth and volumetric losses relative to one another.
+
+# 5. Conclusion
+
+In this work, we proposed a novel approach to monocular 3D reconstruction that can be trained using only single images. The resulting geometry matches or exceeds the performance of models trained with multi-view supervision.
+
+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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+# DreamActor-M1: Holistic, Expressive and Robust Human Image Animation with Hybrid Guidance
+
+Yuxuan Luo* Zhengkun Rong* Lizhen Wang* Longhao Zhang* Tianshu Hu*† Bytedance China
+
+{luoyuxuan, rongzhengkun, wanglizhen.2024, zhanglonghao.zlh, tianshu.hu}@bytedance.com
+
+
+Figure 1. We introduce DreamActor-M1, a DiT-based human animation framework, with hybrid guidance to achieve fine-grained holistic controllability, multi-scale adaptability, and long-term temporal coherence.
+
+
+
+
+
+
+
+
+
+# Abstract
+
+While recent image-based human animation methods achieve realistic body and facial motion synthesis, critical gaps remain in fine-grained holistic controllability, multi-scale adaptability, and long-term temporal coherence, which leads to their lower expressiveness and robustness. We propose a diffusion transformer (DiT) based framework, DreamActor-M1, with hybrid guidance to overcome these limitations. For motion guidance, our hybrid control signals that integrate implicit facial representations, 3D head spheres, and 3D body skeletons achieve robust
+
+control of facial expressions and body movements, while producing expressive and identity-preserving animations. For scale adaptation, to handle various body poses and image scales ranging from portraits to full-body views, we employ a progressive training strategy using data with varying resolutions and scales. For appearance guidance, we integrate motion patterns from sequential frames with complementary visual references, ensuring long-term temporal coherence for unseen regions during complex movements. Experiments demonstrate that our method outperforms the state-of-the-art works, delivering expressive results for portraits, upper-body, and full-body generation with robust long-term consistency.
+
+# 1. Introduction
+
+Human image animation has become a hot research direction in video generation and provides potential applications for film production, the advertising industry, and video games. While recent advances in image and video diffusion have enabled basic human motion synthesis from a single image, previous works like [14, 21, 30, 40, 53, 58, 62] have made great progress in this area. However, existing methods remain constrained to coarse-grained animation. There are still some critical challenges in achieving fine-grained holistic control (e.g., subtle eye blinks and lip tremors), generalization ability to multi-scale inputs (portrait/upper-body/full-body), and long-term temporal coherence (e.g. long-term consistency for unseen garment areas). In order to handle these complex scenarios, we propose a DiT-based framework, DreamActor-M1, to achieve holistic, expressive and robust human image animation with hybrid guidance.
+
+Recent developments in image-based animation have explored various directions, yet critical shortcomings persist in attaining photorealistic, expressive, and adaptable generation for practical applications. While single-image facial animation approaches employ landmark-driven or 3DMM-driven methodologies through GAN [3, 37, 39, 46, 48, 59] or NeRF [57] for expression manipulation, they frequently face limitations in image resolution and expression accuracy. Although certain studies attain robust expression precision via latent face representations [5, 6, 44, 51, 63] or achieve enhanced visual quality with diffusion-based architectures [41, 60], their applicability is typically restricted to portrait regions, failing to meet the broader demands of real-world scenarios. Diffusion-based human image animation [1, 14, 43, 53, 58] are able to generate basic limb articulation, plausible garment deformations and hair dynamics, but neglect the fine-grained facial expressions reenactment. Current solutions remain under-explored in addressing holistic control of facial expressions and body movements while failing to accommodate real-world multi-scale deployment requirements. Furthermore, existing methods fail to maintain temporal coherence in long-form video synthesis, especially for unseen areas in the reference image.
+
+In this work, we focus on addressing multi-scale driven synthesis, fine-grained face and body control, and long-term temporal consistency for unseen areas. Solving these challenges is non-trivial. First, it is very challenging to accurately manage both detailed facial expressions and body movements using a single control signal, especially for the precise control over subtle facial expressions. Second, due to incomplete input data and the inability to generate extended video sequences in a single pass, the model inevitably loses information about unseen regions (such as clothing textures on the back) during the continuation process that relies solely on the reference image and the final frame of prior clips. This gradual information decay
+
+leads to inconsistencies in unseen areas across sequentially generated segments. Third, under multi-scale inputs, the varying information density and focus priorities make it hard to achieve holistic and expressive animation within a single framework. To tackle these issues, we introduce stronger hybrid control signals, and complementary appearance guidance that can fill missing information gaps, and a progressive training strategy with a training dataset including diverse samples at different scales (e.g. portrait talking and full-body dancing).
+
+Specifically, for motion guidance, our core innovation lies in extracting maximally informative yet mutually decoupled control signals from driving videos, followed by their effective integration into the backbone model. We design a hybrid control signals including implicit face latent for fine-grained control of facial expressions, explicit head spheres for head scale and rotation and 3D body skeletons for torso movements and bone length adjustment which achieves robust adaptation across substantial shape variations. For scenarios with limited information (e.g., multi-turn rotations or partial-body references), we introduce complementary appearance guidance by first sampling distinct poses from target movements, then generating multiframe references to provide unseen area textures, and finally propagating these references across video segments to maintain consistent details throughout long-term synthesis. To enable multi-scale adaptation, we train the model with a progressive strategy on a diverse dataset that includes different types of scenes like portrait acting, upper-body talking, and full-body dancing. In summary, our key contributions are as follows.
+
+- We propose a holistic DiT-based framework and a progressive training strategy for human image animation that supports flexible multi-scale synthesis.
+- We design hybrid control signals combining implicit facial representations, explicit 3D head spheres, and body skeletons to enable the expressive body and facial motion synthesis while supporting diverse character styles.
+- We develop complementary appearance guidance to mitigate information gaps of unseen areas between video segments, enabling consistent video generation over long durations.
+
+# 2. Related Works
+
+Recent advancements in human image animation can be broadly categorized into single-image facial animation and body animation, each addressing distinct technical challenges in photorealistic and expressive human motion synthesis.
+
+# 2.1. Single-Image Facial Animation
+
+Early work primarily used GANs for portrait animation via warping and rendering, focusing on motion representations
+
+
+Figure 2. Overview of DreamActor-M1. During the training stage, we first extract body skeletons and head spheres from driving frames and then encode them to the pose latent using the pose encoder. The resultant pose latent is combined with the noised video latent along the channel dimension. The video latent is obtained by encoding a clip from the input full video using 3D VAE. Facial expression is additionally encoded by the face motion encoder, to generate implicit facial representations. Note that the reference image can be one or multiple frames sampled from the input video to provide additional appearance details during training and the reference token branch shares weights of our DiT model with the noise token branch. Finally, the denoised video latent is supervised by the encoded video latent. Within each DiT block, the face motion token is integrated into the noise token branch via cross-attention (Face Attn), while appearance information of ref token is injected to noise token through concatenated self-attention (Self Attn) and subsequent cross-attention (Ref Attn).
+
+
+
+like neural keypoints [12, 37, 48, 59] or 3D face parameters [4, 32]. While effectively decoupling identity and expression features, these methods struggled with subtle and exaggerated expressions. Alternative approaches learned latent representations [5, 6, 44] directly from driving faces, enabling better expression reproduction but suffering from GAN limitations in quality and style adaptation. In recent years, diffusion-based methods have demonstrated strong generative capabilities, leading to significant advancements in subsequent research. EMO [41] first introduced the ReferenceNet into the diffusion-based portrait video generation task. Follow-your-emoji [25] utilized expression-aware landmarks with facial fine-grained loss for precise motion alignment and micro-expression details. Megactor- $\Sigma$ [54] designed a diffusion transformer integrating audio-visual signals for multi-modal control. X-Portrait [50] combined ControlNet for head pose and expression with patch-based local control and cross-identity training. X-Nemo [60] developed 1-D latent descriptors to disentangle identity-motion entanglement. SkyReels-A1 [31] proposed a portrait animation framework leveraging the diffusion transformer [29].
+
+# 2.2. Single-Image Body Animation
+
+MRAA [38] pioneered motion representations for body animation. The advent of latent diffusion [33] has significantly advanced body animation techniques [1, 19, 25, 42, 47, 49]. Animate Anyone [14] introduced an additional ReferenceNet to extract appearance features from reference images. MimicMotion [58] designed a confidence-aware pose guidance mechanism and used facial landmarks to reenact facial expressions.Animate-X [40] employed implicit and explicit pose indicators for motion and pose features, respectively. Instead of using skeleton maps, Champ [62] and Make-Your-Anchors [16] leveraged a 3D human parametric model, while MagicAnimate [53] utilized DensePose [11] to establish dense correspondences. TALK-Act [10] enhanced the textural awareness with explicit motion guidance to improve the generation quality. StableAnimator [43] and HIA [52] addressed the identity preservation and motion blur modeling, respectively. Additionally, some previous studies [21, 30, 55] followed a plugin paradigm, enhancing effectiveness without requiring additional training of existing model parameters. To address missing appearances under significant viewpoint changes,
+
+MSTed [13] introduced multiple reference images as input. MIMO [26] andAnimate Anyone 2 [15] separately modeled humans, objects, and backgrounds, aiming to animate characters with environmental affordance. Apart from UNet-based diffusion, recent works [8, 35] have also begun adapting diffusion transformers [29] for human animation.
+
+# 3. Method
+
+Given one or multiple reference images $I_R$ along with a driven video $V_D$ , our objective is to generate a realistic video that depicts the reference character mimicking the motions present in the driving video. In this section, we begin with a concise introduction to our Diffusion Transformer (DiT) backbone in Sec. 3.1. Following that, we offer an in-depth explanation of our carefully-designed hybrid control signals in Sec. 3.2. Subsequently, we introduce the complementary appearance guidance in Sec. 3.3. Finally, we present the progressive training processes in Sec. 3.4.
+
+# 3.1. Preliminaries
+
+As shown in Fig. 2, our overall framework adheres to the Latent Diffusion Model (LDM) [33] for training the model within the latent space of a pre-trained 3D Variational Autoencoder (VAE) [56]. We utilize the MMDiT [7] as the backbone network, which has been pre-trained on text-to-video and image-to-video tasks, Seaweed [23]. Note that we employ Flow Matching [24] as the training objective.
+
+Unlike the prevailing ReferenceNet-based human animation approaches [14, 15], we refrain from employing a copy of the DiT as the ReferenceNet to inject the reference feature into the DenoisingNet following [22]. Instead, we flatten the latent feature $\widetilde{I}_R$ and $\widetilde{V}_D$ extracted through the VAE, patchify, concatenate them together, and then feed them into the DiT. It facilitates the information interaction between the reference and video frames through 3D self-attention layers and spatial cross-attention layers integrated throughout the entire model. Specifically, in each DiT block, given the concatenated token $T\in \mathbb{R}^{(t\times h\times w)\times c}$ , we perform self-attention along the first dimension. Then, we split it into $T_{R}\in \mathbb{R}^{t_{R}\times (h\times w)\times c}$ and $T_{D}\in \mathbb{R}^{t_{D}\times (h\times w)\times c}$ and reshape them to $T_{R}\in \mathbb{R}^{1\times (h\times w\times t_{R})\times c}$ and $T_{D}\in \mathbb{R}^{t_{D}\times (h\times w)\times c}$ to perform cross-attention along the second dimension.
+
+# 3.2. Hybrid Motion Guidance
+
+To achieve expressive and robust human animation, in this paper, we intricately craft the motion guidance and propose hybrid control signals comprising implicit facial representations, 3D head spheres, and 3D body skeletons.
+
+Implicit Facial Representations. In contrast to conventional approaches that rely on facial landmarks for expression generation, our method introduces implicit facial representations. This innovative approach not only enhances the preservation of intricate facial expression details but also
+
+facilitates the effective decoupling of facial expressions, identity and head pose, enabling more flexible and realistic animation. Specifically, our pipeline begins by detecting and cropping the faces in the driving video, which are then resized to a standardized format $F \in \mathbb{R}^{t \times 3 \times 224 \times 224}$ . A pre-trained face motion encoder $\mathbf{E}_f$ and an MLP layer are employed to encode faces to face motion tokens $M \in \mathbb{R}^{t \times c}$ . The $M$ is fed into the DiT block through a cross-attention layer. The face motion encoder is initialized using an off-the-shelf facial representation learning method [44], which has been pre-trained on large-scale datasets to extract identity-independent expression features. This initialization not only accelerates convergence but also ensures that the encoded motion tokens are robust to variations in identity, focusing solely on the nuances of facial expressions. By leveraging implicit facial representations, our method achieves superior performance in capturing subtle expression dynamics while maintaining a high degree of flexibility for downstream tasks such as expression transfer and re-enactment. It is worth noting that we additionally train an audio-driven encoder capable of mapping speech signals to face motion token. This encoder enables facial expression editing, particularly lip-syncing, without the need for a driving video.
+
+3D Head Spheres. Since the implicit facial representations are designed to exclusively control facial expressions, we introduce an additional 3D head sphere to independently manage head pose. This dual-control strategy ensures that facial expressions and head movements are decoupled, enabling more precise and flexible animation. Specifically, we utilize an off-the-shelf face tracking method [45] to extract 3D facial parameters from the driving video, including camera parameters and rotation angles. These parameters are then used to render the head as a color sphere projected onto the 2D image plane. The sphere's position is carefully aligned with the position of the driving head in the video frame, ensuring spatial consistency. Additionally, the size of the sphere is scaled to match the reference head's size, while its color is dynamically determined by the driving head's orientation, providing a visual cue for head rotation. This 3D sphere representation offers a highly flexible and intuitive way to control head pose, significantly reducing the model's learning complexity by abstracting complex 3D head movements into a simple yet effective 2D representation. This approach is particularly advantageous for preserving the unique head structures of reference characters, especially those from anime and cartoon domains.
+
+3D Body Skeletons. For body control, we introduce 3D body skeletons with bone length adjustment. In particular, we first use 4DHumans [9] and HaMeR [28] to estimate body and hand parameters of the SMPL-X [27] model. Then we select the body joints, project them onto the 2D image plane, and connect them with lines to construct the
+
+
+Figure 3. Overview of our inference pipeline. First, we (optionally) generate multiple pseudo-references to provide complementary appearance information. Next, we extract hybrid control signals comprising implicit facial motion and explicit poses (head sphere and body skeleton) from the driving video. Finally, these signals are injected into a DiT model to synthesize animated human videos. Our framework decouples facial motion from body poses, with facial motion signals being alternatively derivable from speech inputs.
+
+skeleton maps. We opt to use skeletons instead of rendering the full body, as done in Champ [62], to avoid providing the model with strong guidance on body shape. By leveraging skeletons, we encourage the model to learn the shape and appearance of the character directly from the reference images. This approach not only reduces bias introduced by predefined body shapes but also enhances the model's ability to generalize across diverse body types and poses, leading to more flexible and realistic results. The body skeletons and the head spheres are concatenated in the channel dimension, and fed into a pose encoder $\mathbf{E}_p$ to obtain the pose feature. The pose feature and noised video feature are then concatenated and processed by an MLP layer to obtain the noise token.
+
+During inference, to address variations in skeletal proportions across subjects, we adopt a normalization process to adjust the bone length. First, we use a pre-trained image editing model [36] to transform reference and driving images into a standardized A-pose configuration. Next, we leverage RTMPose [18] to calculate the skeletal proportions of both the driving subject and the reference subject. Finally, we perform anatomical alignment by proportionally adjusting the bone lengths of the driving subject to match the skeletal measurements of the reference subject.
+
+# 3.3. Complementary Appearance Guidance
+
+We propose a novel multi-reference injection protocol to enhance the model's capability for robust multi-scale, multiview, and long-term video generation. This approach addresses the challenges of maintaining temporal consistency and visual fidelity across diverse viewing angles and extended timeframes. During training, we compute the rotation angles for all frames in the input video and sort them based on their z-axis rotation values (yaw). From this sorted set, we strategically select three key frames corresponding to the maximum, minimum, and median z-axis rotation angles. These frames serve as representative viewpoints, ensuring comprehensive coverage of the object's orientation. Furthermore, for videos featuring full-body compositions, we introduce an additional step: a single frame is randomly selected and cropped to a half-body portrait format, which
+
+is then included as an auxiliary reference frame. This step enriches the model's understanding of both global and local structural details.
+
+During inference, our protocol offers an optional two-stage generation mode to handle challenging scenarios, such as cases where the reference image is a single frontal half-body portrait while the driving video features full-body frames with complex motions like turning or side views. First, the model is utilized to synthesize a multi-view video sequence from the single reference image. This initial output captures a range of plausible viewpoints and serves as a foundation for further refinement. We apply the same frame selection strategy used during training to select the most informative frames. These selected frames are then reintegrated into the model as the complementary appearance guidance, enabling the generation of a final output that exhibits enhanced spatial and temporal coherence. This iterative approach not only improves the robustness of the model but also ensures high-quality results even under constrained input conditions.
+
+# 3.4. Progressive Training Process
+
+Our training process is divided into three distinct stages to ensure a gradual and effective adaptation of the model. In the first stage, we utilize only two control signals: 3D body skeletons and 3D head spheres, deliberately excluding the implicit facial representations. This initial stage is designed to facilitate the transition of the base video generation model to the task of human animation. By avoiding overly complex control signals that may hinder the model's learning process, we allow the model to establish a strong foundational understanding of the task. In the second stage, we introduce the implicit facial representations while keeping all other model parameters frozen. During this stage, only the face motion encoder and face attention layers are trained, enabling the model to focus on learning the intricate details of facial expressions without the interference of other variables. Finally, in the third stage, we unfreeze all model parameters and conduct a comprehensive training session, allowing the model to fine-tune its performance by jointly optimizing all components. This staged approach
+
+
+Reference Image
+
+
+Driving Image
+
+
+Animate Anyone
+
+
+Champ
+
+
+MimicMotion
+
+
+Dispose
+
+
+Ours
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 4. The comparisons with human image animation works, Animate Anyone [14], Champ [62], MimicMotion [58] and DisPose [21]. Our method demonstrates results with better fine-grained motions, identity preservation, temporal consistency and high fidelity.
+
+
+
+
+
+
+
+
+
+
+
+ensures a robust and stable training process, ultimately leading to a more effective and adaptable model.
+
+# 4. Experiments
+
+# 4.1. Experimental Setups
+
+Implementation Details. Our training weights are initialized from a pretrained image-to-video DiT model [23]. Then, we train the first stage with 20,000 steps, the second stage with 20,000 steps, and the third stage with 30,000 steps. To enhance the model's generalization capability for arbitrary durations and resolutions, during training, the length of the sampled video clips is randomly selected from 25 to 121 frames, while the spatial resolution is resized to an area of $960 \times 640$ , maintaining the original aspect ratio. All stages are trained with 8 H20 GPUs using the AdamW optimizer with a learning rate of $5e^{-6}$ . During inference, each video segment contains 73 frames. To ensure full-video consistency, we use the last latent from the current segment as the initial latent for the next segment, modeling the next segment generation as an image-to-video generation task. The classifier-free guidance (cfg) parameters for
+
+both the references and motion control signals are set to 2.5. Datasets. For training, we construct a comprehensive dataset by collecting video data from the internet, totaling 500 hours of footage. This dataset encompasses a diverse range of scenarios, including dancing, sports, film scenes, and speeches, ensuring broad coverage of human motion and expressions. The dataset is balanced in terms of framing, with full-body shots and half-body shots each accounting for approximately $50\%$ of the data. In addition, we leverage Nersemble [20] to further improve the synthesis quality of faces. For evaluation, we utilize two distinct datasets: the widely-used TikTok dataset [17] and our collected dataset. The TikTok dataset is limited in its diversity of motion patterns and framing. Yet our collected dataset provides a more varied and challenging benchmark, enabling a more robust assessment of the model's generalization capabilities across different scenarios.
+
+Evaluation Metrics. We adhere to established evaluation metrics employed in prior research, including FID, SSIM, LPIPS, PSNR, and FVD. The first four are used to evaluate the generation quality of each frame, while the last one is used to assess the video fidelity.
+
+
+Figure 5. Our comparisons with portrait image animation works, LivePortrait [12], X-Portrait [50], Skyreels-A1 [31] and Runway Act-One [34]. Our method demonstrates more accurate and expressive portrait animation capabilities.
+
+# 4.2. Comparisons with Existing Methods
+
+To comprehensively demonstrate the effectiveness of our work, we conducted experiments on both body animation and portrait animation tasks. Note that our method demonstrates strong performance with just a single reference image in most cases. To ensure fairness in comparison with other methods, we only used multiple reference images in the ablation study, while a single reference image was employed in the comparative analysis. We strongly recommend readers refer to the supplementary video.
+
+Comparisons with Body Animation Methods. As illustrated in Tab. 1, DreamActor-M1 achieves superior overall performance compared to state-of-the-art human image animation approaches on the TikTok dataset. Due to the limited character and motion diversity of the TikTok dataset, we additionally perform the qualitative and quantitative evaluation of DreamActor-M1 with our collected dataset and compare with state-of-the-art body animation methods, including Animate Anyone [14], Champ [62], MimicMotion [58], and DisPose [21], as shown in Tab. 2 and Fig. 4. We can see that our proposed DreamActor-M1 outperforms the current state-of-the-art results.
+
+Comparisons with Portrait Animation Methods. We also compare the DreamActor-M1 with state-of-the-art portrait animation methods, including LivePortrait [12], X-Portrait [50], SkyReels-A1 [31], and Act-One [34], as shown in Tab. 3 and Fig. 5. As shown in Tab. 3, the video-driven results consistently outperform all competing methods across all metrics on our collected dataset.
+
+While facial expressions and head pose are decoupled in our framework, our method can also be extended to audio-
+
+ | FID↓ | SSIM↑ | PSNR↑ | LPIPS↓ | FVD↓ |
| AA [14] | 58.98 | 0.718 | 29.56 | 0.285 | 171.9 |
| Champ [62] | 56.04 | 0.773 | 29.91 | 0.234 | 160.8 |
| MimicMotion [58] | 53.47 | 0.785 | 30.17 | 0.223 | 154.6 |
| DisPose [21] | 47.82 | 0.801 | 29.76 | 0.230 | 158.8 |
| Ours | 38.64 | 0.819 | 31.04 | 0.219 | 131.3 |
+
+Table 1. Quantitative comparisons with body animation methods on TikTok dataset.
+
+ | FID↓ | SSIM↑ | PSNR↑ | LPIPS↓ | FVD↓ |
| AA [14] | 36.72 | 0.791 | 21.74 | 0.266 | 158.3 |
| Champ [62] | 40.21 | 0.732 | 20.18 | 0.281 | 171.2 |
| MimicMotion [58] | 35.90 | 0.799 | 22.25 | 0.253 | 149.9 |
| DisPose [21] | 33.01 | 0.804 | 21.99 | 0.248 | 144.7 |
| Ours | 27.27 | 0.821 | 23.93 | 0.206 | 122.0 |
+
+Table 2. Quantitative comparisons with body animation methods on our collected dataset.
+
+driven facial animation. Specifically, we train a face motion encoder to map speech signals to face motion tokens, leading to realistic and lip-sync animations. As an extended application, we omit quantitative comparisons. Please refer to our supplementary video for more results.
+
+# 4.3. Ablation Study
+
+We conducted comprehensive ablation studies to evaluate the impact of several core components of our method.
+
+Multi-Reference Protocol. We compare two settings: (a) inference with a single reference image, (b) a two-stage inference approach as described in Sec. 3.3, where pseudo
+
+ | FID↓ | SSIM↑ | PSNR↑ | LPIPS↓ | FVD↓ |
| LivePortrait [12] | 31.72 | 0.809 | 24.25 | 0.270 | 147.1 |
| X-Portrait [50] | 30.09 | 0.774 | 22.98 | 0.281 | 150.9 |
| SkyReels-A1 [31] | 30.66 | 0.811 | 24.11 | 0.262 | 133.8 |
| Act-One [34] | 29.84 | 0.817 | 25.07 | 0.259 | 135.2 |
| Ours | 25.70 | 0.823 | 28.44 | 0.238 | 110.3 |
+
+Table 3. Quantitative comparisons with portrait animation methods on our collected dataset.
+
+ | FID↓ | SSIM↑ | PSNR↑ | LPIPS↓ | FVD↓ |
| Single-R | 28.22 | 0.798 | 25.86 | 0.223 | 120.5 |
| Multi-R (pseudo) | 26.53 | 0.812 | 26.22 | 0.219 | 116.6 |
+
+Table 4. Ablation study on multi-reference.
+
+
+Figure 6. Ablation study of 3D skeletons with bone length adjustment (BLA) and implicit face features.
+
+reference images are generated first, followed by multi-reference inference. Results are shown in Tab. 4. It demonstrates that pseudo multi-reference inference outperforms single-reference inference in terms of long-term video generation quality and temporal consistency. This is because during the extended video generation process, the supplementary reference images provide additional visual information about unseen areas, enabling the video generation process to leverage reference details. This helps avoid information loss and thereby maintains consistency throughout the video. Nevertheless, the performance achieved by a
+
+single reference image remains competitive, demonstrating its sufficiency for most scenarios.
+
+Hybrid Control Signals. We further investigate the contribution of our hybrid control signals by ablating key components: (a) substituting 3D head sphere and skeleton with 2D skeleton and 3D mesh (b) substituting implicit facial representations with 2D landmark and 3D facial landmarks. Results are shown in Fig. 6. It reveals a significant performance degradation under these settings, emphasizing the importance of each component in our hybrid control framework. Specifically, the 3D skeletons with bone length adjustment provide more accurate spatial guidance, and the implicit facial representations capture subtle expression details more effectively than traditional landmarks. These findings demonstrate the effectiveness and superiority of our proposed hybrid control signals in achieving high-quality and realistic human image animation.
+
+# 5. Conclusion
+
+In this paper, we present a holistic human image animation framework addressing multi-scale adaptation, fine-grained facial expression and body movement control, and long-term consistency in unseen regions. We employ a progressive training strategy using data with varying resolutions and scales to handle various image scales ranging from portraits to full-body views. By decoupling identity, body pose, and facial expression through hybrid control signals, our method achieves precise facial dynamics and vivid body movements while preserving the character identity. The proposed complementary appearance guidance resolves information gaps in cross-scale animation and unseen region synthesis. We believe these innovations provide potential insights for future research in complex motion modeling and real-world deployment of expressive human animation.
+
+Limitation. While our framework achieves robust human animation, it currently exhibits three key limitations: (1) inherent difficulties in controlling dynamic camera movements, (2) inability to model physical interactions with environmental objects, and (3) instability in bone length adjustment (using [36]) for edge cases, requiring multiple iterations with manual selections for optimal cases. These technical challenges, combined with the unmet needs of multi-character and non-humanoid (e.g., animal) animation, constitute important directions for future research.
+
+Ethics considerations. Human image animation has possible social risks, like being misused to make fake videos. The proposed technology could be used to create fake videos of people, but existing detection tools [2, 61] can spot these fakes. To reduce these risks, clear ethical rules and responsible usage guidelines are necessary.
+
+# Acknowledgment
+
+We extend our sincere gratitude to Shanchuan Lin, Lu Jiang, Yongming Zhu, Zhurong Xia, Jianwen Jiang, Zerong Zheng, Chao Liang, Youjiang Xu, Ming Zhou, Tongchun Zuo, Xin Dong and Yanbo Zheng for their invaluable contributions and supports to this research work.
+
+# References
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+# DreamCube: RGB-D Panorama Generation via Multi-plane Synchronization
+
+Yukun Huang1 Yanning Zhou2 Jianan Wang3 Kaiyi Huang1 Xihui Liu1†
+1The University of Hong Kong 2Tencent 3Atribot https://yukun-huang.github.io/DreamCube/
+
+
+RGB-D Panorama Generation from Single View
+
+
+Panoramic Depth Estimation
+
+
+
+
+3D Gaussian Scene Generation
+Figure 1. In this work, we introduce Multi-plane Synchronization to generalize 2D diffusion models to multi-plane omnidirectional representations (i.e., cubemaps), and DreamCube for RGB-D cubemap generation. The proposed approaches can be applied to different tasks including RGB-D panorama generation, panorama depth estimation, and 3D scene generation.
+
+# Abstract
+
+3D panorama synthesis is a promising yet challenging task that demands high-quality and diverse visual appearance and geometry of the generated omnidirectional content. Existing methods leverage rich image priors from pretrained 2D foundation models to circumvent the scarcity of 3D panoramic data, but the incompatibility between 3D panoramas and 2D single views limits their effectiveness. In this work, we demonstrate that by applying multi-plane synchronization to the operators from 2D foundation models, their capabilities can be seamlessly extended to the omnidirectional domain. Based on this design, we further introduce DreamCube, a multi-plane RGB-D diffusion model for 3D panorama generation, which maximizes the reuse of 2D foundation model priors to achieve diverse appearances and accurate geometry while maintaining multi-view consistency. Extensive experiments demonstrate the effectiveness of our approach in panoramic image generation, panoramic depth estimation, and 3D scene generation.
+
+# 1. Introduction
+
+Humans live in a fully immersive 3D environment. Simulating this immersive experience is crucial for applications such as virtual reality, gaming, and robotics [41, 51, 57]. As a fundamental technology for building 3D world, omnidirectional content synthesis aims to generate visual content that covers a full $360^{\circ} \times 180^{\circ}$ field of view, encompassing both appearance and geometry. Despite this necessity, modern generative models [7, 24, 35] require large amounts of training data, yet the scale of currently available omnidirectional assets remains relatively small compared to conventional perspective images.
+
+Leveraging the rich image priors from pre-trained 2D diffusion models [35], previous works [1, 8, 19, 26, 44-46, 53, 54] explore repurposing diffusion-based image generators to create $360^{\circ}$ panoramas, which circumvents the problem of insufficient panoramic data. While most of these works [1, 8, 45, 46, 53, 54] adopt equirectangular projection (ERP) for panoramas for simplicity, this approach introduces significant challenges. The ERP causes severe spatial distortions near the poles, resulting in a pixel distribution fundamentally different from that of perspective images on
+
+
+Figure 2. Motivation. Previous works [43, 48] on RGB-D panorama generation is based on equirectangular representations and only supports Euclidean depth instead of the more popular Z-depth. However, the distribution of Euclidean depth is quite different from that of RGB images (e.g., circles on flat surfaces as highlighted by orange dashed boxes), which hinders the use of pre-trained 2D diffusion priors. Multi-plane methods [19, 44] support Z-depth, but their adopted FoV overlapping techniques lead to depth ambiguity, as highlighted by red dashed boxes. Different from existing works, our approach supports multi-plane Z-depth generation without using FoV overlapping techniques.
+
+which the pre-trained models were trained. These distortions not only affect visual quality but also limit the transferability of pre-trained knowledge, resulting in suboptimal generation quality particularly at the poles.
+
+Another solution for panoramic synthesis is the multi-plane approach, which utilizes 2D diffusion to generate synchronized multi-perspective images. In general, multiplane images are closer to the in-domain distribution of the pre-trained 2D diffusion models and can natively produce higher resolution panoramas. However, the separate generation of multiple planes leads to severe seam inconsistencies. To the best of our knowledge, all existing works [19, 44] on multi-plane panorama generation adopt field-of-view (FoV) overlapping to improve seam inconsistencies. Although effective to some extent, the overlapping planes actually cause computational redundancy and reduce the effective image resolution. Moreover, we empirically found that FoV-overlapping multi-planes are exhibit significant incompatibilities in non-image domains, such as the latent space of LDM [35] and the Z-depth domain, as shown in Figure 2. These incompatibilities manifest as conflicting, non-unique z-depth values at overlapping regions, leading to the artifacts in the end. These limitations lead to a fundamental question: Can seam inconsistencies be resolved without FoV overlapping?
+
+To address this question, we present the first thorough
+
+Table 1. Comparisons of different panorama generation methods. Omni. refers to Omnidirectional $(360^{\circ}\times 180^{\circ})$
+
+| Methods | Condition | Output | Resolution† | Omni. |
| Text2Light [3] | text | HDR | 512 × 1024 | ✓ |
| LDM3D-Pano [42] | text | RGB-D | 512 × 1024 | ✓ |
| OmniDreamer [1] | image | RGB | 256 × 512 | ✓ |
| Diffusion360 [8] | text/image | RGB | 512 × 1024 | ✓ |
| MVDiffusion [44] | text/text-image | RGB | 256 × 256 × 8‡ | × |
| PanFusion [54] | text/text layout | RGB | 512 × 1024 | ✓ |
| PanoDiffusion [48] | image | RGB-D | 256 × 512 | ✓ |
| CubeDiff [19] | text-image | RGB | 491 × 491 × 6‡ | ✓ |
| DreamCube (Ours) | text-image | RGB-D | 512 × 512 × 6 | ✓ |
+
+$\dagger$ Base resolution without super-resolution or post-processing.
+${}^{ \ddagger }$ Calculated effective resolution accounting for overlapping fields of view.
+
+analysis of 2D diffusion models to identify the causes of seam inconsistencies in multi-plane generation. Our analysis reveals that these inconsistencies are rooted in the translational inequivalence of certain neural operators in the omnidirectional image domain. Surprisingly, we find that by adapting these operators to be omnidirectionally translation-equivalent, existing 2D diffusion models can generate seam-consistent panoramic multi-planes without requiring fine-tuning or FoV overlapping. In this work, we refer to this adaptation as "multi-plane synchronization".
+
+Building on multi-plane synchronization, we introduce DreamCube, a novel framework for generating RGB-Depth (RGB-D) cubemaps from a single view through joint panoramic appearance and geometry modeling. Inspired by previous work on diffusion-based depth estimation [9, 14, 20, 23], we repurpose the pre-trained 2D diffusion model for multi-plane image and depth generation. Unlike previous approaches [42, 48] to equirectangular RGB-D panorama generation, we adopt cubemaps as panorama representation. This choice is significant because pixels in each plane of a cubemap are uniformly distributed (due to perspective projection rather than equirectangular projection) and therefore align with the in-domain distribution of the pre-trained 2D diffusion models. Table 1 compares our approach with existing panorama generation methods across key dimensions. Together with multi-plane synchronization, our method maximally exploits pre-trained 2D diffusion models for joint modeling of panoramic appearance and geometry. The resulting RGB-D cubemaps can be easily lifted to 3D scene, effectively enabling single-view to omnidirectional 3D scene generation.
+
+Our main contributions are as follows:
+
+- We thoroughly analyze the operator incompatibilities of existing 2D diffusion models for panoramic multi-plane generation, and propose a multi-plane synchronization strategy that enables seam-consistent cubemap generation without fine-tuning or FoV overlapping.
+
+- Based on multi-plane synchronization, we further introduce DreamCube, a masked RGB-D cubemap generator from single view for panoramic appearance and geometry generation.
+- Extensive experiments demonstrate the effectiveness of our approach in RGB-D panorama generation, panoramic depth estimation, and 3D scene generation.
+
+# 2. Related Work
+
+2D panorama generation. Panorama image generation aims to create 360-degree panoramas from text prompts or partial images. Early works [3, 30] utilized GAN [10] for panorama generation, while recent diffusion models have enabled more sophisticated panoramic synthesis. Current approaches either iteratively outpaint $360^{\circ}$ panoramas from narrow field-of-view images [2, 26, 27] or directly generate complete panoramas [44-46, 48, 53, 54]. Many methods employ equirectangular projection (ERP) to represent $360^{\circ} \times 180^{\circ}$ views, but face challenges with geometric distortions, particularly in polar regions. Various denoising and decoding strategies [45, 46, 48] have been proposed to reduce stitching artifacts. To avoid polar distortion and leverage pretrained perspective image diffusion models, alternative approaches [19, 44] generate multiple perspective views. CubeDiff [19] introduces a cubemap representation that projects the $360^{\circ}$ view onto six faces of a cube, effectively eliminating severe distortions while maintaining consistency. Yet these multi-plane approaches use FoV overlapping to reduce seam artifacts, which introduces computational redundancy and limits effective resolution.
+
+Generative depth estimation. Various methods explore diffusion models for depth estimation [5, 18, 38, 39, 55]. Marigold [20] converts pretrained Latent Diffusion Models into image-conditioned depth estimators. However, directly applying these depth estimation methods to panoramic images presents challenges: the domain gap between ERP and perspective image representations degrades performance. Alternatively, estimating depth for multiple perspective views independently requires an additional alignment step to ensure consistency. DAC [11] attempts to jointly learn depth in both ERP and perspective spaces within a unified framework, but its effectiveness remains limited.
+
+Joint appearance and geometry modeling. Another line of works jointly models appearance and geometry [6, 9, 23, 25, 50]. This joint modeling strategy has also demonstrated effectiveness in specific domains, such as human-centric scenarios [17, 21, 28]. Following this trend, we jointly model appearance and depth information for panorama generation to enhance scene structure understanding and obtain high-quality depth maps for subsequent 3D scene creation. Unlike previous RGB-D panorama generation methods [42, 48], our approach operates directly on perspective images, better leveraging prior knowledge from pretrained
+
+models while jointly modeling appearance and depth for high-quality panoramic scene creation.
+
+# 3. Multi-plane Synchronization
+
+# 3.1. Preliminary: Panorama Representations
+
+Panorama representations refer to methods of storing 360-degree images or videos, allowing viewers to look in all directions from a single viewpoint. Equirectangular and cubemap formats are the two primary formats due to their compatibility with existing image processing frameworks.
+
+Equirectangular representations project the panoramic content onto a rectangular grid, where the horizontal axis represents the longitude and the vertical axis represents the latitude. This format is one of the most commonly used for storing and transmitting 360-degree images and videos due to its simplicity and compatibility with standard image and video formats. Despite its ease of use, the equirectangular representation suffers from significant distortion, especially near the poles, where the pixels are stretched.
+
+Cubemap representations divide the panoramic scene into six square faces of a cube, each representing a 90-degree field of view. The primary advantage of the cubemap is its uniform distribution of pixels across the entire field of view, which minimizes distortion compared to the spherical representation. However, it can introduce discontinuities at the edges where the cube faces meet, which may require additional processing to ensure seamless transitions. In our work, we adopt the cubemap representation for its minimal distortion and compatibility with pre-trained 2D diffusion models.
+
+# 3.2. Multi-plane Synchronization
+
+Directly applying 2D diffusion models pre-trained on single-view images to multi-plane panoramic representations like cubemaps faces a fundamental limitation: They generate each face independently with no inherent correlation, which leads to discontinuities at the seams of adjacent cube faces. To address this issue, we propose Multi-plane Synchronization, which achieves seamless panoramic generation without the need for fine-tuning or explicitly constructing overlapping regions [19, 44].
+
+To present our multi-plane synchronization, we use U-Net-based diffusion models [35] and six-plane cubemaps throughout this work. The principles established, however, are architecture-agnostic and can be adapted to other diffusion frameworks, such as DiT [31] and alternative panorama representation with minimal modifications.
+
+Analysis of spatial operators. Neural operators should ideally maintain translation-equivalence in omnidirectional representations, but standard operators (e.g., self-attention) in 2D diffusion models break this property. For instance, in standard 2D convolutions, boundary pixels of each cube
+
+
+Figure 3. Results of Multi-plane Synchronization on pre-trained 2D diffusion models: SD2 [35], SDXL [33], and Marigold [20]. Our method enables 2D diffusion to generate multi-plane synchronized omnidirectional image representations without fine-tuning.
+
+
+
+face are padded with zeros instead of information from adjacent faces, resulting in discontinuities at cubemap seams. Therefore, all operators of 2D diffusion involving the spatial domain must be adapted to ensure translation invariance in the omnidirectional domain.
+
+Synchronizing spatial operators to cubemaps. For U-Net-based diffusion models, we adapt three key operators from single-view $(H\times W)$ to multi-plane domains $(M\times H\times W$ , where $M = 6$ for cubemaps): (1) synced attentions - reshaping tokens from $(BM)\times (HW)\times C$ to $B\times (MHW)\times C$ , enabling attention to operate across all faces simultaneously; (2) synced 2D convolutions - replacing zero-padding with geometrically projected pixels from adjacent faces; and (3) synced group normalizations - calculating statistics globally across all planes rather than perview independently.
+
+Remarks. While individual adaptations of these operators exist in previous works-flattened attentions in [19, 40], projective resampling in [30], and tiled group normalizations in [15, 19], none provides a comprehensive solution. Our proposed multi-plane synchronization offers a more complete and systematic adaptation of 2D diffusion models to support the omnidirectional image domain. As shown in Figure 3, our method can be applied to various pre-trained 2D diffusion models, such as Stable Diffusion [35] and Marigold [20], to achieve omnidirectional generation. These results demonstrate the effectiveness and potential of our method in omnidirectional vision tasks such
+
+as panorama generation and panoramic depth estimation.
+
+# 4. Method
+
+In this section, we introduce DreamCube, a masked RGB-D cubemap diffusion model for joint panoramic appearance and geometry generation.
+
+# 4.1. Generative Formulation
+
+We conceptualize the generation of RGB-D cubemap as the production of six colored images $\boldsymbol{x}_c \in \mathbb{R}^{M \times H \times W \times 3}$ and their corresponding depth maps $\boldsymbol{x}_d \in \mathbb{R}^{M \times H \times W}$ , where $M = 6$ denotes the number of cubic views. Each of these views is associated with a specific face of the cubemap, namely front, right, back, left, up, and down. Given single-view RGB-D images and multi-view texts as conditions, our model aims to generate RGB-D images of other cubic views through a synchronous diffusion denoising process.
+
+At training time, we first encode the colored cubemap $\pmb{x}_c$ and the corresponding depth cubemap $\pmb{x}_d$ into latents $\pmb{z}_c \in \mathbb{R}^{M \times H' \times W' \times 4}$ and $\pmb{z}_d \in \mathbb{R}^{M \times H' \times W' \times 4}$ using a pretrained VAE [35]. In particular, the depth inputs $\pmb{x}_d$ are broadcasted to 3-channels to match the configuration of the VAE. Then, the masked Gaussian noises $\pmb{\epsilon}_c^{(t)}$ and $\pmb{\epsilon}_d^{(t)}$ are sampled and injected into $\pmb{z}_c$ and $\pmb{z}_d$ , obtaining $\pmb{z}_c^{(t)}$ and $\pmb{z}_d^{(t)}$ , respectively. Note that the conditional image latent (w.l.o.g., we choose the front view as condition) are kept noise-free throughout the diffusion process. Finally, the image latents
+
+
+Figure 4. Training and inference framework of DreamCube for RGB-D cubemap generation. At training time, RGB-D cube faces are encoded by synced VAE and injected masked Gaussian noises, obtaining image and depth latents. These latents are concatenated with positional encoding and mask as diffusion U-Net's input. The entire U-Net is fine-tuned with $v$ -objective [36] to learn to jointly denoise RGB and depth latents. At inference time, DreamCube receives single-view RGB-D images and multi-view texts as input and generates completed RGB-D cubemap representations via iterative diffusion denoising and synced VAE decoding.
+
+$z_{c}^{(t)}$ and depth latents $z_{d}^{(t)}$ are concatenated with the positional encoding and mask on the channel axis and fed into the diffusion U-Net. We use $v$ -prediction [36] as the learning objective, and the training loss is given as follows:
+
+$$
+\begin{array}{l} \mathcal {L} = \mathbb {E} _ {\boldsymbol {x} _ {c}, \boldsymbol {\epsilon} _ {c} \sim \mathcal {N} (0, I), t \sim \mathcal {U} (T)} \| \boldsymbol {v} _ {c} ^ {(t)} - \hat {\boldsymbol {v}} _ {c} ^ {(t)} \| _ {2} ^ {2} \\ + \mathbb {E} _ {\boldsymbol {x} _ {d}, \boldsymbol {\epsilon} _ {d} \sim \mathcal {N} (0, I), t \sim \mathcal {U} (T)} \| \boldsymbol {v} _ {d} ^ {(t)} - \hat {\boldsymbol {v}} _ {d} ^ {(t)} \| _ {2} ^ {2}, \\ \end{array}
+$$
+
+where $\pmb{v}_c^{(t)}$ and $\pmb{v}_d^{(t)}$ are predicted by the diffusion U-Net.
+
+At inference time, the conditional image latents $\pmb{c}_c \in \mathbb{R}^{1 \times H' \times W' \times 4}$ and depth latents $\pmb{c}_d \in \mathbb{R}^{1 \times H' \times W' \times 4}$ are concatenated with Gaussian noises to get the initial noisy latents $\pmb{z}_c^{(T)}$ and $\pmb{z}_d^{(T)}$ . These noisy latents will be iteratively denoised as the time step decreases from $T$ to 1 to get noise-free cubemap latents $\pmb{z}_c^{(0)}$ and $\pmb{z}_d^{(0)}$ . The final results can be obtained by decoding these latents with VAE.
+
+# 4.2. DreamCube: RGB-Depth Cube Diffusion
+
+As illustrated in Figure 4, DreamCube adopts several designs to enable RGB-D cubemap generation from a single view, which involves depth data processing, omnidirectional position encoding, and multi-plane synchronization.
+
+Depth data processing. Panoramic depth data usually uses the Euclidean distance metric, the depth distribution of which is significantly different from the RGB image distribution (e.g., the circle on the flat wall as shown in Figure 2),
+
+which hinders the joint modeling of RGB images and depth maps. Therefore, unlike previous works [42, 48], DreamCube models the Z-distance, which is more consistent with the diffusion image priors, rather than the Euclidean distance.
+
+Additionally, DreamCube estimates the depth maps of other cubic views based on the conditional view. Even though the conditional depth values lie in the diffusion's indomain range $[-1.0, +1.0]$ , the generated depths of other views may exceed this range, leading to performance degradation. Inspired by recent work on depth inpainting [29], we adopt a depth rescaling strategy. Specifically, we rescale the conditional depth to the range of $[-s, +s]$ before input, where the real number $s$ is less than 1. This strategy creates an additional margin for the depth generation of other views, thus avoiding out-of-domain depth values.
+
+Omnidirectional positional encoding. To ensure geometric consistency and coherent object relationships across generated cube faces, we improve the spatial awareness of LDM [35] by integrating positional encodings derived from the 3D geometry of the cube. Specifically, for each point on a cube face, we project its coordinates onto the unit sphere with $(x,y,z)$ values normalized to $[-1,1]$ . These normalized coordinates are then appended as three additional channels to LDM's latent representations. This encoding strategy encodes spatial information for each latent patch rela
+
+
+Figure 5. Comparison between UV encoding and XYZ encoding for omnidirectional image representations.
+
+tive to its cube face while ensuring smooth omnidirectional transitions - addressing limitations of the UV-based encoding proposed by CubeDiff [19] (see comparisons in Fig. 5).
+
+Multi-plane synchronized diffusion. As described in Sec. 3.2, multi-plane synchronization enhances 2D diffusion models' capability to handle omnidirectional image representations. Specifically, all self-attentions, 2D convolutions, and group normalizations within the diffusion U-Net and VAE are replaced with multi-plane synchronized operators. This strategy enables DreamCube to effectively model multi-plane omnidirectional representations, significantly mitigating issues such as discontinuous seams and inconsistent color tones in cubemap generation.
+
+# 5. Experiment
+
+# 5.1. Datasets
+
+We conduct experiments in two distinct data settings to comprehensively evaluate the performance of our method across various scenarios. Further details of data processing can be found in the supplementary material.
+
+Indoor setting. To ensure fair comparison with prior work, we first evaluate our approach on the Structured3D dataset [56], which provides equirectangular indoor RGB-D panorama with a $512 \times 1024$ resolution. Following the same experimental protocol as PanoDiffusion [48], we utilize their exact data split consisting of 16,930 training, 2,116 validation, and 2,117 test instances. Besides, the SUN360 dataset [49] is also used for out-of-domain evaluation.
+
+General setting. To further evaluate our model's generalization capabilities across diverse environments, we construct a more comprehensive dataset by combining multiple publicly available sources, including Structured3D [56], Pano360 [22], Polyhaven [34], Humus [32], HDRI-Skies [12] and iHDRI [13]. This combined dataset encompasses a broad spectrum of both indoor and outdoor environments, resulting in more than 30,000 panoramic instances. This general setting allows us to evaluate the robustness of our approach across a wider range of scenarios.
+
+# 5.2. RGB-D Panorama Generation
+
+Evaluating RGB-D panorama generation from a single view presents unique challenges due to the absence of standardized benchmarks. We train and test our method on the standard split of the Structured3D [56] dataset following another RGB-D panorama generation work, PanoDiffusion [48]. To comprehensively evaluate the capabilities of our method, we evaluate the RGB panorama quality and depth panorama accuracy separately tailored to each modality's characteristics.
+
+Evaluation protocol for RGB panorama generation. We evaluate our method on both in-domain Structured3D [56] and out-of-domain SUN360 [49] datasets. SUN360 consists of around 1000 panorama images including both indoor and outdoor scenes. We use Fréchet Inception Distance (FID) [16] and Inception Score (IS) [37] to evaluate the visual quality of generated panorama images.
+
+Evaluation protocol for depth panorama generation. Since no ground-truth depths exist for generated panoramas, we propose a reference-based evaluation protocol. We first project our generated RGB-D panoramas into multiple perspective views at randomly sampled viewpoints. For each projected RGB image, we obtain a reference depth map using Depth Anything v2 [52], a state-of-the-art monocular depth estimator. This provides pseudo ground-truth depth for each perspective view. We then compare projected depth maps against these reference depths using standard metrics: $\delta$ -1.25, AbsREL, RMSE and MAE, following the implementation in [4].
+
+Quantitative results for RGB panorama generation. We compare our approach with state-of-the-art panorama generation methods including OmniDreamer [1], LDM3D-Pano [43], Diffusion360 [8], MVDiffusion [44], PanoDiffusion [48], and PanFusion [54]. The comparison results are reported in Table 2. Our method performs competitively on both in-domain and out-of-domain datasets with the best overall ranking. Note that for SUN360, we only
+
+Table 2. Quantitative results on RGB panorama generation compared with state-of-the-art methods, evaluated on both in-domain Sturctured3D and out-of-domain SUN360 datasets.
+
+| Methods | Structured3D | SUN360 | Avg. Rank |
| FID ↓ | IS ↑ | FID ↓ | IS ↑ |
| OmniDreamer† [1] | 97.46 | 3.35 | 128.17 | 2.29 | 7.0 |
| LDM3D-Pano [43] | 32.57 | 6.13 | 72.67 | 4.86 | 3.3 |
| Diffusion360† [8] | 26.23 | 4.85 | 63.03 | 4.21 | 3.5 |
| MVDiffusion [44] | 35.99 | 5.00 | 67.22 | 4.33 | 4.0 |
| PanoDiffusion [48] | 16.20 | 4.04 | 80.02 | 3.91 | 4.8 |
| PanFusion [54] | 44.86 | 6.18 | 84.25 | 4.98 | 3.8 |
| DreamCube (Ours) | 12.58 | 5.50 | 66.56 | 5.35 | 1.8 |
+
+†Including SUN360 as training data.
+
+
+Figure 6. Qualitative results of the proposed DreamCube on RGB-D panorama generation compared with RGB-D panorama generation methods: LDM3D-Pano [43] and PanoDiffusion [48]. The green dashed boxes highlight the input image condition.
+
+
+Figure 7. Qualitative results of the proposed Multi-plane Synchronization on panoramic depth estimation compared with recent panoramic depth estimation methods: Depth Any Camera (DAC) [11] and Depth Anywhere [47].
+
+use it for out-of-domain evaluation while Diffusion360 and OmniDreamer use it for training. Nonetheless, our method significantly outperforms both methods on inception score.
+
+Quantitative results for depth panorama generation. We compare our approach with RGB-D panorama generation methods: LDM3D-Pano [43], PanoDiffusion [48], and panoramic depth estimation method: Depth Any Camera (DAC) [11], and the results are reported in Table 3. Our method outperforms the competing methods consistently on all metrics, demonstrating the superiority of the proposed joint RGB-D cubemap generation in obtaining accurate geometry compared to equirectangular-based RGB-D generation and depth estimation methods.
+
+Qualitative results. We provide visualization results of the generated RGB-D panorama, as shown in Fig-
+
+Table 3. Quantitative results on depth panorama generation compared with RGB-D panorama generation methods: LDM3D-Pano [43], PanoDiffusion [48], and panoramic depth estimation method: Depth Any Camera (DAC) [11].
+
+| Methods | δ-1.25 ↑ | AbsRel ↓ | RMSE ↓ | MAE ↓ |
| LDM3D-Pano [43] | 0.655 | 0.199 | 0.323 | 0.267 |
| PanoDiffusion [48] | 0.695 | 0.160 | 0.301 | 0.255 |
| DAC [11] | 0.751 | 0.139 | 0.266 | 0.220 |
| DreamCube (Ours) | 0.787 | 0.133 | 0.256 | 0.211 |
+
+ure 6. Compared with the equirectangular based RGB-D panorama generation methods: LDM3D-Pano [42] and PanoDiffusion [48], our method is able to obtain more de
+
+
+No Sync. (Baseline)
+
+
++ Synced Self-Attn. (MVDream)
+
+
++ Synced Conv2d (CubeGAN)
+
+
++Synced GroupNorm.
+(ScaleCrafter)
+Figure 8. Ablation analysis of Multi-plane Synchronization. We adopt Stable-Diffusion v2 as baseline model for multi-plane generation, and the text prompt used is "The vast cosmos in the style of Van Gogh, with swirling patterns and vibrant colors."
+
+
++ Synced Self-Attn. & GroupNorm
+(CubeDiff)
+
+
+All Sync.
+(Ours)
+
+tailed and accurate geometry. Moreover, our generated RGB panoramas have fewer artifacts than PanoDiffusion which uses the same training set as ours. We attribute these advantages to the fact that the cubemap representations can better exploit the 2D diffusion's image priors compared to the geometrically distorted equirectangular representations.
+
+# 5.3. Panoramic Depth Estimation
+
+Our proposed Multi-plane Synchronization extends naturally to monocular depth estimation, demonstrating its versatility beyond RGB panorama generation. As shown in Figure 7, applying our synchronization approach to Marigold effectively eliminates the discontinuous seams that occur when processing multi-plane inputs with the original model. Qualitative comparisons with recent panoramic depth estimation methods: Depth Any Camera (DAC) [11] and Depth Anywhere [47] reveal that our approach captures more detailed geometric structures while maintaining the continuity of depth values at left-right seams (which Depth Anywhere fails). These results show that the proposed Multi-plane Synchronization can effectively generalize diffusion-based monocular depth estimation models to multi-plane omnidirectional representations with painless modification and minimal performance loss.
+
+# 5.4. Ablation Study
+
+We perform ablation analysis on the proposed Multi-plane Synchronization to evaluate its effectiveness. More analysis results can be found in the supplementary material.
+
+Ablation analysis of Multi-plane Synchronization. To analyze the impact of different synced operators, we perform different synchronization configurations and provide
+
+the visualization results in Figure 8. Synced self-attention ensures content consistency across faces,ynced group normalization harmonizes color tones, andynced convolutions reduce seam discontinuities. Combining all three operators produces panoramas with seamless transitions, consistent content, and uniform style.
+
+# 6. Conclusion
+
+In this work, we thoroughly analyze the limitations of existing 2D diffusion models when applied to multi-plane panoramic representations, and propose a multi-plane synchronization strategy to painlessly generalize pre-trained 2D diffusion models to the omnidirectional image domain. This strategy ensures translation equivariance in the omnidirectional image domain by adapting the spatial operators in the model without the need for additional fine-tuning or constructing overlapping views. Benefiting from multiplane synchronization, we further introduce DreamCube, which jointly models RGB and depth cube maps by leveraging image priors from pre-trained 2D diffusion. Extensive experiments show that the proposed approach outperforms previous equirectangular-based RGB-D panoramic generation methods and holds potential in panoramic depth estimation and 3D scene generation.
+
+# Acknowledgment
+
+The research work described in this paper was conducted in the JC STEM Lab of Autonomous Intelligent Systems funded by The Hong Kong Jockey Club Charities Trust.
+
+# References
+
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+# DreamDance: Animating Human Images by Enriching 3D Geometry Cues from 2D Poses
+
+Yatian Pang $^{1,3}$ , Bin Zhu $^{1}$ , Bin Lin $^{1}$ , Mingzhe Zheng $^{4}$ , Francis E. H. Tay $^{3}$ , Ser-Nam Lim $^{5,6}$ , Harry Yang $^{4,6}$ , Li Yuan $^{1,2,\dagger}$
+
+$^{1}$ PKU Shenzhen Graduate School $^{2}$ PengCheng Laboratory $^{3}$ NUS $^{4}$ HKUST $^{5}$ UCF $^{6}$ Everlyn
+
+# Abstract
+
+In this work, we present DreamDance, a novel method for animating human images using only skeleton pose sequences as conditional inputs. Existing approaches struggle with generating coherent, high-quality content in an efficient and user-friendly manner. Concretely, baseline methods relying on only 2D pose guidance lack the cues of 3D information like depth and normal maps, leading to suboptimal results. Other works introduce extra representations to provide additional 3D information but inevitably involve a cumbersome and time-intensive process. To address these limitations, DreamDance enriches 3D geometry cues from 2D poses by introducing an efficient diffusion model, enabling high-quality human image animation with various guidance. Our key insight is that human images naturally exhibit multiple levels of correlation, progressing from coarse skeleton poses to fine-grained geometry cues, and further from these geometry cues to explicit appearance details. Capturing such correlations could enrich the guidance signals, facilitating intra-frame coherency and interframe consistency. Specifically, we construct the TikTok-Dance5K dataset, comprising 5K high-quality dance videos with detailed frame annotations, including human pose, depth, and normal maps. Next, we introduce a Mutually Aligned Geometry Diffusion Model to generate fine-grained depth and normal maps for enriched guidance. Finally, a Cross-domain Controller incorporates multi-level guidance to animate human images effectively with a video diffusion model. Extensive experiments demonstrate that our method achieves state-of-the-art performance in animating human images compared to baseline methods.
+
+# 1. Introduction
+
+Human image animation refers to generating dynamic and realistic videos from static human images following a sequence of motion control signals. This field has attracted
+
+
+Figure 1. A summarized comparison between DreamDance and the baseline methods.
+
+significant academic interest due to its diverse applications across industries, including film production, social media, and online retail. Despite the rapid development of generative artificial intelligence, human image animation remains challenging because it requires a comprehensive understanding of both intra-frame coherency and inter-frame consistency.
+
+Recently, diffusion models [24, 58] have demonstrated remarkable potential in image [6, 45, 50, 51] and video [4, 5, 79, 84, 90] generation, unlocking new possibilities for human image animation tasks. Pioneer works such as Disco [64] and Dreampose [33] leverage input images and pose conditions to generate target frames sequentially. However, due to the lack of temporal learning capabilities, these methods often suffer from flickering artifacts and temporal inconsistency across frames. To address these limitations, more recent methods such as MagicAnimate [75] and
+
+AnimateAnyone [28] incorporate temporal attention blocks into the diffusion network to enhance temporal coherence. Despite this improvement, their generation quality remains constrained by coarse control conditions without 3D geometry information, leading to inconsistent and incoherent visual outputs. To obtain rich guidance signals other than original 2D poses, Champ [91] additionally introduces a 3D parametric human model SMPL [39]. By first generating SMPL motions and then rendering them into normal and depth maps, this approach integrates geometric information with pose sequences for human image animation. However, SMPL-based methods present significant drawbacks. First, generating SMPL motions is cumbersome and not user-friendly, as it typically relies on predictions from existing videos, which limits editability and flexibility compared to the more intuitive manipulation of poses using open-source tools like the GUI [43]. Second, the independence between SMPL and pose models can lead to misalignment between control signals, resulting in imprecise adherence to the intended pose sequences. Additionally, SMPL's rendering primarily emphasizes body geometry while neglecting visual details and temporal consistency, which can contribute to temporal incoherence and visual inconsistencies. We summarize existing methods in Figure 1.
+
+To this end, we propose DreamDance, a unified framework for animating human images using only skeleton pose sequences as original guidance signals. Our key insight is the recognition of multi-level correlations inherent in human images, extending from coarse skeleton poses to fine-grained geometry cues, and further to explicit appearance details. Capturing these correlations could enrich the guidance signals, thereby enhancing both intra-frame coherence and inter-frame consistency in the animation process. To achieve this, we first construct a dataset, TikTok-Dance5K, comprising 5,000 high-quality dance videos, each annotated with human pose, depth, and normal maps for every frame. Building on this dataset, we propose a novel framework comprising two diffusion models. Specifically, the Mutually Aligned Geometry Diffusion Model generates detailed depth and normal maps to enrich the guidance signals. To ensure the robustness and effectiveness of the generated guidance signals, we introduce geometry attention and temporal attention modules, which align guidance across modality and temporal dimensions. With the enriched geometry cues, the Cross-Domain Controlled Video Diffusion Model utilizes a cross-domain controller to integrate multiple levels of guidance, animating human images with high quality. Besides, we implement a robust conditioning scheme to reduce the impact of error accumulation in our two-stage generation pipeline. Extensive experiments demonstrate that DreamDance achieves state-of-the-art performance in animating human images, significantly improving both visual coherence and temporal consistency
+
+compared to existing methods. We again highlight the comparison in Figure 1 and show that by eliminating the need for complex and rigid 3D models, our approach provides greater flexibility, ease of use, and finer control over the animation process, establishing it as a highly effective solution for animating human images.
+
+To sum up, this work contributes in the following ways:
+
+- We construct the TikTok-Dance5K dataset, comprising 5,000 high-quality human dance videos with comprehensive visual annotations. It will be made publicly available to support further research in the field.
+- We propose the Mutually Aligned Geometry Diffusion model, which generates detailed depth and normal maps to enrich guidance signals. To ensure robustness, we incorporate geometry and temporal attention modules that align geometric information across modality and temporal dimensions.
+- We introduce the Cross-Domain Controlled Video Diffusion Model, which utilizes a cross-domain controller to integrate multiple levels of guidance for high-quality human image animating. A robust conditioning scheme further mitigates the effects of error accumulation in our two-stage generation pipeline.
+- Our extensive experiments demonstrate that our framework achieves state-of-the-art performance in animating human images, setting a new benchmark for visual coherence and temporal consistency compared to existing methods.
+
+# 2. Related Works
+
+# 2.1. Diffusion Models for Image Generation
+
+Diffusion models have achieved significant success in generating images given various conditions. Notably, Stable Diffusion [50] has demonstrated its potential in producing high-quality images from text prompts as the conditioning input. To introduce additional control over the generation process, ControlNet [87] proposes training an additional copy of the pre-trained diffusion model to incorporate extra control signals, such as pose, depth, and canny edges. Subsequently, many works [42, 54, 80] propose incorporating more complex control signals for enhanced controllability in image generation. In this work, we focus on using pose as the control signal and propose generating fine-grained depth and normal maps to provide supplementary guidance. Several works [38, 44, 48] propose generating geometry maps with diffusion models to improve the quality of the generated 3D geometry. Other works [15, 34] propose to utilize diffusion models for depth and normal estimation tasks. To generate precise human images, Hyperhuman [37] proposes a latent structural diffusion model to jointly capture the human image appearance and geometry relationship. Their diffusion model consists of different expert branches and
+
+only supports text as input conditions. In our work, we propose a novel geometry diffusion model by introducing a geometry attention mechanism and utilizing a reference net for fine-grained reference image control. We also incorporate temporal attention to enable the geometric generation along the temporal dimension.
+
+# 2.2. Diffusion Models for Video Generation
+
+The great potential of diffusion models in image generation has inspired extensive research in applying them to video generation [10, 12, 17, 19, 29, 35, 46, 47, 53, 68, 71, 81, 83, 86]. Pioneer works [12, 25, 26, 35, 56] focus on extending image-based diffusion models using temporal modules to address the dynamics of video sequences and generating videos. Video LDM [5] first pre-train the model on images and then fine-tune it on video data by incorporating temporal layers. Animatediff [20] add additional motion modules into pre-trained text-to-image diffusion models and train them with video data. Stable Video Diffusion (SVD) [4] is a latent video diffusion model for high-resolution imaged-to-video generation. The authors identify and evaluate three different stages for successful training of the video diffusion model and explore a unified strategy for curating video data. In this work, we construct SVD-ControlNet and take Stable Video Diffusion as the base model because it possesses a strong temporal prior and temporal consistency compared to training from scratch or adapting from image diffusion models.
+
+# 2.3. Diffusion Models for Human Image Animation
+
+Human image animation aims to generate dynamic and realistic human motion videos given a static human image and a sequence of control signals [1, 7, 8, 13, 14, 16, 18, 21, 22, 30, 32, 36, 40, 41, 49, 52, 59, 60, 62, 63, 65–67, 70, 72–74, 76, 82, 85, 89]. Recent works utilize the successful diffusion models for this task. DreamPose [33] and DISCO [64] modify the diffusion model to integrate the information from the reference image and control signal. However, they animate the human image in a frame-by-frame manner, which lacks temporal consistency. The following works AnimateAnyone [28], MagicAnimate [75], and MagicPose [9] propose a similar framework that uses a reference network for human feature injection and also utilizes motion modules to enhance temporal consistency. The recent work Champ [91] introduces the use of a 3D parametric human model, SMPL, to provide additional conditions for human image animation by generating normal and depth maps from SMPL motions. However, this approach has limitations, including the complexity of creating SMPL motions, potential misalignment between SMPL and pose models, and the omission of important details like outfits and hair, leading to less coherent generated content. Our method addresses these limitations by proposing a Mutually
+
+Aligned Geometry Diffusion Model to jointly capture human image appearance and geometry relationship, achieving efficiency and high quality.
+
+# 3. Preliminaries and Problem Formulation
+
+# 3.1. Diffusion Models
+
+Diffusion models, as introduced in previous works [24, 57], aim to approximate a data distribution $q(\mathbf{x})$ by learning a probabilistic model $p_{\theta}(\mathbf{x}_0) = \int p_{\theta}(\mathbf{x}_{0:T}) \, \mathrm{d}\mathbf{x}_{1:T}$ . The joint distribution between $\mathbf{x}_0$ and random latent variables $\mathbf{x}_{1:T}$ is defined through a reverse Markov Chain, $p_{\theta}(\mathbf{x}_{0:T}) = p(\mathbf{x}_T) \prod_{t=1}^{T} p_{\theta}(\mathbf{x}_{t-1}|\mathbf{x}_t)$ , where $p(\mathbf{x}_T)$ is modeled as a standard normal distribution, and the transition kernels are expressed as $p_{\theta}(\mathbf{x}_{t-1}|\mathbf{x}_t) = \mathcal{N}(\mathbf{x}_{t-1}; \mu_{\theta}(\mathbf{x}_t,t), \sigma_t^2\mathbf{I})$ . A forward Markov Chain is also constructed as $q(\mathbf{x}_{1:T}|\mathbf{x}_0) = \prod_{t=1}^{T} q(\mathbf{x}_t|\mathbf{x}_{t-1})$ , allowing $\mu_{\theta}(\mathbf{x}_t,t)$ to be defined as: $\frac{1}{\sqrt{\alpha}_t} \left( \mathbf{x}_t - \frac{\beta_t}{\sqrt{1 - \bar{\alpha}_t}} \epsilon_{\theta}(\mathbf{x}_t,t) \right)$ , where the noise predictor $\epsilon_{\theta}$ is trained using the loss function:
+
+$$
+\ell = \mathbb {E} _ {t, \mathbf {x} _ {0}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) \| _ {2} \right], \tag {1}
+$$
+
+with $\bar{\alpha}_t$ as a constant and $\epsilon$ sampled from a standard normal distribution. Building on the foundation of diffusion models, latent diffusion models [50] extend this approach by mapping data into a low-dimensional latent space using a pre-trained variational auto-encoder (VAE) [11]. The diffusion process is then applied within this latent space, which significantly reduces computational costs and allows these models to handle larger datasets and more complex tasks, such as video and 3D generation. In our work, we fine-tune our diffusion models using these advanced latent diffusion models and their variants to achieve our specific goals.
+
+# 3.2. Problem Formulation
+
+Given a human image $X$ and a sequence of driving poses $p_{1:T}$ , we aim to generate a human animation video $Y_{1:T}$ . We propose to capture the correlations in a coarse-to-fine manner, facilitating both intra-frame coherence and inter-frame consistency. Specifically, we first jointly generate fine-grained image $x_{t}$ , depth $d_{t}$ , and normal maps $n_t$ in low-resolution space to enrich guidance for each frame $t$ with a Mutually Aligned Geometry Diffusion Model $G_{1}$ . Then we incorporate multiple guidance to animate the human image utilizing a high-resolution Cross-domain Controlled Video Diffusion Model $G_{2}$ with a cross-domain controller. Note that we drop the low-resolution RGB images $x_{1:T}$ generated in the first stage. The overall pipeline can be formulated as,
+
+$$
+x _ {1: T}, n _ {1: T}, d _ {1: T} = G _ {1} ^ {\text {l o w . r e s}} (X, p _ {1: T}) \tag {2}
+$$
+
+$$
+Y _ {1: T} = G _ {2} ^ {\text {h i g h . r e s}} (X, p _ {1: T}, n _ {1: T}, d _ {1: T})
+$$
+
+
+Figure 2. Overview of DreamDance framework. The Mutually Aligned Geometry Diffusion Model generates detailed depth and normal maps to enrich guidance signals that are mutually aligned across modalities and time. The Cross-domain Controlled Video Diffusion Model utilizes a cross-domain controller to integrate multiple levels of guidance, producing high-quality human animations.
+
+# 4. Method: DreamDance
+
+We propose DreamDance, a unified framework for animating human images with high quality and precise control. As shown in Figure 2, our method consists of two stages according to our problem formulation in Section 3.2. Given the reference image and target poses, the Mutually Aligned Geometry Diffusion Model generates the target normal and depth maps as well as RGB images in the first stage, enriching geometry cues as guidance. Subsequently, the Cross-Domain Controlled Video Diffusion Model utilizes a cross-domain controller to integrate multiple levels of guidance for high-quality human image animating.
+
+# 4.1. Mutually Aligned Geometry Diffusion Model
+
+To enrich geometric information from the reference image given the target poses, we aim to first establish correlations that transition from a coarse-level pose skeleton to fine-grained spatial geometry. However, several challenges arise. 1). The original diffusion model is trained on RGB images, which differ significantly from geometry representations, making it difficult to model these disparate modalities within a unified diffusion process. 2). While the target pose provides the basic human structure, it lacks detailed geometry and appearance information that should be sourced from the reference image. 3). Ground truth RGB images are inherently aligned with their geometric features, necessitating the preservation of this alignment throughout the generation process to ensure coherence and accuracy.
+
+Modeling a Unified Diffusion Process. As shown in Fig-
+
+ure 2 (a.), we model a unified diffusion process that jointly generates depth $\mathbf{d}$ and normal maps $\mathbf{n}$ , along with RGB images $\mathbf{x}$ , all aligned with the target poses $\mathbf{p}$ based on the reference images $\mathbf{i}$ . The unified diffusion model can be trained with a simplified objective:
+
+$$
+\begin{array}{l} \ell = \mathbb {E} _ {t, \mathbf {z}, \mathbf {i}, \mathbf {p}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {\mathbf {t}}; \mathbf {i}, \mathbf {p}) \| _ {2} ^ {2} \right. \tag {3} \\ \mathbf {z} _ {\mathbf {t}} = \operatorname {c o n c a t} \left(\mathbf {x} _ {\mathbf {t}}, \mathbf {n} _ {\mathbf {t}}, \mathbf {d} _ {\mathbf {t}}\right) \\ \end{array}
+$$
+
+where $\epsilon \sim \mathcal{N}(0, I)$ are independent Gaussian noise and $t$ is the sampled timestep that determines the scale of added noise. The noisy latents are obtained by $\mathbf{x}_{\mathbf{t}} / \mathbf{n}_{\mathbf{t}} / \mathbf{d}_{\mathbf{t}} = \alpha_{t}(\mathbf{x} / \mathbf{n} / \mathbf{d}) + \sigma_{t}\epsilon$ and are concatenated along the batch dimension as a unified noisy latent $\mathbf{z}_{\mathbf{t}}$ , which is sent into the denoising UNet to predict the added noise. Given that the original diffusion model has a strong prior in the image domain, which differs from the distribution of depth and normal maps, we introduce a domain embedding to the UNet architecture. This aims to simplify the training process by better accommodating the distinct characteristics of each domain. Specifically, we use a one-hot vector to specify the domain of each sample, which is then encoded using positional encoding. The resulting domain embedding is added to the time embedding in the UNet. We find that incorporating the domain embedding leads to more stable training and faster convergence.
+
+Control with Reference Image and Target Pose. Inspired by [28], we introduce a reference UNet for detailed reference image feature guidance. The spatial attention in the denoising UNet is modified as,
+
+$$
+\begin{array}{l} \mathbf {q} = W _ {q} \cdot \mathbf {x}, \\ \mathbf {k} = W _ {k} \cdot \operatorname {c o n c a t} (\mathbf {x}, \mathbf {x} _ {\text {r e f}}), \tag {4} \\ \mathbf {v} = W _ {v} \cdot c o n c a t (\mathbf {x}, \mathbf {x} _ {\mathrm {r e f}}), \\ \end{array}
+$$
+
+where $\mathbf{x}$ is the noisy features and $\mathbf{x}_{\mathrm{ref}}$ is the detailed injection features from the reference UNet. These features are concatenated along the sequence dimension. Additionally, to guide the diffusion model with the target pose, we employ a lightweight convolutional pose encoder with zero convolution projection to encode the pose embedding following [28, 91]. The pose embedding is added to the noisy latent features after the conv_in layer of the UNet.
+
+Mutual Alignment with Geometry Attention. We now extend the original diffusion model to jointly generate normal and depth maps, along with RGB images, all semantically aligned with the target pose and reference image. However, there is no inherent guarantee that these generated outputs will be mutually consistent. To address this, we propose a geometry attention module that aligns the geometric representations and RGB images during the diffusion process, ensuring coherence across the generated content. The geometry attention is modified based on the self-attention mechanism in which the queries, keys, and values for each different modality are computed as follows,
+
+$$
+\begin{array}{l} \mathbf {q} _ {\mathbf {i}} = W _ {q} \cdot \mathbf {x} _ {\mathbf {i}}, \quad \mathbf {q} _ {\mathbf {n}} = W _ {q} \cdot \mathbf {x} _ {\mathbf {n}}, \quad \mathbf {q} _ {\mathbf {d}} = W _ {q} \cdot \mathbf {x} _ {\mathbf {d}}, \\ \mathbf {k} _ {\mathbf {i}} = W _ {k} \cdot c a t \left(\mathbf {x} _ {\mathbf {i}}, \mathbf {x} _ {\mathbf {n}}, \mathbf {x} _ {\mathbf {d}}\right), \mathbf {v} _ {\mathbf {i}} = W _ {v} \cdot c a t \left(\mathbf {x} _ {\mathbf {i}}, \mathbf {x} _ {\mathbf {n}}, \mathbf {x} _ {\mathbf {d}}\right), \tag {5} \\ \mathbf {k} _ {\mathbf {n}} = W _ {k} \cdot c a t (\mathbf {x} _ {\mathbf {i}}, \mathbf {x} _ {\mathbf {n}}, \mathbf {x} _ {\mathbf {d}}), \mathbf {v} _ {\mathbf {n}} = W _ {v} \cdot c a t (\mathbf {x} _ {\mathbf {i}}, \mathbf {x} _ {\mathbf {n}}, \mathbf {x} _ {\mathbf {d}}), \\ \mathbf {k} _ {\mathbf {d}} = W _ {k} \cdot c a t (\mathbf {x} _ {\mathrm {i}}, \mathbf {x} _ {\mathrm {n}}, \mathbf {x} _ {\mathrm {d}}), \mathbf {v} _ {\mathbf {d}} = W _ {v} \cdot c a t (\mathbf {x} _ {\mathrm {i}}, \mathbf {x} _ {\mathrm {n}}, \mathbf {x} _ {\mathrm {d}}), \\ \end{array}
+$$
+
+where $\text{cat}()$ refers to the concatenation operation along the sequence dimension. The geometry attention module enhances mutual-guided geometric consistency, ensuring the generated geometric information remains stable and reliable. Additionally, we incorporate a temporal attention module to smooth the generated content, promoting temporal consistency. By aligning geometric information across both modality and temporal dimensions, we establish a robust foundation for effective control in the subsequent stages of video generation.
+
+Training Strategy. The training process is conducted in three steps. First, we disable the geometry and temporal attention to train the model using random inputs from different modalities. This allows the model to learn independently from each modality without the complexity of cross-modal and temporal interactions. Next, the geometry attention is activated with the other modules freeze, focusing on aligning the different modalities. Finally, we activate the temporal attention and freeze the other modules, ensuring temporal consistency. This three-step strategy stabilizes the training process by gradually introducing the complexity of multi-modal alignment and temporal consistency, ensuring stable convergence. At this stage, all the training
+
+steps are conducted at a relatively low resolution to balance efficiency and performance effectively. We empirically find this strategy can not only stabilize the process and accelerate convergence but also result in minimal performance loss compared to training at high resolution.
+
+Multi-domain CFG. Classifier-free guidance [23] (CFG) is a technique that enables a balance between sample quality and diversity for diffusion models. Our empirical observations indicate that different domains generated by our diffusion model require distinct optimal guidance scales for best results, especially for normal maps. Thus we propose multi-domain CFG(MCFG) to apply different guidance scales to each domain based on Equation 3 and formulate as follows, $\epsilon_{\theta}(\mathbf{x}_{t};\mathbf{i},\mathbf{p}),\epsilon_{\theta}(\mathbf{n}_{t};\mathbf{i},\mathbf{p}),\epsilon_{\theta}(\mathbf{d}_{t};\mathbf{i},\mathbf{p}) = chunk(\epsilon_{\theta}(\mathbf{z}_{t};\mathbf{i},\mathbf{p}))$
+
+$$
+\begin{array}{l} \tilde {\epsilon} _ {\theta} \left(\mathbf {x} _ {t}; \mathbf {i}, \mathbf {p}\right) = \epsilon_ {\theta} \left(\mathbf {x} _ {t}; \mathbf {i}, \mathbf {p}\right) + s _ {x} \cdot \left(\epsilon_ {\theta} \left(\mathbf {x} _ {t}; \mathbf {i}, \mathbf {p}\right) - \epsilon_ {\theta} \left(\mathbf {x} _ {t}; \varnothing , \mathbf {p}\right)\right) \\ \tilde {\epsilon} _ {\theta} \left(\mathbf {n} _ {t}; \mathbf {i}, \mathbf {p}\right) = \epsilon_ {\theta} \left(\mathbf {n} _ {t}; \mathbf {i}, \mathbf {p}\right) + s _ {n} \cdot \left(\epsilon_ {\theta} \left(\mathbf {n} _ {t}; \mathbf {i}, \mathbf {p}\right) - \epsilon_ {\theta} \left(\mathbf {n} _ {t}; \varnothing , \mathbf {p}\right)\right) \\ \tilde {\epsilon} _ {\theta} \left(\mathbf {d} _ {\mathbf {t}}; \mathbf {i}, \mathbf {p}\right) = \epsilon_ {\theta} \left(\mathbf {d} _ {\mathbf {t}}; \mathbf {i}, \mathbf {p}\right) + s _ {d} \cdot \left(\epsilon_ {\theta} \left(\mathbf {d} _ {\mathbf {t}}; \mathbf {i}, \mathbf {p}\right) - \epsilon_ {\theta} \left(\mathbf {d} _ {\mathbf {t}}; \varnothing , \mathbf {p}\right)\right) \tag {6} \\ \end{array}
+$$
+
+# 4.2. Cross-domain Controlled Video Diffusion Model
+
+With the enriched guidance signals (i.e., depth and normal maps) mutually consistent and aligned with the target pose, we now aim to integrate these various types of guidance into a video diffusion model to animate human images. Note that we drop the low-resolution RGB images generated in the previous stage.
+
+Cross-domain Controller As shown in Figure 2 (b), We introduce a cross-domain controller to integrate multiple guidance signals, enabling high-fidelity and accurate animation of human images. Specifically, each control signal modality—such as depth, normal maps, and pose, is first embedded into the feature space through a series of lightweight, domain-specific convolutional layers. This step captures the essential features of each modality. Next, we employ a similar geometry attention mechanism, as outlined in Equation 5, to integrate these feature vectors, ensuring harmonious interaction across modalities. This unified guidance feature drives the animation process with coherence and precision. Formally, the guidance feature $\mathbf{f}$ for each frame is obtained by
+
+$$
+\mathbf {f} _ {\mathrm {i}} = \operatorname {G e o A t t n} \left(F _ {p} \left(\mathbf {p} _ {\mathrm {i}}\right), F _ {d} \left(\mathbf {d} _ {\mathrm {i}}\right), F _ {n} \left(\mathbf {n} _ {\mathrm {i}}\right)\right), i \in [ 0: T ] \tag {7}
+$$
+
+where $F_{p}, F_{d}, F_{n}$ are the domain-specific convolution encoders. The guidance feature is then added to the noisy latent features after the conv in layer of the SVD ControlNet. SVD ControlNet. To effectively control the video diffusion model generation process, we adapt the ControlNet [87] on the SVD model. Specifically, SVD ControlNet freezes all parameters of the pre-trained SVD, while keeping a trainable copy of selected layers from the original network. These two branches are linked by zero-initialized
+
+| Method | Guidance signals | Image | Video |
| L1↓ | PSNR↑ | SSIM↑ | LPIPS↓ | FID-VID↓ | FVD↓ |
| MRAA [55] | 2D pose | 3.21E-04 | 29.39 | 0.672 | 0.296 | 54.47 | 284.82 |
| DisCo [64] | 2D pose | 3.78E-04 | 29.03 | 0.668 | 0.292 | 59.90 | 292.80 |
| AnimateAnyone [28] | 2D pose | - | 29.56 | 0.718 | 0.285 | - | 171.90 |
| MagicAnimate [75] | 2D densepose | 3.13E-04 | 29.16 | 0.714 | 0.239 | 21.75 | 179.07 |
| Champ [91] | 2D pose + SMPL renderings | 3.02E-04 | 29.84 | 0.773 | 0.235 | 26.14 | 170.20 |
| Ours | 2D pose + normal&depth | 2.89E-04 | 29.90 | 0.798 | 0.233 | 19.86 | 153.07 |
+
+(a) Quantitative comparisons on TikTok dataset.
+
+| Method | Guidance signals | Image | Video |
| L1↓ | PSNR↑ | SSIM↑ | LPIPS↓ | FID-VID↓ | FVD↓ |
| AnimateAnyone [28] | 2D pose | 3.25E-04 | 29.37 | 0.725 | 0.278 | 22.69 | 177.38 |
| MagicAnimate [75] | 2D densepose | 3.47E-04 | 29.09 | 0.712 | 0.291 | 28.23 | 196.77 |
| Champ [91] | 2D pose+ SMPL renderings | 3.19E-04 | 29.60 | 0.746 | 0.243 | 23.83 | 182.25 |
| Ours | 2D pose + normal&depth | 2.83E-04 | 29.85 | 0.788 | 0.233 | 20.37 | 158.24 |
+
+(b) Quantitative comparisons on the proposed dataset.
+
+Table 1. Quantitative comparisons with baselines, with best results in bold and second best results underlined.
+
+convolution layers that gradually incorporate controllable features during training. Empirically, we find that using SVD ControlNet leads to more stable training compared to fine-tuning the entire network.
+
+Robust Conditioning. Since the generated depth and normal conditions from the first stage may contain artifacts, error accumulation becomes a potential issue in our two-stage pipeline, potentially leading to performance degradation. To mitigate this, we propose a simple yet effective dropout strategy for the control signals to enhance robust conditioning. Specifically, we randomly replace control signals across temporal dimensions and modalities with zero-value images, encouraging the model to leverage cues from alternative modalities and temporal frames rather than strictly adhering to the conditions. This approach significantly improves robustness during inference and proves especially effective in enhancing temporal consistency.
+
+# 5. Experiments
+
+# 5.1. TikTok-Dance5K Dataset
+
+Large-scale datasets with high-quality samples are important for video generation tasks. We construct a human dance dataset consisting of around 5K videos to facilitate high-fidelity human image animation. All the samples are collected from TikTok and followed by a manual cleaning process. We preprocess the dataset to obtain pseudo ground truth pose, normal, and depth maps [2, 77, 78]. The dataset is made publicly available with collected video IDs.
+
+
+
+
+
+
+
+
+Reference
+
+
+
+
+
+
+
+
+Animate Anyone
+
+
+
+
+
+
+
+
+MagicAnimate
+
+
+
+
+
+
+
+
+Champ
+
+
+
+
+
+
+
+
+Ours
+Figure 3. Qualitative results comparing to baseline methods. The first two rows are from the TikTok dataset and the last two are from the proposed dataset's testing set.
+
+# 5.2. Implementation Details
+
+To train the geometry diffusion model in the first stage, we initialize both the reference UNet and denoising UNet with Stable Diffusion v1.5. During training, we keep the backbone frozen and only train the ControlNet part with the cross-domain controller. For more details on the training settings, please refer to the Appendix.
+
+# 5.3. Main Results
+
+Baselines. MRAA [55] is the state-of-the-art GAN-based animation method that warps the source image by estimating the optical flow of the driving sequence and then inpaints the occluded regions using a GAN model. DisCo [64] is a baseline diffusion-based animation method that integrates a module of separation conditions for pose, body, and background into a pre-trained diffusion model for human image animation. MagicAnimate [75] andAnimateAnyone [28] are diffusion-based human image animat-ing methods that employ 2D control signals as guidance. Champ [91] is developed based onAnimateAnyone and develops a 3D representation such as SMPL to model the control sequence. The SMPL representation is rendered into depth and normal maps as well as semantic maps. Then combined with 2D skeleton poses, multiple control signals are fused and together guide the animating process.
+
+Evaluation Metrics. Following the evaluation method in previous works, we adopt L1 error, Structural Similarity Index (SSIM) [69], Learned Perceptual Image Patch Similarity (LPIPS) [88], and Peak Signal-to-Noise Ratio (PSNR) [27] to evaluate single-frame image quality. To evaluate video fidelity, we use Frechet Inception Distance with Fréchet Video Distance (FID-FVD) [3] and Fréchet Video Distance (FVD) [61].
+
+Evaluation on the Benchmark Dataset. We evaluate our proposed method on the benchmark dataset TikTok dataset [31] and report metrics in Table 1a. Our method shows state-of-the-art performance compared to baseline methods, achieving lower L1 losses, LPIPS, FID-VID, FVD scores, and higher PSNR, and SSIM values. We also provide qualitative results in Figure 3.
+
+
+
+
+
+
+Reference
+Figure 4. Qualitative results with generated normal and depth.
+Evaluation on the Proposed Dataset. To further evaluate our proposed method, we conduct experiments on the
+
+
+
+
+
+
+Generated Guidance and Frames
+
+
+
+
+
+
+
+
+Figure 5. Qualitative results of animating unseen domain images.
+
+
+
+
+
+testing set of our proposed dataset. We report the evaluation metrics in Table 1b and present qualitative comparisons in Figure 3. Our method achieves state-of-the-art performance compared to various baseline methods. We present more qualitative results with generated normal and depth guidance in Figure 4. We observe that bothAnimateAnyone [28] and MagicAnimate [75] produce low-quality results due to insufficient guidance, while Champ [91] fail to generate accurate details, especially in the hand area. This is because SMPL struggles to reconstruct complex hand poses, leading to imprecise guidance map renderings.
+
+
+
+
+
+
+Reference Image
+
+
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+
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+Generated Frames
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+
+
+
+
+Animating Unseen Domain Images. We present qualitative results of animating images from unseen domains in Figure 5, using the obtained normal and depth conditions. These results demonstrate the generalization capabilities of the proposed method.
+
+
+
+
+Figure 6. Qualitative results of cross-ID animation.
+
+
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+Cross-ID Animation. We animate different human images with the same pose sequence and present in Figure 6.
+
+# 5.4. Ablation studies
+
+Different Conditions. We conduct experiments on different variants of the conditions incorporated in the video diffusion model to show the effectiveness of the proposed method. As shown in Table 2a, comparing different variants
+
+| Guidance | L1↓ | PSNR↑ | SSIM↑ | LPIPS↓ | FID-VID↓ | FVD↓ |
| a). Without Pose | 3.38E-04 | 29.43 | 0.743 | 0.255 | 22.38 | 175.37 |
| b). Without Depth | 3.95E-04 | 29.02 | 0.701 | 0.277 | 24.56 | 193.23 |
| c). Without Normal | 3.67E-04 | 29.24 | 0.723 | 0.263 | 23.28 | 183.84 |
| d). Pose+Normal+Depth | 2.89E-04 | 29.90 | 0.798 | 0.233 | 19.86 | 153.07 |
+
+(a) Ablation studies on different conditions.
+
+| Controller | L1↓ | PSNR↑ | SSIM↑ | LPIPS↓ | FID-VID↓ | FVD↓ |
| Without GeoAttn | 3.36E-04 | 29.48 | 0.767 | 0.242 | 21.93 | 165.27 |
| With GeoAttn | 2.89E-04 | 29.90 | 0.798 | 0.233 | 19.86 | 153.07 |
+
+(b) Ablation studies on the effectiveness of geometry attention.
+
+Table 2. Quantitative ablation studies.
+
+a), b), c) with our method d), we show that the incorporation of multiple conditions achieves robust and best performance. Qualitative comparisons are presented in Figure 7. We observe that without depth or normal maps, the quality of the generation is noticeably flawed. Meanwhile, as originally provided, the pose maps provide refined guidance for facial and hand regions, improving generation quality.
+
+
+
+
+
+
+Reference
+
+
+
+
+
+
+Ours
+
+
+
+
+
+
+w/o. pose
+
+
+
+
+
+
+w/o. depth
+
+
+
+
+Figure 9. Qualitative ablation studies on the effectiveness of proposed modules for geometry alignment. (Please zoom in to view.)
+
+
+w/o. normal
+
+
+Figure 7. Qualitative ablation studies on different conditions.
+
+
+Reference
+w./geo.attn
+w/o. geo.attn
+Figure 8. Qualitative ablation studies on the geometry attention.
+Geometry Alignment. To validate the effectiveness of the proposed geometry attention and the MCFG strategy for ge
+
+
+
+
+Reference
+
+
+
+
+w./geo.attn
+w/o. geo.attn
+
+ometry alignment in the first stage, we show qualitative ablation studies in Figure 9. Without MCFG, the generated normal maps show an over-saturated color that cannot represent normal information effectively. Without the geometry attention, normal and depth maps are not aligned with each other, leading to generation degradation.
+
+
+
+
+GT
+
+
+
+
+Ours
+
+
+
+
+w/o. MCFG
+
+
+
+
+w/o. Geo
+
+
+
+
+GT
+
+
+
+
+Ours
+
+
+
+
+w/o. MCFG
+
+
+
+
+w/o. Geo
+
+Geometry Attention for Conditions Fusion. We conduct an ablation study to evaluate the effectiveness of the proposed geometry attention mechanism for conditions fusion. Quantitative comparisons are presented in Table 2b, demonstrating that including geometry attention significantly enhances performance. Additionally, qualitative comparisons in Figure 8 further illustrate its benefits. We observe geometry attention effectively integrates multiple types of conditions, leading to more robust and high-quality generation.
+
+# 6. Conclusion
+
+This paper introduces DreamDance, a unified framework for animating human images using skeleton pose sequences. By employing innovative two-stage diffusion models, including the Mutually Aligned Geometry Diffusion Model to enrich guidance signals and the Cross-domain Controlled Video Diffusion Model to integrate multiple levels of guidance, DreamDance significantly enhances visual coherence and temporal consistency of the generated video. Extensive experiments demonstrate that the proposed method achieves state-of-the-art performance, offering a flexible and user-friendly solution for realistic human image animating.
+
+Acknowledgment This work was supported in part by the Natural Science Foundation of China (No. 62202014, 62332002, 62425101)
+
+# References
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+[91] Shenhao Zhu, Junming Leo Chen, Zuozhuo Dai, Yinghui Xu, Xun Cao, Yao Yao, Hao Zhu, and Siyu Zhu. Champ: Controllable and consistent human image animation with 3d parametric guidance. arXiv preprint arXiv:2403.14781, 2024. 2, 3, 5, 6, 7
\ No newline at end of file
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+# DreamFuse: Adaptive Image Fusion with Diffusion Transformer
+
+Junjia Huang $^{1,2*}$ Pengxiang Yan $^{3*}$ Jiyang Liu $^{3*†}$ Jie Wu $^{3}$ Zhao Wang $^{3}$ Yitong Wang $^{3}$ Liang Lin $^{1,2,4}$ Guanbin Li $^{1,2,4‡}$ $^{1}$ Sun Yat-sen University, $^{2}$ Peng Cheng Laboratory, $^{3}$ ByteDance Intelligent Creation $^{4}$ Guangdong Key Laboratory of Big Data Analysis and Processing huangjj77@mail2.sysu.edu.cn, wantong1017@163.com linliang@ieee.org, liguanbin@mail.sysu.edu.cn {yanpengxiang.ai, liujiyang.liu, wujie.10, zhaoxu.bit}@bytedance.com https://ll3rd.github.io/DreamFuse/
+
+
+
+
+
+
+
+
+Figure 1. DreamFuse demonstrates adaptive performance across diverse scenarios, including style transfer, wearable items, logo printing, placement and handheld. Notably, when given a text prompt, our method effectively responds by further editing the attributes of the foreground object (e.g., a golden car).
+
+
+
+
+
+# Abstract
+
+Image fusion seeks to seamlessly integrate foreground objects with background scenes, producing realistic and harmonious fused images. Unlike existing methods that directly insert objects into the background, adaptive and interactive fusion remains a challenging yet appealing task. It requires the foreground to adjust or interact with the background context, enabling more coherent integration. To address this, we propose an iterative human-in-the-loop data generation pipeline, which leverages limited initial data with diverse textual prompts to generate fusion datasets
+
+across various scenarios and interactions, including placement, holding, wearing, and style transfer. Building on this, we introduce DreamFuse, a novel approach based on the Diffusion Transformer (DiT) model, to generate consistent and harmonious fused images with both foreground and background information. DreamFuse employs a Positional Affine mechanism to inject the size and position of the foreground into the background, enabling effective foreground-background interaction through shared attention. Furthermore, we apply Localized Direct Preference Optimization guided by human feedback to refine DreamFuse, enhancing background consistency and foreground harmony. DreamFuse achieves harmonious fusion while generalizing to text-
+
+driven attribute editing of the fused results. Experimental results demonstrate that our method outperforms state-of-the-art approaches across multiple metrics.
+
+# 1. Introduction
+
+Foreground-background image fusion is a fundamental and practical task in image editing. Recently, with the rapid development of generation methods based on diffusion models, numerous innovative and imaginative approaches have emerged in this field. Beyond generating images purely driven by text prompts, increasing attention has been directed toward generating customized images guided by specific foreground objects [1, 28, 32, 53] or performing inpainting on designated background regions [45] for image editing and fusion. Going further, several methods aim to achieve harmonious fusion of foreground and background by adjusting details such as lighting [50], shadows [34], and brightness-contrast consistency [38], making the fused images appear more natural. Other approaches [2, 7, 42] strive to enhance fusion by modifying the orientation, pose, or style of the foreground object while preserving its identity attributes, enabling better adaptation to the background. However, most of these methods typically focus on directly placing the foreground object into the background scene. In contrast, practical scenarios often involve more diverse and interactive cases, such as partial occlusions, alternating visibility, or interactions where the object is held, worn, or integrated into the scene.
+
+A major challenge in handling such complex fusion scenarios is the lack of suitable datasets. Existing methods typically rely on object segmentation from images or videos [13, 22] followed by inpainting [27, 31] to reconstruct backgrounds. However, this multi-step process frequently suffers from quality degradation due to imprecise segmentation or suboptimal inpainting, which can introduce artifacts like shadows or residual elements in the background. Moreover, handling partially occluded foregrounds is particularly challenging [36], and segmentation-based data often fails to adjust object pose or perspective to align with the background during fusion. Based on these observations, we propose an Iterative Human-in-the-Loop Data Generation Pipeline to directly generate fused data, including foregrounds, backgrounds, and the fused images, avoiding issues such as incomplete foregrounds and background artifacts. We train a DiT model on curated fused data with text prompts, modifying its attention mechanism to shared attention to ensure identity consistency across fused data. Using this model, we generate multi-scale fused data for various scenarios with diverse prompts, such as placement, handheld interactions, wearable items, logo printing, and style transfer. Throughout the process, we enhance content diversity by incorporating existing LoRA [10] and it
+
+eratively optimize the model through manual selected data. We utilize GPT-4o to filter out low-quality fused data, such as mismatched foregrounds or degraded images, ultimately constructing a dataset of 80,000 high-quality, multi-scene, multi-scale fused image samples.
+
+Another critical challenge in image fusion is ensuring background consistency and foreground harmony. Some approaches [2, 7] rely on masks or bounding boxes for foreground placement, blending the background outside the mask to maintain consistency. However, these approaches often fail to realistically render effects like shadows or reflections beyond the mask, limiting the realism of the fused results. Other methods [20, 40] reconstruct fused images through inversion, improving foreground harmony but often compromising background consistency. To address this trade-off, we propose DreamFuse, an adaptive image fusion framework based on DiT. By incorporating shared attention, we condition the the fused image generation on both the foreground and background while employing positional affine to introduce the foreground's position and scale without restricting its editable regions. Additionally, we employ Localized Direct Preference Optimization (LDPO) to further optimize the foreground and background regions of the fused image, ensuring better alignment with human preferences. Experimental results demonstrate that DreamFuse performs exceptionally well across various scenarios. As shown in Fig. 1, DreamFuse produces highly realistic fusion effects for real-world images. Furthermore, during training, a certain proportion of fused image descriptions is incorporated as prompts. When given a text prompt, DreamFuse effectively responds to the input and enables attribute modifications in the fused scenes, such as turning a car into gold. In summary, our key contributions are threefold:
+
+- We propose an iterative Human-in-the-Loop data generation pipeline and construct a comprehensive fusion dataset containing 80k diverse fusion scenarios.
+- We propose DreamFuse, a fusion framework based on DiT, which leverages positional affine and LDPO strategies to integrate the foreground into the background more naturally and adaptively.
+- Our method outperforms the state-of-the-art methods on various benchmarks and remains effective in real-world and out-of-distribution scenarios.
+
+# 2. Related Work
+
+Customized Image Generation. Customized image generation aims to create user-specific images based on text prompts or reference images. Some methods [5, 6, 14, 28] incorporate reference concepts into specific text prompts, while approaches [8, 39, 46, 52] utilize additional encoders to encode reference images as visual prompts, introducing customized representations for generation. Other methods [12, 32] achieve subject-driven generation by directly
+
+
+Figure 2. The framework of the data generation model and position matching process. The left side of the image illustrates the design structure of our data generation model, while the right side shows the position matching process and data format. We enhance the diversity of fused data generation through flexible and rich prompts combined with various style LoRAs.
+
+concatenating reference and target images during generation. In this paper, we further extend generative diffusion models by fine-tuning on small-scale data to directly generate customized foregrounds, backgrounds, and fused images based on corresponding text prompts.
+
+Image Fusion. The goal of image fusion is to seamlessly integrate an object from a foreground image into a background image. Compared to directly cutting and pasting, some approaches [21, 24, 50, 54] adjust the lighting, shadows, and colors of the pasted foreground region to achieve a more harmonious fusion. Other methods [2, 7, 20, 33, 40-42] focus on altering the perspective, pose, or style of the foreground object to make it fit more naturally into the background image. However, these methods are often restricted to object placement. In this paper, we propose a more versatile fusion approach that supports a variety of scenarios, including hand-held objects, wearable items, and style transformations, enabling more diverse integrations.
+
+Human Feedback Learning. Many methods now leverage human feedback learning to make generated images more aligned with users' preferences. Some approaches [18, 43, 44, 48, 49] train a reward model to understand human preferences and improve the generation quality through reward feedback learning. Others [16, 37, 51] utilize human comparison data to directly optimize a policy that best satisfies human preferences. For the image fusion task, we propose localized direct preference optimization, which focuses on region-specific optimization to enhance both the background consistency and the harmony in fused images.
+
+# 3. Methodology
+
+As shown in the data format in Fig. 2, the image fusion task typically involves the following types of images: a foreground image $F \in \mathbb{R}^{H \times W \times 3}$ with mask $F_{m} \in \mathbb{R}^{H \times W}$ , a background image $B \in \mathbb{R}^{H \times W \times 3}$ , a fused image $I \in$
+
+$\mathbb{R}^{H\times W\times 3}$ , a fused mask $I_{m}\in \mathbb{R}^{H\times W}$ associated with the fused object. The masks $F_{m}$ and $I_{m}$ are primarily used to indicate the position and size of the foreground object. In practical applications, only the centroid and bounding box of the mask are required.
+
+# 3.1. Iterative Human-in-the-Loop Data Generation
+
+Data Startup. Unlike methods [7, 35] that start with a fused image to segment the foreground and generate the background using inpainting, we aim to create higher-quality fusion data with richer scenes and more diverse foreground fusion. To this end, we design an iterative, human-in-the-loop data generation process. We first extract a pair of high-quality foreground $F$ and fused image $I$ from a subject-driven dataset [32]. We then manually refine the inpainting regions to remove the foreground object and its effects, such as reflections and shadows, creating a high-quality background image $B$ . A total of 86 initial samples are curated, and their corresponding descriptions $C$ are generated with GPT-4o. These data are then fed into the data generation model depicted in Fig. 2 for training.
+
+Data Generation Model Design. We adopt Flux [15] as the base model and input our curated fusion samples $G = (F, B, I)$ with prompts $C_G = (C_F, C_B, C_I)$ in batches. The images and prompts are encoded into image embeddings $E_i \in \mathbb{R}^{h \times w \times d}$ and text embeddings $E_c$ , supplemented by learnable tag embeddings to differentiate the foreground and background. In Flux's RoPE [30] mechanism, which uses a 2D position index $P_{idx} = (i, j), \forall i \in [0, h), j \in [0, w)$ to represent image positions, we optionally introduce an offset $\Delta$ to $P_{idx}$ for $F, B,$ and $I$ as follows:
+
+$$
+P _ {i d x} = \left\{ \begin{array}{l l} (i, j), & \text {i f} F, \\ (i, j) + \Delta , & \text {i f} B, \\ (i, j) + 2 \Delta , & \text {i f} I. \end{array} \right. \tag {1}
+$$
+
+
+Figure 3. The framework of the DreamFuse. We apply positional affine transformations to map the foreground's position and size onto the background. The foreground and background are concatenated with the noisy fused image as condition images before DiT's attention layers. Localized direct preference optimization is then used to improve background consistency and foreground harmony.
+
+During training, adding an offset improves the model's ability to generate diverse fused scenes but performs poorly across resolutions, while omitting the offset produces overly consistent results yet adapts well to multi-scale data. Based on this, we use two models—with and without offset—to generate diverse, multi-scale samples. Further details are provided in the supplementary materials.
+
+To establish connections between $F, B$ and $I$ , we modify the original independent attention mechanism in the DiT to a shared attention (SA) mechanism [11]. As shown in Fig. 2, after the text embeddings and image embeddings of each sample are processed through modulation and linear layers, they are concatenated to form the attention query $Q_{g} = [Q_{g}^{c}; Q_{g}^{i}]$ , $g \in G$ , where $c$ and $i$ represent the text and image components. We then concatenate the image components of the key and value across all samples: $K_{g} = [K_{g}^{c}; K_{F}^{i}; K_{B}^{i}; K_{I}^{i}]$ , $V_{g} = [V_{g}^{c}; V_{F}^{i}; V_{B}^{i}; V_{I}^{i}]$ . The shared attention is then computed as:
+
+$$
+S A = \operatorname {s o f t m a x} \left(\frac {Q _ {g} K _ {g} ^ {T}}{\sqrt {d}}\right) V _ {g}, \tag {2}
+$$
+
+where $d$ denotes the dimension. After applying shared attention, the model gains an initial ability to generate similar images. We then fine-tune the model with LoRA [10] to enable the generation of high-quality image fusion samples.
+
+Scene Generalizability and Style Variability. Our initial data only consists of object placement scenes. After fin-tuning the data generation model, it demonstrates the ability to generalize to more diverse scene prompts. In subsequent iterations, we leverage GPT-4o with open-source prompts to generate fusion prompts $C_G$ , expanding foreground objects to include animals, pets, products, portraits, and logos, while categorizing background scenes into indoor and outdoor settings. Fusion scenarios are further diversified to include placement, handheld, logo printing, wearable, and style transfer. Furthermore, we observe that the data
+
+generation model responds effectively to existing style LoRAs. Therefore, we integrate fine-tuned style LoRAs, such as depth of field, realism, and ethnicity, to further enhance fusion data in both scene variety and artistic style, mitigating the stylistic bias of the Flux base model. This expansion process is iterative: the model is fine-tuned on data generated in the previous step, additional data is generated, and high-quality fusion samples are manually curated to serve as input for the next round of fine-tuning.
+
+Position Matching. To determine the position of the foreground object in the background, we use RoMA [4] to perform feature matching between the foreground and the fused image, converting the results into bounding boxes. Then we utilize SAM2 [26] to segment the foreground object from the fused image based on these bounding boxes, yielding $I_{m}$ . For the foreground object, we use an internal segmentation model to obtain $F_{m}$ . The position and size of the foreground object in the background are then calculated using the centroids and bounding boxes of $I_{m}$ and $F_{m}$ .
+
+# 3.2. Adaptive Image Fusion Framework
+
+In image fusion tasks, three key aspects need to be considered: (1) how to model the relationship between the background, foreground, and fused image; (2) how to incorporate the position and size information of the foreground object into the background; (3) how to ensure background consistency and foreground harmony in the fused image.
+
+Condition-aware Modeling. Inspired by the work [32], we model the background and foreground as conditions, with the fused image treated as the denoised target. Given a fixed dataset $\mathcal{D} = \{(c_i,x_f,x_b,x_i)\}$ , each sample consists of a textual description of the fused image $c_{i}$ , along with images representing the foreground $x_{f}$ , background $x_{b}$ and fused image $x_{i}$ . We adopt the Flux-based DiT architecture, using the foreground $x_{f}$ and background $x_{b}$ as conditions with a fix timestep 0. Additionally, most text prompt $c_{i}$ are
+
+randomly dropped out with a probability $p$ during training, replaced with empty strings, while a portion of the prompts is retained to preserve the network's text-responsive capability. The DiT network is tasked with denoising the noisy fused image $x_{i}^{t}$ at timestep $t$ defined as:
+
+$$
+x _ {i} ^ {t} = (1 - t) x _ {i} + t x _ {n}, \tag {3}
+$$
+
+where $x_{n}\sim q(x_{n})$ denotes a noise sample and $t\in [0,1]$ . The DiT model is trained to regress the velocity field $\epsilon_{\theta}(x_i^t,x_f,x_b,t)$ by minimizing the Flow Matching [17] objective $\mathcal{L}_{noise}(\theta)$ :
+
+$$
+\mathbb {E} _ {t, (c _ {i}, x _ {f}, x _ {b}, x _ {i}) \sim \mathcal {D}, x _ {n} \sim q (x _ {n})} [ | | \epsilon - \epsilon_ {\theta} (c _ {i}, x _ {i} ^ {t}, x _ {f}, x _ {b}, t) | | ], \tag {4}
+$$
+
+where the target velocity field is $\epsilon = x_{n} - x_{i}$ . Within the DiT attention mechanism, all components are concatenated as $[Dropout(c_i,p),x_i,x_f,x_b]$ , enabling joint attention computation, as illustrated in Fig. 3. This mechanism effectively integrates background and foreground information into the fused image through the attention layers.
+
+Positional Affine. We explore three approaches to incorporate positional information, as shown in Fig. 4. The most straightforward approach is to directly transform the foreground to match the desired position and size in the background (Fig. 4 (b)). However, this method compresses the information of foreground during scaling, which is unfavorable for inserting small objects. Another approach involves using the placement information of the foreground, such as the mask after positioning, as a condition. This information is encoded via a tokenizer and introduced into the attention computation (Fig. 4 (c)). However, this approach relies heavily on the tokenizer, requiring a large amount of data to optimize its representation of positional information. To leverage the relative positional relationship of the foreground more directly and effectively, we propose the positional affine method shown in Fig. 4 (a).
+
+Specifically, both the foreground and background are assigned 2D position index $P_{idx}^{f}, P_{idx}^{b} = (i,j), \forall i \in [0,h), j \in [0,w)$ to represent their spatial relationships within the image. When placing the foreground in a target region $P_{idx}^{r} = (u,v), \forall u \in [h_r,h_r'), v \in [w_r,w_r')$ of the background, the affine transformation matrix $A$ is computed as follows:
+
+$$
+A = \left[ \begin{array}{c c c} \frac {w _ {r} ^ {\prime} - w _ {r}}{w} & 0 & w _ {r} \\ 0 & \frac {h _ {r} ^ {\prime} - h _ {r}}{h} & h _ {r} \\ 0 & 0 & 1 \end{array} \right]. \tag {5}
+$$
+
+Next, the position index $P_{idx}^{r}$ of the target region is mapped to the foreground with the inverse affine transformation:
+
+$$
+P _ {i d x} ^ {f ^ {\prime}} = A ^ {- 1} \left[ \begin{array}{l} u \\ v \\ 1 \end{array} \right]. \tag {6}
+$$
+
+
+Figure 4. Three ways for injecting positional conditions: (a) using positional affine to map the foreground's position index to its target placement; (b) directly transforming the foreground object to the target position; (c) encoding position mask information with a tokenizer and integrating it into DiT's attention computation.
+
+
+
+
+
+We utilize $P_{idx}^{f'}$ as the new position index of foreground. By employing this positional affine transformation, and leveraging DiT's responsiveness to position index, we directly incorporate the position and size information of the foreground into the target location within the background. This approach eliminates the need to scale or compress the foreground, enabling a more effective and reasonable integration of positional information.
+
+Localized Preference Optimization. In the image fusion process, maintaining background consistency and foreground harmony is crucial. When directly generating the denoised fused image, issues such as inconsistent backgrounds or disharmonious foregrounds can easily arise. To address this, we propose Localized Direct Preference Optimization (LDPO) based on Diffusion-DPO [18, 37], enabling the diffusion network to more effectively learn from human preferences in the context of image fusion.
+
+We construct a dataset $\mathcal{D}' = \{(c_i, x_f, x_b, x_i^w, x_i^l)\}$ consisting of additional fused sample pairs, where $x_i^w$ aligns better with human preferences than $x_i^l$ . For example, as shown in Fig. 3, $x_i^l$ can be a fused image obtained by directly copying and pasting the foreground onto the background. For simplicity, we define the model input as $x_t^{w,l} = (c_i, x_f, x_b, x_i^{t,\{w,l\}})$ . The Diffusion-DPO optimizes a policy to satisfy human preferences via objective $\mathcal{L}_{DPO}(\theta, x_t^{w}, x_t^{l})$ :
+
+$$
+\begin{array}{l} \mathbb {E} \bigg [ \log \sigma \Big (- \frac {\beta}{2} (| | \epsilon^ {w} - \epsilon_ {\theta} (x _ {t} ^ {w}, t) | | ^ {2} - | | \epsilon^ {w} - \epsilon_ {r e f} (x _ {t} ^ {w}, t) | | ^ {2} \\ \left. \left. - \left(\left| | \epsilon^ {l} - \epsilon_ {\theta} \left(x _ {t} ^ {l}, t\right) \right| \right| ^ {2} - \left| | \epsilon^ {l} - \epsilon_ {r e f} \left(x _ {t} ^ {l}, t\right) \right| ^ {2})\right)\right) \Bigg ], \tag {7} \\ \end{array}
+$$
+
+where $\epsilon_{\theta}(\cdot)$ and $\epsilon_{ref}(\cdot)$ denotes the predictions of optimized model and reference model, respectively, $\beta$ is the regularization coefficient and $\sigma$ is the sigmoid function. Intuitively, minimizing $\mathcal{L}_{DPO}$ encourages the predicted velocity field
+
+
+Figure 5. Scene distribution of the fusion dataset, including scenario counts, indoor/outdoor background proportions, and complexity levels.
+
+$\epsilon_{\theta}$ closer to the target velocity $\epsilon^w$ of the chosen data, while diverging from $\epsilon^l$ (the rejected data). However, not all aspects of $x_i^l$ fail to align with human preferences. For instance, in copy-paste fused images, the consistency of the background better aligns with human preferences. Therefore, we adopt a Localized DPO strategy for $x_i^w$ and $x_i^l$ . A localized foreground region $M(f)$ is defined as:
+
+$$
+M (f) = \left\{ \begin{array}{l} 1, \text {i f} f \in \alpha \cdot B b o x \left(x _ {f}\right) \\ 0, \text {o t h e r w i s e}, \end{array} \right. \tag {8}
+$$
+
+where $f$ represents a pixel location, $Bbox(x_{f})$ denotes the region in the bounding box of the foreground object and $\alpha$ is a dilation factor that moderately expands this region. The optimized objective $\mathcal{L}_{LDPO}(\theta ,x_t^w,x_t^l,M)$ is defined as:
+
+$$
+M \cdot \mathcal {L} _ {D P O} (\theta , x _ {t} ^ {w}, x _ {t} ^ {l}) + (1 - M) \cdot \mathcal {L} _ {D P O} (\theta , x _ {t} ^ {l}, x _ {t} ^ {w}). (9)
+$$
+
+We provide the pseudo-code for LDPO in the Appendix. This strategy ensures background consistency while making the foreground more harmonious and aligned with human preferences.
+
+# 4. Experiments
+
+# 4.1. Dataset Analysis
+
+As outlined in Sec. 3.1, we employ an iterative human-in-the-loop data generation pipeline to create approximately $400\mathrm{k}$ image fusion samples. To ensure diversity, we leverage GPT-4o and existing prompt libraries during the prompt generation process to create a wide variety of prompts. After applying quality filtering techniques, including GPT-4o screening and gradient comparison, we curate a final dataset containing $80\mathrm{k}$ high-quality fused image samples. We further analyze the fusion scenarios, background types, and complexity of the filtered dataset, as illustrated in Fig. 5. Notably, over half of the dataset features outdoor backgrounds, and approximately $23\mathrm{k}$ images include hand-held
+
+| Method | CLIP | AES | IR | VR |
| ControlCom [47] | 31.28 | 6.09 | -0.27 | 1.33 |
| TF-ICON [20] | 32.28 | 6.51 | 0.266 | 2.37 |
| Anydoor [2] | 31.80 | 6.27 | 0.02 | 1.31 |
| MADD [7] | 30.36 | 5.94 | -0.72 | 0.61 |
| MimicBrush [3] | 31.71 | 6.27 | -0.33 | 0.83 |
| Ours | 31.93 | 6.55 | 0.35 | 3.27 |
+
+Table 1. Quantitative evaluation results on TF-ICON dataset.
+
+| Method | CLIP | AES | IR | VR |
| ControlCom [47] | 34.23 | 5.76 | 0.48 | 2.20 |
| TF-ICON [20] | 35.21 | 6.06 | 0.86 | 3.88 |
| Anydoor [2] | 35.04 | 6.01 | 1.01 | 4.14 |
| MADD [7] | 33.49 | 5.66 | 0.28 | -0.08 |
| MimicBrush [3] | 34.46 | 6.01 | 0.56 | 3.19 |
| Ours | 35.52 | 6.10 | 1.19 | 5.56 |
+
+Table 2. Quantitative evaluation results on DreamFuse test dataset.
+
+scenarios. Details of the generation pipeline, quality filtering methods, and statistical results are provided in the supplementary materials.
+
+# 4.2. Implementation Details
+
+Hyperparameters. In DreamFuse training, we adopt FluxDev [15] as the base model. The input images are scaled proportionally from their original resolution to a short side of 512 pixels. The training procedure comprises two stages: first, the full DreamFuse 80k dataset is trained for 10k iterations with batch size 1, the Prodigy [23] optimizer, and a LoRA rank of 16. Subsequently, we manually select 15k high-quality samples from the initial dataset for LDPO training. Negative samples $x_{i}^{l}$ in LDPO training consist of two types: copy-paste images and low-quality inference results generated from the selected samples after stage one. We apply the $\mathcal{L}_{LDPO}$ loss to the copy-paste data and $\mathcal{L}_{DPO}$ loss to remaining negative samples. The second stage employs the AdamW [19] optimizer (learning rate $5 \times 10^{-5}$ ) for another 10k iterations. The dropout probability $p$ and dilation factor $\alpha$ is set to $99\%$ and 1.5. The entire training is conducted on 8 NVIDIA A100 GPUs, requiring approximately 24 hours.
+
+**Benchmarks.** We randomly selected 500 unseen samples from the generated dataset as DreamFuse test set to evaluate the model's fusion capabilities across multiple scenarios, including object placement, wearing, logo printing, hand-held and style transfer. Additionally, we evaluated method's performance on out-of-domain data with the TF-ICON [20] dataset, which consists of 332 samples spanning four visual domains: photorealism, pencil sketching, oil painting, and cartoon animation.
+
+Evaluation metrics. We utilize the CLIP [25] score to evaluate the similarity between the fused images and their corresponding descriptive texts, the AES [29] score to assess the aesthetic quality of the fused images, and the Im
+
+
+Condition Images ControlCom TF-ICON Anydoor MmicBrush Ours
+Figure 6. Qualitative comparisons with existing methods. The first row is from the TF-ICON dataset, while the others are from the DreamFuse test set. Our approach achieves a more seamless integration of foreground objects with the background images, resulting in higher visual consistency and realism.
+
+ageReward [43] (IR) score to evaluate alignment, fidelity, and harmlessness. Additionally, we employ the VisionReward [44] (VR) score, which leverages a vision language model [9] (VLM) to evaluate the fused results from multiple perspectives across various questions, better reflecting human preferences.
+
+# 4.3. Comparisons with Existing Methods
+
+Quantitative results. We evaluate several existing state-of-the-art image fusion methods on the TF-ICON and DreamFuse test datasets, including image composition methods such as TF-ICON [20], Anydoor [2], MADD [7] and ControlCom [47], as well as the reference-based fusion method MimicBrush [3]. As shown in Tab. 1, our method outperforms existing approaches across multiple metrics on the TF-ICON dataset, with a notable 0.9 improvement in the VR score compared to the second-best method. The TF-ICON contains both realistic images and images from diverse domain, and our results highlight the robustness and generalization capability of our approach. Similarly, as shown in Tab. 2, our method achieves superior performance on the DreamFuse test set, surpassing the second-best method by 1.4. Our method consistently demonstrates better fusion quality across all scenarios.
+
+Qualitative results. Fig. 6 presents the qualitative visualization results of our method compared with other methods. As shown, our method not only performs well across var
+
+
+Figure 7. User Study: Evaluation from three perspectives: consistency, harmony, and overall quality.
+
+| Method | CLIP | AES | IR | VR |
| Direct Trans. | 35.04 | 6.10 | 0.98 | 4.72 |
| Mask Token. | 35.14 | 6.11 | 1.03 | 4.93 |
| Pos. Affine | 35.22 | 6.13 | 1.07 | 5.28 |
+
+Table 3. Qualitative analysis of three positional incorporation strategies on the DreamFuse test set after the first-stage training.
+
+| DreamFuse | CLIP | AES | IR | VR |
| First-Stage Training | 35.22 | 6.13 | 1.07 | 5.28 |
| w/ LDPO | 35.36 | 6.07 | 1.16 | 5.52 |
| w/ LDPO + LLDPO | 35.51 | 6.10 | 1.17 | 5.58 |
| w/ LDPO + LLDPO + Lnoise | 35.52 | 6.10 | 1.19 | 5.56 |
+
+Table 4. Qualitative analysis of localized preference optimization.
+
+ious fusion scenarios but also excels when the fused foreground object contains reflective surfaces. Specifically, for elements like the mirror in the last row, DreamFuse can perceive the surrounding environment and adaptively adjust the reflections on the mirror, resulting in more natural fusion image. Detailed discussions on fusion effects in real-world scenarios are provided in the supplementary materials.
+
+User study. As shown in Fig. 7, we randomly select 200 samples and conduct a user study with 17 participants to compare our method with Anydoor [2] and TF-ICON [20]. The evaluation focus on three perspectives: the consistency of the fused image's foreground and background with the input, the harmony of the fusion image, and the overall fusion quality. The results demonstrate that our method outperforms existing approaches across all three dimensions, achieving a $64.6\%$ score in overall fusion quality.
+
+# 4.4. Ablation Study
+
+Positional affine. We compare the three positional incorporation strategies discussed in Sec. 3.2. As shown in Tab. 3, the results on the DreamFuse test set after the first-stage training demonstrate that the positional affine approach achieves the highest CLIP and VR scores, reaching 35.215 and 5.278, respectively. This suggests that the positional affine method better preserves the information of foreground objects, outperforming the direct transform and mask tokenizer strategies, which are more prone to information loss of fine-grained details.
+
+Localized preference optimization. In the second stage of
+
+
+Figure 8. Qualitative results about the LDPO. Compared to "w/ $\mathcal{L}_{DPO}$ ", "w/ $\mathcal{L}_{LDPO}$ " leverages copy-paste data to better help the model understand perspective changes in the foreground while maintaining background consistency as much as possible.
+
+training, we employ Localized Direct Preference Optimization (LDPO) to further enhance the model's performance by utilizing two types of paired data: the first type consists of poorly performing and well-performing results generated after the first training stage with different seeds and optimized with the $\mathcal{L}_{DPO}$ , while the second type involves copy-paste data treated as negative samples and optimized with the $\mathcal{L}_{LDPO}$ . As shown in Tab. 4, "w/ $\mathcal{L}_{DPO}$ " refers to training with only the first type of data, "w/ $\mathcal{L}_{LDPO}$ " refers to training with copy-pasted data. Results indicate the LDPO significantly improves fusion performance by achieving an approximate 0.11 increase in IR scores compared to the first-stage results. Further incorporating the $\mathcal{L}$ noise loss results in a comparable performance. LDPO primarily enhances background consistency and foreground harmony, as visually demonstrated in Fig. 8, where using copy-paste data as negative samples allows the model to better capture fusion-related transformations, such as perspective and affine adjustments, rather than simply copying and pasting the foreground, while also improving the consistency of other background regions.
+
+Dropout probability $p$ . To retain the diffusion model's text response capability, allowing it to edit the fused foreground based on the prompt, we include the fusion image's text as a prompt at a dropout probability $p$ . However, we find that when the dropout probability is set too low, such as $80\%$ , the model's response to empty text weakens, resulting in the inability to properly integrate the foreground into the background. As shown in Fig. 9 (a), lower dropout probabilities lead to lower CLIP scores for the fusion results, indicating that the foreground is not well integrated into the background. Therefore, we ultimately chose $p = 99\%$ , which preserves the model's text response capability to a greater extent without compromising its performance.
+
+Dilation factor $\alpha$ . Intuitively, the dilation factor $\alpha$ defines the size of the local harmonious region around the foreground considered during the LDPO process. As shown in Fig. 9 (b), we investigate the impact of $\alpha$ on the model's performance. When $\alpha = 1$ , the model focuses solely on the
+
+
+Figure 9. The effectiveness about the dropout probability $p$ and dilation factor $\alpha$ .
+
+
+
+
+Figure 10. The responsiveness to different prompts.
+
+harmony within the bounding box of the object, disregarding external factors such as shadows or reflections, which are then treated as non-preferred, leading to a performance drop. When $\alpha = 0$ , copy-paste data is entirely treated as samples consistent with human preferences, resulting in a significant decline in the VR score. As $\alpha$ increases, the preference for background consistency gradually diminishes, though it has minimal impact on overall harmony. Based on these findings, we set $\alpha = 1.5$ for LDPO training.
+
+Responsiveness to text prompts. In our experiments, we find that DreamFuse responds effectively to text prompts without additional training. This enables modifications to the attributes of foreground objects or the fusion scene, as shown in Fig. 10.
+
+# 4.5. Conclusion
+
+In this paper, we first propose an iterative human-in-the-loop data generation pipeline to create fusion scenarios that are relatively rare in traditional fusion tasks, making the fusion process more natural and flexible. Using this pipeline, we generated a dataset of 80k fusion data that encompasses various scenarios, including placement, handheld, wearable, and style transfer tasks. Additionally, we introduce DreamFuse, an adaptive image fusion framework with the diffusion transformer. This framework incorporates positional affine transformations to encode the position and size of foreground, employs shared attention mechanisms to establish connections between the foreground and background, and ultimately leverages localized direct preference optimization to further enhance the quality of the fused images. Experimental results show that our method outperforms existing approaches on multiple benchmarks.
+
+# 5. Acknowledgment
+
+This work is supported in part by the National Key R&D Program of China (2024YFB3908503), and in part by the National Natural Science Foundation of China (62322608).
+
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+# DreamLayer: Simultaneous Multi-Layer Generation via Diffusion Model
+
+Junjia Huang $^{1,2*}$ Pengxiang Yan $^{3*}$ Jinhang Cai $^{3}$ Jiyang Liu $^{3}$
+
+Zhao Wang $^{3}$ Yitong Wang $^{3}$ Xinglong Wu $^{3}$ Guanbin Li $^{1,2,4\dagger}$
+
+1Sun Yat-sen University, 2Peng Cheng Laboratory, 3ByteDance Intelligent Creation
+
+$^{4}$ Guangdong Key Laboratory of Big Data Analysis and Processing
+
+huangjj77@mail12.sysu.edu.cn,wantong1017@163.com,liguanbin@mail.sysu.edu.cn
+
+{yanpengxiang.ai, caijinhang, liujiyang.liu, zhaoxu.bit, wuxinglong}@bytedance.com
+
+https://ll3rd.github.io/DreamLayer/
+
+# Abstract
+
+Text-driven image generation using diffusion models has recently gained significant attention. To enable more flexible image manipulation and editing, recent research has expanded from single image generation to transparent layer generation and multi-layer compositions. However, existing approaches often fail to provide a thorough exploration of multi-layer structures, leading to inconsistent inter-layer interactions, such as occlusion relationships, spatial layout, and shadowing. In this paper, we introduce DreamLayer, a novel framework that enables coherent text-driven generation of multiple image layers, by explicitly modeling the relationship between transparent foreground and background layers. DreamLayer incorporates three key components, i.e., Context-Aware Cross-Attention (CACA) for global-local information exchange, Layer-Shared Self-Attention (LSSA) for establishing robust inter-layer connections, and Information Retained Harmonization (IRH) for refining fusion details at the latent level. By leveraging a coherent full-image context, DreamLayer builds inter-layer connections through attention mechanisms and applies a harmonization step to achieve seamless layer fusion. To facilitate research in multi-layer generation, we construct a high-quality, diverse multi-layer dataset including 400k samples. Extensive experiments and user studies demonstrate that DreamLayer generates more coherent and well-aligned layers, with broad applicability, including latent-space image editing and image-to-layer decomposition.
+
+# 1. Introduction
+
+In recent years, text-to-image generation based on diffusion models [1, 3, 4, 22, 24, 27] has demonstrated impressive
+
+
+Figure 1. DreamLayer can handle multiple tasks: (a) Text-to-layer: Given a text input, we use GPT-4 to decompose foreground and background elements, feeding them into DreamLayer to generate a multi-layered image. (b) Image-to-layer: By using inversion to initialize starting latent, DreamLayer can decompose an image based on text prompts. (c) Latent-space editing: During denoising, DreamLayer can respond to editing instructions, producing more harmonious and consistent edited images.
+
+capabilities to create high-quality, detail-rich images from text prompts. However, most methods focus on generating a single, complete image, significantly limiting their potential in applications like content editing and graphic design, which rely heavily on layered compositions. Layered structures are particularly advantageous for images containing multiple objects, as they allow for more flexible editing and creative modifications. This paper investigates the application of diffusion models to generate coherent, multi-layered images through a simple text-driven process.
+
+Recent methods have started to explore the simultaneous generation of layered image structures to better support AI-driven image editing workflows. Most existing methods [42, 45] are limited to the generation of two-layer structures, i.e., foreground and background layers. While certain approaches [11, 42] attempt to model the multi-layer generation task, they lack consideration for the relationship
+
+
+Figure 2. Multi-layer Dataset: Each image consists of a multi-layer structure, including a background and multiple foreground objects, with each foreground object represented as a transparent layer.
+
+between different foreground layers and the background. For instance, LayerDiffusion [42] disregards the spatial relationships between layers when adding new ones, leading to unintended overlaps between layers. LayerDiff [11] attempts to generate multi-layer composite images simultaneously, but it can only generate isolated, non-overlapping layers. These methods typically rely on simple stacking for layer composition, neglecting essential effects like shadows and occlusion, which are important for cohesive multi-layer generation and editing. Furthermore, a significant challenge in multi-layer generation is the lack of large-scale, high-quality open-source datasets. Current approaches and their datasets often rely on randomly stacked segmentation data [37], suffer from limited data volume [32], or lack strictly defined multi-layered images [11].
+
+To address these challenges, we propose a multi-layer data generation pipeline that decomposes images generated by advanced text-to-image models, creating a dataset of $400k$ multi-layer samples, as shown in Fig. 2. In existing text-to-image generation models, when given a text prompt containing a background and multiple foregrounds, the models often demonstrate the ability to automatically arrange objects in a reasonable layout and generate harmonious compositions. Building upon this, we introduce DreamLayer, a framework that utilizes global layer information to guide inter-layer attention and integrates a harmonization mechanism. To address layout issues in foreground layers, we begin by generating a cohesive global image from the full-text prompt. Then, we employ Context-Aware Cross-Attention to extract contextual information from the global image, guiding the generation of foreground layers. To establish connections between layers, we adapt Layer-Shared Self-Attention, which further facilitates the sharing of global information across independent layers. Finally, we apply Information Retained Harmonization to
+
+fuse the composite image in latent space, ensuring a harmonious final result and improving consistency for subsequent editing tasks. DreamLayer enables the generation of multi-layer images with cohesive layouts and seamless integration across layers. It also supports a variety of tasks. As shown in Fig. 1, (a) DreamLayer can perform text-to-layer to generate multi-layer images by adaptively decomposing user text prompts; (b) DreamLayer supports image-to-layer decomposition by initializing the denoising latent via inversion and directing it based on text prompts in a training-free manner; (c) DreamLayer supports user-driven edits during the denoising process, ensuring harmonious edited images. In summary, our key contributions are threefold:
+
+- We introduce DreamLayer, a simultaneous multi-layer generation framework that enhances harmony and consistency across layers via inter-layer interaction.
+- We propose a layer-level harmonization approach to achieve smoother inter-layer blending, making it more adaptable for subsequent editing tasks.
+- The release of a large-scale, high-quality multi-layer dataset, containing $400k$ meticulously curated multi-layer images, covering multiple objects and scenes.
+
+# 2. Related Work
+
+Diffusion based Image Generation. Diffusion models [10, 31] have shown leading performance in generative tasks, including image generation [24, 40, 41, 48], editing [2, 12], inpainting [17], and video generation [7, 47]. These models have evolved from early pixel-space denoising [28] to latent-space denoising [24], with architectures progressing from U-Net [25] to advanced designs like DiT [4, 21]. For multi-layer image generation, Text2Layer [45] uses a latent diffusion model to jointly reconstruct the RGB and alpha channels for two-layer images. LayerDiffusion [42] encodes the alpha channel in the latent manifold and shares
+
+
+Figure 3. The DreamLayer Framework for Multi-Layer Image Generation: During the generation process, background and foreground prompts are combined via layer assign embeddings to form a global prompt $C_t^{k+1}$ . In the attention phase, CACA extracts a context map from the global layer. Subsequently, the contextual information is fused across layers through LSSA, based on the global context map. Finally, IRH fuses the images using the latent image during the denoising process, achieving a harmonious result.
+
+
+Figure 4. Overview of the Attention Mechanism in DreamLayer: (a) Context-Aware Cross-Attention for extracting the global context map and guiding the foreground layer layout; (b) Layer-Shared Self-Attention for establishing inter-layer connections and ensuring consistency.
+
+attention between foreground and background layers to generate multi-layered images. LayerDiff [11] proposes to generate multi-layer composites with layer-collaborative attention. However, these approaches often neglect integrated effects such as shadows and other inter-layer interactions between multiple foreground and background layers.
+
+Controllable Diffusion Model and Image Editing. To enhance controllability in image generation, a range of methods have been developed. Textual Inversion [5] and Dream-Booth [26] enable personalized content generation from a small set of example images. ControlNet [43] and T2I-Adapter [20, 39] introduce conditional signals, using reference images as visual prompts for direct guidance. Other methods [35, 46] utilize bounding boxes to control image layout, while P2P [8] and PnP [33] condition attention layers to manage content and style. To enable more customized image content, some methods [6, 12, 19] leverage inversion
+
+techniques, converting the input image into a noise latent representation, which is then edited and generated in a controlled manner based on text prompts. DesignEdit [13] further segment the latent representations into multiple layers, allowing more flexible spatial editing. However, existing methods typically restrict layers to non-overlapping structures. In this work, we utilize a harmonious global layer to guide the generation of layers and employ independent layers to achieve seamless fusion in the latent space.
+
+# 3. Methodology
+
+**Definitions.** Intuitively, a $k$ -layer image consists of a background layer $I^1$ , $k - 1$ foreground layers $\{I^i\}_{i = 2}^k$ and a global layer $I^{k + 1}$ . Each layer comprises a three-channel color image $I_{c} \in \mathbb{R}^{H \times W \times 3}$ and an alpha channel $I_{\alpha} \in \mathbb{R}^{H \times W \times 1}$ , where the alpha channel indicates the visibility
+
+of the pixels within the color image. Formally, the global layer image $I^{k + 1}$ can be expressed as
+
+$$
+I ^ {k + 1} = \sum_ {i = 1} ^ {k} \left(I _ {\alpha} ^ {i} \cdot I _ {c} ^ {i} \cdot \prod_ {f = i + 1} ^ {k} \left(1 - I _ {\alpha} ^ {f}\right)\right). \tag {1}
+$$
+
+Each layer is associated with a corresponding textual description as a text prompt $\{C_p^i\}_{i = 1}^{k + 1}$ .
+
+Generation of Alpha Channel. For each layer image, we fill the image with a solid gray background based on its alpha channel to obtain an RGB layer. This RGB layer is then encoded into a latent image $z \in \mathbb{R}^{hw \times D}$ and perturbed with noise for $t$ timesteps to produce a noisy latent image $z_{t}$ . With the timestep $t$ and a text prompt $C$ as conditions, the diffusion model trains a network $\epsilon_{\theta}$ to predict the noise added to the noisy latent image $z_{t}$ with
+
+$$
+\mathcal {L} _ {\text {n o i s e}} = \mathbb {E} _ {z _ {t}, t, C, \epsilon \sim \mathcal {N} (0, 1)} \left[ | | \epsilon - \epsilon_ {\theta} (z _ {t}, t, C) | | _ {2} ^ {2} \right], \tag {2}
+$$
+
+where $\mathcal{L}_{noise}$ represents the learning objective of the diffusion model. After $T$ denoising steps, the latent image $z_0$ is decoded by a layer decoder to generate the final transparent layer image with alpha channel. The layer decoder can be diverse, some methods [11, 45] train a 4-channel VAE decoder, while others [42] utilize a VAE decoder combined with a gray-background segmentation model. In this work, we adopt the same layer decoder as used in LayerDiffusion [42]. Notably, we primarily focuses on the layout coherence and overall harmony in multi-layer generation, rather than the accuracy of alpha channel generation.
+
+Overview. As shown in Fig. 3, for multi-layer generation, we simultaneously encode the prompt of background layer and each foreground layer with the text encoder to obtain text embedding $\{C_t^i\in \mathbb{R}^{S\times D}\}_{i = 1}^k$ , where $S$ denotes the sequence length after tokenization. A learnable layer assign embedding is then added to each text embedding. We extract the portion between the [SOS] and [EOS] tokens from each text embedding and concatenate them to form a global embedding $C_t^{k + 1}\in \mathbb{R}^{S\times D}$ , which captures the essential information of all layers and guides the generation of the global layer. All layers are processed in a batch-wise manner during the attention computation of the diffusion model. To fully utilize the information from the global layer, we design three key components: Context-Aware Cross-Attention (CACA), Layer-Shared Self-Attention (LSSA), and Information Retained Harmonization (IRH). These components leverage guidance from the global layer to ensure consistency across background layer and foreground layers, facilitating the generation of harmonious multi-layer images.
+
+# 3.1. Context-Aware Cross-Attention
+
+The key to multi-layer generation is maintaining consistency in layout and proportions across all layers. During the generation process, we align the layout positions of
+
+other layers with the global layer. Utilizing the text embeddings of each layer, we extract relevant information from the cross-attention of the global layer. Formally, as shown in Fig. 4 (a), the global noisy latent image $z_{t}^{j,k + 1}$ in the $j^{th}$ cross-attention mechanism is projected to a query matrix $Q_{c}^{j} = \ell_{Q}(z_{t}^{j,k + 1})$ and the attention map $\mathcal{M}_j\in \mathbb{R}^{hw\times S}$ is then calculated with global embedding as
+
+$$
+\mathcal {M} _ {j} = \operatorname {S o f t m a x} \left(\frac {Q _ {c} ^ {j} \ell_ {K} \left(C _ {t} ^ {k + 1}\right) ^ {T}}{\sqrt {d}}\right), \tag {3}
+$$
+
+where $\ell_{Q},\ell_{K}$ are linear projections and $d$ is the latent dimension. The attention map preserves the spatial layout and geometry of the different foreground objects [8, 44]. Therefore, we extract the cross-attention maps corresponding to each foreground object from $J$ layers in the diffusion model. These maps are combined to create $f$ initial spatial-aware global attention maps $\mathcal{M}_G^f$ :
+
+$$
+\mathcal {M} _ {G} ^ {f} = \operatorname {N o r m} \left(\sum_ {s = 1} ^ {S _ {f}} \sum_ {j = 1} ^ {J} \left(\mathcal {M} _ {j} ^ {s}\right)\right), f = 2, \dots , k \tag {4}
+$$
+
+where $Norm(\cdot)$ denotes the Min-Max Normalization and $S_{f}$ denotes the token length of each foreground's text embedding within the global embedding. To enhance foreground layer context in the extracted attention map, we feed the initial map and the global noisy latent image of $J$ cross-attention mechanism into $N$ context-aware layers $CAL(\cdot ,\cdot)$ to generate global context map $\mathcal{M}_G^{f,n + 1}$ as:
+
+$$
+\mathcal {M} _ {G} ^ {f, n + 1} = C A L \left(\mathcal {M} _ {G} ^ {f, n}, \sum_ {j = 1} ^ {J} z _ {t} ^ {j, k + 1}\right). \tag {5}
+$$
+
+Each context-aware layer consists of a multi-head attention [34] followed by a feed-forward network (FFN). The context map is supervised by the alpha channel of the foreground image with
+
+$$
+\mathcal {L} _ {c} = \sum^ {f} \left| \left| \mathcal {R} \left(I _ {\alpha} ^ {f}\right) - \mathcal {M} _ {G} ^ {f, N} \right| \right| _ {2}, \tag {6}
+$$
+
+where $\mathcal{R}(\cdot)$ denotes the resize operation with interpolation.
+
+After extracting the harmonious layout and geometric information of the foreground layer from the global layer $I^{k + 1}$ , we apply the same way to extract the corresponding spatial-aware attention maps $\mathcal{M}_F^f$ from the foreground-specific layers $(I^i)_{i = 2}^k$ . Next, we implement a layout align loss $\mathcal{L}_{layout}$ to enable the global layer to supervise and guide the local foreground layers, facilitating alignment and coherence between them:
+
+$$
+\mathcal {L} _ {\text {l a y o u t}} = \sum^ {f} \left| \left| \mathcal {M} _ {G} ^ {f, N} - \mathcal {M} _ {F} ^ {f} \right| \right| _ {2}. \tag {7}
+$$
+
+The final objective can be jointly written as
+
+$$
+\mathcal {L} = \lambda_ {\text {n o i s e}} \mathcal {L} _ {\text {n o i s e}} + \lambda_ {c} \mathcal {L} _ {c} + \lambda_ {\text {l a y o u t}} \mathcal {L} _ {\text {l a y o u t}}, \tag {8}
+$$
+
+where $\lambda_{noise},\lambda_c$ and $\lambda_{layout}$ are weight terms.
+
+
+Figure 5. The pipeline of multi-layer data preparation. We utilize GPT-4 to process a randomly selected base prompt, structuring it into a background prompt and multiple foreground prompts. After generating the image using a diffusion model, we apply an open-set detection model GroundingDINO to identify the positions of the foreground objects and use the DepthAnything model to obtain a depth map. Based on the depth order, we sequentially extract the foreground layers and fill in the missing areas with an inpainting model.
+
+# 3.2. Layer-Shared Self-Attention
+
+To further strengthen the connections between layers, we propose a layer-shared self-attention. This approach first integrates global layer information into the foreground layers through the attention map, then processes information from all layers simultaneously within the self-attention mechanism, reinforcing inter-layer relationships and ensuring consistency throughout the multi-layer generation.
+
+Specifically, as shown in Fig. 4 (b), given a layer batch of noisy latent images $\{z_t^{i_1}z_{t + 1}^{k + 1}\}$ and the global context map $\{\mathcal{M}_G^{i,t}\}_{i = 2}^k$ at time step $t$ , we integrate global information into the foreground layers based on the global context map, which is expressed as:
+
+$$
+\tilde {z} _ {t} ^ {i} = z _ {t} ^ {k + 1} \cdot \mathcal {M} _ {G} ^ {i, t} + z _ {t} ^ {i} \cdot (1 - \mathcal {M} _ {G} ^ {i, t}). \qquad (9)
+$$
+
+For a diffusion model with $T$ denoising steps, we execute the process during the first $T_{G}$ steps. Furthermore, to establish interaction between layers, we concatenate all noisy latent images along the sequence dimension to form a joint noise image at each denoising step:
+
+$$
+\tilde {z} _ {t} ^ {c} = \operatorname {c o n c a t} \left(\tilde {z} _ {t} ^ {1}, \dots , \tilde {z} _ {t} ^ {k + 1}\right). \tag {10}
+$$
+
+We then perform linear projections to generate the joint key $K_{s}^{c}$ and value $V_{s}^{c}$ , and apply attention with original layer query $Q_{s}^{i}$ , formally as:
+
+$$
+O _ {s} ^ {i} = \operatorname {S o f t m a x} \left(\frac {Q _ {s} ^ {i} \left(K _ {s} ^ {c}\right) ^ {T}}{\sqrt {d}}\right) V _ {s} ^ {c}, \tag {11}
+$$
+
+where $d$ denotes the latent dimension. The weights of the linear projection are initialized from the original weights.
+
+# 3.3. Information Retained Harmonization
+
+In multi-layer fusion, simply blending layers based on the alpha channel often affects the overall visual quality, as adding foreground objects to the background typically introduces shadow variations in real-world scenarios. To
+
+achieve a more harmonious fusion of the composite image, we propose Information Retained Harmonization, which blends latent during the denoising process and incorporates additional denoising steps, resulting in a more coherent and visually consistent final composite image.
+
+Specifically, during the standard $T$ denoising steps, we retain the noisy latent images between step $T_{H}$ and $T_H^\prime$ , denoted as $\{z_t\}_{t = T_H}^{T_H^{\prime}}$ . After completing the $T$ denoising steps, we obtain the alpha channel $\{I_\alpha^i\}_{i = 2}^k$ of the foreground-specific layer through the layer decoder. We then perform re-denoising for $T - T_{H}$ steps as a harmonization process, and between steps $T_{H}$ and $T_H^\prime$ , we conduct latent-level layer fusion. The formulation is as follows:
+
+$$
+\hat {z} _ {t} ^ {m} = \hat {z} _ {t} ^ {1} \cdot \prod_ {i = 2} ^ {k} \left(1 - I _ {\alpha} ^ {i}\right) + \sum_ {i = 2} ^ {k} \left(z _ {t} ^ {i} \cdot I _ {\alpha} ^ {i} \cdot \prod_ {f = i + 1} ^ {k} \left(1 - I _ {\alpha} ^ {f}\right)\right), \tag {12}
+$$
+
+where $\hat{z}$ represents the noisy latent image obtained during the harmonization steps. During the IRH process, the fused latent is influenced by the foreground objects throughout the denoising steps, allowing for the generation of corresponding shadow details and enhancing the overall coherence of the image. Simultaneously, information from the foreground layers is gradually preserved during denoising, ensuring the consistency of the generated foreground layers.
+
+Additionally, we can edit the layers within the latent space, ensuring a smoother, more harmonious fusion of the layers. This is expressed as follows:
+
+$$
+\begin{array}{l} \hat {z} _ {t} ^ {m} = \hat {z} _ {t} ^ {1} \cdot \prod_ {i = 2} ^ {k} (1 - o p \left(I _ {\alpha} ^ {i}\right)) + \\ \sum_ {i = 2} ^ {k} \left(o p \left(z _ {t} ^ {i}\right) \cdot o p \left(I _ {\alpha} ^ {i}\right) \cdot \prod_ {f = i + 1} ^ {k} \left(1 - o p \left(I _ {\alpha} ^ {f}\right)\right)\right), \tag {13} \\ \end{array}
+$$
+
+where $op(\cdot)$ represents the operations such as resizing, flipping, and moving.
+
+| Methods | Two Layers | Three Layers | Four Layers |
| AES↑ | Clip↑ | FID↓ | AES↑ | Clip↑ | FID↓ | AES↑ | Clip↑ | FID↓ |
| SD v1.5 [24] | 6.930 | 34.678 | 53.950 | 6.363 | 34.222 | 55.198 | 6.367 | 35.000 | 59.149 |
| LayerDiffusion [42] | 6.522 | 32.466 | 63.481 | 6.058 | 30.350 | 67.118 | 5.975 | 29.158 | 79.997 |
| DreamLayer w/o IRH | 6.967 | 34.587 | 51.957 | 6.351 | 34.696 | 58.812 | 6.340 | 34.993 | 57.073 |
| DreamLayer | 7.013 | 34.835 | 50.761 | 6.441 | 35.267 | 54.508 | 6.422 | 35.723 | 53.598 |
+
+Table 1. Quantitative comparison of multi-layer composite image generation. For SD v1.5, we generate the complete image from the global prompt as a composite image.
+
+| Dataset | Images | Resolutions | Classes | Instances |
| MuLAn [32] | 44,860 | 600~800 | 759 | 101,269 |
| DreamLayer | 408,187 | 896~1152 | 1453 | 525,388 |
| -TwoLayer | 305,801 | 896~1152 | 1379 | 305,801 |
| -ThreeLayer | 87,571 | 896~1152 | 1322 | 175,142 |
| -FourLayer | 14,815 | 896~1152 | 1045 | 44,445 |
+
+Table 2. Dataset comparison between MuLAn and DreamLayer.
+
+# 3.4. Dataset Preparation
+
+Fig. 5 illustrates the construction process of our multi-layer dataset. To manage complex layer relationships, we begin with the global layer and employ open-set object detection, depth maps, and inpainting to decompose it into multiple layers. First, we randomly sample a prompt from a large-scale prompt dataset [36] as the base prompt. This base prompt is then processed by the GPT-4 model, which breaks it down into a background prompt $C_p^0$ , several foreground prompts, and a complete global prompt $C_p^{k+1}$ . If the base prompt lacks sufficient foreground objects, GPT-4 selects a suitable category from the Object365 [30] dataset. Next, the global prompt is passed through a powerful image generation diffusion model, such as Flux [15], SD3 [16], or SDXL [22], to generate a complete image. We then use the foreground prompts and the open-set detection model, GroundingDINO [18], to match the text with objects in the image. Grounding DINO predicts bounding boxes based on input text. We match each box with a segmentation mask by computing their IoU, and link the corresponding text to the matched mask. Simultaneously, we generate a depth map of the complete image using the DepthAnything [38] model. Based on the depth map, we extract the object at the forefront using a matting model and fill in the missing areas with an inpainting model. Repeating this process, we determine the sequence of layers using the depth map and extract the corresponding foreground layers. We match the objects and text using segmentation masks and detection boxes, ultimately obtaining transparent images for multi-layers. Current generative models still struggle in generating a larger number of objects, resulting in low data retention. Therefore, we set the final output to 4 layers. Details of the pipeline are in the supplementary materials.
+
+Following this pipeline, we generate a dataset containing millions of multi-layer images. To further improve the quality, we apply both VLM-based (e.g., GPT-40) and human
+
+
+Figure 6. The vote preference percentage in user study. We evaluate our method and LayerDiffusion on three aspects: multi-layer, foreground, and background quality.
+
+quality inspection to filter out samples with (1) background artifacts, (2) incomplete foreground masks, and (3) text-layer mismatches from Grounding DINO errors. The final dataset comprises $300k$ two-layer images, $85k$ three-layer images, and $15k$ four-layer images. As shown in Tab. 2, our dataset contains more samples and encompasses a broader range of classes compared to existing datasets.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Training. We initialize training with the pre-trained weights of Stable Diffusion v1.5 [24] and employ the Custom Diffusion [14] strategy, fine-tuning the K&V linear layers in all attention layers. For foreground layers, additional K&V layers are trained separately. The Context-Aware Cross-Attention is applied in the downsampling layers at a resolution of 16, while Layer-Shared Self-Attention is used in all upsampling layers. Each layer batch is initialized with same timestep noise, and the Layer Embedding is zero-initialized to minimize interference with the original weights. The training is performed over 4 days on 2 A100 GPUs with a batch size of 4 and a learning rate of 2e-6. More details are available in the supplementary materials.
+
+Evaluation. We evaluate DreamLayer on a test set of 3k multi-layer images from our proposed dataset. Aesthetic quality is assessed using the AES Score [29], text-image alignment with the CLIP-Score [23], and distribution similarity with the FID [9].
+
+# 4.2. Comparisons of Multi-Layer Image Generation
+
+Quantitative Comparisons. As shown in Tab. 1, We compare DreamLayer's performance in generating complete layers with results from Stable Diffusion [24] (SD15) and
+
+
+Figure 7. Qualitative comparison of multi-layer image generation. We present the generation results of Layerdiffusion and our method with two-layer, three-layer and four-layer images.
+
+
+Figure 8. Ablation Study on Context-Aware Cross-Attention: Using $\mathcal{L}_{layout}$ supervision to extract layout information from the global image, guiding the generation of foreground layers and reducing overlapping placements.
+
+| DreamLayer | Multi-Layers (Average) |
| LSSA | CACA | AES↑ | Clip↑ | FID↓ |
| | 6.438 | 33.808 | 57.241 |
| ✓ | | 6.471 | 33.727 | 56.598 |
| ✓ | 6.561 | 34.004 | 55.788 |
| ✓ | ✓ | 6.625 | 35.275 | 52.956 |
+
+LayerDiffusion [42]. In this setup, SD15 generates a single complete image based solely on a global prompt. We use LayerDiffusion's background-to foreground approach for three-layer and four-layer images, sequentially adding foreground elements to simulate multi-layer composition. As shown in the table, our method outperforms LayerDiffusion across all three metrics for multi-layer generation, with a notable improvement of around 0.5 in aesthetic score. For composite multi-layer images, our approach also achieves higher aesthetic quality and better text alignment compared to direct full-image generation by SD15.
+
+Qualitative Comparisons. In Fig. 7, we present the multilayer image generation results. Compared to Layerdiffusion [42], our method produces more coherent and appropriately sized foreground layers and achieves a more harmonious blending of the foreground and background.
+
+User Study. As shown in Fig. 6, we perform a user study with 20 subjects on 200 samples to evaluate the multi-layer generation quality of our method and LayerDiffusion [42]
+
+
+Figure 9. Ablation study on IRH. Our harmonization approach, unlike direct blending, generates appropriate shadows for foreground objects, resulting in a more cohesive overall composition.
+
+Table 3. Ablation study on LSSA and CACA.
+
+| TH | 0 | 200 | 400 | 600 | 800 |
| T′H | 0 | 0 | 200 | 400 | 600 |
| Avg AES↑ | 6.553 | 6.568 | 6.600 | 6.625 | 6.615 |
+
+Table 4. Investigation of ${T}_{H}$ and ${T}_{H}^{\prime }$ in IBH.
+
+across three aspects: multi-layer, foreground, and background quality. The results show that our method achieves a preference percentage of $71.34\%$ , $47.84\%$ , $83.03\%$ w.r.t the above three aspects. It indicates our method delivers more cohesive layouts and higher quality, particularly in background and multi-layer images.
+
+# 4.3. Ablation Study
+
+Context-Aware Cross-Attention. CACA extracts the context map information from the global layer and utilizes $\mathcal{L}_{layout}$ to guide the layout of the foreground layer. As shown in Fig. 8, without the layout alignment loss w/o $\mathcal{L}_l$ , foreground objects tend to generate in the same position, leading to overlap and occlusion. We report the qualitative results in Tab. 3. Removing CACA significantly degrades image quality, reducing the overall AES score of the multi-layer generation by 0.154.
+
+Layer-Shared Self-Attention. LSSA is primarily used to maintain consistency across different image layers. As shown in Tab. 3, the absence of LSSA leads to a significant drop in the CLIP score, decreasing by approximately 1.27.
+
+
+Figure 10. Image to Layer Visualization: By leveraging inversion to transfer the input image as the initial noise latent for all layers, DreamLayer can decompose the input with the text prompt.
+
+Information Retained Harmonization. We further investigate the role of IRH in layer composition. As shown in Fig. 9, simply stacking foreground and background layers (Blend) produces unrealistic composite images, lacking texture details like shadows. For example, the chair in Fig. 9 appears to float without a shadow, disrupting visual harmony. With IRH, however, shadows and other details are generated in the background to reflect the presence of foreground objects, resulting in a more natural and cohesive layer composition. For quantitative results, as shown in Tab. 1, "DreamLayer w/o IRH" shows a noticeable decline in aesthetic scores, dropping by 0.1 without IRH.
+
+$T_{H}$ and $T_{H}^{\prime}$ in IBH. We investigate the values of $T_{H}$ and $T_{H}^{\prime}$ in the IBH. We experiment with $T_{H}$ from 800 to 0 steps. As Tab. 4 shows, when $T_{H}^{\prime} < 600$ , IBH is applied near the end of the denoising process, resulting in poor harmonization and low AES score. Conversely, when $T_{H}$ is large (e.g., $T_{H} = 800$ ), IBH over-modifies the background, reducing the AES score. Based on these observations, we selected $T_{H} = 600$ and $T_{H}^{\prime} = 400$ .
+
+# 4.4. Further Application
+
+Image to Layer Within the DreamLayer framework, we can extend it to Image-to-Layer task in a training-free manner. Specifically, we encode the input image into a latent representation as the global latent, then progressively add noise up to the $T$ step latent using an inversion technique [19], which serves as the initial latent for all layers in DreamLayer. To obtain a more accurate initial latent during this inversion process, we isolate global image information using a mask, minimizing the influence of other layers. As shown in Fig. 10, this approach enables us to decompose the input image into separate layers based on text prompts. Detailed steps are provided in the supplementary materials.
+
+Layer Editing In practical applications, DreamLayer can generate multi-layer images and allow users to make harmonious edits to the layers. As described in Eq. (13), we perform these edits within IRH at the latent level, ensuring
+
+
+Figure 11. Layer Editing Visualization: Compared to DesignEdit, DreamLayer can complement objects at the image edges and create more cohesive results when they are flipped or moved.
+
+more cohesive adjustments. For instance, in Fig. 11, when the chair is flipped and moved, the floor shadow is updated to align with its new position, enhancing overall realism. Moreover, when parts of a foreground object extend beyond the image boundary, DreamLayer has the ability of foreground object amodal completion, which can complete the missing sections as needed when repositioned. As shown in Fig. 11, compared to existing methods like DesignEdit [13], DreamLayer successfully restores the out-of-frame areas of objects such as the robot and blue vase after they are moved.
+
+# 5. Conclusion
+
+In this paper, we introduce a large-scale, high-quality multi-layer dataset featuring diverse foreground objects and backgrounds. Building on this, we propose DreamLayer, a framework for simultaneously generating multi-layer images. To address layout consistency among foreground layers, we introduce Context-Aware Cross-Attention, which guides foreground generation using the harmonious layout of a global image. To enhance inter-layer connections, we present Layer-Shared Self-Attention, enabling effective information exchange between layers. Finally, to generate a cohesive composite image, we propose Information Retained Harmonization, which merges layers at the latent level to achieve seamless fusion. DreamLayer support not only multi-layer generation but also layer decomposition for image-to-layer task with inversion, enabling flexible editing within the latent space for harmonious adjustments. Experimental results demonstrate the effectiveness of DreamLayer in multi-layer generation.
+
+# 6. Acknowledgment
+
+This work is supported in part by the National Key R&D Program of China (2024YFB3908503), and in part by the National Natural Science Foundation of China (62322608).
+
+# References
+
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+# DreamRelation: Relation-Centric Video Customization
+
+Yujie Wei $^{1}$ , Shiwei Zhang $^{2,*}$ , Hangjie Yuan $^{2}$ , Biao Gong $^{3}$ , Longxiang Tang $^{2}$ , Xiang Wang $^{2}$ , Haonan Qiu $^{4}$ , Hengjia Li $^{5}$ , Shuai Tan $^{3}$ , Yingya Zhang $^{2}$ , Hongming Shan $^{1,\dagger}$
+
+$^{1}$ Fudan University $^{2}$ Alibaba Group $^{3}$ Ant Group $^{4}$ Nanyang Technological University $^{5}$ Zhejiang University $^{y}$ jwei22@m.fudan.edu.cn, zhangjin.zsw@alibaba-inc.com, hmshan@fudan.edu.cn
+
+Project page: https://dreamrelation.github.io
+
+
+hugging
+
+
+
+
+A bear is hugging with a panda.
+
+
+
+
+
+
+punching
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+cheering
+
+
+
+
+A polar bear is punching a penguin on an icy plain.
+
+
+
+
+
+
+
+
+shaking hands
+
+
+Figure 1. Relational video customization results of DreamRelation. Given a few exemplar videos, our method can customize specific relations and generalize them to novel domains, where animals mimic human interactions.
+
+
+A panda is raising a toast with a red panda in a bamboo grove.
+
+
+A dog is shaking hands with a cat in a cyberpunk city.
+
+
+
+
+
+# Abstract
+
+Relational video customization refers to the creation of personalized videos that depict user-specified relations between two subjects, a crucial task for comprehending real-
+
+world visual content. While existing methods can personalize subject appearances and motions, they still struggle with complex relational video customization, where precise relational modeling and high generalization across subject categories are essential. The primary challenge arises from the intricate spatial arrangements, layout variations, and nuanced temporal dynamics inherent in relations; consequently, current models tend to overemphasize irrelevant visual details rather than capturing meaningful interactions. To address these challenges, we propose DreamRelation, a novel approach that personalizes relations through a small
+
+set of exemplar videos, leveraging two key components: Relational Decoupling Learning and Relational Dynamics Enhancement. First, in Relational Decoupling Learning, we disentangle relations from subject appearances using relation LoRA triplet and hybrid mask training strategy, ensuring better generalization across diverse relationships. Furthermore, we determine the optimal design of relation LoRA triplet by analyzing the distinct roles of the query, key, and value features within MM-DiT's attention mechanism, making DreamRelation the first relational video generation framework with explainable components. Second, in Relational Dynamics Enhancement, we introduce space-time relational contrastive loss, which prioritizes relational dynamics while minimizing the reliance on detailed subject appearances. Extensive experiments demonstrate that DreamRelation outperforms state-of-the-art methods in relational video customization.
+
+# 1. Introduction
+
+Recent advancements in text-to-video (T2V) generation, particularly through powerful video diffusion transformers (DiT) [5, 65, 104], have significantly propelled customized video generation [38, 93, 108]. While existing methods succeed in customizing subject appearances and single-object motions [85, 97, 112], the challenging task of customizing higher-order interactions between subjects (i.e., Relational Video Customization) remains under-explored due to its intrinsic complexity. Enhancing video generation through customized relations is crucial for real-world applications such as filmmaking, enabling a more profound comprehension and production of complex relational visual content.
+
+We formulate the task of Relational Video Customization as follows: given exemplar videos representing a relational pattern , the model aims to generate videos that exhibit the specified relation within the pattern, as shown in Fig. 1. While general text-to-video DiTs like Mochi [79] can generate videos depicting certain relational concepts, they often fail to: (1) produce unconventional or counter-intuitive interactions, such as animals engaging in human-like relationships as illustrated in Figs. 2, even when provided with detailed prompts; (2) generate videos that adhere to precise relational dynamics, such as "two people approaching each other from predefined positions." These issues highlight the need for a novel video generation method to precisely customize desired relations.
+
+A straightforward approach involves adapting existing video subject or motion customization methods to customize relations between subjects. However, while subject customization techniques like Dreamix [62] capture detailed appearances using low-level reconstruction loss, they may hinder high-level relation learning due to severe appearance leakage. Similarly, motion customization methods
+
+
+
+
+"A bear is hugging with a tiger."
+"A bear and a tiger stand on their hind legs, each extending their front legs wide open towards each other in a warm embrace. Both animals lean ......"
+
+
+(a) Results of the base model Mochi.
+"A bear is hugging with a tiger."
+(b) Results of our DreamRelation.
+
+
+Figure 2. (a) General Video DiT models like Mochi [79] often struggle to generate unconventional or counter-intuitive interactions, even with detailed descriptions. (b) Our method can customize a specific relation to generate videos on new subjects.
+Figure 3. Averaged value feature across all layers and frames in Mochi. We identify that the relations encompass intricate spatial arrangements, layout variations, and nuanced temporal dynamics, presenting challenges in relational video customization.
+
+such as MotionInversion [85] excel in transferring single-object motions but struggle to precisely capture relational dynamics between two subjects. We identify that the key challenge stems from the complexity inherent in the relations, which involve intricate spatial arrangements, layout variations, and nuanced temporal dynamics. To illustrate this, we visualize the Value features in Fig. 3 and provide detailed analysis in Sec. 3.3. This tangled nature may prevent accurate modeling of relations and cause models to focus on irrelevant subject appearances. This raises a critical research question: How can we decouple relations and subject appearances while accurately modeling relational dynamics to enhance generalizability?
+
+To that end, we propose DreamRelation, a relational video customization method that personalizes user-specified relations from exemplar videos through two concurrent processes: relational decoupling learning and relational dynamics enhancement. In relational decoupling learning, we decompose the relational pattern from input videos into relational and appearance information using devised relation LoRA triplet, a composite LoRA [32] set comprising relation LoRA sets and subject LoRA sets. To facilitate this decoupling, we introduce hybrid mask train
+
+ing strategy that guides the two types of LoRAs to focus on designated regions with corresponding masks, achieved by a LoRA selection strategy and an enhanced diffusion loss based on masks to amplify the learning in target areas.
+
+Furthermore, building on the MM-DiT [18] architecture, we analyze the query, key, and value features within the full attention, and empirically identify that the query, key, and value matrices serve distinct roles in the relation customization task. This insight motivates our design of relation LoRA triplet, particularly in determining the optimal placement of LoRA components within the model architecture to maximize relational customization effectiveness.
+
+To explicitly enhance relational dynamics learning, we propose a novel space-time relational contrastive loss, which emphasizes relational dynamics while reducing the focus on detailed appearances during training. Concretely, we pull relational dynamics representations closer through frame differences in model outputs of videos depicting the same relation, while distancing them from appearance representations derived from single-frame outputs.
+
+We curate a dataset comprising 26 human interactions from publicly available action recognition datasets [49, 71] to comprehensively evaluate relational video customization. Each video is annotated with a textual prompt, and approximately 20 videos per relation type are randomly selected for training. The evaluation is conducted on diverse subjects using 40 designed textual prompts. Extensive experimental results demonstrate that our DreamRelation outperforms state-of-the-art methods in this task.
+
+Our contributions are summarized as follows:
+
+- We make the first attempt at the Relational Video Customization task by presenting DreamRelation, a method that generates videos depicting customized relations based on the MM-DiT architecture.
+- We devise relation LoRA triplet with hybrid mask training strategy to explicitly decouple relation and subject appearances. To determine the optimal model design of our method, we further analyze the roles of query, key, and value features in MM-DiT full attention.
+- We propose a novel space-time relational contrastive loss to enhance relation learning by emphasizing relational dynamics while reducing focus on appearances.
+- Extensive experimental results demonstrate that DreamRelation achieves state-of-the-art performance on relational video customization.
+
+# 2. Related Work
+
+Text-to-video diffusion models. Text-to-video generative models have achieved breakthroughs in generating high-quality and controllable videos using textual prompts and diverse conditions [1, 3, 4, 7, 17, 24, 29, 41, 48, 56-59, 67, 74-77, 86-90, 98, 103, 107, 109]. VDM [30] introduces diffusion models into video generation by modeling
+
+video distribution in pixel space. ModelScopeT2V [84] and VideoCrafter [11, 13] integrate spatiotemporal blocks for text-to-video generation. With the success of DiT [65] that introduces Transformers [82] as the backbone of diffusion models, the generated video quality has improved with increased parameters [5, 19, 43, 55, 113]. CogVideoX [104] incorporates 3D VAE and expert transformers, enhancing video coherence. Mochi [79] proposes an Asymmetric Diffusion Transformer architecture to scale parameters. HunyuanVideo [42] enhances architecture design and model training, achieving leading performance. These advancements pave the way for relational video customization.
+
+Customized video generation. Building upon achievements in image generation and personalization [8, 15, 16, 21, 28, 35, 44, 66, 69, 70, 92, 99, 110, 115], customized video generation has garnered growing attention [9, 26, 46, 60, 62]. Many studies focus on generating personalized videos using a few subject or facial images [45, 72, 93-97, 108, 111, 114], while others tackle the challenging multi-subject video customization [10, 12, 14, 34, 91]. Besides subject customization, motion customization or motion transfer have also gained significant interest [37, 38, 68, 80, 81, 100, 105, 112]. For example, MotionInversion [85] integrates motion embeddings into the temporal attention of video diffusion models to learn motion dynamics. While these methods effectively capture the subject appearances or single-object motions, the challenging task of customizing interactions between two subjects remains underexplored due to its inherent complexity. In this work, we pioneer this relational video customization task by presenting DreamRelation, which can personalize specific relations and generate diverse videos aligned with text prompts.
+
+Relation generation. Early works on relational image generation focus on human-object interactions using additional conditions like bounding boxes [22, 31, 33]. Recently, inspired by image customization methods, several works have explored relational image customization to personalize user-specific interactions from a few relational images [23, 36, 73]. For instance, ReVersion [36] utilizes inversion techniques to capture relational information in the text embedding space. Despite these advancements, existing methods are confined to the relatively simple relations depicted in images. Direct adaptation of these image-based methods for relational video customization often leads to inaccurate relation modeling since dynamic and sequential interactions cannot be fully represented in a single image. In contrast, we design our method based on Video DiT architecture and precisely model relations through relational decoupling learning and relational dynamics enhancement.
+
+# 3. DreamRelation
+
+Our DreamRelation aims to generate videos depicting a specified relation expressed in a few exemplar videos while
+
+
+Figure 4. Overall framework of DreamRelation. Our method decomposes relational video customization into two concurrent processes. (1) In Relational Decoupling Learning, Relation LoRAs in relation LoRA triplet capture relational information, while Subject LoRAs focus on subject appearances. This decoupling process is guided by hybrid mask training strategy based on their corresponding masks. (2) In Relational Dynamics Enhancement, the proposed space-time relational contrastive loss pulls relational dynamics features (anchor and positive features) from pairwise differences closer, while pushing them away from appearance features (negative features) of single-frame outputs. During inference, subject LoRAs are excluded to prevent introducing undesired appearances and enhance generalization.
+
+aligning with textual prompts, as illustrated in Fig. 4. We begin by introducing preliminaries in Sec. 3.1. We then detail relational decoupling learning and relational dynamics enhancement in Secs. 3.2 and 3.4, respectively, along with an analysis of the query, key, and value features in Sec. 3.3.
+
+# 3.1. Preliminaries of Video DiT
+
+Text-to-video diffusion transformers (DiTs) show growing attention due to their capacity to generate high-fidelity, diverse, and long-duration video. Current Video DiTs [79, 104] predominantly adopt MM-DiT [18] architecture with full attention and employ diffusion processes [28] in latent space with a 3D VAE [39]. Given latent code $\mathbf{z}_0 \in \mathbb{R}^{f \times h \times w \times c}$ from video data $\mathbf{x}_0 \in \mathbb{R}^{F \times H \times W \times 3}$ with its textual prompt $c$ , the optimization process is defined as:
+
+$$
+\mathcal {L} (\theta) = \mathbb {E} _ {\boldsymbol {z}, \epsilon , \boldsymbol {c}, t} \left[ \| \epsilon - \epsilon_ {\theta} (\boldsymbol {z} _ {t}, \boldsymbol {c}, t) \| _ {2} ^ {2} \right], \tag {1}
+$$
+
+where $\epsilon \in \mathcal{N}(0,1)$ is random noise from a Gaussian distribution, and $z_{t}$ is a noisy latent code at timestep $t$ based on $z_{0}$ with the predefined noise schedule. In this work, we choose Mochi [79] as our base Video DiT model.
+
+# 3.2. Relational Decoupling Learning
+
+Relation LoRA triplet. To customize complex relations between subjects, we decompose the relational pattern from exemplar videos into distinct components emphasizing subject appearances and relations. Formally, given a few videos depicting interactions between two subjects, we represent their relational patterns as a triplet $<$ subject, relation, subject>, denoted as $< S_{1}, R, S_{2}>$ for brevity, where $S_{1}$ and $S_{2}$ are two subjects and $R$ is the relation [106].
+
+To differentiate relations and subject appearances in the relational pattern, we introduce relation LoRA triplet, a
+
+composite LoRA set comprising Relation LoRAs to model relational information and two Subject LoRAs to capture appearance information, as depicted in Fig. 4. Specifically, we inject Relation LoRAs into the query and key matrices of the MM-DiT full attention. Concurrently, we design two Subject LoRAs corresponding to the two subjects involved in the relation and inject them into the value matrix. This design is motivated by our empirical findings that the query, key, and value matrices serve distinct roles within the MM-DiT full attention. More details on the analysis are provided in Sec. 3.3. Additionally, we devise an FFN LoRA to refine the outputs of the Relation and Subject LoRAs and inject it into the linear layers of full attention. Note that the two branches of text and vision tokens in MM-DiT are processed by different LoRA sets.
+
+Hybrid mask training strategy. To achieve the decoupling of relational and appearance information in the introduced relation LoRA triplet, we propose hybrid mask training strategy (HMT) to guide Relation and Subject LoRAs to focus on designated regions using corresponding masks. We first employ Grounding DINO [50] and SAM [40] to derive masks for the two individuals in a video, indicated as Subject Masks $M_{S_1}$ and $M_{S_2}$ . Inspired by representative relation detection approaches [78, 101, 102] that utilize minimum enclosing rectangles to delineate subject-object interaction zones, we define the Relation Mask $M_R$ as the union of the two Subject Masks to indicate the relation area. Since the 3D VAE in Video DiT compresses the video's temporal dimensions by a factor of $T_c$ , we average the masks over every $T_c$ frame to represent the latent masks.
+
+We then devise a LoRA selection strategy and an enhanced diffusion loss for better disentanglement during training. Specifically, we randomly select either the Relation LoRAs or one type of Subject LoRAs in relation
+
+
+(a) Visualization of Query, Key, and Value Features in MM-DiT Full Attention. (b) Subspace similarity among the Query, Key, and Value Matrices across different models.
+Figure 5. Features and subspace similarity analysis of MM-DiT. (a) Value features across different videos encapsulate rich appearance information, and relational information often intertwines with these appearance cues. Meanwhile, query and key features exhibit similar patterns that differ from those of value features. (b) We perform singular value decomposition on the query, key, and value matrices of each DiT block and compute the similarity of the subspaces spanned by their top-k left singular vectors, indicating query and key matrices share more common information while remaining independent of the value matrix. This observation holds for both MM-DiT (Mochi [79] and HunyuanVideo [42]) and CrossAttn-based DiT (Wan2.1 [83]) architectures.
+
+LoRA triplet to update for each training iteration. When the Relation LoRAs are chosen, the two Subject LoRAs are trained simultaneously to provide appearance cues, assisting the Relation LoRAs in concentrating on relational information. This process facilitates the decoupling of relational and appearance information. The FFN LoRAs are consistently engaged throughout training to refine outputs from the selected Relation or Subject LoRAs.
+
+Following LoRA selection, we apply the corresponding masks to amplify the loss weight within the focused area, which can be defined as:
+
+$$
+\mathcal {L} _ {\text {r e c}} = \mathbb {E} _ {\boldsymbol {z}, \epsilon , \boldsymbol {c}, t} \left(\lambda_ {m} \mathbf {M} _ {l} + 1\right) \cdot \left\| \epsilon - \epsilon_ {\theta} \left(\boldsymbol {z} _ {t}, \boldsymbol {c}, t\right) \right\| _ {2} ^ {2}, \tag {2}
+$$
+
+where $l \in \{S_1, S_2, R\}$ indicates the selected mask type, and $\lambda_m$ is the mask weight. By employing the LoRA selection strategy and the enhanced diffusion loss, Relation and Subject LoRAs are encouraged to concentrate on their designated area, facilitating effective relation customization and improving the generalization capacity.
+
+Inference. During inference, we exclude Subject LoRAs to prevent undesired appearances and inject only Relation LoRAs and FFN LoRAs into the base Video DiT to maintain learned relations and enhance generalization.
+
+# 3.3. Analysis on Query, Key, and Value Features
+
+To determine the optimal model design, we analyze query, key, and value features and matrices in MM-DiT's full attention via visualization and singular value decomposition, revealing their impacts on relational video customization.
+
+Visualization analysis. We start with two types of videos: a single-subject video with multiple attributes, and a two-subject interaction video, as illustrated in Fig. 5(a). We compute the averaged query, key, and value features across all layers and attention heads at timestep 60, focusing solely on those associated with vision tokens. These features are then reshaped into an $f \times h \times w$ format, and we visualize the averaged features across all frames with shape $h \times w$ . From the observations in Fig. 5(a), we draw two conclusions: 1) Value features across different videos encapsulate
+
+rich appearance information, and relational information often intertwines with these appearance cues. For instance, in the single-subject video, high-value feature responses occur at locations like "blue glasses" and "birthday hat." In the two-subject video, high values are observed both in regions of relations (e.g., handshakes) and appearances (e.g., human face and clothing), indicating the entanglement of relational and appearance information within the features. 2) Query and key features exhibit highly abstract yet similar patterns, distinctly diverging from the value features. Unlike the obvious appearance information in value features, query, and key features exhibit homogeneity across different videos, clearly differing from value features. To further validate this point, we analyze query, key, and value matrices from a quantitative perspective.
+
+Subspace similarity analysis. We further analyze the similarity of the subspace spanned by the singular vectors of the query, key, and value matrix weights from the base Video DiT model Mochi. This similarity reflects the degree of overlap in contained information between two matrices. For the query and key matrices, we apply singular value decomposition to obtain left-singular unitary matrices $U_{Q}$ and $U_{K}$ . Following [32, 52], we select the top $r$ singular vectors from $U_{Q}$ and $U_{K}$ , and measure their normalized subspace similarity based on the Grassmann distance [25] using $\frac{1}{r}\left\|U_{Q}^{\top}U_{K}^{r}\right\|_{F}^{2}$ . The other similarities are calculated in a similar way. The results in Fig. 5(b) demonstrate that the subspaces of the query and key matrices are highly similar, whereas their similarity to the value matrix is minimal. This suggests that the query and key matrices in MM-DiT share more common information while remaining largely independent of the value matrix. In other words, the query and key matrices exhibit a strongly non-overlapping relationship with the value matrix, which facilitates the design of our decoupling learning. This observation aligns with the visualization results in Fig. 5(a). To further verify the generalizability of this finding, we conduct similar analyses on various models, e.g. HunyuanVideo [42] and
+
+Wan2.1 [83]. The results in Fig. 5(b) indicate that the higher similarity between the query and key matrices remains consistent across different MM-DiT models and other DiT architectures (CrossAttn-based DiT).
+
+Building on these observations, we empirically argue that the query, key, and value matrices serve distinct roles in relational video customization, motivating our design of relation LoRA triplet. Specifically, given that value features are rich in appearance information, we inject Subject LoRAs into the value matrix to focus on learning appearances. In contrast, due to the homogeneity observed in the query and key features and their non-overlapping nature with the value matrix, which facilitates decoupling learning, we inject Relation LoRAs into both query and key matrices to disentangle relations from appearances. The results in Tab. 3 confirm our analysis, showing this design achieves optimal performance. We believe our findings can advance video customization research based on DiT architecture.
+
+# 3.4. Relational Dynamics Enhancement
+
+To explicitly enhance relational dynamics learning, we propose a novel space-time relational contrastive loss (RCL), which emphasizes relational dynamics while reducing the focus on detailed appearance during training. Specifically, at each timestep $t$ , we compute the pairwise differences of the model output along the frame dimension, denoted as $\bar{\epsilon} \in \mathbb{R}^{(f-1) \times h \times w \times c}$ . We then reduce dependency on pixel-level information by averaging these differences across the spatial dimensions, resulting in 1D relational dynamics features $A \in \mathbb{R}^{(f-1) \times c}$ , which serve as anchor features. Subsequently, we sample $n_{\mathrm{pos}}$ 1D relational dynamics features from other relation videos as positive samples $P \in \mathbb{R}^{(f-1) \times n_{\mathrm{pos}} \times c}$ . For each frame in $A$ , we sample $n_{\mathrm{neg}}$ 1D features from single-frame model outputs $\epsilon_i \in \mathbb{R}^{1 \times h \times w \times c}$ as negative samples $N \in \mathbb{R}^{(f-1) \times n_{\mathrm{neg}} \times c}$ , which capture appearance information while excluding relational dynamics.
+
+Our objective is to learn representations with relational dynamics by pulling together the pairwise differences from different videos depicting the same relation, while distancing them from spatial features of single-frame outputs to mitigate appearance and background leakage. Following InfoNCE [61, 64] loss, we formulate the proposed loss as:
+
+$$
+\mathcal {L} _ {\mathrm {R C L}} = - \log \sum_ {i = 1} ^ {f - 1} \frac {\sum_ {j = 1} ^ {n _ {\mathrm {p o s}}} \exp \left(\frac {A _ {i} ^ {\top} P _ {i j}}{\tau}\right)}{\sum_ {j = 1} ^ {n _ {\mathrm {p o s}}} \exp \left(\frac {A _ {i} ^ {\top} P _ {i j}}{\tau}\right) + \sum_ {k = 1} ^ {n _ {\mathrm {n e g}}} \exp \left(\frac {A _ {i} ^ {\top} N _ {i k}}{\tau}\right)}, \tag {3}
+$$
+
+where $\tau$ is the temperature hyper-parameter.
+
+Additionally, we maintain a memory bank $\mathcal{M}$ to store and update the positive and negative samples, both randomly selected from the 1D features of the current batch videos and previously seen videos. This online dynamic update strategy can enlarge the number of positive and neg-
+
+ative samples, enhancing the contrastive learning effect and training stability. At each iteration, we store all current anchor features $A$ and the 1D features of $\epsilon_{i}$ into $\mathcal{M}$ . The memory bank is implemented as a First In, First Out queue.
+
+Overall, the training loss $\mathcal{L}_{\mathrm{total}}$ consists of both reconstruction and contrastive learning loss, defined as:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e c}} + \lambda_ {1} \mathcal {L} _ {\text {R C L}}, \tag {4}
+$$
+
+where $\lambda_{1}$ is the loss balancing weight.
+
+# 4. Experiment
+
+# 4.1. Experimental Setup
+
+Datasets. We conduct experiments on the NTU RGB+D Action Recognition Dataset [49, 71]. We select 26 types of human relations, such as handshakes and hugs, each labeled with a text prompt like "A person is shaking hands with a person." For evaluation, we design $10 \times 26$ prompts with uncommon subject interactions, such as "A dog is shaking hands with a cat", to assess generalization to novel domains. More details are provided in Appendix A.
+
+Baselines. Given the absence of existing methods for relational video customization, we define four baseline categories: 1) The base model Mochi. 2) Direct LoRA finetuning. 3) Adapted relational image customization methods. We reproduce ReVersion [36] on Mochi for relational video customization. 4) Motion customization methods, which mostly rely on Temporal Attention Layers that are absent in MM-DiT, face challenges in direct adaptation. Thus, we choose the recent and adaptable MotionInversion [85] as a baseline, reproducing it on Mochi for comparison.
+
+Evaluation metrics. We evaluate our method by focusing on four aspects: 1) Relation Accuracy. Instead of using biased classifiers trained on test sets with limited diversity like previous methods [23, 36], which hinders test accuracy and generalizability, we propose the Relation Accuracy metric to assess relations using advanced Vision-Language Models (VLMs). Specifically, we input generated videos to Qwen-VL-Max [2], a leading VQA model [20, 53], asking if the video matches the specified relation, and converting yes/no responses into relation accuracy percentages. We repeat this process 10 times to calculate the average accuracy. 2) Text Alignment. We employ CLIP image-text similarity (CLIP-T) to measure alignment with text prompts. 3) Temporal Consistency, which computes the average cosine similarity across consecutive frames [17]. 4) Video Quality. We use FVD to evaluate the video quality. The reference videos are 800 videos from the AnimalKingdom test dataset [63].
+
+Implementation details. We adopt Mochi [79] as our base model. We use AdamW [54] optimizer with a learning rate of 2e-4 and weight decay of 0.01. The training iteration is 2400. We set LoRA rank to 16, $\lambda_{m}$ to 50, and $\lambda_{1}$ to 0.01. Generated video resolution is $61\times 480\times 848$ , and the
+
+
+Figure 6. Qualitative comparison results. Our method outperforms all baselines in precisely capturing the intended relation and mitigating appearance and background leakage.
+
+Table 1. Quantitative comparison results.
+
+| Method | Relation Accuracy | CLIP-T | Temporal Consistency | FVD↓ |
| Mochi (base model) [79] | 0.2623±0.04 | 0.3237 | 0.9888 | 2047.37 |
| Direct LoRA finetuning | 0.3258±0.05 | 0.2966 | 0.9945 | 2229.08 |
| ReVersion [36] | 0.2690±0.01 | 0.3013 | 0.9921 | 2682.69 |
| MotionInversion [85] | 0.3151±0.03 | 0.3217 | 0.9855 | 2084.51 |
| DreamRelation | 0.4452±0.01 | 0.3248 | 0.9954 | 2079.87 |
+
+batch size is 1. We set $n_{\mathrm{pos}}$ to 4 and $n_{\mathrm{neg}}$ to 10. The memory bank size is 64, and $\tau$ is 0.07. During inference, we generate 30-fps videos using Euler Discrete method [47, 51] with 64 steps. The classifier-free guidance [27] scale is 6.0.
+
+# 4.2. Main Results
+
+Qualitative results. Qualitative comparisons in Fig. 6 reveal that all baseline methods, including the base model Mochi, fail to generate videos that match the relations defined in exemplar videos. For example, Direct LoRA finetuning struggles with appearance and background leakage, while other methods like MotionInversion cannot capture desired relational dynamics due to the complexity inherent in relations. In contrast, our DreamRelation precisely generates videos with intended relations and diverse subjects, effectively preventing appearance and background leakage.
+
+Quantitative results. Tab. 1 presents the quantitative comparison results. Direct LoRA finetuning improves the base model's Relation Accuracy but suffers from reduced CLIP-T and FVD due to appearance leakage. Inversion-
+
+
+(a) Visualization of Attention Maps.
+
+
+(b) Human evaluation results.
+Figure 7. (a) Our method focuses on the desired relational region. (b) Our method is most preferred by users across all aspects.
+
+based methods like ReVersion and MotionInversion achieve better CLIP-T than finetuning but fail to model desired relations accurately. In contrast, while comparable to the base model in FVD, our DreamRelation consistently surpasses baselines across other metrics, verifying its effectiveness.
+
+Attention map analysis. To verify the effectiveness of our method, we compute averaged attention maps from all layers and heads, extracting values for text tokens of relations like "shaking hands" and all vision tokens [6]. These attention maps are reshaped and visualized in Fig. 7(a). We observe that the base model's attention map for "shaking hands" is messy, leading to poor generation. In contrast, our method's attention map effectively focuses on the relational area, producing more natural results and demonstrating its capability to capture relational information.
+
+User study. We conduct user studies to evaluate our DreamRelation, involving 15 annotators who rate 180 video
+
+
+Figure 8. Qualitative ablation study on each component.
+
+Table 2. Ablation studies on effects of hybrid mask training strategy (HMT), space-time relational contrastive loss (RCL), and each type of LoRA. Removing any of the above components significantly reduces the overall performance.
+
+| Method | Relation Accuracy | CLIP-T | Temporal Consistency | FVD↓ |
| w/o HMT | 0.3574±0.02 | 0.3244 | 0.9938 | 2248.52 |
| w/o RCL | 0.3416±0.03 | 0.3185 | 0.9953 | 2136.95 |
| w/o Relation LoRAs | 0.3626±0.02 | 0.3035 | 0.9950 | 2318.49 |
| w/o Subject LoRAs | 0.3769±0.04 | 0.3147 | 0.9949 | 2408.59 |
| w/o FFN LoRAs | 0.4021±0.03 | 0.3241 | 0.9914 | 2369.98 |
| ours | 0.4452±0.01 | 0.3248 | 0.9954 | 2079.87 |
+
+groups generated by four methods. Each group contains four generated videos, a reference video, and a textual prompt. Evaluations are based on majority votes in three aspects: Relation Alignment, Text Alignment, and Overall Quality. Results in Fig. 7(b) indicate that our method is most preferred by users across all aspects. More details about the user study are provided in Appendix B.
+
+# 4.3. Ablation Studies
+
+Ablation on each component. We perform an ablation study on the effects of each component, as shown in Fig. 8. Without hybrid mask training strategy, the model generates the desired relations but experiences some background leakage due to incomplete decoupling of relational and appearance information. Omitting space-time relational contrastive loss reduces background leakage but results in videos exhibiting inaccurate relations.
+
+Quantitative results in Tab. 2 show that removing hybrid mask training strategy or space-time relational contrastive loss degrades performance across all metrics, confirming that each component is crucial to overall performance; see Appendix C for more ablation studies.
+
+Ablation on each LoRA in relation LoRA triplet. We conduct ablation studies to verify each LoRA's effects. The results in Tab. 2 indicate that removing Relation LoRAs or Subject LoRAs significantly reduces Relation Accuracy and
+
+Table 3. Ablation study of Relation LoRA position.
+
+| Relation LoRA | Subject LoRA | Relation Accuracy | CLIP-T | Temporal Consistency | FVD↓ |
| V | Q, K | 0.3444±0.02 | 0.3225 | 0.9953 | 2233.48 |
| Q | K, V | 0.3921±0.03 | 0.3301 | 0.9951 | 2284.65 |
| K, V | Q | 0.3937±0.04 | 0.3196 | 0.9954 | 2180.27 |
| Q, K | V | 0.4452±0.01 | 0.3248 | 0.9954 | 2079.87 |
+
+Table 4. Effects of space-time relational contrastive loss on motion customization method (MotionInversion).
+
+| Method | Relation Accuracy | CLIP-T | Temporal Consistency | FVD↓ |
| MotionInversion [85] | 0.3151±0.03 | 0.3217 | 0.9855 | 2084.51 |
| MotionInversion + RCL | 0.3633±0.05 | 0.3181 | 0.9862 | 2063.30 |
+
+CLIP-T due to insufficient decoupling of appearance and relational information. Excluding FFN LoRAs also lowers accuracy, highlighting the need for refinement.
+
+Ablation on Relation LoRAs position. To determine the optimal position of Relation LoRAs, we experiment with different settings in the query (Q), key (K), and value (V) matrices, as shown in Tab. 3. Inserting Relation LoRAs to the V matrix results in the lowest Relation Accuracy, likely because V features predominantly exhibit appearance information, making it challenging to accurately capture the desired relations. Placing Relation LoRAs in the Q matrix or KV matrices is suboptimal since the overlapping nature of the QK matrices hinders their ability to process different information separately, which is not conducive to decoupling relations from appearances. In contrast, inserting Relation LoRAs to the QK matrices achieves the best Relation Accuracy, consistent with our analysis of full attention in Fig. 5. Ablation on space-time relational contrastive loss (RCL). To verify the effectiveness of RCL among different methods, we integrate it with MotionInversion [85]. Results in Tab. 4 show that incorporating RCL enhances Relation Accuracy and Temporal Consistency while maintaining comparable CLIP-T, demonstrating its potential for generalization across different methods.
+
+# 5. Conclusion
+
+In this paper, we present DreamRelation, a novel relational video customization method that accurately models complex relations defined in exemplar videos through relational decoupling learning and relational dynamics enhancement. We introduce relation LoRA triplet to decompose relations into appearance and relational information and further enhance this decoupling with hybrid mask training strategy. Our analysis of query, key, and value features in MM-DiT's full attention motivates and offers interpretability for our model design. To further enhance relation dynamics learning, we propose space-time relational contrastive loss, which prioritizes relational dynamics over detailed appearances. Extensive experimental results demonstrate the superior customization capabilities of DreamRelation.
+
+Acknowledgements This work is partially supported by STI2030-Major Projects (No. 2021ZD0200204), National Natural Science Foundation of China (No. 62471148), and Alibaba Group. Special thanks to Zhihang Liu (University of Science and Technology of China) and Boyuan Cao (Fudan University) for sharing their invaluable experience and advice on model analysis.
+
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+# DreamRenderer: Taming Multi-Instance Attribute Control in Large-Scale Text-to-Image Models
+
+Dewei Zhou $^{1}$ , Mingwei Li $^{1}$ , Zongxin Yang $^{2}$ , Yi Yang $^{1*}$
+RELER, CCAI, Zhejiang University $^{1}$ DBMI, HMS, Harvard University
+
+{zdw1999,mingweili, yangyics}@zju.edu.cn {Zongxin Yang}@hms.harvard.edu Project Page: https://limuloo.github.io/DreamRenderer/
+
+
+"A shiny {color} pool ball with number {number}", with combinations as follows: 1) Red, number '1'; 2) Blue, number '2'; 3) Yellow, number '3'; 4) Green, number '4'; 5) Purple, number '5'; 6) Orange, number '6'; 7) Magenta, number '7'; 8) Black, number '8'; 9) Pink, number '9'; 10) Turquoise, number '10'; 11) Gold, number '11'; 12) Silver, number '12'; 13) Maroon, number '13'; 14) Teal, number '14'; 15) Lavender, number '15' and 16) a pure white pool ball.
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+"A regal queen on a gothic throne, holding a sword surrounded by skulls, in a dark medieval fantasy setting with dramatic lighting." 1) Fire word. 2) Ice-covered frozen throne. 3) Brown & golden hair. 4) White skull with mask. 5) Sleek black high-heeled boots. 6) Golden skull.
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+Figure 1. Images generated using DreamRenderer. DreamRenderer is a plug-and-play controller that grants users fine-grained control over the content of each region and instance during depth- or canny-conditioned generation without any training. By leveraging Redux [3] to translate images into text embeddings, it further allows users to seamlessly control generated content based directly on visual inputs.
+
+1) green plant. 2) red bear. 3) orange book. 4) black ball. 5) brown cup. 6) gray cat. 7) yellow hat.
+
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+1) a fire bird. 2) a Lego dog. 3) a ice cat. 4) small waterfall in the woods.
+
+
+
+
+
+# Abstract
+
+Image-conditioned generation methods, such as depth- and canny-conditioned approaches, have demonstrated remarkable abilities for precise image synthesis. However, existing models still struggle to accurately control the content of multiple instances (or regions). Even state-of-the-art models like FLUX and 3DIS face challenges, such as attribute leakage between instances, which limits user control. To address these issues, we introduce DreamRenderer, a training-free approach built upon the FLUX model. DreamRenderer enables users to control the content of each instance via bounding boxes or masks, while ensuring overall visual harmony. We propose two key innovations: 1) Bridge Image Tokens for Hard Text Attribute Binding, which uses replicated image tokens as bridge tokens to ensure that T5 text embeddings, pre-trained solely on text data, bind the correct visual attributes for each instance during Joint Attention; 2) Hard Image Attribute Binding applied only to vital layers. Through our analysis of FLUX, we identify the critical layers responsible for instance attribute rendering and apply Hard Image Attribute Binding only in these layers, using soft binding in the others. This approach ensures precise control while preserving image quality. Evaluations on the COCO-POS and COCO-MIG benchmarks demonstrate that DreamRenderer improves the Image Success Ratio by $17.7\%$ over FLUX and enhances the performance of layout-to-image models like GLIGEN and InstanceDiffusion by up to $26.8\%$ . Project Page: https://limuloo.github.io/DreamRenderer/.
+
+# 1. Introduction
+
+Beyond conventional text-to-image models, image-conditioned generation methods [40, 67], such as depth-and canny-conditioned approaches, have emerged as powerful tools for more controllable content creation, finding applications in animation, game development, visual restoration, and virtual reality [21, 28, 34, 51, 58, 63, 67].
+
+However, existing techniques cannot accurately constrain the content generated within each specific instance (or region), and their performance deteriorates significantly as the number of controlled elements increases. As shown in Fig. 1, even state-of-the-art methods such as FLUX [3] and 3DIS [75, 76] often fail to follow user-specified inputs, leading to unsatisfactory outcomes in which attributes bleed across different instances. Such limitations ultimately hinder more refined and controllable user-directed creation.
+
+To address these challenges and grant users greater creative control, we introduce DreamRenderer, a training-free approach built upon the FLUX model [3]. As illustrated in Fig. 1, DreamRenderer functions as a plug-and-play tool, allowing users to further regulate the content of
+
+each instance via bounding boxes or masks, all while preserving overall visual harmony.
+
+When implementing DreamRenderer, we encounter two main challenges. 1) Ensuring text embeddings bind the correct visual information. Current state-of-the-art text-to-image models [3, 8] employ the T5 text encoder [46], pre-trained purely on textual data, to extract text embeddings lacking intrinsic visual information. These embeddings instead rely on Joint Attention [7, 17, 32, 60] with image embeddings to incorporate visual information [76]. In scenarios where multiple instances are controlled, attribute confusion can easily arise among different instances and regions. 2) Rendering each instance accurately while preserving overall visual harmony. To accurately generate controlled instances, it is necessary to constrain the image tokens' attention masks [43, 53, 56] during Joint Attention. Yet overly restrictive constraints can undermine the resulting image quality, highlighting the need for more nuanced strategies to guide the attention masks of image tokens.
+
+A naive solution to ensure each instance's text embedding binds the correct visual information during Joint Attention is to constrain the tokens (both image and text) of a single instance to attend only to themselves. This strategy effectively simulates a single-instance generation process, thereby preserving the intended visual attributes for each text embedding. However, completely separating each instance's tokens from those of others significantly degrades the image quality, as shown in Fig. 7.
+
+To address the two challenges outlined above, Dream-Assembler introduces two key innovations: 1) Bridge tokens for Hard Text Attribute Binding. Instead of directly using an instance's original image tokens to help text tokens bind the correct attributes, we replicate the instance's image tokens, referred to as Bridge Image Tokens. These bridge tokens are not included in the model's final output but instead simulate a single-instance generation process during Joint Attention, guiding the text embeddings to acquire the correct visual attributes. In other words, each instance's text embedding and Bridge Image Tokens attend only to each other, ignoring all other tokens. 2) Hard Image Binding only applied to vital layers. After ensuring each text embedding accurately captures its instance's visual attributes through Hard Text Attribute Binding, we further ensure each instance's image embedding incorporates the correct visual information. We adopt two types of "image attribute binding": a hard bind, where an instance's image tokens attend exclusively to themselves, and a soft bind, where they can attend to all tokens in the image. From experimental observation, layers near the input and output of FLUX primarily encode global information, while intermediate layers are crucial for rendering each instance. Therefore, we apply hard binding only in these middle layers, and soft binding elsewhere, thus preserving overall visual harmony while
+
+
+Figure 2. The overview of DreamRenderer. (§ 3.3) (a) The pipeline of DreamRenderer. (b) Attention maps in Joint Attention, which includes 1) Hard Text Attribute Binding (§ 3.5), 2) Hard Image Attribute Binding (§ 3.6), and 3) Soft Image Attribute Binding (§ 3.6). In the attention maps shown in (b), rows represent queries and columns represent keys. We use different patterns to distinguish between image tokens, text tokens, and bridge image tokens while different colors for an ice cat, for a fire dog and for the global text tokens and background image tokens) represent tokens from different instances.
+
+
+
+
+
+maintaining precise control over each instance's attributes.
+
+We evaluated DreamRenderer on two widely used benchmarks, COCO-POS [31] and COCO-MIG [73, 74], demonstrating its effectiveness in balancing image quality with fine-grained control. On COCO-POS, we extracted depth maps and canny maps from the COCO dataset as conditional inputs and leveraged their layouts to guide DreamRenderer. The results show that DreamRenderer boosts the Image Success Ratio by $17.7\%$ over the original FLUX model, without sacrificing image quality. On COCO-MIG, we applied DreamRenderer to re-render the outputs of several state-of-the-art layout-to-image models, significantly enhancing both image quality and controllability. Specifically, DreamRenderer increases the Image Success Ratio for GLIGEN [25], InstanceDiffusion [53], MIGC [73], and 3DIS [75] by $26.8\%$ , $19.9\%$ , $8.3\%$ , and $7.4\%$ , respectively.
+
+The key contributions of this paper are as follows:
+
+- We propose DreamRenderer, a training-free method that enables users to control the generation content for each region and instance in image-conditioned generation.
+- We introduce a novel Hard Text Attribute Binding technique, ensuring that text embeddings bind the correct visual attributes during the Joint Attention process.
+- For multi-instance generation, we provide the first in-depth analysis of each layer's potential function in the FLUX model, clarifying which layers handle global operations and which are pivotal for rendering individual in
+
+stances, offering fresh insights for subsequent research.
+
+# 2. Related Works
+
+Text-to-Image Generation. In recent years, text-to-image generation has progressed rapidly [1, 4, 9, 12, 14, 19, 22–24, 26, 27, 29, 35–39, 41, 50, 57, 62, 65, 66], with generative models now producing high-quality images aligned with user descriptions. Early approaches—such as SD1.5 [48] and SDXL [44]—adopted a U-Net-based [20, 39, 49, 68–72] architecture together with a CLIP text encoder [45] for extracting text embeddings, injecting textual information into the network via cross-attention [10, 52] to ensure correspondence between text and output content. Later, the Diffusion Transformer (DiT) [6] structure was introduced, replacing the U-Net with a Transformer, and using AdaLN to incorporate text information. To further refine text control, models like SD3 [8] and FLUX [3] switched to a T5-XXL [46] text encoder, employing Joint Attention to align image and text embeddings and thereby ensure that the final outputs adhere closely to the textual prompts.
+
+Controllable Text-to-Image Generation. With further improvements in image quality, users and researchers have turned their attention to more controllable content generation. Image-conditioned generation methods, like depth- and canny-conditioned techniques [2, 21, 30, 42, 54, 61, 67], provide an outline-based or scene-level structure for generated images. However, current methods lack
+
+the ability to precisely regulate individual regions or instances—particularly in complex scenes with multiple controlled elements—often leading to inaccurate or undesirable results. To address this limitation, we introduce Dream-renderer, a plug-and-play controller that empowers users to specify the generation content of each region or instance with heightened accuracy. In addition, DreamRenderer can be applied to re-render the outputs of layout-to-image [5, 11, 18, 25, 53, 55, 59, 64, 73, 75] models, further enhancing both content fidelity and overall image quality.
+
+# 3. Method
+
+# 3.1. Preliminaries
+
+FLUX. The FLUX [3] model is a state-of-the-art text-to-image generation model that leverages the rectified flow [8, 33] framework to iteratively generate images. In each iteration, FLUX first encodes the text prompt into a text embedding using a T5 text encoder [46], which is trained solely on textual data. This text embedding is then concatenated with a randomly sampled noise-based image embedding; if needed, a control image embedding (e.g., depth or canny) is also included. Subsequently, multiple layers of Joint Attention [7, 32, 76] iteratively refine both the image and text embeddings, ensuring they remain in alignment. Finally, FLUX decodes the refined image embedding through a Variational Autoencoder (VAE) [15], generating an output image that faithfully reflects the user's textual description.
+
+Joint Attention. In Joint Attention, both text and image embeddings are processed simultaneously. Each embedding is first transformed into token representations via a linear layer: the text embedding is converted into $Q_{\mathrm{text}}$ , $K_{\mathrm{text}}$ , and $V_{\mathrm{text}}$ , while the image embedding is mapped to $Q_{\mathrm{image}}$ , $K_{\mathrm{image}}$ , and $V_{\mathrm{image}}$ . These token sets are then concatenated as follows: $Q = Q_{\mathrm{text}} \oplus Q_{\mathrm{image}}$ , $K = K_{\mathrm{text}} \oplus K_{\mathrm{image}}$ , and $V = V_{\mathrm{text}} \oplus V_{\mathrm{image}}$ , where $\oplus$ denotes the concatenation operation. The attention mechanism is subsequently applied to the concatenated tokens.
+
+$$
+\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {S o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V, \tag {1}
+$$
+
+where $d_{k}$ is the dimension of the key vectors. This Joint attention mechanism allows for bidirectional information flow between text and image embeddings, enabling the model to align visual content with textual descriptions.
+
+# 3.2. Problem Definition and Challenges
+
+Problem Definition. Given a depth/canny map, a global prompt, and detailed instance (or region) descriptions, the objective is to generate an image that not only adheres to the global structural constraints of the depth/canny map and global prompt, but also ensures that each controlled instance accurately adheres the specified descriptions.
+
+Challenges. We build DreamRenderer upon the FLUX model (§ 3.1), and there are two main challenges in achiev-
+
+
+Layer-wise Performance Analysis
+Figure 3. Vital Binding Layer Search (§ 3.6). We apply Hard Image Attribute Binding layer by layer and observe that applying it in the FLUX model's input or output layers degrades performance, whereas applying it in the middle layers yields improvements.
+
+ing our objectives: 1) Correctly binding text embedding attributes in multi-instance scenarios. Unlike previous text-to-image models that use CLIP [45], FLUX employs the T5 text encoder, which is pre-trained on pure text data and does not contain visual information. This creates a challenge in ensuring that the text embedding correctly binds the visual attributes of each instance during the Joint Attention process, particularly when multiple instances are involved. 2) Enhancing the overall harmony of the generated image while maintaining correct attributes for each instance. In multi-instance scenarios, the image tokens corresponding to different instances may inadvertently leak attributes [43] during Joint Attention. Our goal is to minimize such leakage while ensuring that the final generated image retains a cohesive and harmonious composition across all instances.
+
+# 3.3. Overview
+
+Fig. 2 illustrates the overview of DreamRenderer. In the Joint Attention mechanism, DreamRenderer introduces a novel Hard Text Attribute Binding (§3.5) algorithm to ensure that the text embedding for each instance correctly binds the relevant visual information. Additionally, to enhance the overall harmony of the generated image while maintaining accurate image embedding attributes for each instance, we conducted an experimental analysis (§3.6) of each layer in FLUX and decided to apply Hard Image Attribute Binding (§3.6) only in the middle layers of the FLUX model. In all other layers, Soft Image Attribute Binding (§3.6) is used.
+
+# 3.4. Preparation
+
+As shown in Fig. 2 (a), DreamRenderer first embeds the input text descriptions for each instance and the global prompt separately through the T5 text encoder. These encoded embeddings are then concatenated to form the complete text embedding for the generation process. Our method requires users to provide either a depth map or a canny edge map
+
+as structural guidance, which serves as the foundation for the spatial arrangement of instances in the generated image. For instance localization, we utilize bounding boxes or masks provided by the user to identify each instance's region within this structural guidance.
+
+# 3.5. Hard Text Attribute Binding
+
+Motivation. When generating a single instance, the FLUX model generally produces images that align with the textual prompt, exhibiting minimal attribute errors. In such scenarios, image and text tokens in Joint Attention focus exclusively on the information of that single instance, thereby enabling the text embedding to bind accurate visual attributes. Building on this insight, we propose that in multi-instance scenarios, the image and text tokens of each instance should primarily attend to themselves rather than to tokens belonging to different instances, allowing the text embedding to effectively bind the correct visual information.
+
+Naive Solution. A straightforward approach to ensure that each instance's text embedding is bound to the correct attributes is to process each instance independently during Joint Attention. In this method, both image and text tokens for a given instance interact exclusively with themselves, remaining isolated from tokens of other instances. However, this complete isolation introduces a significant drawback: it disrupts the visual harmony of the overall image and substantially lowers the quality of the generated result (as shown in Fig. 7).
+
+Bridge Image Token for Advanced Solution. Since strictly isolating original image tokens for each instance in joint Attention degrades the image quality, DreamRenderer proposes an advanced solution: during Joint Attention, an additional copy of each instance's image tokens are created, referred to as Bridge Image Tokens. These Bridge Image Tokens do not contribute to the final output image but serves solely to assist each instance's text embedding in binding the correct visual attributes during the Joint Attention. As shown in Fig. 2, the Bridge Image Tokens and text tokens for each instance align exactly as in a single-instance generation process, ensuring that the visual attributes in the final text embedding are consistent with the textual description. Formally, for the $i$ -th instance, the Hard Text Attribute Binding attention mask $M_{\mathrm{text}}^i$ is defined as:
+
+$$
+M _ {\text {t e x t}} ^ {i} [ q, k ] = \left\{ \begin{array}{l l} 1, & \text {i f} q, k \in \mathcal {T} _ {i} \cup \mathcal {B} _ {i} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {2}
+$$
+
+where $q$ and $k$ are the query and key indices respectively, $\mathcal{T}_i$ and $\mathcal{B}_i$ denote the token indices of the $i$ -th instance's text and Bridge Image Tokens respectively.
+
+# 3.6. Image Attribute Binding
+
+Overview. After ensuring the accuracy of the text embedding's attributes, the next step is to guarantee the correctness of the visual attributes in each instance's image tokens.
+
+As shown in Fig. 2, DreamRenderer employs Hard Image Attribute Binding at the vital binding layer to ensure that each instance is rendered with the correct attributes. In the remaining layers, Soft Image Attribute Binding is used to ensure that all instances ultimately form a coherent image. In the following sections, we will detail the mechanisms of hard and soft image attribute binding and explain how we identify the vital layers for Hard Image Attribute Binding.
+
+Hard Image Attribute Binding. As shown in Fig. 2, the Hard Image Attribute Binding imposes attention mask constraints on each instance's image tokens during Joint Attention. First, it ensures that each instance attends only to its corresponding text token—which, following Hard Text Attribute Binding, contains the correct visual information. Second, to prevent attribute leakage across different image tokens, Hard Image Attribute Binding further restricts each instance's image tokens to attend its own image tokens. For the $i$ -th instance, the Hard Image Attribute Binding mask $M_{\mathrm{hard}}^i$ is constructed as:
+
+$$
+M _ {\text {h a r d}} ^ {i} [ q, k ] = \left\{ \begin{array}{l l} 1, & \text {i f} q \in \mathcal {I} _ {i}, k \in \mathcal {T} _ {i} \cup \mathcal {I} _ {i} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {3}
+$$
+
+where $\mathcal{I}_i$ represents the set of image token indices belonging to the $i$ -th instance, and $\mathcal{T}_i$ represents its corresponding text token indices.
+
+Soft Image Attribute Binding. To ensure the overall coherence of the final generated image, Soft Image Attribute Binding relaxes the constraints imposed by Hard Image Attribute Binding. Specifically, for each instance's image tokens, Soft Image Attribute Binding allows it to attend to the image tokens of the entire image, thereby enhancing the cohesion of the entire scene. For the $i$ -th instance, the Soft Image Attribute Binding mask $M_{\mathrm{soft}}^i$ is constructed as:
+
+$$
+M _ {\text {s o f t}} ^ {i} [ q, k ] = \left\{ \begin{array}{l l} 1, & \text {i f} q \in \mathcal {I} _ {i}, k \in \mathcal {I} _ {\text {a l l}} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {4}
+$$
+
+where $\mathcal{I}_{\mathrm{all}} = \mathcal{I}_{\mathrm{background}} \cup \left(\bigcup_{i=1}^{N} \mathcal{I}_i\right)$ represents the set of all image token indices, $\mathcal{I}_{\mathrm{background}}$ is the set of all image tokens that are not associated with any instance.
+
+Search Vital Binding Layers. As shown in Fig. 3, we applied Hard Image Attribute Binding layer by layer on the FLUX network, which consists of 57 Joint Attention layers, and compared the result obtained using Soft Image Binding across all layers to identify which layers are more suitable for binding specific instance attributes. The results from Fig. 3 indicate that applying Hard Image Binding near the output and input layers of FLUX leads to a significant decrease in performance. Conversely, we observed that implementing hard image attribute binding in the middle layers of FLUX often enhances attribute fidelity. Based on these findings, we argue that the layers at the input and output of FLUX are primarily involved in handling global image information, while the mid-layers play a critical role in ren
+
+
+1) Bread 2) Apple 3) Apple 4) Orange 5) Orange
+
+
+
+
+
+
+1) Chair 2) TV 3) Coach 4) Ship 5) Couch
+
+
+Figure 4. Qualitative Comparison on the COCO-POS benchmark (§ 4.2).
+
+
+
+
+1) Broccoli 2) Broccoli 3) Broccoli 4) Broccoli 5) Spoon
+
+
+
+
+
+
+
+
+
+
+1) Sandwich 2) Sandwich 3) Banana 4) Bowl 5) Apple 6) Apple
+
+Table 1. Quantitative results on COCO-POS benchmark (§ 4.2). SR: Success Ratio of the Entire Image, ISR: Instance Success Ratio, MIoU: Mean Intersection over Union, AP: Average Precision. *: canny-guided. †: depth-guided.
+
+| Method | SR (%)↑ | ISR (%)↑ | MIoU (%)↑ | AP (%)↑ | CLIP↑ |
| FLUX* | 16.38 | 64.95 | 59.71 | 31.88 | 19.03 |
| 3DIS* | 18.07 | 68.78 | 62.97 | 31.36 | 19.46 |
| Ours* | 23.28 | 74.61 | 66.95 | 37.00 | 20.03 |
| FLUX† | 44.83 | 85.13 | 76.86 | 50.72 | 19.82 |
| 3DIS† | 53.88 | 90.33 | 81.26 | 54.26 | 20.23 |
| Ours† | 62.50 | 94.51 | 84.36 | 58.95 | 20.74 |
+
+dering the attributes of instances within the image. Therefore, we perform Hard Image Binding in the mid-layers of FLUX, while employing Soft Image Binding in the remaining layers. This approach optimally balances the fidelity of instance attributes with the overall coherence of the image.
+
+# 4. Experiments
+
+# 4.1. Experiment Setup
+
+Baselines. Beside the FLUX model, we evaluate our method against several state-of-the-art methods for multi-instance generation. Since DreamRenderer is designed as a plug-and-play solution, we conduct experiments by integrating it with existing methods: GLIGEN [25], InstanceDiffusion [53], MIGC [73], and 3DIS [76].
+
+Implementation Details. We perform canny-conditioned and depth-conditioned generation using FLUX.1-Canny [3] and FLUX.1-Depth [3], respectively. For both cases, we sample images over 20 steps. During depth-conditioned generation, we set the Classifier-Free Guidance (CFG) [13] scale to 10.0, while for canny-conditioned generation, the CFG scale is set to 30. In our experiments, for instances whose positions are specified by bounding boxes, we further segment them using the SAM-2 [16, 47] model to obtain more precise instance masks, which is consistent with previous work [75].
+
+Evaluation Benchmarks. We conduct experiments on two widely used benchmarks: 1) COCO-POS Benchmark,
+
+which requires generating images according to specified layouts. We extract depth maps or canny edges from COCO dataset images as conditioning signals and utilize the dataset's inherent layouts for rendering. Models must generate results matching the instance categories at designated locations. Here we compare our approach with training-free rendering methods including Multi-Diffusion and 3DIS. 2) COCO-MIG Benchmark, which tests multi-instance generation with accurate position and attribute control. We evaluate DreamRenderer's integration capabilities with state-of-the-art MIG models by first generating RGB images with these models, then extracting depth maps to combine with layouts for instance rendering. This evaluates DreamRenderer's attribute control effectiveness when applied to existing MIG frameworks.
+
+Evaluation Metrics. We used the following metrics to evaluate the model: 1) Mean Intersection over Union (MIoU): Measures the overlap ratio between the rendered instance positions and the target positions. 2) Local CLIP Score: Assesses the visual consistency of the rendered instances with their corresponding textual descriptions. 3) Average Precision (AP): Evaluates the accuracy of the rendered image's layout. 4) Instance Success Ratio (ISR): Calculates the ratio of correctly rendered instances. 5) Image Success Ratio (ISR): Measures the ratio of images where all instances are correctly rendered.
+
+# 4.2. Comparison with State-of-the-Art Methods
+
+COCO-POS Benchmarks. Tab. 1 presents quantitative results comparing our method against FLUX and 3DIS. Our approach achieves consistent superiority across all metrics in both depth-guided and canny-guided generation scenarios. In the depth-guided setting, DreamRenderer shows a substantial improvement in SR (62.50% vs. 53.88% for 3DIS), indicating more coherent scene structures. The high ISR (94.51%) and MIoU (84.36%) further corroborate its precise instance-level control. In the more demanding canny-guided scenario, DreamRenderer also ex
+
+Table 2. Quantitative results on COCO-MIG benchmark (§ 4.2). $\mathcal{L}_i$ means that the count of instances needed to generate is i.
+
+ | Instance Success Ratio (%)↑ | Mean Intersection over Union (%)↑ | Image Success Ratio (%)↑ |
| Method | L2 | L3 | L4 | L5 | L6 | AVG | L2 | L3 | L4 | L5 | L6 | AVG | L2 | L3 | L4 | L5 | L6 | AVG |
| GLIGEN [CVPR23] | 41.6 | 31.6 | 27.0 | 28.3 | 27.7 | 29.7 | 37.1 | 29.2 | 25.1 | 26.7 | 25.5 | 27.5 | 16.8 | 4.6 | 0.0 | 0.0 | 0.0 | 4.4 |
| +Ours | 75.5 | 73.6 | 67.9 | 62.6 | 66.2 | 67.8 | 64.3 | 63.5 | 58.1 | 54.2 | 56.6 | 58.2 | 57.4 | 45.1 | 27.0 | 11.4 | 13.0 | 31.2 |
| vs. GLIGEN | +33.9 | +42.0 | +40.9 | +34.3 | +38.5 | +38.1 | +27.2 | +34.3 | +33.0 | +27.5 | +31.1 | +30.7 | +40.6 | +40.5 | +27.0 | +11.4 | +13.0 | +26.8 |
| InstanceDiff [CVPR24] | 58.4 | 51.9 | 55.1 | 49.1 | 47.7 | 51.3 | 53.0 | 47.4 | 49.2 | 43.7 | 42.6 | 46.0 | 37.4 | 15.0 | 11.5 | 5.0 | 2.6 | 14.5 |
| +Ours | 77.4 | 75.4 | 72.5 | 65.3 | 67.2 | 70.1 | 68.8 | 66.4 | 63.0 | 57.8 | 57.5 | 61.2 | 58.7 | 45.8 | 34.5 | 13.6 | 17.5 | 34.4 |
| vs. InstanceDiff | +19.0 | +23.5 | +17.4 | +16.2 | +19.5 | +18.8 | +15.8 | +19.0 | +13.8 | +14.1 | +14.9 | +15.2 | +21.3 | +30.8 | +23.0 | +8.6 | +14.9 | +19.9 |
| MIGC [CVPR24] | 74.8 | 66.2 | 67.2 | 65.3 | 66.1 | 67.1 | 64.5 | 56.9 | 57.0 | 55.5 | 57.3 | 57.5 | 54.8 | 32.7 | 22.3 | 12.9 | 17.5 | 28.4 |
| +Ours | 79.7 | 76.3 | 70.6 | 67.7 | 69.4 | 71.4 | 68.8 | 65.0 | 60.3 | 57.6 | 59.3 | 61.0 | 64.5 | 47.7 | 30.4 | 18.6 | 20.1 | 36.7 |
| vs. MIGC | +4.9 | +10.1 | +3.4 | +2.4 | +3.3 | +4.3 | +4.3 | +8.1 | +3.3 | +2.1 | +2.0 | +3.5 | +9.7 | +15.0 | +8.1 | +5.7 | +2.6 | +8.3 |
| 3DIS [ICLR25] | 76.5 | 68.4 | 63.3 | 58.1 | 58.9 | 62.9 | 67.3 | 61.2 | 56.4 | 52.3 | 52.7 | 56.2 | 61.3 | 36.0 | 25.0 | 12.9 | 11.7 | 29.7 |
| +Ours | 79.0 | 77.3 | 71.8 | 68.7 | 69.4 | 71.9 | 69.8 | 68.2 | 63.7 | 61.4 | 61.2 | 63.7 | 63.2 | 52.9 | 29.7 | 18.6 | 18.8 | 37.1 |
| vs. 3DIS | +2.5 | +8.9 | +8.5 | +10.6 | +10.5 | +9.0 | +2.5 | +7.0 | +7.3 | +9.1 | +8.5 | +7.5 | +1.9 | +16.9 | +4.7 | +5.7 | +7.1 | +7.4 |
+
+
+
+
+
+
+
+
+
+
+Figure 5. Qualitative comparison on the COCO-MIG benchmark (§ 4.2).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ceeds the 3DIS by $5.21\%$ in SR. Meanwhile, as shown in Fig. 4, our method does not compromise the original FLUX model's image generation quality—thanks to applying hard image attribute binding only within the vital layers.
+
+Table 3. User study results with 31 participants (1-5 scale) (\$ 4.2).
+
+| Method | Layout Accuracy↑ | Visual Quality↑ |
| FLUX | 3.51 | 3.26 |
| 3DIS | 3.63 | 3.31 |
| Ours | 4.04 | 3.80 |
+
+COCO-MIG Benchmarks. Tab. 2 and Fig. 5 present the results of applying DreamRenderer to various state-of-the-art layout-to-image methods. As shown, DreamRenderer substantially enhances the instance-attribute control accuracy, ultimately boosting the Image Success Ratio by $26.8\%$ over GLIGEN, $19.9\%$ over InstanceDiffusion, $8.3\%$ over MIGC, and $7.4\%$ over 3DIS. Notably, this improvement becomes more pronounced as the number of instances to be controlled increases: for example, DreamRenderer's performance gain over 3DIS is only $2.5\%$ when controlling two instances, but rises to $10.5\%$ when controlling six. These benefits stem from our Hard Text Attribute Binding algorithm, which ensures that each instance's text embedding accurately binds its visual attributes during Joint Attention, even for a large number of instances.
+
+User Study. Tab. 3 shows a user study with 31 partici
+
+pants comparing our method to FLUX [3] and 3DIS [76] on perceptual quality. Participants viewed paired outputs and rated each on (1) Layout Accuracy and (2) Image Quality, using a 5-point scale, in a blind comparison with randomized presentation. Each participant evaluated 17 pairs, with the input layout and text descriptions displayed. The results show that our proposed DreamRenderer not only enhances the FLUX model's layout control capabilities but also generates outputs that are more visually appealing to users.
+
+# 4.3. Ablation Study
+
+Bridge Image Tokens for Hard Text Attribute Binding. Tab. 4 and Fig. 7 present our ablation study on the Hard Text Attribute Binding mechanism. The Naive Solution (§ 3.5) isolates each instance during Joint Attention, disrupting the model's inherent feature distribution and thus causing a performance drop. Introducing Bridge Image Tokens—which are not part of the final output—can effectively address this issue, enabling text tokens to bind the correct attributes and improving accuracy without compromising image quality. As the number of controlled instances increases, the benefit of Hard Text Attribute Binding becomes more pronounced: for example, moving from 2 to 6 instances raises the Instance Success Ratio improvement from $3.5\%$ to $6.2\%$ .
+
+Vital Layers for Image Attribute Binding. Tab. 5 and
+
+Table 4. Ablation study on Hard Text Attribute Binding (§ 3.5). $\mathcal{L}_i$ means that the count of instances needed to generate is i.
+
+| Method | Instance Success Ratio (%)↑ | Mean Intersection over Union (%)↑ | Image Success Ratio (%)↑ | |
| \( \mathcal{L}_2 \) | \( \mathcal{L}_3 \) | \( \mathcal{L}_4 \) | \( \mathcal{L}_5 \) | \( \mathcal{L}_6 \) | \( \mathcal{AVG} \) | \( \mathcal{L}_2 \) | \( \mathcal{L}_3 \) | \( \mathcal{L}_4 \) | \( \mathcal{L}_5 \) | \( \mathcal{L}_6 \) | \( \mathcal{AVG} \) | \( \mathcal{L}_2 \) | \( \mathcal{L}_3 \) | \( \mathcal{L}_4 \) | | \( \mathcal{L}_5 \) | \( \mathcal{L}_6 \) | \( \mathcal{AVG} \) |
| Ours (Full) | 79.0 | 77.3 | 71.8 | 68.7 | 69.4 | 71.9 | 69.8 | 68.2 | 63.7 | 61.4 | 61.2 | 63.7 | 63.2 | 52.9 | 29.7 | 18.6 | 18.8 | 37.1 | |
| Naive Solution | 59.7 | 56.0 | 48.8 | 41.1 | 46.4 | 48.5 | 53.8 | 50.9 | 43.8 | 38.7 | 42.2 | 44.2 | 30.3 | 17.7 | 7.4 | 1.4 | 4.6 | 12.5 | |
| vs. Full | -19.3 | -21.3 | -23.0 | -27.6 | -23.0 | -23.4 | -16.0 | -17.3 | -19.9 | -22.7 | -19.0 | -19.5 | -32.9 | -35.2 | -22.3 | -17.2 | -14.2 | -24.6 | |
| w/o Hard Text Attribute Binding | 75.5 | 72.3 | 68.1 | 64.6 | 63.2 | 67.2 | 66.9 | 65.3 | 60.6 | 58.1 | 56.1 | 60.0 | 58.1 | 41.8 | 24.3 | 11.4 | 9.7 | 29.5 | |
| vs. Full | -3.5 | -5.0 | -3.7 | -4.1 | -6.2 | -4.7 | -2.9 | -2.9 | -3.1 | -3.3 | -5.1 | -3.7 | -5.1 | -11.1 | -5.4 | -7.2 | -9.1 | -7.6 | |
+
+Table 5. Ablation study on Image Attribute Binding (§ 3.6). $\mathcal{L}_i$ means that the count of instances needed to generate is i.
+
+ | Instance Success Ratio (%)↑ | Mean Intersection over Union (%)↑ | Image Success Ratio (%)↑ |
| Method | L2 | L3 | L4 | L5 | L6 | AVG | L2 | L3 | L4 | L5 | L6 | AVG | L2 | L3 | L4 | L5 | L6 | AVG |
| w/o Hard Image Bind | 71.3 | 69.5 | 56.9 | 51.4 | 47.6 | 56.2 | 63.8 | 61.3 | 52.3 | 47.5 | 43.9 | 51.2 | 53.6 | 37.9 | 16.2 | 4.3 | 3.9 | 23.6 |
| Hard Image Bind Input Layer | 71.0 | 68.4 | 56.6 | 52.9 | 50.3 | 57.1 | 62.4 | 60.5 | 50.4 | 47.2 | 45.4 | 50.9 | 51.0 | 34.0 | 14.9 | 5.7 | 5.2 | 22.5 |
| Hard Image Bind Middle Layer (Ours) | 79.0 | 77.3 | 71.8 | 68.7 | 69.4 | 71.9 | 69.8 | 68.2 | 63.7 | 61.4 | 61.2 | 63.7 | 63.2 | 52.9 | 29.7 | 18.6 | 18.8 | 37.1 |
| Hard Image Bind Output Layer | 64.5 | 63.8 | 57.4 | 49.4 | 58.3 | 57.6 | 56.9 | 57.2 | 51.8 | 45.0 | 52.1 | 51.7 | 43.9 | 28.8 | 14.9 | 2.9 | 7.8 | 20.0 |
+
+
+
+
+
+
+
+
+Figure 6. Ablation study on Hard Image Attribute Binding (§ 3.6).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 7. Ablation study on Hard Text Attribute Binding (§ 3.5). We use the same layout from Fig. 1 for testing. Due to space limitations in the main text, additional image results are provided in the Supplementary Materials.
+
+Fig. 6 present our ablation study on the Hard Image Attribute Binding mechanism. Applying Hard Image Attribute Binding at the FLUX input or output layers yields no clear performance gains and substantially degrades image quality, indicating that these layers are critical for the model's global information processing. Imposing instance or region isolation at these stages severely disrupts the intermediate feature distribution, ultimately causing a sharp drop in performance. In contrast, restricting Hard Image Attribute Binding to the mid layers preserves image quality while significantly improving performance—for instance, boosting the Instance Success Ratio by $15.7\%$ . This finding shows that FLUX's mid layers play a pivotal role in deter
+
+mining each instance's visual content, making them more suitable for binding instance's attribute.
+
+# 5. Conclusion
+
+We present DreamRenderer, a plug-and-play method that enables depth- and canny-conditioned generation to control the content of specific regions and instances, without compromising the model's image quality. Our contributions are twofold: (1) we introduce a novel Hard Text Attribute Binding mechanism that employs Bridge Image Tokens, ensuring each instance's text embedding binds the correct visual information during Joint Attention; (2) based on a layerwise analysis of FLUX, we apply hard image binding only to vital layers, achieving precise instance control while preserving global coherence. Experiments on COCO-POS and COCO-MIG show superior results: under depth guidance, DreamRenderer achieves $62.50\%$ SR, $94.51\%$ ISR, and $84.36\%$ MIoU; under the more challenging canny guidance, it still performs well with $74.61\%$ ISR and $66.95\%$ MIoU. DreamRenderer also functions as a re-renderer, boosting layout-to-image accuracy. Being training-free, it generalizes easily across foundation models, offering strong flexibility. Future work will explore its integration with other image-conditioned generation methods.
+
+Acknowledgment. This work was supported by both the Earth System Big Data Platform of the School of Earth Sciences, Zhejiang University, and the National Natural Science Foundation of China (62293554, U2336212).
+
+# References
+
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+# DRIVEAREA: A Closed-loop Generative Simulation Platform for Autonomous Driving
+
+Xuemeng Yang $^{1,\ast}$ , Licheng Wen $^{1,6,7,\ast}$ , Tiantian Wei $^{3,\ast,\dagger}$ , Yukai Ma $^{2,\ast,\dagger}$ , Jianbiao Mei $^{2,1,\ast}$ , Xin Li $^{1,\ast}$ , Wenjie Lei $^{2,\dagger}$ , Daocheng Fu $^{4,1}$ , Pinlong Cai $^{1}$ , Min Dou $^{1}$ , Liang He $^{5}$ , Yong Liu $^{2,\spadesuit}$ , Botian Shi $^{1,\spadesuit}$ , Yu Qiao $^{1}$
+
+$^{1}$ Shanghai Artificial Intelligence Laboratory $^{2}$ Zhejiang University $^{3}$ Technical University of Munich $^{4}$ Fudan University $^{5}$ East China Normal University $^{6}$ Shanghai Innovation Institute $^{7}$ Shanghai Jiao Tong University
+
+Project Page: https://pjlab-adg.github.io/DriveArena/
+
+# Abstract
+
+This paper introduces DRIVEAREA, the first high-fidelity closed-loop simulation system designed for driving agents navigating real-world scenarios. DRIVEAREA comprises two core components: Traffic Manager, a traffic simulator capable of generating realistic traffic flow on any global street map, and World Dreamer, a high-fidelity conditional generative model with infinite auto-regression. DRIVEAREA supports closed-loop simulation using road networks from cities worldwide, enabling the generation of diverse traffic scenarios with varying styles. This powerful synergy empowers any driving agent capable of processing real-world images to navigate in DRIVEAREA's simulated environment. Furthermore, DRIVEAREA features a flexible, modular architecture, allowing for multiple implementations of its core components and driving agents. Serving as a highly realistic arena for these players, our work provides a valuable platform for developing and evaluating driving agents across diverse and challenging scenarios. DRIVEAREA takes a significant leap forward in leveraging generative models for driving simulation platforms, opening new avenues for closed-loop evaluation of autonomous driving systems.
+
+# 1. Introduction
+
+Autonomous driving (AD) algorithms have advanced rapidly in recent decades [1, 6, 25-29, 39, 41], progressing from modular pipelines [13, 21, 23, 44] to end-to-end models [17, 18, 43] and knowledge-driven methods [10, 22, 36]. Despite demonstrating outstanding performance across var
+
+
+Figure 1. Comparison of DRIVEARENA with existing autonomous driving methods and platforms along the dimensions of Interactivity and Fidelity. Interactivity indicates the platform's control over vehicles, Fidelity reflects the realism of driving scenarios. DRIVEARENA uniquely occupies the top-right, being the first simulation platform to generate diverse traffic scenarios and surround-view images with closed-loop controllability for all vehicles. For detailed descriptions of these methods and related works, please refer to the supplementary materials.
+
+ious benchmarks, significant challenges persist in evaluating these algorithms on replayed open-loop datasets, obscuring their real-world efficacy. Public datasets [3, 4, 33], while offering realistic driving data with authentic sensor inputs and traffic behavior, are inherently biased towards simple straight-ahead scenarios. In such cases, an agent can achieve seemingly good performance by merely maintaining its current state, complicating the assessment of actual driving capabilities in complex situations. Furthermore, the agent's current decision does not affect execution or subsequent decisions in the open-loop evaluation, which pre
+
+vents it from reflecting cumulative errors in real-world driving scenarios. Additionally, the static nature of recorded datasets, where other vehicles cannot react to the ego vehicle's behavior, further hinders the evaluation of AD algorithms in dynamic, real-world conditions.
+
+As illustrated in Figure 1, we analyze existing AD methods and platforms, revealing that most of them are inadequate for a high-fidelity closed-loop simulation. Ideally, as an aspect of embodied intelligence, agents should be evaluated in a closed-loop environment, where other agents react to the actions of the ego vehicle, and the ego vehicle receives changed sensor input accordingly. However, existing simulation environments either cannot simulate sensor inputs [12, 19, 37] or have a significant domain gap with the real world [8, 20], making it difficult to seamlessly integrate algorithms into the real world, thus posing a huge challenge for closed-loop evaluation. We believe that the simulator should not only closely reflect the visual and physical aspects of the real world, but also promote the continuous learning and evolution of the model within an exploratory closed-loop system for adapting to diverse complex driving scenarios. To achieve this goal, it is imperative to establish a high-fidelity simulator that complies with physical laws and supports interactive functionalities.
+
+Therefore, we present DRIVEAREA, a pioneering closed-loop simulator based on conditional generative models for training and testing driving agents. Specifically, DRIVEAREA offers a flexible platform that can be integrated with any camera-input driving agent. It adopts a modular design and naturally supports iterative upgrades of each module. DRIVEAREA consists of a Traffic Manager that manages traffic flow and a World Dreamer based on auto-regressive generation. Traffic Manager can generate realistic interactive traffic flow on any road network worldwide, while World Dreamer is a high-fidelity conditional generative model with infinite autoregression. The driving agent should make corresponding driving actions based on the images generated by World Dreamer, and feed them back to Traffic Manager to update the status of vehicles in the environment. The new scene layout will be returned to World Dreamer for a new round of simulation. This iterative process realizes the dynamic interaction between the driving agent and the simulation environment. The specific contributions are as follows:
+
+- High-fidelity Closed-loop Simulation: We introduce DRIVEAREA, the first high-fidelity closed-loop simulation platform for autonomous driving that provides realistic surround images and integrates with vision-based driving agents. It accurately reflects real-world visual and physical properties, allowing agents to continuously learn in complex closed-loop driving scenarios.
+- Controllability and Scalability: Our Traffic Manager can dynamically control all vehicle movements in the sce
+
+narios and feed the scene layouts into World Dreamer, which utilizes a conditional diffusion network to generate realistic images in a stable and controllable manner. Additionally, DRIVEAREA supports simulation using road networks from any city worldwide, enabling the creation of diverse driving scenario images with varying styles.
+
+- Modularized Design: The Driving Agent, Traffic Manager and World Dreamer communicate via network interfaces, enabling a highly flexible and modular framework. This architecture allows each component to be replaced with different methods without requiring specific implementations. Functioning as an arena for these players, DRIVEAREA facilitates comprehensive testing and improvement of both vision-based driving agents and driving scene generative models.
+
+# 2. DRIVEAREA Framework
+
+As illustrated in Figure 2, the framework of our proposed DRIVEAREA comprises two key components: a Traffic Manager functioning as the backend physical engine and a World Dreamer serving as the real-world image renderer. Notably, DRIVEAREA does not rely on pre-built digital assets or reconstructed 3D road models. Instead, the Traffic Manager adapts to road networks of any city in OpenStreetMap (OSM) format [14], which can be directly downloaded from the Internet. This flexibility enables closed-loop traffic simulations on diverse urban layouts.
+
+The Traffic Manager receives ego trajectories output by the driving agent and manages the movement of all background vehicles. Unlike world model approaches [11, 15] that rely on diffusion models for both image generation and vehicle movement prediction, our Traffic Manager utilizes explicit traffic flow generation algorithms [35]. This approach enables the generation of a wider range of uncommon and potentially unsafe traffic scenarios, while also facilitating real-time collision detection between vehicles.
+
+World Dreamer generates realistic camera images that precisely correspond to the Traffic Manager's output. It also allows for user-defined prompts to control various elements of the generated images, such as street view style, time of day, and weather conditions, enhancing the diversity of the generated scenes. Specifically, it employs a diffusion-based model that utilizes the current map and vehicle layouts as control conditions to produce surround-view images. These images serve as input for end-to-end driving agents. Given DRIVEAREA's closed-loop architecture, the diffusion model is required to maintain both cross-view and temporal consistency in the generated images.
+
+The generated multi-view images of the current frame are fed into the end-to-end autonomous driving agents, which can output the ego vehicle's movement. The planned ego trajectory is subsequently sent to DRIVEAREA for the next simulation step. The simulation concludes when
+
+
+Figure 2. Overview of the DRIVEAREA framework. The system consists of two main components: (1) The Traffic Manager, which processes Internet-download HD maps to create diverse urban layouts, manages vehicle movements including background traffic, and handles collision detection. (2) The World Dreamer, an auto-regressive generative model that generates photo-realistic, multi-view camera images corresponding to the simulation state, with controllable parameters following given prompts. The framework operates in a closed loop: generated images are fed to the AD agent, which outputs the planned ego trajectory. The trajectory is then fed back into the Traffic Manager for the next simulation step.
+
+the ego vehicle either successfully completes the entire route, crashes, or deviates from the road. Upon completion, DRIVEAREA performs a comprehensive evaluation process to assess the agent's capabilities.
+
+It is noteworthy that DRIVEAREA employs a distributed modular design. The Traffic Manager, World Dreamer, and AD agent communicate via network using standardized interfaces. Consequently, DRIVEAREA does not mandate specific implementations of individual modules and agents. Our framework aims to function as an "arena" for these "players", facilitating comprehensive testing and improvement of both autonomous driving algorithms and realistic driving scene generative models.
+
+# 3. Methodology
+
+Following DRIVEAREA framework outlined above, we have implemented a preliminary version of DRIVEAREA. In this section, we elaborate on the implementation of each module: Traffic Manager, World Dreamer, and AD agent, while describing necessary details that were not previously mentioned. At the end of this section, we present both the open-loop and closed-loop evaluation metrics for AD agents in DRIVEAREA.
+
+# 3.1. Traffic Manager
+
+Most existing realistic driving simulators [38, 40, 42] rely on limited layouts from public datasets, lacking diversity
+
+for dynamic environments. To address these challenges, we utilize LimSim [9, 37] as the underlying Traffic Manager to simulate dynamic traffic scenarios and generate road and vehicle layouts for subsequent environment generation. LimSim also provides a user-friendly front-end GUI, which directly displays the BEV map and results from World Dreamer and the driving agent.
+
+Our Traffic Manager enables interactive simulations of multiple vehicles in traffic flow, including comprehensive vehicle planning and control. We adopt a hierarchical multi-vehicle decision-making and planning framework, which jointly makes decisions for all vehicles within the flow and reacts promptly to the dynamic environment through a high-frequency planning module [35]. The framework also incorporates a cooperation factor and trajectory weight set, introducing diversity to autonomous vehicles in traffic at both social and individual levels.
+
+Furthermore, our dynamic simulator supports various custom HD maps of any city from OpenStreetMap, facilitating the construction of diverse road graphs for convenient simulation. The Traffic Manager controls the movement of all background vehicles. For the ego vehicle, we provide two distinct simulation modes: open-loop and closed-loop. In closed-loop mode, the driving agent performs planning for the ego vehicle, and Traffic Manager uses the agent-outputted trajectory to control the ego vehicle accordingly. In open-loop mode, the trajectory generated by the driving
+
+agent is not actually used to control the ego vehicle; instead, Traffic Manager maintains control in a closed-loop manner. The details of these two modes are further elaborated in Section 3.4.
+
+# 3.2. World Dreamer
+
+Unlike recent autonomous driving generation methods [38, 40, 42] that use Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3D GS) for environment reconstruction from logged video, we design a diffusion-based World Dreamer. It utilizes control conditions of the map and object layouts from the Traffic Manager to generate geometrically and contextually accurate driving scenarios. Our framework shares several advantages: (1) Better controllability. The generated scenes can be controlled by scene layouts from Traffic Manager, textual prompts, and reference images to capture different weather conditions, lighting, and scene styles. (2) Better scalability. Our framework can be adapted to various road structures without the need to model the scene in advance. In theory, we support the generation for any city using OpenStreetMap layouts. However, we acknowledge that compared to NeRF and 3D GS methods, our WorldDreamer currently exhibits limitations in maintaining strict geometric and semantic consistency due to the absence of explicit 3D model constraints.
+
+We illustrate our diffusion-based World Dreamer in Figure 3. Built upon the stable diffusion pipeline [2], World Dreamer utilizes an effective condition encoding module that accepts a variety of conditional inputs including map and object layouts, text descriptions, camera parameters, ego poses, and reference images to generate realistic surround-view images. Considering the importance of ensuring synthesis scene consistency across different views and time spans for driving agents, we integrate a cross-view attention module, inspired by [11], to maintain coherence across different views. Additionally, we adopt an image auto-regressive generation paradigm to enforce temporal consistency. This approach enables World Dreamer to not only maximally maintain the temporal consistency of the generated videos, but also generate videos of arbitrary length in an infinite stream, which provides great support for autonomous driving simulation.
+
+Condition encoding. Previous work [11] applied the BEV layout as a conditional input to control the output of the diffusion model, increasing the difficulty of the network in learning to generate geometrically and contextually accurate driving scenes. In this work, we introduce more guidance information that helps the model generate high-fidelity surround images. In addition to encoding camera poses for each view, text descriptions, 3D object bounding boxes, and BEV maps using a condition encoder similar to [11], we also explicitly project the map and object layouts onto each camera view to generate layout canvases for more accu
+
+
+Figure 3. The figure illustrates the denoising process employed by World Dreamer. Beginning with randomly sampled noise, the autoregressive model utilizes various conditions—such as multiview layout, BEV map, text prompt, reference image, relative pose, camera parameters, and 3D bounding boxes—to enhance the denoising procedure. The encoders depicted in the figure are distinct, with the color indicating whether each one utilizes a pretrained network or is frozen. Additionally, we incorporate ControlNet to introduce conditional control into the diffusion model.
+
+rate lane and object generation guidance. Specifically, the text embedding $e_{text}$ is obtained by encoding the text descriptions with the CLIP text encoder [31]. The parameters $\mathrm{P} = \{\mathrm{K} \in 3 \times 3, \mathrm{R} \in 3 \times 3, \mathrm{T} \in 3 \times 1\}$ of each camera and the 8 vertices of the 3D bounding boxes are encoded to $e_{cam}$ and $e_{box}$ by Fourier embedding [30], where K, R, T represent camera intrinsic, rotations and translations respectively. The 2D BEV map grid uses the same encoding method as in [11] to obtain the embedding $e_{map}$ . Then, each category of the HD maps and the 3D boxes is projected onto the image plane respectively to obtain the layout canvas. The final feature $e_{layout}$ can be obtained by encoding the layout canvas by the conditional encoding network [46].
+
+Moreover, we introduce a reference condition to provide appearance and temporal consistency guidance. During training, we randomly extract a frame from the past $n$ frames as a reference frame and use the pre-trained CLIP model [31] to extract reference features $e_{ref}$ from the multiview images. These features imply semantic context and are integrated into the conditional encoder through a cross-attention module. To enable the diffusion model to grasp how the ego-car's motion influences background changes, we encode the ego-pose relative to the reference frame within the conditional encoder. The relative pose embedding $e_{rel}$ is encoded by Fourier embedding. By incorporating the above control conditions, we can effectively control the generation of images.
+
+Auto-regressive generation. To facilitate online inference and streaming video generation while maintaining temporal coherence, we have developed an auto-regressive generation pipeline. Specifically, during the inference phase, the previously generated images and the corresponding relative ego pose are used as reference conditions. This approach
+
+guides the diffusion model to generate current surround images with enhanced consistency, ensuring a smoother transition and coherence with the previously generated frames.
+
+This paper presents a simple implementation of World Dreamer. We also verify that extending to a multi-frame auto-regressive version (using multiple past frames as reference and outputting multi-frame images) and adding additional temporal modules can enhance temporal consistency.
+
+# 3.3. Driving Agent
+
+Recent works [24, 45] have demonstrated the challenges in justifying the planning behavior of driving agents through open-loop evaluation on public datasets [3], primarily due to the simplistic nature of driving scenarios presented. While some studies [34] have conducted closed-loop evaluations using simulators like CARLA [8], discrepancies such as appearance and scene diversity persist between these simulations and the dynamic real world. To bridge this gap, our DRIVEAREA provides a realistic simulation platform with the corresponding interfaces for camera-based driving agents [16-18] to perform more comprehensive evaluations, including both open-loop and closed-loop testing. Moreover, by changing the input conditions, such as the road and vehicle layouts, DRIVEAREA could generate corner cases and facilitate these driving agents' evaluation on out-of-distribution scenarios. Without loss of generality, we select two representative end-to-end driving agents, namely UniAD [17] and VAD [18], for open-loop and closed-loop testing in our DRIVEAREA. They utilize surround images to predict motion trajectories for the ego vehicle and other agent vehicles, which can be seamlessly integrated with our Traffic Manager for evaluation. Furthermore, the perceptual outputs, such as 3D detection and map segmentation, contribute to enhancing the validation of realism in our environment generation.
+
+# 3.4. Ego Control Modes and Evaluation Metrics
+
+DRIVEARENA inherently supports "closed-loop" simulation mode of driving agents. That is, the system adopts the trajectory output by the agent at each timestep, updates the ego vehicle's state based on this trajectory, and simulates the actions of background vehicles. Subsequently, it generates multi-view images for the next timestep, thus maintaining a continuous feedback closed-loop. Additionally, recognizing that some AD agents may be unable to perform long-term closed-loop simulation during the development process, DRIVEARENA also supports the "open-loop" simulation mode. In this mode, the Traffic Manager will take over the control of the ego vehicle, while the trajectory output by the AD agent is recorded for subsequent evaluation.
+
+In both open-loop and closed-loop modes, it is crucial to comprehensively evaluate AD agent performance from a results-oriented perspective. Drawing inspiration from
+
+NAVSIM [7] and the CARLA Autonomous Driving Leaderboard [5], DRIVEAREA adopts two evaluation metrics: PDM Score (PDMS) and Arena Driving Score (ADS).
+
+PDMS, initially proposed by NAVSIM [7], evaluates trajectory output at each timestep by aggregating sub-scores according to its original definition:
+
+$$
+\begin{array}{l} \mathrm {P D M S} _ {t} = \underbrace {\left(\prod_ {m \in \{\mathrm {N C} , \mathrm {D A C} \}} \operatorname {s c o r e} _ {m}\right)} _ {\text {p e n a l t i e s}} \tag {1} \\ \times \underbrace {\left(\frac {\sum_ {w \in \{\mathrm {E P} , \mathrm {T T C} , \mathrm {C} \}} \operatorname {w e i g h t} _ {w} \times \operatorname {s c o r e} _ {w}}{\sum_ {w \in \{\mathrm {E P} , \mathrm {T T C} , \mathrm {C} \}} \operatorname {w e i g h t} _ {w}}\right)} _ {\text {w e i g h t e d a v e r a g e}}. \\ \end{array}
+$$
+
+where the penalties include the drive with no collisions (NC) with road users and drivable area compliance (DAC), as well as the weighted average, including ego progress (EP), time-to-collision (TTC), and comfort (C). We implement minor modifications tailored to DRIVEAREA: in score NC, we do not differentiate "at-fault" collisions, and for score EP, we utilize the Traffic Manager's Ego path planner as the reference trajectory instead of the Predictive Driver Model. At the end of the simulation, the final PDM Score is averaged across all simulation frames.
+
+$$
+\mathrm {P D M S} = \frac {\Sigma_ {t = 0} ^ {T} \mathrm {P D M S} _ {t}}{T} \in [ 0, 1 ] \tag {2}
+$$
+
+For open-loop simulations, PDMS serves directly as the evaluation metric for AD agents. However, for agents operating under the "closed-loop" simulation mode, we employ a more comprehensive metric called Arena Driving Score (ADS), which combines the PDMS with route completion:
+
+$$
+\mathrm {A D S} = \mathrm {R} _ {c} \times \text {P D M S} \tag {3}
+$$
+
+where $\mathrm{R}_c \in [0,1]$ represents route completion, defined as the percentage of the route distance completed by an agent. Given that "closed-loop" simulations terminate upon agent collision with other road users or deviation from the road, ADS provides a suitable metric for differentiating agents' driving safety and consistency.
+
+# 4. Experiments
+
+# 4.1. Experimental Setups
+
+For World Dreamer, we use the nuScenes [3] dataset for training. The nuScenes dataset contains data collected from four different cities, covering various lighting and weather conditions, allowing DRIVEAREA to conditionally imitate different appearances. The model is initialized using the pre-trained Stable Diffusion v1.5 [32], and various control conditions are integrated into UNet with a randomly initialized ControlNet [46] to control the denoising process. The
+
+
+Figure 4. Comparison between MagicDrive and DRIVEAREA. Both are used to generate realistic images on the same Carla Town05 Map, with corresponding ground truth lane lines projected onto the images for demonstration. For such large curvatures and wide roads in CARLA, which are atypical scenarios in the nuScenes dataset, MagicDrive struggles to generate images that accurately fit the network. It incorrectly generates pavements and fails to match the road curvature (indicated by yellow arrows). In contrast, DRIVEAREA successfully generates images that accurately represent the road structure.
+
+
+Figure 5. Demonstration of diverse prompts and reference images' influence on identical scenes. The figure features two distinct image sequences generated by DRIVEANA for the same 30-second simulation, each driven by different prompts and reference images. These sequences reveal clear contrasts in weather and lighting conditions while maintaining their individual styles consistently throughout the entire 30-second duration. For more driving scenes under different prompts and reference images, please refer to supplementary materials.
+
+experiment is conducted on 8 NVIDIA A100 (80GB) GPUs with a batch size of $4 \times 8$ and 200K training iterations.
+
+Traffic Manager operates at $10\mathrm{Hz}$ , while the control frequency is set to $2\mathrm{Hz}$ to accommodate the AD agents. Beyond the nuScenes map, we design four distinct routes: sing-route_1, sing-route_2, bos-route_1, bos-route_2. These routes serve to evaluate the AD agent's generalization in both open-loop and closed-loop modes in Section 4.3. In fact, Traffic Manager can download road network data for any area directly from OpenStreetMap and perform simulations, enabling DRIVEAREA to simulate the road network of almost any city worldwide.
+
+# 4.2. World Dreamer Performance Assessment
+
+Fidelity. In this section, we assess the sim-to-real gap between our generated images and the original nuScenes images. We generate $2\mathrm{Hz}$ videos based on the original layout from the nuScenes validation set. For comparative analysis, we use MagicDrive [11] as our baseline, with both methods generating images at a resolution of $224\times 400$ . We then employ UniAD as an evaluator on these images to compute various metrics, including 3D object detection, BEV map segmentation, and planning. The results are summarized in Table 1. It shows that all our indicators are higher than the baseline method, and a few indicators even surpass the performance on the original nuScenes. Furthermore, it
+
+| Data Source | 3DOD | BEV Segmentation mIoU (%) | L2 (m) ↓ | Col. Rate (%) ↓ |
| mAP ↑ | NDS ↑ | Lanes ↑ | Drivable ↑ | Divider ↑ | Crossing ↑ | 1.0s | 2.0s | 3.0s | Avg. | 1.0s | 2.0s | 3.0s | Avg. |
| ori nuScenes | 37.98 | 49.85 | 31.31 | 69.14 | 25.93 | 14.36 | 0.51 | 0.98 | 1.65 | 1.05 | 0.10 | 0.15 | 0.61 | 0.29 |
| nuScenes w/ downsample | 31.20 | 45.22 | 29.19 | 65.83 | 23.51 | 12.99 | 0.60 | 1.10 | 1.85 | 1.18 | 0.08 | 0.28 | 0.66 | 0.34 |
| MagicDrive | 12.92 | 28.36 | 21.95 | 51.46 | 17.10 | 5.25 | 0.57 | 1.14 | 1.95 | 1.22 | 0.10 | 0.25 | 0.70 | 0.35 |
| DRIVEarena | 16.06 | 30.03 | 26.14 | 59.37 | 20.79 | 8.92 | 0.56 | 1.10 | 1.89 | 1.18 | 0.02 | 0.18 | 0.53 | 0.24 |
+
+Table 1. Comparison of generation fidelity. The data synthesis conditions are from the nuScenes validation set. All results are computed by using the official implementation and checkpoints of UniAD. Bold represents the best results, underline represents the second-best results (excluding row 2).
+
+demonstrates our model's superior capability to accurately respond to control signals and strictly adhere to input conditions. To isolate the impact of image resolution, the second row of the table presents results when original nuScenes images are downsampled by a factor of 4 and subsequently upsampled to their original resolution. This processing introduces performance degradation compared to the unmodified nuScenes dataset, suggesting that perceptual metrics would likely improve further as the resolution of generated images increases. These findings establish a solid foundation for deploying our generator as a reliable simulator.
+
+Controllability and Scalability. The Traffic Manager can accept any map downloaded from OpenStreetMap and seamlessly connect to the Carla road network. Combined with Dreamer's excellent following capability, the entire framework demonstrates robust controllability and scalability. The specific results are shown in Figure 4. We used both MagicDrive and our World Dreamer to generate realistic images on the same Carla road network, with the corresponding lane lines projected onto the images. The road style in Carla differs significantly from that of nuScenes. It is rare to encounter roads with such large curvature and such wide roads in nuScenes. Consequently, the performance of MagicDrive, which is based on the nuScenes BEV map, is slightly inferior in these conditions. As indicated by the yellow arrow, MagicDrive struggles to generate curved roads and fit wide roads accurately. DRIVEAREA, however, can produce reasonable pictures that follow the road structure.
+
+Figure 5 presents images generated using different text prompts and reference images on the same road network. Each set of images portrays the surrounding scenery at intervals of 8.5 seconds and 24 seconds respectively, with the layout projected on the image. The images clearly illustrate that the road structure and vehicles strictly adhere to the given control conditions while maintaining excellent consistency in the surrounding view. Furthermore, the road and vehicle layouts adhere to novel out-of-distribution scenario generation methods. Consequently, DRIVEAREA can generate corner cases such as head-on collisions and rear-end collisions. More examples are presented and discussed in supplementary materials.
+
+
+Figure 6. Case studies on open-loop performance of AD agents. Two long-term open-loop simulation sequences are shown: the upper for UniAD on Singapore's left-hand drive network, while the lower for VAD on Boston's right-hand drive network. Each subfigure displays, from left to right: ground truth BEV images from Traffic Manager; World Dreamer-generated images; and agent-predicted BEV images.
+
+# 4.3. Open-loop and Closed-loop Experiments
+
+In this section, we adopt the prevailing end-to-end autonomous driving methods UniAD [17] and VAD [18] as the driving agents to test both the open-loop and closed-loop performance within the DRIVEAREA framework. We utilized the open-source code and pre-trained weights from the two driving agents without additional training. UniAD and VAD operate at $2\mathrm{Hz}$ , outputting a trajectory of 6 path points over the next 3 seconds. Traffic Manager further interpolates this to a $10\mathrm{Hz}$ trajectory.
+
+Open-loop Evaluation. We first assess the performance of driving agents in DRIVEAREA's open-loop mode. The agents are evaluated on three scenarios: 1) the original nuScenes image sequences; 2) World-Dreamer-generated nuScenes image sequences, where the vehicles' trajectory remains identical to nuScenes ground truth, but sur
+
+| Scenario | Driving Agent | NC ↑ | DAC ↑ | EP ↑ | TTC ↑ | C ↑ | PDMS ↑ |
| nuScenes (original) | VAD | 0.915±0.17 | 0.937±0.10 | 0.762±0.18 | 0.848±0.23 | 1.000±0.00 | 0.740±0.18 |
| UniAD | 0.993±0.03 | 0.995±0.01 | 0.914±0.05 | 0.947±0.14 | 0.848±0.21 | 0.910±0.09 |
| nuScenes (generated) | VAD | 0.915±0.16 | 0.942±0.10 | 0.754±0.18 | 0.855±0.23 | 1.000±0.00 | 0.744±0.18 |
| UniAD | 0.993±0.02 | 0.991±0.02 | 0.909±0.05 | 0.951±0.14 | 0.821±0.21 | 0.902±0.09 |
| DRIVEARENA | VAD | 0.807±0.11 | 0.950±0.05 | 0.795±0.13 | 0.800±0.12 | 0.913±0.09 | 0.683±0.12 |
| UniAD | 0.792±0.11 | 0.942±0.04 | 0.738±0.11 | 0.771±0.12 | 0.749±0.16 | 0.636±0.08 |
| nuScenes GT | Human | 1.000±0.00 | 1.000±0.00 | 1.000±0.00 | 0.979±0.12 | 0.752±0.17 | 0.950±0.06 |
+
+Table 2. Performance of driving agents in DRIVEArena's open-loop mode. Evaluation across three scenarios: 1) original nuScenes images sequences; 2) World Dreamer-generated images with nuScenes ground truth trajectories; and 3) DRIVEArena's open-loop mode simulation sequences. Metrics include: no collisions (NC), drivable area compliance (DAC), ego progress (EP), time-to-collision (TTC), comfort (C), and PDM Score (PDMS).
+
+| Route | Driving Agent | PDMS ↑ | RC ↑ | ADS ↑ |
| sing-route_1 | VAD | 0.5315 | 0.0467 | 0.0248 |
| UniAD | 0.7615 | 0.1684 | 0.1282 |
| sing-route_2 | VAD | 0.5147 | 0.0400 | 0.0206 |
| UniAD | 0.7215 | 0.169 | 0.0875 |
| bos-route_1 | VAD | 0.5830 | 0.0604 | 0.0352 |
| UniAD | 0.4952 | 0.091 | 0.0450 |
| bos-route_2 | VAD | 0.5054 | 0.0366 | 0.0185 |
| UniAD | 0.6888 | 0.121 | 0.0835 |
+
+Table 3. Evaluation of Driving Agents' performance in DRIVEAREA's closed-loop mode across four distinct routes. Performance metrics include: PDM Score (PDMS), Route Completion (RC), and Arena Driving Score (ADS).
+
+round images are replaced with World-Dreamer-generated ones; and 3) the four routes defined by DRIVEAREA (i.e., DRIVEAREA's open-loop mode). Our evaluation metrics consist of the PDM Scores and its sub-scores, as detailed in Section 3.4. Additionally, we evaluate trajectories driven by human drivers in nuScenes as the human driver performance. Detailed results are presented in Table 2.
+
+The results show that UniAD performs best on the original nuScenes sequence with a PDMS metric of 0.91, whereas the PDMS metric on the World Dreamer-generated sequence is a surprising 0.902, with a metric drop of less than $1\%$ . We attribute this to both the high fidelity of our World Dreamer-generated images and UniAD's dependence on ego states, as corroborated by [24]. Furthermore, VAD achieves better performance on the World Dreamer simulation sequences with a PDMS of 0.683, demonstrating its better open-loop ability on unseen roadmaps and scenarios. Figure 6 presents the open-loop performance of both driving agents in long simulation sequences. More examples of visualization of the open-loop evaluation can be found in supplementary materials.
+
+Closed-loop Evaluation. We further evaluate the performance of VAD and UniAD in DRIVEAREA's closed-loop mode. In this mode, the trajectory outputted by the driving
+
+agents is directly used for ego vehicle control, and the evaluation metrics include PDM Score (PDMS), Route Completion (RC), and Arena Drive Score (ADS). Our closed-loop experiment was conducted on four pre-defined paths, with two paths selected in Boston and two in Singapore. The simulation time to complete each route was approximately 120 seconds. Detailed results are presented in Table 3.
+
+The results indicate that the PDMS of UniAD-generated trajectories in closed-loop mode (Avg.: 0.667) are comparable to those of the open-loop mode, while the PDMS of VAD-generated trajectories (Avg.: 0.534) has a significant metric drop of 0.149. The Route Completions (RC) of both driving agents are consistently low, with VAD completing just $4.59\%$ and UniAD completing an average of $13.7\%$ of the route. During the evaluation, both agents performed better on straightaways but largely failed to navigate the first turning intersection in the route. While VAD showed better metrics in open-loop mode, it failed to achieve better results when conducting closed-loop experiments. This highlights the inherent flaws of open-loop evaluation in assessing the true capabilities of agents, which could potentially be mitigated by DRIVEAREA.
+
+# 5. Conclusions
+
+This paper introduces a novel closed-loop simulation platform named DRIVEAREA for vision-based driving agents. DRIVEAREA features a modular architecture that seamlessly integrates a Traffic Manager that generates human-like traffic flow and a high-fidelity generative World Dreamer with infinite generation. This integration allows realistic interaction and continuous feedback between driving agents and the simulation environment. DRIVEAREA provides researchers with a valuable testbed for developing and evaluating autonomous driving systems across diverse scenarios, genuinely supporting closed-loop interaction of driving agents in realistic scenarios. This advancement represents a significant advancement in driving simulation technology.
+
+# 6. Acknowledgment
+
+The research was supported by Shanghai Artificial Intelligence Laboratory, the National Key R&D Program of China (Grant No. 2022ZD0160201) and the Science and Technology Commission of Shanghai Municipality (Grant Nos. 22DZ1100102 and 23YF1462900).
+
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+# DriveX: Omni Scene Modeling for Learning Generalizable World Knowledge in Autonomous Driving
+
+Chen Shi $^{1\diamond}$ Shaoshuai Shi $^{2}$ Kehua Sheng $^{2}$ Bo Zhang $^{2}$ Li Jiang $^{1\dagger}$
+
+1The Chinese University of Hong Kong, Shenzhen
+2Didi Chuxing, China
+
+chenshi@link.cuhk.edu.cn jiangli@cuhk.edu.cn
+
+# Abstract
+
+Data-driven learning has advanced autonomous driving, yet task-specific models struggle with out-of-distribution scenarios due to their narrow optimization objectives and reliance on costly annotated data. We present DriveX, a self-supervised world model that learns generalizable scene dynamics and holistic representations (geometric, semantic, and motion) from large-scale driving videos. DriveX introduces Omni Scene Modeling (OSM), a module that unifies multimodal supervision—3D point cloud forecasting, 2D semantic representation, and image generation—to capture comprehensive scene evolution. To simplify learning complex dynamics, we propose a decoupled latent world modeling strategy that separates world representation learning from future state decoding, augmented by dynamic-aware ray sampling to enhance motion modeling. For downstream adaptation, we design Future Spatial Attention (FSA), a unified paradigm that dynamically aggregates spatiotemporal features from DriveX's predictions to enhance task-specific inference. Extensive experiments demonstrate DriveX's effectiveness: it achieves significant improvements in 3D future point cloud prediction over prior work, while attaining state-of-the-art results on diverse tasks including occupancy prediction, flow estimation, and end-to-end driving. These results validate DriveX's capability as a general-purpose world model, paving the way for robust and unified autonomous driving frameworks.
+
+# 1. Introduction
+
+Data-driven learning techniques have significantly advanced autonomous driving, enhancing core tasks like perception [27, 48, 51, 66, 71] and planning [22, 23, 37, 52]. Despite this impressive progress, task-specific models still struggle with complex and out-of-distribution scenarios,
+
+
+(a) World modeling facilitates training
+
+
+(b) World modeling in video space
+
+
+(c) World modeling in spatially-aware latent space
+Figure 1. Comparison of different methods for integrating world models in autonomous driving systems. (a) World modeling serves as a pretraining task or an auxiliary supervision for driving models, without fully capturing general world knowledge. (b) Future prediction is performed in video space to assist downstream tasks, requiring additional 2D-to-3D transformation. (c) Our proposed DriveX framework decodes future states in latent 3D space, learning task-agnostic features that seamlessly benefit driving tasks.
+
+primarily due to their task-specific optimization and reliance on limited human-annotated training data. World models, which predict future environment states based on historical observations and ego actions, have gained increasing attention for their ability to model complex driving environments [1, 11, 12, 32, 44, 55, 56, 62, 63]. By learning generalizable world knowledge from large-scale driving videos, world models hold the potential to improve robustness and safety across various autonomous driving tasks.
+
+Existing world modeling approaches in autonomous driving can be broadly categorized into three strategies, as shown in Figure 1. The first strategy involves using world modeling as a general pretraining step [1, 44, 63], followed by fine-tuning for specific driving tasks. The second strategy treats world modeling as an auxiliary head [12, 31, 34, 62, 72] during task-specific training. While effective, both
+
+strategies struggle to retain general world knowledge and may not fully exploit the world model's potential for detailed spatial and temporal prediction, as the model parameters are ultimately adapted for specific downstream tasks. The third strategy uses world model as a generative model to predict future video sequences [11, 21, 32, 55, 56] by utilizing video generation techniques [17, 24, 54], which are subsequently used for task-specific purposes. Although this approach explicitly provides valuable predictive context by functioning as a world simulator, these generative models frequently struggle with maintaining consistent temporal-spatial coherence and lack adequate 3D spatial information, limiting their practical applications. These challenges motivate us to explore a fundamental question: how can we develop a world model framework that extracts generalizable world representations to benefit various downstream autonomous driving tasks within a unified paradigm?
+
+We argue that an effective world model should excel in two key dimensions: 1) it should perceive the environment by capturing both geometric structure and visual semantics—critical for ensuring that learned representations can be effectively transferred across diverse tasks; and 2) it should accurately model world dynamics, which is essential for decision-making tasks such as planning. In this work, we propose DriveX, a novel world model framework that not only preserves essential world knowledge within a spatially-aware bird's-eye view (BEV) latent space—facilitating general knowledge transfer across multiple downstream tasks—but also captures precise world evolution. As illustrated in Figure 1(c), DriveX demonstrates its extensibility by seamlessly integrating with various autonomous driving tasks.
+
+DriveX distinguishes itself from existing world modeling approaches through two key aspects. First, existing methods face a critical trade-off: prior work either focuses on geometric cues (e.g., point cloud forecasting [26, 63, 70]) or semantic occupancy prediction using manual labels [43, 62, 72], sacrificing either visual details or scalable supervision. To overcome these limitations, we introduce the Omni Scene Modeling (OSM) module, which encodes rich multimodal world knowledge into a bird's-eye view (BEV) latent space. Specifically, OSM integrates 3D point cloud forecasting for geometric fidelity, 2D semantic representations for class-aware reasoning, and image generation for retaining visual texture information. As shown in Table 1, when used as a pretrained feature extractor for end-to-end driving, DriveX maintains robust performance even with frozen parameters. In contrast, ViDAR[63] and DriveWorld[43] experience significant performance degradation when parameters are frozen, highlighting the generalizable knowledge captured by our approach. Moreover, OSM operates in a fully self-supervised manner, leveraging either inherently available labels or those generated by
+
+| Method | Finetuned | Fixed | Gap |
| ViDAR [63] | 83.6 | 77.0 | -6.6 |
| DriveWorld [43]† | 83.7 | 82.2 | -1.5 |
| DriveX | 83.7 | 83.6 | -0.1 |
+
+Table 1. End-to-end driving performance on NAVSIM [8] test set. "Finetuned" refers to training the world model simultaneously, while "Fixed" represents freezing the world model. We observe negligible performance gap in DriveX. $\dagger$ : re-implemented by us.
+
+foundation models [46, 69] for scalable learning.
+
+Second, we introduce a decoupled latent world modeling strategy that separates learning into two key components: world representation learning and latent future decoding. This hierarchical approach first builds a robust spatial representation before modeling temporal evolution, effectively capturing sparse motion signals. In the world representation learning component, we train a world encoder to generate structured BEV features from multi-view historical images. These BEV features are optimized by our OSM module and thus are generalizable across driving tasks. In the latent future decoding component, we train a future decoder to model world evolution in the latent BEV space. Given the pretrained world encoder, the future decoder predicts motion flow and future BEV features based on given ego actions, with self-supervised alignment against the encoded future video frames by the world encoder. To further enhance motion modeling, we also apply OSM loss on the predicted latent features and introduce a dynamic-aware ray sampling strategy that prioritizes motion-salient regions.
+
+To fully exploit DriveX's predictive capabilities in downstream tasks, we introduce the Future Spatial Attention (FSA) paradigm, a lightweight yet effective module that seamlessly integrates DriveX into various driving applications. By acting as a "world simulator", DriveX predicts future latent BEV features over the next few seconds, providing a rich predictive context. FSA then employs task-specific queries to dynamically aggregate relevant contextual information from these features. This streamlined approach improves state-of-the-art performance across diverse tasks such as occupancy prediction, occupancy flow estimation, and end-to-end driving, highlighting DriveX's strong generalization and predictive capabilities.
+
+In summary, our contributions are four-fold: 1) We introduce DriveX, a self-supervised world model that learns generalizable world knowledge in latent space through Omni Scene Modeling with multimodal supervision; 2) We propose a decoupled latent world modeling strategy that separates world representation learning from latent future decoding, enhanced by dynamic-aware ray sampling to prioritize motion-salient regions; 3) We present the Future Spatial Attention (FSA) paradigm, which leverages the pretrained world model to enhance diverse driving tasks within a unified framework; 4) DriveX achieves significant improvements across multiple tasks, achieving a rel
+
+ative $6 \%$ reduction in Chamfer Distance for 3- second future point cloud prediction, along with notable improvements in downstream tasks such as occupancy prediction, occupancy flow estimation, and end-to-end driving.
+
+# 2. Related Work
+
+Point Cloud Forecasting Point cloud forecasting, which aims to predict future point clouds from historical observations, has emerged as a crucial self-supervised learning paradigm in autonomous driving. Early approaches [42, 57, 58] typically project past point clouds into dense range images and leverage LSTM or 3D convolutional networks for future range image prediction. Recent work 4D-Occ [26] decomposes the task into 4D occupancy forecasting and employs differential depth rendering [25, 45] to generate point cloud predictions from occupancy grids. COPILOT4D [70] extends this line of work by incorporating diffusion models [19, 49]. In a different direction, VidAR [63] explores a vision-centric approach by predicting future point clouds from past visual inputs. Unlike existing researches that primarily utilize point cloud forecasting as a pretraining strategy for encoder in downstream tasks, our work adopts a fundamentally distinct perspective: we integrate point cloud forecasting as a component of the world model to learn more generalizable representations.
+
+World Models World models [13, 28], inspired by human cognition, enable intelligent agents to predict future outcomes based on past experiences and current actions. Learning world models has been widely studied to enhance policy function in reinforcement learning [13-16, 47, 60], but their adoption in real-world applications remains limited. Another line of research emphasizes world simulation, aiming to generate high-fidelity future videos in gaming [2, 4, 50] and real-world scenarios [5, 20, 29, 64]. However, these methods often fail to provide consistent and precise spatiotemporal representation. In this work, we target real-world autonomous driving and construct world models directly in the spatial BEV space, enabling transferable representations that support diverse downstream driving tasks.
+
+World Modeling for Autonomous Driving As a complex and safety-critical real-world application, autonomous driving has increasingly attracted interest in world modeling. Leveraging advances in video generation, several approaches [9-11, 21, 32, 55, 56] have demonstrated the capability to synthesize realistic driving sequences across diverse scenarios. However, the generated videos lack comprehensive 3D scene understanding, restricting their applications in downstream tasks. Alternative methods [33, 44, 62, 72] explore future prediction in occupancy space, achieving remarkable progress but relying on costly semantic occupancy annotations. Meanwhile, research on applying world models to real-world driving applications mainly focuses on using world models as auxiliary supervi
+
+sion [31, 34, 34, 63] for autonomous model training, failing to capture task-agnostic world features. Recent works such as LAW [34] and SSR [31] have also explored world modeling in latent BEV space to eliminate the need for manual labels, but are limited to the end-to-end driving task. To address these challenges, we present DriveX, a spatially-aware world model that learns general world knowledge in a self-supervised manner and offers seamless integration with various driving tasks via spatial attention.
+
+# 3. Methodology
+
+In autonomous driving scenarios, world models are typically designed to predict future environmental states from past observations and ego actions, enabling generalized scene understanding. Some approaches leverage world modeling as a pre-training step [26, 63, 70] or as an auxiliary task [17, 24, 54] but often compromise transferability due to reliance on specialized supervision. Another line of world models [11, 32, 55, 56] explores to generate future video sequences but faces challenges in ensuring the spatial and temporal consistency.
+
+To advance the utility of the world model in driving tasks, we propose DriveX, as depicted in Figure 2. DriveX leverages multi-view historical camera video and ego action data to predict future world states within a spatially-aware latent space. To learn general world representation, we propose the Omni Scene Modeling module (described in Sec 3.1), which employs a multimodal supervision strategy to simultaneously encode geometric, semantic, and visual details in a self-supervised manner. To further improve world dynamics modeling, we design a decoupled learning strategy that enables precise motion signal learning based on well-trained BEV latent representations (See Sec 3.2). Finally, we present the Future Spatial Attention (FSA) mechanism (See Sec 3.3), which seamlessly integrates DriveX with various downstream driving tasks.
+
+# 3.1. World Representation Learning
+
+To encode environmental information into latent representations, prior works have explored point cloud reconstruction [26, 63] and occupancy prediction as proxy tasks [43, 62, 72]. However, these specialized objectives fail to fully capture comprehensive scene information (as demonstrated in Table 1). To address this limitation, we design the Omni Scene Modeling (OSM) module that promotes the learning of generalizable representations. Leveraging foundation models [46, 69] and paired multi-view images and point cloud data, this learning process is fully self-supervised.
+
+Temporal Streaming World Encoder. Given a sequence of multi-view images $I_{1:t}$ up to the current timestamp $t$ , we apply a world encoder to compress the multi-view historical observations into a latent BEV representation $B_t \in \mathbb{R}^{H \times W \times C}$ , where $H, W$ and $C$ are the width, height and
+
+
+
+
+
+
+Omni Scene Modeling
+
+
+(a) World Model Learning
+(b) Future Spatial Attention
+Figure 2. Top: An overview of our DriveX framework. The learning process consists of two stages: world representation learning, where the model learns temporal and geometric semantics through Omni Scene Modeling, and latent future decoding, where the model predicts future states in the learned latent space. Both stages are trained in a self-supervised manner. Bottom: Illustration of the FSA paradigm. Various driving tasks can dynamically aggregate information from predicted latent features through FSA.
+
+
+
+number of channels of the feature map, respectively. We follow the BEVFormer [35] paradigm for 2D-to-3D view transformation. Taking previous latent BEV features $B_{t - 1}$ in streaming memory and images $I_{t}$ from $N_{\mathrm{view}}$ cameras as inputs, the world encoder extracts visual information and transforms it into grid-structured BEV features, as follows:
+
+$$
+B _ {t} = \operatorname {T C A} \left(E \left(I _ {t}\right), B _ {t - 1}\right), \tag {1}
+$$
+
+where $E$ denotes the combination of a 2D encoder [18, 39, 53] and a 2D-to-3D transformation network [35]. TCA represents a Temporal Cross-Attention module [74] that achieves interaction between current states and historical latent information. The encoder operates in a streaming manner, continuously caching BEV features in the streaming memory to maintain long-term temporal dependencies.
+
+In this way, we obtain a compact and structured representation $B_{t}$ , where each grid cell corresponds to a specific location in the physical world. The spatial priors of grids in $B_{t}$ facilitate scene dynamics modeling by enabling independent processing of each grid cell. Furthermore, such structured representation ensures strong compatibility with diverse practical applications (detailed in Section 3.3).
+
+Omni Scene Modeling. A well-designed training signal is essential for the world encoder to capture generalizable latent BEV features. To achieve this, we design a omni scene modeling module to compel the world encoder to develop a comprehensive understanding of the environment. Specifically, we categorize the environmental understanding into three aspects: geometric structure, semantic information, and visual details. Then we introduce a multimodal supervision strategy, combining 3D point cloud reconstruction, 2D semantic prediction, and image generation to improve the richness of the latent representation.
+
+To be specific, let $I_{t} \in \mathbb{R}^{N_{\mathrm{view}} \times H_{\mathrm{img}} \times W_{\mathrm{img}} \times 3}$ and $P_{t} \in \mathbb{R}^{N_{p} \times 3}$ represent the multi-view images with shape $(W_{\mathrm{img}}, H_{\mathrm{img}})$ and point clouds with $N_{p}$ points, respectively. Firstly, we cast $N_{r}$ rays from image and LiDAR views by sampling corresponding pixels and points. Each ray can be parameterized as $r_{i} = o_{i} + td_{i}$ , where $o_{i}$ denotes the camera or LiDAR center and $d_{i}$ indicates the ray direction pointing to the sampled pixel or point. Then we sample $n$ waypoints $x_{i} \in \mathbb{R}^{n \times 3}$ along the ray $r_{i}$ . The coordinates of these waypoints are computed as follows:
+
+$$
+x _ {i, j} = o _ {i} + \lambda_ {j} d _ {i}, \tag {2}
+$$
+
+where $i$ and $j$ denotes the index of ray and waypoint, respectively, and $\lambda = \{\lambda_1,\lambda_2,\dots,\lambda_n\}$ represents predefined distances.
+
+The waypoint features $V_{t} \in \mathbb{R}^{N_{r} \times n \times C^{*}}$ are obtained by first transforming the BEV features $B_{t}$ into 3D space through a Channel-to-Height module, yielding volumetric features $F_{t} \in \mathbb{R}^{H \times W \times Z \times C^{*}}$ , followed by a trilinear interpolation operation:
+
+$$
+F _ {t} = \operatorname {R e s h a p e} \left(\operatorname {C o n v} \left(B _ {t}\right), [ H, W, Z, C ^ {*} ]\right), \tag {3}
+$$
+
+$$
+V _ {t} = \operatorname {I t e r p} \left(F _ {t}, X _ {t}\right),
+$$
+
+where Conv denotes 2D convolution layer with input channels $C$ and output channels $ZC^{*}$ , and $X_{t} = \{x_{i}\}_{i = 1}^{N_{r}}$ represents the collection of ray waypoints. Subsequently, for each waypoint $x_{i,j}$ , we utilize a MLP to predict its attribution filed $\alpha_{i,j}\in \mathbb{R}^{N_s + N_c}$ and density field $\sigma_{i,j}\in \mathbb{R}$ :
+
+$$
+\left(\alpha_ {i, j}, \sigma_ {i, j}\right) = \operatorname {M L P} \left(\operatorname {C o n c a t} \left(v _ {i, j}, \operatorname {P E} \left(x _ {i, j}\right)\right), \right. \tag {4}
+$$
+
+where $v_{i,j}$ represents the waypoint features from $V_{t}$ , $N_{s}$ and $N_{c}$ indicate the number of semantic classes and RGB color channels, respectively. PE is the cosine position encoding. Finally, the attribute prediction $\alpha_{i}$ for $r_i$ is accumulated through volume rendering process [45, 61]:
+
+$$
+\tau_ {j} = \exp \left(- \sum_ {l = 1} ^ {j - 1} \sigma_ {i, l} \delta_ {l}\right), \tag {5}
+$$
+
+$$
+\alpha_ {i} = \sum_ {j = 1} ^ {n} \tau_ {j} (1 - \exp (- \sigma_ {i, j} \delta_ {j})) \alpha_ {i, j},
+$$
+
+where $\delta_{j} = \lambda_{j} - \lambda_{j-1}$ ( $\lambda_0 = o_i$ ) represents the distance between two adjacent waypoints, and $\alpha_{i}$ can be decomposed into semantic prediction $s_i \in \mathbb{R}^{N_s}$ and color prediction $c_i \in \mathbb{R}^{N_c}$ . Following the same formulation, the expected depth $d_i$ of $r_i$ is estimated by replacing $\alpha_{i,j}$ with the distance $\lambda_j$ in Eq.(5).
+
+To enable comprehensive scene understanding, we train the world encoder using a multimodal supervision framework, deriving the scene modeling loss $\mathcal{L}_{\mathrm{scene}}$ from both camera and LiDAR perspectives. Specifically, for camera-view rays, we optimize the scene modeling loss $\mathcal{L}_{\mathrm{scene}}^{\mathrm{camera}}$ that integrates semantic segmentation $(\mathcal{L}_{\mathrm{sem}})$ and color reconstruction $(\mathcal{L}_{\mathrm{rgb}})$ objectives. For LiDAR-view rays, we optimize the scene modeling loss $\mathcal{L}_{\mathrm{scene}}^{\mathrm{LiDAR}}$ with only depth estimation $(\mathcal{L}_{\mathrm{depth}})$ :
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {s c e n e}} ^ {\text {c a m e r a}} = \mathcal {L} _ {\text {s e m}} + \mathcal {L} _ {\text {r g b}}, \\ \mathrm {e} ^ {\text {L D A P}} = \end{array} \tag {6}
+$$
+
+$$
+\mathcal {L} _ {\text {s c e n e}} ^ {\text {L i D A R}} = \mathcal {L} _ {\text {d e p t h}},
+$$
+
+where we adopt cross-entropy loss for $\mathcal{L}_{\mathrm{sem}}$ and L2 Loss for both $\mathcal{L}_{\mathrm{rgb}}$ and $\mathcal{L}_{\mathrm{depth}}$ . The ground truth depth and color values are directly acquired from raw sensor data, while semantic labels are automatically generated using foundation models Grounded SAM [46] and OpenSeeD [69], enabling scalable training without manual annotation.
+
+
+(a) Future forecasting pipeline
+
+
+(b) Feature warping
+Figure 3. Illustration of the flow-based future forecasting pipeline. (a) The detailed structures of future decoder, consisting of a future propagation module, a motion head "M", and a refinement 2D convolutional backbone. (b) Grid points with predicted flows are transformed to time $t + k$ coordinates, followed by distance-based interpolation to obtain the future grid features.
+
+# 3.2. Decoupled Latent World Modeling
+
+Instead of jointly learning representation and temporal dynamics, we propose a decoupled strategy, where the world decoder is first trained to generate representative BEV features that reflect a comprehensive understanding of past observations. Building on these spatially-aware features, we then introduce a dynamic future decoder module to model temporal evolution in the latent BEV space, without being burdened by feature learning. Specifically, we employ an explicit flow-based future forecasting strategy to generate future world states in the latent BEV space, along with a dynamic-aware ray sampling strategy to improve learning efficiency in potentially dynamic regions.
+
+Flow-based Future Forecasting. As illustrated in Figure 3, the future decoder predicts future states based on the latent spatial features $B_{t}$ and action condition, i.e., ego-motion. Specifically, the ego-motion to target time $t + k$ is first encoded into an embedding $a_{t + k} \in \mathbb{R}^C$ through a multi-layer perceptron (MLP), which is added to $B_{t}$ to incorporate action information. Then, a future propagation module consisting of stacked deformable attention blocks processes these condition-augmented features and interacts with historical latent features in streaming memory, producing future features $B_{t + k}'$ . The corresponding future grid positions $g_{f}$ are computed by adding current grid positions $g \in \mathbb{R}^{H \times W \times 2}$ with flow fields $f_{t + k} \in \mathbb{R}^{H \times W \times 2}$ , where $f_{t + k}$ is predicted from $B_{t + k}'$ via a motion head. Since $g_{f}$ are expressed in the frame- $t$ coordinate system, we transform them to the target frame $t + k$ as follows:
+
+$$
+g _ {f} ^ {\prime} = T _ {t} ^ {t + k} g _ {f}, \tag {7}
+$$
+
+where $T_{t}^{t + k}$ is the ego-motion transformation matrix from
+
+the current frame to frame $t + k$ . Finally, distance-based interpolation is applied to warp the features into grid-structure future state $\hat{B}_{t+k}$ . In particular, for each grid in $\hat{B}_{t+k}$ , we select $N$ nearest neighbor grids in $B_{t+k}'$ using $g_f'$ , and aggregate the grid features through inverse distance weighted summation. A 2D convolutional backbone is employed to further refine the interpolated features. During training, we supervise the predicted features $\hat{B}_{t+k}$ using ground truth latent representations $B_{t+k}$ extracted by the world encoder:
+
+$$
+\mathcal {L} _ {\text {l a t e n t}} = \left\| B _ {t + k} - \hat {B} _ {t + k} \right\|. \tag {8}
+$$
+
+In this way, we can predict future states at arbitrary times-stamps. Compared to autoregressive methods [63, 72], this direct prediction strategy not only avoids error accumulation but also offers greater flexibility in practice.
+
+Dynamic-aware Ray Sampling. In addition to latent space supervision, we incorporate scene modeling loss $\mathcal{L}_{\mathrm{scene}}$ at future timestamps. However, since the majority of rays belong to static background elements, salient moving objects may be overlooked during training. To bolster the model's understanding of world dynamics, we present a dynamic-aware ray sampling strategy, which leverages an off-the-shelf tracker to identify regions of interest (RoIs) with high dynamic activity, preserving rays within these regions to prioritize motion-salient areas.
+
+Learning Objective To summarize, the overall objective for the future decoder contains latent space alignment and future scene modeling:
+
+$$
+\mathcal {L} _ {\text {f u t u r e}} = \sum_ {k = 1} ^ {F} \left(\omega_ {l} \mathcal {L} _ {\text {l a t e n t}} ^ {k} + \omega_ {s} \mathcal {L} _ {\text {s c e n e}} ^ {k}\right), \tag {9}
+$$
+
+where $\omega_{l}$ and $\omega_{s}$ are the weight coefficients, and $F$ represents the number of future timestamps used for supervision. Notably, the supervision signal $B_{t + k}$ in $\mathcal{L}_{\mathrm{latent}}$ is generated from raw images using Eq.(1), while $\mathcal{L}_{\mathrm{scene}}$ operates without manual annotations, ensuring a fully self-supervised training paradigm in future decoding.
+
+# 3.3. World Model Integration with Task Heads
+
+The fully-trained DriveX model can predict future world evolutions in the latent BEV space, offering valuable insights for a range of autonomous driving tasks. Notably, the generated generic and spatially-aware BEV features are readily compatible with various driving models. As shown in the bottom part of Figure 2, various downstream tasks can directly employ the BEV features from the frozen world model through a lightweight adapter, which enhances $B_{t}$ with latent image features from world encoder using a stack of deformable attention layers. Then, we introduce a Future Spatial Attention (FSA) paradigm that enables future predictions to be incorporated into various autonomous driving models within a unified framework. To illustrate the integration of the DriveX model, we focus on two representative tasks: occupancy prediction and end-to-end driving.
+
+| Method | Modality | Chamfer Distance (m2) ↓ |
| 0.5s | 1.0s | 1.5s | 2.0s | 2.5s | 3.0s |
| 4D-Occ* [26] | L | 0.91 | 1.13 | 1.30 | 1.53 | 1.72 | 2.11 |
| ViDAR [63] | C | 1.01 | 1.12 | 1.25 | 1.38 | 1.54 | 1.73 |
| HERMES [73] | C | - | 0.78 | - | 0.95 | - | 1.17 |
| DriveX-B | C | 0.55 | 0.66 | 0.75 | 0.86 | 0.97 | 1.10 |
+
+Table 2. Point cloud forecasting performance comparison on nuScenes [3] dataset. L and C denote LiDAR and Camera inputs, respectively. $\ast$ : re-evaluated by [62].
+
+Action Prediction. Because the world model's future predictions are conditional on the ego vehicle's future actions, we employ a straightforward strategy to predict these actions for models that don't inherently include this functionality, such as perception models. Specifically, we follow AD-MLP [67] to predict actions based on ego states and historical trajectories, focusing on short-term predictions to simplify the task compared to full trajectory planning. For the end-to-end driving task, we directly adopt the planning head's output as the predicted actions.
+
+Future Spatial Attention Paradigm. To integrate the predicted future BEV features into downstream tasks, we propose a unified Future Spatial Attention (FSA) paradigm. As shown in Figure 2, this paradigm uses task-specific queries to directly aggregate world state information from the predicted future BEV features via standard spatial attention. Concretely, given a query $q$ from the task model and its 3D reference point $p$ , the spatial attention can be formulated as:
+
+$$
+q := q + \sum_ {k = 1} ^ {K} \sum_ {j = 1} ^ {J} A _ {k j} W \hat {B} _ {t + k} \left[ T _ {t} ^ {t + k} \left(p + \Delta p _ {k j}\right) \right], \tag {10}
+$$
+
+where $K$ and $J$ denote the number of future timesteps and sampling positions, respectively. $W$ represents the learnable projection matrix, $A_{kj}$ indicates the normalized attention weight, and $\Delta p_{kj}$ is sample offset. Unlike conventional deformable attention, we transform the sample point $p + \Delta p_{kj}$ to the frame- $(t + k)$ coordinate system for feature sampling from $\hat{B}_{t + k}$ . For simplicity, we omit the explicit expression of attention heads. The key to adapting spatial attention for various downstream tasks lies in the selection of $\Delta p_{kj}$ , which enables the DriveX model to seamlessly integrate with diverse autonomous driving tasks while preserving the integrity of existing architectures.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Dataset. We conduct experiments on two multimodal autonomous driving datasets: nuScenes [3] and NAVSIM [8]. The nuScenes dataset comprises 1,000 driving sequences and supports various autonomous driving tasks. For occupancy prediction and occupancy flow estimation experiments, we utilize the annotations from the FlowOcc3D
+
+| Method | Backbone | Flow Head | mIoU | IoUgeo | mAVE ↓ | others | barrier | bicycle | bus | car | const. veh. | motorcycle | pedestrian | traffic cone | trailer | truck | drive. surf. | other flat | sidewalk | terrain | mannade | vegetation |
| BEVFormer[35] | InternT | X | 36.93 | 68.49 | - | 8.56 | 42.94 | 19.34 | 47.02 | 49.59 | 20.36 | 22.62 | 24.69 | 19.77 | 30.11 | 35.24 | 82.11 | 40.86 | 50.62 | 54.81 | 42.56 | 36.55 |
| CVT-Occ [65] | Res101 | X | 40.34 | - | - | 9.45 | 49.46 | 23.57 | 49.18 | 55.36 | 23.10 | 27.85 | 28.88 | 29.07 | 34.97 | 40.98 | 81.44 | 40.92 | 51.37 | 54.25 | 45.94 | 39.71 |
| ViewFormer [30] | InternT | X | 43.61 | 72.46 | - | 13.82 | 50.32 | 29.49 | 49.24 | 54.52 | 24.34 | 32.72 | 31.09 | 31.49 | 34.44 | 41.62 | 85.47 | 51.27 | 59.03 | 62.15 | 48.33 | 42.06 |
| FB-OCC [36] | InternT | X | 38.69 | 69.95 | - | 11.40 | 41.42 | 24.27 | 46.01 | 49.38 | 24.56 | 27.06 | 28.09 | 25.61 | 32.23 | 38.46 | 80.97 | 42.99 | 50.95 | 56.15 | 40.55 | 37.61 |
| ViewFormer (ViDAR [63])† | InternT | X | 43.72 | 72.88 | - | 13.52 | 50.69 | 29.56 | 49.77 | 54.72 | 25.24 | 32.41 | 31.59 | 31.20 | 34.54 | 42.03 | 85.40 | 51.01 | 58.96 | 62.28 | 48.10 | 42.17 |
| ViewFormer [30] | InternT | X | 43.61 | 72.46 | - | 13.82 | 50.32 | 29.49 | 49.24 | 54.52 | 24.34 | 32.72 | 31.09 | 31.49 | 34.44 | 41.62 | 85.40 | 51.27 | 59.03 | 62.15 | 48.33 | 42.06 |
| ViewFormer (DriveX-S) | InternT | X | 44.38 | 73.61 | - | 14.00 | 51.18 | 30.10 | 50.13 | 55.44 | 26.82 | 33.12 | 32.37 | 32.07 | 35.60 | 43.18 | 85.78 | 50.93 | 59.16 | 62.23 | 49.80 | 42.59 |
| Improvement | | | +0.77 | +1.15 | | | | | | | | | | | | | | | | | | |
| BEVFormer* [35] | InternT | ✓ | 33.61 | 67.41 | 0.695 | 8.44 | 40.80 | 12.57 | 37.70 | 45.76 | 18.44 | 12.14 | 22.52 | 21.25 | 25.97 | 29.40 | 80.92 | 38.19 | 48.56 | 52.58 | 40.98 | 35.07 |
| FB-OCC* [36] | InternT | ✓ | 37.36 | 69.73 | 0.433 | 10.95 | 40.08 | 23.14 | 42.87 | 47.17 | 21.43 | 23.84 | 27.24 | 24.50 | 31.54 | 37.36 | 80.31 | 42.26 | 50.14 | 55.44 | 39.98 | 36.84 |
| ViewFormer (ViDAR [63])† | InternT | ✓ | 42.64 | 72.76 | 0.404 | 13.73 | 49.23 | 29.04 | 46.98 | 52.79 | 21.80 | 29.85 | 30.73 | 30.55 | 34.42 | 41.22 | 85.17 | 50.45 | 58.28 | 61.63 | 47.72 | 41.72 |
| ViewFormer [30] | InternT | ✓ | 42.54 | 72.36 | 0.412 | 13.63 | 49.35 | 28.74 | 46.63 | 52.71 | 21.04 | 29.63 | 30.34 | 30.53 | 34.01 | 41.04 | 85.23 | 50.63 | 58.68 | 61.63 | 47.72 | 41.56 |
| ViewFormer (DriveX-S) | InternT | ✓ | 43.47 | 73.44 | 0.385 | 13.72 | 49.46 | 30.64 | 48.85 | 54.99 | 27.13 | 31.90 | 32.62 | 31.29 | 34.29 | 41.16 | 84.89 | 49.91 | 58.00 | 60.75 | 47.50 | 41.88 |
| Improvement | | | +0.93 | +1.08 | -0.027 | | | | | | | | | | | | | | | | | |
+
+Table 3. 3D occupancy and occupancy flow prediction performance comparison on FlowOcc3D [30]. We report results for models with and without a flow head. Performance gains achieved by our DriveX model are highlighted. \* reported by [30]. $\dagger$ : re-implemented by us.
+
+| Method | Modality | NC ↑ | DAC ↑ | TTC ↑ | Comf. ↑ | EP ↑ | PDMS ↑ |
| Constant Velocity [8] | Camera | 68.0 | 57.8 | 50.0 | 100 | 19.4 | 20.6 |
| Ego Status MLP [8] | Camera | 93.0 | 77.3 | 83.6 | 100 | 62.8 | 65.6 |
| Transfuser* [6] | Camera | 97.4 | 92.8 | 92.4 | 100 | 79.0 | 83.8 |
| PARA-Drive * [59] | Camera | 97.9 | 92.4 | 93.0 | 99.8 | 79.3 | 84.0 |
| UniAD* [22] | Camera | 97.8 | 91.9 | 92.9 | 100 | 78.8 | 83.4 |
| DiffusionDrive-C [38]† | Camera | 97.8 | 92.2 | 92.6 | 99.9 | 78.9 | 83.6 |
| DriveX-S | Camera | 97.5 | 94.0 | 93.0 | 100 | 79.7 | 84.5 |
| Improvement | - | -0.3 | +1.8 | +0.4 | +0.1 | +0.8 | +0.9 |
+
+Table 4. End-to-end planning performance on NAVSIM test split. "PDMS" indicates the predictive driver model score. *: reported by [8]. †: our re-implementation of the camera-based Diffusion-Drive model. The best results are marked in bold.
+
+benchmark [30]. The NAVSIM dataset, built upon OpenScene [7], provides 115k filtered samples for challenging end-to-end driving. We generate image semantic labels for both datasets using 2D foundation models [46, 69], resulting in 15 classes as defined in [68].
+
+Network Architecture. The world encoder consists of an InternImage-Tiny [53] backbone with an FPN neck [39], followed by six encoder layers [35] to extract BEV-space world representations from multi-view images and historical latent states. The future decoder consists of a future propagation module with three deformable attention blocks [35], a motion head, and a 2D CNN backbone for refinement. We develop two variants of the world model: DriveXS, which uses a smaller input image size of $256 \times 704$ , and DriveX-B, which employs a larger size of $900 \times 1600$ . For downstream task verifications, we adopt the ViewFormer [30] head as our baseline for occupancy and flow prediction task, and the DiffusionDrive [38] head for end-to-end driving task. The adapter and FSA are configured with 4 and 3 attention layers, respectively.
+
+Training. The world model adopts a two-step training strategy, with the world encoder first trained for 40 epochs, followed by the future decoder trained for 24 epochs. Both stages utilize the AdamW optimizer [40] and are conducted on 32 NVIDIA H20 GPUs with a total batch size of 32. In
+
+the future decoding training phase, we predict states at 0.5-second intervals over a 3-second horizon. The loss weights $\omega_{l}$ and $\omega_{s}$ in Eq.(9) are set to 1.0 and 0.5, respectively. For ray sampling, we first utilize DetZero [41] to identify moving objects and aggregate point clouds from the time range [-2s, +2.5s] to reconstruct the scene. We then select up to 8000 rays from LiDAR view through voxel-based down-sampling and 10000 rays from image view based on pixel semantics. Additionally, for dynamic-aware ray sampling, we sample up to 2,000 rays within the bounding boxes of moving objects. For downstream tasks, we follow the official training protocols while configuring the world model to predict 2 future frames for 3D occupancy and flow prediction, and 3 frames for end-to-end driving.
+
+# 4.2. Main Results
+
+In this section, we first evaluate our DriveX model in point cloud forecasting task to demonstrate its superior capability in future forecasting. We then benchmark its effectiveness in improving the performance of occupancy prediction, occupancy flow estimation, as well as end-to-end driving.
+
+Point Cloud Forecasting. Following [62, 73], we evaluate on points within the range of $[-51.2\mathrm{m}, 51.2\mathrm{m}]$ on both X and Y axes. As presented in Table 2, our DriveX model outperforms the previous state-of-the-art method HERMES [73] across all timestamps, achieving a reduction of $0.12\mathrm{m}^2$ and $0.09\mathrm{m}^2$ in Chamfer Distance at 1.0s and 2.0s horizons.
+
+Occupancy and Flow Prediction. We verify our DriveX model on the 3D occupancy and flow prediction tasks, employing the state-of-the-art ViewFormer [30] as baseline. As shown in Table 3, for occupancy prediction, the DriveX model boosts ViewFormer's performance by $+0.77 \, \text{mIoU}$ and $+1.15 \, \text{IoU}_{geo}$ , surpassing all previous methods. Notably, while conventional pretrained-based world models like ViDAR [62] show marginal improvements on such a strong baseline, DriveX still delivers substantial gains, which we attribute to its ability to learn a more compre
+
+hensive understanding of the world. To further investigate its effectiveness in modeling world dynamics, we add a flow head for occupancy motion estimation. The model achieves an mAVE of 0.385, reducing the error by $6.5\%$ . The performance gains also remain remarkable for both mIoU $(+0.93)$ and IoUgeo $(+1.08)$ . These improvements highlight the capability of the DriveX model in enhancing downstream models via future scene prediction.
+
+End-to-end Driving. Safely planning for autonomous driving requires accurate anticipation of future consequences. By leveraging a world model, we can comprehensively evaluate possible futures to enhance performance. As shown in Table 4, our DriveX model, based on the re-implemented DiffusionDrive-C [38], boosts the overall PDMS to 84.5, achieving state-of-the-art performance among camera-only end-to-end driving models.
+
+# 4.3. Ablation Study
+
+In this section, we conduct a series of ablation studies on nuScenes [3] dataset to investigate the individual components of our DriveX framework. By default, we use an input image resolution of $256 \times 704$ for efficient training. All models are trained with a batch size of 32 on 32 GPUs.
+
+Omni scene modeling. We first ablate the effects of our omni scene modeling module through occupancy and flow prediction task. As presented in Table 5, DriveX captures only geometric information when supervised solely by depth estimation. Adding semantic supervision enriches the model's semantic understanding, achieving a mIoU of 42.53. However, since the semantic labels from auto-labeling inevitably suffer from information loss, incorporating color reconstruction preserves additional generalizable features, ultimately improving the mIoU to 43.47.
+
+Effect of prediction horizon. Table 6 verifies that the downstream performance gain stems from DriveX's predictive capability. As indicated in the $2^{nd}$ row, DriveX achieves significant improvements of $+0.9$ in mIoU and $-0.03$ in mAVE compared to the baseline without future prediction. While extending the prediction horizon to 4 frames brings further gains, we adopt 2 as the default setting to balance performance and computational cost.
+
+Decoupled training strategy. We ablate the effects of our decouple training strategy in Table 7. For a fair comparison, we train a joint training variant of our DriveX model for 64 epochs, matching the total training duration of the decoupled version. As shown in $1^{st}$ and $2^{nd}$ rows, our decoupled approach significantly improves prediction accuracy, reducing the Chamfer Distance by $0.44\mathrm{m}^2$ for 3.0s predictions. This validates that separating the world model into world encoding and latent future predicting leads to a better modeling of world evolution. Moreover, the integration of dynamic-aware ray sampling strategy enables the model to focus on motion-critical regions, further re
+
+| Sup-D | Sup-S | Sup-C | mIoU | IoUgeo | mAVE ↓ |
| ✓ | | | 3.96 | 59.7 | 1.388 |
| ✓ | ✓ | | 42.53 | 73.1 | 0.396 |
| ✓ | ✓ | ✓ | 43.47 | 73.44 | 0.385 |
+
+Table 5. Ablation study on components of omni scene modeling module. "Sup-D", "Sup-S" and "Sup-C" denote supervision from depth estimation, semantic segmentation, and color reconstruction, respectively.
+
+| Future frames | mIoU | IoUgeo | mAVE ↓ |
| 0 | 42.57 | 72.60 | 0.415 |
| 2 | 43.47 | 73.44 | 0.385 |
| 4 | 43.59 | 73.42 | 0.387 |
+
+Table 6. Effects of prediction horizon in FSA .
+
+| Joint | Decoupled | D-sample | Chamfer Distance (m2) ↓ |
| 1.0s | 2.0s | 3.0s | Avg. |
| ✓ | | | 1.09 | 1.41 | 1.75 | 1.41 |
| ✓ | | 0.83 | 1.03 | 1.31 | 1.06 |
| ✓ | ✓ | 0.80 | 0.99 | 1.28 | 1.02 |
+
+Table 7. Ablation study on decoupled training strategy. "D-Sample" refers dynamic-aware ray sampling.
+
+| Strategy | Chamfer Distance (m2) ↓ |
| 1.0s | 2.0s | 3.0s | Avg. |
| Autoregressive-pred | 0.99 | 1.21 | 1.76 | 1.32 |
| Direct-pred | 0.80 | 0.99 | 1.28 | 1.02 |
+
+Table 8. Comparison of autoregressive and direct prediction strategies for future state prediction.
+
+ducing the average Chamfer Distance to $1.02\mathrm{m}^2$ . Additionally, we compare direct prediction with autoregressive strategies for future decoding in Table 8, where direct prediction demonstrates superior performance, diminishing the average Chamfer Distance from $1.32\mathrm{m}^2$ to $1.02\mathrm{m}^2$ .
+
+# 5. Conclusion
+
+In this paper, we present DriveX, a self-supervised world model that learns generalizable scene dynamics and holistic representations from driving videos. DriveX introduces Omni Scene Modeling, unifying multimodal supervision for comprehensive scene understanding, and employs a decoupled latent modeling strategy to simplify the learning of complex dynamics. Additionally, we develop the Future Spatial Attention paradigm to enhance downstream task adaptability. Extensive experiments on the nuScenes and NAVSIM datasets demonstrate the effectiveness of our approach, paving the way for developing more practical and scalable world models in autonomous driving systems.
+
+# Acknowledgment
+
+This work is supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011434) and CCF-DiDi GAIA Collaborative Research Funds.
+
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+# Driving View Synthesis on Free-form Trajectories with Generative Prior
+
+Zeyu Yang $^{1*}$ Zijie Pan $^{1*}$ Yuankun Yang $^{1*}$ Xiatian Zhu $^{2}$ Li Zhang $^{1\dagger}$ $^{1}$ Fudan University $^{2}$ University of Surrey
+fudan-zvg.github.io/DriveX
+
+# Abstract
+
+Driving view synthesis along free-form trajectories is essential for realistic driving simulations, enabling closed-loop evaluation of end-to-end driving policies. Existing methods excel at view interpolation along recorded paths but struggle to generalize to novel trajectories due to limited viewpoints in driving videos. To tackle this challenge, we propose DriveX, a novel free-form driving view synthesis framework, that progressively distills generative prior into the 3D Gaussian model during its optimization. Within this framework, we utilize a video diffusion model to refine the degraded novel trajectory renderings from the in-training Gaussian model, while the restored videos in turn serve as additional supervision for optimizing the 3D Gaussian. Concretely, we craft an inpainting-based video restoration task, which can disentangle the identification of degraded regions from the generative capability of the diffusion model and remove the need of simulating specific degraded pattern in the training of the diffusion model. To further enhance the consistency and fidelity of generated contents, the pseudo ground truth is progressively updated with gradually improved novel trajectory rendering, allowing both components to co-adapt and reinforce each other while minimizing the disruption on the optimization. By tightly integrating 3D scene representation with generative prior, DriveX achieves high-quality view synthesis beyond recorded trajectories in real time-unlocking new possibilities for flexible and realistic driving simulations on free-form trajectories.
+
+# 1. Introduction
+
+Building virtual driving worlds capable of being engaged with driving policies plays a pivotal role in developing robust autonomous driving systems. It facilitates efficient training data scaling and automatic synthesis of safety-critical long-tail cases, while enabling close-loop evaluation
+
+for end-to-end autonomous driving systems.
+
+In recent years, the burgeoning advancements in novel view synthesis [12, 18] have propelled the prevalence of reconstruction-based driving simulations [3, 34, 35]. These methods aim to reconstruct driving environments from vehicle sensor data typically involving single-trajectory videos from surrounding cameras and synchronized LiDAR point clouds. However, the limited overlap between frames, large textureless regions and illumination variations in large-scale scenes, drastically complicate this task than conventional novel view synthesis. Consequently, despite achieving impressive results in fitting training views and interpolating along recorded trajectories, they still struggle to extrapolate on novel views far from the recorded trajectory, limiting their flexibility and usefulness in many downstream tasks.
+
+Recent works [15, 16, 37] have demonstrated that 2D generative priors can effectively regularize sparse-view reconstruction by synthesizing pseudo ground-truth images for novel view, thereby alleviating the under-constraint nature of this task. However, directly applying these approaches in the driving scenes presents unique challenges due to the limited diversity of trajectories in existing driving video datasets. The training is primarily confined on forward-moving trajectories, while the off-trajectory videos are required for inference. This will introduce a considerable gap, making it infeasible to learn precise explicit pose control, and posing a great challenge to simulate degraded patterns for training a restoration-based model.
+
+To address these challenges, we propose a reconstruction-generation interwined framework for driving view synthesis along free-form trajectories, termed DriveX, which progressively distills video generative prior into the 3D scene representation (i.e., 3D Gaussian Splatting [12]). During this process, a video diffusion model is employed to generate novel trajectory videos as additional supervision for the optimization of scene representation, effectively mitigating the sparse-view issue. This is achieved by leveraging a generative model to restore novel trajectory renderings from the in-training 3D Gaussian model, which ensures the consistency of generated content while eliminating the need for explicit pose condition. Specifically,
+
+
+Figure 1. Though conventional reconstruction-based approaches can well fit views on the recorded trajectory, they struggle to extrapolate onto the views beyond it (top). In contrast, our method significantly improves the synthesis quality on these novel trajectory views by incorporating generative prior (bottom), thereby achieving superior synthesis quality on free-form trajectories.
+
+
+
+
+
+
+
+we design an inpainting-based restoration task where generation is conditioned on the rendered video masked by a geometry-aware unreliability mask. This formulation allows the model to fully leverage its generative capability, freeing it from the task of identifying degraded regions, thus circumventing the complexity of simulating degraded patterns during its training. During the optimization of scene representation, we progressively perform the restoration process and update the generated pseudo ground truth to further enhance consistency of the generated content. As shown in Fig. 1, our approach substantially improves the view synthesis quality in the novel trajectory compared to the state-of-the-art reconstruction-only method [35].
+
+Our contributions are as follows: (i) We propose a novel driving view synthesis framework that seamlessly integrates generative prior into driving scene reconstruction, where a diffusion model is employed to progressively synthesize consistent novel view ground truth for regularizing the optimization of the 3D Gaussian model; (ii) By formulating an inpainting-based restoration task, we disentangle the identification of degraded regions from the generative capability of the diffusion model, thereby simplifying training on driving videos with limited diverse trajectories; (iii) Our DriveX effectively overcomes the sparse-view issue in previous street scene reconstruction methods, enabling high-fidelity view synthesis along free-form trajectories.
+
+# 2. Related works
+
+Reconstruction-based driving view synthesis Early approaches [25, 26, 31, 34, 36] for dynamic urban scenes reconstruction focus on extending neural radiance fields (NeRF) [18] in large scale unbounded scenes. These methods are restricted with low efficiency and blurry rendering performance. Recently, another line of works introduced 3D Gaussian splatting [12] into this task to produce real-time high-fidelity rendering. Some of them [35, 42] leverage its favorable explicit property to decouple the whole scene into the static background and moving foreground
+
+Gaussians, while others modeling the motion of 3D Gaussians with periodic functions [3] or deformation fields [10]. However, driving scenes featured with sparse views, little overlaps, and large textureless areas, making existing methods struggle to generalize to substantively novel views.
+
+Generative-based driving view synthesis. Recently, propelled by the significant advancement of the diffusion model [1, 8, 21-23], many works employ video generators to construct world models [13]. Some of them introduce this paradigm into autonomous driving [5, 6, 9, 14, 17, 28, 29, 41] for simulating the plausible visual outcomes under versatile driving controls. Despite the remarkable diversity of generated results, this approach is constrained by the absence of underlying 3D model. Consequently, they cannot promise geometry and texture consistency for the generated many-trajectory videos of the same scene.
+
+Scene reconstruction with diffusion prior Leveraging generative prior to enhance the reconstruction from sparse view observations [15, 16, 33, 37] has emerged. Extending this paradigm into driving scene reconstruction has been recently attempted [11, 38, 40]. Limited diversity of trajectory in driving scene data poses unique challenges for them. SGD [38] and VEGS [11] contribute to define and tackle pseudo and extrapolated view synthesis in driving scenarios. However, these methods may encounter challenges with accurate pose and detail estimation under novel trajectories. DriveDreamer4D [40] samples novel trajectory video based on single reference frame before training, risking hallucination and inconsistency due to insufficient constraints. StreetCrafter [39] refines the novel view renderings using a controllable video diffusion model guided by LiDAR projections. Meanwhile, FreeSim [4] and Di-fix3D+ [32] directly condition on degraded renderings and employ carefully data curation to train the generative model to adapt on degradation patterns resulted from off-trajectory renderings. In contrast, by crafting an inpainting-based video restoration task, we free the generative model from identifying degraded regions, thereby eliminating the need
+
+
+Figure 2. Schematic illustration of DriveX. Top: Optimizing the scene representation with both recorded trajectory views and generated novel trajectory views as supervision. Bottom: Generative prior integration. During optimization, given a novel view rendering from in-training Gaussian $\mathcal{G}_t$ , a video diffusion model is employed to generate a restored version as pseudo ground truth on novel trajectories, guided by its unreliability mask and accumulated LiDAR projections.
+
+to simulate specific degraded patterns in training.
+
+# 3. Methodology
+
+# 3.1. Preliminary: Driving scene reconstruction
+
+Reconstruction-based driving simulation aims to recover the surrounding scenes from calibrated video $\mathcal{V}_{\mathrm{gt}} = \{I_i\}_{i=0}^F$ recorded along a driving trajectory $\mathcal{T} = \{P_i\}_{i=0}^F$ , where $P_i \in \mathrm{SE}(3)$ is the camera pose at frame $i$ . Then the sensor data can be simulated under the unrecorded actions (e.g. lane change) in the reconstructed environment.
+
+Recently, due to the superior fidelity and efficiency of 3D Gaussian splatting (3DGS) [12], it has been widely employed in numerous street scene reconstruction efforts [3, 10, 35, 42] as a fundamental scene representation. 3DGS represents scenes as a set of 3D Gaussians, denoted $\mathcal{G}$ . The influences of each Gaussian primitive with position $\mathbf{x}_k \in \mathbb{R}^3$ and covariance $\boldsymbol{\Sigma} \in \mathbb{R}^{3 \times 3}$ on any position is given by an unnormalized Gaussian function $G_k(\cdot; \mathbf{x}_k, \boldsymbol{\Sigma})$ weighted by its opacity $o_k \in \mathbb{R}$ . Given any camera pose $P_i$ , it can be rendered by performing splatting and alpha blending on $N$ sorted Gaussians visible at this view:
+
+$$
+I ^ {\prime} = R (\mathcal {G}, P _ {i}) = \sum_ {k = 1} ^ {N} o _ {k} G _ {k} c _ {k} (P _ {i}) \prod_ {j = 1} ^ {k - 1} \left(1 - o _ {j} G _ {j}\right), \tag {1}
+$$
+
+where $R$ represents the differentiable Gaussian rasterizer, $I^{\prime}$ denotes the rendered image, $c_{k}$ is the view-dependent color of the $k$ -th Gaussian. Then the Gaussians $\mathcal{G}$ can be optimized via the photometric loss between rendered images $I_{i}^{\prime}$ and ground truth $I_{i}$ from recorded video $\mathcal{V}_{\mathrm{gt}}$ by:
+
+$$
+\mathcal {L} _ {\mathrm {i m g}} \left(I _ {i} ^ {\prime}, I _ {i}\right) = \lambda \| I _ {i} ^ {\prime} - I _ {i} \| _ {1} + (1 - \lambda) \mathcal {L} _ {\mathrm {S S I M}} \left(I _ {i} ^ {\prime}, I _ {i}\right), \tag {2}
+$$
+
+where $\mathcal{L}_{\mathrm{SSIM}}$ is the SSIM [30] loss and $\lambda$ is a weight.
+
+Following [35], we model the traffic participants in the driving scenes as a dynamic node in the neural scene graph with rigid motion, which can be regarded as static in their own local coordinate frames. The transformation from each object's local frame to the global coordinate frame of the whole scene is parameterized by a series of rotations and transformations, which can be annotated by their tracked bounding boxes. Additionally, cube map is employed to model the sky with infinite distance [3, 35].
+
+Challenges Since the camera configuration in autonomous vehicles is primarily designed for perception tasks, the captured videos often offer limited viewpoints, minimal overlap, and large textureless regions. These inherent properties bring challenges to the reconstruction of the unbounded driving scenes from single-trajectory videos. Fitting the training views at recorded trajectory $\mathcal{T}$ is insufficient to realize satisfactory extrapolation out of $\mathcal{T}$ for novel view synthesis. As a result, existing optimization-based driving scene synthesis approaches struggle to achieve high-quality rendering along novel trajectories $\mathcal{T}' = \{P_i'|P_i'\notin \mathcal{T}\}_{i = 0}^F$ , often leading to obvious degeneration and artifacts.
+
+# 3.2. Novel view regularization with generative prior
+
+Generate consistent novel view via video restoration A promising solution to the aforementioned challenges is to incorporate generative priors as an additional regularization. Large video generative models trained on internet-scale data have developed a strong knowledge of natural video distributions, enabling them to reliably infer and generate novel view content as pseudo ground truth for optimizing 3DGS. To ensure consistency between the generated content and the underlying scene, thereby preventing disruption to optimization, the generation should be appropriately conditioned on the in-training Gaussian model.
+
+Algorithm 1 Iterative refinement
+Require: Initial Gaussian model $\mathcal{G}_0$ , novel trajectories $\mathcal{T}'$ , video diffusion $\mathcal{D}$ , total steps $T$ , warm up steps $T_0$
+1: for $t = 0, \dots, T - 1$ do
+2: $\mathcal{V}_t \gets \{R(\mathcal{G}_t, P_i)\}_{i=0}^F$
+3: Computing loss $\mathcal{L}_{\mathrm{img}}(\mathcal{V}_t, \mathcal{V}_{\mathrm{gt}})$
+4: if $t \geq T_0$ then
+5: $\mathcal{V}_t' \gets \{R(\mathcal{G}_t, P_i')\}_{i=0}^F$
+6: if $(t - T_0) \mod K = 0$ then
+7: $k \gets t$
+8: $\mathcal{V}_{k,\mathrm{refine}}' \gets \mathcal{D}(\mathcal{V}_t', \mathcal{M})$
+9: end if
+10: Computing loss $\mathcal{L}' \gets \mathcal{L}_{\mathrm{img}}(\mathcal{V}_t', \mathcal{V}_{k,\mathrm{refine}}')$
+11: end if
+12: Backwarding loss and updating $\mathcal{G}_{t+1}$
+13: end for
+14: return $\mathcal{G}_T$
+
+To achieve this, we delicately design a video restoration task, which is formulated as recovering clean novel view images $\mathcal{V}$ from the artifact-heavy novel view renderings $\mathcal{V}'$ beyond the recorded trajectory. Within this design, a video generative model can be employed to address this problem effectively. The refined video then serves as additional supervision in the optimization of 3DGS.
+
+Concretely, given a sequence of viewpoints $\mathcal{T}' = \{P_i'\}_{i=0}^F$ along a novel trajectory, a video diffusion model $\mathcal{D}$ is employed to estimate clean version $\mathcal{V}_i$ :
+
+$$
+\mathcal {V} _ {t} ^ {\prime} = \left\{R \left(\mathcal {G} _ {t}, P _ {i} ^ {\prime}\right) \right\} _ {i = 0} ^ {F}, \tag {3}
+$$
+
+$$
+\mathcal {V} _ {t, \text {r e f i n e}} ^ {\prime} = \mathcal {D} \left(\mathcal {V} _ {t} ^ {\prime}\right), \tag {4}
+$$
+
+$$
+\mathcal {L} ^ {\prime} \triangleq \mathcal {L} _ {\mathrm {i m g}} \left(\mathcal {V} _ {t} ^ {\prime}, \mathcal {V} _ {t, \text {r e f i n e}} ^ {\prime}\right), \tag {5}
+$$
+
+where $\mathcal{V}_t^\prime$ is rendered from the Gaussian model $\mathcal{G}_t$ at $t$ -th iteration of optimization through Eq. (1), the refined video $\mathcal{V}_{t,\mathrm{refine}}^{\prime}$ can be regarded as the estimation of $\mathcal{V}$ . Typically, $\mathcal{D}$ takes noise-perturbed images as input, conditioned on the degraded video, and outputs the refined video $\mathcal{V}_{t,\mathrm{refine}}^{\prime}$ . Then $\mathcal{V}_{t,\mathrm{refine}}^{\prime}$ is used as the pseudo ground truth in the novel trajectory loss $\mathcal{L}^{\prime}$ (Eq. (5)) to supervise the novel view renderings as illustrated in Fig. 2.
+
+Iterative refinement The generative model can be employed to provide novel view supervision for enhancing the novel view renderings. In turn, the generation quality also benefits from these improvements, as it is conditioned on $\mathcal{G}_t$ whose enhancements could provide more accurate information to guide the generation process. This co-adapt and reinforced enhancement motivates an iterative refinement in our framework. As outlined in Algorithm 1, we initiate the optimization for $T_0$ steps using conventional reconstruction-based method [35]. Subsequently, we perform video restoration in Eq. (4) based on the in-training
+
+Gaussians $\mathcal{G}_{T_0}$ , and use a buffer to store refined videos for reuse in the following $K$ iterations. To ensure that the generated content can be improved along with the progressively optimized reconstruction results, we update all videos in the buffer every $K$ iterations by performing video restoration conditioned on the latest novel trajectory renderings.
+
+Due to the additional time demands of running the video diffusion model, it is inefficient to set $K = 1$ , i.e., the buffer is updated in every iteration. We set it to 3000 to strike the balance between quality and efficiency. Please refer to Sec. 4.4 for the trade-off between different choice of $K$ . As the generated contents are conditioned on Gaussian model $\mathcal{G}_t$ , they are constrained with the recorded scene, thus ensuring the consistency between the recorded and generated ground truth and leading to stable optimization.
+
+Novel trajectory sampling Another important design space is how to sample the novel trajectory $\mathcal{T}' = \{P_i'\}_{i=0}^F$ to be distilled by video diffusion model. The ideal trajectory should balance the two requirements: (i) maximizing the utility of the generative model, i.e., the generated novel views should contribute as much as possible to enhance reconstruction quality; (ii) minimizing inconsistency between the recorded and generated images to mitigate potential perturbation for Gaussian's optimization. Therefore, we adopt a panning camera trajectory that starts from a recorded front view $P_0' = [R_0|T_0]$ and gradually shifts laterally:
+
+$$
+P _ {i} ^ {\prime} = \left[ R _ {0} \right| \frac {i}{F} s \mathbf {v} + T _ {0} ], \tag {6}
+$$
+
+where $\mathbf{v} \in \mathbb{R}^3$ is the shifting direction, and $s \in \mathbb{R}$ controls the maximum shifting length. This design not only provides novel views beyond the recorded trajectory, but also allows video generation model to extract detailed references from the initial frame. At the early stage of optimization, rendering quality may degrade as the camera deviates from the recorded driving trajectory, which offers limited guidance for the video generation. To address this issue, we initially use a small shifting length $s$ and progressively extend it during optimization, ensuring our method's stability and robustness across diverse scenes.
+
+# 3.3. Inpainting-based video restoration
+
+Under the proposed trajectory sampling scheme with progressively increasing shifted length, degradations in the rendered video caused by the poor extrapolation capabilities of the scene representation are typically localized. Therefore, the key to effective video restoration lies in accurately identifying the artifacts in the rendered videos. Ideally, a well-trained generative model should be capable of automatically identifying and restoring these degraded regions. However, limited viewpoints in driving video datasets make it challenging to simulate degradation caused by off-trajectory rendering while obtaining corresponding ground truth during the training of the generative model. Therefore, we
+
+propose an inpainting-based restoration framework that removes the need for the model to adapt to specific degraded patterns, thereby simplifying the training process.
+
+Specifically, we construct an unreliability mask representing the artifacts via comparing the rendered images with the recorded images, which directly guides the model to focus on refining these unreliable regions while preserving reliable areas. Thus, the Eq. (4) should be revised as:
+
+$$
+\mathcal {V} _ {t, \text {r e f i n e}} ^ {\prime} = \mathcal {D} \left(\mathcal {V} _ {t} ^ {\prime}, \mathcal {M}\right), \tag {7}
+$$
+
+where $\mathcal{M}$ is the mask indicating unreliable regions, and $\mathcal{D}$ is conditioned on the masked video.
+
+Unreliability mask To assess geometry accuracy in novel view rendered images, we derive $\mathcal{M}$ by comparing the rendered images with novel view warped images from the recorded trajectory. Let $I_{\mathrm{ren}} \in \mathcal{V}_t'$ denote a rendered image, and let $I_{\mathrm{rec}}$ represent the recorded image that are "closest" to $I_{\mathrm{ren}}$ . We define a warping operation $\psi$ in Eq. (8) to project a 3D point $p$ onto the image plane given camera pose $P$ :
+
+$$
+(x, y, d) = \psi (p | P), \tag {8}
+$$
+
+where $x, y$ represent the pixel coordinates, and $d$ is the depth (Please refer to Appendix B for details). Note that the refined video starts from a front view on the recorded trajectory, which is selected as the "closest" image for all refined views in the video. Notably, $\psi$ is invertible, allowing us to unproject an image with its corresponding depth map back to 3D points given the camera pose. Consequently, we can obtain a pseudo image $\hat{I}_{\mathrm{ren}}$ under the pose $P_{\mathrm{ren}}$ by sampling the color in $I_{\mathrm{rec}}$ using the warped pixel coordinates $(\mathbf{x}, \mathbf{y}, \mathbf{d})$ from unwarped $I_{\mathrm{ren}}$ to $I_{\mathrm{rec}}$ , as expressed by Eq. (9).
+
+$$
+(\mathbf {x}, \mathbf {y}, \mathbf {d}) = \psi (\psi^ {- 1} (D _ {\mathrm {r e n}} | P _ {\mathrm {r e n}}) | P _ {\mathrm {r e c}}), \tag {9}
+$$
+
+where $D_{\mathrm{ren}}$ is the depth map corresponding to $\hat{I}_{\mathrm{ren}}$ rendered by $\alpha$ -blending each Gaussian center's depth. Since it is hard to guarantee the pixel-wise correspondence between $I_{\mathrm{ren}}$ and $\hat{I}_{\mathrm{ren}}$ , we choose SSIM to evaluate similarity at the patch-structure level. The unreliability mask $\mathcal{M}$ is then obtained by applying a threshold $\tau$ to SSIM score:
+
+$$
+\mathcal {M} = \mathbb {1} \left(\operatorname {S S I M} \left(I _ {\text {r e n}}, \hat {I} _ {\text {r e n}}\right) < \tau\right). \tag {10}
+$$
+
+Because the warping process involves both rendered depth and rendered image, the discrepancy can serve as an indicator of geometric or appearance unreliability.
+
+Since the warped image provides a rough overview of the novel trajectory, making it unnecessary to start denoising from scratch when we refine the videos using Eq. (7). Hence, we perturb warped videos by adding Gaussian noise at some noise level. This not only reduces unnecessary time costs but also avoids color shifts by preserving accurate low-frequency components in original video. Because
+
+autonomous vehicles are typically equipped with surround-view cameras, we include side view on recorded trajectory in the same frame as the auxiliary source images, which is also warped using equation (9) to the regions that are invisible by the front view to ensure well-defined unreliability masks for all areas of the novel view.
+
+Since the sparse depth ground truth in the novel view can be derived from LiDAR measurements, the Gaussian model performs better in depth rendering than in color rendering under novel view, even in the presence of overfitting. This allows the warped images to serve as a reliable anchor for indicating the reliability.
+
+Projected LiDAR as auxiliary condition Additionally, we also utilize colored LiDAR projections as an oracle to guide the generative process. For each novel view requiring restoration, LiDAR points projected onto it are accumulated from its adjacent $\pm 2$ frames, where points belonging to moving objects are aligned to the rendered frame based on their tracked poses. This empirically stabilizes the optimization, especially for those challenging scenes where rendered novel views struggle to provide reliable information in the early optimization. In light of the importance of novel view depth supervision within this framework, we additionally use the accumulated LiDAR point cloud as the depth ground truth for novel views.
+
+# 3.4. Training of generative model
+
+One remaining question is how to obtain a generative prior capable of handling the restoration task in Eq. (7). Due to the limited trajectory in existing driving datasets, precisely simulating degradation in novel trajectory views caused by overfitting has an inherent challenge. Fortunately, our inpainting approach can mitigate this issue by disentangling the degraded pattern from the condition, avoiding the necessity to simulate degraded rendering during training and freeing the model from identifying potential degradations.
+
+Specifically, we employ an edge-aware strategy to generate unreliability masks for the training data. This leads to a more general task which can cover scenarios typically encountered during off-trajectory rendering. Given a RGB image, we first convert it into grayscale. Then its directional derivatives computed using Sobel filters, as the edge intensity at each pixel. The resulting intensity map is normalized to yield a probability distribution over the pixels after adding a baseline offset for background regions. Then a predefined number of pixels is randomly sampled based on the distribution. For each sampled pixel, a $3 \times 3$ patch centered at the pixel is masked out to imitate the structured occlusion. Both front and side-view camera videos are used in training. Because the trajectory of the side-view camera along the moving forward trajectory is similar to the lateral shift of the front cameras adopted in our novel trajectory sampling, as suggested by [4, 27].
+
+
+Figure 3. Qualitative comparisons on novel trajectories. For each method, images are rendered at the novel views with lateral shift of $3m$ to the recorded trajectories.
+
+While there remains a gap between training and inference, it does not substantially hinder the usage. This is because the training process primarily aims at unleashing the generative capability of the diffusion model to adapt on such a masked image inpainting task, rather than fitting specific mask patterns. Actually, even [37] trained only on rendered point clouds can also serve as a competent generative prior for the crafted inpainting-based restoration task. While finetuning the model on driving videos can further adapt it to the style of driving scenarios, thereby significantly improving its robustness as demonstrated in Sec. 4.4.
+
+# 4. Experiments
+
+# 4.1. Experimental setup
+
+Datasets We evaluate our framework and train the diffusion model on driving sequences from large-scale Waymo Open Dataset (WOD) [24]. Each sequence comprises surrounding videos and synchronized LiDAR point clouds capture at $10\mathrm{Hz}$ . For training, we use all sequences from its training and validation set. The quantitative evaluation is conducted on 18 selected sequences, each containing 40 frames. Official bounding boxes are used to crop the point
+
+cloud of dynamic traffic participants and initialize their per-frame pose. For fair comparison, all images are downsampled into $640 \times 960$ in both training and evaluation. More details can be found in Appendix B.
+
+Metrics We evaluate the view synthesis quality on both recorded and novel trajectories. For recorded trajectory, we follow the common practice of reporting the PSNR and SSIM on these views. The test views are held out from every 5 frames. For novel trajectory views, since the ground truth is unavailable, it is infeasible to directly assess the pixel-level fidelity. Therefore, we devised a novel benchmark to comprehensively evaluate the synthesis results at these views. Specifically, the Fréchet Inception Distance (FID) [7] between synthesized views in novel trajectories and the captured images from the original trajectories is employed to assess the realism of synthesized images at the distribution level. Moreover, we report Lane IoU and vehicle AP (Refer to Appendix B for these calculations.) to evaluate the distinguishability and fidelity of two safety-critical high-level traffic components, i.e., road lanes and vehicles, in novel trajectory viewpoints.
+
+Implementation details For the reconstruction with calibrated camera images and LiDAR point clouds, we first
+
+ | ±0m (recorded) | ±1m | ±2m | ±3m | FPS |
| PSNR↑ | SSIM↑ | IoU↑ | AP↑ | FID↓ | IoU↑ | AP↑ | FID↓ | IoU↑ | AP↑ | FID↓ |
| EmerNeRF [36] | 29.60 | 0.8459 | 0.1147 | 0.5101 | 89.43 | 0.0881 | 0.4644 | 102.98 | 0.0735 | 0.4072 | 122.83 | 0.12 |
| S3Gaussian [10] | 29.68 | 0.8670 | 0.0718 | 0.4499 | 115.67 | 0.0401 | 0.4127 | 131.26 | 0.0177 | 0.3812 | 162.03 | 8.4 |
| PVG [3] | 29.98 | 0.8627 | 0.1082 | 0.5444 | 51.86 | 0.0291 | 0.5102 | 86.93 | 0.0170 | 0.4699 | 123.53 | 48 |
| StreetGaussian [35] | 29.76 | 0.8738 | 0.2671 | 0.5919 | 51.87 | 0.2122 | 0.5848 | 70.66 | 0.1720 | 0.5697 | 93.04 | 34 |
| DriveX (ours) | 29.74 | 0.8700 | 0.2880 | 0.5932 | 46.91 | 0.2710 | 0.5901 | 65.52 | 0.2699 | 0.5712 | 79.78 | 34 |
+
+Table 1. Quantitative evaluation on Waymo dataset [24]. We compare images rendered in novel trajectories with different shift lengths, where the IoU and AP are computed between the projected ground truth and those detected on synthesized views by perception models [2, 20]. The inference speeds of all methods are measured on the NVIDIA RTX A6000 GPU.
+
+
+Figure 4. Qualitative comparisons with methods incorporating generative model. The results of DriveDreamer4D [40] and ReconDreamer [19] are downloaded from their project pages. The result of FreeVS [27] is obtained by running its official released code. Compared to other alternatives, our method can more effectively harness the generative prior, significantly reducing hallucinations.
+
+initialize the scene representation [35] by optimizing on the recorded data for $T_0 = 50,000$ steps and then integrate generative priors for following 30,000 steps. For the generation of novel trajectory videos, the initial view $P_0'$ of a novel trajectory $\mathcal{T}'$ is selected from every 3 frames, with shifting length $s$ ranging from $2m$ to $6m$ . The generative model is initialized from [37], and then fine-tuned on WOD [24] for 15,000 iterations with batch size of 24 using 8 RTX A6000 GPUs. During the iterative refinement, the buffer for storing refined videos is updated every $K = 3000$ steps. The refine strength (i.e. the level of noise adding to images) is set to 0.6. The threshold $\tau$ in Eq. (10) is set to 0.65.
+
+# 4.2. Main results
+
+In Tab. 1, we quantitatively compared DriveX with several representative baselines in terms of view synthesis quality and rendering speed. For extrapolated novel views, we synthesized driving videos laterally shifting from the recorded trajectories by $\pm 1m$ , $\pm 2m$ and $\pm 3m$ . The result demonstrates our significant improvement on FID, AP and IoU, surpassing the leading reconstruction-based counterpart [35] with a $14.3\%$ decrease in FID and $56.9\%$ increase
+
+in IoU under the $3m$ shifting length. These enhancements are visually corroborated in Fig. 3, where our approach demonstrates robust rendering quality under large trajectory deviations, where safety-critical scene elements can be more clearly recognized in novel views by incorporating generative priors. Notably, once trained, our model solely relies on the 3DGS for inference, enabling efficient rendering speed. For views on recorded trajectories, our method also achieves comparable performance with the baseline. The slightly lower metrics often result in perceptually negligible impact on synthesized quality. This further indicates our method can seamlessly integrate generative prior by effectively minimizing inconsistencies of generated content.
+
+# 4.3. Comparison with methods incorporating generative prior
+
+In previous section, we compared our methods with popular reconstruction-based approaches as the main results because it is directly built upon these reconstruction-based solutions and primarily aims to address the view extrapolation challenge for them. Although there are some concurrent works [4, 19, 27, 39, 40] sharing a similar scope
+
+
+(a) Ablation on unreliability mask
+
+
+(b) Ablation on iterative refinement
+Figure 5. Ablations on (a) unreliability mask and (b) iterative refinement. (a) shows the initial restored results without (middle left) and with (middle right) unreliability mask (top right). The final rendered results exhibit significant artifacts without mask (bottom left). (b) shows the rendered (top) and restored results at iteration $T_{0}$ (middle left) and $T$ (middle right). It can be seen that single-time refinement can not completely eliminate artifacts (as shown in orange boxes), resulting in inferior final results compared to iterative refinement (bottom). Best viewed with zoom-in.
+
+ | Lane change | Lane shift ±3m |
| NTA-IoU↑ | NTL-IoU↑ | NTA-IoU↑ | NTL-IoU↑ |
| DriveDreamer4D [40] | 0.495 | 53.42 | 0.340 | 51.32 |
| ReconDreamer [19] | 0.554 | 56.63 | 0.539 | 54.58 |
| DriveX (ours) | 0.620 | 58.60 | 0.567 | 58.29 |
| Lane shift ±1m | Lane shift ±3m |
| IoU↑ | AP↑ | IoU↑ | AP↑ |
| FreeVS [27] | 0.2782 | 0.5777 | 0.2723 | 0.5688 |
| DriveX (ours) | 0.2880 | 0.5932 | 0.2699 | 0.5712 |
+
+Table 2. Comparison with methods using generative model. All results are averaged from 8 sequences used in [40]. For lane change, the NTA-IoU and NTL-IoU are evaluated under setting in [19, 40], and we report the best results of [19, 40] from their original paper. lane shift is computed in the same way as our main paper. For FreeVS [27], we run its official released model and measure the results on the same sequences, note that its cropped image size does not essentially impact the results.
+
+with ours, most of them have not released code until our paper submission. Despite that, we try our best to compare with those allowing for a reasonable comparison and report the results in Tab. 2. The results indicate that our method performs better than other alternatives, which is also confirmed by qualitative results in Fig. 4. Compared to DriveDreamer4D [40], our approach substantially eliminates hallucinations and inconsistencies caused by insufficient constraints. Unlike generative-only approach FreeVS [27], our method maintains continuous 3D scene representation, enabling synthesized views to preserve superior detail fidelity and better consistency across frames than those only relying on sparse LiDAR signal. Moreover, our method has significantly faster synthesis speed (34 FPS vs. 0.43 FPS).
+
+# 4.4. Ablation study
+
+Unreliability mask The unreliability mask is designed to guide the generation of video diffusion by directly in-
+
+ | IoU↑ | AP↑ | FID↓ |
| mask all | 0.2153 | 0.6334 | 102.69 |
| w/o mask | 0.2193 | 0.6341 | 76.26 |
| w/ mask | 0.2263 | 0.6389 | 74.34 |
+
+Table 3. Effects of unreliability mask. "mask all", "w/o mask", and "w/ mask" denotes the threshold $\tau$ in Eq. (10) set to 1.0, -1.0, and 0.65, respectively.
+
+| Buffer interval | IoU↑ | AP ↑ | FID↓ | Time↓ |
| 500 | 0.2271 | 0.6392 | 75.33 | 4.8× |
| 3,000 | 0.2263 | 0.6389 | 74.34 | 1.6× |
| 6,000 | 0.2228 | 0.6388 | 75.98 | 1.3× |
| Inf | 0.2194 | 0.6173 | 89.06 | 1.0× |
+
+Table 4. Ablations on buffer intervals. "Inf" denotes the novel trajectory supervision only generated one time at iteration $T_0$ . dicating where the model needs to be retained or repaired. From Tab. 3 and Fig. 5(a) we can observe: (i) When all regions are masked, the video diffusion model can only rely on sparse LiDAR projections as condition, leading to inferior results due to the inability to fully leverage information from the in-training Gaussian representation; (ii) When the mask is disabled, the generative model can still refine the rendered results toward the learned video distribution, but usually with too conservative refinement (it also indicates that the model does not strictly follow the given mask during inpainting); (iii) Equipped with the proposed unreliability mask, our full model achieves superior performance in both quantitative and qualitative ablation.
+
+Iterative refinement The interval of iterative refinement offers the trade-off between quality and efficiency. When the novel trajectory supervision only generated once time at iteration $T_0$ (see Fig. 5(b)), the quality of the novel view is constrained to the in-training Gaussian model, which is overfitted on the recorded trajectory. To the other extreme, we are unable to afford the time cost of running the diffusion at every step. From Tab. 4, it can be seen that even a small interval 500 leads to $4.8 \times$ training time. Hence we finally set the interval to 3,000 to strike the balance.
+
+# 5. Conclusion
+
+In this paper, we present a novel framework that integrates generative priors into the reconstruction of the driving scene from single-trajectory recorded videos, addressing limitations in extrapolating novel views beyond a recorded trajectory. To reasonably leverage the video generative model to provide consistent novel view supervision, we construct a tailored inpainting-based video restoration task to refine the novel view renderings for optimizing the street scene representation. The experiments demonstrate that the proposed method significantly improves the synthesis quality for novel trajectories. These results pave the new way for driving scene synthesis on free-form trajectories.
+
+# Acknowledgments
+
+This work was supported in part by National Natural Science Foundation of China (Grant No. 62376060).
+
+# References
+
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+# DrivingGPT: Unifying Driving World Modeling and Planning with Multi-modal Autoregressive Transformers
+
+Yuntao Chen $^{3}$ Yuqi Wang $^{1,2}$ Zhaoxiang Zhang $^{1,2}$
+
+1 New Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences
+
+$^{2}$ School of Artificial Intelligence, University of Chinese Academy of Sciences
+
+$^{3}$ HKISI, CAS
+
+Project page: https://rogerchern.github.io/DrivingGPT
+
+
+Figure 1. Driving as next token prediction. Our DrivingGPT treat interleaved discrete visual and action tokens of a driving sequence as a unified driving language and leverage multimodal autoregressive transformers to simultaneously perform world modeling and end-to-end planning by standard next token prediction given historical driving tokens. The red rectangle in planning denotes the ego car and the blue line is the generated trajectory while the brown line is the human driving trajectory.
+
+# Abstract
+
+World model-based searching and planning are widely recognized as a promising path toward human-level physical intelligence. However, current driving world models primarily rely on video diffusion models, which specialize in visual generation but lack the flexibility to incorporate other modalities like action. In contrast, autoregressive transformers have demonstrated exceptional capability in modeling multimodal data. Our work aims to unify both driving model simulation and trajectory planning into a single sequence modeling problem. We introduce a multimodal driving language based on interleaved image and action tokens, and develop DrivingGPT to learn joint world modeling and planning through standard next-token prediction. Our DrivingGPT demonstrates strong performance in both action-conditioned video generation and end-to-end planning in the VQ token space for the first time, outperforming strong baselines on large-scale nuPlan and NAVSIM benchmarks.
+
+# 1. Introduction
+
+Driving world models [19, 27, 31, 61, 64, 75] have gained significant attention as model-based searching and planning are widely considered essential paths toward human-level physical intelligence [34]. These models serve multiple purposes, including training data augmentation, rare scenario generation, and contingency planning. Most current world models are developed by fine-tuning existing diffusion models [1, 47], leveraging the generalization capabilities of video generation foundation models. Control signals—such as text, layout, and driving maneuvers—are incorporated through two main approaches: cross-attention between spatial features of diffusion models [36] and control signal features, or channel-level feature modulation techniques like AdaLN [43] and FiLM [44].
+
+Despite advances in driving world models, a fundamen
+
+tal challenge persists: the seamless integration of world modeling and planning in a differentiable framework remains largely unresolved, thereby limiting the full potential of differentiable model-based planning. World models currently base primarily on video diffusion architectures, limiting their ability to generate multiple modalities such as text and action sequences. As a result, achieving true end-to-end integration of driving planning and world modeling within the diffusion model framework continues to be a significant technical challenge. These limitations motivate us to explore alternative architectures that naturally handle multi-modal inputs and outputs and enable end-to-end differentiable planning.
+
+In contrast to diffusion models, autoregressive transformers with next-token prediction training targets have demonstrated exceptional modeling ability in a wide range of tasks tasks including language modeling [5, 16, 54, 59], visual question answering [39, 60], image generation [42, 46, 50, 58, 73], video prediction [20, 62, 69, 70], sequential decision making [9, 48] and robot manipulation [3, 4, 8, 41]. The natural ability of autoregressive transformers to handle sequential data and multiple modalities makes them particularly promising for integrated model-based driving planners.
+
+In this work, we aim to leverage the modeling capabilities of autoregressive transformers for both world modeling and trajectory planning in driving tasks. Specifically, we formulate visual driving world modeling and end-to-end driving trajectory planning as a unified sequence modeling problem. We transform driving video frames into discrete tokens using pretrained VQ-VAEs [58]. Similarly, we convert driving trajectories into frame-to-frame relative actions, which are then quantized into discrete bins. We design a multi-modal driving language by unifying the image and action vocabularies, interleaving image and action tokens on a frame-by-frame basis. We use a Llama-like DrivingGPT architecture with frame-wise 1D rotary embeddings [49] to model the multi-modal driving language through standard next token prediction. Our DrivingGPT demonstrates strong performance for both world modeling and planning tasks while using 1/100 computation and data of previous methods like GAIA-1 [27]. In terms of video generation, our method surpasses the strong SVD baseline [1], outperforming it in metrics such as FID and FVD. Additionally, since video generation in DrivingGPT is jointly trained with the planning task, our approach exhibits a more accurate understanding of action conditions when generating long-horizon videos, as shown in Figure 3. Experiments on the challenging NAVSIM benchmark [15] further demonstrate the effectiveness of the proposed multi-modal driving language as a training target for planning and shows comparable performance with state-of-the-art planners [37]. Our DrivingGPT outperforms the prevalent visual encoder with an MLP trajectory decoder planner in terms of driving scores.
+
+In summary, our key contributions are as follows:
+
+- We propose a multi-modal driving language that unifies the visual world modeling and the trajectory planning problems into a sequence modeling task.
+- We design a DrivingGPT model that successful learns these two tasks via next token prediction simultaneously for the first time in driving.
+- Our DrivingGPT shows strong performance against established baselines both for action-conditioned video generation and end-to-end planning on large-scale real-world nuPlan and NAVSIM datasets.
+
+# 2. Related Works
+
+# 2.1. World Models for Autonomous Driving
+
+World models [23, 24, 34] have gained significant attention in autonomous driving, aiming to predict different future states based on actions. Existing work primarily focuses on generation, whether in 2D video forecasting [19, 27, 31, 61, 63, 64, 71] or 3D spatial predictions [21, 66, 75-77]. Among these, visual modeling has received considerable attention due to its richer and more human-like representational forms. Drive-WM [64] further explores the use of future visual feedback to guide an end-to-end planner. Except GAIA-1 [27] which features an autoregressive next visual token predictor with an additional diffusion image decoder, most of the previous works build on the diffusion models [1, 47]. Although diffusion models have achieved more realistic visual qualities, they still face challenges regarding temporal consistency and longer video generation. Moreover, no previous world modeling works have explored the joint prediction of action and vision modalities. In this paper, we explore autoregressive multimodal prediction, unifying planning and video generation within a single model that can simultaneously output predictions of future states and actions.
+
+# 2.2. Generation with Autoregressive Models
+
+Early works explored the direct autoregressive generation of images at the pixel level [56, 57]. Inspired by VQVAE [58], many methods [18, 35, 74] have encoded continuous images into discrete tokens. Recently, several approaches have drawn on the success of the next-token prediction paradigm used in large language models [54], applying it to image and video generation. In image generation, LlamaGen [50] employs a language model architecture to demonstrate that simple next-token prediction can produce high-quality images. Additionally, VAR [53] adopts a next-scale prediction generation paradigm, distinguishing itself from the sequence modeling approach of traditional language models. In video generation, Loong [65] proposes progressive short-to-long training, exploring the auto-regressive generation of long videos. Meanwhile, VideoPoet [33], Chameleon [52], and Emu3 [62] focus on multi-modal generation, integrating language comprehension with visual generation through
+
+the use of discrete tokens. In this paper, we adopt the multimodal auto-regressive paradigm, and simultaneously output video generation and planning.
+
+# 2.3. End-to-end Autonomous Driving
+
+End-to-end autonomous driving [2, 10, 14, 29, 32, 45, 68] has gained significant attention for its ability to directly generate vehicle motion plans from raw sensor inputs. From the evaluation benchmark, existing methods can be categorized into open-loop and closed-loop settings. For closed-loop evaluations, A broad body of research [11-13, 26, 28, 30] conducts evaluations in simulators, such as CARLA [17], nuPlan [7] and Waymax [22]. Recently, developing end-to-end models on open-loop benchmarks has gained growing attention. On the nuScenes [6] benchmark, UniAD [29] introduces a unified framework that integrates multiple driving tasks and directly generates planning outputs. VAD [32] advances vectorized autonomous driving, achieving improved performance. PARA-Drive [67] designs a fully parallel end-to-end autonomous vehicle architecture, achieving state-of-the-art performance in perception, prediction, and planning, while also significantly enhancing runtime efficiency. SparseDrive [51] explores the sparse representation and proposes a hierarchical planning selection strategy. In this paper, unlike previous BEV-based planning frameworks, We have innovatively explored an autoregressive model paradigm trained using world models, and evaluate it in an open-loop setting on the NAVSIM benchmark [15].
+
+# 3. Driving as Next Token Prediction
+
+Autoregressive transformers trained for next-token prediction have demonstrated remarkable capabilities in diverse domains. In this work, we harness the power of autoregressive transformers for autonomous driving by combining world modeling and trajectory planning. Different from previous autoregressive world models like GAIA-1 [27], our approach converts both visual inputs and driving actions into a discrete driving language, enabling unified modeling through autoregressive transformers, as illustrated in Figure 2.
+
+# 3.1. Problem Formulation
+
+Like many other tasks, the driving problem can be formulated as a Markov Decision Process (MDP), which is a general mathematical framework for decision making in environments with partially random outcomes. An MDP comprises a state space $S$ that reflects all states of the ego vehicle and the environment, an action space $A$ , a random transition function $P(s_{t+1} | s_t, \boldsymbol{a}_t)$ that describes the probability distribution of all possible outcomes given the state and action at time $t$ , and a scalar reward function $R(s_{t+1} | s_t, \boldsymbol{a}_t)$ that shapes the optimal action to take under certain states. In most real-world applications, we can only perceive noisy observations $\boldsymbol{o}_t$ instead of the underlying states $s_t$ . There-
+
+fore, an observation probability function $Z(\boldsymbol{o}_t|\boldsymbol{s}_t)$ is introduced, and the MDP becomes a partially observable MDP (POMDP).
+
+Both the end-to-end policy $\pi (\pmb{a}_t|\pmb {o}_t)$ that predicts future trajectories and the observation space random transition function $P(\pmb{o}_{t + 1}|\pmb {o}_t,\pmb {a}_t)$ that models driving world dynamics are of great importance in autonomous driving. We seek to unify these two challenges into a single sequence modeling task.
+
+# 3.2. Multimodal Driving Sequence Modeling
+
+Inspired by natural language modeling, a general driving sequence could be represented as a series of time-synchronized observation-action pairs $\pmb{o}_1, \pmb{a}_1, \pmb{o}_2, \pmb{a}_2, \dots, \pmb{o}_t, \pmb{a}_t$ with a time horizon of $T$ . Here we need to tokenize both the observation $\pmb{o}_t$ and the action $\pmb{a}_t$ into discrete tokens and form a multimodal driving language before we leverage autoregressive transformers for next token prediction.
+
+Observation Tokenization To make our method simple, we only include the front camera image $\pmb{o}_i \in \mathbb{R}^{3 \times H \times W}$ in our observation space, leaving more advanced sensor setups like surrounding cemaras, LiDARs and IMUs for future exploration. Although pixel-level transformers [42] have shown great potential in modeling images, we still need to strike a balance between the information loss in image compression and the limited context length of transformers when dealing with long driving sequences. To incorporate more frames into our sequence modeling, we leverage VQVAE [18] for down-sampling images $\pmb{o}_i$ of shape $H \times W$ into image tokens $z_i = \{z_{ij} | j = 1, \dots, HW / S^2\}$ of shape $H / S \times W / S$ and of vocabulary size $D$ , here $z_{ij}$ denotes the $j$ -th token of the $i$ -th image.
+
+Action Tokenization What set our method apart from existing driving world modeling works is the ability to generate future driving actions. Unlike most end-to-end driving planners [29, 32] $\pi_{\theta}(\pmb{a}_{t:t+N}| \pmb{a}_{| Model | Type | Fine-tune Dataset | FVD↓ | FID↓ |
| SVD [1] | Diffusion | - | 483.76 | 27.80 |
| CogvideoX [72] | Diffusion | - | 848.87 | 31.78 |
| SVD [1] | Diffusion | navtrain | 227.54 | 24.03 |
| DrivingGPT | Autoregressive | navtrain | 142.61 | 12.78 |
+
+Planning Metrics. We evaluate end-to-end planning performance on the NAVSIM benchmark [15] and report the PDMS. The Predictive Driver Model Score(PDMS) is a combination of five sub-metrics: No At-Fault Collision (NC), Drivable Area Compliance (DAC), Time-to-Collision (TTC), Comfort (Comf.), and Ego Progress (EP). They provide a comprehensive analysis of different aspects of driving performance. All metrics are computed after a 4-second non-reactive simulation of the planner output. We measure the performance of end-to-end planning on the navmini split.
+
+World Modeling Metrics. The quality of video generation is assessed using the Frechet Video Distance (FVD) [55] and the Frechet Inception Distance (FID) [25]. We select 512 videos in the navtest for fast visual quality evaluation.
+
+# 4.3. Video Generation
+
+Comparison of Generated Videos on navtest. We provide the quantitative comparison with several methods on the navtest in Table 1. As many video models only release model weights, we compare our method with their publicly available models. We found that both SVD [1] and CogvideoX [72] tend to generate subtle movements, which results in poor performance in driving scenarios. To ensure a fair comparison, we fine-tune the SVD model on the navtrain set. Previous video models typically rely on diffusion-based approaches, while our method is a pioneer in autoregressive video generation. Notably, our model, trained from scratch, surpasses previous methods in video generation quality.
+
+Long Video Generation. One of the key advantages of autoregressive models is their ability to generate long-duration videos by effectively leveraging historical information, resulting in more coherent video generation. In this experiment, we selected 512 video clips, each containing more than 64 frames, from the navtest dataset for evaluation. While the SVD method struggles to maintain quality when generating longer sequences, as evidenced in Table 2, our method demonstrates a remarkable ability to produce high-quality long-term sequences. The fixed frame number training limitation of SVD leads to a significant drop in image and video quality for longer sequences. In contrast,
+
+our method consistently produces high-quality images and achieves a lower FVD score, indicating a more stable and superior performance.
+
+Moreover, compared to previous diffusion-based methods, our approach can generate more diverse and reasonable scenes. As shown in Figure 3, SVD fine-tuning methods often get stuck repeating past content when generating longer videos, such as being stuck at a red light for an extended period. In contrast, autoregressive methods exhibit significant advantages in generating long videos, leading to notable improvements in both scene content and video quality.
+
+Table 1. Video generation comparison on the navtest. Our model, trained from scratch, surpasses previous methods in video quality.
+
+| Model | Metric | 16 Frames | 32 Frames | 64 Frames |
| SVD | FID | 30.48 | 35.57 | 46.45 |
| FVD | 418.93 | 786.68 | 1079.28 |
| DrivingGPT | FID | 15.04 | 16.30 | 20.45 |
| FVD | 278.11 | 454.28 | 506.95 |
+
+Table 2. Long video generation comparison. The evaluation is conducted on the navtest set with 512 clips.
+
+Mitigating Object Hallucination. Beyond long video generation, another advantage of our method lies in its mitigation of object hallucination phenomena. As depicted in Figure 4, diffusion-based methods, due to their lack of historical information, often suffer from the sudden appearance (red box) and gradual disappearance (green box) of objects. In contrast, our autoregressive approach maintains superior consistency.
+
+# 4.4. End-to-end Planning
+
+Our DrivingGPT's ability to jointly predict future images and driving actions allows for end-to-end planning performance evaluation. To rigorously evaluate the performance of our planner, we choose the more challenging NAVSIM benchmark, which is curated to provide more diverse driving maneuvers than previous nuScenes and nuPlan benchmarks. Furthermore, in light of recent discussion [38] that using the ego status will provide too much privileged information to the planner, we deliberately choose to exclude it from our driving language. Following the NAVSIM setting [15], we condition on the past 2 seconds of observations and actions to predict 4-second future trajectories. As shown in Table 3, our DrivingGPT shows a non-trivial
+
+
+Figure 4. Object hallucination. Top: Diffusion-based methods often exhibit object hallucination phenomena. For instance, when comparing models fine-tuned with SVD, we observe the sudden appearance (red box) and gradual disappearance (green box) of objects. Bottom: In contrast, our autoregressive approach maintains better consistency.
+
+| Method | Input | Aux. Sup. | NC ↑ | DAC ↑ | TTC ↑ | Comf. ↑ | EP ↑ | PDMS ↑ |
| Constant Velocity | Pixels | No | 66.7 | 63.9 | 45.2 | 100.0 | 23.6 | 24.2 |
| ResNet-50 + MLP baseline | Pixels | No | 92.6 | 89.9 | 86.2 | 96.3 | 73.7 | 77.8 |
| Transfuser [13] | Pixels | Yes | 96.2 | 94.8 | 91.0 | 97.8 | 80.6 | 84.6 |
| LAW [37] | Pixels | No | 93.3 | 94.5 | 87.7 | 97.7 | 79.3 | 82.7 |
| DrivingGPT | VAE tokens | No | 98.9 | 90.7 | 94.9 | 95.6 | 79.7 | 82.4 |
+
+advantage over a constant velocity baseline and a simple yet solid end-to-end planner baseline implemented with a ResNet-50 visual encoder and an MLP trajectory decoder. Despite using less informative VQ-VAE tokens as the visual input, our method achieves performance comparable to state-of-the-art planners, including LAW [37], when compared with approaches that do not rely on intermediate supervision. All baselines only uses the front-camera image and make no use of ego status as well. The results highlight the potential for jointly learning world modeling and the planning given considering that our DrivingGPT could only learn representation by reconstructing highly compressed image tokens of the driving environment. We demonstrate trajectories generated under challenging driving scenes by DrivingGPT in Figure 5.
+
+# 4.5. Ablation Study
+
+Comparison of Different Visual Tokenizers. The quality of the visual tokenizer significantly impacts the upper bound of the world model's visual prediction quality. As shown in Table 4, we evaluate several state-of-the-art discrete visual tokenizers on the navtest (NAVSIM test set), a dataset comprising 12,146 video samples. Based on our evaluation, we select LlameGen [50] as the optimal visual tokenizer for our world model.
+
+Table 3. End-to-end planning performance on the NAVSIM benchmark. We show the no at-fault collision (NC), drivable area compliance (DAC), time-to-collision (TTC), comfort (Comf.), and ego progress (EP) subscores, and the PDM Score (PDMS), as percentages. Transfuser results are not fair comparison with other baselines as auxiliary supervision are used.
+
+| Tokenizer | rFVD↓ | rFID↓ | PSNR↑ | SSIM↑ |
| Llama-Gen [50] | 68.40 | 5.67 | 23.09 | 0.652 |
| OpenMAGVIT2 [40] | 96.32 | 6.70 | 15.57 | 0.410 |
| Cosmos Tokenizer | 178.50 | 27.12 | 25.05 | 0.695 |
+
+Table 4. Comparison of different visual tokenizers. The evaluations are conducted on the navtest dataset with an image size of $512 \times 288$ , and a spatial downsampling rate of 16 is applied across all encoders.
+
+Does DrivingGPT Learn or Copy Planning Solutions? Autoregressive transformers are well-known as powerful fitting machines. In this section, we tries to answer the question that does DrivingGPT truly learn to drive or just cut corners by copying or extrapolating history driving maneuvers. We gradually replace the predicted actions(pred.) by DrivingGPT with future actions estimated solely from history actions. We simply copy the last history action as general driving trajectories do not involve any action input change. As shown in Table 5, our DrivingGPT consistently outperform all the variants that simply copy any $x$ , $y$ and $\theta$ history actions. One may notice that copying the previous longitudinal action $x$ gives the worst planning results which is due to that the NAVSIM benchmark contains a lot
+
+
+(a) Unprotected left turn
+
+
+(b) Large curvature turn
+
+
+(c) Merging into traffic
+Figure 5. DrivingGPT planning results in complex driving scenes: (a) Unprotected left turn; (b) Large curvature turn; (c) Merging into traffic; (d) Take better path than human. The red rectangle denotes the ego car, the blue line is the generated trajectory, and the brown line is the human driving trajectory.
+
+
+(d) Take better path
+
+| x | y | θ | NC↑ | DAC↑ | TTC↑ | Comf.↑ | EP↑ | PDMS↑ |
| pred | pred | pred | 98.9 | 90.7 | 94.9 | 95.6 | 79.7 | 82.4 |
| copy | pred | pred | 75.9 | 89.6 | 63.1 | 100.0 | 48.2 | 53.5 |
| pred | copy | pred | 97.8 | 88.4 | 90.6 | 94.7 | 76.2 | 79.4 |
| pred. | pred | copy | 95.8 | 81.8 | 88.1 | 94.6 | 70.7 | 73.1 |
+
+Table 5. Comparison of planning performance when replacing predicted actions with copied history actions for different action components. Here $x, y, \theta$ denotes the longitudinal, lateral and yaw components respectively. Pred stands for using DrivingGPT prediction and copy stands for using the action value of the last history frame. We show the no at-fault collision (NC), drivable area compliance (DAC), time-to-collision (TTC), comfort (Comf.), and ego progress (EP) subscores, and the PDM Score (PDMS), as percentages.
+
+| Dataset | # Sequences | # Frames / Seq | PDMS ↑ |
| nuPlan uniform | 651k | 16 | 74.6 |
| NAVSIM train | 104k | 12 | 82.4 |
+
+of scenes where the ego vehicle is just start to accelerate from a stop and go. Experiment results suggest that our DrivingGPT truly learns how to drive instead of just copying history actions.
+
+Training Data Curation for Planning. Data quality plays the central role when training autoregressive transformers on other tasks like language modeling. So in this section, we study the influence of driving data quality and quantity on the performance of end-to-end planning. As shown in Table 6, models trained on high quality data like NAVSIM with only $100\mathrm{k}$ driving sequences outperform those trained on $650\mathrm{k}$ nuPlan driving sequences. The results suggest that data quality plays a more important role than data quantity in driving language modeling. We hypothesize this is because general driving contains too many trajectories that involve minimum action change and thus provides little information gain.
+
+Position Embedding for Actions. Unlike GAIA-1 [27]
+
+Table 6. Effect of training data curation on planning performance. The results suggest that data quality plays a more important role than data quantity in driving language modeling.
+
+| PosEmb for Image | PosEmb for Action | PDMS ↑ |
| ✓ | | 65.3 |
| ✓ | ✓ | 82.4 |
+
+Table 7. Effect of apply position embedding to tokens of different modalities on planning performance.
+
+and similar methods that use zero position embedding for actions in autoregressive transformers for video generation, we discovered that applying 1D rotary embeddings to both image and action tokens is crucial for achieving strong planning performance, as demonstrated in Table 7.
+
+# 5. Conclusion
+
+In this work, we propose a novel multi-modal driving language that effectively unifies the visual world modeling and trajectory planning into a sequence modeling task. We design a DrivingGPT that could jointly learn to generate image and action tokens for both tasks. Experiments and ablation studies on large-scale nuPlan and NAVSIM benchmarks demonstrates the effectiveness of the proposed DrivingGPT on action-conditioned video generation and end-to-end planning. DrivingGPT clearly shows the viability of unified learning of world modeling and planning with a single model, setting a stepping stone for the future exploration of differentiable model-based planning.
+
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+# DropletVideo: A Dataset and Approach to Explore Integral Spatio-Temporal Consistent Video Generation
+
+Runze Zhang $^{1,\ast}$ , Guoguang Du $^{1,\ast}$ , Xiaochuan Li $^{1,\ast}$ , Qi Jia $^{1,\ast}$ , Liang Jin $^{1,\ast}$ , Lu Liu $^{1}$ , Jingjing Wang $^{1}$ , Cong Xu $^{1}$ , Zhenhua Guo $^{1}$ , Yaqian Zhao $^{1}$ , Xiaoli Gong $^{2}$ , Rengang Li $^{3,1,\dagger}$ , Baoyu Fan $^{2,1,\dagger}$ , IEIT SYSTEMS Co., Ltd. $^{2}$ Nankai University $^{3}$ Tsinghua University Jinan, China Tianjin, China Beijing, China
+
+{zhangrunze, duguoguang, lixiaochuan, jiaqi01, jinliang, liulu06, wangjingjing03, xuong, guozhenhua, zhaoyaqian}@ieisystem.com, gongxiaoli@nankai.edu.cn, lirengangx@gmail.com, fanbaoyu@ieisystem.com
+
+# Abstract
+
+Spatio-temporal consistency is a critical topic in video generation. A qualified generated video segment must ensure plot plausibility and coherence while maintaining visual consistency of objects and scenes across varying viewpoints. Prior research, especially in open-source projects, primarily focuses on either temporal or spatial consistency, or their basic combination, such as appending a camera-movement description after a prompt without constraining its outcomes. However, camera movement may introduce new objects to the scene or eliminate existing ones, thereby affecting the preceding narrative. Especially in videos with numerous camera movements, the interplay between multiple plots becomes increasingly complex. This paper introduces and examines integral spatio-temporal consistency, considering the synergy between plot progression and camera techniques, and the long-term impact of prior content on subsequent generation. Our research encompasses dataset construction through to model development. Initially, we constructed DropletVideo10M, which comprises 10 million videos that feature dynamic camera motion and object actions. With an average length of 206 words, the captions offer detailed accounts of camera movements. Following this, we developed the DropletVideo model, which excels in preserving spatio-temporal coherence during video generation. The work has been open-sourced: https://dropletx.github.io/.
+
+# 1. Introduction
+
+Video generation is a crucial task in AI-generated content (AIGC). Unlike static image generation, video generation
+
+involves dynamic variations across frames, making it significantly more complex. The primary challenge lies in maintaining spatio-temporal consistency, ensuring both spatial coherence within each frame and temporal continuity across consecutive frames. This challenge can be further decomposed into two key aspects:
+
+Temporal Consistency: Ensuring smooth transitions between frames that adhere to physical principles, enabling the video to progress in a plausible and consistent manner. This is exemplified by the consistent depiction of Forest's actions in the blue region of Fig. 1 (b).
+
+Spatial Consistency: Maintaining consistent visual characteristics of objects and scenes (e.g., shape, size, texture, and color) across different viewpoints is essential for spatiotemporal coherence. This is demonstrated in the red region of Fig. 1 (b), where camera rotation or upward movement preserves object consistency.
+
+Studies in video generation have increasingly focused on addressing the challenge of visual transition consistency. Blattmann et al. [8] and Luo et al. [37] have contributed to enhancing image quality and improving event transition plausibility, ensuring greater narrative coherence and accuracy. Cheong et al. [13] and Wang et al. [61] have explored the unification of objects across different viewpoints while accounting for camera movement. Commercial models such as Sora [41] and Kling-1.5 [28] demonstrate strong spatio-temporal consistency. However, these models are closed-source, they restrict public access and limit algorithmic innovation [27].
+
+Recently, research has underscored the importance of spatio-temporal consistency, with a focus on effecting camera angle shifts concurrent with plot progression, as delineated by the light yellow box in Fig. (b). Nonetheless, these inquiries are confined to the realm of composable spatiotemporal consistency, namely appending camera movement descriptions to prompts without circumscribing the move-
+
+
+Text Prompt: A wide symmetrical shot of a painting in a museum. The camera zooms in close to the painting. (Prompts from Movie Gen)
+
+
+Text Prompt: Two people in a canoe on a lake with mountains in the background, camera pans left.
+(Prompts from V'ench++)
+
+
+Plot Description
+
+
+New Plot Description
+
+
+Plot Start Time
+
+
+Camera Movement Description
+
+
+Plot Persistent Impact
+Figure 1. Comparisons between Composable Spatio-temporal Consistency and Integral Spatio-temporal Consistency. (a) Composable Spatio-Temporal Consistency refers to the straightforward combination of temporal and spatial consistency, without limiting the effects of camera movement. Studies such as MovieGen [46] and VBench++ [22] are dedicated to realizing this consistency. (b) Integral Spatio-Temporal Consistency considers the interplay between plot development and camera techniques, along with the enduring influence of antecedent content on subsequent creation. This is because a camera movement may introduce or eliminate objects, thereby overlaying and impacting the preceding storyline.
+
+
+Text Prompt: Forrest Gump, wearing a blue shirt, khaki pants, and a red hat, is running. His attire is distinct from his surroundings. The camera is stationary, angled towards the path. Forrest Gump runs onto the main road, running away into the distance. A row of white mailboxes come into the frame, standing uniformly on the roadside. The camera follows Forrest Gump with a right turn, the main road enters the frame. A blue sports car enters the frame from the right, its rear facing the lens. The car has a streamlined design, its blue color gleaming under the sunlight. The camera continues to pan right, following the blue sports car. The car moves slowly to Forrest Gump's right, keeping a distance.
+
+
+(a) Composable Spatio-Temporal Consistency
+(b) Integral Spatio-Temporal Consistency
+
+ment's consequences. The current benchmark for video generation evaluation, VBench++ [22], includes an assessment of this capability.
+
+However, a camera movement has the potential to introduce new elements or remove existing ones from the scene, thereby altering the preceding narrative. For example, "Forrest's uninterrupted running" while a car enters and exits the frame due to a camera turn, as illustrated in Fig. 1 (b). Besides, in videos featuring numerous camera movements, the interaction among various plot elements becomes increasingly intricate. Therefore, we introduce and explore integral spatio-temporal consistency, focusing on the synergy between plot progression and camera techniques, and the enduring impact of earlier content on subsequent generation. From the perspective of video generation tasks, ensuring this consistency has the potential to advance generated content from single-shot, plot-based videos to more complex, multi-plot narratives.
+
+Our research on this issue encompasses from dataset construction to model development. We propose an open-source integral spatio-temporal consistency video dataset, named DropletVideo-10M. To the best of our knowledge, it is the largest open-source dataset that preserves integral spatiotemporal consistency. A key attribute of DropletVideo-10M is its inclusion of videos featuring both object motion and camera movement. Compared to traditional datasets that
+
+primarily contain videos with object motion alone, such dual-motion video samples are underrepresented in existing datasets. Additionally, to support the training of integral spatio-temporal consistency models, captions must provide meticulously detailed information, including both object motion and camera movement. Traditional video captions often omit such specifics, typically focusing on scenery and plot while failing to capture the nuances of motion, particularly those induced by camera movement. DropletVideo-10M addresses this limitation by providing captions that explicitly describe these motion aspects, including the effects of camera movements. With an average caption length of 206 words, DropletVideo-10M surpasses existing datasets in descriptive depth. DropletVideo-10M offers an extensive collection of videos encompassing both motion types, thereby providing a more balanced and comprehensive dataset for video generation research.
+
+Based on DropletVideo-10M, we propose a pre-trained model, DropletVideo, an open-source foundational model for video generation. It is designed to maintain integral spatiotemporal consistency while simultaneously generating both camera movement and plot progression. DropletVideo also incorporates a variable frame rate sampling strategy, enabling precise control over video generation speed and the tempo of visual transitions. Comprehensive experiments have been conducted, and the results confirm
+
+that DropletVideo effectively preserves content consistency across both temporal and spatial dimensions.
+
+The contributions of this work are as follows:
+
+- We introduce Integral Spatio-Temporal Consistency in video generation, an aspect that has not been previously explored.
+- We have constructed DropletVideo-10M, the largest dataset designed for integral spatio-temporal consistency in video generation.
+- We propose a pre-trained foundational video generation model DropletVideo, which excels in producing videos with integral spatio-temporal consistency.
+- We have open-sourced the dataset, code, and model weights of DropletVideo.
+
+# 2. Related Work
+
+# 2.1. Video-Language Datasets
+
+Several video-language datasets have been introduced in recent years[6, 9, 25, 39, 59, 60, 65]. For instance, Panda70M[9] presents a large-scale dataset with 70 million video clips. MiraData[25] offers a high-quality dataset comprising 788K videos. These works have significantly advanced the field of video generation. Nonetheless, they primarily focus on temporal consistency in videos, overlooking data subject to perspective transformations. On the other hand, to tackle the spatial consistency challenge, several multiview-image[50, 72] and video[33, 75] datasets have been proposed. However, these datasets are limited in frame count and are chiefly applied to multi-view image generation, not video generation.
+
+Recently, an increasing number of researchers have focused on tackling the spatio-temporal consistency problem in video generation, with several datasets being introduced. MV-Video [23] comprises around 115K publicly available animations, including about 53K animated 3D objects, rendered into over 1.8 million multi-view videos. These efforts consider both object and camera movement but neglect the description of the interplay between the two, such as the cumulative plot changes resulting from camera movement.
+
+In comparison, we have curated the world's largest video-language dataset, DropletVideo-10M, as shown in Tab. 1, which addresses the spatio-temporal consistency problem integrally. All videos in DropletVideo-10M involve camera motions and the quantity is $43 \times$ larger than the multi-view images dataset MVImageNet [72], and comparable with the large-scale video generation dataset Panda-70M [9]. Additionally, the average caption of our dataset is 206 words, which is $15.6 \times$ in comparison with Panda-70M [9].
+
+# 2.2. Spatio-temporal Consistent Video Generation
+
+Due to the high continuity and dynamic variability of video data, ensuring both temporal and spatial consistency is a
+
+highly challenging task. As a result, generated videos often fail to meet practical requirements.
+
+Many video generation studies primarily focus on temporal consistency. Blattmann et al. [8] propose a high-resolution video framework utilizing pre-trained Latent Diffusion Models. Videofusion [37] introduces a decomposed diffusion model to improve cross-frame consistency. For spatial consistency, researchers have initially proposed a series of models based on the U-Net architecture [19, 34, 62, 71]. Diffusion Transformer [18] combines the benefits of Visual Transformer and Diffusion Diffusion Model in video generation tasks. Cheong et al. [13] address the low motion accuracy of DiT by introducing camera motion guidance and a sparse camera control pipeline. DiT-based video generation methods have made substantial progress in generating high-quality long videos[4, 5, 61].
+
+Naturally, jointly considering spatio-temporal consistency has become a critical challenge in generation tasks. In 4D generation tasks, spatio-temporal consistency remains a central and unavoidable research focus[24, 31, 42, 68, 70, 73]. Recent advances in video generation research have similarly concentrated on spatial-temporal consistency. Singer et al.[53] leverage pretrained text-to-image diffusion models and introduce pseudo-3D convolutional layers to enhance temporal coherence. ModelScope[57] proposes a hybrid architecture to maintain multi-scale consistency. Qing et al.[47] propose a two-stage framework that explicitly disentangles spatial and temporal modeling. Agrim et al.[16] improve temporal alignment using a cascaded diffusion pipeline with optical flow-guided latent propagation. Chen et al.[10] address spatio-temporal inconsistencies with a training-free approach during diffusion sampling.
+
+However, these methods address either temporal or spatial consistency, or their rudimentary combination. In the work, we attempt to design and train a novel model to ensure the generation with integral spatio-temporal consistency.
+
+# 2.3. Open-Source Landscape of Video Generation
+
+Although large amounts of video generation models[20, 27, 28, 32, 36, 45, 51, 66, 67, 69] are proposed, most of them are commercial closed-source models. Kling v1.6[28] focuses on personalized 10 seconds video creation, leveraging user data to offer tailored templates and effects. Luma Dream Machine[36] combines deep learning and reinforcement learning to generate videos that reflect the emotions and intentions of the user. Meta's Movie Gen[45] explores the potential of text-to-video synthesis with a focus on scalability and accessibility. Runway Gen-3 [51] allows users to generate, edit, and transform videos with simple instructions.
+
+In addition to these commercial models, some of the video generation models in the community are open-sourced. However, their performance lags significantly behind that of commercial models. Moreover, few of them totally open-
+
+Table 1. Comparison with other video-language datasets: DropletVideo-10M offers distinctive benefits. First, it features lengthier text captions than all but MiraData, which, however, is significantly less extensive. Second, it has an average video length of 7.3 seconds, yielding the highest information density per second. Third, DropletVideo-10M focuses both spatial and temporal video and caption attributes. In contrast, datasets like Koala-36M, rich in textual descriptions, neglect the detailed spatial alterations resulting from camera movement.
+
+ | Words | Year | Clips | Avg dur. | Total dur. | Category |
| HowTo100M [39] | 4.0 words | 2019 | 100M | 3.6s | 135Khr | Temporal |
| WebVid-10M [6] | 12.0 words | 2021 | 10M | 18.0s | 52Khr | Temporal |
| HD-VILA-100M [65] | 17.6 words | 2022 | 100M | 11.7s | 760.3Khr | Temporal |
| InternVid [60] | 32.5 words | 2023 | 7M | 13.4s | 371.5Khr | Temporal |
| HD-VG-130M [59] | ~9.6 words | 2024 | 130M | ~5.1s | ~184Khr | Temporal |
| Panda-70M [9] | 13.2 words | 2024 | 70M | 8.5s | 167Khr | Temporal |
| MiraData [25] | 318.0 words | 2024 | 788K | 72.1s | 16Khr | Temporal |
| Koala-36M [58] | 202.1 words | 2024 | 36M | 13.75s | 172Khr | Temporal |
| CO3Dv2 [50] | - | 2021 | 36k | - | - | Spatial |
| DL3DV-10K [33] | - | 2023 | 10K | - | - | Spatial |
| RealEstate-10K [75] | - | 2023 | 10K | - | - | Spatial |
| MVImageNet [72] | - | 2023 | 229K | - | - | Spatial |
| MV-Video [23] | - | 2024 | 1.8M | 2s | 1Khr | Spatio-Temporal |
| DropletVideo-10M (Ours) | 206.0 words | 2025 | 10M | 7.3s | 20.4Khr | Spatio-Temporal |
+
+Table 2. Open-Source Landscape of Video Generation Models. We have open-sourced the model, technology, and data comprehensively, which, to our knowledge, represents the most accessible open-source video generation solution.
+
+| Model | Institute | Year | Model | Tech Solution | Data | Self-Collected Data |
| I2VGen-XL [45] | Alibaba | 2023 | ✓ | ✓ | × | × |
| Animate-Anything [30] | Alibaba | 2024 | ✓ | ✓ | × | × |
| SVD-XT-1.1 [7] | Stability AI | 2024 | ✓ | ✓ | × | × |
| DynamiCrafter [64] | Tencent | 2024 | ✓ | ✓ | ✓ | × |
| CogVideoX [67] | Zhipu AI | 2024 | ✓ | ✓ | × | × |
| HuynyuanVideo [27] | Tencent | 2024 | ✓ | ✓ | × | × |
| OpenSora [74] | HPC-AI Tech | 2024 | ✓ | ✓ | ✓ | × |
| OpenSoraPlan [29] | PKU | 2024 | ✓ | ✓ | ✓ | × |
| WanX [54] | Alibaba | 2024 | ✓ | ✓ | × | × |
| Cosmos [1] | Nvidia | 2025 | ✓ | ✓ | × | × |
| Step-Video [38] | Stepfun | 2025 | ✓ | ✓ | × | × |
| Movie Gen [53] | Meta | 2024 | × | ✓ | × | ✓ |
| Gen-3 [51] | Runway | 2024 | × | × | × | - |
| Sora [41] | OpenAI | 2024 | × | × | × | - |
| Pika [44] | Pika | 2024 | × | × | × | - |
| Vivago [56] | Vivago | 2024 | × | × | × | - |
| Ray2 [36] | Luma AI | 2025 | × | × | × | - |
| Kling [28] | Kwai | 2024 | × | × | × | - |
| Vidu [55] | Vidu | 2024 | × | × | × | - |
| Hailuo [17] | MiniMax | 2024 | × | × | × | - |
| Qingying [2] | Zhipu AI | 2024 | × | × | × | - |
| DropletVideo (Ours) | | 2025 | ✓ | ✓ | ✓ | ✓ |
+
+source their models and training data, as shown in Tab. 2. However, we open-source all about DropletVideo.
+
+# 3. Dataset
+
+We ultimately curated DropletVideo-10M, a spatio-temporal dataset containing 10 million high-quality videos, spanning 2.21 billion frames with a total video length of 20.4K hours. It comprises 600K video samples meticulously selected from high-quality spatio-temporal video clips in OpenVid-1M
+
+[40], MiraData [25], and Pexels [43]. The major remainder of the dataset was compiled according to the procedure detailed in Fig. 2. We have open-sourced it for academic and non-commercial use under the CC BY-NC-SA 4.0 license to facilitate further research on video generation.
+
+# 3.1. Raw Video Collection
+
+We source our videos primarily from YouTube, leveraging its status as a vast content platform with a wide array of video types. We utilize it's search functionality by constructing a
+
+
+Figure 2. The pipeline we proposed to curate the DropletVideo-10M dataset.
+
+set of 6,250 search keywords and collect 2.81 million video links from the search result, an average of 450 links per search term. For comparison, Panda-70M [9], derived from HD-VILA-100M [65], contains approximately 3.3 million video links. The scale of our dataset is therefore comparable to Panda-70M. However, our dataset specifically focuses on videos with spatio-temporal variations, incorporating preliminary human filtering to enhance quality.
+
+# 3.2. Video Segmentation
+
+Internet videos frequently exceed necessary lengths and lack consistent camera movement. To rectify this, we created an automatic extraction tool using a heuristic approach to identify usable segments efficiently. Our camera movement detection program utilizes optical flow estimation between consecutive frames to measure camera motion. It retains segments where the optical flow displacement surpasses a set threshold, extracting continuous sequences to highlight camera movement periods. To maintain sample continuity, we set a maximum Euclidean distance for optical flow between adjacent frames, thereby avoiding abrupt scene changes and hard cuts. This tool is an extension of PySceneDetect [14]. It extracted 107.6 million video clips from 2.81 million raw videos, averaging 38.29 clips per video.
+
+# 3.3. Video Clip Filtering
+
+To facilitate video generation model training, we need to select high-quality spatio-temporal video clips from the automatically segmented videos. Therefore, we developed a novel classification model, which classifies camera motion types based on the observed motion magnitude and style. We define four primary categories: (C1) camera orbiting or target self-rotation, (C2) local horizontal or vertical tilting, (C3) camera tracking a moving target, and (C4) linear camera motion. Additionally, we classify clips with static or near-static camera movement as (C5) and those edited using software, such as transitions or artificial effects, as (C6). To ensure high-quality data, we exclude most C5 clips and all C6 clips from DropletVideo-10M. We manually label 20,000 video clips and train a classification model based on the Video Swin Transformer [35] and categorize clips into the four primary motion types, forming a spatio-temporally aware video dataset. Additionally, we included a small proportion (less than $5\%$ ) of aesthetically pleasing and high-quality
+
+videos from class C5, as these clips contribute to enhancing the overall quality of video generation. Next, we refine the dataset by selecting high-quality videos based on aesthetics and image quality. We utilize the publicly available LAION aesthetics model [52] to compute aesthetic scores and the DOVER-Technical model [63] to evaluate image quality. Only clips surpassing predefined thresholds are retained. Notably, nearly $95\%$ of clips achieve an aesthetic score above 3.5, while approximately $78\%$ exceed a score of 4.0 in image quality, underscoring the dataset's high visual fidelity.
+
+# 3.4. Video Captioning
+
+We employ a video-to-text model to generate captions for video clips. However, existing ones typically produce brief descriptions, which are insufficient for integral spatiotemporal consistency. To address this, we manually compile a dataset of videos with captions detailing objects, scenes, and visual transitions, focusing on camera movement and its impact. Thereafter, we deploy GPT-4 to amend grammatical and spelling errors, facilitating the creation of a dataset for instructionally supervised fine-tuning of models. We selected and fine-tuned InternVL2-8B [11, 12] to achieve the video captioning model using LoRA [21]. The model produces detailed descriptions accurately capturing lens-induced interactions, such as camera movements and content shifts, thus providing precise training data for video generation models. Video segments are annotated with captions of average 206 words, ensuring detailed and precise description.
+
+# 4. The DropletVideo Model
+
+The architecture of DropletVideo is depicted in Fig. 3. Training inputs include a text prompt, a video, a time parameter $T$ and a motion control parameter $M$ . Multi-modal information are input to dedicated encoders: T5 [48] for text and a 3D causal VAE for visual data. These features, along with $T$ and $M$ , are integrated into the modality expert transformer. The output video, according to the specified motion speed, is reconstructed by the denoised latent using via the decoder.
+
+# 4.1. 3D Causal VAE
+
+Different from other auto-encoders, the outputs of VAE's encoder and decoder are subject to parameter-constrained probability density distributions. It is demonstrated by Yang
+
+
+Figure 3. Overview of the DropletVideo Framework. The video is processed by the 3D VAE following adaptive equalization sampling, which is steered by the motion intensity $M$ . The video feature $x_{v}$ is then input into the Modality-Expert Transformer, depicted on the right side of the figure, to facilitate video generation in conjunction with the text encoding $x_{t}$ , and the combined encoding $x_{T\&M}$ of the temporal $T$ and the motion intensity $M$ . The upper left part illustrates the contrast between (a) the traditional sampling approach and (b) our adaptive equalization sampling.
+
+et al. [67] that the 3D structure can reduce the jitter problem in the reconstructed video. Therefore, we apply 3D causal VAE extended with VAE and 3D structure in our framework. It reduces the computation of DropletVideo and ensures the efficiency and continuity of the generated video.
+
+# 4.2. 3D Modality-Expert Transformer
+
+The input for DropletVideo consists of two modalities, textual prompt and video. To ensure smooth embedding of each modality, 3D positional embedding is applied in the transformer architecture, and multi-modal attention is employed to handle text and vision data simultaneously. Full 3D attention is a technique that has evolved with the widespread application of transformers in computer vision, and we apply it to DropletVideo. Compared with the previous separation approach, it can better capture dynamic variations and enhance the semantic consistency and diversity of the content.
+
+# 4.3. Motion Adaptive Generation
+
+To generate videos with diverse motion speeds, we introduce the Motion Adaptive Generation (MAG) strategy within our DropletVideo model. MAG enables the model to adjust dynamically to the target motion speed of the video content. Previous models, which typically employ a fixed frame rate for sampling raw video frames, produce videos with uniform motion speeds, as depicted in Fig. 3 (a). These models initially extract a sub-clip from the source video and then sample frames at a constant frames per second (FPS), which may not satisfy the demand for detailed visual information. In contrast, DropletVideo employs MAG to ensure motion
+
+control in the generated videos. We uniformly sample frames across the entire video stream and utilize detailed caption data for these frames, thereby capturing global dependencies and enriching semantic information, as illustrated in Fig. 3 (b). We introduce the motion intensity $M$ , which is used to control the motion intensity of the generated video. $M$ can be defined as follows
+
+$$
+M = N \times \left(\frac {F P S}{c l i p _ {n}}\right),
+$$
+
+where $FPS$ represents the FPS of the video, $clip_{n}$ represents the number of video frames, $N$ represents the sample number during the training process. In the DropletVideo framework, the MAG strategy modulates input coding in conjunction with time $T$ . Given the distinct feature states of text and video modalities, we independently implement Text Expert AdaLN and Vision Expert AdaLN in their respective latent spaces. These modules facilitate the smooth transmission of the control parameter $M$ to the diffusion transformer, enabling DropletVideo to accurately govern the temporal dynamics of the generated video.
+
+# 5. Experiments
+
+# 5.1. Implementation Details
+
+During training, video resizing was adjusted for varying token lengths. Initially, the maximum token length was 13,312, facilitating the generation of 49 frames at $512 \times 512$ resolution. Subsequently, this was increased to 68,992, allowing for 85 frames at $896 \times 896$ resolution. To reduce
+
+
+
+Text Prompt: The video shows a pair of small boats floating peacefully on a tranquil lake, with a magnificent sunset sky as the backdrop. the boat on the right is slowly chasing the boat on the left, with a soft golden glow reflecting the afterglow of the setting sun. The camera slowly moves from right to left, gradually revealing more background details. The distant city skyline appears hazy and dreamlike under the sunset, with a few tall buildings faintly visible. On the left side of the frame, tree branches sway gently in the breeze, adding a touch of natural movement to the scene. As the camera continues to move left, another small boat is shown quietly moored on the water on the left side, contrasting sharply with the distant city buildings.
+
+
+(a)
+
+Text Prompt: The video presents a serene and beautiful sunset scene, capturing a flock of birds soaring gracefully under the evening sun, creating a stunning visual. The sun is slowly descending towards the horizon, painting the entire sky in warm shades of orange and red. The clouds, illuminated by the sunset, glow in golden hues, adding to the magnificent scenery. At the center of the frame stands a solitary tree, its branches appearing particularly distinct against the backdrop of the setting sun. As the camera moves slowly, a rolling grassland gradually emerges on the left side of the frame. The grassland, bathed in the sunset's afterglow, displays varying shades of light and shadow, adding a rhythmic natural beauty to the scene. As the camera continues to pan left, the flight path of the birds becomes increasingly visible, forming a bright arc under the glow of the sunset and enhancing the dynamic beauty of the composition. Further along, another tree appears in the frame, its silhouette sharply defined under the warm hues of the setting sun, with crisp and well-defined lines.
+
+
+(b)
+Figure 4. DropletVideo facilitates the generation of videos that maintain integral spatio-temporal consistency. New objects or scenes introduced via camera movement are seamlessly integrated and interact logically with the pre-existing scenes.
+
+Text Prompt: The video showcases a chef focusing on the process of cooking in a modern kitchen, with professional kitchen equipment behind him and a clean and tranquil surrounding environment. At the start of the video, the chef is wearing a tall white chef's hat, a black chef's coat, and a white apron, standing in front of the central kitchen counter. The camera focuses on the chef's skillful hands as he uses a bright knife to chop various fresh ingredients on the worktable. These ingredients include red tomatoes, yellow peppers, green cucumbers, and a tall green cauliflower. The vegetables are colorful and neatly arranged. In the background, you can see the metal exhaust hood and several modern stainless-steel kitchen appliances. The kitchen is empty except for the chef, who is working attentively. As the video progresses, the camera slowly pans to the right, and a red apple gradually enters the frame, which is very fresh.
+
+
+(a) Emerging object: a fresh apple
+
+Text Prompt: The video showcases a chef focusing on the process of cooking in a modern kitchen, ... As the video progresses, the camera slowly pans to the right, and a red apple gradually enters the frame, with many droplets of water, indicating its freshness.
+
+
+(b) Emerging object: an apple with many droplets of water
+
+Text Prompt: The video showcases a chef focusing on the process of cooking in a modern kitchen, ... As the video progresses, the camera slowly pans to the right, and a red apple gradually enters the frame, showing slight signs of spoilage with brown spots.
+
+
+(c) Emerging object: an apple with brown spots
+(d) Emerging object: a few bananas with brown spots
+Figure 5. DropletVideo demonstrates advanced controllability in generating scenes where new objects emerge due to camera movement.
+
+Text Prompt: The video showcases a chef focusing on the process of cooking in a modern kitchen, .... As the video progresses, the camera slowly pans to the right, and a few yellow bananas gradually enter the frame on the workbench. The bananas have minor signs of spoilage with a few black spots.
+
+$M = 8$
+$M = 12$
+$M = 16$
+Figure 6. DropletVideo facilitates precision control over video generation speed. Modifying the Input Speed parameter alters the movement speed of both the camera and target.
+
+Text Prompt: A tranquil and beautiful snow scene, with a delicate glass snowflake placed in the center on soft snow. The background is a vast snowy plain dotted with pine trees, and the afterglow of the setting sun in the sky sprinkles a gentle glow. The video begins with the glass snowflake in the center of the frame, with sunlight passing through its transparent body, making it shine with colorful light. The snowflake's design is detailed, with clear edges and corners. The camera slowly rotates to the right around the snowflake, the distant pine trees are naturally distributed, appearing somewhat bent under the weight of the snow on the layered slopes. The camera continues to slowly rotate to the right and around the snowflake, another mountain view gradually comes into sight, with a few tall pine trees standing on the hilltop. On the horizon, the sun is about to set, and the remaining light turns the sky from light blue to warm orange. The camera continues to slowly rotate to the right around the snowflake, finally, the frame stays on the central glass snowflake, where the distant mountain top meets the horizon, and sunlight reflects on the snow.
+
+transition artifacts, the first and last $10\%$ of frames were excluded prior to uniform sampling.
+
+For weight initialization, we utilized the CogVideoXFun [3]. The text encoder was t5-v1_1-xxl [48], with its maximum text tokenizer length to accommodate extended captions. The model architecture, derived from the MMDiT series [15], comprised 42 layers with 48 attention heads, each of 64 dimensions, and a time step embedding dimension of 512. Optimization was performed using Adam [26] with a weight decay of 3e-2 and an epsilon of 1e-10, at a learning rate of 2e-5. $N$ was constant at 85. Training employed bfloat16 mixed-precision via the DeepSpeed [49] framework. For inference, the classifier-free guidance scale was adjusted to 6.5 to improve temporal consistency and motion smoothness in the generated videos.
+
+# 5.2. Integral Spatio-temporal Consistency
+
+Dynamic Scene Generation with Integral Spatiotemporal Consistency. DropletVideo prioritizes integral spatio-temporal consistency in video generation, mitigating spatial distortion due to camera movement. This ensures seamless plot progression and the consistent representation of objects within scenes. Notably, the introduction of new scenes does not disrupt the behavior of existing video objects. Fig. 4 illustrates this concept, clearly demonstrating DropletVideo's ability to preserve the original plot's continuity amidst the emergence of new story elements.
+
+High controllability of Emerging objects. To assess our proj's proficiency in generating videos with integral spatiotemporal consistency, we performed ablation studies centered on the driving prompts. We altered the final sentences of the prompts, maintaining the remainder, to evaluate the system's precision in manipulating the properties of new
+
+objects, as depicted in Fig. 5. The generated videos exemplify DropletVideo's superior capability to convert text descriptions into visual content, maintaining high fidelity to the described attributes. This underscores DropletVideo's nuanced control over the appearance of objects in the videos.
+
+# 5.3. Controllable Motion Intensity
+
+DropletVideo modulates plot progression and camera angle transitions via a parameter $M$ for motion intensity. Elevating this parameter enables a video of consistent length to incorporate additional plot elements. Fig. 6 illustrates video generation outcomes across diverse motion control parameters with a uniform text-image input. At $M = 8$ , camera movement is distinctly more accentuated compared to the others, affording the snowflake a wider array of perspectives. This finding indicates that DropletVideo effectively governs content playback speed while preserving semantic integrity.
+
+# 6. Conclusion
+
+In this paper, we introduce integral spatio-temporal consistency, which refers to the interaction between newly introduced objects due to camera movement and pre-existing ones. We also released the largest spatio-temporal video dataset to date and open-sourced the foundational video generation model, DropletVideo. Experiments demonstrate that our approach exhibits a strong ability to achieve spatio-temporal consistency, surpassing most open-source models and even rivaling some closed-source models.
+
+# 7. Acknowledgments
+
+This work was supported by the Taishan Industrial Experts Program.
+
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\ No newline at end of file
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+# DuCos: Duality Constrained Depth Super-Resolution via Foundation Model
+
+Zhiqiang Yan $^{1}$ Zhengxue Wang $^{2}$ Haoye Dong $^{1}$ Jun Li $^{2}$ Jian Yang $^{2}$ Gim Hee Lee $^{1}$ $^{1}$ National University of Singapore $^{2}$ Nanjing University of Science and Technology
+{yanzq, gimhee.lee}@nus.edu.sg
+
+# Abstract
+
+We introduce DuCos, a novel depth super-resolution framework grounded in Lagrangian duality theory, offering a flexible integration of multiple constraints and reconstruction objectives to enhance accuracy and robustness. Our DuCos is the first to significantly improve generalization across diverse scenarios with foundation models as prompts. The prompt design consists of two key components: Correlative Fusion (CF) and Gradient Regulation (GR). CF facilitates precise geometric alignment and effective fusion between prompt and depth features, while GR refines depth predictions by enforcing consistency with sharp-edged depth maps derived from foundation models. Crucially, these prompts are seamlessly embedded into the Lagrangian constraint term, forming a synergistic and principled framework. Extensive experiments demonstrate that DuCos outperforms existing state-of-the-art methods, achieving superior accuracy, robustness, and generalization. The code is available at https://github.com/yanzq95/DuCos.
+
+# 1. Introduction
+
+Depth super-resolution (DSR) [60] is a fundamental task in computer vision that aims to restore high-resolution (HR) depth data from low-resolution (LR) depth inputs. It plays a crucial role in various downstream applications such as 3D reconstruction [3, 5, 18, 45, 46, 62, 63], augmented reality [35, 39, 47, 55], and robotic sensing [24, 36, 50, 57]. These applications are largely reliant on clear and HR depth predictions. However, depth data typically has much lower resolution than color images due to the differing advancements of color cameras and depth sensors. It is therefore essential to enhance the resolution of low-quality depth data.
+
+Numerous advanced approaches have been developed, often using a reconstruction loss to minimize the discrepancy between depth predictions and ground truth annotations. However, this loss focuses predominantly on global
+
+
+Figure 1. Overview of our DuCos: A highly synergistic system that integrates prompt learning with a Lagrangian duality (LD) based optimization algorithm. It combines the reconstruction loss with geometric consistency and edge preservation constraints to capture both global content and fine-grained local details, and uses foundation models to enhance generalization.
+
+error minimization that relies heavily on pixel-level differences [36, 41, 57]. As a result, it often fails to capture fine-grained local geometric details, leading to blurred or oversmoothed depth recovery [12, 26, 45]. Moreover, the predictions become increasingly inaccurate and unreliable with disturbances such as noise in the input data. In addition, existing DSR solutions often focus on specialized network designs tailored to specific training data distributions. Despite their effectiveness in certain scenarios, these methods may face challenges in generalization across diverse resolutions and conditions.
+
+We propose DuCos, a novel paradigm of duality constrained DSR via foundation model to address the above-mentioned issues. As illustrated in Fig. 1, DuCos establishes a theoretical framework for accurate and robust DSR while integrating prompt learning to enhance generalization. Specifically, our DuCos first reformulates DSR as a constrained optimization problem with the Lagrangian duality (LD) theory [1, 25]. The total LD loss comprises a reconstruction term and a constraint term. The reconstruction term minimizes global errors, while the constraint
+
+term enforces geometric consistency and edge preservation. Guided by theoretical principles, this design allows the model to balance global context and local details, enhancing both accuracy and robustness. Furthermore, our DuCos is a pioneer in leveraging depth foundation models [7, 29, 51] as prompts to boost generalization. Concretely, these prompts consist of correlation fusion (CF) and gradient regulation (GR). CF quantifies the similarity between RGB-D features using the Pearson Correlation Coefficient and subsequently conducts recurrent fusion. Such explicit data statistics facilitate intuitive and effective modeling. In addition, while depth predictions from depth foundation models often exhibit significant errors, they retain remarkably sharp edges. To take advantage of this property, GR computes their gradients to highlight edges and subsequently minimizes the normalized gradient errors, leading to improved accuracy.
+
+We further introduce an alignment loss in CF to enhance the geometric consistency between RGB-D features, and an edge-aware loss is designed in GR to promote edge preservation. These two loss functions are seamlessly integrated into the Lagrangian duality framework as the Lagrangian constraint term, resulting in a highly synergistic system capable of effectively capturing the sparsity and structural characteristics of depth maps.
+
+In summary, our contributions are as follows:
+
+- We present a novel DSR paradigm based on Lagrangian duality theory, reformulating it as a constrained optimization problem to ensure a precise solution with rigorous theoretical foundations.
+- To our best knowledge, we are first to leverage foundation models as DSR prompts and seamlessly integrate them into the Lagrangian duality framework through CF and GR along with their respective constraints.
+- Extensive experiments demonstrate the superiority of our approach over state-of-the-art methods in terms of accuracy, robustness, and generalization on five datasets.
+
+# 2. Related Work
+
+Depth Super-Resolution. Existing methods can be broadly categorized into synthetic DSR and real-world DSR, depending on the nature of the data used. For synthetic DSR, the degradation pattern is well defined [2, 2, 10, 24, 26, 37, 40, 42, 57] since LR depth inputs are typically generated from depth annotations using bicubic interpolation. For example, ATGVNet [30] combines convolutional neural networks with total variation to produce HR depth maps. MS-GNet [8] introduces a multi-scale guidance network to enhance depth boundaries. PMBANet [53] presents a progressive multi-branch fusion network aimed at restoring high-resolution depth while maintaining sharp boundaries. Similarly, SSDNet [57, 58] incorporates discrete cosine transform and spherical contrast refinement to address issues related to fine details. Recently, several guided image filter
+
+ing approaches [12, 16, 41, 60] have been proposed to improve the transfer of guidance information into target depth maps. For example, DKN [12] utilizes deformable kernel networks to model sparse and spatially variant filter kernels, thereby improving the flexibility of filtering. Furthermore, advanced transformer [58] and diffusion [24] techniques are also incorporated to further advance the DSR task. With the increasing technical and practical demands, real-world DSR with unknown degradation patterns emerges. For the first time, FDSR [5] builds a real-world benchmark dataset and a new blind DSR baseline. Subsequently, SFGNet [55] introduces a structure flow-guided model that learns cross-modal flows to effectively propagate the structural information of color images. Most recently, DORNet [43] utilizes self-supervised degradation learning for the first time to model the degradation patterns of real-world data, contributing to significant performance improvements. Unlike these methods that are optimized using a fixed reconstruction loss function, our objective is to develop a highly precise and robust model with stronger theoretical guarantees.
+
+Depth Prompt Learning. A variety of depth estimation foundation models [7, 11, 29, 51, 52, 54] from a single image have been proposed. These models can provide strong priors for various depth perception tasks, including depth matching [9, 44, 61] and depth completion [19, 21, 23, 27, 28, 38]. DEFOM-Stereo integrates Depth Anything v2 [52] into RAFT-Stereo [20] to enhance stereo matching capabilities. FoundationStereo [44] enables robust and accurate zero-shot stereo depth estimation, bridging the gap between simulation and reality. To complete sparse depth maps, DepthPrompting [28] and UniDC [27] design a prompt mechanism that aggregates RGB priors from depth foundation models with depth features from depth-private branches. Marigold-DC [38] injects sparse depth observations as test-time guidance into a pretrained latent diffusion model for monocular depth estimation [11]. Furthermore, DepthLab [21] introduces image-conditioned depth inpainting based on diffusion priors, thereby facilitating various downstream applications. DepthRescaling [23] proposes to rescale Depth Anything predictions using 3D points provided by low-cost depth sensors or techniques. What's more, PromptDA [19] achieves 4K resolution depth estimation from low-quality depth data through concise prompt fusion and scaling designs. All of these depth prompt learning methods provide valuable insights into harnessing the powerful prior knowledge of depth foundation models to benefit image-guided depth perception tasks.
+
+# 3. Our Method: DuCos
+
+Overview. Existing DSR methods focus mainly on specialized network designs. In contrast, our approach seeks to establish a general baseline by harnessing the strong pri
+
+
+Figure 2. Detailed pipeline of DuCos. The color image $\mathbf{I}$ is first processed by a depth foundation model to generate prompt flows, including the intermediate features $\mathbf{F}_i$ and sharp-edged relative depth output $\mathbf{Y}'$ . $\mathbf{F}_i$ is then used to guide depth recovery with Correlative Fusion (CF), and $\mathbf{Y}'$ enhances edges through Gradient Regulation (GR). Moreover, CF and GR are both formulated as constraints on reconstruction loss within the Lagrangian duality framework. Res-G: residual group [56], PCC: Pearson Correlation Coefficient.
+
+ors of depth foundation models, guided by theoretical principles. Fig. 2 shows the pipeline of our DuCos with two key components: prompt learning and Lagrangian duality optimization. For prompt learning, the prompt flow $\mathbf{F}_i$ and $\mathbf{Y}'$ is derived from a depth foundation model given a color image $\mathbf{I}$ . To effectively integrate these prompts, we first design correlative fusion (CF), which iteratively fuses the RGB prompt feature $\mathbf{F}_i$ and the depth feature $\mathbf{D}_i$ by computing their correlation. At the same time, an alignment loss is introduced to reinforce geometric consistency in RGB-D features. Next, we incorporate gradient regulation (GR) with an edge-aware loss to minimize the gradient discrepancies between the HR depth $\mathbf{Y}$ and the sharp-edged depth $\mathbf{Y}'$ . For Lagrangian duality optimization, the auxiliary alignment and edge-aware losses serve as constraint terms, seamlessly integrated with the primary reconstruction loss using Lagrangian duality theory [1, 25].
+
+We give the details of our DuCos in the following sections. Sec. 3.1 elaborates on prompt learning and the corresponding restricted conditions. Sec. 3.2 describes the formulation of DSR as a constrained optimization problem under these restricted conditions, leading to its dual problem which is ultimately solved using Lagrangian duality theory.
+
+# 3.1. Prompt Learning
+
+Correlative Fusion. As illustrated in Fig. 2, the image branch processes the RGB input $\mathbf{I} \in \mathbb{R}^{3 \times H \times W}$ through
+
+a depth foundation model. A notable example is Depth Anything v2 [52], which extracts the prompt flow $\mathbf{F}_i\in$ $\mathbb{R}^{C\times H / p\times W / p}$ across four stages. We follow [52] to set the patch size $p$ as 14. In the depth branch, the initial low-quality depth map undergoes upsampling by bicubic interpolation [5, 41, 57], producing the depth input $\mathbf{X}\in$ $\mathbb{R}^{1\times H\times W}$ . Subsequently, this input is encoded using a $3\times 3$ convolutional head $\mathcal{F}_{\tau_1}(\cdot)$ to generate the feature representation $\mathbf{D}_1\in \mathbb{R}^{C\times H\times W}$ , i.e.:
+
+$$
+\mathbf {F} _ {i} = \mathcal {F} _ {\phi} (\mathbf {I}), \quad \text {f o r} \quad 1 \leq i \leq 4; \tag {1a}
+$$
+
+$$
+\mathbf {D} _ {1} = \mathcal {F} _ {\tau_ {1}} (\mathbf {X}), \tag {1b}
+$$
+
+where $\mathcal{F}_{\phi}(\cdot)$ denotes the depth foundation model.
+
+In the $i$ -th stage, we introduce the correlative fusion module to effectively integrate the RGB-D features $\mathbf{F}_i$ and $\mathbf{D}_i$ . Specifically, the prompt $\mathbf{F}_i$ is resized by deconvolution and interpolation to maintain RGB-D scale consistency, resulting in $\hat{\mathbf{F}}_i \in \mathbb{R}^{C \times H \times W}$ . A residual group [56] is then applied for further feature extraction, yielding $\hat{\mathbf{D}}_i \in \mathbb{R}^{C \times H \times W}$ . This process can be denoted as:
+
+$$
+\hat {\mathbf {F}} _ {i} = \mathcal {F} _ {\delta} (\mathbf {F} _ {i}), \quad \text {f o r} \quad 1 \leq i \leq 4; \tag {2a}
+$$
+
+$$
+\hat {\mathbf {D}} _ {i} = \mathcal {F} _ {\theta} (\mathbf {D} _ {i}), \tag {2b}
+$$
+
+where $\mathcal{F}_{\delta}(\cdot)$ refers to the combined deconvolution and interpolation and $\mathcal{F}_{\theta}(\cdot)$ represents the residual group [56]. Next, we utilize the statistical measure of Pearson Correlation Coefficient to explicitly quantify the relevance between the two
+
+features. Formally, the relevance is given by:
+
+$$
+r = \frac {\sum \left(\hat {\mathbf {F}} _ {i} ^ {j} - \bar {\mathbf {F}} _ {i}\right) \left(\hat {\mathbf {D}} _ {i} ^ {j} - \bar {\mathbf {D}} _ {i}\right)}{\sqrt {\sum \left(\hat {\mathbf {F}} _ {i} ^ {j} - \bar {\mathbf {F}} _ {i}\right) ^ {2}} \sqrt {\sum \left(\hat {\mathbf {D}} _ {i} ^ {j} - \bar {\mathbf {D}} _ {i}\right) ^ {2}}}, \tag {3}
+$$
+
+where $\bar{\mathbf{F}}_i$ and $\bar{\mathbf{D}}_i$ are the mean values of $\hat{\mathbf{F}}_i$ and $\hat{\mathbf{D}}_i$ , respectively. $j$ is the position index of the matrices and $r \in \mathbb{R}^C$ . As we know that $r$ is symmetric with respect to 0, where $r > 0$ indicates positive correlation and $r < 0$ signifies negative correlation. However, convolutional neural networks (CNNs) typically assign higher weight to features with high similarity and lower weight to those with less similarity instead of letting negative correlations cancel out positive ones. We thus apply a sigmoid function $\mathcal{F}_{\sigma}(\cdot)$ to compute the final correlation $\alpha$ of $\hat{\mathbf{F}}_i$ and $\hat{\mathbf{D}}_i$ . Particularly, $\mathcal{F}_{\sigma}(\cdot)$ maps $r$ to a more compact and nonnegative interval of $[\frac{1}{1 + e}, \frac{1}{1 + e^{-1}}]$ . The fused result $\tilde{\mathbf{D}}_i$ is given by:
+
+$$
+\alpha = \mathcal {F} _ {\sigma} (r), \quad \beta = 1 - \alpha , \tag {4a}
+$$
+
+$$
+\tilde {\mathbf {D}} _ {i} = \alpha \hat {\mathbf {F}} _ {i} + \beta \hat {\mathbf {D}} _ {i}. \tag {4b}
+$$
+
+Eq. (4b) adaptively selects regions of $\hat{\mathbf{F}}_i$ that exhibit a strong correlation with $\hat{\mathbf{D}}_i$ while preserving the original components of $\hat{\mathbf{D}}_i$ in areas with low correlation. This mechanism is especially effective for CNNs in probabilistic modeling, where negative correlation does not merely negate positive correlation but rather acts as a diminished weight in the computation. As a result, this approach effectively regulates the flow of information.
+
+Furthermore, the iterative process involving Eqs. (2b)-(4b) refines the depth representation. Specifically, $\hat{\mathbf{D}}_i$ from Eq. (4b) is used to update $\hat{\mathbf{D}}_i$ in Eq. (2b), and this refinement is repeated for three iterations. Afterward, a $3\times 3$ convolution $\mathcal{F}_{\tau_2}(\cdot)$ is applied to obtain $\mathbf{D}_{i + 1}$ , which serves as the input depth feature for the subsequent CF module:
+
+$$
+\mathbf {D} _ {i + 1} = \mathcal {F} _ {\tau_ {2}} (\tilde {\mathbf {D}} _ {i}). \tag {5}
+$$
+
+Overall, by defining $\mathcal{F}_{\psi}(\cdot ,\cdot)$ as the complete CF module, we can unify Eqs. 1-5 into the following expression:
+
+$$
+\mathbf {D} _ {i + 1} = \mathcal {F} _ {\psi} \left(\mathbf {F} _ {i}, \mathbf {D} _ {i}\right). \tag {6}
+$$
+
+Additionally, despite this fusion process, the depth feature often lacks geometric details while the prompt retains richer geometric structures. Moreover, misalignment issues persist even after resizing the prompt to match the resolution of the depth feature. To mitigate these challenges, we introduce a simple yet effective constraint designed to enhance geometric consistency:
+
+$$
+\mathcal {L} _ {c f} = \frac {1}{n} \| \mathcal {H} (\tilde {\mathbf {D}} _ {i}) - \mathcal {H} (\hat {\mathbf {F}} _ {i}) \| _ {2} ^ {2}, \tag {7}
+$$
+
+
+
+
+
+
+
+
+Figure 3. Visual comparisons of foundation models and traditional DSR methods. DA v2: Depth Anything v2 [52] (ViT-L encoder).
+
+
+
+
+
+where $\mathcal{H}(\cdot)$ denotes a combination of a $1 \times 1$ convolution followed by normalization. It reduces the features to a single channel and normalizes them to the range $[0, 1]$ . $n$ is the number of valid pixels.
+
+Finally, given the fused feature $\mathbf{D}_4\in \mathbb{R}^{C\times H\times W}$ produced from the fourth CF module, we conduct a $3\times 3$ convolutional tail $\mathcal{F}_{\tau_3}(\cdot)$ to map the channel $C$ to 1, yielding the final depth prediction:
+
+$$
+\mathbf {Y} = \mathcal {F} _ {\tau_ {3}} (\mathbf {D} _ {4}). \tag {8}
+$$
+
+Gradient Regulation. As shown in Fig. 2, the image branch utilizing a foundation model also produces a depth prediction denoted as $\mathbf{Y}'$ . However, monocular depth estimation is inherently an ill-posed problem since models can only infer the relative depth instead of absolute measurements. Fortunately, as shown in Fig. 3, the visual quality of $\mathbf{Y}'$ remains remarkably high despite its significant error. Notably, $\mathbf{Y}'$ exhibits exceptional clarity and sharp gradient, even surpassing the ground truth depth.
+
+In view of the large discrepancy between the depth values of $\mathbf{Y}'$ and the target $\mathbf{Y}$ , directly fusing these results is not appropriate. Instead, we utilize the gradient representation of $\mathbf{Y}'$ as a constraint to regulate its edges. Specifically, we first adjust the depth discrepancy using Min-Max Normalization $\mathcal{N}(\cdot)$ . We then calculate the first derivative to get their gradient representations:
+
+$$
+\mathcal {G} (\mathbf {Y}) = \sqrt {\left(\frac {\partial \mathcal {N} (\mathbf {Y})}{\partial x}\right) ^ {2} + \left(\frac {\partial \mathcal {N} (\mathbf {Y})}{\partial y}\right) ^ {2}}, \tag {9a}
+$$
+
+$$
+\mathcal {G} \left(\mathbf {Y} ^ {\prime}\right) = \sqrt {\left(\frac {\partial \mathcal {N} \left(\mathbf {Y} ^ {\prime}\right)}{\partial x}\right) ^ {2} + \left(\frac {\partial \mathcal {N} \left(\mathbf {Y} ^ {\prime}\right)}{\partial y}\right) ^ {2}}. \tag {9b}
+$$
+
+Subsequently, we propagate the edge priors from the depth foundation model by minimizing their normalized gradient distances through:
+
+$$
+\mathcal {L} _ {g r} = \frac {1}{n} \| \mathcal {G} (\mathbf {Y}) - \mathcal {G} \left(\mathbf {Y} ^ {\prime}\right) \| _ {1}. \tag {10}
+$$
+
+This constraint allows us to improve the sharpness and overall quality of our estimated depth maps.
+
+# 3.2. Lagrangian Duality Optimization
+
+Given the HR depth prediction $\mathbf{Y}$ and the ground truth $\mathbf{Z}$ , we use the commonly adopted reconstruction loss [5, 24, 45] for optimization:
+
+$$
+\mathcal {L} _ {r e c} = \frac {1}{n} \| \mathbf {Y} - \mathbf {Z} \| _ {1}. \tag {11}
+$$
+
+By integrating Eq. (11) with the two prompts from Eq. (7) and Eq. (10), we can further enhance the optimization of the target depth. Unlike previous DSR methods [36, 37, 41, 58] that introduce additional loss terms as auxiliary constraints, we adopt the Lagrangian duality theory [1, 25] to translate the optimization problem into a constrained form. Specifically, based on Eqs. (7) and (10), the primal problem can be written as:
+
+$$
+\min _ {\omega} \mathcal {L} _ {r e c}, \quad \text {s . t .} \quad \mathcal {L} _ {c f} < \varepsilon_ {1}, \mathcal {L} _ {g r} < \varepsilon_ {2}, \tag {12}
+$$
+
+where $\omega$ indicates the network weight of our DuCos. $\varepsilon_{1}$ and $\varepsilon_{2}$ are small positive values approaching zero, signifying that errors have become negligible. Next, we introduce two Lagrangian multipliers $\lambda$ and $\mu$ to formulate the Lagrangian function as:
+
+$$
+\begin{array}{l} \mathcal {L} (\omega , \lambda , \mu) = \underbrace {\mathcal {L} _ {r e c}} _ {\text {t a r g e t}} + \underbrace {\lambda \mathcal {L} _ {c f} + \mu \mathcal {L} _ {g r}} _ {\text {L a g . c o n s t . t e r m}} \\ = \frac {1}{n} \| \mathbf {Y} - \mathbf {Z} \| _ {1} + \frac {\lambda}{n} \| \mathcal {H} (\tilde {\mathbf {D}} _ {i}) - \mathcal {H} (\hat {\mathbf {F}} _ {i}) \| _ {2} ^ {2} \tag {13} \\ + \frac {\mu}{n} \| \mathcal {G} (\mathbf {Y}) - \mathcal {G} (\mathbf {Y} ^ {\prime}) \| _ {1}, \\ \end{array}
+$$
+
+where $\lambda \geq 0$ and $\mu \geq 0$ according to the Karush-Kuhn-Tucker (KKT) conditions [14]. We then minimize the Lagrangian function to get the dual function:
+
+$$
+\mathcal {D} (\lambda , \mu) = \min _ {\omega} \mathcal {L} (\omega , \lambda , \mu). \tag {14}
+$$
+
+Subsequently, the dual problem corresponding to the primal problem in Eq. (12) is formulated by maximizing Eq. (14):
+
+$$
+\max _ {\lambda , \mu} \mathcal {D} (\lambda , \mu) = \max _ {\lambda , \mu} \min _ {\omega} \mathcal {L} (\omega , \lambda , \mu). \tag {15}
+$$
+
+The dual optimization in Eq. (15) consists of two key steps: Step 1. Fix $\lambda$ and $\mu$ , minimize the Lagrangian function to obtain the optimal network weight:
+
+$$
+\omega^ {*} (\lambda , \mu) = \arg \min _ {\omega} \left(\mathcal {L} _ {r e c} + \lambda \mathcal {L} _ {c f} + \mu \mathcal {L} _ {g r}\right). \tag {16}
+$$
+
+Step 2. Adjust $\lambda$ and $\mu$ , maximize the dual function:
+
+$$
+\lambda^ {*}, \mu^ {*} = \arg \max _ {\lambda , \mu} \mathcal {D} (\lambda , \mu). \tag {17}
+$$
+
+Alg. 1 gives the details of the dual problem optimization in Eq. (15). The Lagrangian duality optimization allows for the flexible integration of multiple constraint conditions and reconstruction objectives. The optimization process is simplified by relaxing the constraints, providing an exact solution when the loss function is convex and an approximate solution when the loss function is non-convex.
+
+Algorithm 1: Dual Problem Solving
+Input: Y, Z, $\tilde{\mathbf{D}}_i$ , $\hat{\mathbf{D}}_i$ , $\mathbf{Y}'$
+1 Initialize learning rate $\eta_{\omega} = 1\mathrm{e - }5$ , $\lambda = 0.01$ , $\mu = 0.05$ , step-length $\eta_{\lambda} = \eta_{\mu} = 0.01$
+2 Set maximum epoch $T$
+3 for epoch $t = 1$ to $T$ do
+4 Step 1: Fix $\lambda$ and $\mu$ , optimize $\omega$
+5 Total Lag. loss: $\mathcal{L}(\omega, \lambda, \mu) = \mathcal{L}_{rec} + \lambda \mathcal{L}_{cf} + \mu \mathcal{L}_{gr}$
+6 Gradients of $\omega$ : $\nabla_{\omega} \mathcal{L}(\omega, \lambda, \mu)$
+7 Update $\omega$ : $\omega \gets \omega - \eta_{\omega} \nabla_{\omega} \mathcal{L}(\omega, \lambda, \mu)$
+8 Step 2: Optimize $\lambda$ and $\mu$
+9 Update $\eta_{\lambda}$ , $\eta_{\mu}$ : $\eta_{\lambda} \gets \eta_{\lambda}(1 - \frac{t}{T})$ , $\eta_{\mu} \gets \eta_{\mu}(1 - \frac{t}{T})$
+10 Update $\lambda$ , $\mu$ : $\lambda \gets \lambda + \eta_{\lambda} \mathcal{L}_{cf}$ , $\mu \gets \mu + \eta_{\mu} \mathcal{L}_{gr}$
+11 Ensure $\lambda$ , $\mu$ to satisfy KKT conditions:
+12 $\lambda \gets \text{clamp}(\lambda, \min = 0)$ , $\mu \gets \text{clamp}(\mu, \min = 0)$
+13 end for
+Output: Optimized parameters $\omega$ , $\lambda$ , $\mu$
+
+# 4. Experiment
+
+# 4.1. Dataset
+
+With the advancement of computer vision, training with simulated data has become a crucial approach to reducing data acquisition costs. Thus, we retrain all methods on the fully simulated Hypersim [31] dataset and evaluate them on the test sets of various DSR datasets: TOFDSR [48], RGB-D-D [5], NYUv2 [34], Middlebury [6, 32], and Lu [22]. The high-quality RGB-D data of Hypersim are produced from 77,400 images across 461 indoor scenes, offering per-pixel geometric labels along with comprehensive scene geometry, material properties, and lighting information. For DSR training, we choose 2,000 RGB-D pairs. Building on previous approaches [5, 57, 58], we use bicubic interpolation to generate LR depth from depth annotations across these five datasets. Additionally, TOFDSR and RGB-D-D also provide real-world LR depth data, enabling the evaluation of the generalization capabilities of the different models. Refer to our appendix for metrics and implementation details.
+
+# 4.2. Comparison with State-of-the-arts
+
+Synthetic DSR. We first evaluate our proposed DuCos on widely used synthetic DSR datasets. As shown in Tab. 1, DuCos consistently delivers superior or highly competitive performance on various datasets and scales. Particularly, in the $\times 2$ case, our DuCos achieves the lowest RMSE and MAE while maintaining the highest $\delta_{1}$ , outperforming second-best methods by an average of $29.1\%$ in RMSE and $29.6\%$ in MAE on all five datasets. Likewise, in the case of $\times 4$ , our DuCos continues to demonstrate its superiority, exceeding the second-best approaches by $14.9\%$ in RMSE and $24.1\%$ in MAE, respectively. As the scale increases to $\times 8$ and $\times 16$ , the performance of all methods naturally degrades due to the loss of information in depth maps with
+
+
+(a) RGB
+
+
+(b) GT/LR Depth
+
+
+(c) DJF
+
+
+(d) DJFR
+
+
+(e) CUNet
+
+
+(f) DKN
+
+
+(g) FDKN
+
+
+(h) FDSR
+Figure 4. Error map comparisons on the synthetic NYU v2 dataset $(\times 4)$ , where warmer colors indicate higher errors.
+
+
+(i) DCTNet
+
+
+(j) DuCos
+
+| Method | Scale | Middlebury | Lu | NYU v2 | RGB-D-D | TOFDSR |
| RMSE | MAE | δ1 | RMSE | MAE | δ1 | RMSE | MAE | δ1 | RMSE | MAE | δ1 | RMSE | MAE | δ1 |
| DJF [15] | ×2 | 1.14 | 0.63 | 98.56 | 1.08 | 0.44 | 99.00 | 2.32 | 0.83 | 99.49 | 1.18 | 0.36 | 99.64 | 2.99 | 0.66 | 98.74 |
| DJFR [16] | 1.22 | 0.58 | 98.42 | 1.39 | 0.45 | 98.94 | 1.87 | 0.51 | 99.68 | 0.98 | 0.27 | 99.74 | 1.58 | 0.28 | 99.57 |
| CUNet [4] | 1.01 | 0.58 | 98.78 | 1.06 | 0.50 | 99.10 | 1.50 | 0.46 | 99.81 | 0.84 | 0.25 | 99.81 | 1.69 | 0.33 | 99.49 |
| FDKN [12] | 1.35 | 0.62 | 98.39 | 1.59 | 0.49 | 98.91 | 2.05 | 0.50 | 99.63 | 1.04 | 0.26 | 99.70 | 1.85 | 0.36 | 99.32 |
| DKN [12] | 1.32 | 0.62 | 98.48 | 1.48 | 0.48 | 99.00 | 1.95 | 0.49 | 99.66 | 0.98 | 0.24 | 99.74 | 1.87 | 0.36 | 99.33 |
| FDSR [5] | 0.94 | 0.51 | 98.89 | 0.94 | 0.39 | 99.14 | 1.74 | 0.57 | 99.70 | 0.91 | 0.26 | 99.76 | 1.55 | 0.40 | 99.24 |
| DCTNet [57] | 1.01 | 0.53 | 98.90 | 1.03 | 0.59 | 99.36 | 1.59 | 0.59 | 99.76 | 0.89 | 0.28 | 99.79 | 0.80 | 0.23 | 99.87 |
| DADA [24] | 1.28 | 0.60 | 98.47 | 1.45 | 0.48 | 99.07 | 2.00 | 0.54 | 99.65 | 1.04 | 0.27 | 99.71 | 1.73 | 0.37 | 99.26 |
| DuCos | 0.81 | 0.46 | 99.28 | 0.65 | 0.26 | 99.68 | 1.20 | 0.37 | 99.88 | 0.74 | 0.22 | 99.85 | 0.52 | 0.13 | 99.94 |
| DJF [15] | ×4 | 1.93 | 1.11 | 97.11 | 1.93 | 1.11 | 98.20 | 3.60 | 1.67 | 99.05 | 1.63 | 0.74 | 99.39 | 3.75 | 1.14 | 98.18 |
| DJFR [16] | 1.83 | 1.04 | 96.91 | 1.85 | 1.02 | 98.36 | 3.27 | 1.14 | 99.04 | 1.54 | 0.48 | 99.35 | 2.97 | 0.58 | 99.00 |
| CUNet [4] | 1.61 | 0.98 | 97.79 | 1.73 | 0.97 | 98.48 | 3.22 | 1.44 | 99.21 | 1.52 | 0.65 | 99.43 | 3.57 | 1.13 | 98.19 |
| FDKN [12] | 1.80 | 0.80 | 97.69 | 2.11 | 0.58 | 98.53 | 3.28 | 0.93 | 99.28 | 1.56 | 0.42 | 99.42 | 2.80 | 0.58 | 98.96 |
| DKN [12] | 1.77 | 0.78 | 97.77 | 2.05 | 0.56 | 98.58 | 3.15 | 0.90 | 99.34 | 1.50 | 0.41 | 99.49 | 2.73 | 0.56 | 99.04 |
| FDSR [5] | 1.72 | 0.84 | 97.69 | 1.95 | 0.56 | 98.52 | 2.94 | 0.85 | 99.39 | 1.41 | 0.40 | 99.51 | 2.41 | 0.51 | 99.07 |
| DCTNet [57] | 1.66 | 0.77 | 97.86 | 1.85 | 0.57 | 98.56 | 2.90 | 0.99 | 99.37 | 1.49 | 0.44 | 99.45 | 2.86 | 0.59 | 98.98 |
| DADA [24] | 1.82 | 0.83 | 97.45 | 2.12 | 0.66 | 98.35 | 3.08 | 0.96 | 99.33 | 1.63 | 0.46 | 99.39 | 2.85 | 0.68 | 98.57 |
| DuCos | 1.45 | 0.68 | 98.30 | 1.38 | 0.41 | 99.08 | 2.60 | 0.81 | 99.49 | 1.27 | 0.36 | 99.60 | 2.09 | 0.33 | 99.58 |
| DJF [15] | ×8 | 3.09 | 1.46 | 94.10 | 3.58 | 1.22 | 95.60 | 5.56 | 2.30 | 97.70 | 2.58 | 0.96 | 98.29 | 5.59 | 1.71 | 96.29 |
| DJFR [16] | 2.82 | 1.25 | 95.31 | 3.24 | 1.07 | 95.86 | 5.20 | 1.94 | 98.21 | 2.61 | 0.93 | 98.25 | 5.11 | 1.35 | 97.16 |
| CUNet [4] | 2.86 | 1.46 | 94.44 | 2.85 | 1.25 | 96.32 | 5.50 | 2.23 | 97.78 | 2.35 | 0.92 | 98.60 | 5.14 | 1.64 | 96.67 |
| FDKN [12] | 2.51 | 1.13 | 96.26 | 2.67 | 0.85 | 97.39 | 4.93 | 1.67 | 98.65 | 2.25 | 0.70 | 98.86 | 4.40 | 0.96 | 98.15 |
| DKN [12] | 2.43 | 1.12 | 96.26 | 2.88 | 0.88 | 97.13 | 4.88 | 1.71 | 98.62 | 2.33 | 0.74 | 98.76 | 4.54 | 1.06 | 97.87 |
| FDSR [5] | 2.41 | 1.13 | 96.24 | 2.69 | 0.86 | 97.35 | 4.82 | 1.69 | 98.57 | 2.25 | 0.73 | 98.72 | 4.28 | 0.95 | 98.06 |
| DCTNet [57] | 2.75 | 1.31 | 95.25 | 3.07 | 1.18 | 96.38 | 4.90 | 2.12 | 98.28 | 2.47 | 0.92 | 98.60 | 5.38 | 1.57 | 97.01 |
| DADA [24] | 2.77 | 1.27 | 95.01 | 3.76 | 1.17 | 96.01 | 4.83 | 1.86 | 98.34 | 2.81 | 0.93 | 98.29 | 5.86 | 1.64 | 96.15 |
| DuCos | 2.23 | 0.97 | 97.07 | 2.67 | 0.72 | 97.86 | 4.61 | 1.52 | 98.86 | 2.23 | 0.66 | 98.89 | 4.60 | 0.92 | 98.30 |
| DJF [15] | ×16 | 5.50 | 2.92 | 84.66 | 6.53 | 2.69 | 88.91 | 9.82 | 4.73 | 93.05 | 4.46 | 2.04 | 94.99 | 8.19 | 3.49 | 90.79 |
| DJFR [16] | 5.16 | 2.61 | 86.39 | 6.46 | 2.38 | 89.66 | 9.50 | 4.28 | 93.63 | 4.36 | 1.84 | 95.48 | 8.06 | 3.06 | 92.20 |
| CUNet [4] | 4.72 | 2.40 | 88.45 | 5.63 | 2.17 | 91.33 | 8.63 | 3.88 | 94.55 | 3.81 | 1.58 | 96.36 | 7.36 | 2.73 | 93.40 |
| FDKN [12] | 4.42 | 2.10 | 90.80 | 5.48 | 1.91 | 92.24 | 7.97 | 3.43 | 95.76 | 3.71 | 1.45 | 96.81 | 7.16 | 2.29 | 94.78 |
| DKN [12] | 4.17 | 1.97 | 91.67 | 5.44 | 1.90 | 91.94 | 7.70 | 3.28 | 96.06 | 3.70 | 1.39 | 97.06 | 7.24 | 2.20 | 95.26 |
| FDSR [5] | 3.97 | 1.81 | 92.52 | 5.23 | 1.67 | 93.44 | 7.29 | 2.91 | 96.86 | 3.44 | 1.24 | 97.37 | 6.85 | 1.91 | 95.96 |
| DCTNet [57] | 5.07 | 2.59 | 86.91 | 5.83 | 2.25 | 90.19 | 9.10 | 4.24 | 94.04 | 4.13 | 1.66 | 96.30 | 8.04 | 2.77 | 93.45 |
| DADA [24] | 4.11 | 2.06 | 90.09 | 6.19 | 2.22 | 90.95 | 7.99 | 3.54 | 95.64 | 4.01 | 1.59 | 96.71 | 7.79 | 2.70 | 93.25 |
| DuCos | 3.96 | 1.69 | 93.52 | 5.18 | 1.59 | 93.89 | 7.37 | 2.82 | 97.12 | 3.44 | 1.16 | 97.61 | 6.90 | 1.77 | 96.51 |
+
+Table 1. Quantitative comparisons on the synthetic DSR benchmarks. The best and second-best results are highlighted.
+
+lower resolution. However, DuCos remains highly effective, preserving lower errors and higher accuracy. Fig. 4 provides a visual comparison with the latest approaches, where the error maps highlight the ability of our DuCos to reconstruct depth with higher precision and thus it captures more accurate boundaries.
+
+Arbitrary-scale DSR. In downstream applications, scaling factors are often variable or unknown. In addition to evaluating DSR methods at fixed integer scales, we thus also
+
+assess their performance on arbitrary scaling factors. As illustrated in Fig. 5, experiments are conducted at $\times 1.5$ , $\times 2.7$ , $\times 3.4$ , $\times 5.3$ , and $\times 11.6$ scales. Our DuCos consistently achieves outstanding results across all scales and datasets. Specifically, compared to all methods on these five scales, DuCos demonstrates significantly superior performance on RMSE, MAE, and $\delta_{1}$ , with average improvements of $20.6\%$ , $22.3\%$ , and 0.47 percent points, respectively. These results further validate DuCos's effectiveness.
+
+
+Figure 5. Comparisons with arbitrary scaling factors on the synthetic DSR datasets. Refer to our appendix for more details.
+
+| Method | RGB-D-D | TOFDSR | RGB-D-D w/ noise | TOFDSR w/ noise |
| RMSE | MAE | δ1 | RMSE | MAE | δ1 | RMSE | MAE | δ1 | RMSE | MAE | δ1 |
| DJF [15] | 5.54 | 3.43 | 93.81 | 5.84 | 2.13 | 96.79 | 7.94 | 5.16 | 84.82 | 11.45 | 7.87 | 67.95 |
| DJFR [16] | 5.52 | 3.51 | 93.58 | 5.72 | 2.10 | 97.03 | 7.50 | 4.83 | 86.25 | 10.92 | 7.39 | 70.46 |
| CUNet [4] | 5.84 | 3.06 | 94.75 | 6.04 | 2.21 | 96.46 | 6.69 | 4.14 | 89.36 | 9.76 | 5.86 | 80.43 |
| FDKN [12] | 5.37 | 2.70 | 96.05 | 5.77 | 2.19 | 97.33 | 6.66 | 4.26 | 90.09 | 8.13 | 4.66 | 86.24 |
| DKN [12] | 5.08 | 2.58 | 96.28 | 5.50 | 2.07 | 97.54 | 6.50 | 4.16 | 90.04 | 7.42 | 4.29 | 88.20 |
| FDSR [5] | 5.49 | 3.10 | 94.77 | 5.03 | 1.67 | 97.61 | 6.39 | 4.07 | 90.69 | 6.31 | 3.17 | 92.74 |
| DCTNet [57] | 5.43 | 3.29 | 93.15 | 5.16 | 2.10 | 96.37 | 6.04 | 3.79 | 90.90 | 7.52 | 4.50 | 86.04 |
| SFG [55] | 3.88 | 1.96 | 97.09 | 4.52 | 1.72 | 97.45 | 5.87 | 3.79 | 89.84 | 5.46 | 2.89 | 93.02 |
| DuCos | 3.68 | 1.54 | 97.87 | 4.29 | 1.15 | 98.67 | 4.14 | 2.00 | 96.76 | 5.20 | 2.20 | 96.44 |
+
+Table 2. Quantitative comparisons on the real-world DSR datasets, including RGB-D-D, TOFDSR and their noisy patterns.
+
+
+Figure 6. Error map comparisons on the real-world RGB-D-D dataset. Please see our appendix for more visualizations.
+
+Real-world DSR. Since the introduction of FDSR [5], realworld DSR has gained increasing attention. Unlike integer or arbitrary scaling, the real-world setting reflects the practical challenges of DSR. Additionally, we assess model robustness by introducing noise to simulate external disturbances. As listed in Tab. 2, DuCos consistently outperforms all competing methods on both datasets. It surpasses the
+
+second-best SFG by $4.2\mathrm{mm}$ in MAE on RGB-D-D, and exceeds SFG by $5.7\mathrm{mm}$ on TOFDSR. Even under noisy conditions², our DuCos maintains its advantage. On average, DuCos outperforms the suboptimal methods by $17.1\%$ in RMSE, $35.6\%$ in MAE, and 4.6 points in $\delta_{1}$ , demonstrating
+
+| Method | NYU v2 | RGB-D-D | TOFDSR |
| RMSE | MAE | δ1.05 | RMSE | MAE | δ1.05 | RMSE | MAE | δ1.05 |
| DJF [15] | 119.41 | 101.14 | 8.53 | 34.48 | 29.93 | 16.26 | 47.98 | 44.30 | 10.94 |
| DJFR [16] | 147.43 | 121.73 | 7.85 | 40.46 | 34.49 | 14.03 | 50.14 | 45.81 | 8.59 |
| CUNet [4] | 133.90 | 108.96 | 7.14 | 35.03 | 30.67 | 15.08 | 50.25 | 46.53 | 8.96 |
| FDKN [12] | 187.53 | 154.15 | 4.26 | 42.37 | 36.91 | 14.04 | 49.34 | 44.88 | 14.28 |
| DKN [12] | 186.10 | 152.74 | 4.33 | 40.38 | 35.15 | 14.40 | 47.27 | 43.34 | 9.58 |
| FDSR [5] | 118.76 | 101.28 | 8.39 | 35.88 | 30.15 | 20.64 | 45.96 | 40.92 | 20.26 |
| DCTNet [57] | 118.45 | 101.30 | 8.20 | 37.85 | 33.25 | 12.82 | 51.58 | 48.41 | 6.88 |
| DuCos | 58.74 | 46.00 | 26.19 | 24.64 | 21.13 | 26.45 | 30.40 | 25.63 | 22.37 |
+
+
+Figure 7. Ablation study of DuCos on the real-world RGB-D-D.
+
+strong robustness against noise. Fig. 6 shows that DuCos recovers a higher-quality depth map near the boundaries and textureless areas.
+
+Compressed DSR. Due to the limitations of consumer-grade depth cameras and bandwidth constraints, restoring accurate depth from compressed sources is crucial. Following GDNet [59], Tab. 3 presents the $\times 8$ results. Our DuCos consistently outperforms all previous methods, achieving average improvements of $37.6\%$ in RMSE, $40.4\%$ in MAE, and 8.5 points in $\delta_{1}$ over the second-best methods. These significant improvements underscore the effectiveness and generalization of our approach in minimizing reconstruction error while substantially enhancing accuracy.
+
+# 4.3. Ablation Study
+
+DuCos designs. Fig. 7 presents the ablation results on the real-world RGB-D-D. The naive model consists of separate image and depth branches, each using four residual groups [56] for feature extraction and fused by element-wise addition. Our introduction of depth foundation models as prompts reduces the RMSE from $3.97\mathrm{cm}$ to $3.86\mathrm{cm}$ . Based on this, CF improves performance by $0.1\mathrm{cm}$ , while GR yields a $0.11\mathrm{cm}$ improvement. Furthermore, combining CF and GR reduces the error of the base model by $0.15\mathrm{cm}$ . Finally, incorporating the LD strategy (red bar) yields the best performance, achieving an RMSE of $3.68\mathrm{cm}$ . Notably, the alignment loss $\mathcal{L}_{cf}$ in CF also leads to performance gains, reducing the RMSE from $3.82\mathrm{cm}$ to $3.76\mathrm{cm}$ . Additionally, normalization in GR mitigates discrepancies between the target depth and the relative depth from the foundation models, further reducing the error by $0.05\mathrm{cm}$ . In summary, each component contributes positively to the entire model.
+
+Table 3. Quantitative comparisons of compressed DSR on NYU v2, RGB-D-D, and TOFDSR datasets.
+
+| Prompt in DuCos | Params. | Time | NYU v2 | Middlebury |
| (M) | (ms) | RMSE | MAE | δ1.05 | RMSE | MAE | δ1.05 |
| DepthFormer [17] | 282.76 | 58.47 | 7.27 | 2.82 | 97.12 | 4.01 | 1.74 | 93.21 |
| UniDepth v2-S [29] | 87.21 | 91.27 | 8.69 | 3.30 | 96.12 | 4.21 | 1.79 | 93.12 |
| UniDepth v2-L [29] | 372.97 | 159.28 | 8.86 | 3.45 | 95.85 | 5.40 | 2.37 | 89.83 |
| DA v2-S [52] | 34.38 | 23.53 | 7.37 | 2.82 | 97.12 | 3.96 | 1.69 | 93.52 |
| DA v2-B [52] | 107.19 | 31.24 | 7.34 | 2.79 | 97.14 | 3.94 | 1.69 | 93.61 |
| DA v2-L [52] | 345.06 | 71.81 | 7.15 | 2.74 | 97.29 | 3.64 | 1.55 | 94.35 |
+
+Table 4. Ablation study of DuCos with different foundation models on the synthetic NYU v2 $(\times 16)$ and Middlebury $(\times 16)$ .
+
+
+Figure 8. Ablation study of CF on the real-world RGB-D-D.
+
+Iteration & fusion in CF. Fig. 8 shows the ablation study of the CF module. As the number of iterations increases, the error progressively decreases. To balance performance and computational complexity, we set the default iteration count to 4. Furthermore, our findings indicate that the fusion based on the Pearson correlation coefficient (PCC) outperforms both addition and concatenation, achieving improvements of $0.02\mathrm{cm}$ and $0.03\mathrm{cm}$ , respectively.
+
+Depth Foundation Models. Tab. 4 lists the ablation study of DuCos using different foundation models as prompts, including DepthFormer [17], UniDepth v2 [29], and DA v2 [52]. The inference time is measured on a single 4090 GPU. The results indicate that heavier prompts generally yield better performance than their smaller counterparts. Among these models, DA v2-L achieves the highest performance. Considering the complexity-performance trade-off, we adopt DA v2-S as the default prompt for DuCos.
+
+# 5. Conclusion
+
+In this paper, we introduce DuCos, a novel DSR paradigm based on Lagrangian duality theory. By formulating DSR as a constrained optimization problem, our DuCos can restore global reconstruction with local geometric consistency, leading to better depth predictions. Furthermore, we pioneer the use of foundation models as prompts, leveraging correlative fusion and gradient regulation to enhance generalization across diverse scenarios. These prompts are seamlessly incorporated into the Lagrangian constraint term, creating a synergistic framework that combines theoretical rigor with practical adaptability. Extensive experiments demonstrate the superiority of our DuCos in terms of accuracy, robustness, and generalization.
+
+# Acknowledgment
+
+This research/project is supported by the National Research Foundation, Singapore, under its NRF-Investigatorship Programme (Award ID. NRF-NRFI09-0008).
+
+# References
+
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+# DuET: Dual Incremental Object Detection via Exemplar-Free Task Arithmetic
+
+Munish Monga $^{1,2}$ Vishal Chudasama $^{1}$ Pankaj Wasnik $^{1,*}$ Biplab Banerjee $^{2}$ $^{1}$ Sony Research India $^{2}$ Indian Institute of Technology, Bombay
+
+{munish.monga, vishal.chudasamal, pankaj.wasnik}@sony.com, getbiplab@gmail.com
+
+
+Figure 1. Comparison of Class Incremental Object Detection (CIOD), Domain Incremental Object Detection (DIOD), and our proposed Dual Incremental Object Detection (DuIOD), where $\checkmark$ : the scenario is addressed, $X$ : the scenario is NOT addressed. CIOD (left) incrementally learns new categories $(\mathcal{C}_1 \to \mathcal{C}_2)$ in a fixed domain but struggles in unseen domains. DIOD (middle), adapts to new domains $(\mathcal{D}_1 \to \mathcal{D}_2)$ but does not detect new classes. In contrast, DuIOD (right) addresses both challenges by learning new object categories while generalizing across evolving domains (zoomed-in for best view).
+
+
+
+
+
+# Abstract
+
+Real-world object detection systems, such as those in autonomous driving and surveillance, must continuously learn new object categories and simultaneously adapt to changing environmental conditions. Existing approaches, Class Incremental Object Detection (CIOD) and Domain Incremental Object Detection (DIOD)—only address one aspect of this challenge. CIOD struggles in unseen domains, while DIOD suffers from catastrophic forgetting when learning new classes, limiting their real-world applicability. To overcome these limitations, we introduce Dual Incremental Object Detection (DuIOD), a more practical setting that simultaneously handles class and domain shifts in an exemplar-free manner. We propose DuET, a Task Arithmetic-based model merging framework that enables stable incremental learning while mitigating sign conflicts through a novel Directional Consistency Loss. Unlike prior methods, DuET is detector-agnostic, allowing models like YOLO11 and RTDETR to function as real-time incremental object detectors. To comprehensively evaluate both retention and adaptation, we introduce the Retention-Adaptability Index (RAI), which combines the Average Retention Index (Avg RI) for catastrophic forgetting and the Average Generalization Index for domain adaptability into a common ground. Extensive experiments on the Pascal Series and Diverse Weather Series demonstrate DuET's effectiveness, achieving a $+13.12\%$ RAI improvement while preserving $89.3\%$ Avg RI on the Pascal Series (4 tasks), as well as a $+11.39\%$ RAI improvement with $88.57\%$ Avg RI on the Diverse Weather Series (3 tasks), outperforming existing methods.
+
+# 1. Introduction
+
+Real-world object detection systems must continuously learn new categories and adapt dynamically to evolving environments without necessitating full retraining. Traditional models, typically trained on static datasets, struggle to perform effectively in dynamic real-world scenarios like autonomous driving and surveillance, where they must recognize novel objects while handling environmental variations. For example, an autonomous vehicle must detect newly introduced road signs under diverse lighting and weather conditions—without forgetting past knowledge, a challenge known as catastrophic forgetting [25, 38, 40].
+
+Existing approaches attempt to address this through Class Incremental Object Detection (CIOD) [9, 19, 20, 28, 40], which learns new object categories while assuming a fixed domain, and Domain Incremental Object Detection (DIOD) [41], which adapts to unseen domains while keeping object categories unchanged. However, these methods operate under restrictive assumptions—CIOD neglects domain shifts, while DIOD assumes a fixed set of object categories. As shown in Figure 1, both approaches fail when faced with simultaneous class and domain shifts, a scenario frequently encountered in real-world applications.
+
+To bridge this gap, we introduce a more practical yet underexplored setting, Dual Incremental Object Detection (DuIOD), where object detectors must incrementally learn new object categories across evolving domains without access to previous training data (exemplar-free). While some works, such as VIL [35], extend incremental learning to both class and domain shifts, they primarily focus on classification tasks and do not address key object detection chal
+
+
+Figure 2. Catastrophic forgetting of $\mathcal{T}_1$ classes in multi-phase experiments for various methods on the DuIOD task. The left plot illustrates catastrophic forgetting in Night Sunny [1:2] classes across three incremental tasks: Night Sunny [1:2] ( $\mathcal{T}_1$ ) → Daytime Sunny [3:4] ( $\mathcal{T}_2$ ) → Daytime Foggy [5:7] ( $\mathcal{T}_3$ ) on the Diverse Weather Series dataset. Similarly, the right plot depicts catastrophic forgetting in Watercolor [1:3] classes across four incremental tasks: Watercolor [1:3] ( $\mathcal{T}_1$ ) → Comic [4:6] ( $\mathcal{T}_2$ ) → Clipart [7:13] ( $\mathcal{T}_3$ ) → VOC [14:20] ( $\mathcal{T}_4$ ) on the Pascal Series dataset.
+
+lenges like spatial feature retention and bounding box refinement, nor do they tackle the background shift problem of IOD [27, 32], where previously learned objects are misclassified as background if unannotated in later tasks, all of which are present in DuIOD. Recently, PD [15] partially addresses domain shifts in object detection but fails to generalize to the broader DuIOD problem.
+
+To tackle the challenges of DuIOD, we propose DuET, a simple yet effective Task Arithmetic (TA) [13] based incremental learning framework for robust object detection across evolving domains. TA paradigm was recently introduced by [13] for modifying pre-trained models via arithmetic operations on task vectors. Formally, a task vector is derived by subtracting the weights of a pre-trained model from those of the same model fine-tuned on a specific task. In DuET, we decompose model parameters into shared parameters, which persist across all incremental tasks, and task-specific parameters, which evolve incrementally. We compute task vectors for both previous and current tasks using the shared parameters. DuET framework is built upon two components: DuET Module & Incremental Head. DuET Module merges these task vectors through dynamic layer-wise retention and adaptation factors, effectively mitigating catastrophic forgetting. Meanwhile, the Incremental Head concatenates task-specific parameters from both past and current tasks, enhancing generalization. Unlike prior methods, DuET is object detector-agnostic, seamlessly integrating with diverse detection backbones. Notably, it enables state-of-the-art real-time object detectors, such as YOLO11 [17] and RT-DETR [29], to function as real-time incremental object detectors.
+
+Additionally, we introduced Directional Consistency Loss to further stabilize incremental updates, which mitigates weight update conflicts during model merging [45, 49]. Moreover, to jointly quantify catastrophic forgetting
+
+and adaptation performance, we propose a new evaluation metric, the Retention-Adaptability Index (RAI).
+
+Our extensive experiments on Pascal Series and Diverse Weather Series datasets demonstrate the effectiveness of DuET in addressing the DuIOD task. As highlighted in Figure 2, CIOD-based methods (e.g., CL-DETR [28]) suffer severe forgetting in unseen domains, while DIOD-based methods (e.g., LDB [41]) fail to retain previously learned categories. Additionally, conventional incremental learning techniques such as LwF [25] and ERD [8] also struggle in this setting. In contrast, DuET significantly mitigates catastrophic forgetting and enables robust incremental learning across both class and domain shifts. We highlight our contributions as:
+
+- To the best of our knowledge, DuET is the first method to tackle DuIOD using the concept of Task Merging.
+- We propose a novel TA-based algorithm which is object detector agnostic, validated YOLO11 and RT-DETR, enabling real-time incremental object detection.
+- We propose Directional Consistency Loss to mitigate sign conflicts during model merging, ensuring stable incremental learning.
+- To quantify both catastrophic forgetting and adaptation performance, we introduce a new evaluation metric, the Retention-Adaptability Index.
+
+# 2. Related Works
+
+Class Incremental Object Detection: CIOD has evolved from early CNN-based methods [2, 8, 22, 27, 34, 36, 37, 40] to Transformer-based approaches [9, 18-20, 28], improving generalization and stability during incremental updates. Initial efforts, such as [40], introduced CIOD via knowledge distillation inspired by incremental classification methods like LwF [25]. Subsequent works explored intermediate feature distillation [3, 4, 10], replay buffers [1, 19, 39], parameter isolation [23, 50], and pseudo-labeling [9, 20, 46].
+
+Transformer-based models, including CL-DETR [28], SDDGR [19], and VLM-PL [20], use Deformable DETR [52] to enhance CIOD. CL-DETR applies knowledge distillation on labels with exemplar replay, SDDGR integrates generative replay via stable diffusion, and VLM-PL employs vision-language pseudo-labeling. However, most CIOD methods rely on exemplars [1, 19, 51] and assume a static domain. In contrast, DuET proposes an exemplar-free, unified approach that prevents catastrophic forgetting while incrementally learning new objects across domains.
+
+Domain Incremental Object Detection: DIOD focuses on adapting to distribution shifts—such as changes in lighting, viewpoints, and weather—while maintaining a fixed object set. LDB [41] tackles DIOD by learning domain biases with frozen base models and employing a nearest-mean classifier for domain selection, while other methods [33, 42, 43] primarily target Domain Incremental Learn
+
+ing through prompt-based strategies, domain statistics, and cross-domain concept alignment.
+
+Although some DIOD methods support exemplar-free adaptation, they assume a consistent class set across domains and struggle with inter-domain class confusion. DuET overcomes these limitations by using task arithmetic-based model merging to incrementally learn class and domain shifts without relying on exemplars.
+
+Task Arithmetic: Task arithmetic has recently emerged as an effective way to modify pre-trained models through simple arithmetic operations on model weights. Task-Arithmetic [13] showed that task vectors—differences between fine-tuned and pre-trained model weights—can steer model behaviour. Extensions like Fisher-Merging [31] and RegMean [16] introduced importance-weighted schemes using Fisher information and inner-product matrices, but they require manual matrix computations. To resolve sign conflicts during model merging, TIES-Merging [45] enforces orthogonality constraints, while DARE [49] reduces interference using dropout and rescaling. EMR-Merging [12] aligns task directions and amplitudes through a tuning-free strategy, and MagMax [30] mitigates forgetting through important parameters selection.
+
+Unlike standard TA or the variants mentioned above, which merge entire task vectors without distinction, DuET applies layer-wise Task merging with dynamically calculated retention-adaptation factors to prevent catastrophic forgetting while improving generalization. In Section 6, we benchmark DuET against existing model-merging baselines and demonstrate its superiority across multiple object detectors in the DuIOD task.
+
+# 3. Methodology
+
+# 3.1. Problem formulation
+
+In exemplar-free DuIOD, our goal is to develop a unified and robust object detection model that incrementally learns new object classes and adapts to evolving domain characteristics without retaining any past training data (exemplars).
+
+Formally, we define a sequence of tasks as $T = \{\mathcal{T}_1,\mathcal{T}_2,\dots ,\mathcal{T}_T\}$ , where each task $\mathcal{T}_t$ introduces a new set of object classes $\mathcal{C}_t$ from a novel domain $\mathcal{D}_t$ . The cumulative set of classes and domains encountered up to task $\mathcal{T}_t$ is denoted by: $\mathcal{C}_{1:t} = \bigcup_{j = 1}^{t}\mathcal{C}_{j}$ and $\mathcal{D}_{1:t} = \bigcup_{j = 1}^{t}\mathcal{D}_{j}$ , respectively. Furthermore, following the typical CIOD & DIOD assumptions [9, 19, 20, 28, 40, 41], we ensure that:
+
+$$
+\mathcal {C} _ {t} \cap \mathcal {C} _ {1: t - 1} = \emptyset , \quad \mathcal {D} _ {t} \cap \mathcal {D} _ {1: t - 1} = \emptyset , \quad \forall t \geq 2 \tag {1}
+$$
+
+$$
+P \left(\mathcal {D} _ {t}\right) \neq P \left(\mathcal {D} _ {t ^ {\prime}}\right) \forall t \neq t ^ {\prime}. \tag {2}
+$$
+
+For each task $\mathcal{T}_t$ , we define the dataset as $\{\mathcal{X}_t,\mathcal{Y}_t\}$ , where $\mathcal{X}_t = \{x_j^t\}_{j = 1}^{\mathcal{N}_t}$ consists of input images from $\mathcal{D}_t$ that contain only objects from $\mathcal{C}_t$ , and $\mathcal{Y}_t = \{y_j^t\}_{j = 1}^{\mathcal{N}_t}$ provides
+
+bounding box annotations exclusively for $\mathcal{C}_t$ . While images in $\mathcal{X}_t$ may include objects from previously learned classes $\mathcal{C}_{1:t-1}$ , these objects remain unlabeled and are treated as background. This results in a fundamental background shift problem [27, 32], where previously learned objects become part of the background in later tasks—an issue absent in prior works like [35].
+
+To maintain an exemplar-free setting, during task $\mathcal{T}_t$ , we have access only to the dataset $\mathcal{D}_t$ and do not retain any images or annotations from previous domains $\{\mathcal{D}_1,\mathcal{D}_2,\ldots ,\mathcal{D}_{t - 1}\}$ . Our objective is to incrementally update the object detection model $\mathcal{M}_{\theta_t}$ , parameterized by $\theta_{t}$ using only data from $\mathcal{D}_t$ , ensuring that $\mathcal{M}_{\theta_t}$ can accurately detect objects from all learned classes $\mathcal{C}_{1:t}$ across all encountered domains $\mathcal{D}_{1:t}$ .
+
+# 3.2. Overview of DuET Approach
+
+To tackle DuIOD, we discuss the DuET approach in this and subsequent sections. As depicted in Figure 3, DuET strategically decomposes model parameters into shared $(\theta_{s})$ and task-specific $(\theta_{\tau_t})$ components, thereby facilitating efficient knowledge transfer and modular adaptation. The DuET framework is built upon two core components:
+
+- DuET Module: This module fuses shared task vectors $(\tau_{\mathrm{old}}$ and $\tau_{\mathrm{curr}})$ through dynamic, layer-wise weighting factors—retention $(\alpha_l)$ and adaptation $(\beta_l)$ —as described in Section 3.4. This design not only preserves previously acquired knowledge but also incorporates new information in a balanced manner, effectively countering catastrophic forgetting.
+- Incremental Head: This component consolidates task-specific parameters from both past and current tasks, thereby enhancing the model's generalization across diverse detection scenarios. Additionally, Directional Consistency Loss $(\mathcal{L}_{\mathrm{DC}})$ , see Section 3.5) enforces alignment in the direction of incremental updates and prevents detrimental sign conflicts.
+
+Unlike prior approaches [8, 15, 25], which are optimized for specific detection backbones, DuET exhibits broad generalization across a variety of object detectors [17, 29, 52] (see Table 3). Moreover, DuET's training and TA algorithm are provided in Algorithms 1 & 2 (suppl.).
+
+# 3.3. Training Strategy
+
+Base Task: $\mathcal{T}_1$ . Consider a generic, pre-trained object detector $\mathcal{M}_{\theta_0}$ parameterized by $\theta_0$ as shown in figure 3. Let Task $\mathcal{T}_1$ introduce new $\mathcal{C}_1$ classes from $\mathcal{D}_1$ domain. We first train this model on the dataset $\{\mathcal{X}_1,\mathcal{Y}_1\}$ for Task $\mathcal{T}_1$ using the standard detection loss, $\mathcal{L}_{\mathrm{Detector}}$ , which is specific to the object detector being considered. After the first update step, the model's parameters become:
+
+$$
+\theta_ {1} \leftarrow \theta_ {0} - \eta \nabla_ {\theta} \mathcal {L} _ {\text {D e t e c t o r}} \left(\theta_ {0}; \mathcal {X} _ {1}, \mathcal {Y} _ {1}\right), \tag {3}
+$$
+
+
+Figure 3. Overview of the proposed DuET framework for exemplar-free Dual Incremental Object Detection (DuIOD). Left: To setup DuIOD task, we illustrate a sequence of three tasks $\{\mathcal{T}_1,\mathcal{T}_2,\mathcal{T}_3\}$ , each introducing new object classes (e.g. $\{car, truck\}, \{person, bus\}, \{rider, bike, motor\}$ ) under different domain shifts (Night Sunny, Daytime Sunny, Daytime Foggy) respectively. A generic object detector $\mathcal{M}_{\theta_0}$ is first fine-tuned on $\mathcal{T}_1$ , yielding parameters $\theta_{1}$ , the parameters of the model at every Task are decomposed into shared $(\theta_s)$ and task-specific $(\theta_{\tau_1})$ parameters. Subsequently, for each incremental Task $(\mathcal{T}_t,t\geq 2)$ , the shared parameters are merged via DuET Module while the Incremental Head concatenates the task-specific parameters from the old and current Task, $\theta_{\tau_t}$ & $(\theta_{\tau_{t - 1}})\mathrm{incre}$ respectively. During the Inference Phase, the merged incremental weights $\theta_{1}, (\theta_{2})_{\mathrm{incre}}$ & $(\theta_3)_{\mathrm{incre}}$ are used to detect objects from the respective cumulative sets of classes $\mathcal{C}_1,\mathcal{C}_{1:2}$ & $\mathcal{C}_{1:3}$ . Top-Right: We depict the decomposition of $\theta_s$ & $\theta_{\tau}$ for a generic, backbone-agnostic object detector $\mathcal{M}_{\theta}$ , with the DuET framework validated across a variety of object detectors (e.g. YOLO11 [17], RTDETR [29]). Bottom-Right: We zoom in on the DuET Module, which merges the old and current shared task vectors $(\tau_{old},\tau_{curr})$ using layer-wise retention $(\alpha_l)$ and adaptation $(\beta_l)$ factors as per equation 12 (zoomed-in for best view).
+
+
+
+where $\eta$ is the learning rate.
+
+At every incremental step, we decompose the model parameters into shared parameters $\theta_{s}$ , which are common across all incremental tasks, and task-specific parameters $\theta_{\tau_t}$ , which evolve with each incremental step. For instance, in YOLO11 [17], the backbone and neck components, responsible for multi-scale feature extraction and feature refinement, constitute $\theta_{s}$ , whereas the detection head, which is responsible for final task-specific object localization and classification, forms $\theta_{\tau_t}$ . Hence, for Task $\mathcal{T}_1$ , we have:
+
+$$
+\theta_ {0} \rightarrow \left[ \theta_ {s _ {0}}, \theta_ {\tau_ {0}} \right], \quad \theta_ {1} \rightarrow \left[ \theta_ {s _ {1}}, \theta_ {\tau_ {1}} \right]. \tag {4}
+$$
+
+After Task $\mathcal{T}_1$ training, following the task vector definition from [13], we compute the first task vector as:
+
+$$
+\tau_ {s _ {1}} = \theta_ {s _ {1}} - \theta_ {s _ {0}}, \tag {5}
+$$
+
+Here $\tau_{s_1}$ effectively captures how the shared parameters must shift to accommodate the first Task, while the remaining parameters, $\theta_{\tau_1}$ constitute the task-specific weights that
+
+help in localization and classification of the newly introduced $\mathcal{C}_1$ classes. As illustrated in Figure 3, for inference on the base task $\mathcal{T}_1$ , we directly employ $\mathcal{M}_{\theta_1}$ .
+
+Incremental Tasks $\{\mathcal{T}_2,\mathcal{T}_3\ldots ,\mathcal{T}_T\}$ . For each incremental task $(\mathcal{T}_t,t\geq 2)$ , the model encounters a new set of classes $\mathcal{C}_t$ from domain $\mathcal{D}_t$ . We follow sequential fine-tuning and initialize $\theta_t\gets \theta_{t - 1}$ , following [30], but this time, we train the model using $\mathcal{L}_{\mathrm{Total}}$ (eq. 3.5), which incorporates a modified Distillation Loss $\mathcal{L}_{\mathrm{Distill}}^*$ to help preserve knowledge from previously learned tasks and Directional Consistency Loss $\mathcal{L}_{\mathrm{DC}}$ to help resolve sign conflicts and encourage stable parameter updates, along with the object-detector loss $\mathcal{L}_{\mathrm{Detector}}$ (see section 3.5). Hence, after every incremental Task $\mathcal{T}_t$ , the model parameters are updated as:
+
+$$
+\theta_ {t} \leftarrow \theta_ {t - 1} - \eta \nabla_ {\theta} \mathcal {L} _ {\text {T o t a l}} \left(\theta_ {t - 1}; \mathcal {X} _ {t}, \mathcal {Y} _ {t}\right). \tag {6}
+$$
+
+As before, we then decompose the updated parameters into:
+
+$$
+\theta_ {t - 1} \rightarrow \left[ \theta_ {s _ {t - 1}}, \theta_ {\tau_ {t - 1}} \right], \quad \theta_ {t} \rightarrow \left[ \theta_ {s _ {t}}, \theta_ {\tau_ {t}} \right]. \tag {7}
+$$
+
+Now, to incorporate the knowledge from current domain $\mathcal{D}_t$ and current classes $\mathcal{C}_t$ into the shared parameters $\theta_s$ without discarding knowledge of older tasks $\mathcal{T}_{1:t - 1}$ , we define two shared task-vectors as:
+
+$$
+\tau_ {\text {o l d}} = \theta_ {s _ {t - 1}} - \theta_ {s _ {0}} ^ {1}, \quad \tau_ {\text {c u r r}} = \theta_ {s _ {t}} - \theta_ {s _ {0}} ^ {1}. \tag {8}
+$$
+
+The shared task vectors, $\tau_{\mathrm{old}}$ and $\tau_{\mathrm{curr}}$ , play a crucial role in capturing the evolution of the shared parameters as the model transitions between tasks. Specifically, $\tau_{\mathrm{old}}$ represents the cumulative update from the initial pre-trained state up to the last incremental phase, effectively embedding the knowledge of all previous tasks. In contrast, $\tau_{\mathrm{curr}}$ captures the immediate update introduced by the current Task. This separation allows us to precisely balance the retention of previously learned features with the integration of new information, thereby mitigating catastrophic forgetting while enhancing the model's generalization capability. By isolating these vectors, the proposed DuET framework benefits from clearly delineating what knowledge needs to be preserved versus what can be adapted.
+
+# 3.4. Fusing task vectors on shared weights
+
+The core of DuET approach lies in the DuET Module, which performs the dynamic integration of $\tau_{\mathrm{old}}$ and $\tau_{\mathrm{curr}}$ to update the shared weights (Figure 3). Although these retention-adaptation factors are empirically motivated, they can be viewed through a stability-plasticity lens in incremental learning. Interpreting $\tau_{\mathrm{old}}^l$ and $\tau_{\mathrm{curr}}^l$ as "directions" in parameter space—one encoding the cumulative shifts for past tasks and the other the shift introduced by the new Task—our layer-wise $\alpha_l$ and $\beta_l$ define a linear combination that balances preserving old knowledge ( $\alpha_l \approx 1$ ) versus integrating new information ( $\beta_l \approx 1$ ). By comparing $\|\tau_{\mathrm{old}}^l\|$ and $\|\tau_{\mathrm{curr}}^l\|$ at each layer, we obtain a first-order approximation of "which update dominates," adaptively favoring retention when $\|\tau_{\mathrm{old}}^l\|$ is large and plasticity when $\|\tau_{\mathrm{curr}}^l\|$ is large. Geometrically, this ensures the merged parameters lie neither too close to the old solution nor fully dominated by new updates, effectively mitigating catastrophic forgetting and enhancing generalization. For each layer $l \in \{1, \dots, \mathcal{L}\}$ , we define a p-factor:
+
+$$
+p _ {l} = \frac {\left\| \tau_ {\text {o l d}} ^ {l} \right\| - \left\| \tau_ {\text {c u r r}} ^ {l} \right\|}{\left\| \tau_ {\text {o l d}} ^ {l} + \tau_ {\text {c u r r}} ^ {l} \right\| + \epsilon}, \tag {9}
+$$
+
+where $\| \cdot \|$ denotes the $\ell_1$ norm and $\epsilon$ ensures numerical stability. Mapping $p_l$ via a hyperbolic tangent scaled by $\gamma$ gives:
+
+$$
+\delta_ {l} = \gamma \tanh \left(p _ {l}\right), \tag {10}
+$$
+
+After clamping $\delta_l$ to $[- \gamma, \gamma]$ , and adding a base coefficient $\alpha_{\mathrm{base}}$ , we define:
+
+$$
+\alpha_ {l} = \alpha_ {\text {b a s e}} + \operatorname {c l a m p} \left(\delta_ {l}, - \gamma , \gamma\right), \quad \beta_ {l} = 1 - \alpha_ {l}. \tag {11}
+$$
+
+Hence, unlike second-order methods (e.g., Fisher Merging [31]) that require computing parameter importance matrices, the p-factor captures a simpler, local notion of importance. It forgoes expensive matrix approximations yet still encodes how far each layer's weights have drifted from the original baseline. Given these per-layer coefficients, the updated shared weights for layer $l$ are:
+
+$$
+\left(\theta_ {s _ {t}} ^ {l}\right) _ {\text {i n c r e}} = \theta_ {s _ {0}} ^ {l} + \alpha_ {l} \tau_ {\text {o l d}} ^ {l} + \beta_ {l} \tau_ {\text {c u r r}} ^ {l}. \tag {12}
+$$
+
+Applying this across all layers yields $(\theta_{s_t})_{\mathrm{incre}}$ . Simultaneously, the Incremental Head concatenates the current task-specific parameters with the previous ones:
+
+$$
+\left(\theta_ {\tau_ {t}}\right) _ {\text {i n c r e}} \leftarrow \left[ \theta_ {\tau_ {t}}; \left(\theta_ {\tau_ {t - 1}}\right) _ {\text {i n c r e}} \right] \tag {13}
+$$
+
+Finally, combining these updated shared and task-specific components produces the overall incremental weights:
+
+$$
+\left(\theta_ {t}\right) _ {\text {i n c r e}} \leftarrow \left[ \left(\theta_ {s _ {t}}\right) _ {\text {i n c r e}}, \left(\theta_ {\tau_ {t}}\right) _ {\text {i n c r e}} \right] \tag {14}
+$$
+
+which initialize the model for the subsequent Task, i.e., $\theta_{t + 1}\gets (\theta_t)_{\mathrm{incre}}$
+
+As illustrated in Figure 3, for inference on incremental tasks ( $t \geq 2$ ), we employ the merged incremental models $\mathcal{M}_{\theta_t}$ , parameterized by the reconstructed weights $(\theta_t)_{\mathrm{incre}}$ , to detect $\mathcal{C}_{1:t}$ classes across domains $\mathcal{D}_{1:t}$ following the evaluation protocol detailed in Section 4.2.
+
+# 3.5. Loss objectives
+
+For the base task $(t = 1)$ , we optimize the object detector using the standard detection loss, $\mathcal{L}_{\mathrm{Detector}}$ , which is specific to the base detector and is responsible for object localization and classification. For incremental tasks $(t \geq 2)$ , we augment $\mathcal{L}_{\mathrm{Detector}}$ with a modified Distillation Loss $\mathcal{L}_{\mathrm{Distill}}^*$ (discussed in Appendix B), along with our Directional Consistency Loss $\mathcal{L}_{\mathrm{DC}}$ (discussed below) scaled by scaling coefficients $\lambda_{\mathrm{Distill}}$ and $\lambda_{\mathrm{DC}}$ respectively.
+
+Formally, the total loss for task $t$ is:
+
+$$
+\mathcal {L} _ {\text {T o t a l}} = \left\{ \begin{array}{l l} \mathcal {L} _ {\text {D e t e c t o r}}, & \text {f o r} t = 1, \\ \mathcal {L} _ {\text {D e t e c t o r}} + \lambda_ {\text {D i s t i l l}} \mathcal {L} _ {\text {D i s t i l l}} ^ {*} + \lambda_ {\text {D C}} \mathcal {L} _ {\text {D C}}, & \text {f o r} t \geq 2. \end{array} \right. \tag {15}
+$$
+
+Directional Consistency Loss $(\mathcal{L}_{\mathrm{DC}})$ . Incremental learning suffers from conflicting weight updates during model-merging [45], which can destabilize the merging of shared parameters. We introduce the Directional Consistency Loss (DC Loss) to address this. This loss penalizes updates in the shared parameter space that diverge in direction relative to previous incremental changes, thus promoting a consistent evolution of the shared task vectors.
+
+Specifically, for $t \geq 2$ , we define the DC Loss between consecutive tasks $t$ and $t - 1$ as:
+
+$$
+\mathcal {L} _ {\mathrm {D C}} = \sum_ {i \in \theta_ {s}} \operatorname {R e L U} \left[ - \left(\left(\tau_ {s _ {t}} ^ {(i)} - \tau_ {s _ {t - 1}} ^ {(i)}\right) \cdot \left(\tau_ {s _ {t - 1}} ^ {(i)} - \tau_ {s _ {t - 2}} ^ {(i)}\right)\right) \right] \tag {16}
+$$
+
+Here, the dot product quantifies the alignment between successive updates: a negative value indicates a sign conflict (i.e., the current update opposes the previous direction), which the ReLU penalizes. This mechanism enforces a more coherent update trajectory for the shared parameters, effectively mitigating catastrophic forgetting. Consequently, the DC Loss remains object-detector agnostic, as it depends solely on the evolution of shared parameter updates
+
+# 4. Experimental Details
+
+# 4.1. Datasets
+
+Following prior works [6, 21, 26, 41, 44], we evaluate DuIOD using two dataset series: Pascal Series and Diverse Weather Series. Pascal Series includes four domains—Pascal VOC [7], Clipart, Watercolor, and Comic [14]. Pascal VOC and Clipart share 20 object categories, while Watercolor and Comic contain six, forming subsets of the former. Similarly, in Diverse Weather Series, we consider three diverse weather conditions—Daytime Sunny, Night Sunny, and Daytime Foggy—with seven common object categories, sourced from BDD-100k [48], FoggyCityscapes [5], and Adverse-Weather [11]. The training sequence followed for both dataset series is provided in Appendix A- Table S1, and dataset statistics are detailed in Appendix G.
+
+# 4.2. Proposed Evaluation Protocol and Metrics
+
+To comprehensively evaluate different methods on the DuIOD task, we propose a new evaluation protocol (see Appendix A- Table S1). Existing metrics such as $\mathcal{F}_{map}$ [4], RSD & RPD [32], and SPmAP [47], primarily assess catastrophic forgetting and do not capture the model's ability to generalize to unseen classes, which is critical for DuIOD. Since DuIOD goes beyond preserving old knowledge (retention), it also demands evaluating how well the model can adapt to unseen categories (adaptability). We introduce the Retention-Adaptability Index (RAI) to address this requirement. RAI is defined as the mean of the Average Retention Index (Avg RI) and Average Generalization Index (Avg GI).
+
+Avg RI quantifies the model's ability to retain past knowledge and is computed as:
+
+$$
+\operatorname {A v g} \mathrm {R I} = \frac {1}{T - 1} \sum_ {i = 1} ^ {T - 1} R I _ {\mathcal {D} _ {i}}, R I _ {\mathcal {D} _ {i}} = \frac {\mathrm {m A P} _ {\text {o l d}} ^ {T T} \left(\mathcal {D} _ {i} \left[ \mathcal {C} _ {i} \right]\right)}{\mathrm {m A P} _ {\text {n e w}} ^ {T i} \left(\mathcal {D} _ {i} \left[ \mathcal {C} _ {i} \right]\right)}. \tag {17}
+$$
+
+Here, $\mathrm{mAP}_{\mathrm{old}}^{\mathcal{T}_T}$ represents the final-task performance on previously learned classes, while $\mathrm{mAP}_{\mathrm{new}}^{\mathcal{T}_i}$ denotes the initial performance when the classes were first encountered. A higher Avg RI implies better retention of past knowledge while lower values indicate catastrophic forgetting.
+
+Similarly, Avg GI quantifies the model's generalization
+
+to unseen classes and is computed as:
+
+$$
+\operatorname {A v g} \mathrm {G I} = \frac {1}{N} \sum_ {\left(\mathcal {D} _ {i}, \mathcal {T} _ {j}\right)} G I _ {\mathcal {D} _ {i}, \mathcal {T} _ {j}}, \quad G I _ {\mathcal {D} _ {i}, \mathcal {T} _ {j}} = \frac {\operatorname {m A P} _ {\text {u n s e e n}} ^ {\mathcal {T} _ {j}} \left(\mathcal {D} _ {i} \left[ \mathcal {C} _ {\text {u n s e e n}} \right]\right)}{\operatorname {m A P} _ {\text {r e f}} \left(\mathcal {D} _ {i} \left[ \mathcal {C} _ {\text {u n s e e n}} \right]\right)}. \tag {18}
+$$
+
+Here, $\mathrm{mAP}_{\mathrm{unseen}}^{\mathcal{T}_j}$ measures model performance on previously unseen classes, while $\mathrm{mAP}_{\mathrm{ref}}$ is the reference mAP obtained by training solely on these unseen classes. A higher Avg GI indicates better adaptability to new categories. A detailed discussion, including metric formulations and rationale, is provided in Appendix A.
+
+Moreover, unlike prior works, we do not consider the upper-bound joint-training baseline, as Avg RI and Avg GI compute relative performance retention and generalization through direct ratio-based comparisons. This ensures that the overall metric (RAI) directly reflects catastrophic forgetting without biases introduced by architecture-specific joint-training performance.
+
+# 5. Results & Discussion
+
+# 5.1. Quantitative Results
+
+To evaluate the effectiveness of the DuET, we compare it against five baselines: Sequential Fine-Tuning, LwF [25] and ERD [8] (common IOD methods), LDB [41] and CL-DETR [28] (current open-source SOTA in DIOD and CIOD). We re-implemented all under the proposed DuIOD setting, reporting the best results across seven experiments—five two-phase and two multi-phase. Results from two two-phase and two multi-phase experiments are in Table 1 and Table 2, while comprehensive results from all experiments are provided in Appendix E. Moreover, as detailed in Appendix C3, DuET maintains a consistent performance irrespective of the randomness in class-domain orders.
+
+We begin with naïve Sequential Fine-Tuning using YOLO11n [17] as the base detector, where we observe severe catastrophic forgetting, with Avg RI $< 1\%$ across all experiments. LwF and ERD, both implemented on YOLO11n by modifying the Ultralytics pipeline [17] to incorporate distillation losses (LwF) and the Elastic Response Selection algorithm (ERD), show moderate RAI improvement but gives poor results in multi-phase experiments (Table 2) compared to DuET. On the DIOD side, $\mathbf{LDB}^2$ with VitDet [24] as the base detector suffers from severe catastrophic forgetting, particularly in cross-domain uneven class shifts (Table 1). On the CIOD side, $\mathbf{CL}\text{-DETR}^2$ with Deformable DETR [52] struggles under severe domain shifts despite having more trainable parameters. In contrast, DuET consistently outperforms all methods despite having significantly fewer trainable parameters (Table 1) while also demonstrating strong generalization across multiple object detection architectures (Table 3).
+
+DuET achieves an RAI improvement of $+9.82\%$ and $+13.12\%$ while preserving $87.44\%$ and $89.30\%$ Avg RI
+
+Table 1. Detailed results of various methods on Daytime Sunny [1:4] $\rightarrow$ Night Sunny [5:7], where the expanded columns ( $T_1$ : Daytime Sunny [1:4], $T_2$ : Night Sunny [5:7]) show mAP@0.5%, best among the columns in bold, second best underlined.
+
+| Method | Base Detector | Trainable Params (M) | T1 Daytime Sunny [1:4] | T2: Night Sunny [5:7] | Avg RI (%) | Avg GI (%) | RAI (%) |
| Old | New | Unseen |
| Daytime Sunny [1:4] | Night Sunny [5:7] | Night Sunny [1:4] | Daytime Sunny [5:7] |
| Sequential FT | YOLO1ln | 2.58 | 49.40±0.3 | 0.00±0.0 | 62.20±0.5 | 12.60±0.4 | 35.90±0.3 | 0.00±0.0 | 45.88±0.6 | 22.94±0.3 |
| LwFECCV'16 [25] | YOLO1ln | 2.58 | 49.40±0.2 | 27.60±0.4 | 0.34±0.6 | 21.30±0.3 | 0.67±0.5 | 55.87±0.3 | 21.88±0.7 | 38.88±0.6 |
| ERDcvPR'22 [8] | YOLO1ln | 2.58 | 49.40±0.5 | 33.00±0.4 | 34.00±0.3 | 26.10±0.6 | 29.10±0.7 | 66.80±0.5 | 53.04±0.3 | 59.92±0.4 |
| LDBAAAI'242[41] | ViDet | 110.52 | 45.30±0.6 | 0.50±0.3 | 15.10±0.4 | 0.30±0.5 | 16.90±0.7 | 1.10±0.2 | 22.41±0.3 | 11.76±0.6 |
| CL - DETRCVPR'232[28] | Deformable DETR | 39.85 | 46.29±0.4 | 27.41±0.5 | 31.94±0.6 | 19.85±0.3 | 32.55±0.4 | 59.21±0.2 | 54.96±0.5 | 57.09±0.4 |
| DuET (Ours) | YOLO1ln | 2.58 | 49.40±0.2 | 43.50±0.1 | 22.20±0.3 | 31.60±0.2 | 27.40±0.1 | 88.06±0.2 | 56.95±0.1 | 72.51±0.2 |
+
+Table 2. Results of two-phase and multi-phase experiments on DuIOD task. Best among the columns in bold, second best underlined.
+
+| Method | Base Detector | VOC [1:10] → Clipart [11:20] | Watercolor [1:3] → Comic [4:6] → Clipart [7:13] → VOC [14:20] | Night Sunny [1:2] → Daytime Sunny [3:4] → Daytime Foggy [5:7] |
| Avg RI (%) | Avg GI (%) | RAI (%) | Avg RI (%) | Avg GI (%) | RAI (%) | Avg RI (%) | Avg GI (%) | RAI (%) |
| Sequential FT | YOLO11n | 0.75±0.2 | 12.86±0.4 | 6.81±0.3 | 0.00±0.0 | 11.05±0.5 | 5.53±0.3 | 0.00±0.0 | 30.51±0.6 | 15.26±0.5 |
| LwF [25] | YOLO11n | 72.64±0.3 | 33.74±0.5 | 53.19±0.4 | 52.66±0.6 | 17.01±0.4 | 34.84±0.3 | 27.94±0.7 | 23.78±0.5 | 25.86±0.6 |
| ERD [8] | YOLO11n | 68.66±0.4 | 43.68±0.3 | 56.17±0.6 | 54.76±0.5 | 41.13±0.4 | 47.95±0.7 | 44.60±0.6 | 39.40±0.5 | 42.00±0.3 |
| LDB² [41] | ViTDet | 66.89±0.5 | 18.76±0.3 | 42.83±0.4 | 86.08±0.6 | 19.57±0.5 | 52.83±0.4 | 50.50±0.6 | 5.42±0.7 | 27.96±0.5 |
| CL-DETR² [28] | Deformable DETR | 68.29±0.3 | 40.72±0.4 | 54.51±0.3 | 71.73±0.5 | 36.63±0.6 | 54.18±0.4 | 64.26±0.3 | 43.46±0.5 | 53.86±0.6 |
| DuET (Ours) | YOLO11n | 87.44±0.2 | 44.54±0.1 | 65.99±0.3 | 89.30±0.2 | 42.60±0.1 | 65.95±0.2 | 88.57±0.2 | 41.92±0.1 | 65.25±0.2 |
+
+Table 3. Results of proposed DuET framework on Daytime Sunny [1:4] $\rightarrow$ Night Sunny [5:7] experiment with different base detectors. Best among the columns in bold, second best underlined.
+
+| Method | Base Detector | Trainable Params (M) | GFLOPs | Avg RI (%) | Avg GI (%) | RAI (%) |
| DuET (Ours) | ViTDet [24] | 110.52 | 1829.61 | 27.55±0.3 | 28.22±0.8 | 27.89±0.5 |
| Deformable DETR [52] | 39.85 | 11.77 | 84.45±0.2 | 33.45±0.1 | 58.95±0.2 |
| RT-DETR-I [29] | 32.00 | 103.4 | 47.73±0.2 | 21.00±0.1 | 34.37±0.2 |
| RT-DETR-x [29] | 65.49 | 222.5 | 56.39±0.2 | 24.15±0.1 | 40.27±0.2 |
| YOLO11n [17] | 2.58 | 6.3 | 88.06±0.2 | 56.95±0.1 | 72.51±0.2 |
| YOLO11x [17] | 56.84 | 194.4 | 96.88±0.2 | 42.41±0.1 | 69.18±0.2 |
+
+Table 4. Ablations of DuET framework with different components and losses on VOC [1:10] $\rightarrow$ Clipart [11:20] with YOLO11n as base detector.
+
+| Seq FT | Incremental Head | DuET Module | L*Distill | LDC | Avg RI (%) | Avg GI (%) | RAI (%) |
| X | X | X | X | X | 0.5 | 9.13 | 4.82 |
| ✓ | X | X | X | X | 0.75 | 12.86 | 6.81 |
| ✓ | ✓ | X | X | X | 24.75 | 33.36 | 29.06 |
| ✓ | ✓ | ✓ | X | X | 75.00 | 37.26 | 56.13 |
| ✓ | ✓ | ✓ | ✓ | X | 87.06 | 37.75 | 62.41 |
| ✓ | ✓ | ✓ | ✓ | ✓ | 87.44 | 44.54 | 65.99 |
+
+on the Pascal Series two-phase and multi-phase experiments, respectively. Similarly, on the Diverse Weather Series, DuET achieves an RAI improvement of $+12.59\%$ and $+11.39\%$ while preserving $88.06\%$ and $88.57\%$ Avg RI on the two-phase and multi-phase experiments, respectively.
+
+# 5.2. Qualitative Analysis
+
+In Figure 4, we present qualitative comparisons of different methods on two-phase experiments, while additional qualitative results on multi-phase experiments are provided in
+
+Appendix E2. In VOC [1:10] $\rightarrow$ Clipart [11:20], LwF and LDB misclassify the cow class (introduced in $\mathcal{T}_1$ : VOC [1:10]) as horse or sheep (both introduced in $\mathcal{T}_2$ : Clipart [11:20]). While ERD and CL-DETR correctly classify it, they exhibit significantly lower confidence scores compared to DuET. A similar pattern is observed for the person and motorbike classes, both introduced in $\mathcal{T}_2$ , where only DuET correctly detects both objects in the unseen VOC [11:20], while competing methods mostly fail.
+
+Similarly, in Daytime Sunny $[1:4] \to$ Night Sunny [5:7], the car class (introduced in $\mathcal{T}_1$ : Daytime Sunny [1:4]) undergoes a severe domain shift when evaluated in unseen Night Sunny [1:4]. As a result, most methods fail to detect a majority of car instances, instead misclassifying them as background, because of the background shift challenge in DuIOD. (see Appendix F for more details). However, DuET effectively overcomes this challenge by correctly detecting most of the car instances (improving $\mathrm{mAP}_{\mathrm{car}}^{\mathcal{T}_2}$ from 49.4 to 71.8). Similar misclassifications are observed for the truck class, introduced in $\mathcal{T}_2$ : Night Sunny [5:7], where most methods struggle to detect it in unseen Daytime Sunny [5:7], while DuET provides consistent detections. These qualitative results highlight the effectiveness of DuET in seamlessly adapting to unseen classes in new domains.
+
+# 6. Main Ablation Studies
+
+This section covers the main ablation studies, while extended ablations, including the impact of loss components, hyperparameter sensitivity analysis, the influence of random class-domain order, and complexity analysis, are provided in Appendix C.
+
+Role of Sequential Fine-tuning. While DuIOD inherently involves sequential learning, we compare independent
+
+
+Figure 4. Qualitative comparisons on two-phase experiments for different methods on the DuIOD task. The top two rows display detection results on unseen classes: Clipart [1:10] & VOC [11:20], for: VOC [1:10] $\rightarrow$ Clipart [11:20] experiment. Similarly, the bottom two rows show detection results on unseen classes: Night Sunny[1:4] & Daytime Sunny[5:7], for: Daytime Sunny[1:4] $\rightarrow$ Night Sunny[5:7] experiment (zoomed-in for best view).
+
+
+Figure 5. Impact of $\mathcal{L}_{DC}$ on (a) improving RAI and (b) reducing sign conflicts across different TA approaches, evaluated on VOC [1:10] $\rightarrow$ Clipart [11:20] using YOLO11n with Incremental Head and sequential fine-tuning.
+
+(first row, Table 4) vs. sequential fine-tuning (second row) in DuET framework, observing a significant improvement in Avg GI and, hence, RAI with the latter, aligning with the findings in [30], highlighting its importance in DuIOD.
+
+Effectiveness of DuET Module and Incremental Head. Next, we evaluate the effectiveness of the DuET Module and Incremental Head in the DuET framework. Incremental Head (third row) brings a substantial improvement in both Avg RI and Avg GI over Seq FT. This highlights the importance of concatenating task-specific parameters from previous and current tasks, thereby enhancing the model's generalization capability. Incorporating the DuET Module further leads to a significant improvement in both Avg RI and Avg GI (fourth row), effectively mitigating catastrophic forgetting while enhancing generalization.
+
+Impact of $\mathcal{L}_{\mathrm{Distill}}^*$ and $\mathcal{L}_{\mathrm{DC}}$ . We further investigate the impact of $\mathcal{L}_{\mathrm{Distill}}^*$ and $\mathcal{L}_{\mathrm{DC}}$ in the proposed DuET approach.
+
+As shown in Table 4 (rows five and six), both losses contribute significantly. While $\mathcal{L}_{\mathrm{Distill}}^*$ brings a substantial improvement in Avg RI by helping to retain knowledge from previous tasks, $\mathcal{L}_{\mathrm{DC}}$ further enhances Avg GI, thereby improving the model's generalization capability. The combination of both losses yields the best performance, achieving the highest Avg RI and Avg GI, highlighting their critical role in the DuET approach.
+
+Comparison with other model-merging algorithms. In Figure 5, we compare the performance of related TA approaches with the proposed approach. The results indicate that $\mathcal{L}_{\mathrm{DC}}$ improves RAI by an average of $9.67\%$ while significantly reducing sign conflicts by an average of $34\%$ , averaged across all TA approaches, with DuET achieving the best overall performance.
+
+# 7. Conclusions
+
+In this paper, we introduced DuET, a task-arithmetic-driven solution for robust IOD, enabling models to learn new object categories while generalizing across evolving domains incrementally. Unlike previous works that focus on either class or domain shifts, DuET integrates both, making it practical for real-world applications like autonomous driving and surveillance. We demonstrated its effectiveness across diverse object detectors like YOLO11 & RT-DETR through extensive experiments on the Pascal Series and *Diverse Weather Series* datasets. Additionally, we proposed Directional Consistency Loss to mitigate sign conflicts and a Retention-Adaptability Index to comprehensively evaluate retention and adaptation. DuET opens a new research direction in IOD, providing a promising framework for continual learning and domain adaptation.
+
+# References
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+# Dual Domain Control via Active Learning for Remote Sensing Domain Incremental Object Detection
+
+Jiachen Sun\* De Cheng\* Xi Yang† Nannan Wang
+
+State Key Laboratory of Integrated Services Networks,
+
+School of Telecommunications Engineering, Xidian University, Xi'an 710071, China
+
+sunjc@stu.xidian.edu.cn, {dcheng, yangx, nnwang}@xidian.edu.cn
+
+# Abstract
+
+Domain incremental object detection in remote sensing addresses the challenge of adapting to continuously emerging domains with distinct characteristics. Unlike natural images, remote sensing data vary significantly due to differences in sensors, altitudes, and geographic locations, leading to data distribution shifts and feature misalignments. These challenges make it difficult for models to generalize across domains while retaining knowledge from previous tasks, requiring effective adaptation strategies to mitigate catastrophic forgetting. To address these challenges, we propose the Dual Domain Control via Active Learning (Active-DDC) method, which integrates active learning strategies to handle data distribution and model feature shifts. The first component, the Data-based Active Learning Example Replay (ALER) module, combines a high-information sample selection strategy from active learning with the characteristic extreme foreground-background ratio in remote sensing images, enabling the selection of highly representative samples for storage in a memory bank. The second component, the Query-based Active Domain Shift Control (ADSC) module, leverages the query vector, a key element for DETR-based detectors, to implement query active preselection and optimal transport matching, thus facilitating effective cross-domain knowledge transfer. Our method achieves optimal performance in domain incremental tasks across four remote sensing datasets, and ablation studies further validate the effectiveness of both components.
+
+# 1. Introduction
+
+Deep learning has greatly advanced remote sensing object detection, but domain-incremental learning remains challenging due to shifting imaging conditions, sensor
+
+
+(a) Data shift and the balancing effect of ALER
+
+
+
+
+(b) Feature shift and the balancing effect of ADSC
+
+
+Figure 1. Data and Feature Shift: (a) Illustrates the data distribution for two-task and four-task settings, along with the combined training data distribution generated by ALER, demonstrating its effectiveness in balancing data distribution shifts. (b) Presents the T-SNE visualization of query features from the Fine-tuning model and the ADSC-trained model on incremental data, highlighting ADSC's capability in mitigating feature shift.
+
+types, and geographic variations. Unlike natural images, remote sensing data exhibit complex distributions, making it difficult for models to generalize across domains while retaining past knowledge. In this setting, models must detect objects in new domains without catastrophic forgetting. However, conventional methods struggle with data distribution shifts and feature misalignment caused by domain changes. These challenges are further amplified in remote sensing, where heterogeneous data sources and extreme foreground-background imbalances complicate adaptation, requiring more effective strategies for knowledge retention and domain adaptation. Traditional object detection methods struggle to generalize across domains, especially when new data from different environments or conditions
+
+becomes available. This issue is particularly pronounced in remote sensing, where large-scale, high-dimensional images introduce both data distribution shifts and feature misalignments.
+
+Incremental object detection methods can be categorized into knowledge distillation-based methods [8, 9, 22, 28, 47], example replay-based methods [8, 9, 16, 26, 27], and adapter-based methods [10, 37, 38, 41, 43]. Knowledge distillation and example replay methods are particularly effective as they do not require additional network parameters, making them popular in incremental learning. While some methods perform well in multi-domain incremental object detection tasks on natural images, remote sensing images present unique challenges, particularly in data and feature distribution.
+
+Remote sensing images are captured under diverse conditions—different sensors, altitudes, and geographic locations—resulting in notable domain shifts across datasets, as shown in Fig. 1(a). Variations in resolution, scale, and spatial layout further hinder model generalization. In contrast, natural images are typically acquired under more consistent settings, leading to relatively stable data distributions.
+
+Remote sensing images also exhibit complex, multiscale characteristics, including objects with diverse shapes and sizes, along with rich contextual cues such as terrain and vegetation, as illustrated in Fig. 1(b). These factors challenge the extraction and alignment of features across domains. By comparison, natural images tend to contain more standardized objects and consistent contexts, making cross-domain knowledge transfer significantly easier.
+
+To address the above challenges, we propose the Dual Domain Control via Active Learning (Active-DDC) framework. The first component, Data-based Active Learning Example Replay (ALER), mitigates data distribution shifts, as illustrated in fig. 1(a). It employs an active learning strategy to select representative samples, which are stored in a memory bank. By preserving essential information from previous domains, ALER effectively minimizes the impact of data distribution shifts as new domains emerge. The second component, Query-based Active Domain Shift Control (ADSC), addresses the feature shift problem inherent in domain-incremental learning, with its control effect on feature migration depicted in fig. 1(b). By leveraging a query selection strategy combined with optimal transport matching, ADSC facilitates knowledge distillation from the previous domain. The class distillation mechanism helps preserve essential features, ensuring that the model effectively retains critical knowledge while adapting to new domains.
+
+The main contributions of this work are summarized as follows:
+
+- To the best of our knowledge, we are the first to formulate the task of domain-incremental object detection for remote sensing images and propose the Active-DDC
+
+method.
+
+- We introduce the Data-based Active Learning Example Replay (ALER) module, which effectively mitigates data migration in incremental tasks and enhances the representativeness of selected examples.
+- We propose the Query-based Active Domain Shift Control (ADSC) module, which addresses feature shifts in incremental tasks and enables effective cross-domain knowledge transfer through query-based preselection and optimal transport matching.
+- Extensive experiments demonstrate that our approach achieves state-of-the-art performance, with ablation studies further validating the effectiveness of our proposed modules.
+
+# 2. Related Work
+
+Incremental Object Detection (IOD). As a typical extension of incremental learning, IOD aims to handle both old and new task data appearing simultaneously in images. In this task, Knowledge Distillation (KD) [4, 15, 29, 39] has been widely adopted for its ability to leverage prior knowledge from new training samples, thereby minimizing discrepancies between the responses of the previous and current models [3, 13, 31, 45]. A pioneering approach, ILOD [36], applies knowledge distillation to Fast R-CNN [11] to retain responses for old classes, effectively mitigating catastrophic forgetting.
+
+Subsequently, knowledge distillation has been extended to various object detection frameworks, including SID [32] on CenterNet [46], RILOD [19] on RetinaNet [24], and ERD [9] on GFLV1 [23]. Further advancements have applied this technique to Faster R-CNN [34], with methods such as CIFRCN [14], Faster ILOD [31], DMC [42], BNC [7], and IOD-ML [17]. More recently, knowledge distillation has been integrated into Transformer-based detectors, leading to methods such as CL-DETR [28], DyQ-DETR [43], and Incremental-DETR [8], leveraging architectures like DETR [2], UP-DETR [6], and Deformable DETR [48].
+
+Exemplar Replay (ER) is another key strategy in incremental object detection [1, 12, 33, 35]. ORE [16] uses an exemplar set for fine-tuning, while AFD [26] introduces adaptive sampling, and CL-DETR [28] applies distribution-preserving calibration. ABR [27] further enhances replay with a mosaic-based approach. However, these methods often rely on exemplars with incomplete annotations, overlooking their informativeness and reliability. In domain-incremental object detection, this limitation weakens cross-domain knowledge transfer, making it harder to address data and feature distribution shifts.
+
+Transformer-based Object Detection. Detection Transformer (DETR) [2] redefines object detection as a set prediction problem, using a transformer-based architecture to model object relationships via global attention.
+
+
+Figure 2. Overview of our Active-DDC framework. During cross-domain adaptation, ALER first selects highly representative samples and stores them in a memory bank. Then, the model is jointly trained using both the memory bank and the new domain data. Finally, ADSC controls query vector shifts to mitigate domain drift. Active-DDC effectively suppresses both data and feature shifts caused by domain changes.
+
+It eliminates the need for hand-crafted components like non-maximum suppression by employing learnable object queries and Hungarian matching [18]. To improve efficiency, Deformable DETR [48] introduces sparse attention on multilevel feature maps, accelerating convergence and enhancing small-object detection. Various DETR variants [6, 20, 25, 30, 49] further refine performance. Our method is built upon the widely adopted Deformable DETR.
+
+# 3. Method
+
+# 3.1. Problem Definition
+
+Object detection primarily focuses on accurately identifying and localizing objects of interest within an image. Let $(x,y)\in \mathcal{D}$ denote a dataset $\mathcal{D}$ , where $x$ represents the images and $y$ corresponds to their ground truth labels. An ideal object detector $F_{\theta}(x)$ should generate a set of predictions $\hat{y}$ from the features $f_{\theta}(x)$ extracted from the input image.
+
+Domain incremental object detection aims to train a model to detect objects across a sequence of $T$ tasks, where each task $\mathcal{D}^t = (x^t,y^t)$ consists of a set of images $x^{t}$ from the $t$ -th domain. The model should be able to detect objects in new domain images $x^{t}$ while preserving its ability to detect objects in previously encountered domains $x^{1:t - 1}$ , without experiencing catastrophic forgetting.
+
+However, domain increment introduces two primary effects: the shift in data distribution and the shift in feature vectors. Specifically, let $\mu_t = \mathbb{E}[x^t]$ represent the mean of the image data in the $t$ -th domain, and $\sigma_t^2 = \operatorname{Var}(x^t)$ represent the variance of image data in the $t$ -th domain.
+
+The distribution of image data in the $t$ -th domain can be expressed as $X^t \sim N(\mu_t, \sigma_t^2)$ . Similarly, $f_\theta^t(x^t)$ denotes the features extracted by the model $F_\theta^t$ in the $t$ -th domain. The shifts in data distribution and feature vectors between the $t$ -th domain and the $(t-1)$ -th domain can be defined as $D(X^t, X^{t-1})$ and $D(f_\theta^t(x^t), f_\theta^{t-1}(x^t))$ , respectively. These two types of shifts contribute to catastrophic forgetting, ultimately causing the detector to perform poorly on data from incremental domains.
+
+# 3.2. Overall Framework
+
+Our proposed Dual Domain Control via Active Learning (Active-DDC) framework is designed to tackle the challenges of domain-incremental object detection by mitigating data distribution shifts and model feature shifts through a combination of active learning and knowledge distillation strategies. Active-DDC consists of two key modules: Data-based Active Learning Example Replay (ALER) and Query-based Active Domain Shift Control (ADSC). As illustrated in fig. 2.
+
+To counteract data distribution shifts, the ALER module leverages an active learning-based high-information sample selection strategy, ensuring that the most representative samples are stored in the memory bank for effective knowledge retention. To address model feature shifts, the ADSC module exploits query vectors in DETR-based detectors, implementing query preselection and an optimal transport-based matching mechanism to achieve effective many-to-many query alignment, thereby enhancing cross-domain knowledge transfer.
+
+Our method is applied to Transformer-based detectors, Deformable-DETR and DETR. Compared to DETR, Deformable-DETR introduces deformable attention, which significantly reduces computational cost and enhances detection performance, particularly for small and dense objects.
+
+# 3.3. Active Learning Example Replay
+
+Example Replay (ER) mitigates data distribution shifts by replaying past samples, reducing variance, preventing overfitting, and accelerating learning. Active learning further enhances this by selecting the most informative samples rather than relying on random selection. To address distribution shifts, we propose Active Learning Example Replay (ALER), which selects representative samples based on factors like representativeness, uncertainty, and difficulty. These samples are stored in a memory bank and trained alongside new task data. By dynamically updating the memory bank, ALER helps retain knowledge from previous domains while adapting to new ones. Figure 2 illustrates the ALER pipeline.
+
+At the start of task $t$ , ALER pre-selects difficult samples based on the false positive rate (FPR) and false negative rate (FNR), which are stored in the memory buffer $B^{t-1}$ for further processing after task $t-1$ training. The memory buffer and bank are denoted as $B$ and $M$ , respectively, with a limited size. Sample selection is crucial for performance. After applying the scoring ranking mechanism, the memory bank $M^{t-1}$ holds highly representative samples. The ranking mechanism considers information complexity, sample difficulty, and foreground-background uncertainty, following active learning principles to score and retain high-scoring samples for joint training with $\mathcal{D}^t$ during task $t$ .
+
+First, based on the active learning strategy of information entropy, images with higher entropy contain more detailed and structured information, while images with lower entropy tend to contain less information and are often simple or flat regions. The information entropy of the image $x$ in the memory buffer is calculated as follows:
+
+$$
+H (x) = - \sum_ {i = 1} ^ {N} p _ {i} \log_ {2} p _ {i}, \tag {1}
+$$
+
+where $p_i$ represents the probability of the $i$ -th color level occurring in the image, and $N$ is the total number of possible color levels.
+
+Inspired by the DyQ-DETR [43] method and the extreme foreground-background ratio in remote sensing images, we then calculate the average foreground-background ratio for each image:
+
+$$
+r _ {\mathrm {a v g}} (x) = \frac {\sum_ {k = 1} ^ {N _ {\mathrm {f g}} (x)} \operatorname {s i z e} (\mathrm {f g} (k))}{N _ {\mathrm {f g}} \cdot \operatorname {s i z e} (x)}, \tag {2}
+$$
+
+where $N_{\mathrm{fg}}(x)$ is the number of foreground objects in image $x$ , and $\mathrm{size}(\cdot)$ represents the dimension calculation.
+
+Subsequently, the score mapping function maps the average foreground-background ratio to the risk level of the sample:
+
+$$
+R (x) = k _ {1} e ^ {- b _ {1} \cdot r _ {\text {a v g}} (x)} + k _ {2} e ^ {- \left(r _ {\text {a v g}} (x) - c _ {1}\right)} + c _ {2}, \tag {3}
+$$
+
+where $r_{\mathrm{avg}}(x)$ represents the average foreground-background ratio of the sample, $k$ , $b$ , and $c$ are the mapping coefficients, respectively. Serving as the risk assessment metric from the DyQ-DETR [43] method. However, our approach places greater emphasis on the difficulty and risk associated with remote sensing images. As a result, the score mapping function assigns a higher value when the average foreground-background ratio $r_{\mathrm{avg}}(x)$ is low.
+
+The final score is composed of both the image information entropy and the foreground-background ratio:
+
+$$
+S (x) = \alpha H (x) + \beta R (x), \tag {4}
+$$
+
+where $\alpha$ and $\beta$ are the information weight and risk weight, respectively. The score $S(x)$ ultimately determines whether image $x$ from the memory buffer $B^{t-1}$ is selected to be loaded into the memory bank $M^{t-1}$ for multiple rounds of training.
+
+During cross-task learning, the model first tests the samples in the memory bank $M^{t-1}$ and stores the difficulty $p_{t-1}$ of the current samples in the memory bank. Then, during the hard sample selection, the difficulty $p_t$ of the new task samples is stored. The ratio of $p_{t-1}$ to $p_t$ is used to determine the number of new task samples to be loaded into the memory bank $M^t$ . When discarding old task samples, the model also uses a score ranking mechanism, where samples with lower scores are discarded.
+
+Based on entropy and foreground-background ratio scores, ALER dynamically selects and discards samples from both new and old tasks. This selective approach helps the model better adapt to new domains while retaining knowledge from previous domains, reducing the impact of data distribution shifts.
+
+# 3.4. Active Domain Shift Control
+
+In incremental object detection, knowledge distillation helps mitigate catastrophic forgetting by transferring knowledge from previous tasks. In DETR-based detectors, query vectors play a crucial role, representing potential detections that interact with image features to predict objects. To address feature shifts, we propose Active Domain Shift Control (ADSC), which integrates knowledge distillation with active learning. ADSC first preselects highly overlapping queries for distillation, then applies optimal transport for multi-to-multi query matching, enhancing knowledge
+
+transfer. This allows the student model to retain essential knowledge while extracting richer semantic information.
+
+In DETR, the query vectors are unordered and dynamic. They do not have any inherent order or explicit category label association, and during training, the query vectors are dynamically adjusted based on the features of the input image. Additionally, the focus of each query may shift as the task progresses. To address this, query Active Preselection is applied to preselect and match query vectors. After the training of task $t - 1$ is completed, we use both the teacher model $F_{\theta}^{t - 1}$ and student model $F_{\theta}^{t}$ to perform detection and calculate the Intersection over Union (IoU) between their predicted boxes. Based on the IoU values, we filter out query vectors with significant overlap for subsequent knowledge distillation. This step effectively removes queries with low semantic relevance, thereby reducing ineffective learning.
+
+To preselect queries, we calculate the Intersection over Union (IoU) between each query and the prediction boxes from the teacher model. Let the predicted boxes from the student model in task $t$ be $b_{s}^{t}$ , and the predicted boxes from the teacher model in task $t - 1$ be $b_{t}^{t - 1}$ . Then, we set a threshold $\mathrm{IoU}_{\mathrm{thresh}}$ , and select queries whose IoU exceeds this threshold for distillation. The final query preselection can be expressed as:
+
+$$
+\begin{array}{l} \left(Q _ {\text {s e l e c t e d}} ^ {t}, Q _ {\text {s e l e c t e d}} ^ {t - 1}\right) = \tag {5} \\ \left\{\left(Q ^ {t}, Q ^ {t - 1}\right) \mid \operatorname {I o U} \left(b _ {s} ^ {t}, b _ {t} ^ {t - 1}\right) > \operatorname {I o U} _ {\text {t h r e s h}} \right\}, \\ \end{array}
+$$
+
+where $Q_{i}$ is the selected query vector, which satisfies the condition that the IoU with the teacher model's predicted box is greater than the set threshold $\mathrm{IoU}_{\mathrm{thresh}}$ .
+
+Our method focuses on the distribution of query vectors between the target and source models. Let $\xi_{t}$ and $\xi_{t - 1}$ represent the query vector distributions of the teacher model $F_{\theta}^{t - 1}$ and the student model $F_{\theta}^{t}$ , respectively. $Q_{i}^{t}$ and $Q_{i}^{t - 1}$ are the individual query elements in these distributions. We construct a cost matrix based on the Intersection over Union (IoU) and cosine similarity, where higher IoU overlap and higher cosine similarity imply lower cost.
+
+The optimal transport (OT) distance between the teacher's and student's query vectors can be expressed as:
+
+$$
+\begin{array}{l} \min _ {\pi} \sum_ {i = 1} ^ {m} \sum_ {j = 1} ^ {n} C \left(q _ {i} ^ {t}, q _ {j} ^ {t - 1}\right) \pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}}, \\ \text {s . t .} \sum_ {i = 1} ^ {m} \pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}} = s _ {i}, \quad \sum_ {j = 1} ^ {n} \pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}} = d _ {j}, \tag {6} \\ \sum_ {i = 1} ^ {m} s _ {i} = \sum_ {j = 1} ^ {n} d _ {j}, \\ \pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}} \geq 0, \quad i = 1, 2, \dots , m, \quad j = 1, 2, \dots , n. \\ \end{array}
+$$
+
+where $C(q_i^t,q_j^{t - 1})$ represents the cost matrix; $q_{i}^{t}\in Q_{\mathrm{selected}}^{t}$
+
+$q_{j}^{t - 1}\in Q_{\mathrm{selected}}^{t - 1}$ denote query vectors from the current task $t$ and the previous task $t - 1$ , respectively. $\pi_{q_i^t,q_j^{t - 1}}$ represents the optimal matching plan for transferring queries; $s_i$ and $d_{j}$ are the distribution constraints. $m$ and $n$ represent the number of pruned Queries in model $t$ and model $t - 1$ respectively.
+
+The cost matrix $C_{q^t,q^{t-1}}$ is determined by both the IoU and cosine similarity:
+
+$$
+C \left(q _ {i} ^ {t}, q _ {j} ^ {t - 1}\right) = \tag {7}
+$$
+
+$$
+\lambda_ {1} \cdot \operatorname {I o U} \left(b _ {i} ^ {t}, b _ {j} ^ {t - 1}\right) + \lambda_ {2} \left(1 - \cos \left(q _ {i} ^ {t}, q _ {j} ^ {t - 1}\right)\right),
+$$
+
+where $b_{i}^{t}$ and $b_{j}^{t - 1}$ are the bounding boxes corresponding to queries $q_{i}^{t}$ and $q_{j}^{t - 1}$ , $\lambda_{1}$ and $\lambda_{2}$ are weighting hyperparameters that balance the contribution of IoU and cosine similarity in the cost calculation.
+
+By introducing entropy regularization, the Sinkhorn algorithm enables the OT problem to be solved efficiently through smoothing. The optimization problem then becomes:
+
+$$
+L _ {O T} ^ {\lambda} \left(q _ {i} ^ {t}, q _ {j} ^ {t - 1}\right) = \min _ {\pi \in U \left(q _ {i} ^ {t}, q _ {j} ^ {t - 1}\right)} \langle \pi , C \rangle - \lambda H (\pi), \tag {8}
+$$
+
+where $\lambda > 0$ is a regularization coefficient and $H(\pi)$ represents the entropy constraint, defined as:
+
+$$
+H (\pi) = - \sum_ {i, j} \pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}} \log \left(\pi_ {q _ {i} ^ {t}, q _ {j} ^ {t - 1}}\right). \tag {9}
+$$
+
+This optimal transport method ensures that the student model learns richer knowledge from the teacher model by aligning query vectors between the target and source, thereby enhancing performance in incremental tasks.
+
+After the optimal transport matching of the query vectors between the target and source models, the loss is computed between the matched query vectors. Let $q_{i}^{t}$ and $q_{i}^{t - 1}$ be the query vectors from the teacher and student models for task $t$ and task $t - 1$ , respectively. The matching loss can be expressed as:
+
+$$
+\mathcal {L} _ {m a t} = \sum_ {\pi_ {q ^ {t}, q ^ {t - 1}}} \mathcal {L} _ {\mathrm {C E}} \left(q ^ {t}, q ^ {t - 1}\right), \tag {10}
+$$
+
+where $\pi_{q^t,q^{t - 1}}$ is the optimal transport plan indicating the matching between the teacher and student queries.
+
+# 3.5. Overall Loss
+
+The training loss of Deformable-DETR mainly consists of two components: the classification loss and the bounding box loss:
+
+$$
+\mathcal {L} _ {\text {d e t}} = \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {b b o x}}, \tag {11}
+$$
+
+ | HRRSD | LEVIR | DIOR | DOTA | Joint Test |
| Methods | mAP | \( AP_{50} \) | mAP | \( AP_{50} \) | mAP | \( AP_{50} \) | mAP | \( AP_{50} \) | mAP | \( AP_{50} \) | \( AP_{75} \) |
| Joint Training (Faster-RCNN) | 72.2 | 97.3 | 58.7 | 87.1 | 51.6 | 79.0 | 42.7 | 65.6 | 45.9 | 73.3 | 51.5 |
| Fine-tuning (Faster-RCNN) | 39.5 | 70.4 | 22.1 | 52.0 | 26.8 | 59.5 | 31.8 | 62.4 | 32.3 | 61.1 | 29.6 |
| Faster-ILOD [31] | 42.2 | 74.9 | 23.2 | 55.0 | 30.9 | 62.6 | 32.6 | 62.1 | 32.7 | 62.2 | 31.1 |
| ORE [16] | 46.1 | 79.2 | 23.9 | 56.9 | 30.8 | 63.9 | 32.6 | 61.0 | 31.3 | 60.3 | 30.0 |
| Joint Training (Deformable-DETR) | 74.3 | 97.8 | 61.7 | 88.6 | 48.7 | 77.0 | 36.3 | 62.1 | 44.4 | 71.2 | 47.3 |
| Fine-tuning (Deformable-DETR) | 36.6 | 71.5 | 22.1 | 50.0 | 26.8 | 59.5 | 32.6 | 61.0 | 31.3 | 60.3 | 30.0 |
| CL-DETR [28] | 47.0 | 78.0 | 23.6 | 52.3 | 28.6 | 61.0 | 35.6 | 60.8 | 32.6 | 61.9 | 31.0 |
| Incre-DETR [8] | 33.8 | 56.6 | 24.5 | 55.6 | 29.7 | 62.4 | 36.9 | 62.9 | 33.8 | 64.0 | 32.2 |
| DyQ-DETR [43] | 52.8 | 86.0 | 26.9 | 59.6 | 26.8 | 59.5 | 36.7 | 61.5 | 34.0 | 63.2 | 32.8 |
| LDB* [37] | 46.5 | 81.9 | 24.0 | 52.3 | 26.9 | 60.7 | 36.8 | 63.0 | 32.4 | 63.3 | 30.8 |
| ours | 49.5 | 86.9 | 29.1 | 63.9 | 32.6 | 69.5 | 35.9 | 62.8 | 36.2 | 67.8 | 35.0 |
+
+Table 1. The table presents the performance comparison of sate-of-the-art methods on four remote sensing datasets. Evaluation metrics include mAP, $\mathrm{AP}_{50}$ , and $\mathrm{AP}_{75}$ . The Joint Test column reports the overall performance across all datasets, indicating the model's ability to retain knowledge from previously encountered domains. The best results for each metric are highlighted in bold. The domain-bias module of the LDB* method is applied to the DETR detector.
+
+ | ALER | ADSC | mAP | \( AP_{50} \) | \( AP_{75} \) |
| Sequence I | - | - | 31.3 | 60.3 | 30.0 |
| ✓ | - | 34.7 | 65.1 | 31.4 |
| - | ✓ | 33.9 | 64.0 | 34.9 |
| ✓ | ✓ | 36.2 | 67.8 | 35.0 |
| Sequence II | - | - | 24.5 | 58.4 | 14.4 |
| ✓ | - | 29.1 | 61.7 | 26.6 |
| - | ✓ | 28.3 | 60.2 | 27.9 |
| ✓ | ✓ | 32.7 | 62.8 | 30.8 |
+
+The final loss of our method is backpropagated by the matching loss and the original detector loss of Deformable DETR:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {m a t}} + \mathcal {L} _ {\text {d e t}}. \tag {12}
+$$
+
+# 4. Experiments
+
+# 4.1. Datasets and Implement Details
+
+To evaluate the effectiveness of our proposed Active-DDC method, we conducted experiments on four widely used remote sensing object detection datasets: HRRSD [44], LEVIR [50], DIOR [21], and DOTA [40].
+
+To simulate domain-incremental object detection in remote sensing, we applied class pruning across all datasets. Specifically, except for LEVIR, we pruned the categories in the other datasets to three classes: ship, airplane, and oil tank. These datasets, collected from heterogeneous sensors and covering diverse and complex detection scenarios, provide a strong benchmark for evaluating our method's performance in domain-incremental object detection. Addition-
+
+Table 2. The ablation study results for the ALER and ADSC modules across two different fine-tuning sequences.
+
+| Sequence I | HR | LE | DI | DO | JT |
| Joint Training | 97.3 | 87.1 | 79.0 | 65.6 | 72.3 |
| Fine-tuning | 71.9 | 52.0 | 59.6 | 62.4 | 63.4 |
| ours | 86.9 | 63.9 | 69.5 | 62.8 | 67.8 |
| Sequence II | LE | HR | DO | DI | JT |
| Fine-tuning | 58.4 | 79.3 | 47.4 | 71.7 | 58.4 |
| ours | 63.4 | 91.5 | 51.7 | 73.9 | 62.8 |
| Sequence III | DI | DO | HR | LE | JT |
| Fine-tuning | 41.0 | 33.6 | 58.4 | 76.5 | 36.6 |
| ours | 48.8 | 40.5 | 74.0 | 85.0 | 42.5 |
+
+Table 3. Performance of our method across different sequences.
+
+ally, images from the DOTA dataset were cropped into a fixed size of $1024 \times 1024$ pixels.
+
+Our proposed method, Active-DDC, is implemented under the MMDetection [5] framework in Python. Unless otherwise stated, all the hyper-parameters follow the default settings of the corresponding student model for both training and testing.
+
+# 4.2. Results and Analysis
+
+To assess the effectiveness of our proposed method, we conduct a comparative evaluation against several state-of-the-art incremental object detection approaches on four widely used remote sensing datasets: HRRSD, LEVIR, DIOR, and DOTA. The evaluation metrics: mAP, $\mathrm{AP}_{50}$ , and $\mathrm{AP}_{75}$ to ensure a comprehensive performance assessment.
+
+As shown in Table 1, our method consistently outperforms existing incremental object detection techniques across all datasets. Notably, it achieves the highest mAP
+
+| Methods | HR | LE | DI | DO | JT |
| Joint Training | 97.8 | 88.6 | 77.0 | 62.1 | 71.2 |
| Fine-tuning | 71.5 | 50.0 | 59.5 | 61.0 | 60.3 |
| ER [31] | 74.3 | 54.4 | 61.2 | 61.0 | 61.1 |
| ABR* [27] | 70.8 | 51.6 | 59.4 | 61.1 | 60.3 |
| RPC [43] | 78.5 | 56.1 | 62.0 | 61.5 | 64.7 |
| our ALER | 79.8 | 56.5 | 62.3 | 61.7 | 65.1 |
+
+Table 4. Comparison of different Example Replay methods.
+
+| Methods | HR | LE | DI | DO | JT |
| Joint Training | 97.8 | 88.6 | 77.0 | 62.1 | 71.2 |
| Fine-tuning | 71.5 | 50.0 | 59.5 | 61.0 | 60.3 |
| DETRDistill [4] | 72.7 | 51.6 | 59.0 | 61.2 | 61.0 |
| KD-DETR [39] | 79.5 | 54.1 | 60.6 | 61.9 | 63.4 |
| our ADSC | 79.8 | 53.9 | 61.6 | 62.0 | 64.0 |
+
+Table 5. Comparison of different Knowledge Distillation methods.
+
+on HRRSD $(49.5\%)$ , LEVIR $(29.1\%)$ , DIOR $(32.6\%)$ , and DOTA $(35.9\%)$ , demonstrating strong adaptability across diverse domains.
+
+Compared to previous methods, our approach significantly surpasses CL-DETR and Incre-DETR, which also employ knowledge distillation, and outperforms DyQ-DETR and LDB, which rely on adaptor-based techniques. For instance, in the joint evaluation, our method outperforms CL-DETR, Incre-DETR, DyQ-DETR, and LDB by 5.9, 3.8, 4.6, and 4.5 percentage points in terms of $\mathrm{AP}_{50}$ , respectively. These results highlight the effectiveness of our ALER and ADSC, which collectively enhance feature transfer mitigation in domain-incremental object detection. In the Joint Test, which evaluates the model's ability to retain knowledge from previously encountered domains, our method achieves the best overall performance. This suggests that our approach effectively alleviates catastrophic forgetting while adapting to new domains.
+
+# 4.3. Ablation Study
+
+Modules ablation study. As shown in Table 2, the ablation study results for the Active Learning Example Replay (ALER) and Active Domain Shift Control (ADSC) modules are presented. The experiments use mAP, $\mathrm{AP}_{50}$ , and $\mathrm{AP}_{75}$ as evaluation metrics, conducted under the Sequence I and Sequence II settings.
+
+In both Sequence I and Sequence II, using ALER or ADSC individually improves performance, indicating that both modules are highly adaptable to different data sequences. The best performance is achieved when ALER and ADSC are combined in both fine-tuning sequences. In Sequence I, mAP increases from $31.3\%$ to $36.2\%$ , $\mathrm{AP}_{50}$ improves by $7.5\%$ , and $\mathrm{AP}_{75}$ increases by $5.0\%$ ; in Sequence
+
+
+Figure 3. The Impact of Domain Increment in Remote Sensing Images on Data Distribution and Model Feature Shifts, and the Balancing Effect of Our Approach on These Impacts.
+
+II, mAP increases from $24.5\%$ to $32.7\%$ , $\mathrm{AP}_{50}$ improves by $4.4\%$ , and $\mathrm{AP}_{75}$ increases by $16.4\%$ . These results demonstrate that our method exhibits strong robustness in domain incremental object detection, effectively mitigating catastrophic forgetting, and consistently improving performance across different task sequences.
+
+Sequences ablation study. As shown in Table 3, our method consistently surpasses Fine-tuning across all sequences and datasets. It enhances individual dataset performance while achieving better overall results in joint tests. The improvements are especially notable in sequences with complex domain shifts, demonstrating the robustness of our approach. However, detection performance remains sensitive to sequence order, influenced by domain difficulty and differences.
+
+ER ablation study. The ER method, a common approach in incremental learning, has many variants. Compared to previous ER methods, our ALER method integrates an informative evaluation strategy based on active learning, which combines the risk and difficulty of remote sensing samples for sampling. This makes our method more advantageous for remote sensing image data with domain shifts. We compare our approach with the ABR [27] method using mixup and mosaic augmentation strategies, as well as the Risk-balanced Partial Calibration (RPC) [43] method. As shown in Table 3, our method outperforms both the ABR and RPC methods across four task datasets and joint tests, demonstrating the superiority of ALER for this task.
+
+KD ablation study. Similarly, knowledge distillation (KD) has been used to mitigate catastrophic forgetting. However, traditional KD methods, which focus on logit or pseudo-label distillation in DETR-based detectors, struggle with feature shifts in domain-incremental object detection. Since queries are unique to DETR-based detectors, query-based KD is gaining attention. KD-DETR [39] introduces dedicated object queries for distillation, using a progressive sampling strategy. DETRDistill [4] constructs soft masks for feature-level distillation by computing the similarity between query embeddings and feature representations. Table 5 compares the performance of DETRDistill, KD-DETR, and our ADSC method in domain-incremental tasks.
+
+
+GT
+
+
+Fine-tuning
+
+
+CL-DETR
+
+
+Incre-DETR
+
+
+DyQ-DETR
+
+
+ours
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 4. Visual detection results of images. The Ground truth, Fine-tuning, CL-DETR, Incre-DETR, DyQ-DETR and ours method are compared respectively. All methods are sequentially trained and evaluated in the joint test.
+
+
+
+
+
+
+
+
+
+
+
+# 4.4. Sensitivity to Hyperparameters
+
+As shown in fig. 3, we conducted a parameter sensitivity analysis. In Eq.(4) and Eq.(7), $\alpha$ and $\beta$ are the information weight and risk weight. $r_1 = \alpha : \beta r_1$ represents the ratio between informativeness and risk. A lower $r_1$ indicates a preference for selecting samples with higher risk but lower informativeness, whereas a higher $r_1$ favors samples with greater informativeness and lower risk. $r_2 = \lambda_1 : \lambda_2$ represents the ratio between IoU weight and cosine similarity weight. A lower $r_2$ indicates a preference for selecting samples with higher IoU overlap but lower similarity. Conversely, a higher $r_2$ favors samples with greater similarity but lower overlap confidence.
+
+# 4.5. Visualization Analysis
+
+As illustrated in fig. 4, we conducted a series of visualization experiments on detection results across different domains. The visualizations clearly highlight the effectiveness of our proposed method in accurately identifying objects under varying domain conditions. Notably, our approach not only maintains high detection precision in newly introduced domains but also effectively mitigates
+
+catastrophic forgetting by retaining critical knowledge from previously learned domains. This demonstrates the model's strong ability to generalize and adapt, ensuring stable, reliable, and consistent performance in domain-incremental object detection scenarios.
+
+# 5. Conclusion
+
+We propose Active-DDC, a novel framework for domain-incremental object detection in remote sensing images. To address domain shifts and catastrophic forgetting, Active-DDC incorporates two key components: ALER and ADSC. ALER uses active learning to select and store representative samples, preserving essential knowledge from past domains. ADSC enhances cross-domain knowledge transfer by using query-based optimal transport to align features. Together, these modules improve model adaptation across various remote sensing datasets. Experimental results show that Active-DDC outperforms existing methods, achieving state-of-the-art performance. Ablation studies confirm the effectiveness of ALER and ADSC in reducing distribution shifts and enhancing model stability.
+
+# 6. Acknowledgments
+
+This work was supported in part by the National Natural Science Foundation of China under Grants 62372348, 62176198, U22A2096 and 62036007, in part by the Key Research and Development Program of Shaanxi under Grant 2024GXZDCYL-02-10, in part by the Key Laboratory of Big Data Intelligent Computing under Grant BDIC-2023-A-004, in part by Shaanxi Outstanding Youth Science Fund Project under Grant 2023-JC-JQ-53, in part by Scientific and Technological Innovation Teams in Shaanxi Province under Grant 2025RS-CXTD-011, in part by the Shaanxi Province Core Technology Research and Development Project under Grant 2024QY2-GJHX-11, in part by the Fundamental Research Funds for the Central Universities under Grant QTZX23042.
+
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+# Dual Reciprocal Learning of Language-based Human Motion Understanding and Generation
+
+Chen Liang, Zhicheng Shi, Wenguan Wang, Yi Yang*
+
+State Key Lab of Brain-Machine Intelligence, Zhejiang University
+
+https://github.com/leonnnop/DRL
+
+# Abstract
+
+Language-based human motion understanding focuses on describing human motions using natural language descriptions. Conversely, human motion generation aims to generate human motions from textual inputs. Despite significant progress in both fields, further advancements are hindered by two primary challenges: i) Both tasks rely heavily on vast amounts of paired motion-language data for model training. However, human labeling is costly, making it increasingly unsustainable as model scales increase. ii) Existing models often learn the two tasks in parallel. The strong reciprocity between them has not been fully explored. In response, this work proposes Dual Reciprocal Learning (DRL) for language-based human motion understanding and generation. DRL establishes a symmetric learning framework where both tasks collaboratively evolve in a closed-loop, bootstrapping manner, effectively leveraging the reciprocity between them. In DRL, the tasks serve as evaluators for each other, enabling the generation of informative feedback signals even with easily acquired unpaired, unidirectional motion or language data. Furthermore, to mitigate dataset-specific bias in existing evaluations, we propose a generalized protocol that extends evaluation to a general-domain cross-modal feature space. Experimental results on standard benchmarks demonstrate that DRL achieves remarkable performance boosts over representative baselines in both tasks across evaluation protocols.
+
+# 1. Introduction
+
+Recent years have witnessed a surge of interest in the convergence of human motion and language modeling, driven by the diverse demands of fields such as robotics [1], game development [2], virtual reality [3, 4], film production [5]. Within this domain, language-based human motion understanding [1, 6-9] and generation [8-16] stand out as pivotal
+
+problems with a long-standing research history in literature. Language-based human motion understanding aims to translate 3D human motions into natural language descriptions or instructions, notably employed for guiding robots or virtual game avatars [1-3]. Conversely, language-based human motion generation focuses on synthesizing desired human motions given the textual guidance. Recent research endeavors have delved deeply into these tasks, centering on sophisticated model architectures [1, 6, 10-14, 16] and training strategies [7, 15]. More recently, a new trend has emerged in scaling up model sizes and capabilities [8, 9], echoing the breakthroughs seen in large foundation models [17-19] to drive further progress in this domain.
+
+While significant advancements have been made in both tasks, two major barriers hinder further progress in the field: ① Despite technological strides, both tasks heavily depend on vast amounts of paired motion-language data for model training. Recent progress indicates a growing trend of utilizing more data to train larger models with increased parameters. However, collection of such data is prohibitively expensive and labor-intensive, potentially limiting related research and applications. Besides, ② existing studies commonly treat the two tasks as separate problems (Fig. 1 (a)), disregarding the significant interdependence between them. While some initial efforts have aimed to connect the tasks using methods such as one-way alignment [20] (Fig. 1 (b)) or in a unified model design [8, 9] (Fig. 1 (c)), these approaches still tackle the two tasks in parallel, with the motion understanding often being viewed as merely a supplementary component to enhance the learning of motion generation. The strong reciprocity between these two tasks remains largely underexplored in current literature.
+
+To respond, in this work, we propose Dual Reciprocal Learning (DRL) for language-based human motion understanding and generation, denoted as T2M (Text-to-Motion) and M2T (Motion-to-Text). DRL establishes a symmetric learning framework where both tasks collaboratively evolve in a closed-loop, bootstrapping manner, effectively capitalizing on their reciprocal relationship, cf., Fig. 1 (d). Specif
+
+
+Figure 1. Previous studies commonly treat language-based human motion understanding (M2T, Motion-to-Text) and generation (T2M, Text-to-Motion) as separate problems, i.e., (a). Even though some initial efforts try to connect the two tasks, i.e., (b) and (c), the strong reciprocity between these two tasks remains largely underexplored. In this work, we propose dual reciprocal learning, wherein the two tasks collaboratively evolve in a closed-loop, bootstrapping manner, i.e., (d). Additional details are provided in §1.
+
+
+
+
+
+ically, we maintain two separate model instances for T2M and M2T. Beginning with either modality (text for T2M or motion for M2T), input data $x$ is first fed into primal model $f$ to derive an intermediary output $f(x)$ in the dual modality, which is then converted back to the primal modality using the dual model $g$ , i.e., $\hat{x} = g \circ f(x)$ . In DRL, the dual model $g$ serves as an evaluator to measure the quality of generated results, and the discrepancy between $x$ and $\hat{x}$ is used as feedback signal for model learning. As seen, the training data is not limited to a specific modality or necessarily to be paired inputs, allowing us to effectively learning with both unpaired text and motion data. DRL cycle can be repeated for an arbitrary number of rounds, facilitating continuous enhancement for both model instances. To define discrepancy measurement, DRL involves evaluating semantic similarity in the embedding space for motion modality and assessing the discrete tokenized space for text modality using non-differentiable metrics, e.g., CIDEr [21].
+
+DRL framework has three distinctive features. First, our proposed DRL allows unimodal unpaired data to play a similar role to the aligned text-motion pairs, that reduces the dependency on labeled pairwise data during training process, thereby alleviating the issue one. Second, distinguished from existing efforts (i.e., Fig. 1 (b) and (c)), where M2T model is either fixed or separately trained, thereby only partially and implicitly exploring reciprocal relationship, DRL enhances both models collectively and collaboratively through mutual feedback. Each task serves as the evaluator for the other, whereby the growth in the model's capabilities corresponds to a proportional increase in the evaluation strengths of both tasks, thereby enforcing further model advancements. Consequently, this iterative process progressively and densely strengthens the reciprocity between the two tasks, mitigating the issue two. Third, DRL is a principled framework that seamlessly integrates with mainstream T2M and M2T models, which allows DRL to adapt continuously alongside advancements in architecture.
+
+For thorough evaluation, we first review conventional evaluation protocol (Ori.) [20], which employs dataset-specific text and motion encoders contrastively trained on each evaluation dataset to measure the feature-space alignment between generated text-motion pairs. While effective within constrained domains, these two specialized encoders introduce inherent evaluation bias: their text-motion alignment favors generations conforming to encoder training set's kinematic distribution and lexical patterns, thus hindering evaluation on semantic richness and kinematic diversity of novel motions. In response, we propose a generalized evaluation protocol (Upd.) that first expands the encoder training corpus to include general-domain data (HumanML3D [20] + Motion-X [22]), and then anchors text-motion alignment to a fixed DistilBERT text encoder [23] to preserve semantic generality while learning motion representations through contrastive objectives analogous to Ori..
+
+We evaluate DRL under both protocols by applying DRL over two representative language-based motion understanding and generation baseline models and test it on the gold-standard benchmark, i.e., HumanML3D [20]. Under Ori. evaluation, DRL achieves consistent improvements of - 0.012 FID and +7.43 CIDEr, confirming its efficacy. While Upd. protocol reveals amplified benefits of -0.024 FID and +0.011 RP Top-1, demonstrating its superior generalization beyond dataset-specific artifacts. Extensive experiments show that even in the absence of paired labels, DRL consistently enhances model performance across various architectures for both tasks simultaneously. This not only reaffirms the utility and versatility of DRL but also highlights its potential in real-world applications where unpaired data sources are more readily accessible.
+
+# 2. Related Work
+
+Human Motion Generation is generally categorized into unconstrained [24-26] and conditional motion synthesis,
+
+and recent studies mainly focus on the latter. Conditional motion synthesis varies by stimulus type, including coarse action label [27-34], acoustic [35-48] and movement trajectory [49]. In recent years, text-to-motion has been a key focus of research in this field. Recent advances in text-to-motion can be categorized into three mainstreams: (i) VAE-based methods [10, 11] are mainly based on distribution alignment between language and motion latent spaces by applying Kullback-Leibler divergences and contrastive loss, using a decoder to generate motions. (ii) Diffusion-based methods [12-14] leverage denoising diffusion models to synthesize human motion distributions from Gaussian noise guided by text conditions. (iii) Autoregressive methods [15, 16, 50, 51], e.g., T2M-GPT [15], predict motion sequences similarly to language models, conditioning on text inputs and previous motion tokens. The latest works, e.g., MotionGPT [8] and AvatarGPT [9], exploit large language models to predict motion token sequences.
+
+Despite promising results, existing approaches primarily focus on designing sophisticated model architectures for SOTA performance on generation quality and text-motion alignment. For instance, MoMask [50] adopts a hierarchical quantization scheme with two well-designed transformers, while BAMM [51] uses a masked transformer with hybrid attention masking to predict randomly masked tokens. However, existing methods still rely on text-motion pairs and are potentially constrained by the limited availability of paired text-motion data. Meanwhile, abundant unpaired motion data remains largely underexplored.
+
+Human Motion Understanding. Compared to motion generation, studies on human motion understanding remain comparatively scarce. InfoGCN [52] and MotionBERT [53] identify the pre-defined action category from motion inputs. Other approaches leverage natural language, with early works [1, 6] using RNN-based models to generate coarse textual descriptions. Later in TM2T [7], transformer is explored operating on discretized motion tokens.
+
+Recent works [8, 9] have introduced unified frameworks for text-to-motion and motion-to-text using pretrained large language models. Among them, AvatarGPT [9] leverages large-scale LLM model with additional video-text data and achieves SOTA performance on semantic richness and expression coherence. However, these unified methods focus more on text-to-motion, only viewing the motion-to-text model as a by-product during training process. In contrast, DRL treats motion-to-text and text-to-motion equally to leverage their intrinsic connections and form a closed loop for end-to-end joint training to bootstrap each other.
+
+Dual Learning [54] originates from neural machine translation (NMT). The core idea involves establishing a two-agent communication game. Each agent, assigned an individual task, is required to map an $x$ from the primal domain to its dual domain $y$ and then recover the original $x$ through
+
+the reverse mapping in dual task, thus producing a feedback signal without parallel data [55, 56]. Dual learning has moderately addressed the dependence of deep learning methods on data annotation and has been successfully applied to a variety of cross-modality generation tasks, such as visual question answering [57, 58], visual acoustic matching [59], and vision language navigation [60]. Noticing that motion generation and understanding have a reciprocal relationship, which is analogous to that of bidirectional language translation, we propose a dual-task bootstrapping framework in which we could emphasize and explore the structural symmetry of two correlated tasks and capitalize on one-sided data samples for yielding informative feedback signals to boost each other.
+
+# 3. Methodology
+
+We propose a dual learning framework, namely DRL, to leverage feedback signals from symmetrical tasks to promote model learning and better exploit unpaired data. We first give a brief preliminary on T2M and M2T tasks (§3.1), then illustrate the general formulation of DRL (§3.2). DRL is a principled framework that is not tied to specific model design. In §3.3, we present one instantiation of DRL, adopting representative architectures drawn from mainstream T2M and M2T models. Finally, in §3.4, we provide the implementation details of the proposed pipeline.
+
+# 3.1. Preliminary: T2M and M2T Tasks
+
+DRL involves two tasks: the primal task motion generation [10] that employs the T2M model $f_{\theta}$ to convert textual inputs into the desired motion sequences. In the dual task, motion understanding [1], M2T model $g_{\phi}$ translates motion sequences back to corresponding textual descriptions.
+
+T2M. Considering paired text-motion data distribution, denoted as $\mathcal{D}^L = \{(t_n,v_n)\}_{n = 1}^N$ , the goal of T2M is to convert the textual description $t_n$ to corresponding motion sequence $v_{n}$ , i.e., to estimate the conditional distribution $f_{\theta}(v_{n}|t_{n})$ . The network parameters $\theta$ are optimized with $\theta^{\star} = \mathrm{argmax}_{\theta}\sum_{(t,v)\in \mathcal{D}}\log P(v|t,\theta) = \mathrm{argmin}_{\theta}\mathcal{L}_{\mathrm{T2M}}(t)$ .
+
+M2T. Contrarily, M2T model $g_{\phi}$ translates motion sequences into text descriptions $g_{\phi}(t_n|v_n)$ , that seeks optimal parameters $\phi^{\star}$ with $\phi^{\star} = \operatorname{argmax}_{\phi}\sum_{(t,v)\in \mathcal{D}}\log P(t|v,\phi) = \operatorname{argmin}_{\phi}\mathcal{L}_{\mathrm{M2T}}(v)$ . As seen, conventionally, both tasks are independently trained on paired text-motion inputs, ignoring the reciprocity between the two tasks while not being able to utilize the unpaired, one-way data.
+
+# 3.2. Dual Reciprocal Learning Framework
+
+Distinct from conventional T2M/M2T models, DRL learns T2M and M2T tasks jointly. The goal is to simultaneously achieve and progressively enhance both motion understanding and motion generation by utilizing paired and unidirectional non-paired data. To achieve such goal, we exploit the
+
+
+Figure 2. Framework overview of DRL. Starting from either task, data samples are first forwarded to another domain, then reversed back to the original. Within this iterative process, two models act as mutual evaluators, providing feedback signals that facilitate collaborative learning even with unpaired data from single modality. $\mathbf{d}(\cdot ,\cdot)$ is the distance measurement. For a comprehensive elaboration, refer to §3.2.
+
+reciprocity between these two tasks, where the input-output spaces of T2M and M2T demonstrate a strong correlation and can alternatively serve as the evaluator for each other.
+
+Starting from either task, we initially transform a unidirectional data sample forward to another domain, then reverse the transfer to original domain. Dual model is utilized to assess the quality of intermediate outputs produced by primal model and transmits an error signal back to the primal, and vice versa. By evaluating results of this two-step transfer, we can assess the quality of both models and refine them correspondingly. This iterative process can be repeated multiple times until both models converge.
+
+More formally, for the primal process starting from text modality, we first sample random text example $t$ and $\hat{v} = f_{\theta}(t)$ is the mid-transition output. Then, dual model $g_{\phi}$ translates $\hat{v}$ to $\tilde{t}$ by mapping $g_{\phi}(\hat{v})$ . The $\tilde{t}$ is expected to be consistent with $t$ in semantic meaning, i.e., achieving a small cycle-consistency error $\Delta_t = \mathbf{d}_t(\tilde{t}, t)$ , where $\mathbf{d}(\cdot, \cdot)$ is the distance measurement. Conversely, starting from the dual task, we have $\tilde{v} = f_{\theta} \circ g_{\phi}(v)$ and $\tilde{v}$ should be akin to $v$ in motion fidelity. Likewise, $\Delta_v$ can be employed to evaluate the discrepancies between $v$ and $\tilde{v}$ . Finally, the errors $\Delta_t$ and $\Delta_v$ can be specified as two reconstruction losses, which are minimized for model training.
+
+As discussed, $t$ and $v$ are not necessarily aligned. This allows exploration of unimodal unpaired data, addresses the over-reliance on labeled data pairs during the training process. More importantly, DRL is general in its formulation. Instantiations of $f_{\theta}, g_{\phi}$ , and $\Delta_{v/t}$ are not restricted to specific model or loss design. In the next section, we demonstrate specific application of DRL on existing models.
+
+# 3.3. Framework Instantiation
+
+Given the labeled collection $\mathcal{D}^L = \{(t_n^L,v_n^L)\}_{n = 1}^N$ , unpaired unimodal text data $\mathcal{U}_T = \{(t_m^U)\}_{m = 1}^M$ and unimodal motion data $\mathcal{U}_V = \{(v_k^U)\}_{k = 1}^K$ , consisting of $N$ aligned text-motion pairs, $M$ and $K$ unimodal data samples, respectively. T2M model $f_{\theta}$ , M2T model $g_{\phi}$ , discrepancy measurement $\Delta_{t / v}$
+
+and framework optimization are instantiated as follows.
+
+T2M Model. Latest methods often follow a quantization-prediction pipeline: Motions are first quantized into discrete motion embeddings using a discrete VAE (e.g., VQ-VAE [61]). Then, a sequence-to-sequence network (e.g., autoregressive or diffusion-based) predicts the quantized motion, conditioned on text feature extracted by large-scale pretrained text encoder (e.g., CLIP [62]). This work adopts a representative architecture as follows.
+
+Define a motion tokenizer composed of an encoder $\mathcal{F}_{\mathrm{Enc}}$ , a decoder $\mathcal{F}_{\mathrm{Gen}}$ , and a learned discrete codebook $Z$ . For a motion sample $v$ , drawn from both labeled and unlabeled motion sets (i.e., $v \in \{v_n^L\}_{n=1}^N \cup \{v_k^U\}_{k=1}^K$ ), it is fed into $\mathcal{F}_{\mathrm{Enc}}$ , which outputs a latent feature sequence. Each element in this sequence is quantized by finding its nearest neighbor vector in $Z$ , yielding a corresponding sequence of indices $s = \operatorname{Index}(Z, \mathcal{F}_{\mathrm{Enc}}(v))$ . The indices $s$ represent the discrete motion codes. The original motion can be approximately reconstructed as $v' \approx \mathcal{F}_{\mathrm{Gen}}(Z[s])$ , where $Z[s]$ maps each index in $s$ back to its corresponding codebook vector.
+
+Next, autoregressive next-index prediction network $\mathcal{F}_{\theta}$ is defined for T2M generation. Given the previous $i - 1$ indices $s_{< i}$ and text condition $c = \mathcal{F}_{\mathrm{CLIP}}(t)$ encoded from text description $t$ , $\mathcal{F}_{\theta}$ predicts the distribution of possible next index $s_i$ : $\mathcal{F}_{\theta}(s_i|c,s_{< i})$ . The text $t$ is the corresponding description for $v$ , which comes either from the ground-truth label $t_n^L$ paired with $v_n^L$ , or is a intermediate output generated for unlabeled motion $v_k^U$ by the dual M2T model $g_{\phi}$ , i.e., $t\in \{t_n^L\}_{n = 1}^N\cup \{g_\phi (v_k^U)\}_{k = 1}^K$ . During T2M training, only parameters of autoregressive network $\mathcal{F}_{\theta}$ are trained.
+
+M2T Model. Similarly, M2T model $\mathcal{F}_{\phi}$ follows an autoregressive next-token prediction paradigm, conditioned on the encoded discrete motion token sequence $s$ : $\mathcal{F}_{\phi}(t_i|s,t_{< i})$
+
+Discrepancy Measurement $\Delta_{t / v}$ . $\Delta_{t / v}$ measures discrepancies between the estimated results and ground-truths. Depending on their formulation, they can be either differentiable or not. For $\Delta_v$ , we compute the cross-entropy between generated motion tokens $\tilde{s}$ and original $s$ : $\Delta_v =$
+
+$\mathcal{L}_{\mathrm{CE}}(s,\tilde{s})$ . Since $\tilde{s}$ is generated by the differentiable prediction network $\mathcal{F}_{\theta}$ (and the motion tokenizer $\mathcal{F}_{\mathrm{Enc}},\mathcal{F}_{\mathrm{Gen}},Z$ is fixed), $\Delta_v$ is differentiable, enabling end-to-end training via backpropagation. For $\Delta_t$ , we define it as sum of normalized CIDEr [21] and BertScore [63] between the generated text $\tilde{t}$ and the reference. Due to its reliance on non-differentiable semantic evaluation metrics, $\Delta_t$ is non-differentiable. In this case, we use reinforcement learning, i.e., policy gradient optimization, where $\Delta_t$ serves as the reward signal.
+
+Two-stage Optimization. To bootstrap DRL, at stage one, the framework is optimized using labeled text-motion pairs $(t^{L},v^{L})\in \mathcal{D}^{L}$ and unlabeled motions $v^{U}\in \mathcal{U}_{V}$ :
+
+$$
+\mathcal {L} _ {\mathrm {S} 1} = \mathcal {L} _ {\text {l a b e l e d}} + \lambda_ {V} \mathcal {L} _ {V}. \tag {1}
+$$
+
+Here, $\mathcal{L}_{\mathrm{labeled}}$ supervises paired data:
+
+$$
+\mathcal {L} _ {\text {l a b e l e d}} = \frac {1}{N} \sum_ {(t ^ {L}, v ^ {L}) \in \mathcal {D}} \left(\mathcal {L} _ {\mathrm {T 2 M}} (t ^ {L}) + \mathcal {L} _ {\mathrm {M 2 T}} (v ^ {L})\right),
+$$
+
+$$
+\mathcal {L} _ {\mathrm {T 2 M}} = - \sum_ {i = 0} ^ {| s ^ {L} |} \log \mathcal {F} _ {\theta} \left(s _ {i} ^ {L} \mid c ^ {L}, s _ {< i} ^ {L}\right), \tag {2}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {M 2 T}} = - \sum_ {i = 0} ^ {| t ^ {L} |} \log \mathcal {F} _ {\phi} \left(t _ {i} ^ {L} \mid s ^ {L}, t _ {< i} ^ {L}\right).
+$$
+
+$\mathcal{L}_V$ leverages unlabeled motions:
+
+$$
+\mathcal {L} _ {V} = \frac {1}{K} \sum_ {v ^ {U} \in \mathcal {U} _ {V}} \triangle_ {v ^ {U}} = \frac {1}{K} \sum_ {v ^ {U} \in \mathcal {U} _ {V}} \mathcal {L} _ {\mathrm {C E}} \left(s ^ {U}, \tilde {s} ^ {U}\right). \tag {3}
+$$
+
+$\mathcal{L}_{\mathrm{labeled}}$ and $\mathcal{L}_V$ are balanced by weighting parameter $\lambda_V$ .
+
+At stage two, DRL utilizes only unlabeled texts $t^U \in \mathcal{U}_T$ to generate feedback and learns via RL. We define a reward measuring text semantic similarity:
+
+$$
+\mathcal {R} \left(\tilde {t} ^ {U}\right) = \operatorname {C I D E r} \left(t ^ {U}, \tilde {t} ^ {U}\right) + \operatorname {B e r t - S} \left(t ^ {U}, \tilde {t} ^ {U}\right), \tag {4}
+$$
+
+which is maximized via policy gradient:
+
+$$
+\mathcal {L} _ {\mathrm {S} 2} = \mathcal {L} _ {T} = - \mathbb {E} _ {\tilde {t} ^ {U} \sim \left(f _ {\theta}, g _ {\phi}\right)} \left[ \mathcal {R} \left(\tilde {t} ^ {U}\right) \right] \tag {5}
+$$
+
+utilizing SCST [64] with PPO [65]. This two-stage design enhances training stability and explores text-motion reciprocity with unpaired data throughout optimization.
+
+# 3.4. Implementation Details
+
+Network Architecture. We adopt VQ-VAE [61] as discrete VAE and CLIP [62] for text condition extraction, and employ the same architecture as [15] for $\mathcal{F}_{\mathrm{Enc}}$ , $\mathcal{F}_{\mathrm{Gen}}$ , $Z$ and $\mathcal{F}_{\mathrm{CLIP}}$ . T2M/M2T autoregressive networks $\mathcal{F}_{\theta} / \mathcal{F}_{\phi}$ are implemented as standard Transformer [66] (See §4.1).
+
+Training. DRL facilitates cyclic propagation of gradients between T2M and M2T models. While this gradient flow could, in theory, iterate indefinitely, we truncate the backpropagation after the first cycle for computational efficiency and implementation stability. We pretrain the motion VQVAE following the same training process to [15] and keep it fixed in DRL learning. $\lambda_{V}$ is set to 1.0.
+
+Reinforcement Learning. RL setups largely follow [67]. We treat T2M-M2T model pair as policy model and add a KL penalty weighted by $\beta$ to constrain the policy's output from deviating too far from that of a frozen pretrained M2T
+
+model obtained in stage one. We disable dropout during policy training [67, 68], and use a batch size of 128, learning rate of $1 \times 10^{-7}$ , $\beta = 0.02$ , $\gamma = 1$ , and four PPO epochs per batch. Other hyperparameters are set to common default.
+
+Inference. Following conventions [8, 15], we adopt probabilistic sampling to generate non-deterministic outputs for both T2M and M2T. Notably, DRL jointly trains T2M and M2T instances with the same FLOPs as baselines, which train each single model in parallel. DRL deploys them independently in inference without adding extra parameters.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Dataset. We use the gold-standard text-motion dataset, HumanML3D [20]. It provides 14,616 motions and 44,970 texts composed by 5,371 distinct words. Each motion is annotated with at least 3 descriptions and is scaled to 20 FPS.
+
+Unimodal Data. We establish unimodal data $(\mathcal{U}_V$ for motion and $\mathcal{U}_T$ for text) with Motion-X [22] dataset. Motion-X comprises 81.1K high-quality, diverse motion clips (including locomotion, object interaction, dancing, and martial arts) paired with 81.1K semi-automatically generated sequence-level text descriptions, of which 13,581 are refined for fine-grained semantics. We randomly select 12K motion clips as $\mathcal{U}_V$ and the full set of 13,581 refined texts as $\mathcal{U}_T$ to balance performance and training cost. Motion samples use the SMPL-X format [69], which includes body, finger, and facial keypoints; to align with HumanML3D's representation, we retain only body keypoints.
+
+Baseline Setting. We set representative baselines (Fig. 1):
+
+- One-way-align Methods [7, 15] perform T2M or M2T separately. We adapt TM2T [7], replacing its T2M and fixed M2T model [70] with same Transformer model from T2M-GPT [15]. This baseline is denoted as $\mathrm{TM2T^{*}}$ .
+- Unified Methods [8, 9] use a single model for both tasks. Original MotionGPT [8] handles additional tasks like motion completion and prediction. We adapt its T5 [71] architecture solely for T2M-M2T, termed MotionGPT*.
+
+Training Details. We adopt the pre-processing, optimizer, and batch size configurations from [15] and [8] for training $\mathrm{TM2T^{*}}$ and $\mathrm{MotionGPT^{*}}$ , respectively. Both baselines are trained for 800K iterations with official learning rate schedule for each. M2T decoding uses a maximum token length of 128. All experiments are conducted on four NVIDIA GeForce RTX 4090 GPUs with PyTorch. More details are available in our github repository1.
+
+Evaluation Protocol. Standard protocol evaluates T2M/M2T outputs in a text-motion aligned embedding space for fidelity, diversity, and cross-modal alignment. Conventional works (Ori.) [20] train separate text and motion encoders
+
+| Method | R Precision ↑ | FID ↓ | MM Dist ↓ | Diversity ↑ | MModality ↑ |
| Top 1 | Top2 | Top3 |
| Real motions | 0.511±.003 | 0.703±.003 | 0.797±.002 | 0.002±.000 | 2.974±.008 | 9.503±.065 | - |
| TM2T [7] [ECCV22] | 0.424±.003 | 0.618±.003 | 0.729±.002 | 1.501±.017 | 3.347±.008 | 9.175±.083 | 2.219±.074 |
| MDM [12] [ICLR23] | 0.320±.005 | 0.498±.004 | 0.611±.007 | 0.544±.044 | 5.566±.027 | 9.559±.086 | 2.779±.072 |
| MLD [14] [CVPR22] | 0.481±.003 | 0.673±.003 | 0.772±.002 | 0.473±.013 | 3.196±.010 | 9.724±.082 | 2.413±.079 |
| T2M-GPT [15] [CVPR23] | 0.491±.003 | 0.680±.003 | 0.775±.002 | 0.116±.004 | 3.118±.011 | 9.761±.081 | 1.856±.011 |
| AttT2M [16] [ICCV23] | 0.499±.003 | 0.690±.002 | 0.786±.002 | 0.112±.006 | 3.038±.007 | 9.700±.090 | 2.452±.051 |
| MoMask [50] [CVPR24] | 0.521±.002 | 0.713±.002 | 0.807±.002 | 0.045±.002 | 2.958±.008 | - | 1.241±.040 |
| BAMM [51] [ECCV24] | 0.525±.002 | 0.720±.003 | 0.814±.003 | 0.055±.002 | 2.919±.008 | 9.717±.089 | 1.687±.051 |
| MotionGPT [8] [NeuRIPS23] | 0.492±.003 | 0.681±.003 | 0.778±.002 | 0.232±.008 | 3.096±.008 | 9.528±.071 | 2.008±.084 |
| AvatarGPT [9] [CVPR24] | 0.510±.005 | 0.702±.005 | 0.796±.003 | 0.168±.008 | - | 9.624±.055 | - |
| TM2T*-T2M | 0.463±.004 | 0.638±.002 | 0.742±.005 | 0.092±.002 | 3.291±.010 | 9.453±.034 | 1.882±.048 |
| TM2T*-T2M + DRL | 0.468±.003 | 0.634±.002 | 0.735±.004 | 0.080±.004 | 3.361±.016 | 9.398±.042 | 2.095±.037 |
| MotionGPT* | 0.487±.004 | 0.677±.005 | 0.776±.004 | 0.363±.005 | 3.112±.009 | 9.430±.045 | 2.280±.040 |
| MotionGPT* + DRL | 0.490±.003 | 0.679±.004 | 0.777±.003 | 0.327±.003 | 3.125±.008 | 9.396±.037 | 2.425±.029 |
+
+Table 1. Quantitative comparison of motion generation (§4.2) on HumanML3D test under Ori. protocol (§4.1). Metrics computed using encoders from [20], which is biased to specific HumanML3D data distribution. ±: 95% confidence interval. Blue: DRL improvements. (*) denotes our re-trained baselines (§4.1); other results directly borrowed from respective papers.
+
+| Method | R Precision ↑ | FID ↓ | MM Dist ↓ | Diversity ↑ | MModality ↑ |
| Top 1 | Top2 | Top3 |
| Real motions | 0.386±.002 | 0.568±.003 | 0.687±.002 | 0.001±.000 | 3.661±.010 | 8.026±.023 | - |
| TM2T*-T2M | 0.370±.002 | 0.552±.003 | 0.666±.003 | 0.063±.002 | 3.651±.034 | 8.101±.048 | 2.091±.035 |
| TM2T*-T2M + DRL | 0.380±.003 | 0.557±.002 | 0.643±.004 | 0.039±.003 | 3.736±.027 | 8.156±.033 | 2.238±.029 |
| MotionGPT* | 0.346±.002 | 0.521±.004 | 0.631±.004 | 0.231±.002 | 3.833±.010 | 8.021±.045 | 2.436±.034 |
| MotionGPT* + DRL | 0.364±.003 | 0.552±.004 | 0.664±.005 | 0.190±.002 | 3.701±.029 | 8.069±.035 | 2.610±.035 |
+
+Table 2. Quantitative comparison of motion generation (§4.2) on HumanML3D test set using Upd. protocol (§4.1). Metrics computed with re-trained encoders on generalized distributions. Decline in RP-3 and MM Dist may stem from diversified outputs, reducing exact matches.
+
+per benchmark using only its training data, limiting the evaluation's generalizability and binding it to dataset-specific biases. To address this, we propose Upd. setup that establishes a unified embedding space:
+
+- Specialized Domain (Ori.): Use dataset-specific, separately pre-trained encoders per benchmark.
+- General Domain (Upd.): Create a unified, generalized embedding space by: (i) Employing a fixed, general-purpose DistilBERT text encoder [23] instead of specialized ones; (ii) Expanding the motion encoder training data to include both HumanML3D and Motion-X, enabling better alignment between diverse motions and texts. This explicitly tackles the Ori. setup's lack of generalization beyond individual benchmarks.
+
+# 4.2. Performance on Motion Generation
+
+Metrics. Following conventions [7], we evaluate: (i) Motion quality via Frechet Inception Distance (FID) [72] between generated and real motions. (ii) Motion diversity using Diversity (DIV), i.e., feature-space variance, and MultiModality (MM), i.e., output variation under identical text prompts. (iii) Text-motion alignment with motion-retrieval
+
+precision (R Precision) [7], i.e., Top-k retrieval accuracy, and Multi-modal Distance (MM Dist). All metrics derive from text/motion encoders and are protocol-dependent.
+
+Quantitative Results. We summarize motion generation results in Tables 1-2, highlighting four key observations for DRL-enhanced models: (i) Though affected by the biased Ori. protocol, DRL achieves impressive improvements in FID, confirming enhanced generation fidelity. (ii) Under Upd. protocol, DRL yields higher R-Precision, reflecting stronger text-motion alignment. (iii) Under both protocols, DRL effectively boosts the overall and class-wise diversity. (iv) A decline in RP Top3 and MM Dist is observed. This may stem from diversified outputs reducing exact matches.
+
+Qualitative Results. As in Fig. 3 (row 1), TM2T $^*$ -T2M + DRL generates an exact throwing motion whereas TM2T $^*$ -T2M fails, indicating DRL's role in enhancing semantic perception and motion diversity. In row 2, motion generated by baseline lacks completeness and precision. It shows simultaneous leg movements and misses a back-to-left motion. In contrast, TM2T $^*$ -T2M + DRL produces a fully aligned motion, demonstrating DRL's benefit for fine-grained semantic understanding and motion generation.
+
+
+A person throws something with right hand.
+
+
+A person side steps, moving one leg at a time to the right and then does the same kind of side step to the left.
+
+Figure 3. Qualitative comparison of $\mathrm{TM2T^{*}}$ and $\mathrm{TM2T^{*} + DRL}$ on motion generation (§4.2).
+
+| Method | R Precision ↑ | MM Dist ↓ | BLEU@1 ↑ | BLEU@4 ↑ | Rouge ↑ | CIDEr ↑ | BertScore ↑ |
| Top 1 | Top2 | Top3 |
| Real Desc. | 0.523 | 0.725 | 0.828 | 2.901 | - | - | - | - | - |
| †TM2T [7] [ECCV22] | 0.516 | 0.720 | 0.823 | 2.935 | 48.90 | 7.00 | 38.10 | 16.80 | 32.20 |
| ‡MotionGPT [8] [NeurIPS23] | 0.543 | - | 0.827 | 2.821 | 48.20 | 12.47 | 37.40 | 29.20 | 32.40 |
| ‡AvatarGPT [9] [CVPR24] | - | - | - | - | 49.28 | 12.70 | 40.44 | 32.65 | 53.58 |
| TM2T*-M2T | 0.288 | 0.449 | 0.547 | 4.790 | 23.65 | 4.42 | 27.94 | 43.47 | 18.03 |
| TM2T*-M2T + DRL | 0.303 | 0.472 | 0.569 | 4.622 | 28.62 | 5.80 | 27.68 | 50.90 | 19.88 |
| MotionGPT* | 0.504 | 0.687 | 0.780 | 3.065 | 43.44 | 6.01 | 34.38 | 5.68 | 23.28 |
| MotionGPT* + DRL | 0.511 | 0.697 | 0.788 | 3.059 | 45.70 | 7.52 | 35.93 | 13.26 | 26.01 |
+
+Table 3. Quantitative comparison of motion understanding (§4.3) on HumanML3D test (Ori. protocol, §4.1). †: TM2T uses an expanded VQVAE codebook in size and dimensions; ‡: Models trained with enhanced scale/strategies/data augmentation. Results of state-of-the-art methods, sourced from [8] and [9] papers, were evaluated using NLG-Eval [73], while we employ NLG-Metricverse [74] following official implementation of [8]. This evaluation setup discrepancy may lead to inconsistencies when comparing their results with ours.
+
+| Method | R Precision ↑ | MM Dist ↓ |
| Top 1 | Top2 | Top3 |
| Real Desc. | 0.384 | 0.572 | 0.685 | 3.591 |
| TM2T* -M2T | 0.199 | 0.324 | 0.420 | 5.145 |
| TM2T* -M2T + DRL | 0.210 | 0.347 | 0.446 | 5.076 |
| MotionGPT* | 0.352 | 0.538 | 0.661 | 3.580 |
| MotionGPT* + DRL | 0.363 | 0.552 | 0.667 | 3.565 |
+
+Table 4. Quantitative comparison of motion understanding (§4.3) on HumanML3D test set under Upd. protocol (§4.1).
+
+# 4.3. Performance on Motion Understanding
+
+Metrics. For motion-to-text evaluation, we assess two aspects: (i) Text-motion alignment via R-Precision and Multimodal Distance (MM Dist), evaluating M2T at embedding level; (ii) Natural language quality using linguistic metrics, i.e., BLEU [75], ROUGE [76], CIDEr [21] and BertScore [63], computed at the text token level with NLGMetricverse [74]. Alignment metrics depend on the evaluation protocol, while linguistic metrics are protocol-agnostic.
+
+Quantitative Results. Table 3 and 4 compare motion understanding performance under different protocols. DRL-enhanced TM2T\*-M2T surpasses its non-DRL version across four linguistic metrics, most notably in CIDEr (50.90
+
+vs 43.47), demonstrating significant gains in semantic accuracy. Under the Upd. protocol, consistent improvements in motion-text alignment metrics confirm DRL's capability to strengthen cross-modal alignment.
+
+Qualitative Results. Fig. 4 (left) shows TM2T-M2T* + DRL correctly identifies subtle picking-up gestures with detailed descriptions, while TM2T*-M2T outputs irrelevant content. On the right, the baseline merely tracks trajectory, whereas TM2T*-M2T + DRL captures full-body semantics to correctly recognize dancing with precise and concise descriptions. These contrasts demonstrate DRL's role in enhancing fine-grained motion perception, holistic semantic understanding, rich and concise semantic expression.
+
+# 4.4. Diagnostic Experiments
+
+For in-depth analysis, we perform a set of ablative studies with $\mathrm{TM2T^{*}}$ -T2M and $\mathrm{TM2T^{*}}$ -M2T under Upd. protocol.
+
+Dual Learning. We first validate the significance of both unpaired data and reciprocal relations within our DRL framework. Table 5a (row 1) reports the result of a baseline model trained solely on paired text-motion data. Next, we implement our dual-learning bootstrapping process using only the paired data, i.e., training two models with $\mathcal{L}_V$ and $\mathcal{L}_T$ exclusively on text-motion pairs, without incorporating any unpaired data. This yields notable improve
+
+
+Figure 4. Qualitative comparison of $\mathrm{TM2T^{*} - M2T}$ to $\mathrm{TM2T^{*} - M2T + DRL}$ on motion understanding (§4.3). Gray indicates irrelevant texts.
+
+(a) Dual Learning
+
+| Method | Text-to-Motion | Motion-to-Text |
| FID ↓ | R TOP1 ↑ | MModality ↑ | BLEU@4 ↑ | CIDEr ↑ |
| Baseline (w only DL) | 0.063 | 0.370 | 2.091 | 4.42 | 43.47 |
| DRL w/o additional data | 0.048 | 0.376 | 2.156 | 5.11 | 47.28 |
| DRL w Uv | 0.043 | 0.377 | 2.192 | 5.45 | 48.07 |
| DRL w Uv + UT | 0.039 | 0.380 | 2.238 | 5.80 | 50.90 |
+
+(b) Unpaired Data Size
+
+| Data Size
+UV | Text-to-Motion | Motion-to-Text |
| FID ↓ | R TOP1 ↑ | MModality ↑ | BLEU@4 ↑ | CIDEr ↑ |
| 3k | 0.056 | 0.367 | 2.106 | 4.75 | 45.02 |
| 5k | 0.048 | 0.371 | 1.171 | 5.32 | 47.45 |
| 9k | 0.039 | 0.380 | 2.238 | 5.80 | 50.90 |
| 12k | 0.031 | 0.388 | 2.265 | 5.97 | 52.23 |
+
+(c) Paired Data Reliance
+
+| Data Ratio | Text-to-Motion | Motion-to-Text |
| FID ↓ | R TOP1 ↑ | MModality ↑ | BLEU@4 ↑ | CIDEr ↑ |
| DL | 0.063 | 0.370 | 2.091 | 4.42 | 43.47 |
| 1/2DL+UT+UV | 0.064 | 0.367 | 1.977 | 4.36 | 38.70 |
| 1/4DL+UT+UV | 0.071 | 0.361 | 1.970 | 4.30 | 30.16 |
| 1/8DL+UT+UV | 0.105 | 0.349 | 1.853 | 4.26 | 22.75 |
+
+(d) Training Strategy
+
+| Training Strategy | Text-to-Motion | Motion-to-Text |
| Stage One | Stage Two | FID ↓ | R TOP1 ↑ | MModality ↑ | BLEU@4 ↑ | CIDEr ↑ |
| L + Lv + LT | 0.134 | 0.352 | 2.677 | 4.74 | 39.52 |
| L | Lv + LT | 0.060 | 0.371 | 2.107 | 4.89 | 45.08 |
| L + Lv | L + Lv + LT | 0.051 | 0.377 | 2.179 | 5.22 | 47.95 |
| L + Lv | LT | 0.039 | 0.380 | 2.238 | 5.80 | 50.90 |
+
+Table 5. A series of ablation studies on HumanML3D test set [20]. All the experiments are conducted under Upd. evaluation protocol.
+
+ment (row 2), suggesting that the structural symmetry between primal and dual tasks alone provides valuable training signals. Further incorporating unpaired motion data during dual learning yields additional gains (row 3). Finally, leveraging both unpaired text and motion data within DRL achieves the greatest improvement (row 4), demonstrating the full efficacy of the DRL framework.
+
+Unpaired Data Size. Then, we investigate the impact of unpaired motion data volume within DRL. Table 5b demonstrates that increasing unpaired motion data consistently boosts performance, evidencing DRL's scalability. To balance performance and computational resources, we incorporate 9k motion samples in DRL by default.
+
+Paired Data Reliance. Furthermore, we analyze DRL's reliance on paired data. Using a fixed amount of unpaired data and progressively decreasing amounts of paired data (Table 5c), we observe that the performance of the DRL-enhanced TM2T $^*$ -T2M model remains comparable to the baseline model's even when paired data is reduced to one-fourth of the original amount. This demonstrates that DRL reduces the dependency on paired data.
+
+Training Strategy. Finally, we study the influence of different training strategies in Table 5d. $\mathcal{L}$ denotes $\mathcal{L}_{\mathrm{labeled}}$ . We investigate four alternatives: (i) Initialize and maintain $\mathcal{L} + \mathcal{L}_V + \mathcal{L}_T$ throughout training; (ii) Stage One: $\mathcal{L}$ ;
+
+Stage Two: $\mathcal{L}_V + \mathcal{L}_T$ ; (iii) Stage One: $\mathcal{L} + \mathcal{L}_V$ ; Stage Two: $\mathcal{L} + \mathcal{L}_V + \mathcal{L}_T$ ; (iv) The DRL strategy proposed in §3.3. In practice, we find our proposed strategy leads to more stable convergence and superior results. We use this by default.
+
+# 5. Conclusion
+
+In this work, we propose Dual Reciprocal Learning (DRL) framework for language-based human motion understanding and generation. By fostering the strong reciprocity relationship with collaborative dual learning, DRL reduces data dependency, enhances model performance, and shows great promise for real-world applications where labeled pairs are harder to acquire. We further propose a generalized protocol that extends existing evaluation to a general-domain cross-modal feature space, mitigating dataset-specific bias.
+
+Acknowledgement. This work was supported by the National Science and Technology Major Project (No. 2023ZD0121300), Zhejiang Provincial Natural Science Foundation of China (No. LD25F020001), Fundamental Research Funds for the Central Universities (226-2025-00057), and the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (No.VRLAB2025A02), China Postdoctoral Science Foundation (No. 2025T180421), and the Postdoctoral Fellowship Program of CPSF (No. GZC20251066).
+
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+# Dual Recursive Feedback on Generation and Appearance Latents for Pose-Robust Text-to-Image Diffusion
+
+Jiwon Kim1 Pureum Kim1 SeonHwa Kim1 Soobin Park2 Eunju Cha2* Kyong Hwan Jin1*
+1Korea University Sookmyung Women's University
+
+{jwonkim, pureum_kim, sunkim0062, kyong_jin}@korea.ac.kr, {psb1219j, eunju.cha}@sookmyung.ac.kr
+
+# Abstract
+
+Recent advancements in controllable text-to-image (T2I) diffusion models, such as Ctrl-X and FreeControl, have demonstrated robust spatial and appearance control without requiring auxiliary module training. However, these models often struggle to accurately preserve spatial structures and fail to capture fine-grained conditions related to object poses and scene layouts. To address these challenges, we propose a training-free Dual Recursive Feedback (DRF) system that properly reflects control conditions in controllable T2I models. The proposed DRF consists of appearance feedback and generation feedback that recursively refines the intermediate latents to better reflect the given appearance information and the user's intent. This dual-update mechanism guides latent representations toward reliable manifolds, effectively integrating structural and appearance attributes. Our approach enables fine-grained generation even between class-invariant structure-appearance fusion, such as transferring human motion onto a tiger's form. Extensive experiments demonstrate the efficacy of our method in producing high-quality, semantically coherent, and structurally consistent image generations. Our source code is available at https://github.com/jwonkm/DRF.
+
+# 1. Introduction
+
+Recent advancements in diffusion models [4, 10, 20, 24, 28] have led to rapid progress in the field of image generation. Among these developments, the need to generate images that accurately reflect a user's intended expression has emerged, resulting in various approaches for incorporating user intent into Text-to-Image (T2I) generation and Imaged-to-Image (I2I) translation tasks.
+
+Text-to-Image (T2I) techniques have been developed to synthesize realistic and creative images solely from textual descriptions. However, T2I methods often face limitations in controlling the spatial composition of the gener
+
+
+Figure 1. Flowchart of Dual Recursive Feedback (DRF). Illustration of a diffusion-based generative model with latent feedback mechanisms (DRF) for controlling both appearance and generation latent in class-invariant text-to-image synthesis. The proposed method refines latent updates to achieve fine-grained control, improving results with desired structural and appearance attributes.
+
+ated images, making the representation of complex structures challenging. To address this, T2I models have progressively incorporated conditional guidance techniques, enabling more detailed control over the desired image attributes. For instance, approaches such as ControlNet [32] leverage specific structures (e.g., pose, edge, or depth) to provide users with finer control, thus allowing the generated images to align more precisely with user intent. Beyond T2I generations, a line of research known as Image-to-Image (I2I) translation [7, 8, 12, 30] extends generating capabilities by taking an existing source image as input, and then transforming it according to a text query. Since this approach leverages the structural or contextual elements of the original image, I2I offers more precise control than T2I. Nonetheless, a technical trade-off between reliability and diversity still remained.
+
+Another strategy for reflecting both the structure to be incorporated into the generated image and the appearance to be preserved is to use dedicated images as prompts for each aspect, such as IP-Adapter [31] and Ctrl-X [14]. By directly specifying what structures and appearance the user wants, these methods can better integrate the user's intent into the generated results. However, such techniques still
+
+
+Figure 2. Cross-domain Pose transfer via Dual Recursive Feedback(DRF). Our DRF demonstrates robust pose generations based on structures (mesh, skeleton). The first row illustrates human pose structures and their application to penguin (appearance) images, generating semantically consistent with a given penguin appearance. Similarly, the second example presents human skeleton-based structures applied to a tiger (appearance), demonstrating the adaptability of motion synthesis across different poses.
+
+suffer from the need to retrain models every time or the dependence on categorical similarity between the two images. As a result, they may fail to generate appropriate images in class-invariant setups where the categories of structure and appearance are very different or where there is a significant structural mismatch between structure and appearance. This indicates that the conventional approaches do not offer a universally reliable solution yet.
+
+To address these issues, we propose a model called Dual Recursive Feedback (DRF) that successfully exploits the flexibility of score guidance to synthesize the image with the given structure and appearance, even under extreme conditions. A structure image and an appearance image are provided as inputs, thereby eliminating the need for additional training or guidance mechanisms. Then, we recursively refine the resulting latent space by adjusting a text-conditioned score describing the appearance to accurately reflect the identity, as shown in Fig. 1. Owing to appearance feedback, the appearance leakage can be resolved even if the structure and appearance differ significantly. Furthermore, latent values derived from injecting both images are also updated to align with the user's intended prompt, which is referred to as generation feedback. By recursively applying appearance and generation feedbacks to the intermediate latents, the final output with the proposed method enables to reflect the user's intent. Moreover, our framework is compatible with various T2I models, where it consistently outperforms the baseline models in terms of quality.
+
+In summary, our main contributions are as follows:
+
+- We present a novel method that employs dual recursive feedback to preserve appearance fidelity and structural integrity while excelling at pose transfer, enabling high-quality image generation that accurately reflects user intent—even in class-invariant setups.
+- Our method not only generates images where the appearance image is adapted to follow the structure outlined by the structure image, but also allows for diverse scenarios by manipulating the prompt to align the structure's object: guiding the structure image to adopt the textures and colors of the appearance image.
+
+# 2. Related works
+
+# 2.1. Controllable Text-to-Image diffusion
+
+Text-to-Image (T2I) models have continued to evolve by incorporating conditional guidance methods for more precise image generation. ControlNet [32], which augments a pretrained T2I diffusion model with spatial conditional control, allowing users to specify additional constraints—such as layout, pose, and shape—to reflect a desired spatial composition. However, this approach requires fine-tuning multiple models when controlling numerous spatial factors, thereby increasing both model count and training overhead. By contrast, FreeControl [17] imposes no additional training demands on the pretrained T2I model and generally adheres well to textual descriptions; however, it depends solely on
+
+
+
+
+Figure 3. Flowchart of DRF. The backbone of our algorithm starts from the generation latent obtained from the Ctrl-X [14] framework. DRF iteratively updates by obtaining guided noise $\epsilon_{\theta}^{a}$ and $\epsilon_{\theta}^{g}$ through appearance and generation feedback. The distillation function derived from these two noises is combined to update the generation latent.
+
+gradient-based manipulation in the latent space to minimize loss, resulting in significant computational costs and GPU usage. To facilitate faster and more lightweight T2I operations, Ctrl-X [14] has been introduced, injecting separate images for structure and appearance into a pretrained diffusion model, using feed-forward feature replacement to preserve structure and self-attention layers to align generated features with appearance image statistics. While this method increased efficiency, it remains less effective at consistently maintaining the target appearance features. For instance, though Ctrl-X demonstrates robust performance when both source images belong to the same category (e.g., appearance: "horse", structure: "a mesh of horse"), its performance degrades when dealing with class-invariant setups, resulting in subpar generation results.
+
+# 2.2. Score distillation sampling
+
+Score Distillation Sampling (SDS) [21] is a direct, gradient-based optimization approach to diffusion models. The pretrained text-image diffusion model's implicit image distribution and denoising-direction score are inverted to adjust images toward a desired text condition iteratively. Due to the noisy gradients in SDS, which frequently cause oversaturated colors and overly smoothed regions, Delta Denoising Score (DDS) [8] and Identity-preserving Distillation Sampling (IDS) [12] were subsequently introduced to mitigate these effects. Notably, IDS employs a fixed-point regularization (FPR) method, which preserves the original image's identity throughout the editing process, resulting in high-quality image generation. Nevertheless, because FPR strongly constrains the source image to maintain its identity, the degree of editing becomes limited, yielding lower prompt alignment compared to prior approaches [8, 19, 21].
+
+# 3. Methodology
+
+# 3.1. Preliminaries
+
+Diffusion models and sampling guidance. The forward diffusion process is to gradually add Gaussian noise, $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ , to a clean image $\mathbf{z}_0$ across $T$ timesteps:
+
+$$
+\mathbf {z} _ {t} = \sqrt {\alpha_ {t}} \mathbf {z} _ {0} + \sqrt {1 - \alpha_ {t}} \epsilon , \quad t \in \{1, \dots , T \}, \tag {1}
+$$
+
+where $\alpha_{t}$ is the cumulative product of noise variances at step $t$ , and $\mathbf{z}_t$ denotes the resulting noisy image at that step. Then, the diffusion model learns to denoise the data step by step to reconstruct the output image. Sampling guidance modifies the standard denoising procedure to incorporate user constraints. In classifier-free guidance (CFG) [9], the model obtains both conditional $\epsilon(x_t|c)$ and unconditional $\epsilon(x_t|\varnothing)$ noise predictions, leveraging their difference to strongly enforce the desired condition:
+
+$$
+\epsilon_ {\theta} ^ {\omega} \left(\mathbf {z} _ {t}, y, t\right) = (1 + \omega) \epsilon_ {\theta} \left(\mathbf {z} _ {t}, y, t\right) - \omega \epsilon_ {\theta} \left(\mathbf {z} _ {t}, \varnothing , t\right). \tag {2}
+$$
+
+Score guidance models. Approaches like IDS [12] tackle directional ambiguity by preserving the identity of the original image. In IDS, FPR is proposed to modify the current latent for the adjustment of the text-conditioned score to the original latent as follows:
+
+$$
+\mathbf {z} _ {t} ^ {\text {o r g}} \leftarrow \mathbf {z} _ {t} ^ {\text {o r g}} - \lambda \nabla_ {\mathbf {z} _ {t} ^ {\text {o r g}}} \mathcal {L} _ {\mathrm {F P R}}, \tag {3}
+$$
+
+where
+
+$$
+\mathcal {L} _ {\mathrm {F P R}} = d \left(\mathbf {z} ^ {\text {o r g}}, \mathbf {z} _ {0 | t} ^ {\text {o r g}}\right). \tag {4}
+$$
+
+$d(\mathbf{x},\mathbf{y})$ denotes any metric to compare $\mathbf{x}$ and $\mathbf{y}$ . $\mathbf{z}_{0|t}^{\mathrm{org}}$ is the posterior mean associated with the original image given by:
+
+$$
+\mathbf {z} _ {0 | t} ^ {\mathrm {o r g}} = \mathbb {E} \left[ \mathbf {z} _ {0} ^ {\mathrm {o r g}} \mid \mathbf {z} _ {t} ^ {\mathrm {o r g}} \right] = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {z} _ {\mathbf {t}} ^ {\mathrm {o r g}} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\theta} ^ {\omega}\right). \tag {5}
+$$
+
+
+Figure 4. Comparison of Appearance feedback only and DRF. When only Appearance feedback is executed without Generation feedback, the excessive emphasis on appearance image occurs.
+
+However, this strong correction overly retains the original content, limiting the generated image's ability to align with the target prompt.
+
+Notations. For the controllable Text-to-Image (T2I) generation using the pretrained diffusion models, the appearance image $\mathbf{I}^a$ and the structure image $\mathbf{I}^s$ can be used. For the sake of simplicity, the notations for images, latents and other components required during the image synthesis are summarized in Tab. 1.
+
+| Notation | Description | Notation | Description |
| Ig | Generation image | zgt-1 | Generation latent |
| Ia | Appearance image | z0a | Clean latent of Ia |
| Ia | Structure image | zt | Noisy latent of Ia at time t |
| ft | Convolutional feature from Ia | zprev | Previous generation latent in recursion |
| ht | Self-attention-based appearance feature | At | Self-attention map derived from Ia |
+
+Table 1. Notation Summary for DRF
+
+# 3.2. Dual Recursive Feedback (DRF)
+
+The flowchart of the proposed method is illustrated in Fig. 3. In T2I diffusion models where $\mathbf{I}^a$ and $\mathbf{I}^s$ serve as controllable elements, our method robustly transforms the generated image $\mathbf{I}^g$ on a class-invariant dataset while retaining the features of $\mathbf{I}^a$ and adhering to the structure of $\mathbf{I}^s$ .
+
+We begin by injecting $\mathbf{I}^a$ and $\mathbf{I}^s$ into the T2I model without guidance and then focus on the resulting output latent $\mathbf{z}^g$ as in [14]. Specifically, $\mathbf{z}^g$ incorporates $f_t^s$ and $A_t^s$ reflecting structural information from $\mathbf{I}^s$ , as well as an appearance latent $h_t^a$ transferred from $\mathbf{I}^a$ . Hence, $\mathbf{z}^g$ can be expressed as:
+
+$$
+\mathbf {z} _ {t - 1} ^ {g} = \operatorname {C r t} - X \left(\mathbf {z} _ {t} ^ {g} \mid t, y, f _ {t} ^ {s}, A _ {t} ^ {s}, h _ {t} ^ {a}\right). \tag {6}
+$$
+
+We observed that when $\mathbf{I}^a$ and $\mathbf{I}^s$ belong to class-invariant setup-different categories or exhibiting significant structural discrepancies-, simply separating appearance and structural information within the attention map is insufficient to yield $\mathbf{I}^g$ that correctly reflects both features of $\mathbf{I}^a$ and $\mathbf{I}^s$ , as shown in the third column of Fig. 4. To address this limitation, we propose leveraging a score guidance method on $\mathbf{z}^g$ during the generation. We refer to this technique as Dual Recursive Feedback (DRF).
+
+Appearance Feedback. To address "appearance leakage" issue reported in FreeControl [17] and misalignment of appearance features noted in Ctrl-X [14], gradient based on the latents associated with the appearance, such as $\mathbf{z}_t^a$ and $\mathbf{z}^a$ , needs to be investigated. As analyzed in IDS [12], the text-conditioned score $\epsilon_{\theta}^{a}$ computed from $\mathbf{z}_t^a$ cannot always
+
+
+Figure 5. Outputs according to the forward process of appearance latent. When structure and appearance images are given, third and fourth column show the outputs of DRF with $\tilde{\mathbf{z}}_t^a$ and $\mathbf{z}_t^a$ for appearance feedback.
+
+be guaranteed as a gradient to $\mathbf{z}^a$ , leading to a loss of appearance identity. Thus, our method employs the concept of a fixed point—inspired by numerical analysis—to guide the gradient updates toward $\mathbf{z}^a$ .
+
+Unlike IDS, which translates the given source to the target by optimizing the latent with a randomly sampled time step $t \sim \mathcal{U}(0,1)$ , our method generates the output from the initial noise $\mathbf{z}_1 \sim \mathcal{N}(0,\mathbf{I})$ for timestep $t = 1,\dots ,0$ . Since the posterior mean $\mathbf{z}_{0|t}^a$ in the large timestep has insufficient information on $\mathbf{z}_0^a$ , the difference between $\mathbf{z}_{0|t}^a$ and $\mathbf{z}_0^a$ increases, causing excessive guidance to $\mathbf{z}_0^a$ , shown in last column of Fig. 5. We avoid the excessive difference by modifying Eq. (1) to compute modified stochastic latent $\tilde{\mathbf{z}}_t^a$ as following:
+
+$$
+\tilde {\mathbf {z}} _ {t} ^ {a} = \sqrt {\frac {\alpha_ {t}}{\alpha_ {t - 1}}} \mathbf {z} _ {0} ^ {a} + \sqrt {1 - \frac {\alpha_ {t}}{\alpha_ {t - 1}}} \epsilon . \tag {7}
+$$
+
+By designing a loss that minimizes the difference between $\mathbf{z}^a$ and $\mathbf{z}_{0|t}^a = \mathbb{E}[\mathbf{z}_0|\tilde{\mathbf{z}}_t^a]$ calculated from the score $\epsilon_{\theta}^{a} = \epsilon_{\theta}^{\omega}(\tilde{\mathbf{z}}_t^a,y^a,t)$ , we ensure that the appearance information remains intact:
+
+$$
+\mathcal {L} _ {\mathrm {a p p}} = d \left(\mathbf {z} _ {0 | t} ^ {a}, \mathbf {z} _ {0} ^ {a}\right), \tag {8}
+$$
+
+Even though the overemphasis on the appearance image is mitigated by the modified stochastic latent, considering only appearance feedback may hinder its seamless integration in $\mathbf{I}^g$ , as demonstrated in the fourth column of Fig. 4.
+
+Generation Feedback. To further address appearance overfitting, we incorporate generation feedback to $\mathbf{z}^g$ . This ensures a more balanced fusion of appearance signals and ultimately improves the generation quality, as shown in the third column of Fig. 4. Specifically, as the feedback is iteratively applied in a recursive manner, the score $\epsilon_{\theta}^{g}$ updated by the previous gradient modifies $\mathbf{z}_{\mathrm{prev}}^g$ . We treat $\mathbf{z}_{\mathrm{prev}}^g$ as another fixed point so that the current update direction can be aligned with $\mathbf{z}_{\mathrm{prev}}^g$ , allowing for more efficient image synthesis. A loss for the output feedback is designed to minimize the difference between $\mathbf{z}_{\mathrm{prev}}^g$ and $\mathbf{z}_{0|t}^g$ as follows:
+
+$$
+\mathcal {L} _ {\text {g e n}} = d \left(\mathbf {z} _ {0 | t} ^ {g}, \mathbf {z} _ {\text {p r e v}} ^ {g}\right). \tag {9}
+$$
+
+Training - free methods
+Training - based methods
+
+| Structure | Appearance | DRF (Ours) | Ctrl-X[14] | FreeControl[17] | Uni-Control[22] | ControlNet[32] + IP-Adapter[31] | T2I-Adapter[18] + IP-Adapter[31] |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
+
+Figure 6. Qualitative results of appearance and structure control. DRF successfully generates fused images that preserve the characteristics of the appearance and structural images.
+
+Dual Recursive Feedback. We combine the appearance feedback loss Eq. (8) and the generation feedback loss Eq. (9) to formulate our final Dual Recursive Feedback (DRF). Using the structural information from the initial steps contains sufficient information [14]; however, due to the nature of initializing the initial latent $\mathbf{z}_T^g$ with random Gaussian noise, the structure of the image generated in the first inference step may not align with $\mathbf{I}^s$ [30]. Therefore, we applied the DRF to the intermediate 20 steps after the first five steps, considering both the efficiency and generation quality. The discussion and experimental evaluation of the DRF application steps are detailed in the supplementary. As we progress through multiple iterations of DRF at each step, $\mathbf{z}_t^g$ is successively refined, incorporating more corrective feedback and thus becoming increasingly aligned with both the appearance and structure constraints.
+
+To balance appearance and generation feedback, we adopt an exponential weighting scheme that progressively amplifies the generation-feedback weight as the recursive iterations $(i)$ advance:
+
+$$
+w _ {\text {i t e r}} ^ {(i)} = \sqrt {\frac {\exp \left(k \frac {i}{N - 1}\right) - 1}{\exp (k) - 1}}. \tag {10}
+$$
+
+An empirical comparison of alternative weighting strategies is presented in the supplementary.
+
+Namely, appearance feedback is more crucial at the beginning so that the identity of the appearance can be reflected properly in the output, even in complex cases. As the number of iterations increases, the generation feedback is taken more into account to achieve the output that better matches the user's intent. To this end, the $DRF$ loss is defined as follows:
+
+# Algorithm 1 Dual Recursive Feedback
+
+Require: $\mathbf{z}_0^a$ , $\mathbf{z}_{t-1}^g$ , $y^a$ : Prompts of appearance, $y^g$ : Prompts of generation, $\omega$ , $\lambda$ , $\rho$ , $k$ , $N$ : balancing parameters & constants
+
+1: $\epsilon \sim \mathcal{N}(0,\mathbf{I})$
+2: for $i = 1, \dots, N$ do
+3: $\mathbf{z}_t^g\gets \sqrt{\frac{\alpha_t}{\alpha_{t - 1}}}\mathbf{z}_{t - 1}^g +\sqrt{1 - \frac{\alpha_t}{\alpha_{t - 1}}}\epsilon$
+4: $\bar{\mathbf{z}}_t^a\gets \sqrt{\frac{\alpha_t}{\alpha_{t - 1}}}\mathbf{z}_0^a +\sqrt{1 - \frac{\alpha_t}{\alpha_{t - 1}}}\epsilon$
+5: $\epsilon_{\theta}^{a},\epsilon_{\theta}^{g}\gets \epsilon_{\theta}^{\omega}(\tilde{\mathbf{z}}_{t}^{a},y^{a},t),\epsilon_{\theta}^{\omega}(\mathbf{z}_{t}^{g},y^{g},t)$
+6: $\mathbf{z}_{0|t}^a, \mathbf{z}_{0|t}^g \leftarrow \mathbb{E}[\mathbf{z}_0 \mid \tilde{\mathbf{z}}_t^a], \mathbb{E}[\mathbf{z}_0 \mid \mathbf{z}_t^g]$
+
+7: $w_{\mathrm{iter}}^{(i)} = \sqrt{\frac{\exp\left(k\frac{i}{N - 1}\right) - 1}{\exp(k) - 1}}$
+8: $\mathcal{L}_{\mathrm{DRF}}^{(i)}\gets d(\mathbf{z}_{0|t}^a,\mathbf{z}_0^a) + \rho w_{\mathrm{iter}}^{(i)}d(\mathbf{z}_{0|t}^g,\mathbf{z}_{\mathrm{pre}}^g)$
+9: $\epsilon \gets \epsilon -\lambda \nabla_{\epsilon}\mathcal{L}_{\mathrm{DRF}}^{(i)}$
+10: $\mathbf{z}_{\mathrm{prev}}^g\gets \mathbf{z}_{0|t}^g$
+11: end for
+12: return $\mathbf{z}_t^{g*}$
+
+$$
+\mathcal {L} _ {\mathrm {D R F}} ^ {(i)} \leftarrow d \left(\mathbf {z} _ {0 | t} ^ {a}, \mathbf {z} _ {0} ^ {a}\right) + \rho w _ {\text {i t e r}} ^ {(i)} d \left(\mathbf {z} _ {0 | t} ^ {g}, \mathbf {z} _ {\text {p r e v}} ^ {g}\right), \tag {11}
+$$
+
+where $\rho$ is a hyper-parameter.
+
+Note that the injection noise $\epsilon$ is added to $\mathbf{z}_{t - 1}^{g}$ and $\mathbf{z}^a$ to obtain the stochastic latent $\mathbf{z}_t^g$ and $\tilde{\mathbf{z}}_t^a$ , which can be considered as the connection between $\mathbf{z}_t^g$ and $\tilde{\mathbf{z}}_t^a$ . Thus, we updated the injection noise $\epsilon$ in the direction that minimizes the DRF loss over multiple recursive steps:
+
+$$
+\epsilon \leftarrow \epsilon - \lambda \nabla_ {\epsilon} \mathcal {L} _ {\mathrm {D R F}} ^ {(i)}. \tag {12}
+$$
+
+With the modified noise $\epsilon$ in Eq. (12), the fully refined $\mathbf{z}^{g*}$ can be provided. Extensive sensitivity analyses for the hyper-parameters are reported in the supplementary. Consequently, this final $\mathbf{z}^{g*}$ retains the essential features of the appearance image while being appropriately corrected at each step to preserve the structure as well, thereby generating a high-quality image that honors both sets of constraints.
+
+# 4. Experiments
+
+Baselines. We compare our method against recent controllable T2I diffusion models [14, 17, 18, 22, 31, 32] as baselines. For all experiments except Uni-ControlNet and T2I-Adapter, we use the SDXL [20] model optimized for $512 \times 512$ images to ensure a fair comparison. The implementations of the baselines are conducted by referring to the official source code provided for each respective method.
+
+Dataset. Structure images, sourced from prior studies [5, 11, 34], comprise $30\%$ ControlNet-supported conditions (e.g., Canny, skeleton), $51\%$ in-the-wild conditions (e.g., 3D mesh, point cloud), and $19\%$ natural images. Appearance images are collected from open-source datasets [1, 26] and generated images. Text prompts for structure, appearance, and generation are defined by combining templates with manual annotations.
+
+Evaluation metrics. Structure and appearance control are evaluated using widely adopted metrics in T2I diffusion models. Specifically, DINO Self-sim [29] metric quantifies structure preservation by computing the self-similarity distance between the structure image and the generated output in the DINO-ViT [2] feature space, while the DINO-I [25] metric assesses appearance transfer through cosine similarity of the DINO-ViT tokens. CLIP score [23] measures text-image similarity for prompt-based control generation.
+
+In addition, categorical fidelity is quantified by a successive rate. Each synthesized image is passed through an ImageNet-pretrained ResNet-18 [6], whose top-1 prediction is compared with the target class (e.g., "tiger," ImageNet class 292). A concordant prediction is counted as a success; any discrepancy is deemed a failure. The reported score is the proportion of successes averaged over the evaluation set.
+
+# 5. Results
+
+# 5.1. Qualitative results
+
+We evaluate the proposed method against baselines in three appearance-structure fusion scenarios. (1) As the first to fourth rows of Fig. 6 demonstrate, our approach reliably aligns the appearance image with diverse structure types (mesh, skeleton, canny, 3D) while preserving its key features. In contrast, baselines often fail by losing appearance details or generating incoherent results. (2) The last two rows in Fig. 6 show that simply adjusting the prompt for the structure object allows us to inject texture and color from the appearance image into the structure image without sacrificing the structure's essential objects or attributes. (3) Lastly, when applying an illustrative style of appearance image to the structure image as depicted in Fig. 7, our method remains robust and versatile, consistently producing high-quality results across different styles.
+
+We also demonstrate that controllable T2I generation can be achieved solely from a structure image by first producing a text-guided image, then using it as DRF's appearance reference as shown in Fig. 8.
+
+# 5.2.Quantitative results
+
+As reported in Tab. 2, we evaluate Self-Sim [29], CLIP score [23], and DINO-I [25] on four structure datasets. While our method often attains the best scores, each metric focuses on a single aspect—similarity to either structure, appearance, or the prompt—so we additionally measure a successive rate (procedure in Sec. 4) that quantifies how faithfully both images are fused. Notably, our approach achieves the highest successive rate, even on a dataset with a lower DINO-I score, demonstrating robust generation performance.
+
+We also conduct a user study on 20 comparison sets that include five different structure datasets (real images,
+
+
+Figure 7. Qualitative results of Style images. DRF outperforms the baselines with appearance image style to structure image.
+
+| Method | Mesh [5] | Pose | Point cloud [11] | Canny | Successive Rate |
| Self-Sim ↓ | CLIP ↑ | DINO-I ↑ | Self-Sim ↓ | CLIP ↑ | DINO-I ↑ | Self-Sim ↓ | CLIP ↑ | DINO-I ↑ | Self-Sim ↓ | CLIP ↑ | DINO-I ↑ |
| T2I-Adapter+IP-Adapter [18, 31] | 0.2374 | 0.3062 | 0.6627 | 0.2949 | 0.2865 | 0.5304 | 0.1749 | 0.2708 | 0.4224 | 0.0457 | 0.3192 | 0.6467 | 0.9718 |
| ControlNet+IP-Adapter [31, 32] | 0.2024 | 0.3320 | 0.6068 | 0.3035 | 0.2904 | 0.6857 | 0.1328 | 0.2966 | 0.3169 | 0.0497 | 0.3164 | 0.5875 | 0.8873 |
| Uni-ControlNet [22] | 0.2188 | 0.2997 | 0.6232 | 0.3348 | 0.3077 | 0.6450 | 0.1302 | 0.2836 | 0.2918 | 0.0421 | 0.3160 | 0.5530 | 0.7605 |
| FreeControl [17] | 0.1503 | 0.3270 | 0.7288 | 0.2839 | 0.2880 | 0.6162 | 0.1445 | 0.2928 | 0.2552 | 0.0533 | 0.3084 | 0.7381 | 0.9152 |
| Ctrl-X [14] | 0.1542 | 0.3464 | 0.7139 | 0.2332 | 0.3429 | 0.7378 | 0.1205 | 0.3295 | 0.2654 | 0.0493 | 0.3075 | 0.7335 | 0.9577 |
| DRF (Ours) | 0.1532 | 0.3492 | 0.7342 | 0.2294 | 0.3503 | 0.7391 | 0.1114 | 0.3282 | 0.2923 | 0.0473 | 0.3102 | 0.7135 | 0.9859 |
+
+Table 2. Quantitative results Compared with baselines. Metrics measured with various structures (Mesh, Pose, Point cloud, Canny). DINO-ViT self-similarity [29] is lower-better $(\downarrow)$ , CLIP [23] and DINO-I [25] are higher-better $(\uparrow)$ .
+
+sketches, meshes, poses, and 3D) against five baselines. Participants evaluated how well each method (1) matched the text prompt, (2) preserved structure details, and (3) retained appearance characteristics. As Tab. 4 shows, our method outperforms all baselines in every category, indicating it not only aligns with the text prompt but also maintains core features of both the structure and appearance images.
+
+We measure inference time, preprocessing time, and peak GPU memory usage (Tab. 5). Although our dual recursive approach involves multiple fixed points and thus a higher runtime than Ctrl-X [14], the overhead can be reduced by applying DRF only at selected iterations. This enables a flexible trade-off between speed and performance. Moreover, because our method requires no training, the slight loss of efficiency can be compensated for by the gain in performance.
+
+
+"A photo of a bear / panda / tiger smile looking in front"
+
+
+"A photo of a cat / dalmatian dog / pink bunny sitting on the grass "
+Figure 8. Qualitative results of conditional Text-to-Image. Our method shows that T2I is possible using images produced by diffusion, even when an appearance image is not given.
+
+# 6. Discussions
+
+# 6.1. Plug-and-Play enhancement with DRF
+
+Our method can be integrated into existing T2I models in a plug-and-play manner, leading to performance improvements. Specifically, we add DRF process to the baseline model [31, 32] and observe improved image quality. As shown in Fig. 9, incorporating our process leads to enhanced fine-grained details (row 1) while simultaneously producing images that more closely align with both the structure and the specified prompt.
+
+
+Figure 9. Plug-and-Play of DRF. Applying DRF to ControlNet + IP-Adapter [31, 32] yields better results than using baseline alone.
+
+# 6.2. Scheduler-Agnostic DRF
+
+Our approach is scheduler-agnostic, extending beyond the default DDIM scheduler [27] to operate effectively with a broad family of diffusion schedulers. As reported in Tab. 3,
+
+| Steps | DPM-Solver++ (Multi-step) [16] + DRF | UniPC [33] + DRF | DPM-Solver (Single-step) [15] + DRF | DDIM [27] + DRF (Ours) |
| Clip ↑ | Self-Sim ↓ | DINO-I ↑ | Time (s) | Clip ↑ | Self-Sim ↓ | DINO-I ↑ | Time (s) | Clip ↑ | Self-Sim ↓ | DINO-I ↑ | Time (s) | Clip ↑ | Self-Sim ↓ | DINO-I ↑ | Time (s) |
| 5 | 0.3117 | 0.2126 | 0.444 | 8.80 | 0.3076 | 0.2129 | 0.646 | 8.78 | 0.1885 | 0.2622 | 0.544 | 8.64 | 0.3267 | 0.1613 | 0.549 | 7.68 |
| 10 | 0.3256 | 0.1605 | 0.826 | 15.56 | 0.3324 | 0.1898 | 0.765 | 16.06 | 0.3070 | 0.2398 | 0.706 | 16.04 | 0.3394 | 0.1917 | 0.768 | 13.52 |
| 20 | 0.3202 | 0.2449 | 0.843 | 29.81 | 0.3023 | 0.1653 | 0.622 | 30.15 | 0.3449 | 0.1721 | 0.870 | 29.51 | 0.3270 | 0.2061 | 0.854 | 25.33 |
| 30 | 0.3204 | 0.1904 | 0.846 | 43.27 | 0.3074 | 0.1832 | 0.792 | 42.86 | 0.3242 | 0.2207 | 0.770 | 44.15 | 0.3492 | 0.1204 | 0.891 | 35.74 |
| 40 | 0.3290 | 0.2225 | 0.776 | 61.14 | 0.2912 | 0.1667 | 0.762 | 58.68 | 0.3019 | 0.2337 | 0.827 | 57.54 | 0.3249 | 0.1628 | 0.836 | 47.87 |
| 50 | 0.3395 | 0.1864 | 0.851 | 70.45 | 0.2925 | 0.1790 | 0.717 | 72.35 | 0.3474 | 0.1895 | 0.840 | 70.78 | 0.3343 | 0.1533 | 0.863 | 58.50 |
+
+Table 3. Scheduler-agnostic performance of DRF. Quantitative results for DRF combined with four diffusion schedulers [15, 16, 27, 33]. DRF delivers consistently strong fidelity regardless of the solver, and pairing it with the faster DPM-Solver++ cuts latency by roughly $\times 3$ relative to DDIM while preserving perceptual quality.
+
+| User Preference Rate (%) |
| Method | Text (†) | Structure (†) | Appearance (†) |
| T2I-Adapter + IP-Adapter [18, 31] | 7.528 | 8.092 | 11.43 |
| ControlNet + IP Adapter [31, 32] | 16.02 | 12.90 | 14.14 |
| Uni-ControlNet [22] | 10.61 | 10.98 | 9.302 |
| FreeControl [17] | 12.93 | 14.83 | 17.63 |
| Ctrl-X [14] | 17.37 | 9.441 | 13.75 |
| DRF (Ours) | 35.52 | 43.73 | 33.72 |
+
+Table 4. User study shows that our method achieved the highest rates over all questions for controllable T2I.
+
+| Method | Training | Inference latency (s) | Peak GPU memory usage (GiB) |
| T2I-Adapter + IP-Adapter [18, 31] | ✓ | 11.07 | 4.45 |
| ControlNet + IP Adapter [31, 32] | ✓ | 23.39 | 13.68 |
| Uni-ControlNet [22] | ✓ | 18.74 | 8.73 |
| FreeControl [17] | ✗ | 154.76 | 18.69 |
| Ctrl-X [14] | ✗ | 15.52 | 13.07 |
| Ours-DRF N = 1 | ✗ | 29.69 | 18.71 |
| Ours-DRF N = 3 | ✗ | 56.87 | 18.71 |
+
+coupling our method with the multi-step DPM-Solver++ [16] reduces the sampling budget from 40 steps ( $\sim$ 47 sec.) under DDIM to 10 steps ( $\sim$ 15 sec.) while maintaining high perceptual fidelity. Thus, although the baseline DDIM already yields strong image quality, its latency bottleneck can be decisively mitigated by adopting faster solvers without compromising performance.
+
+# 6.3. DRF on Stable Diffusion
+
+To verify the advantages of our method extend beyond its native SDXL [20] backbone, we port the plug-in to two architecturally distinct Stable Diffusion [24] variants: (i) $\epsilon$ -prediction SD 1.5, which directly regresses additive noise, and (ii) v-prediction SD 2.0, where the network estimates latent velocity. Quantitative results in Tab. 6 show that our method preserves, and in some cases improves, image quality while delivering a substantial reduction in GPU memory consumption on both backbones. Additionally, based on validation of the schedulers natively embedded within each backbone (Sec. 6.2), our method demonstrates compatibility irrespective of the underlying model architecture.
+
+# 7. Limitation
+
+Computational cost. DRF adopts a dual framework of appearance feedback and generation feedback, inevitably
+
+Table 5. Inference efficiency DRF, as a training-free method, exhibits variations in inference time depending on the number of iterations $N$ .
+
+| Metrics | Clip ↑ | Self-Sim ↓ | DINO-I ↑ | Time (s) | GPU memory (GiB) |
| SD 1.5 [24] + DRF | 0.3108 | 0.1820 | 0.6176 | 35.17 | 5.87 |
| SD 2.0 [24] + DRF | 0.2934 | 0.2166 | 0.453 | 30.83 | 6.28 |
| SDXL [20] + DRF (Ours) | 0.3331 | 0.1586 | 0.6957 | 58.23 | 18.98 |
+
+Table 6. Cross-backbone DRF. Plug-in DRF from SDXL [20] to SD 1.5 and SD 2.0 [24] preserves fidelity while reducing GPU memory.
+
+increasing computational overhead and prolonging inference time. Adjusting the number of DRF iterations can mitigate this cost, but higher iteration counts produce sharper images at the expense of additional resources.
+
+Preservation of detail. DRF treats appearance and structure images as controllable T2I elements while providing generation guidance through user-defined prompts. While it handles most appearance images effectively. However as shown in Fig. 10, it can struggle to retain fine-grained details for data such as the faces of ordinary individuals that the pretrained model did not encounter during training.
+
+
+Figure 10. Weakness of appearance detail preservation.
+
+# 8. Conclusion
+
+DRF is a training-free T2I diffusion framework that provides recursive feedback to each control component for effective control of appearance and structure. This feedback mechanism ensures that the final generation output aligns coherently with both the appearance image and the text-conditioned score, resulting in high-quality generated images. By employing a dual feedback strategy, DRF resolves the longstanding issues in prior T2I methods, the loss of appearance fidelity, and the inability to produce stable image generations across diverse datasets.
+
+Moreover, DRF exhibits robust performance in preserving structure and reflecting the intended appearance, as demonstrated in tasks such as pose transfer and image synthesis on class-invariant datasets. We further show that our approach can be seamlessly integrated into other T2I diffusion models, thereby offering a foundation for broader advancements in diffusion model sampling.
+
+# Acknowledgments
+
+This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.RS-2021-II212068, Artificial Intelligence Innovation Hub) and by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2024-00335741, RS2024-00357197).
+
+# References
+
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+# Dual-Expert Consistency Model for Efficient and High-Quality Video Generation
+
+Zhengyao Lv $^{2,3*}$ Chenyang Si $^{1\ddagger*}$ Tianlin Pan $^{1,4}$ Zhaoxi Chen $^{5}$ Kwan-Yee K. Wong $^{2}$ Yu Qiao $^{3}$ Ziwei Liu $^{5\dagger}$
+
+$^{1}$ Nanjing University $^{2}$ The University of Hong Kong $^{3}$ Shanghai Artificial Intelligence Laboratory $^{4}$ University of Chinese Academy of Sciences $^{5}$ S-Lab, Nanyang Technological University cszy98@gmail.com chenyang.si@nju.edu.cn pantianlin23@mails.ucas.ac.cn zhaoxi001@ntu.edu.sg kykwong@cs.hku.hk yu.qiao@siat.ac.cn ziwei.liu@ntu.edu.sg
+
+
+Figure 1. Comparison of visual results between our DCM (4 steps), the original HunyuanVideo, and other competing methods (left). Comparison of latency and VBench score across different methods (right). Latency is measured on two A100 GPUs under the video synthesis configuration of 129 frames at $1280 \times 720$ resolution.
+
+
+
+# Abstract
+
+Diffusion Models have achieved remarkable results in video synthesis but require iterative denoising steps, leading to substantial computational overhead. Consistency Models have made significant progress in accelerating diffusion models. However, directly applying them to video diffusion models often results in severe degradation of temporal consistency and appearance details. In this paper, by analyzing the training dynamics of Consistency Models, we identify a key conflicting learning dynamics during the distillation process: there is a significant discrepancy in the optimization gradients and loss contributions across different timesteps. This discrepancy prevents the distilled student model from achieving an optimal state, leading to compromised temporal consistency and degraded appearance details. To address this issue, we propose a parameter-efficient Dual-Expert Consistency Model (DCM), where a semantic expert focuses on learn
+
+ing semantic layout and motion, while a detail expert specializes in fine detail refinement. Furthermore, we introduce Temporal Coherence Loss to improve motion consistency for the semantic expert and apply GAN and Feature Matching Loss to enhance the synthesis quality of the detail expert. Our approach achieves state-of-the-art visual quality with significantly reduced sampling steps, demonstrating the effectiveness of expert specialization in video diffusion model distillation. Our code and models are available at https://github.com/Vchitec/DCM.
+
+# 1. Introduction
+
+Diffusion Models [8] have achieved remarkable progress in image and video synthesis [45, 48, 63]. However, they require multiple iterations to model the probability flow Ordinary Differential Equation (ODE) [52] and rely on increasingly large denoising networks, resulting in substantial computational overhead that limits their practicality in real-world applications.
+
+To mitigate this constraint, Consistency Distillation [54]
+
+has emerged as an efficient knowledge distillation framework to reduce the sampling timesteps. It leverages a pretrained diffusion model as the teacher and trains a student model to directly map any point along the ODE trajectory to the same solution, thereby ensuring the self-consistency property. Despite enabling few-step sampling, it often struggles with visual quality, particularly in challenging video synthesis, leading to distorted layouts, unnatural motion, and degraded details.
+
+To ground this inherent issue, we analyzed the sampling dynamics of video diffusion models, as shown in Fig. 2 (a). Our key observations are that the differences between adjacent steps are substantial in the early stages of sampling, whereas the changes become more gradual in the later stages. This discrepancy arises because the early steps primarily focus on synthesizing semantic layout and motion, while the later steps emphasize refining fine details. These findings suggest that the student model may learn different patterns and exhibit distinct learning dynamics when trained on high-noise and low-noise samples. We visualized the magnitude and gradient of the consistency loss during the distillation process and observed significant differences between high and low noise levels, as shown in Fig. 2 (b). This variation indicates that jointly distilling a single student model to capture both semantic layout and fine-detail synthesis may introduce optimization interference, potentially leading to suboptimal results.
+
+To validate this assumption, we trained two expert denoisers. We first divide the ODE trajectory of the pretrained model into two phases: the semantic synthesis phase and the detail refinement phase. We then train two distinct student expert denoisers, each responsible for fitting one of these sub-trajectories. During inference, we dynamically select the corresponding expert denoiser based on the noise level of samples to predict the next position in the ODE trajectory. The results demonstrate that the combination of the two student expert denoisers achieves better performance, thereby confirming the validity of our hypothesis.
+
+However, this straightforward baseline involves training two student models which is not efficient enough. To further enhance parameter efficiency, we analyze the parameter differences between the two expert denoisers and identify that the primary differences lie in 1) embedding layers where the input parameters include timesteps, and 2) the linear layers within the attention layers. Based on this insight, we propose a parameter-efficient Dual-Expert Consistency Model (DCM). Specifically, we first train a semantic expert denoiser on the semantic synthesis trajectory. We then freeze this expert and introduce a new set of timestep-dependent layers, incorporating a LoRA [11] into the linear layers of the attention blocks. Subsequently, we fine-tune these newly added layers on the detail refinement trajectory. In this manner, we decouple the optimization of the two ex
+
+pert denoisers with minimal additional parameters and computational cost, achieving visual results comparable to those obtained with two separate experts.
+
+Given the differing training dynamics of the semantic and detail expert denoisers, we introduce distinct optimization objectives beyond the original consistency loss. To enforce temporal coherence in the semantic expert denoiser, we introduce a Temporal Coherence Loss, which guides it to capture motion variations across frames. To enhance the fine-grained content synthesized by the detail expert denoiser, we introduce a generative adversarial (GAN) [4] loss and incorporate a Feature Matching loss. Specifically, we alternately optimize the student model and the discriminator in the feature space, encouraging the generator to synthesize visual content that aligns with the output distribution of the teacher model. The Feature Matching term enhances supervision over intermediate features, thereby stabilizing the GAN training.
+
+Our proposed DCM accelerates sampling while preserving both semantic and detail quality, as shown in Fig. 1. In summary, our contributions are as follows:
+
+- We analyze the training dynamics of Consistency Models and identify a key conflict in the distillation process: discrepancies in loss contributions and optimization gradients across noise levels hinder optimal learning, leading to suboptimal visual quality.
+- We propose a parameter-efficient Dual-Expert Consistency Model that decouples the expert denoisers distillation, mitigating the conflict and improving visual quality with minimal parameter and computational cost.
+- To enhance visual quality, we introduce Temporal Coherence Loss for the semantic expert and GAN loss with Feature Matching term for the details expert, improving both temporal consistency and detail quality.
+
+# 2. Related Work
+
+# 2.1. Diffusion Models For Video Synthesis
+
+Video Diffusion Models have witnessed rapid advancements with diffusion models [2, 8, 9], driving a wide range of visual content generation applications[12, 13, 70-72]. Building on the Diffusion Transformer (DiT) [45] pretraining, a notable breakthrough is the development of high-fidelity video diffusion models [10, 20-22, 42, 44, 55, 63]. However, scaling these models for long videos incurs significant training and inference costs. LTX-Video [7] designed Video-VAE that achieves a high compression ratio for efficient self-attention. Pyramid flow [15] introduced a unified pyramidal flow matching algorithm for efficient video generative modeling. The acceleration method based on sparse attention [68, 69] and feature cache [41, 73] has also improved inference efficiency. Moreover, while efficient fast diffusion samplers [17, 28, 32, 33, 52] reduce inference steps, further reduction often severely degrades per
+
+
+(a) Visualization of the video synthesis sampling process
+
+
+(b) The trend of training loss and gradient norm
+Figure 2. Visualization of the video synthesis process and the trend of loss variation. (a) In the early stages of sampling, the results change significantly and rapidly, whereas in the later stages, the changes become gradual and smooth. (b) During distillation, the loss and gradient norm of the student model exhibit significant differences between samples with high and low noise levels.
+
+
+
+formance. Diffusion distillation offers a promising way to reduce sampling steps while maintaining visual quality.
+
+# 2.2. Diffusion Model Distillation
+
+Diffusion distillation [37] aims to distill knowledge from pre-trained diffusion models to student models, reducing inference cost. Prior works can be generally classified into two categories based on their distillation mechanisms.
+
+Trajectory-preserving distillation methods exploit the fact that diffusion models learn an Ordinary Differential Equation (ODE) trajectory and aim to predict the exact teacher output in fewer steps. Among the earliest studies on diffusion distillation, Luhman et al. [34] and DSNO [74] proposed training the student model using noise-image pairs precomputed by the teacher model with an ODE solver. Progressive distillation [43, 49] reduces the final number of sampling steps by iteratively applying the distillation process to halve the number of sampling steps of previous model. Instaflow [29, 30] progressively learns straighter flows, enabling accurate one-step predictions over larger distances. Consistency models [27, 31, 35, 36, 53, 54, 75], BOOT [5] and TRACT [1] learn to map samples along the ODE trajectory to another point to achieve self-consistency. The consistency trajectory model [18] was designed to mitigate discretization inaccuracies and accumulated estimation errors in the multistep consistency model sampling. PCMs [57] phase the ODE trajectory into several sub-trajectories and only enforce the self-consistency property on each sub-trajectory, thus alleviating the limitations of CMs. TCM [23] generalizes consistency training to the truncated time range to prevents the truncated-time training from collapsing to a trivial solution. Trajectory-preserving distillation enables stable optimization but can degrade visual quality, leading to blurriness or distortions when sampling with fewer steps.
+
+Distribution-matching distillation methods bypass the ODE trajectory and aim to train the student model to generate samples whose distribution aligns with that of the teacher diffusion model. Some methods reduce the distribution gap between the student and teacher models through adversarial training [3, 16, 26, 40, 50, 51, 61, 62]. Other methods [38, 39, 64-66, 76] achieve diffusion distillation
+
+by score distillation [46]. Notably, DMD [65] aligns the one-step generator with the distribution of teacher model by minimizing an approximate KL divergence, whose gradient is the difference between the target and synthetic distribution score functions. Recently works [19, 25, 47] have also tried to integrate the advantages of trajectory-preserving and distribution-matching methods. Hyper-SD [47] introduced the trajectory-segmented consistency distillation and used DMD [65] for one-step generation enhancement.
+
+Previous works have primarily focused on distilling image synthesis diffusion models, with some efforts [24, 58, 67] extending to the distillation of small-scale video synthesis models [6, 59]. However, these methods are limited to synthesizing low-resolution and short-sequence videos. Seaweed-APT [26] proposed adversarial post-tuning against real data following diffusion pre-training for one-step high-resolution 2-second duration video generation. A recent work [66] extended DMD [65] for video synthesis in four sampling steps. Due to the inherent complexity of video synthesis and the increasing model scale, research on diffusion distillation for video synthesis remains limited, and its performance is yet to be fully explored.
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+Diffusion Model is a generative framework with a forward and reverse process.
+
+In the forward process, noise is progressively added to clean data $\pmb{x}_0 \sim p_{\mathrm{data}}(\pmb{x}_0)$ , degrading the signal:
+
+$$
+q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {0}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t}; \sqrt {\alpha_ {t}} \boldsymbol {x} _ {0}, \sqrt {1 - \alpha_ {t}} \boldsymbol {I}\right), \tag {1}
+$$
+
+where $\{\alpha_t\}_{t=1}^T$ controls the noise schedule.
+
+The reverse process, typically parameterized by a UNet or transformer $\epsilon_{\theta}$ , is trained to predict the noise:
+
+$$
+\mathcal {L} _ {D M} = \mathbb {E} _ {\boldsymbol {x}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \left| | \epsilon - \epsilon_ {\theta} (\boldsymbol {x} _ {t}, t) | | _ {2} ^ {2} \right]. \right. \tag {2}
+$$
+
+During inference, a clean sample $\pmb{x}_0$ can be recovered through iterative denoising:
+
+$$
+p \left(\boldsymbol {x} _ {t - 1} \mid \boldsymbol {x} _ {t}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t - 1}; \mu_ {\theta} \left(\boldsymbol {x} _ {t}, t\right), \Sigma_ {\theta} \left(\boldsymbol {x} _ {t}, t\right)\right), \tag {3}
+$$
+
+
+
+
+
+
+(b) VBenchmark metric for different variants
+
+
+(a) Variants trained on data with different noise levels
+
+
+(c) Example visual results of different variants
+
+
+Figure 3. Comparison of the visual quality of denoiser variants trained at different noise level samples. By optimizing two expert denoisers to decouple the distillation process into semantic learning and detail learning, and combining them during inference, we achieve the best quantitative and qualitative visual results.
+
+
+
+where $\mu_{\theta}$ and $\Sigma_{\theta}$ are learned parameters.
+
+Consistency Distillation utilizes a pre-trained model $\epsilon_{\theta}$ as the teacher $F_{T}$ to distill its knowledge into a student model $F_{S}$ initialized with $\epsilon_{\theta}$ , allowing for faster sampling with fewer steps [54]. Specifically, consistency distillation trains the student model $F_{S}$ to directly map any point $\boldsymbol{x}_{t_n}$ on the solution trajectory of the ODE solver $\Phi$ to its endpoint $\boldsymbol{x}_{t_{end}}$ . The learning objective can be formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {C D} = \mathbb {E} _ {\boldsymbol {x}, t _ {n}} \| \Phi \left(\boldsymbol {x} _ {t _ {n}}, F _ {S} \left(\boldsymbol {x} _ {t _ {n}}, t _ {n}, c\right), t _ {e n d}\right) - \tag {4} \\ \left. \Phi \left(\hat {\boldsymbol {x}} _ {t _ {n - 1}}, F _ {S} ^ {-} \left(\hat {\boldsymbol {x}} _ {t _ {n - 1}}, t _ {n - 1}, c\right), t _ {e n d}\right) \right\| _ {2} ^ {2}. \\ \end{array}
+$$
+
+Here, $F_{S}^{-}$ is the exponential moving average (EMA) of $F_{S}$ and $\hat{\pmb{x}}_{t_{n - 1}}$ is the next point on the ODE solution trajectory computed by the teacher model $F_{T}$ :
+
+$$
+\hat {\boldsymbol {x}} _ {t _ {n - 1}} = \Phi (\boldsymbol {x} _ {t _ {n}}, F _ {T} (\boldsymbol {x} _ {t _ {n}}, t _ {n}, c), t _ {n - 1}). \tag {5}
+$$
+
+Consistency distillation has garnered widespread attention and research [35, 47, 57] due to its ease of stable training.
+
+3.2. Suboptimal Solution in Consistency Distillation Although consistency distillation has demonstrated promising results in class-conditioned image synthesis and text-to-image model distillation, it falls short in more challenging video synthesis diffusion models, where issues arise such as distorted layouts, unnatural motion, and degraded details.
+
+Due to the limited capacity of the student model, consistency distillation struggles to address these issues simultaneously. By tracking the video synthesis process, we find that in the early stages of sampling, the sampling results vary significantly and rapidly, whereas in the later stages, the transitions become more gradual and smooth, as shown in Fig. 2 (a). In the early stages of sampling, rapid changes
+
+establish the semantic layout and motion of the video, while in the later stages, the model gradually refines the details with smooth adjustments. These findings imply that the student model may learn different patterns with distinct training dynamics when distilled with high-noise and low-noise samples. By visualizing the trends of consistency loss and gradient norm during distillation, we find significant differences in the student model when distilled with high- and low-noise samples, as shown in Fig. 2 (b). This suggests that jointly optimizing a student model for both semantic and fine-grained details synthesis may introduce inefficient optimization, constraining its fitting capacity and leading to suboptimal performance.
+
+To validate our hypothesis, we conducted an experiment on the HunyuanVideo [20] text-to-video diffusion model. Specifically, we divided the ODE solution trajectory $(\pmb{x}_N,\pmb{x}_{N - 1},\dots ,\pmb{x}_1,\pmb{x}_0)$ of the pre-trained model into two sub-trajectories, using $t_\kappa$ as the boundary (we set $N = 50$ and $\kappa = 37$ by default). The first part $\left(\{\pmb{x}_{t_i}\}_{i = \kappa}^N\right)$ primarily focuses on synthesizing the semantic layout and motion, while the second part $\left(\{\pmb{x}_{t_j}\}_{j = 0}^\kappa\right)$ emphasizes semantic refinement and high-quality detail generation. As shown in Fig 3 (a), we optimized two distinct student models, semantic expert denoiser $F_{\mathrm{SemE}}$ and details expert denoiser $F_{\mathrm{DetE}}$ to fit each sub-trajectory:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {S e m E}} = \mathbb {E} _ {\boldsymbol {x}, t _ {m} \in [ t _ {\kappa}, t _ {N} ]} | | \Phi (\boldsymbol {x} _ {t _ {m}}, F _ {\mathrm {S e m E}} (\boldsymbol {x} _ {t _ {m}}, t _ {m}, c), t _ {\kappa}) - \\ \left. \Phi \left(\hat {\boldsymbol {x}} _ {t _ {m - 1}}, F _ {\mathrm {S e m E}} ^ {-} \left(\hat {\boldsymbol {x}} _ {t _ {m - 1}}, t _ {m - 1}, c\right), t _ {k}\right) \right\| _ {2} ^ {2}, \tag {6} \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {D e t E}} = \mathbb {E} _ {\boldsymbol {x}, t _ {n} \in [ t _ {0}, t _ {\kappa} ]} | | \Phi (\boldsymbol {x} _ {t _ {n}}, F _ {\text {D e t E}} (\boldsymbol {x} _ {t _ {n}}, t _ {n}, c), t _ {0}) - \tag {7} \\ \left. \Phi (\hat {\boldsymbol {x}} _ {t _ {n - 1}}, F _ {\mathrm {D e t E}} ^ {-} (\hat {\boldsymbol {x}} _ {t _ {n - 1}}, t _ {n - 1}, c), t _ {0}) \right| _ {2} ^ {2}. \\ \end{array}
+$$
+
+Expert denoiser $F_{\mathrm{SemE}}$ is optimized to synthesize coherent
+
+
+Figure 4. The training process of DCM consists of two stages. In the semantic learning stage, we train SemE on high-noise samples with consistency loss and temporal coherence loss as the learning objectives. In the detail learning stage, we initialize DetE with the weights of SemE and introduce a set of time-dependent layers and LoRA. DetE is then trained on low-noise samples, where only the newly added layers and LoRA are updated. The learning objectives in this stage include consistency loss, GAN loss, and Feature Matching loss.
+
+
+Figure 5. Weight difference distribution between expert denoisers. We employ the normalized L1 distance to quantify the difference between the weights.
+
+semantic layouts and motion, while expert denoiser $F_{\mathrm{DetE}}$ learns to generate high-quality details. During inference, we dynamically switch the expert denoiser based on the sampling stage. To assess the impact of each expert denoiser and the effectiveness of decoupled training, we evaluate four variants: a) VCM: The vanilla consistency model is used throughout the sampling process. b) SemE + VCM: SemE is applied in the first sub-trajectory, transitioning to VCM in the second. c) VCM + DetE: VCM is applied initially, followed by DetE. d) SemE + DetE: SemE and DetE are integrated for the sampling process. According to the Fig. 3 (b) and (c), SemE and DetE have respectively learned to model semantics and details, each outperforming VCM in their respective aspects. This validates our hypothesis, demonstrating that decoupled optimization is superior to jointly training a single model for both tasks.
+
+# 3.3. Parameter-efficient Dual-Expert Distillation
+
+While training two expert denoisers improves video quality, it significantly increases model parameters and GPU memory consumption during inference. Through the analysis of parameter similarity between the two expert denoisers, we found that the primary differences in model parameters lie
+
+in the embedding layers $\Psi$ where the input parameters include timesteps and the linear layers within the attention layers $\Lambda$ , as illustrated in Fig. 5.
+
+Based on the above observations, we propose the parameter-efficient Dual-Expert distillation strategy, as illustrated in Fig. 4. Specifically, our training scheme is divided into two stages. 1) Initialize the semantic expert denoiser $F_{\mathrm{SemE}}$ with the teacher model $F_{T}$ and optimize all its parameters on the sub-trajectory $\{\pmb{x}_{t_i}\}_{i = \kappa}^N$ . 2) Use the optimized $F_{\mathrm{SemE}}$ as the initialization of $F_{\mathrm{DetE}}$ and freeze it. Then add a new set of timestep-dependent embedding layers $\Psi$ and LoRA [11] $\Lambda^{\dagger}$ of attention blocks. Optimize the newly added parameters $(\Psi$ and $\Lambda^{\dagger})$ on its sub-trajectory $\{\pmb{x}_{t_j}\}_{j = 0}^{\kappa}$ . In this way, we significantly reduce the number of parameters required for decoupling the optimization process of semantic modeling and detail learning, with minimal computational cost, while maintaining the visual quality of the synthesized videos.
+
+# 3.4. Expert-specific Optimization Objective
+
+In addition to the consistency objectives mentioned in Eq. 6 and Eq. 7, we also designed expert-specific optimization objectives for the semantic expert denoiser $F_{\mathrm{SemE}}$ and details expert denoiser $F_{\mathrm{DetE}}$ , as shown in Fig. 4.
+
+Temporal Coherence Loss To enhance the temporal coherence in the video synthesized by the semantic expert denoiser $F_{\mathrm{SemE}}$ , we introduce the Temporal Coherence Loss $\mathcal{L}_{TC}$ , which emphasizes and guides the $F_{\mathrm{SemE}}$ to focus on the variations and motion at corresponding positions among different frames:
+
+$$
+\boldsymbol {x} _ {t _ {\kappa}} = \Phi (\boldsymbol {x} _ {t _ {m}}, F _ {\text {S e m E}} (\boldsymbol {x} _ {t _ {m}}, t _ {m}, c), t _ {\kappa}),
+$$
+
+$$
+\hat {\boldsymbol {x}} _ {t _ {\kappa}} = \Phi \left(\hat {\boldsymbol {x}} _ {t _ {m - 1}}, F _ {\text {S e m E}} ^ {-} \left(\hat {\boldsymbol {x}} _ {t _ {m - 1}}, t _ {m - 1}, c\right), t _ {\kappa}\right), \tag {8}
+$$
+
+$$
+\mathcal {L} _ {T C} = | | \left(\boldsymbol {x} _ {l: L} ^ {t _ {\kappa}} - \boldsymbol {x} _ {0: L - l} ^ {t _ {\kappa}}\right) - \left(\hat {\boldsymbol {x}} _ {l: L} ^ {t _ {\kappa}} - \hat {\boldsymbol {x}} _ {0: L - l} ^ {t _ {\kappa}}\right) | | _ {2} ^ {2}.
+$$
+
+Here $\pmb{x}_{l:L}^{t_{\kappa}}$ represents the video latents from the $l$ -th to the $L$ -th channel along the temporal axis. This temporal coherence loss encourages the semantic expert denoiser $F_{\mathrm{SemE}}$ to preserve consistent motion and spatial relationships between frames, ensuring more fluid videos synthesis.
+
+Generative Adversarial Loss The effectiveness of the generative adversarial (GAN) [4] loss in high-quality detail synthesis has been validated in many distribution-matching distillation methods. We introduce the GAN loss into the training of the details expert denoiser and incorporate a Feature Matching loss to stabilize the training. We first obtain $\boldsymbol{x}_{t_0}$ and $\hat{\boldsymbol{x}}_{t_0}$ with the details expert denoiser $F_{\mathrm{DetE}}$ , teacher model $F_T$ and ODE solver $\Phi$ :
+
+$$
+\begin{array}{l} \boldsymbol {x} _ {t _ {0}} = \Phi (\boldsymbol {x} _ {t _ {n}}, F _ {\mathrm {D e t E}} (\boldsymbol {x} _ {t _ {n}}, t _ {n}, c), t _ {0}), \\ \hat {\boldsymbol {x}} _ {t _ {0}} = \Phi (\hat {\boldsymbol {x}} _ {t _ {n - 1}}, F _ {\mathrm {D e t E}} ^ {-} (\hat {\boldsymbol {x}} _ {t _ {n - 1}}, t _ {n - 1}, c), t _ {0}), \tag {9} \\ \end{array}
+$$
+
+Then we perform the forward process and apply noise to them to obtain fake sample $\pmb{x}_{\text{fake}}$ and real sample $\pmb{x}_{\text{real}}$ with Eq. 1. We use a frozen teacher model as the feature extraction backbone $\Omega$ , extracting intermediate features with a fixed stride for calculating the GAN loss and Feature Matching loss $\mathcal{L}_{FM}$ . During training, we iteratively update the parameters of $F_{\mathrm{DetE}}$ and the discriminator head $f_{D}$ :
+
+$$
+\begin{array}{l} \mathcal {L} _ {F M} = \mathbb {E} _ {\boldsymbol {x}, t _ {n}} \left\| \Omega (\boldsymbol {x} _ {f a k e}) - \Omega (\boldsymbol {x} _ {r e a l}) \right\| _ {2} ^ {2}, \\ \mathcal {L} _ {G} = \mathbb {E} _ {\boldsymbol {x}, t _ {n}} [ 1 - f _ {D} (\Omega (\boldsymbol {x} _ {f a k e})) ] + \mathcal {L} _ {F M}, \\ \mathcal {L} _ {D} = \mathbb {E} _ {\boldsymbol {x}, t _ {n}} [ f _ {D} (\Omega (\boldsymbol {x} _ {\text {f a k e}})) ] + \mathbb {E} _ {\boldsymbol {x}, t _ {n}} [ 1 - f _ {D} (\Omega (\boldsymbol {x} _ {\text {r e a l}})) ]. \tag {10} \\ \end{array}
+$$
+
+The integration of the GAN loss in combination with Feature Matching loss provides a robust framework for training the details expert denoiser $F_{\mathrm{DetE}}$ , stabilizing its learning process and improving the quality of detail synthesis.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Backbones and Baselines We utilize HunyuanVideo [20] and CogVideoX [63] as the base models for distillation. The HunyuanVideo has 13 billion parameters, and CogVideoX has 2 billion parameters. Since most prior distillation methods for diffusion models have not been applied to video synthesis, we follow the official implementations of LCM [35] and PCM [57] to implement these two methods on the selected base models as baselines for comparison.
+
+Implementation Details For HunyuanVideo, we selected trajectories with 50 Euler steps and used the default sampling parameters from diffusers. The distillation was conducted on 129-frame video sequences at a resolution of $1280 \times 720$ with a batch size of 6. For the semantic expert denoiser, we performed 1000 iterations of distillation with a learning rate of $1e - 6$ , while for the details expert denoiser, we trained for 1000 iterations with a learning rate of $5e - 6$ . For CogVideoX-2B, we selected trajectories with 50 DDIM
+
+steps. The distillation was conducted on 29-frame video sequences at a resolution of $720 \times 480$ with a batch size of 4. In the first-stage fine-tuning, we distilled for approximately 1000 steps, while in the second-stage fine-tuning, we distilled for around 500 steps, both with a learning rate of $1e - 6$ . All experiments were conducted on 24 NVIDIA A100 80GB GPUs.
+
+Evaluation Metrics For video quality evaluation, we use VBench [14] as our assessment metric. VBench is a comprehensive benchmark suite for video generative models, designed to align closely with human perception and offer valuable insights from multiple perspectives. Additionally, we conducted a user study to help evaluate the visual quality of the generated videos.
+
+# 4.2. Main Results
+
+Quantitative Comparison Table 1 presents the quantitative comparison of our method with LCM and PCM on HunyuanVideo and CogVideoX. We generate videos using the prompts provided by VBench to evaluate their performance in terms of semantic alignment and visual quality. It can be observed that on HunyuanVideo, our method achieves a VBench score comparable to the baseline with 4-step sampling, significantly outperforming LCM and PCM. In terms of efficiency, our method incurs a nearly identical latency cost per inference step compared to LCM and PCM.
+
+Table 1. Comparison of efficiency and visual quality of different methods. The latency of HunyuanVideo was measured on two A100 GPUs, and that of CogVideoX on a single A100 GPU.
+
+| Method | Step | Lat.(Sec.) | VBranch |
| Total | Quality | Semantic |
| Hunyuan | 50 | 1504.5 | 83.87 | 85.00 | 79.34 |
| LCM | 4 | 120.68 | 80.33 | 80.83 | 78.32 |
| PCM | 4 | 120.89 | 80.93 | 81.94 | 76.90 |
| Ours | 4 | 121.52 | 83.83 | 85.12 | 78.67 |
| LCM | 8 | 242.80 | 81.49 | 82.35 | 78.03 |
| PCM | 8 | 242.96 | 81.63 | 82.78 | 77.00 |
| Ours | 8 | 244.72 | 83.86 | 85.00 | 79.32 |
| CogVideoX | 50 | 76.50 | 80.59 | 81.93 | 75.23 |
| LCM | 4 | 3.22 | 78.88 | 80.07 | 74.12 |
| PCM | 4 | 3.23 | 79.09 | 80.33 | 74.14 |
| Ours | 4 | 3.31 | 79.99 | 81.35 | 74.56 |
| LCM | 8 | 6.42 | 79.34 | 80.64 | 74.21 |
| PCM | 8 | 6.42 | 79.70 | 80.98 | 74.60 |
| Ours | 8 | 6.58 | 80.26 | 81.57 | 75.03 |
+
+Qualitative Comparison Fig. 6 presents a comparison of the videos generated by our method and those produced by the original model, LCM and PCM. The results demonstrate that our method maintains high semantic and detail quality in synthesized videos while reducing the number of inference steps. Additional qualitative results are provided in the supplementary material for further reference.
+
+
+Prompt: A panda wearing a chef's hat and a red apron stands in a cozy kitchen filled with wooden cabinets and colorful utensils. The panda chops vegetables on a wooden cutting board, its furry paws. Next, it stirs a bubbling pot on the stove. The kitchen is warmly lit, with pots and pans hanging from a rack above. The panda then tastes the soup with a wooden spoon.
+
+
+
+
+
+
+
+
+
+
+
+
+Prompt: A golden retriever with a shiny coat stands by a serene crystalclear stream in a lush forest, its tongue lapping up the refreshing water. The sunlight filters through the dense canopy, casting dappled light on the dog's fur. As the dog drinks, droplets of water glisten on its whiskers, and its tail wags contentedly.
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 6. Visual quality comparison of different methods. Differences are highlighted in boxes.
+
+
+
+User Study To further evaluate the effectiveness of our method, we conduct a human evaluation to assess the perceived visual quality of the generated videos. Specifically, we randomly select 30 videos for each model. During the evaluation, each rater is presented with a text prompt along with two videos generated by different distillation methods, displayed in a randomized order to eliminate bias. Following the protocol of human preference evaluation in HunyuanVideo [20], the professional raters are asked to choose the video they perceive to have superior text alignment, motion quality, and visual quality. Each sample is evaluated by fifty independent raters, and the aggregated voting results are summarized in Table 2. As one can see, compared to other distillation methods, the raters significantly prefer the videos generated by our method.
+
+Table 2. User preference study. The numbers represent the percentage of raters who favor the videos synthesized by our method.
+
+| Method comparison | HunyuanVideo | CogVideoX |
| Ours vs. LCM | 82.67% | 75.33% |
| Ours vs. PCM | 77.33% | 72.67% |
+
+# 4.3. Ablation Study
+
+To thoroughly evaluate both the effectiveness of our method, we conduct extensive ablation studies based on
+
+HunyuanVideo, as shown in Table 3. All experiments were conducted on 29-frame videos with a resolution of $1280 \times 720$ . Inference is performed with 4 sampling timesteps.
+
+Table 3. Impact of different components of our method.
+
+ | Variants | VBatch |
| OD | PE | TC | GF | Total | Quality | Semantic |
| (1) | | | | | 80.30 | 80.74 | 78.36 |
| (2) | ✓ | | | | 83.08 | 84.20 | 78.59 |
| (3) | ✓ | ✓ | | | 83.03 | 84.16 | 78.53 |
| (4) | ✓ | ✓ | ✓ | | 83.42 | 84.63 | 78.63 |
| (5) | ✓ | ✓ | | ✓ | 83.71 | 84.99 | 78.59 |
| (6) | ✓ | ✓ | ✓ | ✓ | 83.80 | 85.10 | 78.62 |
+
+Effect of Optimization Decoupling (OD) Through Experiments (1) and (2), decoupling the optimization of semantic and detail modeling significantly improves the semantic and quality scores. As shown in Fig. 7, the optimized decoupled model synthesizes videos with better semantic and detail quality, where the motion of characters and facial details appear more natural.
+
+Effect of Parameter-Efficient dual-expert distillation (PE) Through Experiments (2) and (3), we observe that compared to simply decoupling the optimization into two separate model training processes, the parameter-efficient
+
+
+Figure 7. Impact of optimization decoupling and parameter-efficient distillation.
+
+
+Figure 8. Impact of temporal coherence loss.
+
+
+Figure 9. Impact of the GAN loss and Feature Matching term.
+
+Dual-Expert distillation significantly reduces both the parameters and memory requirements, with minimal computational overhead, while preserving visual quality. The last two rows of Fig. 7 also demonstrate that our parameter-efficient Dual-Expert method does not result in a significant degradation in visual quality.
+
+Effect of Temporal Coherence Loss (TC) By comparing Experiments (3) and (4), or (5) and (6), we observe that the introduction of Temporal Coherence loss improves the quality scores of the synthesized videos. As shown in Fig. 8, the introduction of the TC loss enables more natural motion in the video and enhances its consistency.
+
+Effect of GAN and Feature Matching Loss (GF) By comparing Experiments (3) and (5), or (4) and (6), we observe that the introduction of GAN Loss improves the quality scores of the synthesized videos. As shown in Fig. 9, the introduction of the GAN loss and Feature Matching term enhances the realism of the details in the synthesized video. Selection of $\kappa$ In this paper, we determine the value of $\kappa$
+
+
+Figure 10. Impact of different $\kappa$ .
+
+based on the inference process. Fig. 10 (left) illustrates the L1 distance between adjacent time-step sampling results in HunyuanVideo during the sampling process. It can be observed that from approximately step 37 onward, the L1 Distance decreases to a very small value. We interpret this as the point where the semantic content and layout are established, and the remaining steps focus on synthesizing high-frequency details. Therefore, we set $\kappa = 37$ as the default value. To evaluate the impact of different $\kappa$ values, we experimented with $\kappa = 28, 35, 37, 39, 46$ . As shown in Fig. 10 (right), the results indicate that as $\kappa$ deviates from the transition point between semantic synthesis and detail synthesis, the video quality gradually deteriorates. It further validates the effectiveness of our optimization decoupling strategy.
+
+# 5. Conclusion and Discussion
+
+In this paper, we identify a key optimization conflict in consistency distillation for video synthesis: there exists a significant discrepancy in the optimization gradients and loss contributions across different timesteps. Distilling the entire ODE trajectory into a single student model fails to balance these aspects, leading to degraded motion consistency and coarse synthesis quality. To address this issue, we propose a parameter-efficient Dual-Expert distillation framework that decouples semantic learning from fine-detail refinement. Additionally, we introduce a Temporal Coherence loss to enhance motion consistency for the semantic expert and apply GAN and Feature Matching loss to improve synthesis quality for the detail expert. Our method significantly reduces sampling steps while achieving state-of-the-art visual quality, demonstrating the effectiveness of expert specialization in video diffusion model distillation.
+
+Limitation Although our method achieves favorable results with 4 steps inference, it still struggles to produce satisfactory outcomes with fewer steps (e.g., 2) due to limited training data and iterations. We will further explore high-quality synthesis with fewer steps in future work.
+
+# 6. Acknowledgement
+
+This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOE-T2EP20221-0012, MOE-T2EP20223-0002), and 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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+
+
+
+
+
+(a) Method
+
+
+(b) Applications
+Figure 1. Dual-Process Distillation. Our method distills deliberation into a feed-forward image generation process. When generating an image, we ask a VLM questions about that image and backpropagate the resulting gradient to update the weights of the image generator (a). The flexibility of a VLM allows us to implement many control tasks through visual prompts (b). We construct our method such that it supports off-the-shelf VLMs and image generators without special re-training.
+
+# Abstract
+
+Prior methods for controlling image generation are limited in their ability to be taught new tasks. In contrast, vision-language models, or VLMs, can learn tasks in-context and produce the correct outputs for a given input. We propose a dual-process distillation scheme that allows feed-forward image generators to learn new tasks from deliberative VLMs. Our scheme uses a VLM to rate the generated images and backpropagates this gradient to update the weights of the image generator. Our general framework enables a wide variety of new control tasks through the same text-and-image based interface. We showcase a handful of applications of this technique for different types of control signals, such as commonsense inferences and visual prompts. With our method, users can implement multimodal controls for properties such as color palette, line weight, horizon position, and relative depth within a matter of minutes. Project page: https://dual-process.github.io.
+
+# 1. Introduction
+
+Current large language models have demonstrated competence across many domains and the ability to learn new tasks in-context [9], yet when trained multi-modally to jointly generate image and text, either fail to achieve the fidelity of image-only generation [12, 73, 75] or are inaccessible to academic experimentation [57]. Conversely, contemporary image generation models are near photorealistic, but can be frustratingly hard to communicate with. Inspired in part by cognitive science models, we propose a dual-process architecture [34, 69], combining a knowledge-rich multimodal language model with a visually precise image generator. The former is akin to a "cognitive" or "System 2" component, and the latter plays the role of a "reflex" or "System 1" module. This dual-process idea is also present in some early works in image generation. Classifier guidance [16], which uses an external classifier to steer image generation, can also be interpreted as embedding System 2 deliberation into a System 1 process. However, using this type of guidance requires specialized classifiers for each type of signal or control, and therefore is not easily extensible to new uses.
+
+
+Figure 2. Diagram of Dual-Process Distillation. Given an input prompt and question to check, we feed the predicted clean image to the VLM to rate. Our method then backpropagates this loss to update LoRA [29] weights on the image generator.
+
+On the other hand, vision-language models (VLMs) have proven to be generally applicable, capable of simulating many different discriminators within the same model. Simply by adjusting the input prompt, VLMs can perform different tasks such as optical character recognition [40], object detection [4], and image scoring [13, 44]. VLMs can not only be prompted with text but also multimodal inputs, or mixtures of images and text, such as visual prompts [11].
+
+In this work, we propose a dual-process scheme that combines a deliberative VLM and feed-forward image generator, illustrated in Figure 1. We implement this scheme with gradient-based distillation and low-rank adaptation [29], where we update the weights of the image generator based on the VLM's ratings of its outputs. We demonstrate a handful of possible use cases of our method, such as visual prompting with a desired color palette, line weight, horizon position, or relative depth. We also evaluate our method on improving commonsense understanding and physical accuracy in image generation, where we find that our method significantly outperforms baselines such as prompt expansion.
+
+# 2. Related Work
+
+Classifier Guidance. Guidance methods use an external discriminator to introduce new capabilities missing in the base model. Dhariwal and Nichol [16] first demonstrated this idea with an ImageNet [15] classifier, and follow-up works explore other discriminators to support each newly proposed control task. These works investigate classic depth, segmentation, and object detection models for spatial controls [5, 35], as well as aesthetics and safety rating models for more abstract controls [66, 79]. Other works also look at re-using the image generator itself as a kind of discriminator [18, 42, 49, 76, 81]. Most similar to our work, Nguyen et al. [55] and Jiang et al. [32] investigate image captioning models [17, 41] for improved text-conditional generation. We focus on the novel use of modern VLMs as the most general form of these discriminators, given their ability to simulate many different tasks within the same model [2, 46]. Furthermore, we show that VLMs can newly support multi
+
+modal controls jointly defined with image and text, or visual prompts [11], compared with the image or text-only controls from prior work.
+
+Inference-Time Search. Recent works in inference time search improve the output quality of language models by generating a substantial number of samples and post-hoc filtering with a verifier [8, 70, 82]. Inspired by these works, recent research in image generation investigates rejection or importance sampling during the denoising process [51, 68]. In contrast with these search methods, we compute a gradient through the verifier. This denser learning signal enables our method to discover long-tail images that would normally be extremely challenging to sample, for example variations of objects influenced by subtle physical laws, which we demonstrate on the CommonsenseT2I benchmark [22].
+
+Model Fine-tuning. There exist fine-tuning methods that use the image generator's original objective to learn a narrower subdistribution. To condition the model on spatial controls like pose or depth images, ControlNet [87] trains on a paired dataset of real images and their extracted controls. To produce personalized outputs, Dreambooth [64] fine-tunes on a small image set representative of a given subject. Distillation methods circumvent the need for reference images by using outputs from the image generator itself as the supervision signal. Prior work has proposed such methods to speed up sampling [50, 65, 86], serve as an image prior for 3D generation [60, 78], or learn a concept direction [23]. Unlike these works, rather than optimizing with the original pixel-space objective, our method optimizes with a language-space objective derived from the VLM.
+
+Reinforcement learning methods optimize with reward functions derived from some external model, similar to classifier guidance. Prior work explores policy optimization approaches to increase aesthetic preferences or prompt alignment of generated images [7, 21, 36, 77, 84, 85]. Most relevant to our work, Black et al. [7] uses VLM-generated captions to improve image-text faithfulness. In contrast, we use the VLM to produce numerical ratings, a more general formulation that enables novel use cases like visual prompting (see Sec. 4.3). Furthermore, our method is significantly cheaper than reinforcement learning methods, because we compute a gradient through the reward model. While prior work requires at least four hours of training on 50k samples [7], our method can enforce novel controls after optimizing for one minute on a single sample (see Sec. 4.4).
+
+VQA Scoring. There is also a growing in interest in the usage of VLMs for scoring image-text alignment. Compared with CLIP [61], VLMs offer a more accurate and interpretable scoring framework. Recent works frame scoring as a VQA, or visual question answering, task [1], where one can ask the VLM different questions to evaluate the correctness of an image [13, 14, 38, 44, 85, 88]. Lin et al. [44] shows that answer probability, derived from the logits
+
+output by the VLM, can serve as a continuous metric, where lower and higher scores correlate with human judgement. Rather than using the VLM as an evaluation metric, we use it as a signal to improve the generated images themselves.
+
+# 3. Dual-Process Distillation
+
+# 3.1. Preliminaries
+
+Many image generation models are formulated as a denoising process that transforms samples from a simple Gaussian distribution to the target data distribution. Among these, diffusion models [28, 71] have emerged as a popular theoretical framework. Rectified flows [3, 19, 45, 48] offer an alternative but equivalent theoretical formulation [25]. Specifically, the forward process is viewed as a linear interpolation between the data point $x_0$ and the noise $\epsilon$ , for $t \in [0,1]$
+
+$$
+z _ {t} = (1 - t) x _ {0} + t \epsilon \tag {1}
+$$
+
+Therefore, at sampling time, the reverse process is
+
+$$
+z _ {t ^ {\prime}} = z _ {t} + \hat {u} \cdot \left(t ^ {\prime} - t\right) \tag {2}
+$$
+
+for $t' < t$ , where a neural network is often used to parameterize the estimated velocity $\hat{u} = g_{\phi}(z_t) = \hat{\epsilon} - \hat{x}_0$ . This neural network is trained with a corresponding conditional flow matching objective [45]
+
+$$
+\mathcal {L} _ {\mathrm {C F M}} (\mathbf {x}) = \mathbb {E} _ {t \sim \mathcal {U} (0, 1), \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I})} \left[ \| \hat {\mathbf {u}} - \mathbf {u} \| _ {2} ^ {2} \right] \tag {3}
+$$
+
+While our experiments primarily focus on Flux [39], a state-of-the-art rectified flow model, our method is broadly applicable. We demonstrate its efficacy on both single-step and multi-step generators in Table 1.
+
+# 3.2. Approach
+
+Loss Formulation. In this work, we show that many visual control tasks can be formulated as visual question answering. As such, we propose a simple and general VQA loss, based on the same language modeling objective used for visual instruction tuning [46]. Our loss mainly differs in the object being optimized: visual instruction tuning optimizes the VLM, while our method optimizes the image input, through the image generator. More formally, our goal is to optimize the image generator $G_{\phi}$ such that it produces images where the VLM $D_{\theta}$ , when given a question $S_{q}$ , is most likely to output the desired answer $S_{a}$ . This can be written as the following autoregressive loss:
+
+$$
+\mathcal {L} _ {\mathrm {V Q A}} = - \sum_ {i = 1} ^ {L} \log D _ {\theta} \left(S _ {a, i} \mid G _ {\phi} \left(z _ {t}\right), S _ {q}, S _ {a, < i}\right) \tag {4}
+$$
+
+We illustrate our full pipeline in Figure 2. Most importantly, we still compute gradients through the VLM, which gives a denser signal than reinforcement learning.
+
+Clean Image Estimate. For multi-step models, the image generator may output noisy images that would otherwise be uninterpretable to an off-the-shelf VLM. In these cases, instead of directly feeding $G_{\phi}(z_t)$ , we compute a clean image estimate, following the same insight as prior work [5, 72]. In the case of rectified flow models, this estimate can be computed by setting $t' = 0$ in Equation 2
+
+$$
+\hat {x} _ {0} = z _ {t} - G _ {\phi} \left(z _ {t}\right) \cdot t \tag {5}
+$$
+
+Distillation Scheme. Here, we describe our procedure for distilling the VQA loss from the VLM into the image generator. For rectified flow models, we take a partially noised image and denoise it with the image generator in a single forward pass. However, we do not assume access to any reference images, but we also need images for the VLM to rate. We simply obtain these images by generating them with the image generator with no gradient flow. We then rate these images with the VLM, and backpropagate this loss to update LoRA [29] weights on the image generator. We optimize these weights for each (prompt, question, answer) triplet, on $n$ seeds which correspond to unique images, where $n$ is a hyperparameter to tune.
+
+VLM Input Formatting. Finally, we discuss how we format the input to the VLM, which is crucial for achieving good results. VLMs and LLMs are notoriously sensitive to input format [67], where it is challenging to obtain meaningful ratings if the inputs are poorly formatted. However, as open-source models improve, we expect this to become less of an issue. First, we always use the default question answering template that was used to instruction tune the VLM. We primarily word questions such that they have a clear Yes or No answer, and append "Answer with Yes or No." to the question. We find this yields interpretable probabilities for the extent to which the control was satisfied, simply by exponentiating the VQA loss, using a similar idea as Lin et al. [44]. Our system can also be extended to more open-ended question-answer pairs, but we anticipate this requires in-context learning examples to obtain a reliable answer format, which we leave for future work. Second, we also support visual prompts where we feed not only a question but also an instructional image, described further in Sec. 4.3. Rather than feeding the image instruction as a separate image, we choose to overlay it on top of the generated image from the image generator. Much like how such overlays are easier for people to rate, where they can directly compare the generated contents with the spatial instruction, we find that this format is more helpful for the VLM. Furthermore, this means that our system is also applicable to most VLMs, as it does not require multi-image support.
+
+# 4. Experiments
+
+# 4.1. Experimental Details
+
+In all experiments, we use Flux Schnell [39] as our base image generator unless otherwise specified. By default we run Schnell as a single-step model, but we also validate our method in the multi-step setting in Table 1. For each experiment, we utilize the VLM that demonstrates the strongest performance for the given task. Our method uses VLMs off-the-shelf without additional fine-tuning, which makes it easy to switch between different models. We use LoRA [29] to optimize the weights, with a rank between 8-16 and alpha that is $5\mathrm{x}$ the rank. A high alpha value is crucial; if it is set too low, the VLM cannot observe the full effect of the LoRA and rate images correctly. For optimization, we use Adam [37] with a learning rate of $5e^{-5}$ for up to 100 iterations. We optimize with $n = 100$ seeds unless otherwise specified. We run all experiments on a single 80GB Nvidia A100 GPU, which takes at most three minutes. Our method can run on as little as two 24GB Nvidia RTX 4090 GPUs when implemented on smaller models, e.g., switching out Flux Schnell [39] (12B params) for Sana [83] (1.6B params).
+
+# 4.2. Commonsense Inferences
+
+Setup. Even after training on millions of images, image generators still struggle with basic associations, or commonsense. For example, if a user prompts for a pen placed in a cup of water, many models do not know that the pen should appear bent due to the law of refraction. We evaluate whether our method can fix these knowledge gaps on CommonsenseT2I [22], a benchmark for evaluating commonsense in text-to-image models. Given an underspecified prompt, the image generator should generate an image that aligns with a held-out description of the expected inference. To improve the image generator, we feed the generated images to the VLM to verify whether they satisfy the inference, and optimize the weights to maximize this score. For the VLM, we use Idefics2 [40], a late-fusion VLM that achieves superior performance on OK-VQA, a knowledge-centric question answering benchmark [52]. We automatically generate the questions used to check these inferences using GPT4o [56]. We then compare our method against the base prompt and prompt expansion. Since our method is orthogonal and complementary to prompting, we can apply the learned weights on top. For prompt expansion we use GPT4o, following the same procedure as DALL-E 3 [6]. We compare performance following the same protocol as Fu et al. [22], which uses GPT4o to provide binary (yes or no) judgements of image correctness.
+
+Our method improves on top of prompt expansion. We report quantitative results in Table 1. Both Flux Schnell and Dev perform poorly when prompted with the base prompt, with an average accuracy of $24\%$ or less, demonstrating
+
+that the model inherently lacks commonsense understanding. Our method, when applied on top, improves performance by at least $20\%$ . There are also many cases where prompt expansion is insufficient; our method improves prompt expansion by at least $11\%$ . In these cases, the model completely fails to visually represent the phenomenon, regardless of the amount of explanation. This might be because the phenomenon is uncommon and underrepresented in the training data, and explicitly teaching the model with feedback is helpful.
+
+Commonsense needs verification over suggestion. We show qualitative examples in Figure 3. The base prompt simply generates the primary object while ignoring other information that imply subtle inferences. Sometimes the expanded prompt introduces conflicting information (top half of Figure 3). Although we use GPT4o for both expansion and question generation, the model can produce better inferences when instructed to check for correctness rather than simply adding more detail. Finally, even if the expanded prompt explicitly includes the correct inference, the image generator can still fail (bottom half of Figure 3). Since our method is verification centric, it is better at enforcing the inference rather than leaving it as a suggestion.
+
+# 4.3. Visual Prompting
+
+Setup. The default interface of image generators is restricted to text, due to its reliance on static text embeddings [62, 63]. In contrast, VLMs can process arbitrary multimodal inputs, including visual prompts [10] where the instruction is jointly defined in image and text. This multimodal instruction is more conceptual, for example pointing at a spatial location and annotating what should be there. Unlike spatial control [87], where the image generator should exactly copy the structure of the input image, in visual prompting the model needs to reason about what the instruction is asking for. To implement control with visual prompts, we overlay the image instruction on top of the generated image, which is jointly fed with the text instruction to the VLM. We use Qwen2.5-VL [4] for our VLM, as it is specifically trained on data related to spatial understanding and object grounding. Next, we will discuss some specific use cases that can be implemented as visual prompts. See Table 6 of the Appendix for the image generator prompts of each example.
+
+Color Palette. Here, our objective is to produce an image that adheres to a given color palette. To achieve this, we overlay the palette at the bottom of the generated image and query the VLM to verify that the colors match. We display qualitative examples in Figure 4. We control with three distinct color palettes, which we call dark academia, pastel, and retro. Evidently, our method is able to faithfully replicate the colors on naturalistic and artistic scenes with varying lighting conditions and 3D effects.
+
+Line Weight. We now explore using our method to control line weight in cartoons. We draw a red line at the bottom
+
+| Generator | Method | Animal Behaviors | Biological Laws | Daily Items | Human Practices | Physical Laws | Avg |
| Flux Schnell (single-step) | Base Prompt | 41.7 | 4.4 | 23.8 | 28.3 | 24.0 | 24.4 |
| Base Prompt + Ours | 59.7 | 48.5 | 34.5 | 41.7 | 38.3 | 44.5 |
| Expanded Prompt | 70.8 | 57.4 | 29.8 | 53.3 | 42.4 | 50.7 |
| Expanded Prompt + Ours | 66.7 | 79.4 | 59.5 | 54.4 | 50.0 | 62.0 |
| Flux Dev (multi-step) | Base Prompt | 29.2 | 4.4 | 14.3 | 24.4 | 16.8 | 17.8 |
| Base Prompt + Ours | 47.2 | 44.1 | 31.0 | 56.7 | 28.6 | 41.5 |
| Expanded Prompt | 55.6 | 48.5 | 33.3 | 46.7 | 36.7 | 44.2 |
| Expanded Prompt + Ours | 77.8 | 51.5 | 53.6 | 62.2 | 45.9 | 58.2 |
+
+Table 1. CommonsenseT2I Evaluation. We evaluate on all 150 pairs from the benchmark and report the percentage of correct generations, both per-category and on average. We sample Flux Schnell as a single-step model (t=1) and Flux Dev as a multi-step model (t=28).
+
+| Base Prompt | Expanded Prompt | + Ours (Automatic Questions) |
| A bookshelf just assembled | | ...multiple shelves stocked with an assortment of books... | | Is the bookshelf empty? | |
| A full cup of water tipped over on a table | | ...water droplets are in mid-air, showing motion... | | Is the water spilling out of the cup onto the table? | |
| A potted plant kept in a dark room for a week | | ...leaves appear wilted and pale... yellowish or drooping... | | Does the plant look unhealthy or wilted? | |
| A cup of oil mixed with water | | ...showing the distinct separation between the two liquids... | | Are there visible layers or separation between the oil and water? | |
+
+Figure 3. Commonsense Inferences. When the base prompt fails, prompt expansion can be unhelpful. Our method, which uses an automatically generated question to verify the inference, can be applied on top of prompting to fix these cases. The top two rows show cases where prompt expansion fails to capture implied properties given the short prompt, whereas the bottom two rows show cases where the expanded prompt contains the correct phenomenon but the generated image does not. Our method helps in both situations.
+
+of the generated image and ask the VLM if the line is representative of the image's line weight. In Figure 5 we show qualitative examples, where our method can make the line weight thinner or thicker based on the overlaid line. Through visual prompting, we can create visual abstractions and bind different meanings based on the question. In this case we use lines to denote the desired edge thickness, whereas in the next section we use them to denote spatial position.
+
+Horizon Position. Lines can also be used to control the po
+
+sition of the horizon. We overlay a red line on the generated image and ask the VLM to check if the horizon of the scene is aligned. We show qualitative examples in Figure 6, where our method is able to raise and lower the horizon according to the image instruction. These examples make it clear why overlaying the image instruction is helpful; one can check the spatial alignment simply by assessing the distance between the actual horizon and the red line.
+
+Relative Depth. We now show how points can be used to
+
+
+Figure 6. Horizon Position. We use red lines to specify the position of the horizon, or the boundary at which the earth and sky meet. The same visual abstraction can be bound with different meanings; lines can be used to specify both line weight and horizon position.
+
+specify relative depth. We place two red points, labeled as Point A and Point B, and use the VLM to verify which point is in the foreground vs. background or which point is closer vs. further from the camera. As seen in Figure 7, our method is able to move around two subjects to enforce the control. In the first case, our method shrinks the dog to ensure that Point A lies on the background rather than the dog. The second case imposes the reverse control, where Point A should now lie on the foreground and Point B on the background. Our method enlarges the dog and creates empty space to its right to satisfy the visual prompt. Finally, in the last case our method is able to adjust the depth ordering of the two subjects, where both animals start at roughly the same distance from the camera then the dog is moved in front of the sheep. These examples also demonstrate how our method is able to follow truly multimodal instructions, where the VLM needs to distinguish between the two points
+
+by associating the red labels on the image instruction and the references to the labels in the question.
+
+Visual Composition. We now show how visual prompting can be used to control composition with abstract art. This setting is inspired by the work of Piet Mondrian, who is best known for his abstract De Stijl paintings comprised of simple primary colors and lines. Mondrian paintings can be interpreted as highly abstracted Dutch landscapes, with elements like trees and the horizon reduced to vertical and horizontal lines [80]. In Figure 8 we show how our method can be used to perform the inverse problem and produce
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 8. Visual Composition. We use abstract paintings from Piet Mondrian [53, 54] to control visual composition. We also annotate additional instructions for how to interpret the painting in red.
+
+
+
+
+Figure 7. Relative Depth. We use two red points to specify relative depth ordering. We also annotate these points with text labels, which are referred to in the question.
+
+
+
+images that match the structure of these paintings. To make the task more clear, we annotate the paintings with additional instructions in red. We point to specific elements and instruct that "this line represents vertical object like a tree" or "this region is a large expanse like a field." Our method is able to follow these instructions and produce images with the desired composition, such as a wheat field in the boxed region or a lighthouse aligned with a vertical line. Note that there exists no paired data of abstract to landscape paintings, yet this transformation is possible when framed as a discriminative comparison task with our method.
+
+
+
+
+
+
+
+
+
+
+
+# 4.4. Optimizing Latents vs. Weights
+
+Setup. Although latent optimization may seem significantly cheaper than weight optimization, we show that this is not the case. We compare both approaches for guiding image generation, using our VLM loss (see Equation 4). Unlike the previous experiments, here we follow the setup of Eyring et al. [20], where the goal is to optimize a single seed such that the final image adheres to the input control. While this setup is originally designed to optimize latents, we can use the same gradients to instead optimize model weights, with near-identical implementations. For our VLM, we use Idefics2 [40].
+
+Computational Cost Comparison. In Table 2 we compare the computational cost of latent and weight optimization. The gradient computation through the VLM, with respect to the clean image estimate $\hat{x}_0$ , is identical for both methods. The cost slightly differs for the computation through the image generator, or the gradient of the clean image estimate $\hat{x}_0$ with respect to the input noise $z_t$ . In this case, optimizing the weights increases the VRAM usage by $5\%$ . However, weight optimization also benefits from compute amortization. After one minute of optimization upfront, every subsequent application of the weights is more than $200\mathrm{x}$ faster.
+
+
+Was the image taken from the perspective of a robot vacuum?
+A living room, taken from the perspective of a robot vaccum
+
+
+(a) Single Sample Optimization
+
+
+
+
+(b) Prompt and Seed Generalizations
+Figure 9. Weight Generalizations. We show that latent and weight optimization can achieve comparable results in a controlled single sample optimization setting in (a). We then show that these same weights can generalize to new seeds and prompts in a single inference pass, whereas latent optimization would need to be re-run with significant computational cost, in (b).
+
+| Metric | Latents | Weights |
| VLM VRAM | 21GB | 21GB |
| Image Generator VRAM | 42GB | 44GB |
| Optimization Time | 56s | 66s |
| Inference Time | 56s | 0.3s |
+
+Table 2. Computational Cost Comparison. We compare the memory and runtime cost of latent and weight optimization, averaged over 100 runs.
+
+Weight Generalizations. In Figure 9, we show an example of controlling with an unusual visual perspective. We optimize latents and weights with the same gradients, on a single seed and single prompt, and they yield similar results (Figure 9a). However, these same weights can also generalize to unseen seeds and prompts, unlike latent optimization. The optimized weights can apply the same perspective control to new scenes in a single inference pass, making the camera appear lower to the ground and raising the horizon (Figure 9b). Note that this single-sample setting for weight optimization is unusual. Traditional fine-tuning methods typically optimize on multiple seeds and reference images [64], whereas we show it is possible to optimize the weights in an extremely data-limited setting on a single seed without any reference images.
+
+
+
+# 5. Limitations
+
+Since our method relies on feedback from a model, it is susceptible to reward hacking [24, 30, 58], where the VLM exploits ambiguities in the task specification to achieve high reward. In Figure 10, we show two examples of such misinterpretations. When a red line is used to specify line width, our method may simultaneously change the line color from black to red. When the prompt is ambiguous, for example whether the points are bound to subjects or other elements in the scene, the model may produce an unintended but technically correct result. However, this same phenomenon could also be a useful tool for understanding how VLMs behave. One could use our method to mine adversarial images [26] where VLMs differ from human judgements; for example, cases where VLMs are blind to some visual property or are over-relying on certain visual cues. These automatically generated images could then be used as additional training data to improve the VLM's robustness.
+
+# 6. Conclusion
+
+We proposed a method that distills the deliberative ability of VLMs into image generators. Our method improves accuracy on challenging image generation tasks that require commonsense understanding, and provides new ways to control models through multimodal visual prompting. Our method is designed to be broadly applicable, and can utilize arbitrary off-the-shelf VLMs, selected based on their strengths for a given task. As open-source VLMs scale and improve in visual understanding and instruction following, we anticipate that our method can be used as a flexible and general framework for improving image generation.
+
+
+Figure 10. Limitations. Our method can misinterpret the visual prompt, for example changing line color when only line weight is specified or aggressively raising the ground level to satisfy a depth constraint.
+
+
+
+
+
+# Acknowledgements
+
+We would like to thank Anastasis Germanidis, Yining Shi, Alexander Pan, Chung Min Kim, Boyi Li, and David Chan for helpful discussions and feedback. We would also like to thank the folks at Stochastic Labs, especially Vero Bollow, Alexander Reben, and Joel Simon, for previewing early prototypes of this work. Authors were supported in part by the NSF, DoD, and/or the Berkeley Artificial Intelligence Research (BAIR) industrial alliance program.
+
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+# Dual-Rate Dynamic Teacher for Source-Free Domain Adaptive Object Detection
+
+Qi He $^{1,2}$ , Xiao Wu $^{1,2*}$ , Jun-Yan He $^{3}$ , Shuai Li $^{4}$
+
+$^{1}$ Southwest Jiaotong University, Chengdu, China
+
+$^{2}$ Engineering Research Center of Sustainable Urban Intelligent Transportation, Chengdu, China
+
+3 Meituan Inc., Shenzhen, China, 4 The Hong Kong Polytechnic University, Hong Kong, China
+
+{qihe96,wuxiaohk,junyanhel1989}@gmail.com, novak.li@connect.polyu.hk
+
+# Abstract
+
+Source-Free Domain Adaptive Object Detection transfers knowledge from a labeled source domain to an unlabeled target domain while preserving data privacy by restricting access to source data during adaptation. Existing approaches predominantly leverage the Mean Teacher framework for self-training in the target domain. The exponential moving average (EMA) mechanism in the Mean Teacher stabilizes the training by averaging the student weights over training steps. However, in domain adaptation, its inherent lag in responding to emerging knowledge can hinder the rapid adaptation of the student to target-domain shifts. To address this challenge, Dual-rate Dynamic Teacher (DDT) with Asynchronous EMA (AEMA) is proposed, which implements group-wise parameter updates. In contrast to traditional EMA, which simultaneously updates all parameters, AEMA dynamically decomposes teacher parameters into two functional groups based on their contributions to capture the domain shift. By applying a distinct smoothing coefficient to two groups, AEMA simultaneously enables fast adaptation and historical knowledge retention. Comprehensive experiments carried out on three widely used traffic benchmarks have demonstrated that the proposed DDT achieves superior performance, outperforming SOTA methods by a clear margin. The codes are available at https://github.com/qih96/DDT.
+
+# 1. Introduction
+
+Object detection is a critical component of computer vision, significantly contributing to a myriad of tasks [14, 24, 46]. Large-scale labeled datasets [20, 27] serve as the foundation for successful object detection. However, due to the domain gap between the training and testing domains, deploying the trained detector to the unseen domain often leads to performance degradation. Moreover, annotating large
+
+
+Figure 1. EMA synchronously updates parameters, while AEMA uses decoupled method to control adaptability to target domain and stability on long-term knowledge.
+
+amounts of data for special scenes is time consuming and labor intensive. Therefore, Domain Adaptive Object Detection (DAOD) [3] has been introduced. It leverages existing labeled source domain data and unlabeled target domain data to train a well-adapted target domain detector.
+
+In real-world applications, data security and privacy concerns often restrict the re-access of DAOD to source domain data. To address such demands, Source-Free DAOD (SF-DAOD) [19] has been proposed, which transfers knowledge of the pre-trained source detector to the unlabeled target domain, without accessing the source data during adaptation.
+
+SF-DAOD methods [10, 17, 31] leverage the Mean Teacher [30] to generate pseudo-labels to train the unlabeled target domain. The Mean Teacher framework incorporates a teacher model that serves as a globally smoothed version of the student model. All teacher parameters are updated simultaneously based on the student parameters using an Exponential Moving Average (EMA) with a high smoothing coefficient. EMA can stabilize the teacher model
+
+
+Figure 2. The framework of the proposed DDT. For student optimizing, DDT fuses pseudo-labels from teacher and student to guide optimization via joint detection loss minimization. For teacher updating, it employs gradient-informed parameter grouping (based on detection loss gradients) and asynchronously updates grouped parameters via group-specific EMA smoothing.
+
+by aggregating historical student weights, which has been proven to be valuable for noise reduction in single-domain learning environments [28, 34, 41]. However, this advantage introduces a disparity between stability and adaptability in the context of cross-domain adaptation, particularly within the source-free mode. The teacher model's significant reliance on the student model's past parameters hinders its capacity to adapt swiftly to new patterns in the target domain. Therefore, the pseudo-labels produced by the teacher, which are informed by obsolete knowledge, progressively contradict the adaptation efforts of the student within the target domain. This ongoing misalignment not only impedes the student's ability to acquire essential domain-specific features but also exacerbates the accumulation of errors originating from inaccurate pseudo-labels.
+
+Recent studies have identified critical limitations in relying solely on teacher-generated pseudo-labels. The utilization of teacher knowledge associated with low-confidence predictions is explored in LPU [4], rather than relying solely on high-confidence pseudo-labels. In PETS [21], a dual teacher framework with static and dynamic teachers is proposed to improve the reliability of pseudo-labels, while DRU [17] mitigates label noise through dynamic retraining-updating strategy. However, these approaches do not address the core problem: The synchronous update paradigm inherent in conventional EMA is inadequate for SF-DAOD.
+
+Unlike conventional EMA, which uniformly updates all parameters, in this paper an Asynchronous EMA (AEMA) mechanism is novelly proposed to quickly adapt to new knowledge in emerging domains without sacrificing the stability of the learned knowledge structure. It dynamically categorizes parameters according to their importance to the
+
+target domain and assigns group-specific smoothing coefficients, as illustrated in Figure 1. Parameters with larger gradients indicate higher impacts on reducing prediction errors, which are prioritized during optimization. Inspired by the Lottery Ticket Hypothesis [8], the parameters are delineated into two categories: target-responsive and stability-preserving parameters, which correspond to critical parameters for domain adaptation and those essential for maintaining the integrity of temporal knowledge, respectively. To prioritize rapid adaptation of these critical parameters, a lower smoothing coefficient is assigned to the target-responsive group, enabling agile updates in response to target domain shifts. In contrast, the stability-preserving parameters are governed by a higher smoothing coefficient, which introduces inertia to their updates and prevents catastrophic forgetting. This dual-rate update strategy improves the adaptability of the teacher model and ensures its overall stability at the same time.
+
+To address these limitations in Mean Teacher, a Dual-rate Dynamic Teacher (DDT) framework is proposed for SF-DAOD, which harmonizes model stability and adaptability through the AEMA mechanism. Following the previous work DRU [17], DDT takes weak, strong, and masked images as inputs to leverage the advantage of weak-strong augmentation. To capture comprehensive domain knowledge, the pseudo-labels of the teacher and the student for weak images are integrated. The importance of each parameter is quantified by the magnitude of its backpropagated gradient through the teacher detection loss function, which measures the discrepancy between the predictions from the teacher and the integrated pseudo-labels. The parameter grouping of AEMA is guided by the above parameter im
+
+portance. The teacher is updated via AEMA to perform an asynchronous update with the student. The student is optimized with the detection loss between predictions (strong and masked images) and integrated pseudo-labels. By adjusting the smoothing coefficients based on the importance, DDT can quickly adapt to new knowledge in emerging domains without sacrificing the stability of the learned knowledge structure.
+
+The contributions are summarized as follows:
+
+- Dual-rate Dynamic Teacher with AEMA is proposed for SF-DAOD, which implements a dual-rate updating mechanism to balance the stability of historical knowledge and adaptability of emerging domain knowledge.
+- AEMA dynamically decomposes the teacher parameters into target-responsive and stability-preserving parameters, which accelerates the adaptation of new knowledge and maintains the stability of old knowledge.
+- Experimental results demonstrate that the proposed DDT achieves state-of-the-art performance in SF-DAOD and shows effectiveness in other domain adaptation tasks.
+
+# 2. Related works
+
+# 2.1. Source-Free Domain Adaptation
+
+Source-Free Domain Adaptation (SFDA) aims at transferring knowledge from the source domain to the target domain without accessing the data from the source domain. All SFDA approaches utilize pseudo-labeling technology to adapt the source pre-trained model to the target domain. These methods can be grouped into two categories: non-contrastive and contrastive. Non-contrastive methods [29, 45] use pseudo-labels to align a few samples with trusted pseudo-labels with other data or leverage the target data manifold to generate high-quality pseudolabels. Contrastive methods [32, 42] use variant-enhanced contrastive learning to improve feature representations.
+
+The base task of SFDA is classification, while Source-Free Domain Adaptive Object Detection (SF-DAOD) works for object detection. The differences between two tasks are huge, e.g., the number of objects per image. Although the training manner of SFDA and SF-DAOD is similar, SFDA methods are difficult to apply directly to SF-DAOD.
+
+# 2.2. Domain Adaptive Object Detection
+
+The goal of Domain Adaptive Object Detection (DAOD) is to transfer the knowledge of data from the labeled source domain to the unlabeled target domain in the object detection task. Mainstream DAOD methods can be mainly divided into feature alignment and self-training. Feature alignment [25, 33] uses the Gradient Reverse Layer to align the source and target domains. Self-training [39, 44] mainly leverages weak-strong augmentation and mean teacher framework for teacher-student mutual learning. CMT [1]
+
+optimizes object-level features via contrastive learning. To mitigate the bias that the majority class brings to minority classes, CAT [16] applies an instance-level mixup, which prioritizes the model's attention towards minority classes.
+
+DAOD methods rely on the source data to align or calibrate the target domain. Since SF-DAOD does not use the source data during adaptation, DAOD methods (which require source data) cannot be used directly to SF-DAOD.
+
+# 2.3. Source-Free Domain Adaptive Object Detection
+
+In consideration of data security and privacy protection, Source-Free DAOD (SF-DAOD), as an extension of DAOD, aims to adapt the source domain knowledge to the target domain without accessing the source domain data during the adaptation phase. Only the source pre-trained detector and unlabeled target domain data are accessible. SF-DAOD methods [6, 17, 31] use self-training to learn the target domain data, in which weak-strong augmentation and mean-teacher framework have shown superior advantages in this field. IRG [31] uses a graph structure to learn better features of the target domain under the mean teacher. To improve the stability of the mean teacher framework, PETS [21] proposes a multi-teacher framework to integrate useful knowledge between dynamic and static teachers. LPLD [37] leverages low-confidence pseudo-labels provided by the teacher to the student to explore more knowledge about the target domain. Moreover, DRU [17] introduces a dynamic retraining-update mean teacher to overcome the noisy pseudo-labels provided by the teacher.
+
+Existing methods overlook a critical flaw in the SF-DAOD mean teacher framework. EMA updates all parameters synchronously, creating a conflict between preserving learned knowledge and adapting to new domains. To address this, our DDT assigns different smoothing coefficients to parameters based on their roles of preserving temporal knowledge and capturing domain shift.
+
+# 3. Dual-rate Dynamic Teacher
+
+The Mean Teacher framework and the proposed method are outlined in this section.
+
+# 3.1. Mean Teacher Framework
+
+The Mean Teacher framework [30] has been widely used in semi-supervised learning and unsupervised learning to provide stable self-training for unlabeled data. It consists of a pair of identical network teacher and student. The teacher is updated from the student using EMA, which averages the student over the training steps. The teacher is able to resist disturbances during training and produce more accurate predictions than the student. Therefore, using the pseudolabels provided by the teacher to supervise the learning of unlabeled data can cope with potential model collapse.
+
+In SF-DAOD, the source domain data are used to train a source detector. At the beginning of adaptation, the source detector weights are utilized to initialize the teacher and the student. During the adaptation phase, pseudo-labels, which are predictions of the teacher with a high confidence (exceeding a specified threshold), are utilized to guide the student on unlabeled data from the target domain. The student is optimized with the gradient descent algorithm.
+
+$$
+\theta_ {s} \leftarrow \theta_ {s} - \beta \cdot \frac {\partial \mathcal {L} _ {\text {d e t}} \left(\operatorname {p r e d} s _ {s} , P L _ {t}\right)}{\partial \theta_ {s}}, \tag {1}
+$$
+
+where $\theta_{s}$ denotes the student parameters, $\beta$ is the learning rate, $\mathcal{L}_{\text{det}}(\text{pred}s_s, PL_t)$ refers to the detection loss, which contains the classification loss ( $\mathcal{L}_{\text{cls}}$ ) and the regression losses ( $\mathcal{L}_{\text{L1}}$ and $\mathcal{L}_{\text{giou}}$ ), between the predictions of the student $\text{pred}s_s$ and the pseudo-labels of the teacher $PL_t$ .
+
+The teacher updates its parameters using the EMA weights of the student.
+
+$$
+\theta_ {t} \leftarrow \alpha \cdot \theta_ {t} + (1 - \alpha) \cdot \theta_ {s}, \tag {2}
+$$
+
+where $\theta_{t}$ denotes the parameters of the teacher, and $\alpha$ is the smoothing coefficient.
+
+# 3.2. Dual-Rate Dynamic Teacher
+
+The framework of the Dual-Rate Dynamic Teacher is illustrated in Figure 2. DDT classifies teacher parameters into two categories: target-responsive and stability-preserving parameters. It assigns a lower smoothing coefficient to target-responsive parameters to embrace rapid adaptation and gives a higher smoothing coefficient to stability-preserving parameters to maintain historical knowledge.
+
+# 3.2.1. Integration of Knowledge
+
+To enhance the acquisition of domain knowledge, the pseudo-labels generated by both teacher and student models are combined. The teacher model focuses on maintaining stable knowledge through gradual updates, whereas the student model rapidly adapts to new patterns in the target domain. This integration compensates for their differences caused by different learning strategies. By integrating the teacher's capacity for long-term knowledge retention with the student's aptitude for short-term pattern adaptation, this approach reduces individual model biases and strengthens the overall learning process. In particular, the teacher model's historical consistency serves to mitigate the student model's tendency to overfit to ephemeral patterns, while the adaptability of the student model helps alleviate the rigidity of the teacher model. The resulting integration of consistent historical understanding and flexible pattern recognition fosters more reliable and robust domain knowledge acquisition, ultimately bridging the gap between generalization and domain-specific adaptation.
+
+Given that both the teacher and the student identify a significant number of identical objects, the Non-Maximum Suppression (NMS) is implemented to prevent the assignment of duplicate labels to a single object. Taking into account the pseudo-labels provided by the teacher $PL_{t}$ and those of the student $PL_{s}$ , the integrated pseudo-labels $PL$ can be described as follows:
+
+$$
+P L = n m s \left(c a t \left(P L _ {t}, P L _ {s}\right)\right), \tag {3}
+$$
+
+where $nms$ is NMS operation, and $cat(PL_t, PL_s)$ means concatenating detection labels from $PL_t$ and $PL_s$ . Pseudolabels $PL_t$ and $PL_s$ are obtained by filtering predictions with thresholds of $th_t$ and $th_s$ , respectively.
+
+# 3.2.2. Asynchronous Exponential Moving Average
+
+AEMA achieves asynchronous updates of teacher parameters by employing parameter grouping alongside a dual rate update mechanism. It comprises two steps: gradient-aware parameter importance ranking and group-wise updating.
+
+The parameter importance ranking requires defining a measurable proxy to quantify the significance of each parameter during domain adaptation. This is accomplished by analyzing the gradient descent algorithm. The amplitude of the gradients serves as an intrinsic indicator of the contribution of a parameter to the minimization of losses. The optimization objective minimizes the detection loss between the teacher predictions and the aggregated pseudolabels. As a result, the importance metric can derive from backpropagation gradients. Parameters exhibiting substantial gradient magnitudes are indicative of elevated domain adaptation priority, thereby requiring prioritized updates to effectively facilitate knowledge acquisition within the target domain. In contrast, parameters with smaller gradients are identified as stability-preserving components, which play a critical role in maintaining the consistency of historical knowledge. The importance $s(\theta_t)$ can be formulated as:
+
+$$
+s \left(\theta_ {t}\right) = \left| \frac {\partial \mathcal {L} _ {d e t} \left(p r e d s _ {t} , P L\right)}{\partial \theta_ {t}} \right|, \tag {4}
+$$
+
+where $|\cdot|$ denotes the absolute value. Notably, the teacher gradients are exclusively employed for parameter grouping and are not utilized within the gradient descent process.
+
+The parameters of the teacher model can be categorized into two distinct groups based on their capacity for swift adaptation to novel domain knowledge: target-responsive parameters and stability-preserving parameters. Inspired by Network Pruning [5, 8], only a few parameters are essential for network learning. Given the importance of each parameter, the parameters of highest importance are selected as target-responsive parameters $\mathcal{P}_{TR}$ , and others are indicated as stability-preserving parameters $\mathcal{P}_{SP}$ .
+
+For group-wise asynchronous updating, a reduced smoothing coefficient is allocated to target-responsive parameters to facilitate swift adaptation to distributional
+
+ | Method | Detector | person | rider | car | truck | bus | train | motor | bicycle | mAP |
| Source Only | DefDETR | 40.0 | 41.2 | 47.0 | 13.0 | 29.1 | 6.5 | 21.5 | 38.0 | 29.5 |
| DAOD | SW-Faster [25] | FRCNN | 32.3 | 42.2 | 47.3 | 23.7 | 41.3 | 27.8 | 28.3 | 35.4 | 34.8 |
| CR-DA-DET [35] | FRCNN | 32.9 | 43.8 | 49.2 | 27.2 | 45.1 | 36.4 | 30.3 | 34.6 | 37.4 |
| TIA [43] | FRCNN | 34.8 | 46.3 | 49.7 | 31.1 | 52.1 | 48.6 | 37.7 | 38.1 | 42.3 |
| TDD [11] | FRCNN | 39.6 | 47.5 | 55.7 | 33.8 | 47.6 | 42.1 | 37.0 | 41.4 | 43.1 |
| CAT [16] | FRCNN | 44.3 | 57.1 | 63.7 | 40.8 | 66.0 | 49.7 | 44.9 | 53.0 | 52.5 |
| SFA [33] | DefDETR | 46.5 | 48.6 | 62.6 | 25.1 | 46.2 | 29.4 | 28.3 | 44.0 | 41.3 |
| MTTrans [39] | DefDETR | 47.7 | 49.9 | 65.2 | 25.8 | 45.9 | 33.8 | 32.6 | 46.5 | 43.4 |
| DA-DETR [40] | DefDETR | 49.9 | 50.0 | 63.1 | 24.0 | 45.8 | 37.5 | 31.6 | 46.3 | 43.5 |
| MRT [44] | DefDETR | 52.8 | 51.7 | 68.7 | 35.9 | 58.1 | 54.5 | 41.0 | 47.1 | 51.2 |
| SF-DAOD | SED (Mosaic) [19] | FRCNN | 33.2 | 40.7 | 44.5 | 25.5 | 39.0 | 22.2 | 28.4 | 34.1 | 33.5 |
| A2SFOD [6] | FRCNN | 32.3 | 44.1 | 44.6 | 28.1 | 34.3 | 29.0 | 31.8 | 38.9 | 35.4 |
| LODS [18] | FRCNN | 34.0 | 45.7 | 48.8 | 27.3 | 39.7 | 19.6 | 33.2 | 37.8 | 35.8 |
| PETS [21] | FRCNN | 42.0 | 48.7 | 56.3 | 19.3 | 39.3 | 5.5 | 34.2 | 41.6 | 35.9 |
| IRG [31] | FRCNN | 37.4 | 45.2 | 51.9 | 24.4 | 39.6 | 25.2 | 31.5 | 41.6 | 37.1 |
| LPLD [37] | FRCNN | 39.7 | 49.1 | 56.6 | 29.6 | 46.3 | 26.4 | 36.1 | 43.6 | 40.9 |
| SF-UT [10] | FRCNN | 40.9 | 48.0 | 58.9 | 29.6 | 51.9 | 50.2 | 36.2 | 44.1 | 45.0 |
| DRU [17] | DefDETR | 48.3 | 51.5 | 62.5 | 26.2 | 43.2 | 34.1 | 34.2 | 48.6 | 43.6 |
| DDT (ours) | DefDETR | 49.3 | 53.0 | 65.4 | 25.8 | 43.0 | 39.7 | 40.0 | 47.9 | 45.5 |
+
+Table 1. Comparison with the state-of-the-art methods for the adaptation task of Foggy Adaptation. "Source Only" refers to the source-trained model. "FRCNN" denotes Faster R-CNN [23], and "DefDETR" represents Deformable DETR.
+
+changes within the target domain, while an elevated smoothing coefficient is designated for stability-preserving parameters to maintain the integrity of historical knowledge. This dual-rate strategy reflects their distinct roles, where target-responsive parameters prioritize agility, which dynamically aligns with evolving target patterns. Because stability-preserving parameters emphasize inertia, they mitigate abrupt deviations from consolidated historical knowledge. By decoupling update rates based on parameter roles, the proposed approach balances plasticity for adaptation and stability for long-term consistency. The update of each parameter by AEMA can be described as follows.
+
+$$
+\left\{ \begin{array}{l} \theta_ {t} ^ {i} \leftarrow \alpha_ {1} \cdot \theta_ {t} ^ {i} + (1 - \alpha_ {1}) \cdot \theta_ {s} ^ {i}, \quad i f \quad \theta_ {t} ^ {i} \in \mathcal {P} _ {T R}, \\ \theta_ {t} ^ {i} \leftarrow \alpha_ {2} \cdot \theta_ {t} ^ {i} + (1 - \alpha_ {2}) \cdot \theta_ {s} ^ {i}, \quad i f \quad \theta_ {t} ^ {i} \in \mathcal {P} _ {S P}, \end{array} \right. \tag {5}
+$$
+
+where $\theta_t^i$ and $\theta_s^i$ denote the $i$ -th parameter of the teacher and the student, respectively. $\alpha_{1}$ and $\alpha_{2}$ are the smoothing coefficients for $\mathcal{P}_{TR}$ and $\mathcal{P}_{SP}$ , respectively.
+
+# 3.2.3. Training Objective
+
+Following previous work DRU [17], the Masked Image Consistency (MIC) [12] is used to facilitate the learning of context relations of unlabeled data in the training phase. Given the strong augmented image $x^{S}$ , the masked image $x^{M}$ is generated by $x^{M} = \mathcal{M} \odot x^{S}$ , where $\mathcal{M}$ is a patch mask sampled from a uniform distribution, and $\odot$ denotes element-wise multiplication.
+
+The total training objective is formulated as follows.
+
+$$
+\mathcal {L} = \mathcal {L} _ {d e t} ^ {S} (p r e d s _ {s} ^ {S}, P L) + \mathcal {L} _ {d e t} ^ {M} (p r e d s _ {s} ^ {M}, P L), \tag {6}
+$$
+
+where $\text{preds}_s^S$ and $\text{preds}_s^M$ denote predictions of the student with $x^S$ and $x^M$ , respectively.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. Following previous works [6, 17, 21], DDT is validated on four datasets: Cityscapes [7], FoggyCityscapes [26], BDD100K [38], and Sim10K [15]. Cityscapes consists of real-world urban scenes and includes eight common categories. FoggyCityscapes is a real-world urban scene with foggy, which is generated by applying a synthetic fog filter to the original Cityscapes images. BDD100K comprises 100,000 real-world images under six different conditions. Similarly to previous work [6, 17, 21], the "daytime" subset is extracted, with 36,728 training images and 5,258 validation images. Sim10K is a simulation dataset generated by the GTA-V game engine.
+
+Adaptation Tasks. DDT is applied to three widely used adaptation tasks. 1) Normal to Foggy Adaptation: Cityscapes $\rightarrow$ FoggyCityscapes, which means Cityscapes as the source domain and FoggyCityscapes with the highest fog density (0.02) as the target domain, 2) Cross Scene Adaptation: Cityscapes $\rightarrow$ BDD100K, and 3) Synthetic to Real Adaptation: Sim10K $\rightarrow$ Cityscapes.
+
+# 4.2. Implement Details
+
+The proposed DDT is built on Deformable DETR [47]. The batch size is fixed at 8 for all domain adaptation tasks. The
+
+ | Method | Detector | truck | car | rider | person | motor | bicycle | bus | mAP |
| Source Only | DefDETR | 18.9 | 58.2 | 28.3 | 42.0 | 15.7 | 18.8 | 21.7 | 29.1 |
| DAOD | DA-Faster [3] | FRCNN | 14.3 | 44.6 | 26.5 | 29.4 | 15.8 | 20.6 | 16.8 | 24.0 |
| SW-Faster [25] | FRCNN | 15.2 | 45.7 | 29.5 | 30.2 | 17.1 | 21.2 | 18.4 | 25.3 |
| CR-DA-DET [35] | FRCNN | 19.5 | 46.3 | 31.3 | 31.4 | 17.3 | 23.8 | 18.9 | 26.9 |
| AQT [13] | DefDETR | 17.3 | 58.4 | 33.0 | 38.2 | 16.9 | 23.5 | 18.4 | 29.4 |
| O2net [9] | DefDETR | 20.4 | 58.6 | 31.2 | 40.4 | 14.9 | 22.7 | 25.0 | 30.5 |
| MTTrans [39] | DefDETR | 25.1 | 61.5 | 30.1 | 44.1 | 17.7 | 23.0 | 26.9 | 32.6 |
| MRT [44] | DefDETR | 24.7 | 63.7 | 30.9 | 48.4 | 20.2 | 22.6 | 25.5 | 33.7 |
| SF-DAOD | SED (Mosaic) [19] | FRCNN | 20.6 | 50.4 | 32.6 | 32.4 | 18.9 | 25.0 | 23.4 | 29.0 |
| PETS [21] | FRCNN | 19.3 | 62.4 | 34.5 | 42.6 | 17.0 | 26.3 | 16.9 | 31.3 |
| A2SFOD [6] | FRCNN | 26.6 | 50.2 | 36.3 | 33.2 | 22.5 | 28.2 | 24.4 | 31.6 |
| LPU [4] | FRCNN | 24.5 | 55.2 | 38.9 | 41.4 | 20.9 | 30.4 | 23.2 | 33.5 |
| DRU [17] | DefDETR | 27.1 | 62.7 | 36.9 | 45.8 | 22.7 | 32.5 | 28.1 | 36.6 |
| DDT (ours) | DefDETR | 28.7 | 66.1 | 40.3 | 49.4 | 29.3 | 34.1 | 29.1 | 39.6 |
+
+Table 2. Results of Cross Scene Adaptation.
+
+ | Method | Detector | AP of car |
| Source Only | DefDETR | 48.9 |
| DAOD | TDD [11] | FRCNN | 53.4 |
| PT [2] | FRCNN | 55.1 |
| SFA [33] | DefDETR | 52.6 |
| O2net [9] | DefDETR | 54.1 |
| DA-DETR [40] | DefDETR | 54.7 |
| MTTrans [39] | DefDETR | 57.9 |
| MTM [44] | DefDETR | 58.1 |
| SF-DAOD | SED(Mosaic) [19] | FRCNN | 43.1 |
| IRG [31] | FRCNN | 43.2 |
| A2SFOD [6] | FRCNN | 44.0 |
| PETS [21] | FRCNN | 57.8 |
| LPLD [37] | FRCNN | 49.4 |
| SF-UT [10] | FRCNN | 55.4 |
| DRU [17] | DefDETR | 58.7 |
| DDT (ours) | DefDETR | 60.6 |
+
+Table 3. Results of Synthetic to Real Adaptation.
+
+teacher is updated with AEMA. The smoothing coefficients are set to $\alpha_{1} = 0.997$ , $\alpha_{2} = 0.9996$ for most tasks, except that $\alpha_{1} = 0.9997$ , $\alpha_{2} = 0.9999$ for Cityscapes $\rightarrow$ BDD100K. The top $10\%$ of the parameters are selected as target-responsive parameters. The thresholds of pseudo-labels are $th_{s} = 0.5$ , $th_{t} = 0.4$ . The student is optimized with the Adam optimizer with an initial learning rate of $2e^{-4}$ . Following DRU [17], the MIC module is adopted, where the patch size $b = 64$ and the mask ratio $r = 0.5$ . Mean Average Precision (mAP) with a threshold of 0.5 is used as an evaluation metric.
+
+# 4.3. Comparison with SOTA Methods
+
+The proposed DDT is validated against state-of-the-art approaches in three challenging SF-DAOD adaptation tasks.
+
+1) Normal to Foggy Adaptation. As weather conditions exhibit frequent fluctuations that pose substantial challenges, object detectors are required to demonstrate reliability. To address this issue, the detection model is transferred from the Cityscapes to FoggyCityscapes scenario, which is illustrated in Table 1. Compared to DRU with the same detector framework, DDT improves the performance for difficult categories (e.g., "train" and "motor"), in which more pseudo-labels are generated by the teacher with better adaptability. DDT achieves state-of-the-art performance.
+
+2) Cross Scene Adaptation. The dynamic change of scene in real-world applications, especially within autonomous driving contexts, address domain shift challenges is crucial. The result of Cityscapes $\rightarrow$ BDD100K is listed in Table 2, in which the proposed DDT outperforms the previous SOTA method by $3\%$ mAP and achieves the best performance in all categories.
+3) Synthetic to Real Adaptation. Due to the lower cost of annotating synthetic data compared to acquiring real-world data, training object detectors on synthetic datasets, followed by the application of domain adaptation techniques to real-world scenarios, has emerged as a cost-effective approach. As demonstrated in Table 3, our DDT framework demonstrates superior performance compared to existing methodologies. DDT also outperforms the DefDETR-based DAOD methods by at least $2\%$ mAP.
+
+# 4.4. Ablation Studies
+
+Ablation studies are conducted on the Foggy Adaptation.
+
+Effect of individual component. The effect of the proposed modules is listed in Table 4. By applying the integration of knowledge with the Mean Teacher, performance is improved from $39.8\%$ to $41.3\%$ . The proposed AEMA uses inconsistent smoothing coefficients, which improves the mAP from $39.8\%$ to $44.6\%$ . When both integration
+
+
+Figure 3. The statistics of target-responsive parameters.
+
+
+Figure 4. EMA with different coefficients.
+
+
+
+| MT | MIC | Integration | AEMA | mAP |
| ✓ | ✓ | | | 39.8 |
| ✓ | ✓ | ✓ | | 41.3 |
| ✓ | ✓ | | ✓ | 44.6 |
| ✓ | ✓ | ✓ | ✓ | 45.5 |
| ✓ | | | | 37.4 |
| ✓ | | ✓ | ✓ | 43.2 |
+
+and AEMA are combined, it achieves a $5.7\%$ improvement. In addition, DDT also improves the baseline from $37.4\%$ to $43.2\%$ when the MIC module is removed. This illustrates that each component significantly contributes to the enhancement of adaptive capabilities.
+
+Student gradient guidance. As listed in Table 5, the student's gradient remains effective in driving the AEMA update because the teacher is an ensemble of the student over training steps. However, the inherent local temporal inconsistency between the teacher and the student renders this approach less optimal compared to the direct utilization of the teacher gradient.
+
+Analysis for target-responsive parameters. The statistics of target-responsive parameters are illustrated in Figure 3. We can see that around $70\%$ parameters are hardly chosen (frequency $\leq 1\%$ ) and about $9\%$ parameters are frequently selected (frequency $\geq 20\%$ ) during training. On the right, the frequency, where it is $\geq 20\%$ , is provided for the backbone, encoder, and decoder of DefDETR. In the early stage of training, the target-responsive parameters are concentrated mainly on the backbone to adapt to the low-level change. They are then shifted to the encoder and decoder to enhance semantic consistency. The experiment verifies the effectiveness of AEMA. It demonstrates the capability of AEMA to facilitate hierarchical parameter updating via gradient-based decoupling, effectively addressing the adaptability-stability dilemma.
+
+Sensitivity for target-responsive parameters. The selection ratio and the smoothing coefficient $(\alpha_{1})$ are studied for the target-responsive parameters, which are listed in Ta
+
+Table 4. The effect of each component. "MT" denotes the Mean Teacher framework.
+
+| Methods | mAP |
| Grouped by student gradient | 45.3 |
| Grouped by teacher gradient | 45.5 |
+
+Table 5. Grouping under different guidance.
+
+ | 5% | 10% | 15% | 20% |
| mAP | 45.1 | 45.5 | 45.2 | 44.3 |
+
+Table 6. Comparison with different selection ratios.
+
+ble 6. Too few or too many target-responsive parameters can affect the teacher update. $10\%$ is a suitable ratio for selecting target-responsive parameters. The results of AEMA with different $\alpha_{1}$ are illustrated in Figure 4 (solid lines). A powerful adaptation in the early stage is achieved when $\alpha_{1} = 0.996$ . A more stable training process is obtained when $\alpha_{1} = 0.998$ , which has a relatively poor result due to the accumulation of errors. A suitable $\alpha_{1}$ (0.997) better harmonizes adaptivity and stability, having the best performance.
+
+Comparison with EMA. AEMA is compared with EMA with different smoothing coefficients, which is shown in Figure 4 (dashed line). The teacher model with a lower smoothing coefficient (e.g., $\alpha = 0.998$ ) initially achieves good performance by rapidly incorporating new knowledge from target-domain pseudo-labels. However, in later training stages, this aggressive adaptation amplifies noise from error-prone pseudo-labels, destabilizing historical knowledge and causing performance degradation. In contrast, a higher smoothing coefficient (e.g., $\alpha = 0.9996$ ) stabilizes the teacher model but sacrifices adaptability. The slow teacher updates prevent the student from learning domain-specific features, as the pseudo-labels fail to reflect emerging knowledge. This phenomenon highlights the need for a balanced approach to harmonize stability and adaptability. Using group-wise updates to meet demand, AEMA achieves obvious advantages compared to traditional EMA in SF-DAOD.
+
+Sensitivity for thresholds of pseudo-labels. As shown in Table 7, varying the thresholds for the student and teacher models impacts performance. The combination of a threshold of 0.5 for the student and 0.4 for the teacher achieves the highest mAP. The student model lacks long-term knowledge, which requires a higher threshold to effectively filter out noisy predictions compared to the teacher model.
+
+Effect of the number of groups. From Table 8, we can see that two groups achieve the best performance. To main
+
+
+Figure 5. The cyan oval dashed boxes indicate objects missed by the EMA teacher due to insufficient target-domain knowledge, while the red oval dashed boxes show failures of the student model caused by inadequate historical knowledge preservation.
+
+| Thresholds | mAP |
| th_s = 0.4, th_t = 0.4 | 44.4 |
| th_s = 0.5, th_t = 0.5 | 42.9 |
| th_s = 0.4, th_t = 0.5 | 44.6 |
| th_s = 0.5, th_t = 0.4 | 45.5 |
+
+Table 7. Different thresholds of pseudo-labels.
+
+| # of groups | mAP |
| 1 | 41.3 |
| 2 | 45.5 |
| 3 | 44.7 |
| 4 | 44.0 |
+
+tain the robustness of the hyperparameter, linear interpolation between $\alpha_{1}$ and $\alpha_{2}$ is used to obtain group-specific $\alpha$ . For example, the parameter grouping follows $[10\%, 10\%, 80\%]$ for 3 groups, and the corresponding $\alpha$ are $[\alpha_{1}, (\alpha_{1} + \alpha_{2}) / 2, \alpha_{2}]$ .
+
+Generalization ability of AEMA. To study the generalization of AEMA, it is applied to SFDA (the same adaptation mode, different base tasks) and DAOD (the same base task, different adaptation modes). 1) Application of AEMA to SFDA. The proposed AEMA is integrated into the Mean Teacher-based TransDA [36] for SFDA. As presented in Table 9, TransDA+AEMA improves performance. 2) Application of AEMA to DAOD. As listed in Table 10, integrated MRT+AEMA increases performance. It indicates that AEMA is robust to the improvement of Mean Teacher in cross-domain learning.
+
+Qualitative visualization. The detection results are visualized to demonstrate the quality of the proposed DDT. The EMA teacher $(\alpha = 0.9996)$ is updated during DDT training. As shown in Figure 5, the EMA teacher fails to detect certain objects (cyan oval dashed boxes) due to insufficient emerging knowledge detected by the AEMA teacher and the student, while the student misses others (red oval
+
+Table 8. Effect of the number of groups.
+
+| Method | Avg |
| TransDA [36] | 83.0 |
| TransDA + AEMA | 84.2 |
+
+Table 9. Average accuracy on VisDA [22] for SFDA.
+
+| Method | mAP |
| MRT [44] | 51.2 |
| MRT + AEMA | 51.6 |
+
+Table 10. Normal to foggy adaptation in DAOD manner.
+
+dashed boxes) requiring historical consistency detected by the EMA and AEMA teachers. Our AEMA resolves this duality by balancing emerging knowledge learning and historical knowledge preservation. Therefore, the EMA teacher is capable of detecting objects that the EMA teacher and the student do not detect, exhibiting enhanced robustness in domain adaptation tasks.
+
+# 5. Conclusion
+
+To address the limitations of Exponential Moving Average (EMA) caused by domain adaptation, we propose a novel Dual-rate Dynamic Teacher (DDT) framework, equipped with an Asynchronous EMA (AEMA) updating strategy. The AEMA strategy enables asynchronous updates of teacher parameters to capture the domain change, achieving a balance between rapid adaptation to the target domain and retention of historical knowledge. In addition, the integration of knowledge between the teacher and the student captures a comprehensive domain knowledge to improve the student's optimization and teacher updating. Experimental results in three adaptation tasks validated the effectiveness of DDT, and extensive ablation studies provided deeper insight into its mechanisms, underscoring its potential for robust domain adaptation.
+
+# 6. Acknowledgement
+
+This work was supported in part by the National Natural Science Foundation of China (Grant No. 62372387), and Special Research Funding under Yibin Municipal-University Dual Agreement (No. YBSCXY2024010012, YBSCXY2024010006).
+
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+# Dual-S3D: Hierarchical Dual-Path Selective SSM-CNN for High-Fidelity Implicit Reconstruction
+
+Luoxi Zhang $^{1,*}$ , Pragyan Shrestha $^{1}$ , Yu Zhou $^{3}$ , Chun Xie $^{2}$ , Itaru Kitahara $^{2,*}$
+
+1Graduate School of Science and Technology, University of Tsukuba, Japan
+2Center for Computational Sciences, University of Tsukuba, Japan
+3Department of Data Science and Artificial Intelligence, Hong Kong Polytechnic University, China
+
+{zhang.luoxi, shrestha.pragyan, xie.chun, kitahara.itaru}@image.iit.tsukuba.ac.jp, {xie.chun, kitahara.itaru}@ccs.tsukuba.ac.jp, zy-yu.zhou@connect.polyu.hk
+
+# Abstract
+
+Single-view 3D reconstruction aims to recover the complete 3D geometry and appearance of objects from a single RGB image. Due to incomplete image information and ambiguity, this task remains challenging. Existing methods struggle with the trade-off between local detail and global topology, and with interference from early RGB-depth fusion in signed distance function optimization. To address these challenges, we propose Dual-S3D, a novel framework for single-view 3D reconstruction. Our method employs a hierarchical dual-path feature extraction strategy based on stages that utilize convolutional neural networks to anchor local geometric details. In contrast, subsequent stages leverage a Transformer integrated with selective state-space model to capture global topology, enhancing scene understanding and feature representation. Additionally, we design an auxiliary branch that progressively fuses precomputed depth features with pixel-level features to decouple visual and geometric cues effectively. Extensive experiments on the 3D-FRONT and Pix3D datasets demonstrate that our approach significantly outperforms existing methods—reducing chamfer distance by $51\%$ , increasing F-score by $33.6\%$ , and improving normal consistency by $10.3\%$ —thus achieving state-of-the-art reconstruction quality. Code is available here.
+
+# 1. Introduction
+
+The single-view 3D reconstruction aims to recover the three-dimensional geometry and appearance of a scene from a single RGB image and its corresponding camera parameters, providing critical support for applications in virtual reality [15], autonomous driving [4], robotics [24], and more.
+
+Since a single image captures only partial information, the model must reconstruct the visible regions and infer the structure of occluded areas, posing significant uncertainty and a challenge for high-fidelity reconstruction.
+
+Current mainstream approaches primarily rely on convolutional neural networks (CNNs), transformers, or statespace models (SSMs) for feature extraction, yet they face two significant issues. First, balancing local detail with global topology is challenging: conventional CNNs can capture fine local geometric features (e.g., edges and corners) [10], but their inherent local bias limits the construction of overall topology. In contrast, transformers or SSMs excel at modeling long-range dependencies [30] but often overlook fine details [25]. Naively stacking these modules can lead to feature conflicts and substantially increase computational costs. Second, many methods use the same RGB features for decoding both geometry and texture [40]. This approach allows rich texture signals in highly textured regions to interfere with geometric recovery, destabilizing signed distance function (SDF) optimization [36] and reducing reconstruction accuracy.
+
+To address these challenges, we propose Dual-S3D, a hierarchical dual-path implicit reconstruction framework that uses CNN priming for local detail and SSM-guided global fusion. Our framework takes the input image and camera pose and directly predicts the SDF values and color for each 3D point via end-to-end training. The overall architecture is divided into two main stages:
+
+In the feature encoding stage, we adopt a hierarchical dual-path feature extraction strategy based on a selective SSM [11]. The initial stages employ CNNs to capture local geometric details. In contrast, the subsequent stages use a transformer integrated with the selective SSM to capture the overall topology [20], thus enhancing the understanding of
+
+
+Figure 1. Overview of the Dual-S3D framework, showing the dual-path feature extraction architecture, selective attention module, implicit representation, and rendering network.
+
+the scene and the representation of the features. Additionally, we design an auxiliary branch that progressively fuses precomputed depth features with pixel-level features [28], effectively decoupling and integrating visual and geometric cues for different training stages. In the decoding stage, we combine a multi-layer perception (MLP) with neural radiance fields (NeRF) for implicit representation decoding, modeling volume density as a function of the SDF to jointly recover geometry and texture.
+
+Our main contributions are as follows:
+
+1. First Application of a Selective SSM-CNN Hybrid Encoding Module for Single-View 3D Reconstruction: We introduce, for the first time, a hybrid encoding module that integrates a selective SSM with CNN priming into single-view 3D reconstruction, effectively balancing local detail extraction with global topology and addressing the long-standing issue of insufficient global information capture.
+2. Dual-Branch Feature Extraction Structure: We design an auxiliary branch that progressively fuses precomputed depth and RGB features, enabling effective decoupling of visual and geometric information and significantly improving geometric recovery in high-texture regions.
+3. Outstanding Reconstruction Performance: Extensive experiments on the 3D-FRONT and Pix3D datasets demonstrate that our method significantly outperforms existing approaches in key metrics such as Chamfer distance, F-score, and NC, achieving SOTA reconstruction quality.
+
+# 2. Related Work
+
+Single-View 3D Reconstruction Techniques. Single-view 3D reconstruction is a fundamental problem in computer vision, aiming to infer the complete 3D shape of an object from a single RGB image despite inherent ambiguity due to limited viewpoints. Early methods, such as voxel grids [6, 37, 44] and graph cuts [3], leveraged geometric priors to reconstruct simple structures but faced limitations in complex scenes. Recent advances in neural implicit representations, such as Occupancy Networks [22] and NeRF [2, 23, 43], have enabled continuous, high-quality reconstructions by implicitly modeling 3D shapes through neural networks. However, these methods struggle with complex backgrounds and occlusions, reducing accuracy and detail fidelity. To improve reconstruction, various NeRF variants, like Zero123 [19], were introduced to better capture geometric details. Despite these developments, challenges persist in balancing global and local feature extraction for fine-grained reconstructions in complicated environments. Based on these insights, we propose a selective SSM to achieve efficient global and local feature extraction, enhancing accuracy and fidelity in complex scenarios.
+
+Image Feature Extraction in 3D Reconstruction. Feature extraction is crucial in single-view 3D reconstruction, directly impacting the model's ability to capture both local details and global structure. Traditional methods relying on CNNs [38], including MGN [16], LIEN [39], and InstPIFu [5], effectively capture local details through convolutional layers. However, due to the limited receptive field of CNNs, these methods struggle to capture the global context, resulting in incomplete reconstructions in occluded or complex scenes. Transformer architectures such as vi
+
+sion transformer (ViT) have been introduced to address this, providing long-range dependency modeling for improved structural understanding. Despite their ability to capture global context, Transformers are computationally expensive, with a quadratic complexity that limits scalability in high-resolution tasks. Our proposed selective SSM model leverages a linear complexity self-attention mechanism, achieving efficient global feature extraction while maintaining the accuracy for detailed reconstructions.
+
+Dual-Path vs. Single-Path Feature Extraction. Traditional single-view 3D reconstruction methods typically use a single-path architecture, where a unified network (e.g., a CNN [16, 39] or transformer [33]) extracts both geometric and texture features from the RGB image. However, this approach often fails to decouple modality-specific cues, leading to interference that degrades geometric accuracy and destabilizes SDF optimization [5]. Recent studies reveal that entangled feature learning in single-path designs can cause modality competition, especially under occlusions or textureless regions [42]. In contrast, dual-path architectures—demonstrated in cross-modal fusion for scene understanding and RGB-D reconstruction—process different modalities separately before fusion. This paradigm aligns with findings in monocular 3D detection [26], where decoupled depth and semantic branches improve geometric reasoning. Motivated by these successes, we adopt a dual-path strategy in which one branch extracts high-level semantic features from the RGB image. At the same time, an auxiliary path processes precomputed depth and pixel-level cues. The multi-modal feature decoupling theory in [1] further supports the design, showing that separated pathways reduce cross-modal noise. This approach effectively mitigates interference, yielding more robust and precise 3D reconstructions.
+
+# 3. Method
+
+In this section, we introduce the details of the proposed Dual-S3D framework, which is designed to achieve high-fidelity implicit reconstruction by effectively capturing fine local details and global structure. Dual-S3D consists of an overall architecture, a main feature extraction module, an auxiliary path for feature extraction and training strategy, a point sampling and volume rendering strategy, an implicit plus rendering network decoder, and a multi-stage training strategy with comprehensive loss functions. Each subsection begins with a brief description to clarify its role in the overall 3D reconstruction task.
+
+# 3.1. Framework Overview
+
+As illustrated in Fig. 1, Dual-S3D takes a single-view image, camera pose, and 2D and 3D bounding boxes as input. Combined with volume rendering, it directly predicts SDF values and colors for each 3D point via end-to-end training,
+
+
+Figure 2. Selective mixer module overview.
+
+enabling high-fidelity implicit reconstruction. The overall pipeline is divided into two main stages:
+
+Feature Encoding Stage: We adopt a hierarchical dualpath feature extraction strategy guided by selective statespace models. The main branch integrates a CNN with an SSM module to capture both local geometric details and global topological structure. Meanwhile, an auxiliary path processes precomputed depth features alongside pixel-level cues, aligning them with the input image and dynamically fusing them with RGB features to effectively decouple visual and geometric information.
+
+Decoding Stage: An MLP combined with NeRF-inspired techniques decodes the encoded features into an implicit representation. In this stage, the volume density is modeled as an SDF-related function, and volume rendering is applied to recover view-dependent colors.
+
+Additionally, we design a point sampling update strategy that refines the distribution of sampled points near object surfaces through SDF evaluation, error quantification, $\beta$ -adjustment, and probability density function/cumulative distribution function (PDF/CDF)-based resampling. Furthermore, an Eikonal loss is incorporated to explicitly constrain the gradients of the SDF, thereby enhancing reconstruction accuracy.
+
+# 3.2. Primary Path Feature Extraction
+
+The primary path feature extraction module is designed to capture fine local details and the overall structural context from the input image, thereby providing a robust foundation for 3D reconstruction. Initially, a CNN processes the input image to perform downsampling and convolution, extracting low-level features $F_{\mathrm{low}}$ that capture local geometric cues such as edges and corners. These features are subsequently partitioned into multiple local windows $\{W_i\}_{i=1}^N$ to enable localized processing.
+
+Initially, a CNN processes the input image to perform downsampling and convolution, extracting low-level features $F_{\mathrm{low}}$ that capture local geometric cues such as edges and corners. This CNN consists of stacked residual convolutional blocks (ConvBlock), where each block includes two consecutive $3\times 3$ convolutions with batch normalization
+
+tion (BN) and GELU activation:
+
+$$
+X ^ {\prime} = \operatorname {G E L U} (\mathrm {B N} (\operatorname {C o n v} _ {3 \times 3} (X))), \tag {1}
+$$
+
+$$
+F _ {\text {l o w}} = X + \lambda \cdot \operatorname {B N} \left(\operatorname {C o n v} _ {3 \times 3} \left(X ^ {\prime}\right)\right), \tag {2}
+$$
+
+where $\lambda$ is a learnable scaling factor to stabilize training. Residual connections are incorporated to preserve spatial information, and optional DropPath regularization enhances generalization. This hierarchical convolutional encoding establishes a strong feature representation basis for subsequent feature processing.
+
+Within each window, the features $X \in \mathbb{R}^{B \times L \times D}$ are first projected to an inner dimension $D_{\mathrm{inner}}$ using a linear layer. This projection is formulated as
+
+$$
+X _ {\text {i n n e r}} = \operatorname {L i n e a r} (X) \in \mathbb {R} ^ {B \times L \times D _ {\text {i n n e r}}}, \tag {3}
+$$
+
+and the resulting tensor is split along the channel dimension:
+
+$$
+\left[ X _ {a}, X _ {b} \right] = \operatorname {S p l i t} \left(X _ {\text {i n n e r}}\right). \tag {4}
+$$
+
+where $\mathrm{Split}(\cdot)$ is the split operation. The branch $X_{a}$ is then processed with a 1D convolution to capture local continuity and is subsequently fed into the selective SSM function:
+
+$$
+Y _ {a} = \mathcal {S} \left(X _ {a}, d t, A, B, C, D\right), \tag {5}
+$$
+
+where $S(\cdot)$ is selective scan function; $dt$ and $A, B, C, D$ are the parameters governing the state-space dynamics [12]. In contrast, $X_{b}$ retains the unaltered local features. The outputs from both branches are concatenated and then mapped back to the original feature dimension:
+
+$$
+Y = \operatorname {L i n e a r} \left(\operatorname {c o n c a t} \left(Y _ {a}, X _ {b}\right)\right) \in \mathbb {R} ^ {B \times L \times D}. \tag {6}
+$$
+
+Algorithm 1 provides the pseudocode for the SSSM mixer module.
+
+Subsequently, a series of Transformer blocks is applied to the windowed features to perform global feature fusion via self-attention. This facilitates cross-window information exchange and reinforces overall topology modeling. Finally, a window reverse operation reassembles the processed local windows into a complete feature map. This integrated design preserves fine local details while incorporating global context, ensuring accurate geometric recovery and structural consistency.
+
+# 3.3. Auxiliary Path for Feature Extraction
+
+We introduce an auxiliary path dedicated to processing depth information to mitigate the interference that occurs when RGB features are directly used for geometry and texture decoding. This branch extracts high-resolution depth priors and aligns them with the input image at the 2D pixel level.
+
+Algorithm 1 Selective SSM Mixer Module
+Require: Input feature tensor $\mathbf{X}\in \mathbb{R}^{B\times L\times D}$
+Ensure: Enhanced feature tensor $\mathbf{Y}\in \mathbb{R}^{B\times L\times D}$
+1: $\mathbf{X}_{\mathrm{inner}}\gets \mathrm{Linear}(\mathbf{X})$ {Project to $D_{\mathrm{inner}}$ }
+2: $[\mathbf{X}_a,\mathbf{X}_b]\gets \mathrm{split}(\mathbf{X}_{\mathrm{inner}})$ {Channel splitting}
+3: $\mathbf{X}_a^{\mathrm{conv}}\gets \mathrm{Conv1D}(\mathbf{X}_a)$ {Local continuity modeling}
+4: $\Delta \gets \mathrm{dt\_proj}(\mathbf{X}_a^{\mathrm{conv}})$ {Time step projection}
+5: $\mathbf{Y}_a\gets S(\mathbf{X}_a^{\mathrm{conv}},\Delta ,\mathbf{A},\mathbf{B},\mathbf{C},\mathbf{D})$
+6: $\mathbf{Y}\gets \mathrm{Linear}(\mathrm{concat}(\mathbf{Y}_a,\mathbf{X}_b))$ {Feature fusion}
+7: return Y
+
+Mathematical Formulation: Let $uv \in \mathbb{R}^{B \times N_{uv} \times 2}$ denote the 2D image coordinates. Given an image size $(W, H)$ , we define a scaling factor:
+
+$$
+s _ {c} = \frac {s}{(W , H)}, \tag {7}
+$$
+
+where $s$ is a predefined constant (corresponding to latent_scaling). The normalized coordinates are computed as:
+
+$$
+u v ^ {\prime} = u v \times s _ {c} - 1. \tag {8}
+$$
+
+When the auxiliary path is active, a pretrained depth network extracts the depth prior:
+
+$$
+\mathbf {Z} = \mathcal {F} _ {\theta} (I) \in \mathbb {R} ^ {B \times C \times H ^ {\prime} \times W ^ {\prime}}, \tag {9}
+$$
+
+with $H' = H / s$ and $W' = W / s$ . In the color stage, the depth features are fused with the primary branch's RGB features $\mathbf{F}_{\mathrm{low}} \in \mathbb{R}^{B \times C \times H' \times W'}$ :
+
+$$
+\mathbf {M} = \alpha \odot \mathbf {Z} + (1 - \alpha) \odot \mathbf {F} _ {\text {l o w}}, \tag {10}
+$$
+
+where $w_{\alpha}\in \mathbb{R}$ is a learnable scalar, and $\odot$ denotes elementwise multiplication. Finally, pixel-aligned features $\mathbf{S}$ is obtained using a grid-sampling operation $\mathcal{G}$ ,
+
+$$
+\mathbf {S} = \mathcal {G} (\mathbf {M}, u v ^ {\prime}), \tag {11}
+$$
+
+we obtain pixel-aligned features with shape $(B,C,N_{uv})$
+
+This auxiliary path, through coordinate alignment and dynamic feature fusion from Eq. 7, 9, 8, 10, 11, effectively decouples and integrates visual and geometric cues, significantly improving geometric recovery in high-texture regions. For a detailed pseudocode of the feature extraction process in this branch, please refer to Algorithm 2.
+
+# 3.4. Point Sampling and Volume Rendering
+
+High-fidelity reconstruction relies on precise 3D point sampling. For each camera ray, we first uniformly sample $N$ points $\{z_i\}_{i=1}^N$ along the depth range, applying random perturbations during training to enhance robustness. These sampled points are then mapped to the object coordinate system and evaluated with an implicit network to obtain
+
+Algorithm 2 Auxiliary Path Feature Extraction
+Require: Normalized coordinates $uv\in \mathbb{R}^{B\times N_{uv}\times 2}$ , input image
+1
+2: if Auxiliary path is enabled and in color stage then
+3: $\alpha \leftarrow \sigma (w_{\alpha})$ {Compute dynamic fusion weight}
+4: $\mathbf{M}\gets \alpha \odot \mathbf{D} + (1 - \alpha)\odot \mathbf{F}$
+5: else
+6: M $\leftarrow$ D
+7: end if
+8: $uv^{\prime}\gets uv\times \frac{s}{(W,H)} -1$ {Normalize coordinates}
+9: S $\leftarrow \mathcal{G}(\mathbf{M},uv^{\prime})$ {Bilinear interpolation}
+10: return S
+
+their SDF values, where $f(\mathbf{x}) \approx 0$ indicates proximity to the object surface.
+
+To convert the SDF values into volume densities, we employ a Laplace density function:
+
+$$
+\rho (\mathbf {x}) = \exp \left(- \frac {| f (\mathbf {x}) |}{\beta}\right), \tag {12}
+$$
+
+where $\beta$ is a parameter controlling the rate of density decay. Given the distance $\delta$ between adjacent samples, the opacity $\alpha$ , which denotes the probability of ray absorption in the interval, is computed as
+
+$$
+\alpha = 1 - \exp \left(- \rho (\mathbf {x}) \delta\right), \tag {13}
+$$
+
+Finally, the pixel color $C$ is obtained by accumulating the contributions of each sample along the ray:
+
+$$
+C = \sum_ {i = 1} ^ {N} T _ {i} \alpha_ {i} c _ {i}, \quad \text {w h e r e} \quad T _ {i} = \prod_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j}\right). \tag {14}
+$$
+
+Here, $c_{i}$ denotes the color at the $i$ th sample, and $T_{i}$ is the accumulated transmittance from the ray's origin to the $i$ th sample, reflecting the probability that the ray reaches that sample without being occluded.
+
+To adaptively refine the sampling density, we construct a PDF from $\alpha$ and derive the corresponding CDF. Inverse transform sampling is then applied to insert additional points near the object surface, updating the original sample set. This strategy enhances the accuracy of SDF prediction while enabling view-dependent color recovery.
+
+# 3.5. Implicit and Rendering Network Decoding
+
+In the decoding stage, we employ an MLP combined with NeRF-inspired techniques to decode the encoded features:
+
+Implicit Network: The encoded features are mapped to SDF values $f(\mathbf{x})$ for each 3D point. These SDF values are then converted to volume densities $\rho(\mathbf{x})$ using the density function described above.
+
+Rendering Network: Implemented as an MLP, this network takes position-encoded view direction information and the implicit features to predict the color $c(\mathbf{x})$ of each sample.
+
+Volume Rendering: Using the formulas described in the point sampling section, $\alpha$ and transmittance are computed for each sample, and the weighted sum of colors produces the final pixel color.
+
+# 3.6. Training Strategy and Loss Functions
+
+To mitigate interference between geometry and texture decoding, we adopt a multi-stage training strategy:
+
+Early Stage: The model primarily relies on precomputed depth features for geometry reconstruction, reducing the negative impact of rich RGB texture information on SDF optimization.
+
+Later Stage: RGB features are gradually introduced and dynamically fused with depth features via learnable weights, promoting joint optimization of geometry and texture.
+
+The overall loss function is defined as:
+
+$$
+\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\mathrm {s d f}} + \lambda_ {2} \mathcal {L} _ {\text {n o r m a l}} + \lambda_ {3} \mathcal {L} _ {\text {d e p t h}} + \lambda_ {4} \mathcal {L} _ {\text {c o l o r}} + \lambda_ {5} \mathcal {L} _ {\text {e i k}}, \tag {15}
+$$
+
+where $\mathcal{L}_{\mathrm{sdf}}$ , $\mathcal{L}_{\mathrm{normal}}$ , and $\mathcal{L}_{\mathrm{depth}}$ correspond to the reconstruction quality, normal consistency (NC) accuracy, and depth accuracy losses, respectively. In the texture training stage, $\mathcal{L}_{\mathrm{color}}$ evaluates the texture quality, and $\mathcal{L}_{\mathrm{eik}}$ enforces SDF smoothness. The weights $\lambda_{i}$ are dynamically adjusted following a curriculum schedule, which balances these terms to ensure stable convergence and high-precision reconstruction.
+
+# 4. Experiment
+
+# 4.1. Experimental Setup
+
+Dataset. We evaluate our approach on two datasets: the synthetic 3D-FRONT dataset [9] and the real-world Pix3D dataset [31]. 3D-FRONT contains 29,659 indoor scene images split as in [17] (74.52% training, 16.88% testing, 8.6% validation), while Pix3D comprises 10,026 images (6,931 for training, 2,778 for validation, and 2,762 for testing). This blend of synthetic and real-world data ensures a robust evaluation of our framework.
+
+Training Settings. Experiments were run on a single NVIDIA H100 GPU (batch size30) using PyTorch on Ubuntu 22.04. We trained the model for 200 epochs with an initial learning rate of 6e-5, reduced to 1e-5 at epoch 120 via StepLR, ensuring efficient memory use and stable convergence.
+
+Evaluation Metrics. To evaluate the model's performance, we employed several metrics: CD [8], F-Score [14], Peak Signal-to-Noise Ratio (PSNR) [32], Intersection over Union (IoU) [29], and NC [21, 34].
+
+
+
+
+
+
+
+
+
+
+Input image
+
+
+
+
+
+
+
+
+
+
+MGN
+
+
+
+
+
+
+
+
+
+
+LIEN
+
+
+
+
+
+
+
+
+
+
+InstPIFu
+
+
+
+
+
+
+
+
+
+
+SSR
+
+
+
+
+
+
+
+
+
+
+Ours
+
+
+
+
+
+
+
+
+
+
+Figure 3. Qualitative results of indoor object reconstruction are shown, with 3D-FRONT [9] samples in the top three rows and Pix3D samples in the bottom two. Our model generates smoother surfaces and finer details than previous methods.
+
+
+
+
+
+
+
+
+
+
+Oursmesh
+GT
+
+# 4.2. Experiment Results
+
+Efficiency Comparison. To evaluate computational efficiency, we replace our SSM Mix module with a standard ViT Base under identical settings (input resolution [32,32], 512 channels, 15 hidden layers, 1024-dimensional embeddings) and measure on an NVIDIA 3090 GPU over 2,000 test samples. FLOPs, parameter count and inference time are summarized in Table 1, demonstrating our model's clear efficiency gains over ViT based modules.
+
+Table 1. Efficiency comparison on a single NVIDIA 3090 GPU.
+
+| Encoder | FLOPs (G) ↓ | Params ↓ | Infer_time(s) ↓ |
| ViT Base | 1,136.5G | 292.0M | 3.51 |
| Ours | 669.8G (↓ 41.1%) | 191.1M (↓ 34.5%) | 1.52 |
+
+Table 2. Evaluation of object reconstruction on the 3D-FRONT dataset [9].
+
+| Metrics | Models | bed | chair | sofa | table | desk | nightstand | cabinet | bookshelf | mean |
| CD↓ (51.0%) | MGN [16] | 15.48 | 11.67 | 8.72 | 20.90 | 17.59 | 17.11 | 13.13 | 10.21 | 14.07 |
| LIEN [39] | 16.81 | 41.40 | 9.51 | 35.65 | 26.63 | 16.78 | 11.70 | 11.70 | 28.52 |
| InstPIFu [5] | 18.17 | 14.06 | 7.66 | 23.25 | 33.33 | 11.73 | 6.04 | 8.03 | 14.46 |
| SSR [35] | 4.96 | 10.52 | 4.53 | 16.12 | 25.86 | 17.90 | 6.79 | 3.89 | 10.45 |
| Dual-S3D (ours) | 3.68 | 5.94 | 3.45 | 10.20 | 28.23 | 9.10 | 5.00 | 5.45 | 6.60 |
| F-Score ↑ (33.6%) | MGN [16] | 46.81 | 57.49 | 64.61 | 49.80 | 46.82 | 47.91 | 54.18 | 54.55 | 55.64 |
| LIEN [39] | 44.28 | 31.61 | 61.40 | 43.22 | 37.04 | 50.76 | 69.21 | 55.33 | 45.63 |
| InstPIFu [5] | 47.85 | 59.08 | 67.60 | 56.43 | 48.49 | 57.14 | 73.32 | 66.13 | 61.32 |
| SSR [35] | 76.34 | 69.17 | 80.06 | 67.29 | 47.12 | 58.48 | 70.45 | 85.93 | 71.36 |
| Dual-S3D (ours) | 82.63 | 82.00 | 85.24 | 77.53 | 48.84 | 71.44 | 78.00 | 81.66 | 80.85 |
| NC ↑ (10.3%) | MGN [16] | 0.829 | 0.758 | 0.819 | 0.785 | 0.711 | 0.833 | 0.802 | 0.719 | 0.787 |
| LIEN [39] | 0.822 | 0.793 | 0.803 | 0.755 | 0.701 | 0.814 | 0.801 | 0.747 | 0.786 |
| InstPIFu [5] | 0.799 | 0.782 | 0.846 | 0.804 | 0.708 | 0.844 | 0.841 | 0.790 | 0.810 |
| SSR [35] | 0.896 | 0.833 | 0.894 | 0.838 | 0.764 | 0.897 | 0.856 | 0.862 | 0.854 |
| Dual-S3D (ours) | 0.933 | 0.900 | 0.921 | 0.886 | 0.780 | 0.936 | 0.878 | 0.842 | 0.901 |
+
+Geometric and Quantitative Evaluation. Quantitative re
+
+Table 3. Evaluation of object reconstruction on the Pix3D dataset [31].
+
+| Metrics | Methods | bed | bookcase | chair | desk | sofa | table | tool | wardrobe | misc | mean |
| CD↓ (8.68%) | MGN | 22.91 | 33.61 | 56.47 | 33.95 | 9.27 | 81.19 | 94.70 | 10.43 | 137.50 | 44.32 |
| LIEN | 11.18 | 29.61 | 40.01 | 65.36 | 10.54 | 146.13 | 29.63 | 4.88 | 144.06 | 51.31 |
| InstPIFu | 10.90 | 7.55 | 32.44 | 22.09 | 8.13 | 45.82 | 10.29 | 1.29 | 47.31 | 24.65 |
| SSR | 6.31 | 7.21 | 26.23 | 28.63 | 5.68 | 43.87 | 8.29 | 2.07 | 35.03 | 21.79 |
| Dual-S3D (ours) | 4.38 | 6.69 | 27.35 | 23.84 | 5.04 | 34.14 | 11.37 | 1.89 | 38.09 | 19.90 |
| F-Score ↑ (9.91%) | MGN | 34.69 | 28.42 | 35.67 | 65.36 | 51.15 | 17.05 | 57.16 | 52.04 | 10.41 | 36.20 |
| LIEN | 37.13 | 15.51 | 25.70 | 26.01 | 49.71 | 21.16 | 5.85 | 59.46 | 11.04 | 31.45 |
| InstPIFu | 54.99 | 62.26 | 35.30 | 47.30 | 56.54 | 37.51 | 64.24 | 94.62 | 27.03 | 45.62 |
| SSR | 68.78 | 66.69 | 55.18 | 42.49 | 71.22 | 51.93 | 65.38 | 91.84 | 46.92 | 59.71 |
| Dual-S3D (ours) | 75.04 | 66.96 | 59.28 | 45.43 | 75.03 | 57.67 | 61.91 | 93.62 | 48.40 | 63.70 |
| NC ↑ (12.6%) | MGN | 0.737 | 0.592 | 0.525 | 0.633 | 0.756 | 0.794 | 0.531 | 0.809 | 0.563 | 0.659 |
| LIEN | 0.706 | 0.514 | 0.591 | 0.581 | 0.775 | 0.619 | 0.506 | 0.844 | 0.481 | 0.646 |
| InstPIFu | 54.99 | 62.26 | 35.30 | 47.30 | 56.54 | 37.51 | 64.24 | 94.62 | 27.03 | 6.83 |
| SSR | 0.825 | 0.689 | 0.693 | 0.776 | 0.866 | 0.835 | 0.645 | 0.960 | 0.599 | 0.778 |
| Dual-S3D (ours) | 0.826 | 0.712 | 0.710 | 0.814 | 0.911 | 0.861 | 0.701 | 0.968 | 0.673 | 0.806 |
+
+Table 4. Results on Pix3D by using training on 3D-FRONT.
+
+| Methods | CD ↓ | F-Score ↑ | PSNR ↑ | IoU ↑ | NC ↑ |
| InstPIFU | 33.71(+9.06) | 38.23(-7.39) | 16.77(-6.11) | 0.309(-0.081) | 0.511(-0.172) |
| SSR | 29.55(+7.76) | 41.17(-18.58) | 18.79(-6.38) | 0.332(-0.047) | 0.626(-0.164) |
| Dual-S3D(ours) | 25.32(+5.4) | 49.43(-14.27) | 22.41(-3.75) | 0.353(-0.071) | 0.667(-0.139) |
+
+sults (Tables 2 and 3) combined with qualitative comparisons (Figure 3) clearly demonstrate that Dual-S3D significantly outperforms several SOTA implicit reconstruction methods [5, 16, 35, 41] that rely primarily on learning implicit fields via volumetric rendering losses. These implicit methods consistently yield better smoothness, completeness, and detail fidelity compared to traditional approaches. Recently, other approaches such as PushNet [27] adopt fundamentally different paradigms, predicting sparse point clouds via push-pull refinement supervised by CD losses. Due to substantial differences in input modalities, supervision mechanisms and output formats, a direct fair compar-
+
+
+Figure 4. Multi-angle visualization of reconstructed normal maps for objects from $-90^{\circ}$ to $90^{\circ}$ .
+
+
+Figure 5. Fully rendered scene compositions integrating both geometry and texture. The results showcase visually realistic reconstructions with high fidelity in texture and geometry.
+
+son is challenging and beyond the current scope. Therefore, we did not include those methods like PushNet [27] in the quantitative benchmarks presented here.
+
+To further assess robustness and portability, we directly apply the model trained on 3D-FRONT to Pix3D for inference and evaluation; as shown in Table 5, our method still outperforms SSR [35] and InstPIFU [5], highlighting the potent portability of the Dual-S3D model.
+
+In Table 5, we compare our method with Zero-1-to-3 [19] and Shape-E [13], which also utilize large-scale pretrained priors for 3D reconstruction. The results show that Dual-S3D outperforms these baselines regarding CD, F-Score, and NC metrics, indicating higher reconstruction fidelity. This suggests that among methods relying on pretrained priors, our Dual-S3D framework more effectively captures shape and texture details with greater precision and consistency compared to Zero-1-to-3's [19] diffusion-based 2D priors and Shape-E's [13] textured mesh generation.
+
+Muti-View and Scene Reconstruction. We further illustrate our reconstruction results with extensive visualizations in our supplementary material. Additionally, we obtain multi-view scene reconstructions by reassembling scenes based on a known world coordinate system, as shown in Figure 5. Figure 4 also presents additional viewpoints of the reconstructed objects, clearly demonstrating the enhanced smoothness and consistency of the geometric structures.
+
+Experiments Analysis. A critical component contributing to superior performance is integrating the Selective SSM mechanism [7]. This mechanism employs a selective scanning operation to adapt to input features dynamically, filtering out irrelevant information while capturing essential
+
+Table 5. Quantitative comparison of our model with Zero-1-to-3 [19] and Shape-E [13] on CD, F-Score, and NC metrics.
+
+| Methods | CD | F-Score | NC |
| Zero-1-to-3 [19] | 39.27 | 30.07 | 0.624 |
| Shape-E [13] | 29.16 | 39.86 | 0.686 |
| Dual-S3D (ours) | 6.60 | 80.85 | 0.901 |
+
+
+Figure 6. The SDF loss convergence on the validation set for Ablation Experiment 1, 2, and our Dual-S3D method.
+
+contextual dependencies. Consequently, spatial consistency and noise robustness are enhanced, resulting in smoother surfaces and an average improvement of $11.45\%$ in the NC metric. As a result, our model yields 3D reconstructions with fewer artifacts and greater visual coherence.
+
+In addition, the dual-path architecture of Dual-S3D leverages an auxiliary path to decouple the focus between geometric and RGB reconstructions, thereby reducing the interference of color information during early training stages. This design leads to more accurate feature extraction and improved reconstruction outcomes. Overall, experimental results demonstrate that Dual-S3D achieves SOTA performance on both the 3D-FRONT [9] and Pix3D [31] datasets, with each module contributing significantly to reconstruction accuracy, structural completeness, and surface smoothness.
+
+# 5. Ablation Experiments
+
+We conduct three ablation experiments to investigate the impact of our auxiliary path, multi-stage training strategy, and texture finetuning stage on the final 3D reconstruction performance. All metrics are compared with our complete Dual-S3D model.
+
+# 5.1. Ablation Setup
+
+We define three experimental configurations:
+
+- Exp 1 (No Auxiliary Path): The auxiliary path is removed entirely, leaving only the primary RGB path for reconstruction. This experiment tests the role of decoupling geometry and color features via a secondary branch.
+
+
+Figure 7. Qualitative comparison of texture reconstruction. The first row shows the results of Ablation Experiment 3, while the second row presents the visualization results of Dual-S3D.
+
+Table 6. Evaluation results for ablation experiments compared with our Dual-S3D model.
+
+| Configuration | CD | F-Score | PSNR | IoU | NC |
| Exp 1 (No Auxiliary Path) | 9.48 | 75.87 | 29.23 | 0.561 | 0.880 |
| Exp 2 (Single-Stage Training) | 9.91 | 75.36 | 28.85 | 0.561 | 0.871 |
| Exp 3 (No Texture Finturn Stage) | 6.87 | 80.3 | 29.99 | 0.607 | 0.907 |
| Full Model (Dual-S3D) | 6.60 | 80.85 | 30.04 | 0.612 | 0.900 |
+
+- Exp 2 (Single-Stage Training): The multi-stage strategy (SDF then color) is disabled, so geometry and texture features are learned jointly from the beginning. This setup assesses whether simultaneously introducing RGB and depth features hinders convergence.
+- Exp 3 (No Texture Finetune Stage): The depth prior is still used to guide geometry reconstruction, but shallow RGB features are not integrated in the subsequent texture finetuning phase. This experiment examines the contribution of additional RGB feature refinement for texture quality.
+
+# 5.2. Ablation Results
+
+Table 6 compares the results of our three ablation experiments with the full Dual-S3D model. For Exp 1 and Exp 2, the geometry metrics show a notable drop, indicating that removing the auxiliary path or training geometry and color simultaneously can significantly degrade shape accuracy. In contrast, Exp 3 achieves geometry metrics comparable to the whole model, suggesting that omitting the final texture finetuning stage has minimal impact on the structural reconstruction. However, as shown in Figure 7, Exp 3's texture appears coarse, lacking fine pixel-level detail. To better quantify these differences, we evaluated SSIM and LPIPS on 1,250 test samples (8 categories), including comparisons to recent methods One-2-3-45 [18] and Zero-123 [19]. Results in Table 7 demonstrate that our complete model achieves the highest SSIM and good LPIPS, confirming its superior texture fidelity.
+
+# 5.3. Ablation Analysis
+
+We further illustrate the convergence of SDF loss in Figure 6 for Exp 1, Exp 2, and the full Dual-S3D. In Exp 2
+
+Table 7. Texture metrics (SSIM, LPIPS) on 1,250 test samples.
+
+| Method | Ours | Abl. Exp3 | One-2-3-45 | Zero-123 |
| SSIM ↑ | 0.83 | 0.61 | 0.76 | 0.78 |
| LPIPS ↓ | 0.14 | 0.28 | 0.25 | 0.12 |
+
+(Single-Stage Training), introducing geometry and color from the outset causes interference between RGB and depth features, which slows down and impairs the model's geometric learning, reflected in a higher SDF loss curve. Exp 1 (No Auxiliary Path) also hinders convergence because features inevitably overlap and degrade reconstruction quality without a dedicated branch to handle geometry or color.
+
+Regarding Exp 3, Figure 7 shows that while geometry remains intact mainly—thanks to the continued use of the depth prior—texture details are lost, manifesting as large color patches rather than fine-grained texture patterns. This outcome highlights the importance of incorporating shallow RGB features during the finetuning phase for improved texture fidelity.
+
+In general, these findings confirm the following.
+
+- The auxiliary path is crucial for decoupling geometric and RGB features, thus avoiding early interference and preserving fine structural details.
+- The multi-stage training strategy stabilizes convergence by separating geometry optimization from texture learning.
+- The texture finetuning stage leverages shallow RGB features to refine color details, contributing to a more realistic and visually coherent 3D reconstruction.
+
+# 6. Conclusion
+
+We presented Dual-S3D, a single-view 3D reconstruction framework that leverages multi-stage training and an auxiliary path to address shortcomings in local geometry and global topology extraction. Experiments on the 3D-FRONT and Pix3D datasets demonstrate that Dual-S3D significantly outperforms current methods in key metrics, including CD, F-Score, and NC. Ablation studies further validate that our dual-path design and staged training effectively mitigate early RGB-depth coupling, resulting in more stable and high-fidelity reconstructions.
+
+However, our model's performance declines when evaluated on real-world datasets with limited data (e.g., Pix3D), underscoring the critical impact of data scale and realism on single-view 3D reconstruction. We will explore semi-supervised and self-supervised training schemes to enhance model generalization and accuracy under scarce data conditions. We believe these advancements will open new opportunities for applications in virtual reality, autonomous driving, and other areas with stringent 3D reconstruction requirements.
+
+Acknowledgment. This achievement was supported by JST SPRING, Grant Number JPMJSP2124, and received partial funding from the JSPS Grant-in-Aid for Scientific Research (Grant Number 25K03146). This work was supported by MEXT Promotion of Development of a Joint Usage/Research System Project: Coalition of Universities for Research Excellence Program (CURE) Grant Number JP-MXP1323015474.
+
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+# Dual-Temporal Exemplar Representation Network for Video Semantic Segmentation
+
+Xiaolong Xu $^{1}$ , Lei Zhang $^{1,2*}$ , Jiayi Li $^{1}$ , Lituan Wang $^{1}$ , Yifan Guan $^{1}$ , Yu Yan $^{1}$ , Leyi Zhang $^{1}$ , Hao Song $^{1}$ , Sichuan University, Tianfu Jincheng Laboratory
+
+xilo@stu.scu.edu.cn, leizhang@scu.edu.cn
+
+# Abstract
+
+Video semantic segmentation aims to assign a class label for each pixel in every video frame. Existing methods predominantly follow the reference-target interaction paradigm, focusing on extracting local temporal contexts while neglecting the integration of global temporal information. Moreover, complex dynamics and varying lighting conditions introduce inter-frame intra-class discrepancies in feature representations, leading to unstable predictions. In this paper, we propose a novel framework, the Dual-Temporal Exemplar Representation Network (DTERN), which utilizes the strong representational capability of cluster centers, i.e., exemplars, to effectively model both local and global temporal information. DTERN consists of two core modules: 1) the Local Temporal Exemplar Module (LTEM), which constructs local exemplars to capture local temporal contexts, ensuring stable and reliable predictions. 2) the Global Temporal Exemplar Module (GTEM), which introduces learnable global exemplars to dynamically model global temporal information, thereby improving the effective consistency of segmentation. Furthermore, we observe that the existing Video Consistency (VC) metric fails to evaluate segmentation accuracy and lacks sensitivity to small-object segmentation. To this end, we propose Video Effective Consistency (VEC) to comprehensively evaluate temporal consistency and segmentation effectiveness. Experiments on VSPW and Cityscape demonstrate that DTERN outperforms state-of-the-art methods. The code is available at https://github.com/zlxilo/DTERN.
+
+# 1. Introduction
+
+Video semantic segmentation (VSS) involves assigning semantic labels to all pixels in a video. The core of VSS lies in effectively leveraging temporal information. Existing methods mainly focus on modeling the temporal rela
+
+
+Figure 1. Comparison of existing VSS methods with DTERN. (a) Approaches using the reference-target interaction paradigm model only the local temporal information. (b) CFFM++ further models global temporal information by constructing non-learnable global exemplars. (c) DTERN models both local and global temporal information by constructs learnable exemplars.
+
+tionship between reference and target frames through the reference-target interaction paradigm (Fig. 1a).
+
+Most of the existing VSS methods rely on optical flow to capture temporal relationships. Typically, optical flow is extracted by dedicated networks [7, 16] to warp the reference frame features into alignment with the target frame features, followed by a simple aggregation process [9, 14, 25, 35, 47]. Additionally, recent research [18, 31, 34, 41] has introduced the self-attention mechanism to model interactions between frames, enabling the target frame to be dynamically updated based on the reference frames. Meanwhile, researchers have explored approaches to achieve efficient and stable video semantic segmentation by reusing frame
+
+features [1, 21, 29] and improving reference frame selection strategies [38]. However, the above methods mainly focus on extracting local temporal contexts, while the utilization of global temporal information remains insufficient. To mine global temporal contexts, CFFM++ [33] constructs non-learnable global exemplars through a pre-trained encoder to model global temporal information, further improving segmentation performance (Fig. 1b). Nevertheless, CFFM++ is a multi-stage training framework that increases the training burden, while the effectiveness of the global temporal context mining with non-learnable exemplars is constrained by the performance of the pre-trained encoder. Moreover, these works fail to address the inter-frame intraclass discrepancies caused by complex factors such as lighting and occlusion, resulting in unstable predictions.
+
+To address the above issues, we propose DTERN, which adopts a new interaction paradigm (Fig. 1c) that leverages the strong representational capability of cluster centers to model both local and global temporal information. Specifically, DTERN consists of two core modules: the Local Temporal Exemplar Module (LTEM) and the Global Temporal Exemplar Module (GTEM). The sequential LTEMs progressively enhance the target frame features, with each LTEM constructing local exemplars to model local temporal information. To achieve this, a Selection and Aggregation Module is designed to selectively construct and adaptively aggregate cluster centers, generating local exemplars within each LTEM, thereby mitigating prediction instability. Furthermore, to dynamically capture high-quality spatial and semantic information from each input frame, a Cluster Assignment Module is proposed to simulate the cluster assignment process. In GTEM, learnable tokens representing frame-level cluster centers (FCC) and video-level cluster centers (VCC) are introduced. During training, VCC progressively aggregates local temporal context from the updated target frame features to derive global temporal information, which is then used to further update the target frame features, improving the effective consistency of segmentation. Furthermore, we introduce the Video Effective Consistency (VEC) to address the limitations of the Video Consistency (VC) metric, which fails to evaluate segmentation accuracy and exhibits insufficient sensitivity to small-object segmentation.
+
+In summary, our work has the following main contributions:
+
+- To exploit temporal information and mitigate unstable predictions caused by inter-frame intra-class discrepancies, we propose DTERN to learn local and global temporal information by leveraging the strong representational capability of cluster centers.
+- We propose Video Effective Consistency (VEC), a novel evaluation metric for video semantic segmentation. This dual-focus metric simultaneously assesses temporal con
+
+sistency and segmentation effectiveness.
+
+- We evaluate DTERN on the large-scale video semantic segmentation datasets VSPW and Cityscapes. DTERN outperforms several state-of-the-art methods.
+
+# 2. Related Work
+
+# 2.1. Image Semantic Segmentation
+
+Image semantic segmentation is a core computer vision task that assigns semantic labels to every pixel in an image. While traditional methods relied on handcrafted features and shallow models, significant advancements in this field have been driven by Convolutional Neural Networks. Modern approaches [2, 3, 8, 12, 13, 15, 23, 26, 28, 42, 46, 48] leverage end-to-end deep neural networks for efficient scene segmentation and have achieved remarkable success. However, video data is more common in real-world scenarios, which has led to increasing research attention on VSS.
+
+# 2.2. Video Semantic Segmentation
+
+VSS performs pixel-level classification for each frame. Current approaches mainly model temporal relationships between reference and target frames, utilizing local temporal information to improve segmentation performance.
+
+VSS approaches mostly utilize optical flow to capture temporal information. Specifically, NetWarp [9] and STTGU [25] employ feature warping to align features from reference frames to the target frame via optical flow and fuse them with the target frame features. ETC [22] uses optical flow to align the segmentation results of the reference and target frames and employs a temporal loss function to enforce consistency constraints. DFF [47] and Accel [17] propagate features from reference frames to the target frame via optical flow, reducing computational costs. Researchers also utilize self-attention mechanisms to model temporal information. Specifically, CFFM [31] introduces a coarse-to-fine feature mining method that learn both static and dynamic contextual information simultaneously. TMANet [34] uses self-attention mechanisms to capture the relationships between the current frame and the memorized frames. STT [18] dynamically captures the temporal relationships through a sparse self-attention mechanism. LMANet [27] enhances the segmentation performance by leveraging semantic information from past frames. Different from the above approaches, [1, 29] reuse high-level features directly. DVSNet [38] utilizes a dynamic key-frame selection strategy. CFFM++[33] generates global exemplars via clustering to enhance target frame features, improving the video semantic segmentation performance. Efficient VSS [17, 19, 38, 47] run costly networks only on reference frames (fine-tuning non-keyframe features), while HighPerformance VSS [18, 22, 24, 31, 33] exploit temporal continuity to boost accuracy [11].
+
+The above VSS approaches mainly follow the reference-target interaction paradigm for local temporal information mining. However, this paradigm fails to utilize global temporal information across entire videos. Though CFFM++ has learned global temporal information, the non-learnable global exemplars generated by the pre-trained encoder limit its performance. Moreover, intra-class discrepancies among frames may lead to inconsistent semantic propagation, resulting in unstable predictions. This paper proposes a novel end-to-end VSS framework that leverages the strong representational capability of cluster centers to capture local and global temporal information.
+
+# 2.3. Difference with CFFM++
+
+We observe that recent work, CFFM++ [33], also employs global exemplars to model global temporal information for VSS. However, there are key differences between CFFM++ and our approach. CFFM++ adopts a multi-stage training framework and models global temporal information using non-learnable global exemplars generated by a pre-trained encoder, which limits the model's ability. In contrast, DERN models both local and global temporal contexts through trainable exemplars within an end-to-end training framework, providing greater flexibility and adaptability.
+
+# 3. Methods
+
+# 3.1. overview
+
+As shown in Fig. 2a, DTERN includes a shared encoder, $N$ LTEMs, a GTEM, and a segmentation head. Given a video clip with $T$ frames $\{\mathbf{I}_{t_k} \in R^{3 \times H \times W}\}_{k=1}^T$ . The target frame is $I_{t_T}$ and previous frames $\{\mathbf{I}_{t_k} \in R^{3 \times H \times W}\}_{k=1}^{T-1}$ are reference frames. The encoder extracts multi-level features $\{\mathbf{Z}_{t_k}^v \in R^{C_v \times H_v \times W_v}\}_{v=1}^V$ for each frame. The convolutional layers then fuse these features to produce encoded outputs $\{\mathbf{F}_{t_k} \in R^{D \times H_t \times W_t}\}_{k=1}^T$ . For the $l$ -th LTEM, $\{\mathbf{F}_{t_k}^l\}_{k=1}^{T-1}$ and enhanced target frame features $\{\widetilde{\mathbf{F}}_{t_T}^{l-1} \in R^{D \times H_t \times W_t}\}$ from the last LTEM are fed into the module, which generates local exemplars $\{\widetilde{\mathbf{C}}^l \in R^{M \times D}\}$ and enhanced target frame features $\widetilde{\mathbf{F}}_{t_T}^l$ . The GTEM enhances target frame features with global exemplars to improve temporal consistency and gets output $\{\widetilde{\mathbf{O}} \in R^{D \times H_t \times W_t}\}$ . Finally, $\widetilde{\mathbf{O}}$ is processed through the segmentation head to produce the final segmentation result.
+
+# 3.2. Local Temporal Exemplar Module
+
+LTEM models local temporal information by constructing local exemplars and using them to enhance the target frame features. Specifically, LTEM consists of three submodules: Cluster Assignment Module (CAM), Selection and Aggregation Module (SAM), and Feature Enhancement Module
+
+(FEM). For the multi-frame input features of the $l$ -th LTEM, the CAM generates cluster assignments $\mathbf{A}_{t_j}^l$ for each frame. Based on these assignments, the SAM constructs cluster centers for each frame and completes the formation of local exemplars $\widetilde{\mathbf{C}}^l$ by aggregating the cluster centers of the reference and target frames. The FEM leverages these local exemplars to enhance the target frame features.
+
+CAM. As shown in Fig. 2b, CAM consists of two branches: Parallel Deep Convolutional Branch (PDCB) and Axial Decomposition and Correction Branch (ADCB). Specifically, due to intricate variations in illumination intensity, object morphology, and other factors within and across frames in video data, directly employing simply stacked convolutional layers is insufficient to capture high-quality texture features. To address this, the PDCB adopts a multibranch design with parallel depthwise convolutions of varying kernel sizes. The extracted multi-scale features are aggregated to construct intra-frame texture feature. This process is formulated as:
+
+$$
+L _ {t _ {j}} ^ {l} = \mathcal {F} _ {\text {a g g}} \left(\sum_ {i = 1} ^ {n} \operatorname {D W C o n v} _ {k _ {i}} \left(x _ {t _ {j}} ^ {l}\right) + x _ {t _ {j}} ^ {l}\right) \tag {1}
+$$
+
+where $\mathcal{F}_{\mathrm{agg}}$ represents a point-wise convolutional layer, $\mathrm{DWConv}_{k_i}$ represents a depthwise convolution with a kernel size of $k_{i}$ , and $x_{t_j}^l$ represents the output of the shallow convolutional layers processed from $F_{t_i}^l$ .
+
+The ADCB extracts spatial features via horizontal and vertical pooling. Then, small-kernel 1D convolution is applied along the orthogonal axis (e.g. vertical for horizontal pooling and vice versa) to refine the extracted features with small-scale axial corrections. The output at height $h$ can be formalized as:
+
+$$
+G _ {t _ {j}} ^ {l} (h) = \psi_ {k _ {x} \times 1} \left(\frac {1}{W} \sum_ {i = 0} ^ {W} y _ {t _ {j}} ^ {l} (h, i)\right) \tag {2}
+$$
+
+where $y_{t_j}^l = \psi_{1\times 1}(F_{t_j}^l)$ . Similarly, the output at width $w$ can be formalized as:
+
+$$
+G _ {t _ {j}} ^ {l} (w) = \psi_ {1 \times k _ {y}} \left(\frac {1}{H} \sum_ {i = 0} ^ {H} y _ {t _ {j}} ^ {l} (w, i)\right) \tag {3}
+$$
+
+After performing small-scale axial corrections separately along each axis, the features are aggregated by summation. Subsequently, two orthogonal 1D convolutions with larger kernels are applied to achieve large-scale edge corrections. This process can be expressed as:
+
+$$
+G _ {t _ {j}} ^ {l} = \psi_ {1 \times k _ {g}} \left(\psi_ {k _ {g} \times 1} \left(G _ {t _ {j}} ^ {l} (c, h) + G _ {t _ {j}} ^ {l} (c, w)\right)\right) \tag {4}
+$$
+
+By applying corrections to the feature map across multiple directions and scales, the model achieves enhanced accuracy of cluster assignment.
+
+
+(a)DTERN
+
+
+(b) CAM
+
+
+(c) SAM
+
+
+(d) FEM
+Figure 2. Overview of DTERN (three input frames illustrated, with $I_{t_3}$ as the target frame). (a) DTERN consists of a shared encoder, $N$ LTEMs, a GTEM, and a segmentation head. Each LTEM includes three submodules: CAM, SAM, and FEM. (b) CAM consists of PDCB and ADCB, which jointly perform cluster assignment for each frame. (c) SAM merges the cluster assignments through feature selection and aggregates the cluster centers of the reference and target frames to construct local exemplars. (d) FEM enhances the target frame feratures using local exemplars. (e) GTEM dynamically updates global exemplars to learn global temporal information.
+
+
+(e) GTEM
+
+A sigmoid function is applied to the ADCB output to generate a weight matrix, which is then used to enhance the texture features extracted by the PDCB. The final cluster assignment is obtained as:
+
+$$
+\mathbf {A} _ {t _ {j}} ^ {l} = \psi_ {1 \times 1} \left(L _ {t _ {j}} ^ {l} \odot \sigma \left(G _ {t _ {j}} ^ {l}\right) + L _ {t _ {j}} ^ {l}\right) \tag {5}
+$$
+
+where $\sigma$ denotes the sigmoid function, $\odot$ denotes the Hadamard product, $A_{t_j}^l\in R^{M\times H_t\times W_t}$ and $\mathbf{M}$ is the predefined number of clusters.
+
+SAM. Considering the discrepancies in cluster assignments between adjacent LTEMs, we employ feature selection [30] to selectively merge these assignments. Specifically, we first concatenate all cluster assignments and flatten them along both temporal and spatial dimensions $A_{t}^{l} = \text{ flatten}([A_{t_{1}}^{l}, A_{t_{2}}^{l}, \ldots, A_{t_{T}}^{l}])$ . The selection operation is $\widetilde{A_{t}^{l}} = \phi \cdot A_{t}^{l} \cdot \text{sim}(A_{t}^{l}, \xi)$ , where $\xi$ represents the task embedding, and $\text{sim}(\cdot)$ denotes the cosine similarity function. We perform a mean operation on the cluster assignments of two adjacent layers to bring them closer together $\widehat{\mathbf{A}_{t}^{l}} = \text{Avg}(\widetilde{A_{t}^{l}}, \widetilde{A_{t}^{l-1}})$ . Then, we reshape the result along the temporal dimension to recover the cluster assignments for
+
+each frame. Through matrix multiplication, we construct cluster centers for each frame as:
+
+$$
+\mathbf {C} ^ {l} = \delta \left(\widehat {\mathbf {A} _ {t} ^ {l}}\right) \otimes f l a t t e n \left(F _ {t} ^ {l}\right) ^ {\top} \tag {6}
+$$
+
+where $F_{t}^{l}$ denotes the outcome of concatenating all frame features along the temporal dimension, the flattening operation is executed along the spatial dimension, $\delta$ is the softmax function and the cluster centers $\mathbf{C}^l\in R^{T\times M\times D}$ .
+
+As video data tends to be complex and variable, direct summing or averaging cluster centers across different frames may lead to erroneous feature alignment and unstable predictions. Video information can be divided into static regions, which capture consistent areas across consecutive frames, and dynamic regions, which highlight the content specific to the current frame. We hypothesize that the variations in cluster centers align with the inter-frame variations. Therefore, the local exemplars $\widetilde{\mathbf{C}^l}$ can be constructed by aggregating the cluster centers of the reference and target frames based on their similarity.
+
+We define $w_{t_j}^l$ as the similarity between the cluster centers of the $j$ -th frame and the target frame in the $l$ -th LTEM,
+
+while $\widetilde{\mathbf{C}^l}$ is denoted as:
+
+$$
+\widetilde {\mathbf {C}} ^ {l} = \mathbf {C} _ {t _ {T}} ^ {l} + \sum_ {j = 0} ^ {T - 1} w _ {t _ {j}} ^ {l} \mathbf {C} _ {t _ {j}} ^ {l} \tag {7}
+$$
+
+where $\widetilde{\mathbf{C}}^l\in R^{M\times D}$ and $\mathbf{C}_{t_T}^l$ denotes the cluster centers of the target frame. We compute the similarity between cluster centers using the following formula:
+
+$$
+w _ {t _ {j}} ^ {l} = \sigma \left(\partial + \beta \cos \left(\mathbf {C} _ {t _ {T}} ^ {l}, \mathbf {C} _ {t _ {j}} ^ {l}\right)\right) \tag {8}
+$$
+
+where $\cos(\cdot)$ denotes the cosine function, and $\partial$ and $\beta$ are trainable parameters that are initialized to 0 and 1.
+
+FEM. To enhance the features of the target frame with the local exemplars $\widetilde{\mathbf{C}^l}$ , we first map the target frame features $F_{t_T}^l$ to a query $\{\pmb {Q}_i^l\in R^{H_tW_t\times D}\}$ through the linear layer.
+
+$$
+Q _ {i} ^ {l} = F C \left(F _ {t _ {T}} ^ {l}, W _ {\text {q u e r y}}\right) \tag {9}
+$$
+
+where $W_{query}$ represents the weights of the linear layer $FC$ . Similarly, $\widetilde{\mathbf{C}^l}$ is mapped to key $\{K_i^l \in R^{M \times D}\}$ and value $\{V_i^l \in R^{M \times D}\}$ through the linear layer. Then, we update the target frame features using:
+
+$$
+\widetilde {\mathbf {F} _ {t _ {T}} ^ {l}} = \delta \left(\frac {Q _ {i} ^ {l} K _ {i} ^ {l} {} ^ {\top}}{\sqrt {c}}\right) V _ {i} + F _ {t _ {T}} ^ {l} \tag {10}
+$$
+
+Since the predefined cluster number is typically smaller than the number of tokens $(M << H_{t}W_{t})$ , our approach is expected to reduce the complexity from quadratic to linear.
+
+Traditional methods for mining local temporal information predominantly rely on the reference-target interaction paradigm. However, they neglect inter-frame intra-class discrepancies caused by complex video variations, leading to unstable predictions. In contrast, we utilize local exemplars to model local temporal information, which can more effectively leverage consistent temporal information and enhance the accuracy and consistency of segmentation.
+
+# 3.3. Global Temporal Exemplar Module
+
+To mine global temporal information for improving effective consistency in segmentation, GTEM introduces learnable tokens: frame-wise cluster centers $\{FCC\in R^{T_g\times M_g\times D}\}$ and video-wise cluster centers $\{VCC\in R^{M_g\times D}\}$ . $FCC$ denotes the cluster centers of each frame input to the GTEM, interacting with the corresponding frame features to perform cluster assignments. $VCC$ serves as the video-level cluster centers as well as the global exemplars. We leverage VCC to progressively model global temporal information from local temporal information contained in the updated target frame features. Specifically, we first apply linear transformations to the target frame features and $FCC$ as follows:
+
+$$
+d _ {x} = F C \left(\widetilde {\mathbf {F} _ {t _ {T}}}, W _ {x}\right) d _ {y} = F C \left(F C C, W _ {y}\right) \tag {11}
+$$
+
+To simulate cluster assignment, we calculate the affinity between FCC and the target frame features, subsequently deriving a probability distribution through softmax normalization as:
+
+$$
+S _ {x, y} = \delta \left(d _ {x} \otimes d _ {y} ^ {\top}\right) \tag {12}
+$$
+
+We align the local temporal information with the global temporal information contained in VCC by matrix multiplication.
+
+$$
+\widetilde {d _ {x}} = S _ {x, y} \otimes V C C \tag {13}
+$$
+
+To strengthen the correlation between local and global temporal information, we further update the target frame features as:
+
+$$
+\widetilde {\mathbf {O}} = \delta \left(\frac {\varphi_ {q} \left(\widetilde {\mathbf {F} _ {t _ {T}}}\right) \varphi_ {k} ^ {\top} \left(\widetilde {d _ {x}}\right)}{\sqrt {c}}\right) \varphi_ {v} \left(\widetilde {d _ {x}}\right) + \widetilde {\mathbf {F} _ {t _ {T}}} \tag {14}
+$$
+
+where $\varphi (\cdot)$ denotes a linear transformation operations. The $\widetilde{\mathbf{O}}$ will be fed into the segmentation head for processing to obtain the final segmentation result.
+
+Through the utilization of global temporal information, GTEM improves the effective consistency of video semantic segmentation.
+
+# 4. Experiment
+
+# 4.1. Experimental Setup
+
+Datasets. The proposed approach is primarily evaluated on VSPW [24], the largest dataset for video semantic segmentation. The dataset includes 2,806 training clips, 343 validation clips, and 387 testing clips. It covers 124 semantic categories, such as people, cars, and roads, with annotations surpassing those of previous video semantic segmentation (VSS) datasets. To validate the generalization of DTERN, we also conduct experiments on the Cityscapes dataset [6], which includes 2975 training clips, 500 validation clips, and 1275 testing clips covering 19 categories. Unlike VSPW, Cityscapes features higher resolution and is annotated every 30 frames, making it suitable for semi-supervised tasks. Implementation details. Similar to Segformer [37], we use the MiT backbone pre-trained on ImageNet-1K as the encoder. Following prior works [31, 33], Our model adopts a $T = 4$ four-frame input configuration: for the target frame at time $t$ , the input frame sequence is $\{t - 9, t - 6, t - 3, t\}$ . In the ADCB of the CAM, we set the kernel sizes as $\{k_x, k_y\} = 3$ and $k_g = 11$ . For the PDCB, the kernel sizes are configured as $\{k_1, k_2, k_3, k_4\} = \{13, 11, 9, 7\}$ when the backbone adopts MiT-B0, otherwise, they are set to $\{k_1, k_2, k_3, k_4\} = \{11, 9, 7, 5\}$ . In the VSPW experiments, the number of clusters for the MiT-B0, MiT-B1, MiT-B2, and MiT-B5 are set to 250, 200, 150, and 124. In the Cityscapes experiments, the number of clusters for the MiT-B0 and MiT-B1 are set to 60 and 45. All data preprocessing procedures and training strategy are consistent with
+
+| Methods | Type | Backbone | Params (M)↓ | mIoU↑ | Weighted IoU↑ | VEC8↑ | VEC16↑ | FPS↑ | Sources |
| SegFormer [37] | Image | MiT-B0 | 3.8 | 33.1 | 57.1 | 30.1 | 31.3 | 96.1 | NeurIPS (2021) |
| MRCFA [32] | Self-attention | MiT-B0 | 5.2 | 35.2 | 57.9 | 33.4 | 34.5 | 42.3 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B0 | 4.7 | 35.2 | 58.8 | 32.6 | 33.9 | 44.2 | CVPR (2022) |
| CFFM++ [33] | other | MiT-B0 | 5.7 | 35.9 | 58.9 | 33.2 | 34.4 | 42.0 | TPAMI (2024) |
| TFC [21] | other | MiT-B0 | 4.5 | 32.9 | - | - | - | - | AAAI (2024) |
| Ours | - | MiT-B0 | 8.2 | 35.9 | 59.8 | 33.4 | 34.5 | 31.3 | - |
| SegFormer [37] | Image | MiT-B1 | 13.8 | 37.7 | 59.5 | 33.8 | 35.0 | 88.2 | NeurIPS (2021) |
| MRCFA [32] | Self-attention | MiT-B1 | 16.2 | 38.9 | 60.0 | 35.8 | 37.1 | 33.0 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B1 | 15.5 | 38.3 | 60.1 | 35.8 | 37.0 | 32.8 | CVPR (2022) |
| CFFM++ [33] | other | MiT-B1 | 16.5 | 39.9 | 60.7 | 37.5 | 38.1 | 31.3 | TPAMI (2024) |
| TFC [21] | other | MiT-B1 | 14.5 | 36.7 | - | - | - | - | AAAI (2024) |
| TDSNet [39] | other | MiT-B1 | 15.4 | 39.2 | 60.2 | - | - | - | Inf. Sci. (2025) |
| Ours | - | MiT-B1 | 18.1 | 40.3 | 61.3 | 37.8 | 39.0 | 27.2 | - |
| PSPNet [44] | Image | ResNet-101 | 70.5 | 36.5 | 58.1 | - | - | 32.5 | CVPR (2017) |
| OCRNet [40] | Image | ResNet-101 | 58.1 | 36.7 | 59.2 | - | - | 34.5 | ECCV (2020) |
| Mask2Former [4] | Image | Swin-S | 68.9 | 42.1 | 63.1 | - | - | - | CVPR (2022) |
| MPVSS [35] | Optical-flow | Swin-S | 108.0 | 40.4 | 62.0 | - | - | - | NeurIPS (2023) |
| ETC [22] | Optical-flow | OCRNet | 58.1 | 37.5 | 59.1 | - | - | 25.1 | ECCV (2020) |
| NetWarp [36] | Optical-flow | OCRNet | 58.1 | 37.5 | 58.9 | - | - | 6.2 | ECCV (2018) |
| TCBst-ocr [24] | other | ResNet-101 | 58.1 | 37.4 | 59.3 | - | - | 8.1 | CVPR (2021) |
| SegFormer [37] | Image | MiT-B2 | 24.2 | 44.1 | 63.7 | 40.3 | 41.5 | 54.2 | NeurIPS (2021) |
| MRCFA [32] | Self-attention | MiT-B2 | 27.3 | 45.3 | 64.7 | 42.3 | 43.8 | 24.4 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B2 | 26.5 | 45.0 | 64.4 | 42.7 | 44.3 | 23.6 | CVPR (2022) |
| CFFM++ [33] | other | MiT-B2 | 28.5 | 45.5 | 64.7 | 43.1 | 44.7 | 22.5 | TPAMI (2024) |
| DCFM (K=1) [45] | other | MiT-B2 | 24.8 | 45.0 | 64.3 | - | - | - | TCSVT (2024) |
| TDSNet [39] | other | MiT-B2 | 26.5 | 45.9 | 65.1 | - | - | - | Inf. Sci. (2025) |
| Ours | - | MiT-B2 | 29.1 | 46.1 | 65.2 | 43.3 | 45.2 | 20.6 | - |
| SegFormer [37] | Image | MiT-B5 | 82.1 | 48.9 | 66.5 | 46.0 | 47.6 | 25.0 | NeurIPS (2021) |
| MRCFA [32] | Self-attention | MiT-B5 | 84.5 | 49.9 | 66.0 | 45.9 | 46.8 | 11.4 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B5 | 85.5 | 49.3 | 66.5 | 47.1 | 48.2 | 10.6 | CVPR (2022) |
| CFFM++ [33] | other | MiT-B5 | 87.5 | 50.1 | 66.5 | 47.6 | 48.7 | 10.4 | TPAMI (2024) |
| TFC [21] | other | MiT-B5 | 82.8 | 48.3 | - | - | - | - | AAAI (2024) |
| DCFM (K=1) [45] | other | MiT-B5 | 82.1 | 49.5 | 66.0 | - | - | - | TCSVT (2024) |
| Ours | - | MiT-B5 | 86.3 | 50.3 | 66.7 | 48.1 | 49.3 | 10.6 | - |
+
+Table 1. Comparison with the state-of-the-art methods on the val set of VSPW [24]. The best results under each setting are highlighted in bold. The FPS is computed on a single NVIDIA GeForce RTX 4090.
+
+those described in [31, 33]. The code is built on mmsegmentation [5] codebase.
+
+Evaluation metrics. Following previous works [4, 21, 24, 31, 33, 39], we primarily employ the mean IoU and the weighted IoU as the main measures of segmentation performance. Previous works [21, 31, 33, 39] have adopted video consistency (VC) to evaluate the smoothness of the predicted segmentation maps. Formally, $\mathbf{V}\mathbf{C}_C$ is computed as follows:
+
+$$
+\mathrm {V C} _ {C} = \frac {\left(\bigcap_ {i = 1} ^ {C} Q _ {t + i}\right) \cap \left(\bigcap_ {i = 1} ^ {C} Q _ {t + i} ^ {\prime}\right)}{\left(\bigcap_ {i = 1} ^ {C} Q _ {t + i}\right)} \tag {15}
+$$
+
+where $\{\mathbf{Q}_{t + i}\}_{i = 1}^{C}$ are the ground truth frames, $\{\mathbf{Q}_{t + i}'\}_{i = 1}^{C}$ are the predicted labels.
+
+We observe that the VC metric solely focuses on prediction consistency while neglecting the accuracy of segmentation and exhibiting insensitivity to small-object segmentation. For instance, a prediction of all zeros would result in a VC metric of 1, which is clearly undesirable. We introduce constraint 1: predictions must be effective:
+
+$$
+\mathrm {V C} _ {C} ^ {\prime} = \frac {\left(\bigcap_ {i = 1} ^ {C} Q _ {t + i} \cap \bigcap_ {i = 1} ^ {C} Q _ {t + i} ^ {\prime}\right)}{\left(\bigcap_ {i = 1} ^ {C} Q _ {t + i}\right)} \tag {16}
+$$
+
+The corrected VC' metric considers both temporal consistency and segmentation accuracy. We further introduce con
+
+strain 2: we compute the mean IoU for consistent regions. Ultimately, our VEC metric is expressed as:
+
+$$
+\operatorname {V E C} _ {C} = \frac {1}{N _ {c}} \sum_ {k = 1} ^ {N _ {c}} \left(\frac {\left(\bigcap_ {i = 1} ^ {C} \left(Q _ {t + i} = k\right) \cap \bigcap_ {i = 1} ^ {C} \left(Q _ {t + i} ^ {\prime} = k\right)\right)}{\left(\bigcap_ {i = 1} ^ {C} \left(Q _ {t + i} = k\right) \cup \bigcap_ {i = 1} ^ {C} \left(Q _ {t + i} ^ {\prime} = k\right)\right)}\right) \tag {17}
+$$
+
+where $N_{c}$ denotes the category number. The VEC ensures both temporal consistency and segmentation effectiveness.
+
+# 4.2. Segmentation Results
+
+Performance on the VSPW: A comparison of DTERN with the state-of-the-art methods on the VSPW dataset is shown in Tab. 1. As in previous work [31, 33, 39], we also report the complexity of the models and categorize the models into two groups: small models (with less than 20M parameters) and large models (with more than 20M parameters). For small model, DTERN significantly outperforms the baseline SegFormer [37], achieving a $2.8\%$ improvement in mIoU when using MiT-B0 as the backbone. DTERN also exhibits superior segmentation consistency, with $\mathrm{VEC}_8$ and $\mathrm{VEC}_{16}$ increasing by $3.3\%$ and $3.2\%$ . When using the MiT-B1 as the backbone, DTERN achieves a $2.6\%$ improvement in mIoU over SegFormer, with $\mathrm{VEC}_8$ and $\mathrm{VEC}_{16}$ increasing by $4.0\%$ . For larger models with MiT-B2 and MiT-B5 as the backbone, DTERN still significantly outperforms the baseline. DTERN provides consis
+
+
+Figure 3. Qualitative results. From top to bottom: the input frames, the ground truth (GT), DTERN predictions, CFFM++ [33] predictions and CFFM [37] predictions.
+
+tent performance improvement across all backbones, indicating the effectiveness of the proposed framework.
+
+Performance on the Cityscapes: We also report the performance on the val set of the Cityscapes in Tab. 2. Similar to VSPW, DTERN also achieves better segmentation results than the baseline SegFormer[37]. When using MiT-B0 as the backbone, DTERN achieves a $2.6\%$ improvement in mIoU over the baseline SegFormer, reaching $74.5\%$ mIoU. With the deeper MiT-B1 as the backbone, the mIoU increases by $1.9\%$ , achieving $76.0\%$ mIoU.
+
+Comparison with state-of-the-art methods: Under the same backbone, DTERN outperforms self-attention-based models such as CFFM [31] and CFFM++ [33] in terms of mIoU, weighted IoU, $\mathrm{VEC}_{8}$ , and $\mathrm{VEC}_{16}$ . For example, in the VSPW experiments, DTERN achieves improvements of $0.7\%$ , $2.0\%$ , $1.1\%$ and $1.0\%$ over CFFM when using MiT-B0, MiT-B1, MiT-B2, and MiT-B5 as backbones, respectively. Compared to CFFM++, DTERN achieves comparable mIoU results with MiT-B0 while demonstrating superior mIoU performance in all other cases. Additionally, DTERN achieves the best $\mathrm{VEC}_{8}$ and $\mathrm{VEC}_{16}$ scores across all backbones. DTERN constructs local exemplars to model local temporal information, effectively enhancing the accuracy and stability of predictions. Moreover, by leveraging global exemplars to capture global temporal information, DTERN further improves the effective consistency of segmentation.
+
+Qualitative results: We present qualitative examples of results in Fig. 3. We compare the predictions of DTERN with CFFM++ and CFFM on MiT-B1. It can be observed that the CFFM, which employs a reference-target interaction paradigm, produces unstable predictions even for adjacent frames where the same region (the black-box region) belongs to the same category. Although CFFM++ improves prediction consistency, consecutive prediction errors across frames. In contrast, DTERN demonstrates significantly improved segmentation accuracy and temporal consistency, delivering superior quantitative and qualitative results.
+
+| Methods | Type | Backbone | Params (M)↓ | mIoU↑ | Sources |
| FCN [23] | Image | MobileNetV2 | 9.8 | 61.5 | CVPR (2015) |
| PSPNet [44] | Image | MobileNetV2 | 13.7 | 70.2 | CVPR (2017) |
| DFF [47] | Optical-flow | ResNet-101 | - | 68.7 | CVPR (2017) |
| GRFP [25] | Optical-flow | ResNet-101 | - | 69.4 | ECCV (2018) |
| DVSN [38] | Optical-flow | ResNet-101 | - | 70.3 | ECCV (2018) |
| Accel [17] | Optical-flow | ResNet-101 | - | 72.1 | ECCV (2019) |
| ETC [22] | Optical-flow | ResNet-18 | 13.2 | 71.1 | ECCV (2020) |
| SegFormer [37] | Image | MiT-B0 | 3.7 | 71.9 | NeurIPS (2021) |
| MRCAF [32] | Self-attention | MiT-B0 | 4.2 | 72.8 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B0 | 4.6 | 74.0 | CVPR (2022) |
| CFFM++ [33] | Self-attention | MiT-B0 | 5.1 | 74.3 | TPAMI (2024) |
| Ours | - | MiT-B0 | 7.7 | 74.5 | - |
| SegFormer [37] | Image | MiT-B1 | 13.8 | 74.1 | NeurIPS (2021) |
| MRCFA [32] | Self-attention | MiT-B1 | 14.9 | 75.1 | ECCV (2022) |
| CFFM [31] | Self-attention | MiT-B1 | 15.4 | 75.1 | CVPR (2022) |
| CFFM++ [33] | other | MiT-B1 | 15.9 | 75.7 | TPAMI (2024) |
| DCFM* [45] | other | MiT-B1 | - | 74.4 | TCSVT (2024) |
| TDSNet [39] | other | MiT-B1 | - | 75.7 | Inf. Sci. (2025) |
| Ours | - | MiT-B1 | 17.8 | 76.0 | - |
+
+# 4.3. Ablation Study
+
+For a fair comparison, we follow the training strategy in [31, 33] and conduct ablation studies with MiT-B1 on the VSPW dataset [24].
+
+Effectiveness of GTEM: We conduct ablation experiments on GTEM to study its effect on the model. As shown in Tab. 3, the inclusion of the GTEM module results in a $0.2\%$ improvement in both $\mathrm{VEC}_8$ and $\mathrm{VEC}_{16}$ . This demonstrates that GTEM enhances the effective consistency of segmentation by capturing global temporal information through global exemplars. The slight decrease in mIoU can be attributed to the reference frame selection strategy, which enables the model to extract rich global temporal information relevant to the target frame. While GTEM further enhances segmentation consistency by exploiting global temporal information across the entire video, its stronger emphasis on global contexts may inadvertently dilute fine-grained details in the target frame features.
+
+Table 2. Comparison with recent efficient VSS models on the Cityscapes val set [6]. The best results are highlighted in bold.
+
+| # | GTEM | SAM | CAM | mIoU↑ | VEC8↑ | VEC16↑ |
| PDCB | ADCB |
| a | | ✓ | ✓ | ✓ | 40.4 | 37.6 | 38.8 |
| b | ✓ | | ✓ | ✓ | 40.0 | 37.1 | 38.0 |
| c | ✓ | ✓ | | | 39.7 | 36.7 | 37.8 |
| d | ✓ | ✓ | ✓ | | 38.3 | 35.6 | 36.6 |
| e | ✓ | ✓ | | ✓ | 39.6 | 37.1 | 38.1 |
| f | ✓ | ✓ | ✓ | ✓ | 40.3 | 37.8 | 39.0 |
+
+Table 3. Ablation study of proposed blocks .
+
+Effectiveness of CAM: To demonstrate the gain of CAM, we replace it with ResBlock with comparable parameters. As illustrated in Tab. 3, CAM achieves a $0.6\%$ improvement in mIoU. This demonstrates that the proposed CAM enables more accurate cluster assignments compared to traditional stacked convolutional layers, leading to a significant improvement in segmentation performance. We also report ablation experiments on the dual-branch architecture of CAM. The results indicate that the removal of either the PDCB or ADCB leads to performance degradation. We ob
+
+| # | Num | mIoU↑ | VEC8↑ | VEC16↑ |
| a | 32 | 39.3 | 36.1 | 37.1 |
| b | 124 | 39.7 | 37.2 | 38.1 |
| c | 200 | 40.3 | 37.8 | 39.0 |
| d | 2048 | 39.6 | 37.0 | 37.9 |
+
+Table 4. Ablation study on the number of cluster centers.
+
+| Method | Pearson↑ | Spearman↑ | Kendall↑ |
| CFFM | CFFM++ | CFFM | CFFM++ | CFFM | CFFM++ |
| Video Consistency | 59.4 | 61.4 | 59.7 | 61.0 | 42.2 | 43.5 |
| Video Effective Consistency | 88.1 | 88.2 | 88.0 | 88.1 | 71.6 | 71.5 |
+
+Table 5. Correlations between measured TC and ground-truth TC.
+
+| Methods | mIoU↑ | VEC8↑ | VEC16↑ | Sources |
| ClusterFormer [20] | 38.0 | 34.9 | 36.3 | NeurIPS (2023) |
| PaCaViT [10] | 39.7 | 36.8 | 38.5 | CVPR (2023) |
| Ours | 40.3 | 37.8 | 39.0 | - |
+
+Table 6. Ablation study on clustering strategy.
+
+serve a sharp drop in mIoU when the ADCB is removed, which indicates the benefits of non-local features. When both branches are incorporated, DTERN achieves optimal performance with a $40.3\%$ mIoU. This highlights the synergistic improvement between the two branches. Furthermore, we provide a visualization of our cluster assignments generated by CAM in Fig. 4.
+
+Effectiveness of SAM: To validate the benefits of SAM, we substitute our cluster center aggregation strategy with direct summation across frames. The experimental results in Tab. 3 demonstrate that this additive operation causes a $0.3\%$ mIoU degradation. Complex variations between video frames may cause spatial discrepancies in cluster centers and lead to unstable predictions, which SAM effectively mitigates, resulting in improved model performance.
+
+Influence of the number of cluster centers: Table 4 explores the impact of the cluster-category cardinality relationship ( $K$ vs. $C$ ) on segmentation performance: the optimal mIoU is achieved when $K$ is slightly larger than $C$ (e.g., $K = 200$ ); $K < C$ (e.g., $K = 32$ ) limits feature discriminability, leading to inter-class confusion (with a $1\%$ drop in mIoU); when $K = C$ , rigid correspondences reduce performance in complex scenes (with a $0.6\%$ drop in mIoU); and $K >> C$ (e.g., $K = 2048$ ) introduces computational redundancy and overfitting (with a $0.7\%$ drop in mIoU). The results indicate that a moderate number of clusters ( $K > C$ ) can generate finer-grained feature representations for complex scenes, enhancing flexibility and expressive power.
+
+Effectiveness of VEC: To validate the effectiveness of the VEC, we conduct experiments based on the Measuring Temporal Consistency [43] to evaluate VC and VEC. As shown in Tab. 5, in terms of Pearson, Spearman, and Kendall correlation coefficients, VEC exhibits significantly stronger correlation with the ground-truth TC compared to the video consistency measure. We also demonstrate the
+
+
+Figure 4. Qualitative results of our cluster assignments. Different cluster assignments effectively focus on different category regions. For certain categories, we generate diverse cluster assignments.
+
+
+Figure 5. Qualitative comparison of VC and VEC metrics using CFFM++ predictions.
+
+qualitative analysis of the VC and VEC in Fig. 5.
+
+Effectiveness of clustering strategy: In Tab. 6, we also compare our clustering strategy with recently adopted clustering strategies [10, 20] in image segmentation. Our strategy outperforms the others. The efficacy of our approach stems from its capability to address two inherent challenges: 1) complex variations in illumination, object morphology, and other scene dynamics that render traditional stacked convolutions inadequate for precise cluster assignments, and 2) prediction instability caused by cluster assignment discrepancies between adjacent LTEMs and interframe cluster center variations. Our CAM improves cluster assignment accuracy and SAM mitigates instability, ultimately enhancing segmentation performance.
+
+# 5. Conclusion
+
+For video semantic segmentation, the effective utilization of both local and global temporal information is crucial. In this paper, the primary contributions are two folds: 1) a novel Video Effective Consistency metric for evaluating temporal consistency and segmentation effectiveness simultaneously and 2) the Dual-Temporal Exemplar Representation Network (DTERN), leveraging the strong representational capability of cluster centers to effectively model local and global temporal information and achieving more accurate and efficient segmentation results. To the best of our knowledge, this is the first work to implement end-to-end video semantic segmentation by utilizing exemplars. DTERN introduces two key modules: the Local Temporal Exemplar Module and the Global Temporal Exemplar Module. The former constructs local exemplars to model local temporal information, enabling stable prediction of the target frame, thereby enhancing segmentation accuracy. The latter leverages global exemplars to dynamically learn global temporal information, improving the effective consistency of segmentation. With a limited increase in parameters, DTERN achieves improved segmentation performance.
+
+# 6. Acknowledgments
+
+This work was supported by the National Science Fund for Distinguished Young Scholars, PR China under Grant No. 62025601, Transformation Foundation of Tianfu Jincheng Laboratory (2025ZH013) and National Natural Science Foundation of China under Grant 62376174.
+
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+# Dual-level Prototype Learning for Composite Degraded Image Restoration
+
+Zhongze Wang Haitao Zhao* Lujian Yao Jingchao Peng Kaijie Zhao East China University of Science and Technology, China
+
+{zzwang, lujiangyao, pjc, kjzhao}@mail.ecust.edu.cn, Haitaozhao@ecust.edu.cn
+
+# Abstract
+
+Images captured under severe weather conditions often suffer from complex, composite degradations, varying in intensity. In this paper, we introduce a novel method, Dual-Level Prototype Learning (DPL), to tackle the challenging task of composite degraded image restoration. Unlike previous methods that rely on fixed embeddings to characterize degradation types, DPL maintains a number of degradation-level prototypes to represent the specific degradation scenes dynamically. Furthermore, considering the diverse factors influencing each degradation type, factor-level prototypes are incorporated to capture variations in individual degradation factors. Image features are matched with both degradation-level and factor-level prototypes, producing detailed scene embeddings that enhance the network's understanding of composite degradations. These scene embeddings are then processed through Dual Scene Embedding Transformer Blocks to guide the restoration process. To further refine the prototype distribution, we propose a Prototype Scatter Learning Loss, which enables prototypes within the same degradation to learn more information and push prototypes between different degradations to be separate. Additionally, we introduce a new dataset named Variable Composite Degradation (VCD) dataset which contains images with different intensities of each type of composite degradation to validate the efficacy of our method. Extensive experiments demonstrate that DPL significantly outperforms existing methods in restoring images with composite degradations.
+
+# 1. Introduction
+
+Image restoration in severe weather conditions—such as haze, rain, snow, and low light—is crucial, as these factors degrade image quality and impact downstream tasks [34, 68]. Existing restoration methods, whether based on priors [16, 24, 29, 30, 67, 76] or deep learning [26, 46, 51, 52, 54, 59], typically follow a one-to-one paradigm, addressing a single degradation type per model. Recent works [33, 43, 47] attempt to generalize across degradation types, formulating a one-to-many task. However, these methods
+
+
+(a) Previous methods
+
+
+(b) Our DPL
+Figure 1. The main idea of our DPL. Note that the different line thicknesses in (b) represent different values of matching results.
+
+restore only one degradation type at a time, limiting real-world applicability where multiple degradations co-occur.
+
+In practice, images captured in adverse weather often exhibit composite degradations, such as rain coexisting with low light and haze due to water vapor. Addressing such cases in a unified model is more practical than solving individual degradations separately. Han et al. [23] approached this as a Blind Image Decomposition (BID) task, treating composite degradations as mixtures of unknown domains and decomposing them into source images. Subsequent works [49, 50, 69] refined BID-based restoration, yet their reliance on explicit visual component predictions introduces redundancy, limiting efficiency and scalability.
+
+A more intuitive approach is to make the model aware of degraded scenes. Guo et al. [22] train an embedder aligning image embeddings with text embeddings of degradation types, enabling degradation recognition. However, as shown in Fig. 1 (a), for images affected by haze and rain, embeddings for "heavy haze + light rain" and "light haze +
+
+heavy rain” collapse into the same “haze + rain” category, hindering the model's ability to distinguish different intensity combinations—a key aspect of composite degradation restoration. Moreover, degradation intensity depends on multiple factors. For example, haze can be described by the atmospheric scattering model (ASM) [15, 39]. Haze intensity is influenced by multiple physical parameters, such as depth, scattering coefficient, and global atmospheric light. Such factor-based perspective generalizes to other degradations (e.g., low light: illumination, noise; rain/snow: streak density, snow scale). Thus, factor-level descriptions are essential.
+
+To address these challenges, we propose Dual-level Prototype Learning (DPL) for composite degradation image restoration. Our method maintains two prototype levels: degradation-level prototypes, characterizing different degradation types, and factor-level prototypes, capturing underlying degradation factors. As illustrated in Fig. 1 (b), image features are matched to these dual levels, generating degradation-level and factor-level embeddings. These embeddings are processed by our Dual Scene Embedding Transformer Blocks, enhancing degradation understanding.
+
+Optimizing prototypes is the key in prototype learning. Prior methods [9, 53, 72, 73] primarily use Euclidean or cosine distances between prototypes, focusing on pairwise relationships. This limits effectiveness since each degradation comprises multiple prototypes. Instead, we introduce a Prototype Scatter Learning Loss $(\mathcal{L}_{psl})$ to capture overall prototype distribution. Scatter [3, 18, 19] measures data dispersion, offering a more holistic separation metric than direct pairwise comparisons.
+
+Furthermore, existing composite degraded image datasets [22, 23] lack degradation intensity variations within the same scene. To evaluate our method's ability to model variable degradation levels, we construct the Variable Composite Degradation (VCD) dataset, featuring diverse degradation intensities within identical backgrounds. In summary, the contributions are as follows:
+
+- The proposed Dual-level Prototype Learning constructs two sets of prototypes to describe degradation at both the degradation level and the factor level.
+- A Dual Scene Embedding Transformer Block is proposed to utilize two levels of description embedding to guide complex image restoration.
+- A novel Prototype Scatter Learning loss is introduced to optimize the prototype distribution via scatter analysis to lead the prototype learn more degradation information.
+
+# 2. Related Works
+
+Composite Degraded Image Restoration. Before researchers shifted focus to image restoration in composite degradation scenes, most studies addressed single-degradation tasks. These include models handling a specific degradation (one-to-one) [1, 5, 11, 12, 16, 21, 24, 25, 36, 38,
+
+45, 51, 52, 57, 62–64, 71, 74] and models addressing multiple single degradations (one-to-many) [33, 41, 43, 47]. Recently, researchers recognized that real-world images often suffer from a combination of degradations, prompting studies on composite degradation restoration [22, 23, 49, 50]. Quan et al. [44] propose to remove rain streak and snow together, but their method targets specific degradation types. Han et al. [23] pioneered treating composite degradation as a blind image decomposition (BID) task, decomposing a degraded image into its clear and degradation components. However, BID diverges from our goal, as we only seek to predict clear images—an approach later adopted by BID-based methods [49, 50].
+
+For complex inputs, understanding their components enhances restoration performance. Guo et al. [22] propose learning fixed embeddings from degraded texts and aligning image embeddings during training for automatic degradation matching at inference. However, degradation intensities vary, and fixed embeddings fail to differentiate inputs with the same degradation but different intensities, reducing robustness. Additionally, degradation factors are complex, making a single embedding insufficient for comprehensive characterization. To address these challenges, we propose Dual-level Prototype Learning, a novel framework for composite degradation restoration.
+
+Prototype Learning. Prototype learning has recently been applied to computer vision tasks [7, 9, 10, 17, 35, 40, 55, 72, 73]. Zhou et al. [72, 73] propose a prototype-based network for instance segmentation, addressing the limitations of using a single weight or query vector for classification. Liu et al. [35] integrate prototype learning with an orthogonal constraint for few-shot instance segmentation, using orthogonal loss to separate prototypes and facilitate novel class recognition. Chen et al. [10] apply prototype learning to low-level vision, employing multiple prototypes to model snowfall at different scales. Existing methods primarily optimize prototypes through contrastive learning [6], either to expand representational diversity or prevent prototype collapse [20, 27]. Instead, we introduce a scatter-based approach, optimizing prototypes by analyzing their overall distribution.
+
+# 3. Method
+
+The basic framework of DPL is a transformer-based U-Net. As shown in Fig. 2 (a), a composite degraded image is input to the encoder and we get image features, which are matched to dual-level prototypes. The matching results are aggregated to dual-level scene embeddings and both embeddings are fed into the decoder to get the restored image.
+
+# 3.1. Dual-level Prototypes
+
+Given two instances have the same types of composite degradation, but different intensities of each degradation, we aim to obtain differentiated scene embeddings by maintaining dual-level prototypes, i.e., making the scene embed
+
+
+(a) Overall Pipeline
+
+
+(b) Feature-Prototype Matching
+Figure 2. Overall pipeline of our proposed DPL.
+
+
+(c) DSCA
+
+dings reflect both the type of degradation and the intensity of degradation. In this subsection, we describe the initialization of the prototypes and feature-prototype matching.
+
+Prototype Initialization. For $N$ types of degradations, each degradation is described from the degradation level using a $C$ -dimensional prototype, which is called degradation-level prototype $\mathbf{P}_{deg} \in \mathbb{R}^{N \times C}$ , $\mathbf{P}_{deg} = [p_{deg}^{1}, \dots, p_{deg}^{N}]$ . In some other prototype-based methods [61, 72, 73], the prototype is usually initialized by random sampling from a Gaussian distribution. In our method, it is desired to speed up the convergence of the network by distinguishing the prototypes with different degradations from the very beginning of training. Following OneRestore [22], we encode the corresponding degraded text by a pre-trained text encoder, normalize it and set it as the initial degradation-level prototype of the corresponding degradation:
+
+$$
+p _ {d e g} ^ {i} := \operatorname {n o r m} \left(E _ {T} \left(\text {t e x t} ^ {i}\right)\right), \text {s . t .} i \in [ 1, \dots , N ] \tag {1}
+$$
+
+where $E_{T}(\cdot)$ stands for a pre-trained text encoder, and in this method, the commonly used Glove [42] is introduced to encode degradation texts. Note that we only use the text information in the initialization of degradation-level prototypes and no longer use it in either the subsequent training or inference phases.
+
+Considering that each degradation is influenced by a number of different factors, we also introduce a second level of prototype to characterize the degradation at the factor-level. Each degradation we describe with $K$ $C$ -dimensional prototypes, and because of the correlation between the various degradations, we additionally construct a public set of prototypes parallel to the factor-level prototypes of each independent degradation $(\mathbf{P}_{fac}\in \mathbb{R}^{(N + 1)\times K\times C},K$ is set to 8 in our setting). The initialization of $\mathbf{P}_{fac}$ is as follows:
+
+$$
+p _ {f a c} ^ {i j} := p _ {d e g} ^ {i} + \epsilon^ {i j},
+$$
+
+$$
+p _ {f a c} ^ {(N + 1) j} := \frac {1}{N} \sum_ {i = 1} ^ {N} p _ {d e g} ^ {i} + \epsilon^ {(N + 1) j}, \tag {2}
+$$
+
+$$
+\mathrm {s . t .} \epsilon^ {i j} \in \mathcal {N} (0, \sigma^ {2}), i \in [ 1, \dots , N ], j \in [ 1, \dots , K ]
+$$
+
+where $\epsilon^{ij}$ denotes random Gaussian noise.
+
+Feature-Prototype Matching. The input degradation image is used by the image encoder to get the image features, we want to match the image features to the individual prototypes, get the weight of each match, and finally aggregate them to achieve the description of the image scene. Given an flatten image feature $\mathbf{F} \in \mathbb{R}^{HW \times C}$ and the $\mathbf{P}_{deg} \in \mathbb{R}^{N \times C}$ , we perform the feature-prototype matching
+
+and gain the matching matrix $\mathbf{Q}_{deg} \in \mathbb{R}^{HW \times N}$ . The $\mathbf{Q}_{deg}$ is optimized by maximizing the similarity between pixelwise image features and the prototypes:
+
+$$
+\max _ {\mathbf {Q} _ {d e g}} \operatorname {T r} \left(\mathbf {Q} _ {d e g} \mathbf {P} _ {d e g} \mathbf {F} ^ {T}\right) \tag {3}
+$$
+
+In the case of a strict matching problem, the above objectives are required to be under the following conditions:
+
+$$
+\mathbf {Q} _ {d e g} \in \{0, 1 \} ^ {H W \times N}, \mathbf {Q} _ {d e g} \mathbf {1} ^ {N} = \frac {H W}{N} \mathbf {1} ^ {H W}, \mathbf {Q} _ {d e g} ^ {T} \mathbf {1} ^ {H W} = \mathbf {1} ^ {N} \tag {4}
+$$
+
+where $\mathbf{1}^N$ and $\mathbf{1}^{HW}$ stand for vectors of all ones of the corresponding dimensions. These restrictions constrain each pixel-level feature to match to only one prototype, which is contrary to our desire to match to multiple prototypes, and this optimization problem is time-consuming to solve directly [48]. To fit our aim and facilitate the optimization problem, one feasible solution is as follows:
+
+$$
+\max _ {\mathbf {Q} _ {d e g}} \operatorname {T r} (\mathbf {Q} _ {d e g} \mathbf {P} _ {d e g} \mathbf {F} ^ {T}) + \varepsilon h (\mathbf {Q} _ {d e g}),
+$$
+
+$$
+\text {s . t .} \mathbf {Q} _ {d e g} \in \mathbb {R} _ {+} ^ {H W \times N}, \mathbf {Q} _ {d e g} \mathbf {1} ^ {N} = \frac {H W}{N} \mathbf {1} ^ {H W}, \mathbf {Q} _ {d e g} ^ {T} \mathbf {1} ^ {H W} = \mathbf {1} ^ {N} \tag {5}
+$$
+
+where the $\varepsilon h(\mathbf{Q}_{deg})$ is an entropy regularization term, and the factor $\varepsilon > 0$ is a parameter which controls the smoothness of the distribution. With the soft assignment relaxation, the optimization fit our purpose and can be solved as:
+
+$$
+\mathbf {Q} _ {d e g} = \operatorname {d i a g} (\mathbf {u}) \exp \left(\frac {\mathbf {P} _ {d e g} \mathbf {F} ^ {T}}{\varepsilon}\right) \operatorname {d i a g} (\mathbf {v}) \tag {6}
+$$
+
+where $\mathbf{u} \in \mathbb{R}^N$ and $\mathbf{v} \in \mathbb{R}^{HW}$ are renormalization vectors. And eq. (6) can be solved by a few steps of Sinkhorn-Knopp iterations [14]. The process is efficient on GPU and only takes about 1 ms for 1024 pixel-level feature vectors matching to 4 prototypes on an RTX 4090 GPU. Similarly, the matching result $\mathbf{Q}_{fac} \in \mathbb{R}^{HW \times (N + 1)K}$ between image features and factor-level prototypes can also be calculated.
+
+# 3.2. Dual-level Scene Embedding Transformer Block
+
+To further improve the network's perception of the scene at both levels and to help the network improve image restoration in composite degradation scenes, we introduce the Dual-level Scene Embedding Transformer Block (DSETB). In this subsection, we describe the process obtaining the degradation-level and factor-level scene embedding. Then the DSETB based on Dual-level Scene Cross Attention (DSCA) is introduced.
+
+Dual-level Scene Embedding. After obtaining the two feature-prototype matching results, we proceed to derive
+
+
+Prototype Space
+
+Purpose: $\mathrm{Tr}(\Psi_b)\uparrow$
+
+$$
+\operatorname {T r} \left(\Psi_ {w n}\right) \uparrow
+$$
+
+$$
+\operatorname {T r} \left(\Psi_ {w f}\right) \downarrow
+$$
+
+Objective:
+
+$$
+\mathcal {L} _ {p s l} = \left[ \mathrm {T r} (\Psi_ {w f} ^ {\prime - 1} (\Psi_ {b} + \beta \Psi_ {w n}) \right] ^ {- 1}
+$$
+
+$\times \times$ : Prototypes $\bigcirc$ : Within-degradation-farthest neighbor
+
+$\bigcirc$ : Within-degradation-nearest neighbor $\Longleftrightarrow$ : Push away
+
+$\bigcirc$ : Between-degradation neighbor
+
+Figure 3. Illustration of the Prototype Scatter Learning. Take prototypes of two degradations as an example.
+
+two levels of scene embedding. The degradation-level scene embedding $\mathbf{emb}_{deg} \in \mathbb{R}^{1 \times C}$ can be calculated as:
+
+$$
+\mathbf {e m b} _ {d e g} = \frac {1}{H W} \sum_ {i = 1} ^ {N} \left(\mathbf {Q} _ {d e g} ^ {i: T} \mathbf {P} _ {d e g}\right) \tag {7}
+$$
+
+Specifically, for each pixel, we compute a weighted average of the matched prototypes based on the matching results. We then perform an average pooling over all pixels to obtain the degradation-level embedding for this instance. Similarly, we further calculate its factor-level scene embedding:
+
+$$
+\mathbf {e m b} _ {f a c} = \frac {1}{H W} \sum_ {i = 1} ^ {(N + 1) K} \left(\mathbf {Q} _ {f a c} ^ {i,:} ^ {T} \mathbf {P} _ {f a c} ^ {\prime}\right) \tag {8}
+$$
+
+where $\mathbf{P}_{fac}^{\prime}\in \mathbb{R}^{(N + 1)K\times C}$ denotes the result of $\mathbf{P}_{fac}$ flatten the first two dimension. Subsequently, the two scene embeddings are input to the decoder DSETBs together with the image features. One DSETB is composed of our newly proposed DSCA, as well as the conventional Self-Attention (SA) and Feed-forward Network (FFN) [64].
+
+Dual-level Scene Cross Attention. The structure of DSCA is illustrated in Fig. 2 (c). In DSCA, we convert scene embeddings into queries $(\mathbf{Q}\mathbf{u}_{deg},\mathbf{Q}\mathbf{u}_{fac})$ , while keys (Key) and values (Val) are computed from image features by linear layers. The formulation of the DSCA can be defined as:
+
+$$
+\begin{array}{l} \mathrm {D S C A} (\mathbf {Q u e} _ {\text {d e g}}, \mathbf {Q u e} _ {\text {f a c}}, \mathbf {K e y}, \mathbf {V a l}) \\ = \operatorname {S o f t m a x} \left(\frac {\operatorname {R e p e a t} \left(\mathbf {Q u e} _ {d e g} + \mathbf {Q u e} _ {f a c}\right) \mathbf {K e y} ^ {T}}{\lambda}\right) \mathbf {V a l} \tag {9} \\ \end{array}
+$$
+
+where $\lambda$ is a temperature factor and we set it to be learnable. For more network details please refer to the Suppl.
+
+# 3.3. Prototype Scatter Learning Loss
+
+Purpose. Given a set of factor-level prototypes, we aim for these prototypes to capture unique information relative to
+
+each other while maintaining distances among prototypes of different degradations. In line with this objective, we compute the following scatter matrices. Specifically, we define three types of scatter matrices. (Note that in this subsection, unless otherwise specified, $p$ in the formulas represents a factor-level prototype.)
+
+Between-degradation Scatter Matrix. Firstly, we aim for prototypes with different levels of degradation to be as distinct from each other as possible. That is, the scatter between prototypes of different degradation should increase. Thus we calculate between-degradation scatter matrix, which represents the scatter of each factor prototype with the nearest prototype from a different degradation:
+
+$$
+\Psi_ {b} = \frac {1}{(N + 1) K} \sum_ {i = 1} ^ {N + 1} \sum_ {j = 1} ^ {K} \left[ p ^ {i j} - p _ {N N} ^ {p \notin p ^ {i,:}} \left(p ^ {i j}\right) \right] \left[ p ^ {i j} - p _ {N N} ^ {p \notin p ^ {i,:}} \left(p ^ {i j}\right) \right] ^ {T} \tag {10}
+$$
+
+where $p_{NN}^{p \notin p^{i,:}}(p^{ij})$ denotes the nearest prototype to $p^{ij}$ that is not in the same degradation as $p^{ij}$ .
+
+Within-degradation-nearest Scatter Matrix. Since different prototypes within the same degradation level represent distinct influencing factors, we also aim for these prototypes to be separated, i.e., to increase within-degradation scatter. The within-degradation-nearest scatter matrix denotes the scatter of each prototype with the nearest prototype from a same degradation:
+
+$$
+\Psi_ {w n} = \frac {1}{(N + 1) K} \sum_ {i = 1} ^ {N + 1} \sum_ {j = 1} ^ {K} \left[ p ^ {i j} - p _ {N N} ^ {p \in p ^ {i:}} \left(p ^ {i j}\right) \right] \left[ p ^ {i j} - p _ {N N} ^ {p \in p ^ {i:}} \left(p ^ {i j}\right) \right] ^ {T} \tag {11}
+$$
+
+where $p_{NN}^{p \in p^{i,:}}(p^{ij})$ denotes the nearest prototype to $p^{ij}$ that is in the same degradation as $p^{ij}$ .
+
+Within-degradation-farthest Scatter Matrix. We aim to learn diverse information by increasing the two types of scatter mentioned above. However, simultaneously increasing both between-degradation and within-degradation scatter can destabilize the prototype distribution. To address this, we introduce a constraint to limit the expansion of the prototype distribution. Specifically, we require the scatter between a prototype and the farthest prototype within the same degradation to be minimized:
+
+$$
+\Psi_ {w f} = \frac {1}{(N + 1) K} \sum_ {i = 1} ^ {N + 1} \sum_ {j = 1} ^ {K} \left[ p ^ {i j} - p _ {F N} ^ {p \in p ^ {i,:}} \left(p ^ {i j}\right) \right] \left[ p ^ {i j} - p _ {F N} ^ {p \in p ^ {i,:}} \left(p ^ {i j}\right) \right] ^ {T} \tag {12}
+$$
+
+where $p_{FN}^{p \in p^{i,:}}(p^{ij})$ denotes the farthest prototype to $p^{ij}$ that is in the same degradation as $p^{ij}$ .
+
+Objective Function. In summary, as is shown in Fig. 3, our goal is to maximize between-degradation scatter and within-degradation-nearest scatter, while minimizing within-degradation-farthest scatter. Inspired by classical
+
+
+Figure 4. Examples of VCD. The image in the upper right corner is the ground truth, and the rest are degraded images with different combinations and intensities degradation. Each clear image in the VCD corresponds to 111 degraded images.
+
+Linear Discriminant Analysis (LDA) [58, 70], we formulate the objective function in the form of a ratio-trace:
+
+$$
+\mathcal {L} _ {p s l} = \left[ \operatorname {T r} \left(\Psi_ {w f} ^ {\prime} \right. ^ {- 1} \left(\Psi_ {b} + \beta \Psi_ {w n}\right)\right) ] ^ {- 1} \tag {13}
+$$
+
+where $\Psi_{wf}^{\prime -1}$ denotes the inverse of $\Psi_{wf}^{\prime}$ and $\Psi_{wf}^{\prime} = \Psi_{wf} + \xi E$ . The item $\xi E$ is to ensure reversibility and $\xi$ is set to $10^{-6}$ . The hyper-parameter $\beta$ is set to 0.5. And research [2, 66] prove that such ratio-trace form can be optimized by optimizers based on gradient descent [4, 31, 37]. The total loss function is: $\mathcal{L} = \mathcal{L}_{L1} + \gamma_1\mathcal{L}_{per} + \gamma_2\mathcal{L}_{psl}$ , where the $\mathcal{L}_{L1}$ and the $\mathcal{L}_{per}$ are the L1 loss and perceptual loss [28], respectively, between the output and ground truth. The hyper-parameters $\gamma_{1}$ and $\gamma_{2}$ are set to 0.2 and 10.
+
+Factor-level prototypes are updated with the gradient of the network, while degradation-level prototypes do the momentum update with the mean of the factor-level prototypes of the corresponding degradation and the public prototypes, with the momentum being set to 0.99.
+
+# 4. Experiments
+
+# 4.1. Variable Composite Degradation Dataset
+
+Since the currently available composite degraded image restoration datasets do not contain data that composite different intensities of degradation, we contribute Variable Composite Degradation (VCD) dataset. The clear backgrounds (ground truths) are selected from the clear images of RESIDE SOTS-outdoor [32], LOLv2 [60] and Rain100H [25]. According to OneRestore [22], we synthesize our degraded data. Unlike OneRestore, for each clear background and each combination of degradation, the VCD has a diverse range of degraded images with varying intensities of degradation. Regarding the scale, the training set for VCD contains clear images of 100 scenes and their corresponding 11,100 degradation images. The test set, on the other hand, contains 20 scenes and 2220 degradation images, respectively. Some examples of VCD are shown in Fig. 4. For more data displays and specific parameter settings of the synthesized data, please refer to the Suppl.
+
+Table 1. Quantitative comparison of DPL with the state-of-the-art image restoration methods on several datasets. Best results are bolded and second best results are underlined. Cells where results are not available are replaced by "-". "OneRestore†" denotes using the corresponding scene description text as additional input.
+
+| Method | CDD-11 [22] | VCD | BID-task.II [23] | IVIPC DQA [56] |
| PSNR (dB) ↑ | SSIM ↑ | PSNR (dB) ↑ | SSIM ↑ | PSNR (dB) ↑ | SSIM ↑ | NIQE ↓ | BRISQUE ↓ |
| One-to-One | MIRNet [63] | 25.97 | 0.874 | 19.05 | 0.623 | 24.62 | 0.810 | 3.972 | 28.44 |
| MIRNetv2 [65] | 25.37 | 0.834 | 19.95 | 0.640 | 24.88 | 0.813 | 3.810 | 28.38 |
| Restormer [64] | 26.99 | 0.865 | 22.90 | 0.739 | 28.82 | 0.888 | 4.101 | 28.62 |
| Fourmer [71] | 23.44 | 0.789 | 21.75 | 0.727 | 26.51 | 0.840 | 5.157 | 29.09 |
| NAFNet [8] | 24.13 | 0.796 | 20.14 | 0.690 | 25.53 | 0.847 | 5.430 | 29.83 |
| OKNet [13] | 26.33 | 0.861 | 21.62 | 0.708 | 27.71 | 0.883 | 4.746 | 27.38 |
| One-to-Many | AirNet [33] | 23.75 | 0.814 | 19.13 | 0.612 | 25.98 | 0.836 | 5.013 | 28.16 |
| TransWeather [47] | 23.13 | 0.781 | 20.55 | 0.656 | 27.66 | 0.847 | 4.653 | 26.79 |
| WeatherDiff [41] | 22.49 | 0.799 | 21.31 | 0.700 | 26.91 | 0.812 | 5.418 | 27.74 |
| PromptIR [43] | 25.90 | 0.850 | 23.75 | 0.737 | 29.17 | 0.899 | 3.941 | 26.82 |
| WGWSNet [75] | 26.96 | 0.862 | 23.89 | 0.749 | 28.33 | 0.883 | 4.239 | 28.49 |
| One-to-Composite | BIDeN [23] | 26.03 | 0.837 | 22.83 | 0.717 | 28.20 | 0.902 | 4.079 | 29.61 |
| CPNet [49] | - | - | - | - | 31.50 | 0.927 | - | - |
| OneRestore [22] | 28.47 | 0.878 | 23.91 | 0.780 | 30.69 | 0.897 | 3.861 | 28.29 |
| OneRestore † [22] | 28.72 | 0.882 | 23.99 | 0.781 | 31.06 | 0.909 | - | - |
| DPL (ours) | 29.55 | 0.884 | 25.27 | 0.802 | 32.22 | 0.936 | 3.786 | 25.01 |
+
+
+
+
+
+
+Degraded
+
+
+
+
+
+
+Restormer
+
+
+
+
+
+
+AirNet
+
+
+
+
+
+
+OneRestore
+Figure 5. Visual comparison of various SOTA image restoration methods on CDD-11[22] (the top-2 rows, low-light&haze&snow and low-light&haze&rain), VCD (the third row, haze&snow). Please zoom in for a better view.
+
+
+
+
+
+
+DPL (ours)
+
+
+
+
+
+
+Clear
+
+# 4.2. Datasets and Metrics
+
+We conduct experiments on several datasets to evaluate the performance of our method on CDIR. The datasets include VCD, CDD-11 [22], BID-task.II [23]. Despite our proposed VCD dataset, CDD-11 is an image restoration dataset with composite degradations. It contains 1383 clear backgrounds, and each clear image corresponds to 11 fixed intensities of single or composite degradation. BID-task.II
+
+is the dataset of blind image decomposition for real-world application scenarios, which is oriented to composite degraded image restoration of driving scenarios. In addition, to validate the performance of our method in real-world scenarios, we also perform a comparison on the IVIPC DQA [56] dataset, a dataset containing 206 images of real-world rain scenes, against the model trained on CDD. Commonly used image quality evaluation metrics: PSNR (dB) and
+
+
+Figure 6. Visual comparison of various SOTA image restoration methods on real-world degraded dataset. Please zoom in for a better view.
+
+
+
+
+
+
+
+
+
+Table 2. Ablation studies of our DPL.
+
+| Method | Module | Metrics |
| Pdeg | Pfac | DSETB | Lpsl | PSNR (dB) | SSIM |
| Baseline | | | | | 20.59 | 0.740 |
| (a) | ✓ | | | | 21.10 | 0.761 |
| (b) | ✓ | ✓ | | | 22.71 | 0.770 |
| (c) | ✓ | ✓ | ✓ | | 23.08 | 0.782 |
| (d) | ✓ | ✓ | ✓ | ✓ | 25.27 (+2.19) | 0.802 (+0.020) |
+
+SSIM are employed to evaluate the performance of DPL. For real-world degraded images, non-reference image quality evaluation metrics NIQE and BRISQUE are introduced.
+
+# 4.3. Performance Evaluation
+
+We compare DPL with several SOTA image restoration methods. In addition to the one-to-composite methods (BIDeN [23], CPNet [49], OneRestore [22]), the one-to-one (MIRNet [63], MIRNetv2 [65], Restormer [64], Fourmer [71], NAFNet [8] and OKNet [13]) and one-to-many (AirNet [33], TransWeather [47], WeatherDiff [41], PromptIR [43] and WGWSNet [75]) methods are also introduced for performance comparison.
+
+Quantitative Evaluation. The quantitative comparison of different methods is recorded in Table 1. Our DPL achieved the best quantitative results on all four datasets. The results above illustrate that DPL for different intensities of composite degradation can perform best on the VCD dataset, in addition to beating other SOTA methods on single-intensity datasets, showing favorable generalization.
+
+Qualitative Evaluation. The qualitative comparison between various SOTA methods is displayed in Fig. 5 and 6. The one-to-one method Restormer [64] and one-to-many method AirNet [33] are not effective in restoring composite degraded images. Specifically, Restormer and AirNet cannot determine the type of degradation and incomplete removal of degradation. Faced with complex inputs, their results will have artifacts, color distortion, loss of detail and blurring. For the one-to-composite method OneRestore [22], which relies on fixed embedding, its results will deteriorate when it extracts embedding of the wrong type of degradation, e.g., in the first example of Fig. 5, it does less enhancement for low-light degradation; in the second ex
+
+
+(a) Degradation-level matching result of instance 1
+
+
+
+
+Figure 7. Illustration of matching results for combinations of degradation of different intensities.
+
+
+
+ample, there are some regions where the rain streaks are incompletely removed. Unlike OneRestore, our DPL gets dynamic scene embeddings that can better guide the restoration by matching image features to dual-level prototypes. Thus our DPL achieves more satisfactory restoration results that are close to the corresponding clear images. On real data as shown in Fig. 6, other methods fail to remove rain streaks and haze caused by rain, while DPL significantly remove the degradation, showing that DPL holds better robustness and ability to cope with the composite degradation of real scenes. More visual results are shown in Suppl.
+
+# 4.4. Ablation Studies and Discussion
+
+In this section, we conduct ablation experiments to demonstrate the effectiveness of our proposed individual modules. The overall quantitative results are displayed in Table 2, where our baseline is a basic transformer-based U-Net. Experiments are performed on the VCD dataset
+
+Effectiveness of Scene Embedding via Dual-level Prototypes. The dual-level prototypes are introduced to characterize degradation scenarios. According to Table 2, the introduction of $\mathbf{P}_{deg}$ alone brings about a gain of $0.51\mathrm{dB}$ PSNR and 0.021 SSIM. Whereas, the introduction of both $\mathbf{P}_{deg}$ and $\mathbf{P}_{fac}$ is able to bring about an increase of $2.12\mathrm{dB}$
+
+
+Degraded
+
+
+Clear
+
+
+w/o DSETB
+Figure 8. Ablation study of DSETB.
+
+
+w/ DSETB (Ours)
+Figure 9. T-SNE visualization of $\mathbf{P}_{fac}$ in different settings.
+
+PSNR and 0.030 SSIM compared to the baseline.
+
+In addition, to demonstrate the motivation we showed in Fig. 1 (b), we visualized the feature-prototype matching results for two instances of the same background with the same degradation combination but different degradation intensities, and the histograms are shown in Fig. 7. It demonstrates that the matching results of our method can accurately determine the degradation types, keeping the weights of the non-existent types low. Moreover, as the intensity of degradation changes, the corresponding weights also change, proving the feasibility of our motivation and the effectiveness of our DPL.
+
+Effectiveness of DSETB. The comparison of the results with and without the use of DSETB is recorded in variants (b) and (c) of Table 2. The use of DSETB brings an improvement of $0.37\mathrm{dB}$ PSNR and 0.012 SSIM over no use. This indicates that the interaction of two levels of scene embeddings and image features is significant. If the scene embedding is simply used as a token for regular self-attention computation, the network becomes less effective in perceiving the type and intensity of degradation. Fig. 8 gives a set of visual comparisons that show that using DSETB can handle complex degradation scenarios better than not.
+
+Effectiveness of Prototype Scatter Learning. The proposed $\mathcal{L}_{psl}$ is introduced to optimize the prototypes and avoid prototype collapse. Table 2 demonstrates that with $\mathcal{L}_{psl}$ , the restoration performance can be improved by 2.19 dB on PSNR and 0.020 on SSIM. We further analyze the proposed $\mathcal{L}_{psl}$ and compare it with several loss variants:
+
+$$
+\mathcal {L} _ {v a r 1} = \left[ \mathrm {T r} (\Psi_ {b} + \beta \Psi_ {w n}) \right] ^ {- 1}
+$$
+
+$$
+\mathcal {L} _ {v a r 2} = - \operatorname {T r} \left(\Psi_ {w f} ^ {\prime} ^ {- 1} \left(\Psi_ {b} + \beta \Psi_ {w n}\right)\right) \tag {14}
+$$
+
+$$
+\mathcal {L} _ {v a r 3} = \operatorname {T r} \left(\Psi_ {w f}\right) - \operatorname {T r} \left(\Psi_ {b} + \beta \Psi_ {w n}\right)
+$$
+
+where $\mathcal{L}_{var1}$ is the variant that does not use the within-degradation-farthest scatter for constraint, $\mathcal{L}_{var2}$ is the variant in which $\mathcal{L}_{psl}$ does not use the inverse form, and $\mathcal{L}_{var3}$ is the variant that does not use the ratio-trace form. The results of the comparison are presented in Table 3. The re
+
+Table 3. Ablation studies of our ${\mathcal{L}}_{psl}$ .
+
+| Metrics | Objective |
| Lvar1 | Lvar2 | Lvar3 | Lpsl |
| PSNR (dB) | 19.68 | 21.19 | 23.62 | 25.27 (+1.65) |
| SSIM | 0.693 | 0.766 | 0.791 | 0.802 (+0.011) |
+
+sults illustrate that using all three variants of the objective function causes deterioration in the results. Due to the lack of the $\Psi_{wf}$ constraint, using $\mathcal{L}_{var1}$ expands both $\mathrm{Tr}(\Psi_b)$ and $\mathrm{Tr}(\Psi_{wn})$ to infinity, giving worse results than baseline. Since all scatter matrices are semi-positive definite, the negative sign in $\mathcal{L}_{var2}$ causes the loss function to optimize to negative infinity during the optimization process, resulting in unstable network training. $\mathcal{L}_{var3}$ uses the difference form however, it still has no guarantee that it will not be optimized to negative infinity. We therefore choose the form presented in the previous section for the objective function, which ensures that the lower bound of the loss is zero. Further, we compare $\mathcal{L}_{psl}$ with the standard losses: contrastive loss and center loss. The results are shown in Tab. 4 and Fig. 9. The contrastive loss causes uneven prototype distributions due to pairwise constraints, while center loss separates classes but limits within-class diversity. $\mathcal{L}_{psl}$ holistically optimizes prototype scattering, ensuring between-class separation and within-class diversity. This enables richer feature and ideal distribution learning.
+
+Table 4. Comparison with standard prototype learning losses.
+
+| Objective | contrastive loss | triplet loss | center loss | ours |
| PSNR (dB) ↑ | 24.81 | 24.03 | 23.08 | 25.27 |
| SSIM ↑ | 0.799 | 0.767 | 0.761 | 0.802 |
+
+# 5. Conclusion
+
+We propose DPL, a framework for addressing composite degraded image restoration challenge under severe weather. DPL captures degradation scene information through dual-level prototypes. DSETB is introduced to enable the learned scene embeddings to assist subsequent image restoration, combined with $\mathcal{L}_{psl}$ for enhancing the representation ability of prototypes. A VCD dataset is further proposed to validate DPL's performance and generalization. DPL advances image restoration in challenging environments and holds potential for broader applications in multifaceted image processing tasks.
+
+# Acknowledgments.
+
+This work is supported by the National Natural Science Foundation (NSFC) under Grant 62173143.
+
+# References
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+# DualReal: Adaptive Joint Training for Lossless Identity-Motion Fusion in Video Customization
+
+Wenchuan Wang, Mengqi Huang, Yijing Tu, Zhendong Mao*
+University of Science and Technology of China
+
+{wenc_k, huangmq, tuyijing}@mail.ustc.edu.cn, zdmao@ustc.edu.cn
+
+
+Identity
+A cat
+
+
+Motion
+A person is doing TaiChi
+
+
+plushie grey sloth\*
+
+
+A person is lifting
+
+
+A dog\*
+
+
+A person is playing guitar
+
+
+A cat \* wrapped in woolen scarf is doing TaiChi on glacier plateau
+
+
+Customized Video
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+A plushie grey sloth * wearing rain boots is lifting a barbell in a stormy wetland
+A dog * sporting round sunglasses on a sandy beach is playing guitar
+Figure 1. Generated customization results of our proposed novel paradigm DualReal. Given identity images and motion videos, DualReal generates high-quality customized identity and motion simultaneously, without compromising the consistency of either dimension.
+
+
+
+
+
+
+
+# Abstract
+
+Customized text-to-video generation with pre-trained large-scale models has recently garnered significant attention by focusing on identity and motion consistency. Existing works typically follow the isolated customized paradigm, where the subject identity or motion dynamics are customized exclusively. However, this paradigm completely ignores the intrinsic mutual constraints and synergistic interdependencies between identity and motion, resulting in identity-motion conflicts throughout the generation process that systematically degrade. To address this, we introduce DualReal, a novel framework that employs adaptive joint training to construct interdependencies between dimensions collaboratively. Specifically, DualReal is composed of two
+
+units: (1) Dual-aware Adaptation dynamically switches the training step (i.e., identity or motion), learns the current information guided by the frozen dimension prior, and employs a regularization strategy to avoid knowledge leakage; (2) StageBlender Controller leverages the denoising stages and Diffusion Transformer depths to guide different dimensions with adaptive granularity, avoiding conflicts at various stages and ultimately achieving lossless fusion of identity and motion patterns. We constructed a more comprehensive evaluation benchmark than existing methods. The experimental results show that DualReal improves CLIP-I and DINO-I metrics by $21.7\%$ and $31.8\%$ on average, and achieves top performance on nearly all motion metrics. Page: https://wenc-k.github.io/dualreal-customization
+
+# 1. Introduction
+
+Video constitutes a spatiotemporal embodiment of the real world, where the spatial subject identity and the temporal motion dynamics form mutually constrained yet synergistic dimensions for physical modeling. This mutuality manifests through their inherent interdependence, i.e., maintaining stable subject identities across frames restricts motion possibilities, while enforcing certain motion trajectories conversely necessitates corresponding topological transformations of identity representation (e.g., $180^{\circ}$ viewpoint rotation leads to identity transformation from frontal to dorsal profiles).
+
+Video customized generation [24, 50, 52, 53, 58], which aims to mimic the user-specified concepts (i.e., subject identities, dynamic motions, or both) beyond linguistic expressibility, significantly enhances the controllability of video synthesis systems. This task greatly expands the applicability scope of pre-trained text-conditioned video models to cinematic production, personalized avatars, etc., attracting growing interest from academic and industrial communities. The primary challenge of customized video generation lies in two interdependent dimensional objectives, i.e., (1) identity consistency, i.e., the target subject should closely match the given reference in all frames, while minimizing temporal motion artifacts, and (2) motion consistency, i.e., the subject motion should closely match the given reference across frames, while minimizing spatial identity artifacts.
+
+As a rapidly emerging research frontier, existing video customized methodologies currently focus on either identity or motion independently. VideoBooth [24] achieves subject identity-driven generation by injection of reference image embedding, whileAnimateDiff [12] achieves the animation of static outputs into videos by appending trainable temporal modules to personalized text-to-image models. Recently, DreamVideo [52] employs independent training for each dimension (i.e., identity or motion) and directly blends their parameters during inference to achieve both the identity and motion customization simultaneously, demonstrating promising results to combine specific subject identity and motion patterns. Essentially, current works typically follow the isolated customized paradigm, where the subject identity or motion dynamics are customized exclusively.
+
+However, the existing isolated customized paradigm completely ignores the intrinsic mutual constraints and synergistic interdependencies between identity and motion, resulting in identity-motion conflicts throughout the generation process that systematically degrade either motion coherence, subject fidelity, or both dimensions simultaneously. The reason is that the step-by-step diffusion video synthesis process itself, by nature, with different denoising steps dynamically reweights their spatiotemporal focus, i.e., progressively refines identity details across frames, enabling complete modeling through increasing denoising
+
+
+Figure 2. Visual analysis of isolated training paradigm. We select different identities with the same motion pattern, fix the number of identity training steps, and gradually increase the number of motion training steps to achieve two-dimensional customization. The red box marking the relative optimal position of the same identity's fidelity. Experiments show that (1) adding motion prior significantly damages identity consistency; (2) We cannot find a universal step to minimize identity degradation from the positions of the red boxes for different identities.
+
+steps. The existing isolated customized paradigm violates this natural progression through indiscriminate dimensional over-specialization across all time steps, since they enforce uniform step sampling during motion/identity customized training, thereby inducing conflicting optimization trajectories between motion and identity accuracy. Consequently, existing methodologies inevitably cause mutual performance deterioration, that is, motion customization undermines the pre-trained video model's inherent identity priors, or vice versa. As shown in Fig. 2, (1) adding the motion prior irreversibly reduced identity fidelity, indicating that isolated training fails to resolve dimensional conflicts during inference and leads to performance degradation; and (2) as motion training steps increased, optimal fidelity for different identities occurred unpredictably, suggesting that no universal number of training steps minimizes degradation. In summary, the existing paradigm does not meet the consistency and flexibility requirements of video customization tasks.
+
+In this paper, we introduce DualReal, a novel framework that, for the first time, employs adaptive joint training to collaboratively construct interdependencies between identity and motion, which meets the consistency requirements of customized video generation in both identity and motion, as shown in Fig. 1. Technically, DualReal is composed of two complementary units: (1) Dual-aware Adaptation dynamically switches the training step (i.e., either identity
+
+or motion) to learn the current information, guided by the other dimension prior. It also employs a regularization strategy to prevent dimensional knowledge leakage by blocking the parameter updates of the non-training dimension using gradient masking, thereby achieving effective joint training; (2) **StageBlender Controller** operates through coordinated utilization of denoising-stage progression and Diffusion Transformer (DiT) layer-depth variations during training. By adaptively allocating hierarchical focus (i.e., fine-grained adjustments for identity patterns and motion dynamics), it resolves dimensional competition across processing stages. This granularity-aware guidance ultimately achieves dimensional lossless fusion.
+
+Our contributions can be summarized as follows:
+
+Concepts. For the first time, we (1) point out that the isolated paradigm causes mutual performance deterioration (identity fidelity and motion coherence) because it ignores the intrinsic constraints and synergistic; (2) present DualReal, a novel paradigm that employs adaptive joint training to collaboratively construct interdependencies.
+
+Technology. The proposed DualReal framework consists of two components: (1) Dual-aware Adaptation, which alternates between identity and motion training phases, leveraging dimension-specific guidance and regularization to prevent information leakage and enable joint training; (2) StageBlender Controller, which adaptively coordinates denoising stages and DiT depths to guide modes at different granularities, resolving conflicts and enabling seamless fusion of identity and motion patterns.
+
+Performance We constructed a more comprehensive evaluation benchmark than existing methods. The experimental results show that DualReal improves CLIP-I and DINO-I metrics by $21.7\%$ and $31.8\%$ on average, and achieves top performance on nearly all motion quality metrics, demonstrating the efficiency of our framework.
+
+# 2. Related Work
+
+# 2.1. Text-to-video Diffusion Models
+
+Recent advances in generative models have significantly improved the quality and versatility of synthetic content[9, 16, 19, 20, 42, 59]. DQVAE [20] generates images autoregressively in a more effective coarse-to-fine order. Text-to-video generation aims to generate realistic videos based on prompts and has recently received growing attention [1, 12, 32, 34, 46, 48, 49, 54, 56, 57]. Current text-to-video generation architectures primarily fall into two categories [33, 37]. UNet-based video diffusion frameworks utilize hierarchical enc-dec with spatiotemporal learning [3, 12, 16, 17, 42, 48, 54], e.g., Video diffusion models [16] pioneered diffusion model applications in video generation through pixel-space video distribution modeling. Make-A-Video [42] andAnimateDiff [12] augment pretrained text
+
+to-image models with motion modules. Recent advances in scalability drive the shift toward transformer-based architectures with joint spatiotemporal modeling [23, 25, 30, 32, 56], achieving revolutionary progress in video generation. Sora [32] introduces the diffusion-transformer framework, achieving cinematic-quality extended video synthesis with temporal stability. CogVideoX [56] introduces an expert transformer for enhanced text-video feature fusion. While diffusion transformers exhibit strong generative capacities, their architectural constraints in spatiotemporal decoupling inherently limit dynamic concept embedding.
+
+# 2.2. Generation Model Customization
+
+Generation Model Customization has emerged as a pivotal strategy[7, 21, 29, 41, 43]. In contrast to domain-agnostic generation frameworks, customized visual synthesis exhibits superior adaptability in addressing personalized visual requirements via parametric adaptation mechanisms[6, 8, 10, 13, 20, 38, 39, 51]. Textual inversion [10] aligns visual-textual semantics through text embedding optimization. Dreambooth [38] through full model fine-tuning of diffusion architectures to inject subject-specific priors. RealCustom[21, 29] disentangles similarity from controllability by precisely limiting subject influence to relevant parts only. Building upon these foundational approaches, contemporary video customization research explores analogous methodologies[2, 5, 11, 14, 28, 31, 36, 52, 53]. MotionBooth [53] proposes a comprehensive video diffusion model fine-tuning coupled with attention map manipulation for motion control during inference. DreamVideo [52] develops decoupled adapter training with joint inference mechanisms, coordinating subject customization and motion preservation during generation.
+
+# 3. Methodology
+
+Given a series of identity-specific images and motion sequences, DualReal through an innovative joint training framework, synthesizes coherent motion while preserving full-frame identity fidelity, as detailed in Fig. 3. During training, DualReal dynamically switches optimization focus between identity and motion, adjusting the module parameters through specific guidance. To address the key challenges: (1) enabling joint identity-motion interaction modeling in unified parameter spaces. (2) mitigating attribute leakage risks in alternating training dimensions. We propose the Dual-aware Adaptation architecture with a complementary regularization strategy in Sec. 3.2, forming an integrated framework for parameter-shared adaptation. Moreover, we propose StageBlender Controller, which leverages the denoising stages and DiT depths to guide different dimensions with adaptive granularity, avoiding conflicts at various stages and ultimately achieving high-fidelity fusion of identity and motion in Sec. 3.3.
+
+
+Figure 3. Overall framework of DualReal. At each training step, we first dynamically switch the training step $Z$ (i.e., identity or motion) to determine the data processing path. The specific data undergoes noise injection and combines with the text embeddings. StageBlender Controller governs two-dimensional adapters' contributions in Dual-Aware Block (DA-Block) through time-aware conditioning of current denoising step and fused feature representations. In DA-Block, the training-stage adapter learns the current information guided by the frozen dimension prior, and employs a regularization strategy to avoid dimensional knowledge leakage, achieving joint training. Both branches engage in residual connections with DiT outputs.
+
+# 3.1. Preliminary
+
+DiT-based Models. Most DiT-based models [25, 30, 32, 56] process concatenated conditioning prompt and spatiotemporal visual tokens through transformer layers, establishing multi-modal coupling between text-guided semantic contexts and visual representations in latent space. Despite achieving remarkable capabilities in generic generation scenarios, this architecture fundamentally constrains conventional personalization frameworks that demand decoupled control along spatial-temporal axes [50, 53].
+
+# 3.2. Dual-aware Adaptation
+
+To achieve joint training of identity and motion while resolving dimensional conflicts, we innovatively proposed Dual-aware Adaptation, which leverages the prior from one dimension to guide the training of the other while preventing information leakage through a regularization strategy, as shown in the lower half of Fig. 3.
+
+Joint Identity-Motion Optimization. Different from some approaches that fine-tune the whole diffusion model [38], DualReal first dynamically switches the training step (i.e., motion-focused or identity-focused) with the predefined hyperparameter ratio before each denoising iteration; the corresponding data is then sent to the DiT. The input of $i$ -th block is the joint feature $f_{\mathrm{in}}^i = [f_{\mathrm{text}}^i, f_{\mathrm{visual}}^i] \in \mathbb{R}^{B \times (n_t + n_v) \times c}$ , where $n_t, n_v$ represent the number of text and visual tokens respectively. The adapters employ the bottleneck architecture with skip connections [52]:
+
+$$
+f _ {\mathrm {i d}} ^ {i} = \sigma \left(f _ {\mathrm {i n}} ^ {i} * \mathbf {W} _ {\mathrm {d o w n}} * \mathbf {W} _ {\mathrm {u p}}\right), \tag {1}
+$$
+
+$$
+f _ {\mathrm {m o}} ^ {i} = \sigma \left(\left(f _ {\mathrm {i n}} ^ {i} * \mathbf {W} _ {\text {c o n d}}\right) * \mathbf {W} _ {\text {d o w n}} ^ {\prime} * \mathbf {W} _ {\text {u p}} ^ {\prime}\right), \tag {2}
+$$
+
+where the activation function $\sigma$ corresponds to GELU [15], $\mathbf{W}$ and $\mathbf{W}'$ denote the identity and motion linear projection weights, respectively, both operating on hidden dimension $d$ . The weight $\mathbf{W}_{\mathrm{cond}} \in \mathbb{R}^{e \times c}$ of conditional linear maps
+
+reference image embedding to the latent space [52].
+
+Through StageBlender Controller constraint (Sec. 3.3), the motion adapter outputs are scaled by weight coefficient $\omega_{i}$ , with identity outputs weighted by the complementary coefficient $(1 - \omega_{i})$ . The modulated features are aggregated into the output of DiT blocks through residual connections. The above process can be formulated as:
+
+$$
+\hat {f} _ {\text {o u t}} ^ {i} = \omega_ {i} * f _ {\mathrm {m o}} ^ {i} + (1 - \omega_ {i}) * f _ {\mathrm {i d}} ^ {i} + f _ {\mathrm {d i t}} ^ {i}, \tag {3}
+$$
+
+where $f_{\mathrm{d}\mathrm{it}}^{i}$ denotes the output of the $i$ -th DiT layer and $\hat{f}_{\mathrm{out}}^{i}$ indicates the aggregated output of the final block. This parametric constraint intrinsically balances feature contributions across blocks and denoising stages, while structurally enforcing dedicated attention to either identity preservation or motion dynamics during adaptation.
+
+Regularization Strategy. A critical challenge in joint dimensional training arises from the significant distribution shift across different training dimensions, where unconstrained optimization usually causes destructive interference between cross-dimension knowledge observed in previous work [53, 55]. For example, fine-tuning the motion adapter with static images during the temporal training phase irreversibly degrades its dynamic generation capability, with analogous effects occurring during identity adaptation. To resolve this, we employ regularization with the gradient mask $M$ to activate only the corresponding adapter parameters based on a binary selector variable $Z \in \{0,1\}$ , optimizing motion coherence(i.e., through motion adapter), or preserving identity consistency(i.e., through identity adapter), which can be formulated as:
+
+$$
+\theta^ {(t + 1)} = \theta^ {(t)} - M \odot \nabla_ {\theta} \mathcal {L}, \tag {4}
+$$
+
+$$
+M = Z \cdot M _ {m} + (1 - Z) \cdot M _ {i}. \tag {5}
+$$
+
+The mask conditions are defined as:
+
+$$
+\left\{ \begin{array}{l} M _ {m} [ l ] = 1 \Longleftrightarrow M _ {m} \cdot \theta [ l ] = \theta_ {m}, \\ M _ {i} [ k ] = 1 \Longleftrightarrow M _ {i} \cdot \theta [ k ] = \theta_ {i}, \end{array} \right. \tag {6}
+$$
+
+where $\mathcal{L}$ denotes the video diffusion reconstruction loss. The adapter parameters $\theta$ are split into motion $(\theta_{m})$ and identity $(\theta_{i})$ components using binary masks $M_{m}$ and $M_{i}$ .
+
+Simultaneously, we keep a frozen adapter in a waiting state to inform modal expertise for active adapters during forward propagation, enabling two-dimensional features referencing within current data streams. The features from the frozen adapter act as intrinsic regularization to constrain dimension overfitting, thereby facilitating mutual reference learning without interference.
+
+# 3.3. StageBlender Controller
+
+Furthermore, in order to resolve dimensional competition across the processing stage, we propose the StageBlender
+
+
+Figure 4. Illustration of proposed StageBlender Controller, which employs an Adaptive LayerNorm mechanism that modulates text-visual feature based on timestep-conditional embeddings, then maps the feature to multiple groups after residual gated connections. These scaled weights are subsequently routed to their respective DA-Blocks for processing.
+
+Controller that governs dimensional contributions through time-aware conditioning of block-level scaling coefficients, which empowers the DA-Block to adaptively allocate specific dimension shares (i.e., achieve granularity decoupling) through the mechanism detailed in Fig. 4. Specifically, this module dynamically generates multiple sets of scaling weights according to denoising timestep embedding and the fused text-visual features. For the input feature $f_{\mathrm{in}} = [f_{\mathrm{text}}^{1}, f_{\mathrm{visual}}^{1}] \in \mathbb{R}^{B \times (n_t + n_v) \times c}$ , the processing flow first extracts salient features through pooling, then adaptively modulates them via DiT Adaptive LayerNorm [56] with injected timestep embeddings $t$ . This operation can be formulated as:
+
+$$
+f ^ {\prime} = \operatorname {P o o l i n g} \left(f _ {\text {i n}}, \dim = 1\right) * \mathbf {W}, \tag {7}
+$$
+
+$$
+f ^ {\prime \prime} = \operatorname {M L P} \left(\operatorname {L a y n e r N o r m} \left(f ^ {\prime}\right)\right) * \alpha + \beta , \tag {8}
+$$
+
+where the $\mathbf{W} \in \mathbb{R}^{c \times t_{\mathrm{dim}}}$ denotes the weight matrix with $t_{\mathrm{dim}}$ as the channel dimension of timestep embedding, and $\alpha, \beta$ are defined as:
+
+$$
+\mathbf {h} = \operatorname {M L P} (\operatorname {S i L U} (\mathbf {t})) , \tag {9}
+$$
+
+$$
+\alpha , \beta , \gamma = \mathbf {h} _ {: d}, \mathbf {h} _ {d: 2 d}, \mathbf {h} _ {2 d: 3 d}. \tag {10}
+$$
+
+The computed weight coefficients are then integrated to enable gated fusion between the timestep and visual text tokens, as formulated below:
+
+$$
+f _ {g} = f ^ {\prime \prime} + \gamma * f ^ {\prime}. \tag {11}
+$$
+
+Through empirical analysis of DiT-based denoising architectures, we observe that deeper blocks inherently special-
+
+
+Figure 5. Qualitative comparison with existing methods. Compared with other methods, DualReal achieves high identity consistency with coherent motion, demonstrating the advantage of joint training in balancing pattern conflicts.
+
+
+
+ize in processing concrete, fine-grained features. To enhance hierarchical decoupling, we implement a downward-propagating MLP that transforms integrated features into weight groups, as formalized below:
+
+$$
+\underbrace {\omega^ {(1)} , \dots , \omega^ {(n)}} _ {\text {W e i g h t s g r o u p s}} = \operatorname {s o f t m a x} \left(\Gamma \cdot \left(\mathrm {M L P} \left(f _ {g}\right)\right)\right), \tag {12}
+$$
+
+where $\Gamma$ is the projection operator: $\mathbb{R}^L\to \mathbb{R}^n$ . The $L$ denotes the DiT block depth, and $n$ specifies the number of disentangled weight groups; each group then sequentially controls its assigned layers via parameter assignment.
+
+# 4. Experiment
+
+# 4.1. Setup
+
+Datasets. The evaluation datasets are divided into two components: identity images and motion videos. For identity customization, 50 subjects are strictly selected from previous works [26, 27] and Internet collections (including pet, plush, etc.), with each subject containing 3-10 images. For motion customization, 21 motion sequences with challenging dynamic patterns are collected from public datasets [44, 45]. Additionally, each case is provided with 50 various
+
+prompts containing different editability (i.e., decoration or environment) to evaluate the method's editability and scene versatility sequentially.
+
+Baselines. Among existing methods, DreamVideo [52] achieves customization of both identity and motion. For fair comparison, we implement two approaches from the same DiT backbone: (1) CogVideoX-5B [56]: Sequential full-parameter fine-tuning with identity then motion data as in the DreamBooth [38] paradigm. (2) LoRA fine-tuning [18]: Separate training of two LoRA modules for identity and motion, then fuse their parameters during inference. Additionally, the identity module of MotionBooth [53] introduces irrelevant random videos during training to preserve the model's motion capability, so we compare our approach with this method as well. In summary, we evaluate our results against DreamVideo, CogVideoX-5B, LoRA fine-tuning, and MotionBooth to provide a more comprehensive performance analysis.
+
+Evaluation metrics. We use seven metrics across three dimensions. (1) Text-Video Consistency is measured by CLIP-T scores, computed as the CLIP [35] cosine similarity between text prompts and all generated frames. (2) Identity Fidelity is quantified using DINO-I and CLIP-I scores, which assess feature similarity between generated frames and ref
+
+| Method | Text Consistency | Identity Similarity | Motion Quality |
| CLIP-T ↑ | CLIP-I ↑ | DINO-I ↑ | T.Flickering ↑ | T.Cons ↑ | Motion Smoothness ↑ | Dynamic Degree |
| MotionBooth [53] | 0.317 | 0.566 | 0.459 | 0.962 | 0.972 | 0.973 | 10.95 (-1.07) |
| LoRA [18] | 0.323 | 0.425 | 0.286 | 0.956 | 0.976 | 0.973 | 25.34 (+13.32) |
| CogVideoX-5B [56] | 0.336 | 0.521 | 0.424 | 0.947 | 0.973 | 0.965 | 26.51 (+14.49) |
| DreamVideo [52] | 0.278 | 0.458 | 0.334 | 0.949 | 0.963 | 0.968 | 8.841 (-3.18) |
| DualReal (Ours) | 0.323 | 0.629 | 0.551 | 0.965 | 0.983 | 0.978 | 14.96 (+2.94) |
+
+erence identity images via DINO ViTS/16 [4] and enhanced CLIP [40] embeddings, respectively. (3) Temporal Motion Quality is evaluated with four metrics: T-Cons [9] for temporal consistency, Motion Smoothness (MS) for global fluidity, Temporal Flickering (TF) for high-frequency inconsistencies measured by mean absolute differences between adjacent frames, and Dynamic Degree (DD) leveraging RAFT optical flow estimation [47] to quantify motion intensity (We quantify the method's deviation from the benchmark to determine the intensity consistency of movement). Notably, MS, TF, and DD are adopted from the comprehensive video benchmark VBench [22].
+
+# 4.2. Main Results
+
+Qualitative results. Qualitative experiments in Fig. 5 show that while MotionBooth maintains identity fidelity, it fails to model motion patterns effectively. DreamVideo suffers from pattern conflicts during inference, resulting in inconsistent identity. Similarly, CogVideoX-5B and LoRA struggle to preserve identity due to their decoupled training methods. In contrast, DualReal achieves high identity consistency with coherent motion, demonstrating the advantage of joint training in balancing pattern conflicts.
+
+Quantitative results. As shown in Tab. 1, DualReal achieved average improvements of $21.7\%$ on CLIP-I and $31.8\%$ on DINO-I, recorded the best results on three motion quality metrics (T.Cons, Motion Smoothness, and Temporal Flickering), and ranked second on CLIP-T. Although our DD metric for quantifying motion intensity is not high, we evaluated all motion data and found an average DD of 12.02. Our metric deviates slightly from it, proving there is no collapse in motion amplitude. Overall, our method significantly enhances motion coherence and identity fidelity while preserving text consistency, further validating our adaptive joint training approach.
+
+Table 1. Quantitative comparison of personalization video generation for customized subject and motion. We highlight the best and second-best values for each metric. “T.Cons” and “T.Flickering” denote Temporal Consistency and Temporal Flickering, respectively. Compared with other methods, DualReal achieved average improvements of $21.7\%$ on CLIP-I and $31.8\%$ on DINO-I, recorded the best results on three motion quality metrics (T.Cons, Motion Smoothness, and Temporal Flickering), and ranked second on CLIP-T. The motion datasets achieve an average Dynamic Degree of 12.02, and parenthetical values quantify the current method's deviation from this benchmark to determine the intensity consistency of movement.
+
+| Settings | CLIP-T | CLIP-I | DINO-I | DD |
| w/o Dual-aware Adaptation | 0.334 | 0.616 | 0.647 | 3.51(-5.53) |
| w/o StageBlender Controller | 0.346 | 0.619 | 0.652 | 5.70(-3.31) |
| w/o Weight Groups | 0.335 | 0.662 | 0.766 | 5.83(-3.12) |
| ours | 0.333 | 0.674 | 0.771 | 6.34(-2.70) |
+
+Table 2. Quantitative ablation studies on each component. We implement Dual-aware Adaptation removal by separately training the two modalities and directly blending their parameters during inference, following the approach of DreamVideo. The motion datasets achieve an average Dynamic Degree of 9.04.
+
+| Group Cardinality | CLIP-T | CLIP-I | DINO-I | DD |
| n=1 | 0.335 | 0.662 | 0.766 | 5.83 (-3.21) |
| n=2 | 0.343 | 0.632 | 0.660 | 5.49 (-3.55) |
| n=42 | 0.336 | 0.631 | 0.706 | 6.24 (-2.80) |
| ours(n=7) | 0.333 | 0.674 | 0.771 | 6.34 (-2.70) |
+
+Table 3. Quantitative ablation studies of group cardinality. The results suggest that very small groups may lack sufficient context and overly large groups may dilute crucial details, making balanced group cardinality essential for optimal performance.
+
+# 4.3. Ablation Studies
+
+We evaluate our method by conducting ablation studies on a smaller evaluation subset, with the observed trends aligning with those of the main evaluation set. Additional ablation results are provided in the supplementary.
+
+Quantitative experiment. The ablation study in Tab. 2 shows that removing Dual-aware Adaptation or the Stage-Blender Controller slightly increases the text consistency metric CLIP-T but significantly decreases identity similarity and motion intensity, highlighting the need for joint dimension training and granular control. Additionally, metric
+
+
+Figure 6. Qualitative ablation studies on each component. (1) Omitting Dual-aware Adaptation introduces artifacts on the subject's hands and chin, significantly reducing clarity. Using fixed weights for the dimensional adapters without the StageBlender Controller causes the hands to become overly adapted to the motion pattern, and removing weight grouping reduces identity fidelity and background detail.
+
+changes diminish slightly when weight groups are removed. Qualitative experiment. Qualitative results in Fig. 6 reveal that omitting Dual-aware Adaptation produces artifacts on the hands and chin, degrading clarity. Using fixed weights for the dimensional adapters without the StageBlender Controller (i.e., direct fusion at inference) overfits the hands to motion patterns. Removing weight grouping (i.e., uniform block modulation) weakens identity fidelity and background detail. These observations confirm that every component is essential for high-quality customized generation. Effectiveness of group cardinality. As shown in Tab. 3, CLIP-I and DINO-I performance declines when group cardinality is either very small or very large, while a balanced group size $(n = 7)$ yields the best results. This suggests that very small groups may lack sufficient context and overly large groups may dilute crucial details, making balanced group cardinality essential for optimal performance.
+
+# 4.4. Visual analysis of StageBlender Controller
+
+As Fig. 7 shows, shallow blocks (Groups 1-6, blue) progressively increase identity weights during denoising, emphasizing early identity preservation. In contrast, the deepest block (Group 7, red) steadily raises motion weights to enhance motion modeling. Overall (orange dashed line), as
+
+
+Figure 7. Controller Visual Analysis. We show the Identity Weights trends across denoising steps for different block depths. (1) As denoising progresses, the diffusion model's emphasis shifts monotonically between identity and motion, with a growing focus on identity(orange dashed line); (2) The deepest block group exhibits an inverse pattern, i.e., with the denoising process increasingly prioritizing motion coherence modeling.
+
+denoising advances, the model increasingly prioritizes identity preservation over motion generation, highlighting the distinct roles of different network depths. These observations further confirm that: (1) as denoising progresses, the diffusion model's emphasis shifts monotonically between identity and motion, with a growing focus on identity; (2) DiT networks of different depths divide the tasks of modeling identity and motion differently at each denoising step, with the deepest network focusing on motion patterns and showing increased enhancement as denoising advances.
+
+# 5. Conclusion
+
+In this paper, we propose DualReal, a novel approach for customized video generation given a subject and motion. DualReal adaptively trains identity and motion jointly, resolving dimensional conflicts and enabling universal sample customization. Our framework leverages the prior from one dimension to guide the training of the other, while preventing information leakage through a regularization strategy. Simultaneously, we use a controller to guide the high-fidelity fusion of modes based on various denoising stages and DiT depths. Evaluated on a more comprehensive evaluation benchmark, our method improves CLIP-I and DINO-I metrics by $21.7\%$ and $31.8\%$ , and achieves top performance on nearly all motion quality metrics, demonstrating the efficiency of our adaptive joint training framework.
+
+# 6. Acknowledgment
+
+This research is supported by Artificial Intelligence National Science and Technology Major Project 2023ZD0121200, and National Natural Science Foundation of China under Grant 62222212 and 623B2094.
+
+# References
+
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+# DuoCLR: Dual-Surrogate Contrastive Learning for Skeleton-based Human Action Segmentation
+
+Haitao Tian
+University of Ottawa, Canada
+htian026@uottawa.ca
+
+# Abstract
+
+In this paper, a new contrastive representation learning framework is proposed to enhance action segmentation via pretraining using trimmed (single action) skeleton sequences. Unlike previous representation learning works that are tailored for action recognition and that develop isolated sequence-wise representations, the proposed framework focuses on exploiting multi-scale representations in conjunction with cross-sequence variations. More specifically, it proposes a novel data augmentation strategy, "Shuffle and Warp", which exploits diverse multi-action permutations. The latter effectively assist two surrogate tasks that are introduced in contrastive learning: Cross Permutation Contrasting (CPC) and Relative Order Reasoning (ROR). In optimization, CPC learns intra-class similarities by contrasting representations of the same action class across different permutations, while ROR reasons about inter-class contexts by predicting relative mapping between two permutations. Together, these tasks enable a Dual-Surrogate Contrastive Learning (DuoCLR) network to learn multi-scale feature representations optimized for action segmentation. In experiments, DuoCLR is pretrained on a trimmed skeleton dataset and evaluated on an untrimmed dataset where it demonstrates a significant boost over state-the-art comparatives in both multi-class and multi-label action segmentation tasks. Lastly, ablation studies are conducted to evaluate the effectiveness of each component of the proposed approach.
+
+# 1. Introduction
+
+Contrastive learning [4, 5, 18] opens a new opportunity for taking advantage of the growing volume of unlabeled data for learning a rich latent feature representation aware of underlying data structures and semantics without human annotations. This approach effectively reduces the need for extensive labeled data in downstream task fine-tuning. In human-centric video understanding, human skeleton data
+
+
+Figure 1. Limitation of traditional skeleton-based contrastive learning. (a): Distinct feature similarity matrices obtained from feature extraction on trimmed (upper) vs. untrimmed (lower) skeleton videos. Entry (i, j) represents the feature similarity (Eq. (1)) between action classes i and j. The feature extractor is learned on NTU RGB+D using AimCLR [18]. Trimmed and untrimmed videos are both sampled from PKU Part 1. For untrimmed videos, action-specific features are extracted via post-segmentation in the feature space using frame annotations (detailed in Sec. 3.3). (b): Trend of contrastive learning performance (detailed in Table 1) in skeleton action segmentation by publication year.
+
+
+
+[12, 29, 35] has become a widely used modality in contrastive learning as it depicts the trajectories of key body joints and provides a compact and robust depiction of human motion that is resilient to environmental variations. Existing research primarily involves trimmed (single action) skeleton sequences into contrastive learning, where the model treats each sequence as an instance and learns intra-action temporal representations (i.e., similarities) through instance discrimination [6, 9, 46, 47]. The learned representations have been effectively transferred into trimmed-sequence-based downstream tasks such as action recognition [1, 9, 17, 20, 28, 38, 42, 48, 54] and action retrieval [13, 18, 24, 34, 49].
+
+However, complex human-centric video understanding applications such as action segmentation often involve untrimmed long skeleton videos exhibiting multiple actions and complex action correlations. While focusing on sequence-wise instance discrimination tasks, traditional contrastive learning generally neglects the exploitation of inter-sequence temporal dependencies (i.e., contexts) that
+
+
+Figure 2. The proposed contrastive learning framework for action segmentation utilizes multi-action permutations. For example, six single-action skeleton sequences are randomly shuffled and warped into two sequences, Permutation 1 and Permutation 2, with three shared actions. Such a data augmentation introduces dynamic cross-sequence variations that enhance learning in two ways: i) CPC contrasts intra-class instance across different permutations, promoting permutation-invariant representations despite changing contexts (e.g., "Put on a hat" appears in both permutations but in different contexts); ii) ROR captures inter-class dependencies by mapping one permutation to another (e.g., learning the transformation from (b, a, c) to (c, b, a)).
+
+are critical for action segmentation. To highlight this limitation, Fig. 1a experimentally verifies that a state-of-the-art contrastive learning paradigm [18], which learns isolated sequence-wise representations, may lead to significantly different feature representations when applied to trimmed and untrimmed videos. We hypothesize that such a discrepancy results from the extraction of inconsistent action representations from dynamic action contexts permuted in untrimmed sequences, which leads to suboptimal transfer learning performance to action segmentation tasks (as illustrated in Fig. 1b).
+
+In this work, a new contrastive learning framework is proposed to improve action segmentation on untrimmed videos by pretraining on trimmed skeleton videos. First, the framework leverages multi-action permutations to fulfill cross-sequence data augmentation. Previous single-action augmentations use simple sequence-wise modifications, e.g., spatial transformation [9, 18] and temporal scaling [25, 49], that generate low-level context-free data variations. This work rather introduces "Shuffle and Warp" to exploit high-level contextual variations: (1) "Shuffle" treats trimmed skeleton sequences as modular action elements that can be sampled and shuffled, introducing dynamic cross-sequence variations; and (2) "Warp" leverages geometrical transformations to concatenate the shuffled sequences into a view-consistent permutation of actions.
+
+Second, two new surrogate tasks ensure multi-scale representation learning. To fully exploit the temporal variations present in multi-action permutations, this work
+
+introduces two contrastive learning surrogate tasks, Cross Permutation Contrasting (CPC) and Relative Order Reasoning (ROR). As conceptually illustrated in Fig. 2, CPC learns permutation-invariant intra-class similarities via instance discrimination where the representation of the same action class should be similar regardless of context variations arising from their neighboring segments. ROR focuses on the permutation-aware inter-class contexts by predicting the temporal mapping between action permutations, encouraging the model to learn relative positioning among actions, thereby adding a complementary regularization to the feature space.
+
+Lastly, a hierarchical network facilitates sliding-window-free transfer learning. We amalgamate the key heuristics into a Dual-Surrogate Contrastive LeaRning (DuoCLR) network that can be trained end-to-end. Unlike previous works [7, 28, 48, 50] relying on a single visual encoder, DuoCLR employs a cascaded structure [16] composed of a visual encoder and a temporal encoder. The additional temporal encoder enables a large temporal receptive field, allowing the model to capture long-range action dependencies without requiring sliding-window operations [7, 11, 48] on untrimmed skeleton videos. As a result, DuoCLR surpasses state-of-the-art methods in action segmentation (Fig. 1b). After pretraining, both encoders can be jointly fine-tuned as a feature extractor for downstream tasks.
+
+The original contributions of the work are threefold. First, a new contrastive learning framework for skeleton data-based representation learning enables trimmed sequences to learn a fine-grained representation for action segmentation. Second, a new data augmentation strategy, "Shuffle and Warp", for skeleton data introduces variations in between data sequences to improve feature learning. Third, the framework builds upon a dual-contrastive approach by combining CPC and ROR. It focuses on instance coherence and instance correlation, both critical for action segmentation. The project is available at: https://htian026.github.io/DuoCLR, which contains code implementation.
+
+# 2. Related work
+
+Skeleton-based Action Segmentation. Compared to skeleton action recognition [6, 14, 25, 44, 46, 47] that aims at sequence-wise action classification, skeleton action segmentation [2, 3, 16, 26, 31] is inherently more challenging as the model must aggregate both action patterns and contexts among multiple actions permuted in a single sequence. To tackle the difficulty, recent research [16, 21, 21, 26] proposes to optimize an end-to-end model that incorporates frame-wise action classification into supervised training. Yet, training an action segmentation model from scratch relies heavily on frame-level
+
+annotations that are costly and time-consuming to generate [12, 29]. In this work, we circumvent the data annotation usage by leveraging trimmed skeleton videos for pretraining, where a contrastive learning network can leverage numerous action permutations to pre-learn a feature extractor relevant to action segmentation, and quick fine-tuning to untrimmed videos.
+
+Skeleton Data Augmentation is primarily achieved by single-action skeleton modifications. For instance, studies [1, 7, 18, 20, 24, 28, 38, 42, 49, 53] delve into designing more effective single-action augmentations, e.g., "Shear", "Crop", "Spatial Flip", "Spatial Rotate", "Spatial Jitter", "Axis Mask", "Gaussian Noise", and "Gaussian Blur", demonstrating the effectiveness of carefully involving multiple augmentations in representation learning [18, 49]. Recent works also leverage multi-action skeleton augmentations, e.g., "Latent Action Composition" [48] and "Skeleton Actionlet" [28] are proposed to mix spatiotemporal statistics of two sequences; "Skeleton-Mix" [8, 19, 28, 30, 43, 51] is proposed to generate a synthetic sequence by merging both data and label from two sequences into a composable sequence. SCS [39] proposes a temporal skeleton stitching scheme to generate multi-action stitched sequences. However, it imposes an offline data generation process requiring time-consuming frame registration operations. In contrast, this work proposes utilizing online multi-action permutations, "Shuffle and Warp", a new data augmentation scheme which will be detailed in Section 3.2.
+
+Skeleton-based Representation Learning [4, 5] is primarily achieved by learning action similarities from augmented skeleton views via effective surrogate tasks such as instance discrimination [1, 7-9, 13, 17-20, 24, 28, 42, 49, 53, 54], jigsaw puzzles [27, 37], adversarial learning [52], and language-video contrasting [21]. However, prior works mainly produce sequence-level representations, which are effective for simplified downstream tasks like action recognition but may be insufficient for action segmentation, where fine-grained feature representations are crucial. Recent efforts [7, 11, 48] attempt to mitigate this by applying sliding windows to generate fixed-length action clips from untrimmed sequences, enabling the use of standard action recognition models. However, this strategy introduces noisy boundaries, leading to degraded segmentation accuracy (experimentally verified in Section 4.3). These limitations highlight the need for a contrastive learning paradigm tailored for action segmentation.
+
+# 3. Dual-Surrogate Contrastive Learning
+
+# 3.1. Overview
+
+Let $X \in \mathbb{R}^{T \times V \times C}$ be a trimmed skeleton video with $T$ skeleton frames $V$ skeleton joints, and $C$ spatial dimensions, which covers the motion of a single action class. A
+
+contrastive learning paradigm aims to use trimmed skeleton videos to pretrain a feature extraction network $\mathcal{F}$ by which the features of the same action class should be similar. In previous studies [18, 20, 24], feature similarity between two sequences, $X_{i}$ and $X_{j}$ , is calculated as:
+
+$$
+\operatorname {s i m} \left(\mathcal {F} \left(X _ {i}\right), \mathcal {F} \left(X _ {j}\right)\right) = \frac {\mathcal {F} \left(X _ {i}\right) \mathcal {F} \left(X _ {j}\right)}{\left| \mathcal {F} \left(X _ {i}\right) \right| \left| \mathcal {F} \left(X _ {j}\right) \right| \cdot \tau} \tag {1}
+$$
+
+where $\tau$ acts as the temperature parameter. This work aims to pretrain a $\mathcal{F}$ using Dual-Surrogate Contrastive Learning (DuoCLR) and customize a task-specific (action segmentation) layer $\mathcal{C}$ for a target dataset composed of a small number of frame-wise labeled and untrimmed videos. Section 3.2 describes the Shuffle and Warp data augmentation technique for generating dynamic multi-action permutations. Section 3.3 details the network structure of $\mathcal{F}$ . In Sections 3.4 and 3.5, DuoCLR introduces two surrogate tasks (as conceptually depicted in Fig. 3), Cross Permutation Contrasting (CPC) and Relative Order Reasoning (ROR), respectively.
+
+# 3.2. Multi-Action Permutations
+
+Capturing temporal contexts is critical for action segmentation as it requires the model to discern the state of actions over a single untrimmed skeleton sequence. Since trimmed skeletal data lacks such context, Shuffle and Warp is introduced to generate dynamic multi-action permutations to support improved contrastive learning for action segmentation.
+
+Temporal Shuffling was previously utilized to generate single-action augmentation where segments of a trimmed sequence are shuffled to solve a jigsaw puzzle task for action recognition [27, 33]. In this work, we rather involve multiple trimmed sequences at each augmentation of temporal shuffling to introduce cross-sequence variations. Specifically, let $\mathcal{X} = \{X^{(a)}, X^{(b)}, X^{(c)}, \ldots\}$ be a set of trimmed skeleton sequences sampled from a data batch, we can generate a multi-action permutation as:
+
+$$
+\operatorname {S h u f f l e} (\mathcal {X}, \mathcal {P}) = \operatorname {c o n c a t} \left(X ^ {\mathcal {P} [ 1 ]}, X ^ {\mathcal {P} [ 2 ]}, X ^ {\mathcal {P} [ 3 ]}, \dots\right) \tag {2}
+$$
+
+where the function "Shuffle" first permutes the elements of $\mathcal{X}$ according to the permutation $\mathcal{P}$ , e.g., $\mathcal{P} = (b, c, a, \ldots)$ , and then generates a single sequence using the tensor concatenation operation "concat". The proposed data augmentation supports both labeled and unlabeled skeleton data where $a, b, c, \ldots$ denotes action classes while labeled and sequence indices while unlabeled (discussed in Section 4.3).
+
+Temporal Warping. However, skeleton sequences collected under different imaging configurations may lead to unnecessary data variations in the skeleton scale and poses [35]. A representation learning network may use such intricacies to develop shortcuts to fulfill the surrogate task of
+
+
+Figure 3. Computational workflow of the proposed DuoCLR approach. Trimmed single-action skeleton videos are augmented by using "Shuffle and Warp" on the input. In DuoCLR, the two surrogate tasks, "ROR" and "CPC", share the feature encodings, $z_{i}^{(n)}$ and $z_{j}^{(n)}$ , while fulfilling different pipelines for representation learning. By solving simultaneous CPC and ROR, the network learns a fine-grained action representation for action segmentation.
+
+
+
+
+
+contrastive learning [18, 38]. To tackle the issue, temporal warping is newly proposed to eliminate the unnecessary data variations by using a pairwise sequence concatenation operation. Specifically, given two heterogenous sequences $X_{i}\in \mathbb{R}^{T_{i}\times V\times C}$ and $X_{j}\in \mathbb{R}^{T_{j}\times V\times C}$ , it uses a rotation $\mathcal{R}\in \mathbb{R}^{C\times C}$ , a translation $\mathcal{T}\in \mathbb{R}^{C\times 1}$ , and a scaling factor $s\in \mathbb{R}$ , to map $X_{j}$ into the camera configuration of $X_{i}$ . In this way, "Warp" is defined as:
+
+$$
+\operatorname {W a r p} \left(X _ {i}, X _ {j}\right) = \operatorname {c o n c a t} \left(X _ {i}, s \left(X _ {j} * \mathcal {R} + \mathcal {T}\right)\right) \tag {3}
+$$
+
+where $*$ denotes the batched dot product. Details regarding parameters estimation and sequence operation are available in supplementary material.
+
+At last, we use "Shuffle and Warp" to generate the multi-action permutation $\mathcal{H}$ as follows
+
+$$
+\mathcal {H} = \operatorname {W a r p} (\operatorname {S h u f f l e} (\mathcal {X}, \mathcal {P})), \tag {4}
+$$
+
+which denotes that $\mathcal{H}$ is generated by recursively operating the "Warp" operation on shuffled $\mathcal{X}$ under $\mathcal{P}$ .
+
+# 3.3. Feature Extraction
+
+In this work, the feature extraction network $\mathcal{F}$ is composed of a visual encoder and a temporal encoder, as illustrated in Fig. 3.
+
+Visual Encoder. It is common in the research community [13, 17, 20, 25, 28, 28] to use a graph convolutional network (GCN) [46] as a visual encoder to parse intermediate skeleton feature embeddings. In this work, we removed the temporal pooling layer of GCN to keep the feature's temporal resolution, i.e., $\mathrm{GCN}:\mathbb{R}^{T\times V\times C}\to \mathbb{R}^{T\times C_1}$ . However, a vanilla GCN may be limited by their small temporal receptive fields [16], thus not exploiting contextual structures that are relevant to action segmentation.
+
+Temporal Encoder. In order to effectively capture action relationships, we stack a temporal encoder onto the visual encoder to constructs $\mathcal{F}$ . The temporal encoder adopts a temporal convolution network [15] that utilizes a series of dilated temporal convolutions to aggregate long-range temporal contexts of the hidden state from the visual encoder, i.e., $TCN: \mathbb{R}^{T \times C_1} \to \mathbb{R}^{T \times C_2}$ .
+
+At last, given a skeleton sequence input $X$ , its hidden feature representation $h$ is obtained as:
+
+$$
+h = \underbrace {(\mathrm {T C N} \circ \mathrm {G C N})} _ {\mathcal {F}} (X) \tag {5}
+$$
+
+Multi-grained feature projections. DuoCLR differs from prior contrastive learning works that input single-action sequences. DuoCLR rather utilizes multi-action permutations for feature extraction prior to contrastive learning. As illustrated in Fig. 3, DuoCLR uses Shuffle and Warp (Eq. (4)) to generate a pair of multi-action permutations $\mathcal{H}_i$ and $\mathcal{H}_j$ of $\mathcal{X}$ with two random permutations $\mathcal{P}_i$ and $\mathcal{P}_j$ . Using Eq. (5), it obtains multi-action representations $h_i = \mathcal{F}(\mathcal{H}_i)$ and $h_j = \bar{\mathcal{F}} (\mathcal{H}_j)$ , where $\bar{\mathcal{F}}$ denotes a moving average of the feature extractor $\mathcal{F}$ and we follow the same implementation introduced in [18]. For notation simplicity, let's assume the cardinality of $\mathcal{X}$ is 3, e.g., $\mathcal{X} = X^{(a)},X^{(b)},X^{(c)}$ , and assume $\mathcal{P}_i = (b,a,c)$ and $\mathcal{P}_j = (c,b,a)$ . In this way, DuoCLR generates multi-grained feature projections for contrastive learning by treating the feature representations, $h_i$ and $h_j$ , as concatenations of action-wise encodings: $h_i = \text{concat}(h_i^{(b)},h_i^{(a)},h_i^{(c)})$ and $h_j = \text{concat}(h_j^{(c)},h_j^{(b)},h_j^{(a)})$ . Furthermore, an MLP-based projection head is used to generate local and global feature projections:
+
+$$
+z _ {i} ^ {(n)} = M L P [ \phi (h _ {i} ^ {(n)}) ]; z _ {i} = M L P [ \phi (h _ {i}) ] \qquad (6)
+$$
+
+where $n = a, b, c$ and $\phi$ denotes the temporal average pooling operation. Likewise, it generates $z_{j}^{(n)}$ and $z_{j}$ .
+
+# 3.4. Cross Permutation Contrasting (CPC)
+
+While treating each action within a permutation as an instance, individual instances of the same action class can have different contextual neighbors (e.g., the action "Put on a hat" in Fig. 2 may appear next to different actions in each permutation). Traditional methods [18, 25, 28, 48] overlook such information and learn isolated sequence-wise representations, thereby achieving suboptimal transferability in action segmentation (as illustrated in Fig. 1). In this work, DuoCLR utilizes multi-action permutations as data augmentation and employs Cross Permutation Contrasting (CPC) for self-supervised representation learning. Since the augmentation of action permutations expose the network to numerous action temporal contexts, CPC learns permutation-invariant temporal coherence where intra-class representations from the different permutations should be pulled together while inter-class representations should be pushed away.
+
+Permutation Bank-based Instance Discrimination. In implementation, CPC employs local feature projections $z_{i}^{(n)} \in \mathbb{R}^{C_{3}}$ and $z_{j}^{(n)} \in \mathbb{R}^{C_{3}}$ as positive pairs and formulates class-specific memory banks $\mathcal{N} = \{\mathcal{N}^{(m)}\}$ to store negative instances, each updated with $z_{j}^{(m)}$ where $m \neq n$ . Afterwards, it learns short-term invariant representations for each instance regardless of surrounding context changes by optimizing a InfoNCE loss [5]:
+
+$$
+\mathcal {L} _ {\mathcal {N}} ^ {(n)} = - \log \frac {\operatorname {s i m} \left(z _ {i} ^ {(n)} , z _ {j} ^ {(n)}\right)}{\operatorname {s i m} \left(z _ {i} ^ {(n)} , z _ {j} ^ {(n)}\right) + \sum_ {z ^ {-} \in \mathcal {N}} \operatorname {s i m} \left(z _ {i} ^ {(n)} , z ^ {-}\right)} \tag {7}
+$$
+
+where $z^{-}$ is a negative sample from the memory bank.
+
+Second, CPC also involves a permutation (multi-action) memory bank $\mathcal{M}$ in contrastive learning, which is updated by $z_{j}$ . When $\mathcal{H}_i$ and $\mathcal{H}_j$ share the same permutation, i.e., $\mathcal{P}_i = \mathcal{P}_j$ , it treats each permutation as an instance and encourages the network to learn long-term invariant representations of permutations. It calculates the similarity between permutation-wise positive pair, $z_{i} \in \mathbb{R}^{C_{3}}$ and $z_{j} \in \mathbb{R}^{C_{3}}$ , and optimizes the second InfoNCE loss as:
+
+$$
+\mathcal {L} _ {\mathcal {M}} = - \log \frac {\operatorname {s i m} \left(z _ {i} , z _ {j}\right)}{\operatorname {s i m} \left(z _ {i} , z _ {j}\right) + \sum_ {z ^ {-} \in \mathcal {M}} \operatorname {s i m} \left(z _ {i} , z ^ {-}\right)} \tag {8}
+$$
+
+Upon the formulation of Eq. (7) and Eq. (8), the final objective for CPC is formulated as:
+
+$$
+\mathcal {L} _ {C P C} = \lambda \sum_ {n = a, b, c, \dots} \mathcal {L} _ {\mathcal {N}} ^ {(n)} + (1 - \lambda) \mathcal {L} _ {\mathcal {M}} \tag {9}
+$$
+
+where $\lambda$ is equals to 1 if $\mathcal{P}_i\neq \mathcal{P}_j$ , and O otherwise.
+
+# 3.5. Relative Order Reasoning (ROR)
+
+Order reasoning of action videos is a fundamental task in video representation learning. Traditional approaches primarily focus on chronological order prediction within a single-action class, where models learn temporal coherence by reordering shuffled video frames [23] or clips [27, 33, 45]. However, in multi-action sequences, the order is inherently ambiguous, making traditional approaches not applicable. To address this, we introduce Relative Order Reasoning (ROR), a novel paradigm that leverages multi-action permutations. Instead of predicting a single "correct" order, ROR focuses on "relative" mapping between paired action permutations and learns the capability of discerning the latent state of actions over long skeleton sequences, thus regularizing the feature space from a complementary direction to CPC.
+
+In implementation, DuoCLR solves ROR via classification upon the mapping between $\mathcal{H}_i$ and $\mathcal{H}_j$ . Specifically, since each pair of action permutations share the same actions, the relative mapping between the paired permutations is uniquely determined. For example, let $|\mathcal{P}_j|$ (where $\mathcal{P}_j = (c,b,a)$ ) be the action granularity of $\mathcal{H}_j$ , there exist $|\mathcal{P}_j|! = 6$ factorial orders: $\{(c,b,a),(c,a,b),(b,c,a),(b,a,c)\ldots\}$ . The mapping from $\mathcal{H}_i$ to $\mathcal{H}_j$ is represented by the one-hot class label $\mathbf{1}(\mathcal{P}_i|\mathcal{P}_j) = [0,0,0,1,0,0]^T$ while $\mathcal{P}_i = (b,a,c)$ .
+
+Positional Encodings. For optimization, ROR calculates Positional Encodings (PE) of $\mathcal{H}_i$ and $\mathcal{H}_j$ . It uses local projections $z_i^{(n)} \in \mathbb{R}^{C_3}$ and $z_j^{(m)} \in \mathbb{R}^{C_3}$ (obtained via Eq. (6)) to calculate pair-wise feature comparison $z_{ij}^{(n,m)} = \left|z_i^{(n)} - z_j^{(m)}\right|$ . Second, it generates the concatenation of $\{z_{ij}^{(n,m)} | n \in \mathcal{P}_i, m \in \mathcal{P}_j\}$ to obtain fine-grained position relations between $\mathcal{H}_i$ and $\mathcal{H}_j$ :
+
+$$
+P E \left(\mathcal {H} _ {i}, \mathcal {H} _ {j}\right) = \operatorname {c o n c a t} \left(z _ {i j} ^ {(b, c)}, z _ {i j} ^ {(b, b)}, z _ {i j} ^ {(b, a)}, z _ {i j} ^ {(a, c)}, \dots\right). \tag {10}
+$$
+
+Such an operation allows the network to infer relative positioning of $\mathcal{H}_i$ and $\mathcal{H}_j$ by comparing their temporal structures in feature space, which is also illustrated in Fig 3. Afterwards, ROR utilizes a fully connected layer, $FC: \mathbb{R}^{C_3 \times |\mathcal{P}_j|^2} \to \mathbb{R}^{|\mathcal{P}_j|!}$ , to optimize a Cross-Entropy loss:
+
+$$
+L _ {R O R} = - \mathbf {1} \left(\mathcal {P} _ {i} \mid \mathcal {P} _ {j}\right) \cdot \log \left(F C \left(P E \left(\mathcal {H} _ {i}, \mathcal {H} _ {j}\right)\right)\right) \tag {11}
+$$
+
+DuoCLR Loss. The final loss function for DuoCLR combines CPC and ROR losses, with a weighting factor $\alpha$ to balance their contributions:
+
+$$
+L = \mathcal {L} _ {C P C} + \alpha \mathcal {L} _ {R O R} \tag {12}
+$$
+
+The implementation of DuoCLR upon Eq. (12) leads to an expressive representation $\mathcal{F}$ that is fully transferable to action segmentation and will be comprehensively evaluated in Section 4.
+
+
+Figure 4. Transfer learning in skeleton-based human action segmentation. (a): Hierarchical structure introduced in Sec. 3.3. (b) and (c): Common structures used in existing works. See more details in supplementary material.
+
+# 4. Experiments
+
+This section studies the application of DuoCLR in action segmentation. DuoCLR first involves a trimmed dataset for pretraining, followed by an evaluation phase where an untrimmed dataset is used to test the action segmentation performance. The study experimentally demonstrates the effectiveness of the proposed DuoCLR approach in comparison to state-of-the-art methods.
+
+# 4.1. Implementations
+
+- Datasets. Three trimmed skeleton datasets are considered for pretraining in DuoCLR: NTU RGB+D (NTU) [35], Toyota Smarthome (TS) [12] and Kinetics-400 (K4) [22]. Three untrimmed skeleton datasets are involved for evaluating the pre-trained models in the application of action segmentation, including PKU Multi-Modality Dataset (PKU) [29] (We use both versions: PKU1 and PKU2), Toyota Smarthome Untrimmed (TSU) [11], and Charades (CR) [36]. We report on mean Average Precision at IoU thresholds 0.1 $(\mathrm{mAP}_{0.1})$ and 0.5 $(\mathrm{mAP}_{0.5})$ [48], Top1 Accuracy (Acc) [46], mean Intersection over Union (mIoU) [28], and per-frame mAP (mAP) [11] for cross-view (CV) and cross-subject (CS) test cases of all untrimmed datasets.
+- Pretraining. We adopt ST-GCN [46] as the skeleton visual encoder and MS-TCN [15] as the skeleton temporal encoder. In the pretraining, we use the entire (both training and testing) set of a trimmed dataset to learn the feature extractor $\mathcal{F}$ . We adopt the same hyper-parameter values as in previous works [18, 20, 38], i.e., $C_3$ is set as 128 and $\tau$ in Eq. (1) as 0.07. The sizes of the two memory banks, $\mathcal{N}^{(m)}$ and $\mathcal{M}$ , are set as 684 and 32,768, respectively. More details are available in supplementary material.
+- Evaluation. We consider two popular downstream tasks: multi-class action segmentation [16, 29] and multi-label (composite) action segmentation [11, 48], in each of which we learn a frame-wise classification (frame annotating) layer $\mathcal{C}$ over the pre-learned $\mathcal{F}$ (as illustrated in Fig. 4a). In multi-class segmentation, each skeleton frame is annotated with one action label. $\mathcal{C}$ is composed of a $1 \times 1$ convolution and SoftMax layer. It is optimized by the multi-class Cross-Entropy loss function with one-hot en
+
+| Models | Method Pretrain Eval. | CS% | CV% |
| NTU→PKU1: | | | | mAP.1 | mAP.5 | mAP.1 | mAP.5 |
| Baseline-I[46] | Linear | NTU | PKU1 | 56.0 | 50.3 | 56.7 | 54.9 |
| LAC [48] | Linear | Poetics | PKU1 | 61.8 | - | 62.4 | - |
| DuoCLR | Linear | NTU | PKU1 | 85.2 | 74.3 | 84.7 | 77.5 |
| Baseline-II [16] | F-T | - | PKU1 | 89.6 | 86.4 | 92.1 | 88.9 |
| MS2L [27] | F-T | NTU | PKU1 | - | 50.9 | - | - |
| CMD [32] | F-T | NTU | PKU1 | - | 59.4 | - | - |
| CrossSCLR [24] | F-T | NTU | PKU1 | - | 60.1 | - | - |
| PCM3 [50] | F-T | NTU | PKU1 | - | 61.8 | - | - |
| Hi-TRS [7] | F-T | NTU | PKU1 | - | 63.5 | - | - |
| USDRL [41] | F-T | NTU | PKU1 | - | 75.7 | - | - |
| LAC [48] | F-T | Poetics | PKU1 | 92.6 | 90.6 | 94.6 | - |
| DuoCLR | F-T | NTU | PKU1 | 94.4 | 90.1 | 96.8 | 94.8 |
| NTU→PKU2: | | | | mIoU | Acc | mIoU | Acc |
| Baseline-I [46] | Linear | NTU | PKU2 | 30.7 | 47.2 | 26.4 | 44.7 |
| AimCLR [18] | Linear | Poetics | PKU2 | - | - | 15.7 | 39.8 |
| ActCLR [28] | Linear | NTU | PKU2 | - | - | 21.4 | 51.3 |
| DuoCLR | Linear | NTU | PKU2 | 54.5 | 73.9 | 50.9 | 68.8 |
| Baseline-II [16] | F-T | - | PKU2 | 50.9 | 69.3 | 45.6 | 66.0 |
| Hi-TRS [7] | F-T | NTU | PKU2 | - | - | - | 55.0 |
| LaSA [21] | F-T | - | PKU2 | - | 73.4 | - | 69.4 |
| DuoCLR | F-T | NTU | PKU2 | 66.1 | 82.6 | 56.3 | 79.2 |
+
+Table 1. Experimental comparison in the multi-class skeleton-based action segmentation task. Evaluation methods include Linear Evaluation and Fine-tune (F-T) Evaluation.
+
+| Models | Methods | Modality | TS → CS(%) | TSU CV(%) | K4 → CR mAP(%) |
| MS-TCT [10] | F-T | RGB | 33.7 | - | 25.4 |
| Baseline-I [46] | Linear | Skeleton | 18.2 | 11.4 | 6.1 |
| LAC [48] | Linear | Skeleton | 20.8 | 18.3 | 14.3 |
| DuoCLR | Linear | Skeleton | 24.1 | 19.8 | 19.1 |
| Baseline-II [16] | F-T | Skeleton | 28.3 | 20.3 | 21.8 |
| LAC [48] | F-T | Skeleton | 36.8 | 23.1 | 28.0 |
| DuoCLR | F-T | Skeleton | 35.1 | 26.3 | 33.9 |
+
+Table 2. Experimental comparison in the composite skeleton-based action segmentation task.
+
+coded frame annotations of the evaluation dataset. In composite action segmentation, each skeleton frame could be labeled with multiple action labels (e.g., "Cooking" and "Stirring"). $\mathcal{C}$ is composed of a $1 \times 1$ convolution and Sigmoid layer and is optimized using the binary Cross-Entropy loss with multi-hot encoded frame annotations of the evaluation dataset. In both applications, we use SGD to update $\mathcal{C}$ with Nesterov momentum 0.9 and learning rate 0.05.
+
+# 4.2. Results
+
+In the multi-class action segmentation task, we use NTU RGB+D for pretraining while using two datasets, PKU1 and PKU2, as the target for evaluation. A similar setting is considered in composite action segmentation where the trimmed TS and K4 are used as the pretraining domain while TSU and CR are used for evaluation. As with previous works, we use Linear Evaluation [24], where $\mathcal{F}$ is fixed while training $\mathcal{C}$ , and Fine-tune (F-T) Evaluation [24], where $\mathcal{F}$ and $\mathcal{C}$ are trained jointly, to evaluate our approach. We report the experimental results in Table 1 and Table 2.
+
+- Comparison to State-of-the-art Methods. We first
+
+| Models | Methods | 5% of PKU1 | 10% of PKU1 |
| CS(%) | CV(%) | CS(%) | CV(%) |
| Baseline-I | Linear | 33.9 | 36.0 | 41.6 | 42.7 |
| DuoCLR | Linear | 58.4 | 41.3 | 70.0 | 72.8 |
| Baseline II | Fine-Tune | 47.4 | 49.5 | 56.4 | 58.1 |
| LAC[48] | Fine-Tune | 73.9 | 75.4 | 79.8 | 81.1 |
| DuoCLR | Fine-Tune | 74.6 | 77.5 | 81.9 | 84.2 |
+
+Table 3. Semi-supervised evaluation $(\mathrm{mAP}_{0.1})$ with a low proportion of samples from the target domain.
+
+| Model | PKU1 | PKU2 | TSU | Charade |
| DuoCLR | 63% | 59% | 55% | 42% |
+
+compare the proposed DuoCLR to recent state-of-the-art methods[13, 14, 27, 47, 48] that involve a similar "trimmed-to-untrimmed" learning scenario. Experimental results demonstrate that DuoCLR outperforms most state-of-the-art comparatives across both multi-class (Table 1) and composite (Table 2) action segmentation tasks. We conclude that, since prior methods are limited in exploiting sequence-independent representations, the resultant feature space preserves a low transferability to action segmentation. In contrast, our model benefits from two efficient surrogate tasks, leading to better performance.
+
+- Linear and Fine-tune Evaluation. A vanilla supervised pretraining paradigm involves learning a feature space $\mathcal{F}$ via a conventional end-to-end action recognition model [46] using trimmed skeleton videos without data augmentation. We treat such a paradigm as a baseline model (Baseline-I in Table 1 and Table 2) while making comparison with DuoCLR in Linear Evaluation. Experimental results demonstrate that our model significantly outperforms Baseline-I, which validates the effectiveness of the proposed DuoCLR approach in learning expressive action representations for the action segmentation tasks. We also compare DuoCLR with Baseline-II, an action segmentation model [16] that can be trained end-to-end on untrimmed datasets. DuoCLR, when fine-tuned, achieves substantial performance improvements over Baseline-II, as shown in Table 1 and Table 2 for both multi-class and composite tasks. This outcome highlights the advantage of incorporating DuoCLR's pre-trained features, which enhance the model's adaptability and performance in segmentation.
+
+- Semi-supervised Evaluation The last experiment examines the transferability of our model while using fewer data samples in evaluation. Specifically, the experiment varies the ratios (5% and 10%) of samples from the target domain involved in ransfer learning (i.e., Linear and Finetune Evaluation). Experimental results in Table 3 demonstrate that the model's performance tends to increase monotonically along with the ratio of samples from the target domain. Table 4 suggests that DuoCLR can save up to 63% labeled data to reach the compatible performance compared
+
+Table 4. The ratio of labeled data is saved while reaching the same performance with the vanilla model that was trained on $100\%$ data.
+
+| NTU to PKU1 | Method | CS (%) | CV (%) |
| Baseline-I | Linear | 56.0 | 60.3 |
| CPC | Linear | 83.9 | 85.1 |
| ROR | Linear | 76.7 | 79.5 |
| CPC+ROR (DuoCLR) | Linear | 85.2 | 84.7 |
+
+Table 5. Ablation study of two surrogate tasks: CPC (Cross Permutation Contrasting), ROR (Relative Order Reasoning), and combined DuoCLR. Results are reported as $\mathrm{mAP}_{0.1}$ .
+
+| PKU1 to PKU2 | Methods | Pretraining | CS(%) | CV(%) |
| Baseline-II | Fine-Tune | - | 69.3 | 66.0 |
| DuoCLR | Linear | Trimmed PKU1 | 78.1 | 76.0 |
| DuoCLR | Fine-Tune | Trimmed PKU1 | 78.0 | 77.6 |
+
+Table 6. Experimental results (Acc) of pretraining using untrimmed datasets.
+
+
+Figure 5. Feature clusters visualization by t-SNE [40]
+
+to full-supervised learning.
+
+# 4.3. Ablation studies
+
+- Effectiveness of Surrogate Tasks. To assess the independent and combined effectiveness of these tasks, we conduct experiments using each task individually and in combination, pretraining on NTU and evaluating on PKU1. First, either surrogate task demonstrates a significant performance improvement compared to the vanilla supervised pretraining paradigm (Baseline-I) as summarized in Table 5. In Fig. 5b and Fig. 5c, CPC and ROR demonstrate their independent effectiveness at learning more separate feature clusters compared to Baseline-I (Fig. 5a). Second, CPC achieves superior effectiveness over ROR likely because it directly enforces instance-level similarity, which is critical for clustering. Last, DuoCLR achieves its best learning result when combining the two tasks, i.e. $85.2\%$ and $84.7\%$ on the benchmarks of CS and CV, meanwhile demonstrating the best separability in feature clustering (Fig. 5d).
+
+- Pretraining with Untrimmed Datasets. It is also effective to apply DuoCLR to an untrimmed dataset for representation learning. In this experiment, we consider PKU1 as the pretraining dataset where we trim each sequence into separate single-action sequences using their associated frame annotations. By applying "Shuffle and Warp" to these trimmed sequences, DuoCLR learns a feature extractor, $\mathcal{F}$ , which is then evaluated on the original untrimmed PKU2 dataset. As shown in Table 6, DuoCLR outperforms the vanilla end-to-end supervised model (Baseline-II) in both linear and fine-tune evaluation protocols, showcasing the benefit of pretraining.
+
+| NTU to PKU1 | Shear, Crop | Shuffle | Warp | Supervised | CS% |
| DuoCLR | | ✓ | ✓ | ✓ | 85.2 |
| DuoCLR-I | ✓ | | | ✓ | 58.3 |
| DuoCLR-II | | ✓ | | ✓ | 73.8 |
| DuoCLR-unsup | ✓ | ✓ | ✓ | | 81.6 |
| DuoCLR-III | ✓ | ✓ | ✓ | ✓ | 87.1 |
+
+Table 7. Experimental comparison of DuoCLR and its variants using different skeleton data augmentation strategies.
+
+| Encoder | Classifier | Method | Params | Previous | Ours |
| GCN | Sequence-wiseˆ | F-T | 837K | 63.5 [7] | 77.6 |
| GCN | Frame-wiseˆ | Linear | 13.3K | 61.8 [48] | 81.9 |
| GCN+TCN | Frame-wiseˆ | Linear | 13.3K | - | 85.2 |
+
+Table 8. Experimental comparison between two types of classifiers. For $\hat{C}$ , the sliding window size is set as 300.
+
+- Effectiveness of Data Augmentation. We learn a new model (DuoCLR-I) by incorporating two classical skeleton augmentations, "Shear" and "Crop" [24], with NTU used for pretraining and PKU1 for evaluation. As shown in Table 7, DuoCLR-I achieves an accuracy of $58.3\%$ , suggesting that traditional augmentations alone provide limited transferability for action segmentation tasks. Our "Shuffle and Warp" method, however, is scalable to previous augmentations as we observe an orthogonal performance increase $(1.3\%$ over regular DuoCLR in PKU1) with the model DuoCLR-III after combining two types of augmentation. Additionally, we perform an ablation study on the roles of "Shuffle" and "Warp" individually. The DuoCLR-II variant, which uses only "Shuffle" (Eq. (2)), achieves an accuracy of $73.8\%$ . When compared to DuoCLR, which uses both "Shuffle" and "Warp", the results demonstrate the importance of "Warp" which reduces irrelevant variations.
+- Pretraining with Unlabeled Datasets. DuoCLR also supports unsupervised pretraining. For this approach, labeled proxies are created using sequence subscripts within each data batch. To learn an unsupervised DuoCLR model (DuoCLR-unsup, Table 7), we complement the augmentation with "Shear" and "Crop" to compensate for the lack of explicit labels. As seen in Table 7, regular DuoCLR outperforms the unsupervised variant (81.6% vs. 85.8% accuracy). This performance gap is likely due to the challenge of accurately identifying negative pairs in an unsupervised setting, which can lead to noise to the learning process.
+- DuoCLR is general to different network structures. Fig. 4 illustrates two network structures commonly used in skeleton action segmentation: 1) Siding-window-free structure (Fig. 4b) composed of a GCN encoder $\hat{\mathcal{F}}$ and a framewise classifier $\mathcal{C}$ ; 2) sliding window based structure (Fig. 4c) composed of a $\hat{\mathcal{F}}$ and a sequence-wise classifier $\hat{\mathcal{C}}$ while using sliding windows to pre-segment input sequences. Fig. 4a illustrates the network proposed in Sec. 3.3. For evaluation, we train three DuoCLR models with different structures and conclude the experimental results in Table 8). It
+
+
+Figure 6. The confusion matrices obtained by ROR on different action granularities.
+
+demonstrates that DuoCLR is effective for different structures while suppassing previous works with clear margins.
+
+- Effectiveness of Action Granularity. In this study, we treat the action granularity $(\mathcal{G})$ of action permutations as a hyperparameter and learn how it affects optimizations of DuoCLR. In practice, setting a high value of $\mathcal{G}$ will introduce diverse action contexts, however, it can also lead to high computational complexity, e.g., $o(\mathcal{G})!$ for ROR while the size of the FC layer grows. In experiments, we increase $\mathcal{G}$ from 1 to 5 while preserving other implementations parameters as defined in Table 1. We illustrate confusion matrices (showing how ROR is good at mapping permutations) and similarity matrices (showing how CPC is good at learning consistent features) in Fig. 6, where Acc values evaluate the transferability of the resultant (CPC+ROR) network on PKU 2. While $\mathcal{G} = 1$ , it degrades to a vanilla contrastive learning model [18]. While $\mathcal{G}$ increases, each model is capable of learning at different action granularity and and the best model is achieved when $\mathcal{G}$ is around 4.
+
+# 5. Conclusions
+
+This paper introduces a dual-surrogate contrastive learning (DuoCLR) framework while exploiting fine-grained extraction on action representations for skeleton data-based human action segmentation. It applies "Shuffle and Warp" to generate various multi-action permutations where two surrogate tasks, Cross Permutation Contrasting and Relative Order Reasoning, learn permutation-invariant intra-class similarities and permutation-aware inter-class contexts. The learned action representations can be represented by a feature extractor which can be entirely transferred into action segmentation. Experimental results demonstrate that 1) DuoCLR enables training with both unlabeled and labeled trimmed skeleton videos; 2) DuoCLR outperforms state-of-the-art methods in multiple tasks; 3) DuoCLR can save $42\% -63\%$ frame-level labeled data to reach the compatible fully-supervised performance in action segmentation; 4) DuoCLR supports learning with RGB videos that can lead to better action segmentation performance compared to previous RGB based approaches.
+
+# 6. Acknowledgments
+
+This research was supported in part by MITACS Accelerate and NSERC Discovery grants. The authors would like to express their sincere gratitude to Dr. Pierre Payeur for his invaluable contributions to this work. Dr. Payeur provided consistent supervision throughout the research and played a key role in project administration and funding acquisition. His thoughtful input during the review and editing process was instrumental to the successful completion of this work. The authors also gratefully acknowledge the collaboration of the Sensing and Machine Vision for Automation and Robotic Intelligence (SMART) laboratory and Spectronix Inc.
+
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+# DuoLoRA : Cycle-consistent and Rank-disentangled Content-Style Personalization
+
+Aniket Roy $^{1,2*}$ , Shubhankar Borse $^{2\dagger}$ , Shreya Kadambi $^{2\dagger}$ , Debasmit Das $^{2}$ , Shweta Mahajan $^{2}$ , Risheek Garrepalli $^{2}$ , Hyojin Park $^{2}$ , Ankita Nayak $^{2}$ , Rama Chellappa $^{1}$ , Munawar Hayat $^{2}$ , Fatih Porikli $^{2}$ $^{1}$ Johns Hopkins University, $^{2}$ Qualcomm AI Research‡
+
+# Abstract
+
+We tackle the challenge of jointly personalizing content and style from a few examples. A promising approach is to train separate Low-Rank Adapters (LoRA) and merge them effectively, preserving both content and style. Existing methods, such as ZipLoRA, treat content and style as independent entities, merging them by learning masks in LoRA's output dimensions. However, content and style are intertwined, not independent. To address this, we propose DuoLoRA—a content-style personalization framework featuring three key components: (1) rank-dimension mask learning, (2) effective merging via layer priors, and (3) Constyle loss, which leverages cycle-consistency in the merging process. First, we introduce ZipRank, which performs content-style merging within the rank dimension, offering adaptive rank flexibility and significantly reducing the number of learnable parameters. Additionally, we incorporate SDXL layer priors to apply implicit rank constraints informed by each layer's content-style bias and adaptive merger initialization, enhancing the integration of content and style. To further refine the merging process, we introduce Constyle loss, which leverages the cycle-consistency between content and style. Our experimental results demonstrate that DuoLoRA outperforms state-of-the-art content-style merging methods across multiple benchmarks. Project: https://github.com/aniket004/DuoLoRA.git
+
+# 1. Introduction
+
+Text-to-image diffusion models [6, 27, 31] have recently attracted significant interest due to their broad range of applications. These models can produce images with desired content and style, overcoming the limitations of earlier approaches that required extensive training data for neural style transfer [13]. They can generate specific images from just
+
+
+
+
+Figure 1. Content and style personalization using DuoLoRA provides (1) adaptive rank flexibility, (2) significantly fewer trainable parameters, and (3) better content-style merging.
+
+one or two reference images, but blending both content and style remains challenging.
+
+Recently, parameter-efficient fine-tuning (PEFT) methods like Low-Rank Adapters (LoRA) [17] have become popular. These methods can capture unique characteristics with a small amount of data. Consequently, content-style personalization can be reframed as a LoRA merging task, where individually trained LoRAs are combined to achieve efficient content-style blending. For example, ZipLoRA [29] merges
+
+content and style by learning masks over the LoRA output dimensions, assuming that content and style are independent concepts. This approach provides adequate control over the diffusion model. However, the requirement for fine-tuning during inference is a drawback. Additionally, using the same rank for both content and style LoRAs may not be optimal, as content and style may have different representational requirements depending on each layer.
+
+In this work, we ask: How can we enable adaptive rank flexibility to reduce fine-tuning costs while increasing the separation between content and style distributions? To achieve adaptive rank flexibility across the layers of the diffusion UNet, we analyze the SDXL model architecture [3, 10]. We observe that UNet layers, with smaller resolutions, primarily influence content generation, suggesting that content merges should have higher rank in these layers than style merges. Conversely, the layers, with larger resolutions, are more crucial for style generation, and the rank constraint should be adjusted accordingly [3, 10].
+
+Within this context, we introduce DuoLoRA, a framework for effective content-style merging, composed of three components: (1) ZipRank, which learns masks within the rank dimension, (2) improved merging via layer priors, and (3) Constyle loss, which leverages cycle-consistency across content and style. In ZipRank, we propose learning masks in the rank dimension rather than the output dimension, allowing for adaptive rank adjustment and a substantial reduction in learnable parameters. To facilitate layer-wise rank-adaptive merging, we apply rank constraints during content-style merging, informed by our observations as prior knowledge. This rank constraint is formulated as a nuclear norm minimization problem under a $l1$ sparsity constraint, improving content-style blending with fewer parameters. To further disentangle content and style, we introduce Constyle loss, which leverages cycle-consistency across content and style. This approach, inspired by CycleGAN's [45] treatment of content and style as separate domains optimized through domain translation with minimized reconstruction loss, enables balanced content-style merging. Unlike ZipLoRA, which treats content and style independently, our cycle-consistency loss accounts for their interdependent nature, resulting in improved content-style blending.
+
+In summary, the contributions of this paper are as follows:
+
+- We address content-style personalization as a LoRA merging problem, where we propose learning masks in the rank dimension instead of the output dimension, allowing for adaptive rank flexibility with significantly fewer learnable parameters.
+- We analyze the SDXL architecture's layer prior information, finding that layers with lower resolutions primarily contribute to content generation, while layers with higher resolutions focus on style generation. Based
+
+on these insights, we introduce explicit rank constraints through nuclear norm minimization under a sparsity constraint to improve merging.
+
+- We introduce Constyle loss, leveraging the cycle-consistency across content and style, and we validate this approach across various benchmarks.
+
+# 2. Related work
+
+Personalization. Personalizing text-to-image diffusion models has recently attracted significant attention. Early approaches, such as Textual Inversion [11], focus on learning a text token that represents a particular concept, while Dreambooth [27] updates network parameters for personalization. Custom Diffusion [22] makes the process more efficient by fine-tuning only the cross-attention modules. However, these methods typically handle only a single concept or object. In contrast, some approaches aim to personalize both content and style. StyleDrop [31] uses the Muse transformer network to align the style of generated images with a reference image. Other recent style learning methods are - Rb-modulation [26], Instantstyle [36], IP-adapter [42], Magic-insert [28], StyleAlign [16], LoRA-composer [41], Paircustomization [20], [1, 2, 4, 5, 7–9, 14, 17–19, 21, 23–25, 30, 32–40, 43].
+
+LoRA merging. LoRA [17] has proven particularly effective for learning from small datasets. Individual LoRA models are trained for each concept or style, and these concepts can then be combined through LoRA merging. Methods like Concept-Sliders [12] and ControlNet [44] also utilize LoRA merging, though their approaches are primarily suited for text-based editing. Recently, Shah et al. [29] introduced a method for LoRA merging by learning orthogonal masks in the output space of the layer.
+
+# 3. Method : DuoLoRA
+
+# 3.1. Problem statement
+
+We address the problem of customizing both content and style from few examples and generate variations conditioned on text prompt. We investigate the problem through the lens of merging individual concepts, where such individual concepts are learned using LoRAs. Therefore we cast the concept-style personalization as a LoRA merging problem (as shown in Fig. 1). However, content and style are not orthogonal, rather those are intertwined concepts. Therefore, entangling such concepts remains challenging.
+
+In order to efficiently merge content and style specific LoRAs, we first learn masks in the rank dimension, with UNet layer-prior informed initialization, explicit rank and sparsity constraint. To further improve performance, we use content-style cycle-consistent merging. We explain this as follows.
+
+
+Figure 2. Overview of DuoLoRA. It consists of three components - (1) ZipRank: learning the mask in rank dimension, (2) layer-prior based merging identifying content-dominant and style-dominant blocks of SDXL UNet, (3) cycle-consistency based merging using Constyle loss.
+
+# 3.2. ZipRank: Merging in Rank space
+
+We start with providing background on LoRA.
+
+Low-Rank Adaptation (LoRA): In LoRA [17], we fine-tune neural networks by approximating weight updates using low-rank matrices. Specifically, the weight update matrix $\Delta W$ is parameterized as: $\Delta W = AB = U_r\Sigma_rV_r^\top$ , where $A \in \mathbb{R}^{d_{\mathrm{out}} \times r}$ , $B \in \mathbb{R}^{r \times d_{\mathrm{in}}}$ , and $r$ is the rank of the approximation.
+
+Blending LoRAs optimally presents a significant challenge. A straightforward approach is to use simple arithmetic merging, but this is not efficient. ZipLoRA [29] (Fig. 1) uses the Zipit [34] operation across model weights through learnable masks in the output dimension as defined below, ensuring the masks in the weight space remain orthogonal.
+
+Definition 1. Output Dimension Masking (ZipLoRA [29]): Here we apply a mask to the output dimension by defining a diagonal mask matrix $M_{out} \in \mathbb{R}^{d_{out} \times d_{out}}$ with entries $n_{ii} \in \{0,1\}$ . The output-masked approximation is:
+
+$$
+\Delta W _ {o u t} = M _ {o u t} A B = M _ {o u t} U _ {r} \Sigma_ {r} V _ {r} ^ {\top}.
+$$
+
+Let $d_{s} = \sum_{i=1}^{d_{out}} n_{ii}$ be the number of active output units.
+
+Our approach, however, focuses on learning masks in the rank dimension (ZipRank, Fig. 2), which greatly reduces the
+
+number of learnable parameters and provides adaptive rank flexibility across the LoRA adapters.
+
+Definition 2. Rank Dimension Masking (ZipRank): We apply a mask to the rank dimension by defining a diagonal mask matrix $M_r \in \mathbb{R}^{r \times r}$ with entries $m_{ii} \in \{0,1\}$ . The rank-masked approximation is:
+
+$$
+\Delta W _ {r a n k} = A M _ {r} B = U _ {r} M _ {r} \Sigma_ {r} V _ {r} ^ {\top}.
+$$
+
+Let $S$ denote the set of indices $i$ where $m_{ii} = 1$ , and $s = |S|$ is the number of active rank components.
+
+Rank space masking serves two primary motivations: (1) enabling adaptive rank flexibility during LoRA merging and (2) reducing the number of learnable parameters. Unlike ZipLoRA, which targets poorly aligned columns, ZipRank addresses cross-concept interference by modulating the contributions of specific rank components in the latent space, allowing for more nuanced control over concept overlap. In this approach, different concepts (e.g., subject vs. style) are encoded in distinct subspaces within the rank space. Rather than reducing the effective rank, rank-space masking adjusts the relative importance of specific feature interactions, providing fine-grained control without entirely nullifying components. ZipRank is designed to separate the style and content adapters while minimizing the number of learnable
+
+Prompt = "a dog in the watercolor painting style"
+
+
+$\mathbf{a} = 0.001$
+
+
+$a = 0.005$
+
+
+$\alpha = 0.01$
+
+
+$\alpha = 0.1$
+
+
+$\alpha = 1.0$
+
+Prompt = "a cat on a chair in the style of impressionism"
+
+
+$a = 0.001$
+
+
+$\alpha = 0.1$
+
+
+$\alpha = 0.2$
+
+
+$\alpha = 0.23$
+Figure 3. SDXL selective weight scaling. The scaling parameter $(\alpha)$ has been applied to the content-dominant blocks (up_block.2, down_block.2, and mid_block). We observe that with a smaller $\alpha$ , the model fails to generate the content and instead focuses solely on the style. In contrast, increasing $\alpha$ allows the model to generate the content specified in the prompt.
+
+
+$\alpha = 0.25$
+
+parameters. This approach reduces overfitting, especially when training on small datasets, and introduces adaptive rank flexibility during the merging of LoRAs. We have also shown that under the same parameter budget, the approximation error resulting from rank dimension masking is less than or equal to that from output dimension masking in Theorem 1 (supplementary).
+
+# 3.3. Layer priors
+
+# 3.3.1. How content style is encoded in SDXL
+
+Understanding how content, style, and similar information are encoded within a diffusion UNet is crucial for enabling both local and global edits. We hypothesize that in SDXL, layers with low resolutions (e.g.,up_block.2, down_block.2, mid_block, with resolution $< 32$ ) capture localized updates, such as content details, while layers with high resolutions (e.g.,up_block.1, down_block.1, with resolution $>= 32$ ) capture global updates, such as the overall style of the image.
+
+This hypothesis is motivated by the structural design of the SDXL model: layers with low resolutions, typically in the earlier stages of the U-Net, focus on small, localized regions, allowing them to encode essential spatial details, shapes, and structures. This fine-grained attention enables accurate representation of core content elements, like objects and scene layouts, aligning closely with the input prompt.
+
+In contrast, layers with high resolutions, often in deeper sections of the model, capture style by blending and harmonizing details across larger regions. This broader scope makes them well-suited for encoding global stylistic features like color gradients, textures, and lighting. Such attributes require a coherent application across the image rather than precision in spatial detail. Consequently, high resolutions are believed to play a crucial role in generating the overall aesthetic and mood of the image, supporting their role in
+
+style encoding.
+
+To verify the hypothesis, we use a layer-freezing simulation via weight scaling. This method allows us to selectively reduce the contributions of specific layers during inference, enabling us to observe the distinct roles that different resolutions play in image generation.
+
+We begin by identifying the layers in the SDXL U-Net architecture associated with low and high resolutions. Layers such as up_block.2, down_block.2, and mid_block have resolutions smaller than 32, while layers like up_block.1 and down_block.1 have resolutions larger than 32.
+
+Next, we apply selective weight scaling to simulate a "freezing" effect. We scale the outputs of either low- or high-resolution layers by a small factor, $\alpha$ (e.g., 0.1), to reduce their influence in the generation process. Scaling down the low-resolution layers diminishes their impact on content details, while scaling down the high-resolution layers lessens the effect on style features.
+
+For instance, when using the prompt, $p =$ "A cat on a chair in the style of impressionism" during inference, we scale down the weights of the low-resolution layers (up_block.2, down_block.2, and mid_block) by a scalar factor $\alpha$ . By varying $\alpha$ , as shown in Fig. 3, we observe that lower values of $\alpha$ generate the style but fail to capture the object (i.e., the "cat"). As we increase $\alpha$ , the object becomes visible in the generated image. This trend, illustrated in Fig. 3, supports our hypothesis that low-resolution layers (up_block.2, down_block.2, and mid_block) contribute to content generation, while layers with higher resolution (up_block.1 and down_block.1) contribute to style. These observations align with prior findings in the literature [3].
+
+Recent works, like B-LoRA [10], have identified specific layers involved in content (W4 in SDXL) and style (W5 in SDXL). However, these findings are highly specific and may not generalize widely. Rather than adhering strictly to these findings, we incorporate this knowledge in a more generalized way by blending content-style LoRAs. In SDXL, we observe that layers up_block.2, down_block.2, and mid_block, which have lower resolutions $(\leq 32)$ , are more involved in content generation. Conversely, layers up_block.1 and down_block.1, with higher resolutions $(\geq 32)$ , contribute more to style generation. Building on this observation, we apply a prior-informed initialization strategy and implicit rank constraint during the merging process. For instance, during merging, we enforce sparsity along with the implicit rank constraint.
+
+# 3.3.2. Prior-informed merger initialization
+
+Instead of initializing the merger masks ( $m_c$ and $m_s$ in Fig. 2) in the rank dimension with all ones, we incorporate layer-specific information to enhance the merging process. To this end, we use the observation of content-style encoding
+
+in SDXL architecture made earlier. To capture the dominance of content and style in different layers, the masks for the merged LoRAs are initialized using content $(T_{\mathrm{content}})$ and style $(T_{\mathrm{style}})$ thresholds. In content-dominant layers, more ones are assigned to content merger $m_c$ than style merger $m_s$ , while the reverse is applied in style-dominant layers. The process begins with a normalized random vector, using thresholds to determine priority for content or style based on their ranks, defaulting to all ones when ranks are equal. For other layers, LoRAs are initialized with all ones to adaptively balance content and style merging. As demonstrated in Tab. 8, this adaptive initialization improves performance. The threshold ablation is shown in Tab. 7, and the detailed algorithm is provided in the supplementary.
+
+
+
+
+
+
+(a) Histogram of rank across low resolution layers in style merger.
+(c) Histogram of rank across low resolution layers in content merger.
+Figure 4. Rank analysis. We plot the frequency of ranks across low-resolution layers (i.e., up_block.2, down_block.2, and mid_block with a resolution $< 32$ ) and high-resolution layers (resolution $>= 32$ ) in content and style mergers post-training. The rank distribution confirms that in SDXL UNet architecture, for low-resolution layers, $\text{Rank}(m_c) > \text{Rank}(m_s)$ , while for high-resolution layers, $\text{Rank}(m_s) > \text{Rank}(m_c)$ .
+
+
+(b) Histogram of rank across high resolution layers in content merger.
+(d) Histogram of rank across high resolution layers in style merger.
+
+Algorithm 1: Rank-constrained Layer-prior Merging
+Output: Loss $\mathcal{L}_{\mathrm{layer\_prior}}$ for merging layers
+```txt
+Input: SDXL-UNet, content merger $(m_c)$ , style merger $(m_s)$
+```
+
+if Resolution(SDXL-UNet layer) < 32 then
+else
+```txt
+$/ / \operatorname{Rank}(m_c) > \operatorname{Rank}(m_s)$ $\mathcal{L}_{\text{layer\_prior}} \gets ||m_c||_1 + \lambda \max(0, \| m_s \|_* - \| m_c \|_*)$ ;
+```
+
+end
+```txt
+$/ / \operatorname{Rank}(m_s) > \operatorname{Rank}(m_c)$ $\mathcal{L}_{\text{layer\_prior}} \gets ||m_s||_1 + \lambda \max(0, \|m_c\|_* - \|m_s\|_*)$
+```
+
+# 3.3.3. Prior-informed rank constraint
+
+Based on our observations in Sec. 3.3.1, we propose to use the explicit layer-specific rank constraints during merging. In Fig. 4, we plot the frequency of ranks across low (i.e., up_block.2, down_block.2, and mid_block with $< 32$ resolution) and high-resolution $(>=32$ resolution) layers in content and style mergers post training. Through the distribution of the ranks, we can verify that for low resolution layers, $\operatorname{Rank}(m_c) > \operatorname{Rank}(m_s)$ , and for high resolution layers, $\operatorname{Rank}(m_s) > \operatorname{Rank}(m_c)$ holds in SDXL UNet architecture.
+
+Therefore, for the content-dominant layers, we apply the constraint $\mathrm{Rank}(m_c) \geq \mathrm{Rank}(m_s)$ during merging, and for the style-dominant layers, we reverse this constraint. In Lemma 1, we demonstrate that this rank constraint simplifies to a nuclear norm minimization problem under a sparsity constraint.
+
+Lemma 1. Let $m_c \in \mathbb{R}^{m \times n}$ be a matrix representing the content merger and $m_s \in \mathbb{R}^{m \times n}$ be a matrix representing the style merger. The problem of minimizing the $l_1$ -norm of $m_c$ subject to a rank constraint on $m_c$ can be written as:
+
+$$
+\min \| m _ {c} \| _ {1} \quad \text {s u b j e c t t o} \quad \operatorname {r a n k} \left(m _ {c}\right) > \operatorname {r a n k} \left(m _ {s}\right)
+$$
+
+This problem is non-convex due to the rank constraint. A convex relaxation can be achieved by approximating the rank of a matrix using the nuclear norm $\| \cdot \|_{*}$ , which is the sum of the singular values of the matrix. Thus, the original problem can be relaxed to:
+
+$$
+\min \| m _ {c} \| _ {1} \quad \text {s u b j e c t t o} \quad \| m _ {c} \| _ {*} > \| m _ {s} \| _ {*}
+$$
+
+where $\| m_c\|_*$ denotes the nuclear norm of $m_c$ , and $\| m_s\|_*$ is the nuclear norm of $m_s$ .
+
+This relaxed problem can be approached via a Lagrangian penalty formulation:
+
+$$
+\mathcal {L} \left(m _ {c}, m _ {s}, \lambda\right) = \| m _ {c} \| _ {1} + \lambda \max \left(0, \| m _ {s} \| _ {*} - \| m _ {c} \| _ {*}\right)
+$$
+
+for some penalty parameter $\lambda \geq 0$ , which enforces the constraint $\|m_c\|_* > \|m_s\|_*$ in the limit as $\lambda \to \infty$ .
+
+Proof. Proof is provided in the supplementary material.
+
+Consequently, in the content-dominant layers (i.e., up_block.2, down_block.2, and mid_block), LoRAs are merged using the layer prior loss $\mathcal{L}_{\text{layer\_prior}}$ .
+
+$$
+\mathcal {L} _ {\text {l a y e r} \_ \text {p r i o r}} = \| m _ {c} \| _ {1} + \lambda \max (0, \| m _ {s} \| _ {*} - \| m _ {c} \| _ {*}) \tag {1}
+$$
+
+where $m_{s}$ and $m_{c}$ represent the style and content mergers, respectively. Similarly, for the style-dominant layers, the process is reversed, as outlined in Algorithm 1.
+
+# 3.4. Constyle loss : Cycle-consistent merging
+
+To further improve the content-style alignment, we introduce Constyle loss, leveraging the cycle-consistency between content and style. Inspired by CycleGAN [45], where content and style are transformed across domains with minimized reconstruction loss, we add and then remove style from content, ensuring minimal reconstruction error during LoRA merging. Similarly, content is added and removed from style images, as illustrated in Fig. 2. Both processes provide feedback on the required blending while upholding rank constraints. Next, we describe cycle-consistent merging in detail (color coded for better explanation, refer to Fig. 2).
+
+The cycle-consistent merging is performed as follows:
+
+# 1. Generate Individual LoRAs:
+
+- Content LoRA: Given a set of content images $I_{c}$ , we learn a content LoRA $\mathbf{L}_{\mathbf{c}}$ , and tokens $\langle \mathbf{V1} \rangle$ , $\langle \mathbf{S1} \rangle$ using the prompt $\mathbf{p}_{\mathbf{c}} = \text{"a} \langle \mathbf{V1} \rangle$ object in $\langle \mathbf{S1} \rangle$ style".
+- Style LoRA: For a (small) set of style images $I_{s}$ , we learn a style LoRA $\mathbf{L}_{\mathrm{s}}$ , and tokens $\langle \mathbf{V2} \rangle$ , $\langle \mathbf{S2} \rangle$ using the prompt $\mathbf{p}_{\mathrm{s}} = "\text{a} < \mathbf{V2}>$ object in $\langle \mathbf{S2} \rangle$ style".
+
+2. Cycle-Consistency Across Style: Starting with a content image $I_{c}$ , we add noise to create its noisy latent. During the denoising process, the style prompt "a object in style" is injected via the style LoRA $\mathbf{L}_{\mathrm{s}}$ to produce a style-infused image $I_{cs}$ . This image $I_{cs}$ is then re-noised and denoised with the content prompt $\mathbf{p}_{\mathbf{c}}$ (via $\mathbf{L}_{\mathrm{s}}$ ) to remove style, resulting in the reconstructed content image $I_{csc}$ . To mitigate mode collapse from limited examples, we also generate a variant $I_{cc}$ by denoising $I_{c}$ solely with the content LoRA $\mathbf{L}_{\mathrm{c}}$ using $\mathbf{p}_{\mathbf{c}}$ . We enforce cycle-consistency in style by minimizing the loss (Fig. 2):
+
+$$
+\mathcal {L} _ {\text {c y c l e \_ s t y l e}} = \mathrm {M S E} \left(I _ {c c}, I _ {c s c}\right)
+$$
+
+3. Cycle-Consistency Across Object (Content): In a similar manner, starting with a style image $I_{s}$ , we add noise and then denoise using a content prompt "a object in style" (via the content LoRA $\mathbf{L}_{\mathbf{c}}$ ) to obtain a content-injected style image $I_{sc}$ . Next, we remove the injected object by denoising $I_{sc}$ with the style prompt $\mathbf{p}_{\mathbf{s}}$ via the content LoRA $\mathbf{L}_{\mathbf{c}}$ , yielding $I_{scs}$ . Additionally, we generate a variant $I_{ss}$ by denoising $I_{s}$ with the style LoRA $\mathbf{L}_{\mathbf{s}}$ using $\mathbf{p}_{\mathbf{s}}$ . The cycle-consistency in content is enforced by minimizing (Fig. 2):
+
+$$
+\mathcal {L} _ {\text {c y c l e _ c o n t e n t}} = \operatorname {M S E} \left(I _ {s s}, I _ {s c s}\right)
+$$
+
+The merged LoRA $L_{m}$ is then trained by minimizing the following loss:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {c o n s t y l e}} = \left\| \left(D + L _ {m}\right) \left(I _ {c}, \mathbf {p} _ {\mathbf {c}}\right) - \left(D + \mathbf {L} _ {\mathbf {c}}\right) \left(I _ {c}, \mathbf {p} _ {\mathbf {c}}\right) \right\| \\ + \left\| \left(D + L _ {m}\right) \left(I _ {s}, \mathbf {p} _ {\mathbf {s}}\right) - \left(D + \mathbf {L} _ {\mathbf {s}}\right) \left(I _ {s}, \mathbf {p} _ {\mathbf {s}}\right) \right\| \\ + \left(\mathcal {L} _ {\text {c y c l e \_ s t y l e}} + \mathcal {L} _ {\text {c y c l e \_ c o n t e n t}}\right) \\ \end{array}
+$$
+
+where $D$ is the text-to-image diffusion model and $\lambda_{cycle}$ (set to 0.1) controls the weight of the cycle-consistency losses. The overall loss used during merging is given by
+
+$$
+\mathcal {L} = \lambda_ {\text {l a y e r} _ {-} \text {p r i o r}} \mathcal {L} _ {\text {l a y e r} _ {-} \text {p r i o r}} + \lambda_ {\text {c y c l e}} \mathcal {L} _ {\text {c o n s t y l e}}
+$$
+
+which is further used to train the layer masks. During inference, the merged tokens are provided in the prompt (e.g., "a object in style running") to the diffusion model with merged LoRA $L_{m}$ , generating images that blend the desired content and style. Detailed algorithm is provided in the supplementary.
+
+# 3.5. Multi-concept stylization
+
+We further extend our approach to handle multi-concept stylization. Given concepts $C_1, \ldots, C_n$ and style $S$ , we first merge individual concept-style LoRAs, $< C_1, S >$ , $< C_n, S >$ , using DuoLoRA/baselines and then combine them via naive merging: $C_{1,2,\dots,n,S} = \alpha_1 < C_1, S > +\dots + \alpha_n < C_n, S >$ , where $\alpha_i = 1/n$ . During inference, we use directional prompting (i.e., object in left/right etc) with the merged LoRA $C_{1,2,\dots,n,S}$ , using prompt $p = "a < C1 > object on the left and a < C2 > object on the right.. in < S > style"$ . In this way, we extend DuoLoRA for multiple concepts.
+
+# 4. Experiments
+
+Dataset. We experiment on four datasets (datasets and splits provided in supplementary).
+
+(1) Dreambooth-SyleDrop: We choose diverse set of content images from the Dreambooth dataset [27], which consists of images of 30 subjects with 4-5 images per subjects. Style images are chosen from StyleDrop [31] dataset, where a single image is used per style.
+(2) Subjectplop: subjectplop [28] contains a single image for both content and style.
+(3) Subjectplop-StyleDrop: We also benchmark on cross dataset, i.e., contents are taken from subjectplop dataset [28], and style images are taken from StyleDrop [31] dataset. Note here also, the content and style contains a single image.
+(4) Custom101-StyleDrop: We conduct experiments on the real-world object-centric Custom101 dataset [22] (with 101 objects like human faces and everyday items) using styles from the Styledrop dataset [31].
+
+Metrics. For content similarity, we use DINO similarity score [27], i.e., the average pairwise cosine similarity of DINO ViT-B/6 embeddings of the content and generated images. For style similarity, we use the CLIP-I metric [27], which is the average pairwise cosine similarity between CLIP embeddings of the style and generated images. Text similarity (CLIP-T [27]) is computed as the average cosine similarity between CLIP's text and prompt embeddings. We also report the Contrastive Style Descriptor-style (CSD-s) metric [32], which is more appropriate to evaluate style similarity.
+
+Table 1. Performance comparison of content and style merging across different datasets and methods
+
+| Method | Dreambooth + StyleDrop | Subjectplop | Subjectplop + StyleDrop | Custom101 + StyleDrop | # Params (M) | Param storage (MB) | Training time (m) |
| DINO | CLIP-I | CLIP-T | CSD-s | DINO | CLIP-I | CLIP-T | CSD-s | DINO | CLIP-I | CLIP-T | CSD-s | DINO | CLIP-I | CLIP-T | CSD-s |
| Naïve Merging | 0.47 | 0.64 | 0.266 | 0.44 | 0.48 | 0.59 | 0.263 | 0.30 | 0.42 | 0.49 | 0.274 | 0.12 | 0.40 | 0.39 | 0.204 | 0.18 | - | - | - |
| B-LoRA [10] (ECCV'24) | 0.45 | 0.57 | 0.281 | 0.28 | 0.64 | 0.57 | 0.275 | 0.32 | 0.63 | 0.56 | 0.281 | 0.14 | 0.49 | 0.51 | 0.263 | 0.25 | - | - | - |
| ZipLoRA [29] (ECCV'24) | 0.53 | 0.65 | 0.285 | 0.41 | 0.75 | 0.62 | 0.288 | 0.35 | 0.87 | 0.56 | 0.289 | 0.16 | 0.54 | 0.58 | 0.286 | 0.30 | 1.33 | 6.5 | 5.48 |
| ZipRank | 0.53 | 0.64 | 0.287 | 0.42 | 0.71 | 0.62 | 0.291 | 0.35 | 0.86 | 0.56 | 0.296 | 0.17 | 0.56 | 0.58 | 0.295 | 0.32 | 0.07 | 0.35 | 5.28 |
| ZipRank + Layer-Priors | 0.54 | 0.67 | 0.293 | 0.45 | 0.73 | 0.63 | 0.310 | 0.37 | 0.90 | 0.56 | 0.302 | 0.18 | 0.59 | 0.60 | 0.307 | 0.35 | 0.07 | 0.35 | 6.02 |
| DuoLoRA | 0.56 | 0.69 | 0.314 | 0.48 | 0.78 | 0.65 | 0.318 | 0.40 | 0.90 | 0.58 | 0.319 | 0.20 | 0.61 | 0.62 | 0.316 | 0.37 | 0.07 | 0.35 | 6.38 |
+
+
+Figure 5. Qualitative Results on Dreambooth + StyleDrop.
+
+Implementation details. In all our experiments, we have used SDXL v1.0 as our base model. To train the content and style LoRAs, we use Dreambooth finetuning with LoRA of rank 64. We update the LoRA weights using Adam optimizer for 1000 steps with batch size of 1 and learning rate of 5e-4. The text encoder of SDXL remains frozen during the LoRA finetuning.
+
+During the merging, we train the mergers in the rank dimension for 100 steps, with both the layer-prior loss $(\mathcal{L}_{layer\_prior})$ and the cycle loss $(\mathcal{L}_{constyle})$ , with Adam optimizer and a learning rate of 0.01. The hyperparameters are chosen as follows, $\lambda_{cycle} = 0.01$ and $\lambda_{layer\_prior} = 0.1$ .
+
+Baselines. For personalized stylization, we compare our method with the following baselines. (1) Naive merging: The content and style adapters are added together with a blending scalar parameter during inference. This merging is training free. (2) B-LoRA [10]: Specific blocks are learnt for content and style in SDXL. (3) ZipLoRA [29]: A weighting vector is learned at the output dimension of each adapter, such that their similarity is reduced. We used the parameters from ZipLoRA paper [29]. and (4) Paircustomization [20].
+
+Quantitative and Qualitative Results. We compare our method with Naive merging, B-LoRA and ziplora baselines. Tab. 1 shows the comparison with different datasets and baseline methods. Our method outperforms the SOTA in all the DINO, CLIP and CSD metrics. Qualitative results are shown in Fig. 5, Fig. 6 and Fig. 7. Visually it is also evident that our method outperform the baselines. We also compare
+
+
+Figure 7. Qualitative Results on Subjectplop (best viewed in color).
+
+
+Figure 8. Recontextualization through prompts.
+
+DuoLoRA with Pair-customization [20] in Tab. 2, using their test set for a fair evaluation since their approach requires paired object and stylized images (details and qualitative results in supplementary). To demonstrate that DuoLoRA generated images are not biased toward the content of the style images, we measured the DINO similarity between the content, style, and generated images. On the Dreambooth-StyleDrop benchmark, the average DINO similarity is 0.56 w.r.t content images and 0.25 w.r.t style images, indicating minimal content bias from the style images.
+
+Recontextulization. Tab. 1 and Fig. 8 show DuoLoRA successfully recontextualizes through text prompts, measured by CLIP-T, (e.g., “a $<\mathrm{V}>$ object in $<\mathrm{S}>$ style riding a bicycle”) while seamlessly blending content and style (more in supplementary). Fig. 8 also demonstrates that our blending preserves the model’s finer text-based editing capabilities,
+
+
+Figure 9. Multi-concept stylization comparison (2 concepts).
+
+such as depicting "sleeping" through closed eyes.
+
+Table 2. Comparison with [20]
+
+| Method | DINO | CLIP-I | CSD-s | Method | DINO | CLIP-I | CSD-s | #Params |
| Paircustomization [20] | 0.56 | 0.65 | 0.47 | ZipLoRA | 0.53 | 0.65 | 0.41 | 1.33M |
| DuoLoRA | 0.62 | 0.69 | 0.50 | DuoLoRA | 0.57 | 0.73 | 0.50 | 1.33M |
+
+Multi-concept stylization. The multi-concept stylization results are visualized in Fig. 9,10, where our method shows qualitative improvements over the baselines in preserving both content and style details. For instance, as shown in Fig. 9, naive merging often loses details of either content, style, or both. Similarly, ZipLoRA struggles to retain content details, while our method successfully captures and maintains both content and style elements. We combine 2, 3, 4 concepts from Dreambooth dataset and styles from StyleDrop dataset and the results are shown in Tab. 4, Fig. 9 and Fig. 10. Details and more results are in the supplementary.
+
+Other diffusion models. We evaluate DuoLoRA on the SSD-1B [15] and Segmind-Vega [15] architectures, demonstrating its generalizability across architectures (Tab. 5).
+
+Runtime and storage. We compare runtime and extra storage required for the mergers in DuoLoRA vs baselines in Tab. 1 on an NVIDIA A6000 (24GB RAM). Our method slightly increase training time while reducing extra storage requirements compared to the baselines.
+
+User study. Since perceptual metrics are not always reliable, we also conducted a human preference study using Amazon Mechanical Turk (AMT) for assesing the content-style alignment. We asked 50 unbiased users rank our method against baselines (i.e., "Naive merging", "B-LoRA", "ZipLoRA", "DuoLoRA", "None is satisfactory"), totaling 1000 questionnaires. The aggregate responses in Tab. 6 show that DuoLoRA generated images significantly outperformed the baselines by a large margin (50%). Further details are provided in the Supplementary.
+
+Ablations. We perform ablations on the loss and initialization when applied to content (Dreambooth dataset) and
+
+Table 4. Multi-concept comparison
+
+| Method | 2-concepts | 3-concepts | 4-concepts |
| DINO | CLIP-I | CSD-s | DINO | CLIP-I | CSD-s | DINO | CLIP-I | CSD-s |
| Naïve Merging | 0.38 | 0.63 | 0.35 | 0.35 | 0.56 | 0.30 | 0.28 | 0.55 | 0.25 |
| ZipLoRA | 0.40 | 0.64 | 0.42 | 0.38 | 0.60 | 0.34 | 0.29 | 0.58 | 0.31 |
| DuoLoRA | 0.45 | 0.66 | 0.47 | 0.40 | 0.64 | 0.39 | 0.32 | 0.63 | 0.35 |
+
+Table 5. Comparison w.r.t architectures
+
+| Method | SSD-1B | Segmind-Vega |
| DINO | CLIP-I | CSD-s | #params(M) | DINO | CLIP-I | CSD-s | #params(M) |
| Naïve Merging | 0.35 | 0.55 | 0.38 | - | 0.33 | 0.57 | 0.42 | - |
| ZipLoRA | 0.42 | 0.65 | 0.46 | 0.61 | 0.40 | 0.67 | 0.50 | 0.26 |
| DuoLoRA | 0.44 | 0.71 | 0.52 | 0.03 | 0.41 | 0.72 | 0.56 | 0.02 |
+
+
+Figure 10. Multi-concept stylization (4 concepts).
+
+Table 6. User study
+
+| None | Naive merging | B-LoRA | ZipLoRA | DuoLoRA |
| 0.0% | 10% | 18% | 22% | 50% |
+
+Table 7. Ablation of content and style threshold $\left( {{T}_{\text{content }},{T}_{\text{style }}}\right)$
+
+| Method | λlayer_prior | T_content | T_style | DINO | CLIP-I | CSD-s |
| ZipRank | 0.1 | - | - | 0.53 | 0.64 | 0.42 |
| ZipRank + Init | 0.1 | 0.1 | 0.0 | 0.56 | 0.65 | 0.43 |
| ZipRank + Init | 0 | 0.75 | 0.50 | 0.57 | 0.64 | 0.41 |
| ZipRank + Init | 0 | 1 | 0.75 | 0.53 | 0.64 | 0.42 |
| ZipRank + Init | 0.1 | 0.75 | 0.50 | 0.50 | 0.64 | 0.44 |
| ZipRank + Init | 0.1 | 1 | 0.75 | 0.47 | 0.64 | 0.43 |
+
+Table 8. Ablations of components
+
+| ZipRank | Merger Initialization | Nuclear Norm loss | Sparsity loss | Cycle Loss (Style) | Cycle Loss (Content+Style) | DINO | CLIP-I | CSD-s |
| ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | 0.530 | 0.647 | 0.424 |
| ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | 0.560 | 0.652 | 0.435 |
| ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | 0.577 | 0.637 | 0.400 |
| ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | 0.516 | 0.679 | 0.476 |
| ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | 0.542 | 0.670 | 0.458 |
| ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | 0.507 | 0.704 | 0.519 |
| ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 0.560 | 0.693 | 0.482 |
+
+Table 9. Ablation of parameters
+
+| Parameters (λlayer_prior/λcycle) | 0/0 | 0/1 | 0/0.01 | 1/0 | 0.1/0 | 0.1/0.1 | 0.01/0.01 | 0.1/0.01 | 1.0/0.01 |
| DINO | 0.53 | 0.45 | 0.47 | 0.57 | 0.55 | 0.52 | 0.48 | 0.51 | 0.56 |
| CLIP-I | 0.64 | 0.70 | 0.68 | 0.63 | 0.64 | 0.64 | 0.65 | 0.66 | 0.69 |
| CSD-s | 0.42 | 0.52 | 0.48 | 0.40 | 0.42 | 0.43 | 0.45 | 0.46 | 0.48 |
+
+style (StyleDrop dataset) in Tab. 8. Ablation of initialization parameters ( $T_{content}$ and $T_{style}$ ) is also provided in Tab. 7. We also present a hyperparameter sensitivity analysis on Dreambooth-StyleDrop in Tab. 9 w.r.t loss coefficients ( $\lambda_{layer\_prior}$ , $\lambda_{cycle}$ ). With same number of parameters compared to baseline (ZipLoRA), DuoLoRA obtains better performance gains in Tab. 3. More ablation results are provided in the supplementary material.
+
+Limitations. At present, our approach handles only two concepts simultaneously, limiting its applicability for merging multiple concepts jointly. We aim to address this limitation in future work.
+
+# 5. Conclusion
+
+We investigate content and style personalization via LoRA merging, introducing DuoLoRA—a content-style personalization framework with three core components: (1) learning a mask in the rank dimension, (2) merging informed by layer priors, and (3) Constyle loss that leverages cycle-consistency between content and style. By learning the mask in the rank dimension, DuoLoRA enables adaptive rank flexibility with a significant reduction in trainable parameters (19x fewer). To further refine the merging process, we apply explicit rank constraints informed by layer priors and adaptive initialization. Additionally, we introduce Constyle loss, which uses content-style cycle-consistency to enhance merging. Experiments across multiple benchmarks show that our approach outperforms state-of-the-art methods.
+
+# 6. Acknowledgement
+
+A. Roy and R. Chellappa acknowledge support through a fellowship from JHU + Amazon Initiative for Interactive AI (AI2AI) and ONR MURI grant N00014-20-1-2787.
+
+# References
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+# DyGS-SLAM: Real-Time Accurate Localization and Gaussian Reconstruction for Dynamic Scenes
+
+Xinggang Hu $^{1,2}$ Chenyangguang Zhang $^{2}$ Mingyuan Zhao $^{3}$ Yuanze Gui $^{4}$ Xiangkui Zhang $^{1}$ Xiangyang Ji $^{2*}$
+
+$^{1}$ Dalian University of Technology $^{2}$ Tsinghua University $^{3}$ University of Chinese Academy of Sciences $^{4}$ Beijing University of Technology hxg@mail.dlut.edu.cn, zcyg22@mails.tsinghua.edu.cn, zhaomingyuan21@mails.ucas.ac.cn, guiyuanze@mails.bjut.edu.cn, zhangxk@dlut.edu.cn, xyji@tsinghua.edu.cn
+
+# Abstract
+
+In dynamic scenes, achieving accurate camera localization and reconstructing a long-term consistent map containing only the static background are two major challenges faced by Visual Simultaneous Localization and Mapping (VSLAM). In current traditional dynamic VSLAM systems, the methods used to handle dynamic objects are primarily designed for localization; if applied to reconstruction, they are prone to introducing motion artifacts. Meanwhile, mask compensation strategies in NeRF- or 3DGS-based dynamic VSLAM systems also face challenges, such as the inability to completely eliminate dynamic object artifacts and low real-time performance. To address these issues, we leverage object detection to extract semantic information and propose a dynamic feature detection algorithm based on both geometry and appearance. This algorithm accurately identifies known and unknown moving objects and determines their actual motion states. To mitigate the issue of insufficient detection box coverage, we design a dynamic object box correction algorithm based on clustering and Gaussian mixture models to comprehensively identify moving object regions. Furthermore, to overcome the limitations of sparse features in texture-scarce environments, we introduce a feature densification strategy based on image texture complexity, enhancing reconstruction quality while maintaining real-time performance. Extensive experimental evaluations demonstrate that our system achieves state-of-the-art localization and reconstruction performance in dynamic scenes and can run in real time on resource-constrained devices.
+
+# 1. Introduction
+
+VSLAM has been widely applied in fields such as mobile robotics [8, 48] and augmented reality [2, 40]. Traditional VSLAM systems [4, 9, 22, 31] primarily focus on geometric
+
+
+
+
+
+
+
+
+(a)
+(A)
+Figure 1. Overview. **Baseline (Top):** (a) Semantic segmentation mask; (b) Compensation mask; (c) Fused mask; (d) Limitations of feature extraction; (e) Rendering results. **Ours (Bottom):** (A) Object detection results; (B) Dynamic feature identification; (C) Dynamic object box correction; (D) Feature densification; (E) Rendering results.
+
+
+(d)
+(D)
+
+
+(e)
+(E)
+
+mapping, utilizing point clouds and voxels for sparse reconstruction. While these approaches provide relatively accurate environmental representations, they exhibit limitations in terms of visual quality and dense reconstruction. Recently, NeRF [26] and 3DGS [18] have been integrated into SLAM systems [11, 12, 25, 29, 36, 43, 45] to achieve higher accuracy and continuity in map representation. However, the geometric constraints that SLAM systems rely on are fundamentally based on static assumptions. Consequently, both traditional VSLAM and neural-rendering-based VSLAM [25] (i.e., NeRF- or 3DGS-based VSLAM) suffer from significant degradation in localization accuracy and mapping quality when applied to dynamic environments.
+
+In dynamic scenes, VSLAM faces two major challenges: mitigating the impact of dynamic elements on camera localization and constructing a long-term consistent map containing only static elements. Several existing neural-rendering-based VSLAM systems have proposed solutions for dynamic scenes. A common approach is to use semantic segmentation to extract Potential Moving Objects (PMOs, determined by the semantic labels of detection results).
+
+To address under-segmentation in semantic segmentation and the inability to recognize Unknown Moving Objects (UMOs, moving objects that are not labeled in the training dataset) (Fig. 1(a)), existing methods generate compensation masks using SAM [30], depth guidance [42], motion detection [15, 41], or photometric residuals [20]. However, these methods still suffer from the following limitations (Fig. 1(b)): (1) The edges of the compensation masks are inaccurate; (2) The methods may fail when object motion is subtle or when the target shares similar depth, color, or texture features with the background; (3) The computational cost of generating the masks is high. These limitations result in residual dynamic artifacts in the reconstructed map (Fig. 1(c) and (e)) and hinder the real-time performance of the system. We observe that object detection algorithms can effectively overcome the edge segmentation accuracy and real-time performance limitations of mask-based methods. However, applying object detection to dynamic object handling still faces two major challenges (Fig. 1(A)): (1) The inability to recognize UMOs; (2) The inability to determine the true motion state of PMOs. In reconstruction, issue (1) introduces ghosting artifacts of UMOs; in localization, issue (1) causes interference from dynamic features, while issue (2) leads to insufficient localization constraints due to the erroneous removal of static features. To address these challenges, we leverage object detection algorithms to identify PMOs while incorporating both geometric and appearance constraints to detect dynamic features (Fig. 1(B)). This enables the identification of dynamic features belonging to UMOs and determines the actual motion state of PMOs. Our approach remains effective even in scenarios where dynamic feature recognition lacks matching associations between consecutive frames. Furthermore, considering that semantic detection boxes and dynamically identified regions sometimes fail to fully cover moving objects [14, 49], we propose a dynamic object box correction algorithm based on clustering and Gaussian mixture models (GMM) (Fig. 1(C)). This algorithm effectively compensates for the local coverage deficiency of detection boxes, improving the completeness of moving object coverage.
+
+The real-time performance of SLAM systems and their deployability on resource-constrained devices are crucial factors. For neural-rendering-based VSLAM, balancing reconstruction quality and real-time performance remains a significant challenge. Frame-to-frame-based systems [11, 17, 25, 43] are limited in real-time performance and consume excessive computational resources. Sparse feature-based methods [12, 28, 34] perform well in terms of real-time efficiency but struggle to maintain reconstruction quality. The main reason is that feature extraction is highly dependent on image texture: in texture-rich regions, sufficient and reasonable Gaussian features can be extracted to support reconstruction; however, in low-visual-quality
+
+or texture-deficient areas, especially under uneven lighting, uniform textures, or smooth surfaces, feature extraction faces significant limitations, and in some regions, effective feature points cannot be obtained at all (Fig. 1(d)), leading to poor reconstruction quality for certain environmental details. To address these issues, we propose feature densification in texture-deficient regions based on image texture complexity (Fig. 1(D)), effectively compensating for the insufficiency of sparse features while balancing reconstruction quality and real-time performance (Fig. 1(E)).
+
+In summary, we aim to propose a 3DGS-SLAM system capable of accurate localization and long-term consistent map reconstruction containing only static backgrounds in dynamic scenes, while ensuring real-time operation on resource-constrained devices (referred to as DyGS-SLAM). Notably, the proposed method is designed to be plug-and-play, making it easily integrable into any VSLAM approach based on sparse feature points. The main contributions of this work are as follows:
+
+- Dynamic Feature Detection (DFD): Leveraging the advantages of geometric and appearance features, it effectively identifies dynamic features belonging to UMOs and determines the true motion state of PMOs.
+- Dynamic Object Box Correction (DOBC): Based on clustering and GMM, the approach refines bounding boxes for more precise coverage of moving objects, working in conjunction with the dynamic feature detection algorithm to benefit both localization and reconstruction.
+- Adaptive Feature Densification (AFD): Based on image texture complexity, it reasonably supplements sparse feature points, ensuring both reconstruction quality and real-time performance.
+- Extensive evaluation demonstrates that our approach achieves state-of-the-art localization and reconstruction performance in dynamic scenes while enabling real-time operation on low-performance portable devices.
+
+# 2. Related Work
+
+1) Traditional VSLAM for Dynamic Scenes: When semantic information is not available as a prior, common geometric methods for identifying and handling dynamic features primarily include epipolar constraints [1, 21], optical flow residuals [5, 19], and projection residuals [35, 50]. These methods are generally efficient in detecting and processing dynamic elements; however, they are prone to errors in dynamic feature identification, which limits their localization accuracy. With the advancement of deep learning, recent studies have integrated semantic and geometric constraints for dynamic feature identification and processing. These approaches can be categorized into three main types: (1) utilizing geometric constraints to further determine the actual motion status of semantically prior moving objects [39, 44, 46]; (2) leveraging geometric constraints to supple
+
+ment the motion determination of UMOs [3, 14, 37]; (3) using geometric constraints to assess whether features belonging to semantically prior moving objects are indeed in motion [6, 13, 47]. These methods have achieved excellent localization accuracy. However, these methods primarily focus on localization tasks and generally do not consider dense and stable reconstruction. The proposed geometric methods become ineffective in the absence of inter-frame feature matching constraints and lack sufficient attention to the complete identification of moving regions, leading to dynamic object artifacts when applied to reconstruction. In contrast, our method robustly and accurately identifies dynamic object regions, while simultaneously contributing to both visual localization and Gaussian reconstruction.
+
+2) Neural-Rendering-Based VSLAM for Dynamic Scenes: The high-precision reconstruction and efficient rendering capabilities of NeRF [26] and 3DGS [18] have driven the application of neural-rendering-based VSLAM in dynamic scenes. Gassidy [38] integrates rendering loss flow analysis to handle dynamic environments; however, this method suffers from certain latency issues and fails to completely eliminate the influence of dynamic objects, which degrades localization accuracy and introduces reconstruction artifacts. GARAD-SLAM [24] removes dynamic points using conditional random fields. However, its theoretical foundation is similar to traditional SLAM approaches that rely purely on geometric methods for dynamic feature identification, making it prone to missing moving or potentially moving objects. Additionally, many studies introduce semantic segmentation to provide prior information. For instance, DOARS [23] employs semantic segmentation to extract masks of dynamic objects, but due to the inherent under-segmentation problem in semantic segmentation, a significant number of artifacts remain in the reconstructed scene. To mitigate these limitations, various methods have been proposed to compensate for semantic segmentation masks. DN-SLAM [30] combines optical flow estimation and SAM for fine-grained segmentation; NID-SLAM [42] proposes a depth-guided semantic mask enhancement method; RoDyn-SLAM [15] adopts a motion mask generation approach to filter out invalid sampled rays; DG-SLAM [41] introduces an adaptive motion mask generation strategy that integrates semantic priors; DGS-SLAM [20] iteratively updates photometric residuals to generate masks. However, the compensation masks generated by the above methods still suffer from inaccurate edges, failure in cases of subtle motion or similar features between the target and background, and high computational overhead, resulting in residual dynamic object artifacts in the reconstructed map and limiting the real-time performance of the system. In contrast, we propose a dynamic feature detection method and a dynamic object box correction algorithm that, combined with semantic priors provided by object detection,
+
+accurately identify dynamic regions. This approach effectively overcomes the imprecise dynamic object region estimation and real-time performance limitations of existing methods, enabling precise visual localization and Gaussian reconstruction under high real-time conditions.
+
+# 3. Method
+
+Given a series of RGB-D frames $\{I_i, D_i\}_{i=1}^N$ , where $I_t \in \mathbb{R}^3$ and $D_t \in \mathbb{R}$ , our method (Fig. 2) aims to accurately estimate camera poses $\{\xi_i\}_{i=1}^N$ , where $\xi_t \in SE(3)$ , under dynamic disturbances and reconstruct a long-term consistent Gaussian map containing only the static background. First, we apply a dynamic feature detection algorithm (DFD, Sec. 3.1) that integrates geometric projection constraints, depth consistency verification, and appearance similarity detection. Then, we refine the bounding boxes of UMOs and PMOs using a clustering and GMM-based correction method (DOBC, Sec. 3.2) to achieve more accurate and comprehensive coverage of moving objects. Finally, based on the results of DFD and DOBC, we perform a two-stage camera pose estimation (Sec. 3.3) and Gaussian mapping with adaptive feature densification (AFD) based on image texture complexity (Sec. 3.4).
+
+# 3.1. Dynamic Feature Detection
+
+In our method, object detection provides semantic priors, while dynamic feature detection aims to determine the actual motion status of features. This enables the identification of UMOs and the determination of the actual motion state of PMOs. The proposed DFD algorithm is illustrated in Fig. 2(C).
+
+For a feature point $p_i$ that has a corresponding match in the adjacent frame $F_j$ , its motion is first determined using the reprojection constraint:
+
+$$
+E _ {\text {p r o j}} \left(p _ {i}\right) = \left\| p _ {i \rightarrow j} - p _ {j} \right\|, \tag {1}
+$$
+
+where $p_{i\rightarrow j}$ denotes the reprojected position of $p_i$ from the current frame $F_{i}$ to the adjacent frame $F_{j}$ , and $p_j$ represents the actual matched position of $p_i$ in $F_{j}$ . If $E_{\mathrm{proj}}(p_i)$ exceeds a predefined threshold, the point is classified as a potential dynamic feature. When the number of dynamic points exceeds a certain threshold relative to the number of foreground points within the PMO's bounding box, the PMO is determined to be in an actual moving state.
+
+For feature points $p_i$ without a corresponding match in $F_j$ , although they do not impact localization accuracy, they are reconstructed into 3D points and integrated into the Gaussian reconstruction. To determine whether such points are dynamic, we leverage a combination of reprojection depth residuals and image patch similarity. This approach integrates geometric and appearance information, effectively mitigating the limitations of using a single constraint under specific conditions.
+
+
+Figure 2. DyGS-SLAM system architecture. The pipeline consists of: RGB-D data stream input (A), initial pose estimation (B), dynamic feature detection (DFD) (C), dynamic object box correction (DOBC) (D), refined pose estimation and sparse 3D point generation (E), and Gaussian reconstruction (F) with adaptive feature densification (AFD).
+
+The reprojection depth residual $R_{D}(p_{i})$ is defined as:
+
+$$
+R _ {D} \left(p _ {i}\right) = \left| D _ {j} \left(p _ {i \rightarrow j}\right) - D _ {i} \left(p _ {i}\right)\right|, \tag {2}
+$$
+
+where $D_{i}(p_{i})$ and $D_{j}(p_{i\rightarrow j})$ denote depth values of point $p_i$ in $F_{i}$ and its reprojected counterpart in $F_{j}$ , respectively.
+
+In frames $F_{i}$ and $F_{j}$ , image patches $A$ and $B$ are extracted centered at points $p_{i}$ and $p_{i\rightarrow j}$ , respectively. The cosine similarity between these patches is defined as:
+
+$$
+S _ {\cos} (A, B) = \frac {\sum_ {u , v} A (u , v) \cdot B (u , v)}{\sqrt {\sum_ {u , v} A (u , v) ^ {2}} \cdot \sqrt {\sum_ {u , v} B (u , v) ^ {2}}}, \tag {3}
+$$
+
+where $A(u,v)$ and $B(u,v)$ represent the intensity values of pixel $(u,v)$ in patches $A$ and $B$ , respectively.
+
+The weighted scoring function $\Phi(p_i)$ is constructed as:
+
+$$
+\Phi (p _ {i}) = \alpha \cdot \frac {R _ {D} (p _ {i})}{e _ {\mathrm {t h}}} + \beta \cdot \left(1 - S _ {\cos} (A, B)\right), \tag {4}
+$$
+
+where $\alpha$ and $\beta$ are weight parameters for geometric and appearance information, respectively, and $e_{\mathrm{th}}$ is a normalization factor for the depth residual. A scoring threshold $\Phi_{\mathrm{th}}$ is set to determine whether $p_i$ is dynamic.
+
+# 3.2. Dynamic Object Box Correction
+
+Object detection boxes and dynamic features (Sec. 3.1) sometimes fail to fully cover moving objects. The primary reasons include: (1) Object detection algorithms may miss complex postures or detailed parts such as hands or feet [49]; (2) Due to the influence of camera viewing angles and the complexity of object motion, dynamic feature detection methods may only identify part of an object's features as dynamic [14]. To address this issue, we propose a dynamic object box correction method based on clustering and GMM, as illustrated in Fig. 2(D).
+
+First, we cluster dynamic features that are identified by the motion detection algorithm but are not within the PMO bounding boxes. We then construct the minimum bounding box enclosing the clustered feature points. Next, to determine whether points surrounding the box belong to the object, we employ GMM to model the depth distribution of foreground points within the box. Specifically, for PMO bounding boxes obtained via semantic recognition, foreground points are clustered using DBSCAN. For boxes of UMOs identified by the dynamic feature detection algorithm, all dynamic features within the box are considered as foreground points.
+
+We assume that the depth values of foreground points,
+
+denoted as $X = \{x_{1}, x_{2}, \ldots, x_{n}\}$ , follow a GMM, with the probability density function $p(x)$ defined as:
+
+$$
+p (x) = \sum_ {k = 1} ^ {K} \pi_ {k} \cdot \mathcal {N} \left(x \mid \mu_ {k}, \sigma_ {k} ^ {2}\right), \tag {5}
+$$
+
+where $K$ is the number of Gaussian components, $\pi_{k}$ is the weight of the $k$ -th Gaussian component, and $\mathcal{N}(x|\mu_k,\sigma_k^2)$ represents the probability density function of the $k$ -th Gaussian component with mean $\mu_{k}$ and variance $\sigma_k^2$ .
+
+We estimate the model parameters $\theta = \{\pi_k, \mu_k, \sigma_k^2\}_{k=1}^K$ using the Expectation-Maximization (EM) algorithm to maximize the log-likelihood function:
+
+$$
+L (\theta) = \sum_ {i = 1} ^ {n} \log \left(\sum_ {k = 1} ^ {K} \pi_ {k} \cdot \mathcal {N} \left(x _ {i} \mid \mu_ {k}, \sigma_ {k} ^ {2}\right)\right). \tag {6}
+$$
+
+For a set of candidate points surrounding the detection box, denoted as $Y = \{y_{1}, y_{2}, \ldots, y_{m}\}$ , we input the depth value $y_{j}$ of each candidate point into the trained GMM model and compute its probability density $p(y_{j})$ :
+
+$$
+p \left(y _ {j}\right) = \sum_ {k = 1} ^ {K} \pi_ {k} \cdot \mathcal {N} \left(y _ {j} \mid \mu_ {k}, \sigma_ {k} ^ {2}\right). \tag {7}
+$$
+
+If $p(y_{j})$ exceeds a predefined threshold $T$ , the candidate point $y_{j}$ is classified as belonging to the moving object. Once all candidate points belonging to the moving object are identified, the bounding box is refined accordingly.
+
+# 3.3. Two-Stage Camera Pose Estimation
+
+In the tracking thread, we adopt a two-stage coarse-to-fine optimization strategy to achieve robust localization in dynamic environments. Specifically, we extract ORB feature points from image frames and establish 2D-3D correspondences through map point projection matching. To mitigate dynamic disturbances, we employ a two-stage feature filtering strategy during pose estimation.
+
+In the first stage, the DBSCAN algorithm is used to extract foreground points within the bounding boxes of PMOs and mark them as dynamic points, which are excluded during pose estimation (Fig. 2(B)). In the second stage, leveraging the refined dynamic information obtained in the first stage, we further optimize the pose. Specifically, foreground points within the corrected bounding boxes of actually moving PMOs and UMOs are marked as dynamic, and only static feature points are used for optimization.
+
+We optimize the camera pose by minimizing the reprojection error through Bundle Adjustment (BA):
+
+$$
+\{R, t \} = \arg \min \sum_ {i \in \mathcal {M}} \psi \left(\| \mathbf {u} _ {i} - \pi (R \mathbf {X} _ {i} + t) \| _ {\boldsymbol {\Sigma}} ^ {2}\right), \quad (8)
+$$
+
+where $\Sigma$ is the scale-dependent covariance matrix of keypoints, $\pi (\cdot)$ represents the 3D-to-2D projection function,
+
+$\psi$ is the Huber loss function, and $\mathcal{M}$ denotes the final set of selected static matching points. This method employs Levenberg-Marquardt optimization, effectively improving tracking accuracy and stability.
+
+# 3.4. Gaussian Mapping and Adaptive Feature Den-sification
+
+After obtaining accurate dynamic object regions, precise camera poses, and sparse 3D points, we perform Gaussian mapping, as shown in Fig. 2(F). We adopt the Gaussian mapping strategy from Photo-SLAM [12] and introduce a masking matrix $M$ when computing the photometric loss $\mathcal{L}$ between the rendered image $I_{r}$ and ground truth $I_{gt}$ to constrain the impact of dynamic object regions on optimization:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {m a s k e d}} = (1 - \lambda) \| M \odot \left(I _ {r} - I _ {g t}\right) \| _ {1} \tag {9} \\ + \lambda (1 - \operatorname {S S I M} (M \odot I _ {r}, M \odot I _ {g t})), \\ \end{array}
+$$
+
+where $M$ is set to 0 in the regions of the corrected bounding boxes of PMOs and UMOs, and 1 elsewhere, and $\odot$ denotes element-wise multiplication.
+
+Feature extraction may fail or degrade in low-visual-quality or texture-deficient scenes, limiting environmental detail reconstruction. To address this, we introduce an adaptive feature densification method based on image texture complexity during Gaussian mapping.
+
+To identify texture details within image patches, we design a metric combining gradient magnitude and local variance to capture edge features and grayscale variations. Given the gradient mean $\bar{G}_{\mathrm{block}}$ and local variance $\sigma_{\mathrm{block}}^2$ , the texture complexity $C_{\mathrm{block}}$ of an image patch is defined as:
+
+$$
+C _ {\text {b l o c k}} = w _ {G} \cdot \bar {G} _ {\text {b l o c k}} + w _ {V} \cdot \sigma_ {\text {b l o c k}} ^ {2}, \tag {10}
+$$
+
+where $\bar{G}_{\mathrm{block}}$ measures edge intensity and is computed using the Sobel operator:
+
+$$
+\bar {G} _ {\text {b l o c k}} = \frac {1}{N} \sum_ {(x, y) \in \text {b l o c k}} \sqrt {\left(\frac {\partial I}{\partial x}\right) ^ {2} + \left(\frac {\partial I}{\partial y}\right) ^ {2}}. \tag {11}
+$$
+
+A larger $\bar{G}_{\mathrm{block}}$ indicates richer edge information in the image patch. The local variance $\sigma_{\mathrm{block}}^2$ reflects the intensity variation and is defined as:
+
+$$
+\sigma_ {\text {b l o c k}} ^ {2} = \frac {1}{N} \sum_ {(x, y) \in \text {b l o c k}} \left(I (x, y) - \bar {I} _ {\text {b l o c k}}\right) ^ {2}, \tag {12}
+$$
+
+where $\bar{I}_{\mathrm{block}}$ is the mean intensity of the patch. Higher variance indicates richer texture details. The weights $w_{G}$ and $w_{V}$ balance the contributions of gradient and variance.
+
+Based on texture complexity, we design a nonlinear adaptive sampling strategy that adjusts the number of sampling points according to the complexity value:
+
+$$
+n = n _ {\max } \cdot \left(1 - e ^ {- \beta \cdot C _ {\mathrm {b l o c k}}}\right), \tag {13}
+$$
+
+
+Figure 3. Feature Densification Results. Green and blue points represent extracted ORB feature points, where green points have matching correspondences in adjacent frames, while blue points do not. Red points denote densified features based on image texture complexity. Only green points are used for pose estimation, while all points contribute to Gaussian mapping.
+
+where $n_{\mathrm{max}}$ is the maximum number of sampling points, and $\beta$ controls the impact of complexity on the number of sampled points. Finally, we employ uniform random sampling to ensure even distribution of sampled points, achieving comprehensive texture coverage, as illustrated in Fig. 3.
+
+# 4. Experiments
+
+In this section, we compare DyGS-SLAM with other state-of-the-art (SOTA) SLAM systems on the TUM RGB-D dataset [33] and the BONN RGB-D Dynamic dataset [27]. The evaluation metrics primarily include the quality of Gaussian mapping and localization accuracy. Additionally, we assess the generation of dynamic object bounding boxes and conduct ablation studies to demonstrate the contributions of each designed module. Finally, we evaluate the real-time performance and resource consumption of our system to showcase its practical applicability. All experiments are conducted on a laptop equipped with an i9-12900H CPU, an RTX 3060 GPU (6GB VRAM), and 16GB of system memory. Details on the experimental parameter settings can be found in the appendix.
+
+# 4.1. Evaluation of Dynamic Object Box Generation
+
+We evaluate the performance of our dynamic object box generation on the balloon2 and mv_box2 sequences from the BONN dataset. As shown in Fig. 4, these scenes contain both PMOs and UMOs, such as cardboard boxes and balloons. Experimental results demonstrate that our proposed DFD (Sec. 3.1) effectively identifies dynamic features, while DOBC (Sec. 3.2) ensures that the bounding boxes accurately and comprehensively cover moving objects. This provides strong support for precise localization and long-term consistent environmental reconstruction.
+
+# 4.2. Evaluation of Reconstruction Performance
+
+Due to the absence of ground truth images with dynamic objects removed, a quantitative comparison of rendering quality is not feasible. To demonstrate the reconstruction performance of our system in dynamic scenes, we conduct a
+
+
+Figure 4. Qualitative Results of Dynamic Object Box Generation. (A) Semantic detection box; (B) Red points represent detected dynamic points (Sec. 3.1); (C) Dynamic points outside the boxes of PMOs are clustered into different groups (colored in yellow, pink, etc.); (D) Minimum boxes enclosing dynamic point clusters; (E) Corrected boxes for PMOs and UMOs (Sec. 3.2).
+
+
+Figure 5. Visual Comparison of Rendered Images on TUM and BONN Datasets.
+
+qualitative evaluation of rendered images by comparing our approach with other state-of-the-art methods using consistent viewpoints. As shown in Fig. 5, even when compared with the most advanced 3DGS-based dynamic SLAM system, DG-SLAM [41], our method exhibits significant advantages in both geometric and texture details. In particular, our approach excels in image sharpness and artifact suppression. This improvement is attributed to our care
+
+fully designed DFD, DOBC, and AFC algorithms, which enable precise and comprehensive dynamic object removal while leveraging adaptive feature densification based on image texture complexity. As a result, despite using sparse points, our method achieves highly competitive Gaussian reconstruction and rendering performance.
+
+It is important to note that most related works have not been open-sourced, and the test sequences used in their evaluations vary, which limits direct experimental comparisons. Therefore, we make our best effort to compare against approaches that use either the same test sequences or have publicly available implementations. Additionally, we compare our rendering results with Photo-SLAM [12] on static scene datasets (TUM [33] and ICL-NUIM [10]), where the experimental results further validate the effectiveness of our proposed AFC. More experiments on mapping and rendering performance can be found in the appendix.
+
+# 4.3. Evaluation of Localization Performance
+
+To comprehensively evaluate the tracking performance of our method, we conducted a comparative analysis under both highly dynamic and mildly dynamic scenarios. As shown in Tabs. 1 and 2, in complex dynamic scenes, unlike current dynamic SLAM systems based on NeRF or 3DGS that predominantly focus on reconstruction performance, our system demonstrates not only strong competitiveness in reconstruction and rendering but also superior tracking performance. In most sequences, the results are nearly optimal or suboptimal, and the average localization accuracy across the two datasets reaches the best level. This can be attributed to our proposed DFD and DOBC algorithms, which precisely identify the actually moving PMOs and UMOs, in conjunction with a two-stage coarse-to-fine pose estimation strategy that ensures stable and accurate tracking even in complex environments.
+
+# 4.4. Ablation Study
+
+To evaluate the effectiveness of each proposed module, we conduct an ablation study by removing the following components: (1) w/o-DFD, (2) w/o-DOBC, and (3) w/o-AFD. Tab. 3 presents the localization results of the ablation study, while Fig. 6 illustrates the mapping results.
+
+- w/o-DFD: The presence of some UMOs in the scene introduces dynamic features, and the inability to determine the true motion state of PMOs leads to the erroneous removal of static features, which together result in a severe decline in localization accuracy (Tab. 3). Furthermore, the reconstructed scene exhibits noticeable ghosting artifacts from UMOs (Fig. 6(A)).
+- w/o-DOBC: Since the bounding boxes of PMOs and UMOs sometimes fail to fully cover moving objects, this omission negatively impacts camera pose estimation accuracy (Tab. 3). It also leads to insufficient removal of
+
+| Method | w_xyz | w_hs | w(static) | w_rpy | s_xyz | s_hs | Avg |
| ORB3 [4] | 36.2 | 46.2 | 38.6 | 68.7 | 1.0 | 2.6 | 32.2 |
| Dyna [3] | 1.6 | 2.7 | 1.2 | 4.3 | 1.5 | 1.8 | 2.2 |
| LC-CRF [7] | 1.9 | 3.0 | 2.8 | 5.1 | 1.3 | 2.6 | 2.8 |
| Crowd [32] | 1.7 | 3.6 | 0.7 | 4.4 | 1.7 | 2.5 | 2.4 |
| ReFusion [27] | 9.8 | 10.6 | 1.9 | 11.2 | 3.4 | 4.7 | 6.9 |
| ESLAM [16] | 43.5 | 61.7 | 7.5 | 57.3 | 3.4 | 6.3 | 30.0 |
| SplaTAM [17] | 156.2 | 231.2 | 49.1 | 143.7 | 1.7 | 13.9 | 99.3 |
| Photo [12] | 29.2 | 42.1 | 9.2 | 48.9 | 1.1 | 1.9 | 22.1 |
| Rodyn [15] | 8.3 | 5.6 | 1.7 | 4.5 | 5.1 | 4.4 | 4.9 |
| NID [42] | 7.2 | 7.0 | 6.3 | 67.8 | 2.6 | 5.5 | 16.1 |
| DN [30] | 1.7 | 2.8 | 0.8 | 3.2 | 2.7 | 4.3 | 2.6 |
| DOARS [23] | 24.6 | 16.5 | / | 33.1 | 1.5 | 9.8 | 17.1 |
| DGS [20] | 4.1 | 5.5 | 0.6 | / | / | 4.1 | 3.6 |
| Gassidy [38] | 3.5 | 3.7 | 0.6 | / | / | 2.4 | 2.6 |
| DG [41] | 1.6 | / | 0.6 | 4.3 | 1.0 | / | 1.9 |
| Ours | 1.5 | 2.5 | 0.7 | 3.2 | 1.1 | 1.7 | 1.8 |
+
+Table 1. RMSE of ATE Comparison [cm] on TUM RGB-D Dataset with SOTA Algorithms. The best result is highlighted in bold, and the second-best result is indicated by an underline. / indicates that the method is not open-source and the corresponding data is not provided in the paper. The methods compared include: traditional VSLAM methods [3, 4, 7, 27, 32]; neural-rendering-based static VSLAM systems [12, 16, 17]; neural-rendering-based dynamic VSLAM systems [15, 20, 23, 30, 38, 41, 42].
+
+| Method | ball | ball2 | box1 | box2 | crowd | crowd2 | ps_tk | ps_tk2 | Avg |
| ORB3 [4] | 5.8 | 17.7 | 32.0 | 3.5 | 49.6 | 98.9 | 70.7 | 77.9 | 44.5 |
| Dyna [3] | 3.0 | 2.9 | 4.9 | 3.9 | 2.6 | 2.8 | 6.1 | 7.8 | 4.3 |
| LC-CRF [7] | 2.7 | 2.4 | 7.9 | 18.6 | 2.7 | 9.8 | 4.6 | 4.1 | 6.6 |
| ReFusion [27] | 17.6 | 25.3 | 7.7 | 17.8 | 4.9 | 6.1 | 28.9 | 46.5 | 19.4 |
| ESLAM [16] | 22.6 | 36.2 | 19.0 | 17.7 | 41.6 | 114.2 | 48.0 | 51.4 | 43.8 |
| SplaTAM [17] | 35.5 | 36.1 | 63.7 | 19.0 | 194.5 | 358.2 | 149.7 | 91.2 | 118.5 |
| Photo [12] | 7.2 | 16.2 | 37.3 | 4.4 | 71.5 | 68.2 | 57.8 | 99.1 | 45.2 |
| Rodyn [15] | 7.9 | 11.5 | 6.7 | 12.6 | 8.8 | 7.8 | 14.5 | 13.8 | 10.5 |
| NID [42] | 7.3 | 10.1 | 14.2 | 9.6 | 6.8 | 7.4 | 5.5 | 10.3 | 8.9 |
| DN [30] | 3.1 | 2.6 | 2.7 | 12.0 | 2.5 | 2.9 | 3.8 | 4.3 | 4.2 |
| DGS [20] | 2.9 | 6.0 | / | 8.8 | / | / | 9.8 | 11.1 | 7.7 |
| Gassidy [38] | 2.6 | 7.6 | / | 5.4 | / | / | 10.3 | 13.0 | 7.8 |
| DG [41] | 3.7 | 4.1 | / | 3.5 | / | / | 4.5 | 6.9 | 4.5 |
| Ours | 2.9 | 2.6 | 2.1 | 3.1 | 1.9 | 2.8 | 4.3 | 4.9 | 3.1 |
+
+Table 2. RMSE of ATE Comparison [cm] on BONN RGB-D Dataset with SOTA Algorithms. The best result is highlighted in bold, and the second-best result is indicated by an underline. / indicates that the method is not open-source and the corresponding data is not provided in the paper.
+
+moving objects, resulting in residual artifacts in the reconstructed scene (Fig. 6(B)).
+
+- w/o-AFD: The limitations of feature extraction algorithms in low-visual-quality or texture-deficient regions result in suboptimal reconstruction quality for certain environmental details (Fig. 6(C)).
+
+
+
+
+
+
+Figure 6. Comparison of Rendered Images in Ablation Study.
+
+| Method | ball | ball2 | mv_box1 | mv_box2 | s_xyz | s_half | Avg |
| w/o-DFD | 3.9 | 3.7 | 4.3 | 4.7 | 1.5 | 2.2 | 3.4 |
| w/o-DOBC | 3.2 | 2.8 | 3.0 | 3.9 | 1.2 | 1.8 | 2.7 |
| Ours | 2.9 | 2.6 | 2.1 | 3.1 | 1.1 | 1.7 | 2.3 |
+
+# 4.5. Real-Time Performance Evaluation
+
+The real-time performance of a SLAM system and its deployability on resource-constrained devices are crucial indicators of its reliability. As shown in Tab. 4, compared to other systems whose real-time performance is severely limited due to high computational overhead, our system not only demonstrates significant advantages in both localization and reconstruction performance but also achieves real-time operation on a portable laptop, highlighting its strong potential for practical applications. The speed advantage of our approach primarily stems from: (1) Utilizing sparse feature points for Gaussian reconstruction while incorporating a densification strategy to balance quality and efficiency. (2) Optimizing dynamic object handling through DFD and
+
+DOBC, which improves target detection efficiency and outperforms semantic segmentation and compensation mask generation methods.
+
+Table 3. Ablation Study on Localization Accuracy (RMSE of ATE) [cm]. The best results are in bold.
+
+| Method | Running FPS ↑ | GMU GB ↓ | System Configuration |
| CPU | GPU |
| Rodyn [15] | 1.2 | 4 | i7-13700K | RTX 3090Ti |
| DGS [20] | 1.6 | / | R7 3800XT | TITAN RTX |
| DG [41] | 1.5 | 9 | / | RTX 3090Ti |
| Ours | 33.9 | 2.9 | i9-12900H | RTX 3060 |
+
+Table 4. Comparison of Frame Rate and GPU Memory Usage (GMU) with Related Systems. / indicates that the original paper did not provide the corresponding information. Additionally, the reported data exclude the time for semantic segmentation in DGS-SLAM [20] and DG-SLAM [41], and the execution time of the optical flow fusion module in Rodyn-SLAM [15].
+
+# 5. Conclusion
+
+Summary: This study proposes an innovative 3DGS-SLAM system that achieves high-precision localization and long-term consistent map reconstruction containing only static backgrounds in dynamic scenes, while also being capable of real-time operation on resource-constrained devices. By leveraging a dynamic feature identification algorithm that integrates geometric and appearance information, we accurately identify unknown moving objects and determine the actual motion states of potential moving objects. Additionally, the proposed dynamic object box correction algorithm, based on clustering and GMM, effectively enhances the completeness of moving object coverage. Furthermore, to improve the adaptability of sparse feature extraction, we design a feature densification strategy based on texture complexity, which enhances reconstruction quality while maintaining real-time performance. Experimental results demonstrate that our system outperforms existing methods in both localization and mapping under dynamic scenarios and can run stably on low-performance portable devices. This provides an efficient and reliable solution for SLAM technology in dynamic environments.
+
+Limitations: While this study offers new insights to the research field and achieves compelling results, there are still several inherent limitations: 1) If PMOs remain stationary throughout the entire observation period, removing them from the reconstruction may lead to noticeable reconstruction holes due to insufficient viewpoints for compensation. However, if removal is based solely on the actual motion state of PMOs, intermittently moving PMOs may leave artifacts in the generated map. 2) For non-PMOs, if they move from one location to another, the system may mistakenly reconstruct them in both locations. In the future, we will work towards addressing these limitations and further explore semantic Gaussian reconstruction in dynamic scenes.
+
+# Acknowledgements
+
+This work was supported by the National Key R&D Program of China under Grant 2018AAA0102801, PCL-CMCC Foundation for Science and Innovation Grant No. 2024ZY1C0040.
+
+# References
+
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+
+ments. In 2013 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pages 209-218. IEEE, 2013. 2
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+# DyWA: Dynamics-adaptive World Action Model for Generalizable Non-prehensile Manipulation
+
+Jiangran Lyu $^{1,2}$ , Ziming Li $^{1,2}$ , Xuesong Shi $^{2}$ , Chaoyi Xu $^{2}$ , Yizhou Wang $^{1,3,4,\dagger}$ , He Wang $^{1,2,\dagger}$
+
+$^{1}$ Center on Frontiers of Computing Studies, School of Computer Science, Peking University $^{2}$ Galbot
+
+3Inst. for Artificial Intelligence, Peking University 4State Key Laboratory of General Artificial Intelligence, Peking University
+
+https://oku-epic.github.io/DyWA/
+
+
+Figure 1. Illustration of the high-level idea and generalization ability of DyWA. Given a target object's 6D pose and single-view object point cloud, our non-prehensile manipulation policy aims to rearrange the object without grasping. Left: Our key insight is to enhance action learning by jointly predicting future states while adapting to dynamics from historical trajectories. (For clarity, rendered images are used for visualization, while the actual visual input consists of partial point clouds.) Right: After being trained in simulation, our policy achieves zero-shot sim-to-real transfer and generalizes across diverse dynamic properties, including variations in object geometry, object physical property (e.g., slipperiness and non-uniform mass distribution), and surface friction.
+
+# Abstract
+
+Nonprehensile manipulation is crucial for handling objects that are too thin, large, or otherwise ungraspable in unstructured environments. While conventional planning-based approaches struggle with complex contact modeling, learning-based methods have recently emerged as a promising alternative. However, existing learning-based approaches face two major limitations: they heavily rely on multi-view cameras and precise pose tracking, and they fail to generalize across varying physical conditions, such as changes in object mass and table friction. To address these challenges, we propose the Dynamics-Adaptive World Action Model (DyWA), a novel framework that enhances action learning by jointly predicting future states while adapting to dynamics variations based on historical trajectories. By unifying the modeling of geometry, state, physics,
+
+and robot actions, DyWA enables more robust policy learning under partial observability. Compared to baselines, our method improves the success rate by $31.5\%$ using only single-view point cloud observations in the simulation. Furthermore, DyWA achieves an average success rate of $68\%$ in real-world experiments, demonstrating its ability to generalize across diverse object geometries, adapt to varying table friction, and robustness in challenging scenarios such as half-filled water bottles and slippery surfaces.
+
+# 1. Introduction
+
+Non-prehensile manipulation—such as pushing, sliding, toppling, and flipping—greatly extends the capabilities of robotic manipulators beyond traditional pick-and-place operations. These dexterous actions enable robots to handle tasks where grasping is infeasible or inefficient due to object geometry, clutter, or workspace constraints. Over the years, significant progress has been made in this area, particularly
+
+through planning-based approaches [34, 36, 40, 51]. While effective, these methods typically rely on prior knowledge of object properties, such as mass, friction coefficients, or even complete CAD models, which limits their practicality in real-world applications. Recently, learning-based methods [54] have emerged as a promising alternative, improving generalization across diverse unseen objects. In this paradigm, policies are trained in simulation and then deployed zero-shot in the real world. For instance, HACMan [56] leverages vision-based reinforcement learning (RL) on object surface point clouds to determine contact locations and motion directions for executing action primitives. Similarly, CORN [8] employs a teacher-student distillation framework, where a teacher policy is first trained using RL with privileged state knowledge and then distilled into a vision-based student policy.
+
+However, these methods face two key limitations that hinder robust real-world deployment. First, as noted by [10], they rely heavily on multi-view cameras for accurate object geometry and on precise pose tracking modules for state estimation. In practical settings, nevertheless, multi-view setups may be unavailable, and tracking modules are often imperfect, leading to unreliable state information. Second, these approaches struggle to generalize across diverse physical conditions, such as variations in object mass and table friction, as their models primarily focus on geometry while overlooking the underlying dynamics.
+
+In contrast, we argue that a generalizable non-prehensile manipulation policy in a realistic robotic setting should not only accommodate diverse object geometries but also adapt to varying physical properties, all while relying solely on a single-camera setup without the need for additional tracking modules.
+
+To achieve this objective, we first experiment with the popular teacher-student policy distillation framework under this challenging setting. Our experiments reveal that while the RL teacher policy, when given oracle information, achieves high performance across diverse dynamic conditions, the distilled student policy, relying on partial observations, suffers from a significant performance drop. We then identify three key factors contributing to this issue. First, severe partial observability from single-view setting harms action learning by omitting critical geometric cues. Second, the Markovian student model inherently learns only an averaged behavior across diverse physical variations, resulting in suboptimal performance. Third, conventional distillation methods supervise only latent features and final actions, which is insufficient to capture the underlying dynamics necessary for effectively learning contact-rich action.
+
+To address the first two issues, we introduce a Dynamics Adaptation Module, inspired by RMA [20], which encodes historical observation-action pairs to model dynamic properties, incorporating both sufficient geometric and physical
+
+knowledge. For the third issue, we extend conventional action learning by enforcing the joint prediction of actions and their corresponding future states. This reformulation transforms the conventional action model into a world action model, introducing additional supervisory signals beyond those provided by the teacher. This synergistic learning paradigm improves imitation loss optimization and significantly enhances overall success rates. Finally, to guide the world action model with the dynamics embedding adequately, we bridge the two parts using Feature-wise Linear Modulation (FiLM) conditioning. In short, we propose a novel policy learning framework that jointly predicting future states while adapting dynamics from historical trajectories. We term our approach DyWA (Dynamics-Adaptive World Action Model).
+
+We conduct extensive experiments in both simulation and the real world to evaluate the effectiveness and generalization of our policy, comparing it against baseline methods. To address the lack of a unified benchmark for non-prehensile manipulation, we build a comprehensive benchmark based on CORN, varying camera views (one or three) and the presence of a ground-truth pose tracker. Our method demonstrates the superiority of its model design across different settings, with a $31.5\%$ improvement in success rate than baselines. Furthermore, comprehensive ablation studies validate the synergistic benefits of dynamics adaptation and world modeling when jointly learning actions. Finally, real-world experiments show that DyWA generalizes across object geometries at a $68\%$ success rate and adapts to physical variations like table friction. It also achieves robustness in handling non-uniform mass distributions (e.g., half-filled water bottles) and slippery objects. Additionally, we showcase its applications combined with VLM, which assists human or grasping models with thin or wide objects.
+
+In summary, this work makes the following contributions:
+
+- We propose DyWA, a novel policy learning approach by jointly predicting future states, with adaptation of dynamics modeling from historical trajectories.
+- We improve generalizable non-prehensile manipulation, reducing dependence on multi-camera setups and pose tracking modules while ensuring robustness across varying physical conditions.
+- We provide a comprehensive simulation benchmark for generalizable non-prehensile manipulation. Our approach surpasses all baseline methods, and we showcase its effectiveness through several real-world applications.
+
+# 2. Related Works
+
+# 2.1. Non-prehensile Manipulation
+
+Non-prehensile manipulation refers to the process of manipulating objects without grasping them [33]. This form of
+
+
+Figure 2. Our World Action Model processes the embeddings of the current observation (partial point cloud, end-effector pose, and joint state) and the goal point cloud (transformed from the initial partial observation) to predict the robot action and next state. Additionally, an adaptation module encodes historical observations and actions, decoding them into the dynamics embedding that conditions the model via FiLM. A pre-trained RL teacher policy (right) supervises both the action and adaptation embedding using privileged full point cloud and physics parameter embeddings.
+
+manipulation involves complex contact interactions among the robot, the object, and the environment, posing significant challenges for state estimation, planning, and control [6, 16, 35, 52]. A line of prior work has employed planning-based approaches, either by relaxing contact mode decision variables [34] or by introducing complementarity constraints to manage contact mode transitions [36, 40, 51]. However, these planners typically assume prior knowledge of object properties, such as mass, friction coefficients, or even complete CAD models, which limits their practical applicability.
+
+In contrast, learning-based methods [54] offer a promising alternative by enabling generalization without relying on known physical parameters. Nonetheless, most existing works are constrained either by the complexity of the manipulation skills—such as being limited to 2D planar pushing [9, 10, 39, 49, 53]—or by limited generalization across diverse object types [19, 23, 55]. Recent advances employing point cloud observations, such as HACMan and its variants [18, 21, 56], as well as CORN [8], have demonstrated the feasibility of 6D object rearrangement, capturing more complex object interactions while generalizing to a wide range of unseen geometries. However, as highlighted by [10], these methods rely on multi-view cameras and object state estimation through accurate pose tracking modules. In contrast, our method achieves accurate end-to-end 6D nonprehensile manipulation with generalization across diverse object geometry, varying physics condition using only one single-view camera in the real world.
+
+# 2.2. World Models
+
+World models [13] learn compact representations of the environment and predict future states conditioned on action sequences. They have been widely studied in domains
+
+such as gaming [12, 14, 15, 44] and autonomous driving [4, 17, 47].
+
+In robotic manipulation, jointly modeling future observations and actions has shown strong empirical performance [3, 11, 48, 50, 57]. We adopt the term world action model to characterize this class of policy learning methods with world model attribute, distinguishing it from prior work such as JOWA [5].
+
+# 3. Method
+
+# 3.1. Task Formulation
+
+Following HACMan and CORN, we focus on the task of 6D object rearrangement via non-prehensile manipulation. The robot's objective is to execute a sequence of non-prehensile actions (i.e., pushing, flipping) to move an object on the table to a target 6D pose. We define the goal pose $\mathbf{G}$ as a 6DoF transformation relative to the object's initial pose, assuming both are stable on the table. The task state $S_{t}$ at timestep $t$ is represented by the relative transformation between the object's current pose and the goal pose. Observations include the partial point cloud $P_{t}$ , joint states $J_{t}$ , and end-effector pose $E_{t}$ .
+
+# 3.2. Pipeline Overview
+
+Our training pipeline follows a standard teacher-student distillation framework. Due to the difficulty of obtaining high-quality demonstrations for our task, we first train a state-based RL policy with additional privileged information—i.e., the full object point cloud, task state, and physical parameters—as the teacher policy. For consistency, we adopt the same reward design as CORN, as elaborated in the supplementary material. To obtain a vision-based policy suitable for real-world deployment, we introduce our
+
+Dynamics-adaptive World Action Model, which serves as the student policy distilled from the teacher policy. Unlike the teacher, our student model relies solely on limited observations that are feasible to obtain in real-world settings.
+
+In the following sections, we detail the design of the world action model (Sec. 3.3) and the dynamics adaptation mechanism (Sec. 3.4). To enable adaptive force interaction in this contact-rich manipulation, we further incorporate a variable impedance controller (Sec. 3.5). Once trained (Sec. 3.6), our model can be transferred from simulation to the real world in a zero-shot manner, without requiring real-world fine-tuning.
+
+# 3.3. World Action Model
+
+Definition. A world action model refers to a policy model that jointly predicts actions and forecasts the corresponding future states. Although the current action is not provided as an explicit input, the model exhibits world model characteristics by implicitly conditioning on the current policy action prediction.
+
+Observation and Goal Encoding. Our model takes observation and goal description as input, encoding different modalities using individual encoders. For the partial point cloud observation, we process it using a simplified PointNet++ [41] to obtain $\mathbf{f}_t^P$ . The architectural details are provided in the supplementary material. For robot proprioception, we separately encode joint positions and velocities $(\mathbf{f}_t^J)$ and the end-effector pose $(\mathbf{f}_t^E)$ using shallow MLPs. For the Goal Description, instead of relying on the unknown task state $S_{t}$ , we construct a visual goal representation by transforming the initial point cloud $P_0$ to the goal pose, yielding $P_G = \mathbf{G}P_0$ . This goal point cloud is then encoded using the shared network with the observation point cloud encoder.
+
+State-based World Modeling. We enforce the end-to-end model that jointly makes action decisions and predicts their outcomes, creating a synergistic learning process that, in turn, improves action learning. Specifically, the observation and goal embeddings are processed through MLPs to produce both the action $\mathbf{A}_t$ and the next task state $S_{t + 1}$ , with supervision signals separately derived from the teacher policy and simulation outcomes. Our object-centric world model represents the environment using task state $S_{t + 1}$ instead of high-dimensional visual signals, enabling the policy to focus on task-relevant dynamics. To represent rotations, we adopt the 9D representation [22, 25], and define the world model loss as:
+
+$$
+\mathcal {L} _ {\mathrm {w o r l d}} = \left\| \mathbf {T} _ {t + 1} - \hat {\mathbf {T}} _ {t + 1} \right\| _ {2} ^ {2} + \left\| \mathbf {R} _ {t + 1} - \hat {\mathbf {R}} _ {t + 1} \right\| _ {1} \quad (1)
+$$
+
+where $\mathbf{T}_{t + 1}\in \mathbb{R}^3$ and $\mathbf{R}_{t + 1}\in SO(3)$ are the predicted translation and rotation, while $\hat{\mathbf{T}}_{t + 1}\in \mathbb{R}^3$ and
+
+$\hat{\mathbf{R}}_{t + 1}\in SO(3)$ denote the ground-truth transformation obtained from simulation outcomes after action execution. Additionally, we employ an imitation loss, defined as the L2 loss between the predicted action and the teacher action:
+
+$$
+\mathcal {L} _ {\text {i m i t a t i o n}} = \left\| \mathbf {A} _ {t} ^ {s} - \mathbf {A} _ {t} ^ {t} \right\| ^ {2} \tag {2}
+$$
+
+# 3.4. Dynamics Adaptation
+
+To enhance the world model's ability to adapt to diverse dynamics, we extract abstract representations of environmental variations from historical trajectories. Our approach distills teacher knowledge regarding full point cloud and physical parameter into an adaptation embedding, which is subsequently decoded into the dynamics embedding. This embedding then conditions the world action model through a learnable feature-wise linear modulation mechanism.
+
+Adaptation Embedding. We design an adaptation module that processes sequential observation-action pairs to compensate for missing geometry and physics knowledge in the current partial observation. Specifically, at each timestep, we concatenate the observation embeddings $f_{t}^{O} = \{f_{t}^{P}, f_{t}^{J}, f_{t}^{E}\}$ with the previous action embedding $f_{t-1}^{A}$ , where the action embedding is obtained via a shallow MLP. We construct an input sequence of $L$ past observation-action tuples which is then processed by a 1D CNN-based adaptation module, for extracting a compact adaptation embedding:
+
+$$
+\mathbf {z} _ {t} = \operatorname {E m b e d} \left(\left[ \operatorname {c o n c a t} \left(\mathbf {f} _ {t - i - 1} ^ {O}, \mathbf {f} _ {t - i - 2} ^ {A}\right) \right] _ {i = 1} ^ {L}\right) \tag {3}
+$$
+
+To ensure meaningful representation learning, we supervise the adaptation embedding using the concatenation of the full point cloud embedding and physics embedding from the teacher encoder.
+
+$$
+\mathcal {L} _ {\mathrm {a d a p t}} = \left\| \mathbf {z} _ {t} ^ {\text {G e o , P h y}} - \operatorname {c o n c a t} \left(\mathbf {f} _ {t} ^ {\text {G e o}}, \mathbf {f} _ {t} ^ {\text {P h y}}\right) \right\| ^ {2} \tag {4}
+$$
+
+Dynamics Conditioning. Once the adaptation embedding is obtained, we decode it into the dynamics embedding, which serves as a conditioning input for the world action model via Feature-wise Linear Modulation (FiLM). FiLM [38] dynamically modulates the intermediate feature representations of the world action model by applying learned scaling and shifting transformations, allowing the model to adapt to varying dynamics. Each FiLM block consists of two shallow MLPs which take the dynamics embedding as input and output the modulation parameters $\gamma$ and $\beta$ for each latent feature $f$ :
+
+$$
+\operatorname {F i L M} (f | \gamma , \beta) = \gamma f + \beta \tag {5}
+$$
+
+We integrate FiLM blocks densely in the early layers of the world action model while leaving the final layers uncondi
+
+tioned. The technique that has proven highly effective in integrating language guidance into vision encoders [1, 7]. In our case, this mechanism allows the dynamics embedding to selectively influence feature representations, enabling adaptive adjustments to the model's behavior based on the underlying dynamics.
+
+# 3.5. Action Space with Variable Impedance
+
+To enable adaptive force interaction between the robot and object, we employ variable impedance control [8] as the low-level action execution mechanism. This allows the robot to dynamically regulate the interaction force based on task demands. Specifically, the action space of our policy consists of the subgoal residual of the end effector, $\Delta T_{ee} \in SE(3)$ , along with joint-space impedance parameters. The joint-space impedance is parameterized by positional gains $(P \in \mathbb{R}^7)$ and damping factors $(\rho \in \mathbb{R}^7)$ , where the velocity gains are computed as $D = \rho \sqrt{P}$ . To execute the commanded end-effector motion, we first solve for the desired joint position using inverse kinematics with the damped least squares method [2]:
+
+$$
+q _ {d} = q _ {t} + I K (\Delta T _ {e e}) \tag {6}
+$$
+
+Then, the desired joint position $q_{d}$ and impedance parameters $K, D$ are applied to a joint-space impedance controller to generate impedance-aware control commands for the robot. We utilize the widely adopted Polymetis API [24] for implementation.
+
+# 3.6. Training Protocol
+
+The overall learning objective is formulated as the sum of the imitation loss, world model loss, and adaptation loss:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {i m i t a t i o n}} + \mathcal {L} _ {\text {w o r l d}} + \mathcal {L} _ {\text {a d a p t}} \tag {7}
+$$
+
+We begin by training the teacher policy for 200K iterations in simulation using PPO. Subsequently, we employ DAgger [43] to train the student policy under teacher supervision for 500K iterations. To enhance robustness and generalization, we introduce domain randomization during training by varying the object's mass, scale, and friction, as well as the restitution properties of the object, table, and robot gripper. The object scale is adjusted such that its largest diameter remains within a predefined range. To further improve sim-to-real transfer, we inject small perturbations into the torque commands, object point cloud, and goal pose when training the student policy.
+
+# 4. Experiments
+
+# 4.1. Benchmarking Tabletop Non-prehensile Rearrangement in Simulation
+
+We evaluate our method alongside several baselines within a unified simulation environment to enable a fair comparison of their performance. Although prior works [8, 56] have
+
+
+Figure 3. Loss curves during the distillation process. We adopt DAgger which starts with teacher action for execution and gradually adds the weights of student action so that the initial loss declines rapidly. Left: Comparison of imitation loss between using only Dynamics Adaptation and incorporating the World Model. Right: Comparison of World Model loss between using only the World Model and integrating Dynamics Adaptation.
+
+
+
+developed their own simulation environments for training and validating non-prehensile manipulation policies, there remains a lack of a standardized benchmark for evaluating both existing and future approaches. To bridge this gap, we establish a comprehensive benchmark based on the CORN setting. Specifically, we adopt the IsaacGym simulation environment and utilize 323-object asset from DexGraspNet [46] for training. Additionally, we enrich the task setting by introducing an unseen object test set, consisting of 10 geometrically diverse objects, each scaled to five different sizes, resulting in a total of 50 evaluation objects. Furthermore, we introduce two additional perception dimensions: (i) single-view vs. multi-view (three-camera) observations and (ii) whether known object poses for constructing the task state $S_{t}$ . Both the training and testing environments are fully randomized w.r.t. dynamics properties including mass, friction, and restitution.
+
+Task Setup. At the beginning of each episode, we randomly place the object in a stable pose on the table. The robot arm is then initialized at a joint configuration uniformly sampled within predefined joint bounds, positioned slightly above the workspace to prevent unintended collisions with the table or object. Next, we sample a random 6D stable goal pose on the table, ensuring it is at least $0.1\mathrm{m}$ away from the initial pose to prevent immediate success upon initialization. To guarantee valid initial and goal poses for each object, we precompute a set of stable poses, as detailed in the supplementary. An episode is considered successful if the object's final pose is within $0.05\mathrm{m}$ and 0.1 radians of the target pose.
+
+Baselines. We evaluate our approach against two state-of-the-art baselines: HACMan and CORN, which represent primitive-based and closed-loop methods, respectively. Since HACMan was originally implemented in the MuJoCo simulator, we re-implemented it within our benchmark for
+
+| Methods | Action Type | Known State (3 view) | Unknown State (3 view) | Unknown State (1 view) |
| Seen | Unseen | Seen | Unseen | Seen | Unseen |
| HACMan [56] | Primitive | 3.8(42.2) | 5.7(39.4) | 3.0(23.6) | 4.1(26.5) | 1.5(17.9) | 2.9(18.3) |
| CORN [8] | Closed-loop | 86.8 | 79.9 | 46.0 | 47.8 | 29.0 | 29.8 |
| CORN (PN++) | Closed-loop | 87.3 | 84.3 | 76.1 | 75.7 | 50.7 | 49.4 |
| Ours | Closed-loop | 87.9 | 85.0 | 85.8 | 82.3 | 82.2 | 75.0 |
+
+Table 1. Quantitative results measured by success rate in the simulation benchmark. For HACMan, we also reports its performance given 3 DoF planar goal(i.e. $[\Delta x, \Delta y, \Delta \theta]$ ) in parentheses. Note that the third track with unknown state and single view camera is the most realistic and challenging track for fully comparison of each methods.
+
+| Methods | W.M. | D.A. | FiLM | Seen | Unseen |
| DAgger [43] | X | X | X | 59.9 | 57.5 |
| World Model | ✓ | X | X | 61.6 | 59.4 |
| RMA [20] | X | ✓ | X | 65.6 | 57.9 |
| Ours w/o W.M. | X | ✓ | ✓ | 70.0 | 63.7 |
| Ours w/o FiLM | ✓ | ✓ | X | 73.3 | 59.4 |
| Ours | ✓ | ✓ | ✓ | 82.2 | 75.0 |
+
+Table 2. Ablation study on the most challenging evaluation track, i.e., unknown state with single-view observation. W.M. means World Model and D.A. means Dynamics Adaptation.
+
+a fair comparison. However, because it requires strict perpoint correspondence as input, its success rate is extremely low in the unknown state setting. CORN shares the same simulation environment as our method, allowing us to train and evaluate it directly with minimal modifications. To ensure a fair comparison, we further enhanced CORN by replacing its shallow MLP-based point cloud encoder with the same vision backbone as ours. Additionally, for settings where the current object pose is unknown, we provided all methods with the same goal point cloud representation to maintain consistency.
+
+Results. As shown in Table 1, our method consistently outperforms all baselines across all three evaluation tracks. In particular, we achieve a significant performance gain over previous approaches, with at least a $31.5\%$ improvement in success rate. Notably, the performance gap is most pronounced in challenging scenarios involving unknown states and single-view observations, where our method's dynamics modeling capability plays a crucial role. Compared to HACMan, our approach benefits from its closed-loop execution and variable impedance control, enabling more robust dexterous manipulation. While HACMan relies on predefined motion primitives, its adaptability to complex geometries and variations in physics are limited. Moreover, our method surpasses CORN due to our adaptation mechanism refines the world model based on historical trajectories, allowing the policy to adjust effectively to variations in
+
+object properties such as mass, friction, and scale. These results highlight the effectiveness of our strong generalization capabilities in diverse rearrangement tasks.
+
+# 4.2. Ablation Study
+
+We conduct ablation studies on the most challenging evaluation track, i.e., unknown state with single-view observation. Our goal is to systematically analyze the contribution of each key module to the overall performance.
+
+Synergy between Next State Prediction and Action Learning. To analyze the optimization process, we visualize the loss curve during training and compare the approach that uses only dynamics adaptation (i.e., RMA) with that adding World Modeling. Our results show that during the distillation, simultaneous learning of the next state improves action loss convergence, confirming the synergy between world modeling and action learning. Additionally, we discuss the integration of the world model in the RL teacher policy, which is elaborated in the supplementary material.
+
+On the Complementarity of Dynamics Adaptation and World Modeling. We investigate the individual and combined effects of dynamics adaptation and world modeling. Our results (Table 2) show that using only the world model or dynamics adaptation, i.e. RMA, provides only marginal improvements over the naive DAgger baseline, with success rates increasing by just $1.7\%$ and $5.7\%$ , respectively. However, when both modules are used together, the performance jumps significantly from $59.9\%$ to $73.3\%$ . This improvement can be attributed to the complementary nature of these components. Without dynamics adaptation, the world model lacks sufficient information to reason about the dynamic effects of interaction. Conversely, using only dynamics adaptation also provides limited benefits due to the absence of a sufficiently structured learning target. These findings highlight the complementarity of world modeling and dynamics adaptation, demonstrating that their combination is a non-trivial yet highly effective design choice.
+
+| Methods | Normal | Slippery YCB-Bottle | Non-uniform Mass | Avg. |
| Mug | Bulldozer | Card | Book | Dinosaur | Chips Can | Switch | Half-full Bottle | Coffee jar |
| CORN w tracking | 1/5 | 3/5 | 4/5 | 4/5 | 2/5 | 0/5 | 2/5 | 0/5 | 0/5 | 2/5 | 18/50 (36%) |
| Ours | 3/5 | 4/5 | 4/5 | 4/5 | 3/5 | 2/5 | 4/5 | 3/5 | 4/5 | 3/5 | 34/50 (68%) |
+
+Table 3. Quantitative results in the real world. Each cell shows the number of successful trials out of 5 attempts. Our method consistently achieves high success rates across diverse objects.
+
+| Methods | μ1 | μ2 | μ3 | μ4 |
| S.R. ↑ | Avg. Time ↓ | S.R. ↑ | Avg. Time ↓ | S.R. ↑ | Avg. Time ↓ | S.R. ↑ | Avg. Time ↓ |
| Ours w/o D.A. | 3/5 | 65 s | 3/5 | 81 s | 4/5 | 96 s | 3/5 | 124 s |
| Ours | 4/5 | 45 s | 4/5 | 50 s | 4/5 | 49 s | 4/5 | 51 s |
+
+Table 4. Experiments on different surface friction, with progressive friction levels, ${\mu }_{1} < {\mu }_{2} < {\mu }_{3} < {\mu }_{4}$ .
+
+Effectiveness of FiLM Conditioning. We further evaluate the role of Feature-wise Linear Modulation (FiLM) in bridging adaptation embeddings and the world action model. Our results indicate that FiLM provides a more effective and structured conditioning mechanism than direct input concatenation. Specifically, incorporating FiLM into RMA boosts performance from $65.6\%$ to $70.0\%$ . More notably, when all three modules (world modeling, dynamics adaptation, and FiLM) are used together, the success rate reaches $82.2\%$ , with FiLM contributing an additional $8.9\%$ improvement. We also discuss different methods for conditioning in the supplementary whose conclusion consists with our claims. This reinforces FiLM as a lightweight and effective choice for integrating adaptation embeddings.
+
+# 4.3. Real-World Experiments
+
+To evaluate the real-world applicability of our method, we conduct experiments on a physical robot setup. Our goal is to validate the zero-shot transferability of our policy from simulation to the real world and compare its performance against prior methods.
+
+Real-World Setup Our experimental setup is illustrated in the supplementary. We use a Franka robot arm for action execution and a RealSense D435 camera positioned at a side view to capture RGB-D images. We evaluate our approach on 10 unseen real-world objects, including both slippery objects and those with non-uniform mass distribution such as a half-filled bottle. Before each episode, we first place the object at the target goal pose and record its point cloud. Then, we reposition the object in a random stable pose and allow our policy to execute the manipulation task. Upon completion, we use Iterative Closest Point (ICP) to measure the pose error between the final object position and the recorded target pose. For symmetric objects where direct ICP alignment is ambiguous, we relax the success criteria along the symmetric axes and compute errors only in translation and relevant rotational components.
+
+Generalization across Diverse Objects. We evaluate our model's generalization ability by comparing it with CORN, which relies on an external tracking module for object pose estimation in real-world experiments. As shown in Figure 4 and Table 3, our method achieves accurate manipulation across diverse objects without external pose tracking, significantly outperforming CORN with an average success rate of $68\%$ versus $36\%$ . CORN struggles with precise execution due to occlusions in single-view partial point clouds and inaccuracies in real-world pose estimation. Additionally, our model demonstrates robust performance on slippery objects and those with non-uniform mass, where CORN fails. We validate the generalization ability of our model and compare our method against CORN, which depends on an external tracking module to estimate object poses in real-world experiments.
+
+Robustness to Surface Friction Variations. To assess the effectiveness of dynamics adaptation, we conduct experiments on surfaces with varying friction coefficients. We select four tablecloths (Figure 1) with progressive friction levels, i.e. $\mu_1, \mu_2, \mu_3, \mu_4$ and use the bulldozer toy as the test object. Additionally, we report the average execution time for successful episodes. As shown in Table 4, the model without dynamics adaptation exhibits significant performance degradation when interacting with surfaces of different friction levels, leading to erratic execution times. In contrast, our policy with dynamics adaptation maintains consistent success rates while ensuring stable execution times across all surface conditions. This highlights the robustness of our approach in handling diverse real-world contact dynamics.
+
+# 4.4. Applications
+
+We present a practical manipulation system that integrates Vision-Language Models (VLMs), our non-prehensile policy, and a grasping model [45]. By leveraging VLMs, our goal-conditioned policy can be executed based on natural
+
+
+Figure 4. Qualitative Results in the real world. The goal pose is shown transparently.
+
+
+Figure 5. By integrating with Vision-Language Models (VLMs), our goal-conditioned policy can be executed based on natural language instructions.
+
+
+Figure 6. Our policy helps grasping a thin card and broad cracker box.
+
+language instructions. Specifically, we utilize SoFar [42], a model capable of generating semantic object poses from language commands, to specify goals for our policy. As shown in Figure 5, given the command "Put the grip of the electric drill into a person's hand", SoFar generates the target transformation of the drill (e.g., rotation $\Delta \theta = 122^{\circ}$ and translation $\Delta x, \Delta y = [0.54, 0.09]$ ), which is then used as the goal for our policy. This enables natural, instruction-driven object handovers, highlighting the potential of our approach in human-robot interaction.
+
+Additionally, we showcase the system outperforms or complements traditional prehensile manipulation. As illustrated in the third row of Figure 4, a standard pick-and-place strategy struggles to flip a tiny switch due to gripper-table
+
+collisions, whereas our policy enables efficient rearrangement in a single continuous motion. Furthermore, our policy serves as an effective pre-grasping step in the system. As shown in Figure 6, certain objects are inherently difficult to grasp due to their geometry—for example, a thin card lying flat on a surface or a broad cracker box exceeding the gripper's maximum span. Our system can firstly reorient these objects into grasp-friendly configurations, significantly improving grasp success rate.
+
+# 5. Conclusion, Limitations, and Future Works
+
+In this work, we present a novel policy learning approach that jointly predicts future states while adapting dynamics from historical trajectories. Our model enhances generalizable non-prehensile manipulation by reducing reliance on multi-camera setups and pose tracking modules while maintaining robustness across diverse physical conditions. Extensive simulation and real-world experiments validate the effectiveness of our approach. However, our method also has certain limitations since it relies solely on point clouds as the visual input modality. It struggles with symmetric objects due to geometric ambiguity, and faces challenges with transparent and specular objects, where raw depth is incomplete. A promising direction is to incorporate additional appearance information [26-32] to provide richer visual cues.
+
+# Acknowledgements
+
+We thank Yixin Zheng for organizing the code release, and Junhao Yang for assistance with rendering. We also appreciate the valuable suggestions and discussions from Jiayi Chen, Jiazhao Zhang, Mi Yan and Shenyuan Gao. This work was supported in part by National Science and Technology Major Project (2022ZD0114904) & NSFC-6247070125.
+
+# References
+
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+# DynFaceRestore: Balancing Fidelity and Quality in Diffusion-Guided Blind Face Restoration with Dynamic Blur-Level Mapping and Guidance
+
+Huu-Phu Do $^{1*}$ , Yu-Wei Chen $^{1*}$ , Yi-Cheng Liao $^{1}$ , Chi-Wei Hsiao $^{2}$ , Han-Yang Wang $^{2}$ , Wei-Chen Chiu $^{1}$ , Ching-Chun Huang $^{1\dagger}$
+
+$^{1}$ National Yang Ming Chiao Tung University, Taiwan $^{2}$ MediaTek Inc., Taiwan
+
+# Abstract
+
+Blind Face Restoration aims to recover high-fidelity, detail-rich facial images from unknown degraded inputs, presenting significant challenges in preserving both identity and detail. Pre-trained diffusion models have been increasingly used as image priors to generate fine details. Still, existing methods often use fixed diffusion sampling timesteps and a global guidance scale, assuming uniform degradation. This limitation and potentially imperfect degradation kernel estimation frequently lead to under- or over-diffusion, resulting in an imbalance between fidelity and quality. We propose DynFaceRestore, a novel blind face restoration approach that learns to map any blindly degraded input to Gaussian blurry images. By leveraging these blurry images and their respective Gaussian kernels, we dynamically select the starting timesteps for each blurry image and apply closed-form guidance during the diffusion sampling process to maintain fidelity. Additionally, we introduce a dynamic guidance scaling adjuster that modulates the guidance strength across local regions, enhancing detail generation in complex areas while preserving structural fidelity in contours. This strategy effectively balances the trade-off between fidelity and quality. DynFaceRestore achieves state-of-the-art performance in both quantitative and qualitative evaluations, demonstrating robustness and effectiveness in blind face restoration.
+
+# 1. Introduction
+
+Blind face restoration (BFR) involves recovering high-fidelity, detail-rich facial images from degraded inputs with unknown kernels [24, 33]. The main difficulty lies in enhancing facial details while preserving the individual's identity, as shown in Fig. 1. Although GAN-based approaches [1, 22, 39] are effective at adding fine details, they
+
+
+Figure 1. Blind face restoration demands both high fidelity and rich detail. Compared to other SOTA methods that leverage GAN priors, codebook priors, or diffusion priors, our proposed method, DynFaceRestore (denoted as an asterisk), demonstrates superior image fidelity (PSNR↑) and quality (FID↓) on the CelebA-Test.
+
+often introduce artifacts. Recently, diffusion models (DM) [13] have demonstrated great generative capabilities to create more realistic details. However, DMs can still compromise fidelity in the restored faces.
+
+Previous approaches [10, 37, 40] have effectively demonstrated the use of pre-trained diffusion models (DM) with high-quality (HQ) image priors to generate realistic facial details. Typically, [37, 40] apply DM for fine detail enhancement after mitigating degradation and recovering the structural information of low-quality (LQ) images using a restoration model. Meanwhile, [5, 10] aims to maintain image structures by guiding the DM through the measurement model. Despite these advancements, these methods still face challenges in maintaining fidelity. Below, we outline possible reasons for this limitation.
+
+First, these methods assume that all LQ inputs exhibit uniform degradation severity and thus use a fixed starting timestep for diffusion sampling in image restoration. This approach often results in under- or over-diffusion when the DM adds details, as illustrated in Fig. 2. Sec
+
+
+Figure 2. Using Difface [40] as an example, let $RM$ represent Difface's restoration model and $p\Theta$ the diffusion model. In the t-SNE plot, green and red points denote the features of $x_{400}^{0}$ sampled from $p\Theta(x_{400}^{0}|\hat{y})$ and $p\Theta(x_{400}^{0}|x_{0})$ , respectively. Here, $\hat{y}$ , the LQ image restored by $RM$ , is used for diffusion guidance. Difface initiates the diffusion process at a fixed $t = 400$ , resulting in under-diffusion (right) for severely degraded LQ images and just enough diffusion for mildly degraded LQ images (left). This underscores the importance of selecting an appropriate starting step.
+
+ond, in blind settings, imperfect kernel estimation and arbitrary kernel forms frequently cause kernel mismatch issues, which misguide the diffusion sampling process. Third, high-frequency regions like hair and wrinkles benefit from stronger DM influence to enhance perceptual quality. In contrast, low-frequency regions, like facial contours, require greater guidance from the observed image to preserve fidelity. However, existing methods [5, 10, 37] that incorporate guidance into DM generally apply a uniform scale factor across all pixels, overlooking region-specific variations. This lack of localized adjustment can lead to suboptimal perceptual quality or fidelity loss, hindering the balance between detail enhancement and structural integrity.
+
+In this paper, we introduce DynFaceRestore, which leverages a pre-trained diffusion model to enhance fine details while preserving fidelity through multiple Dynamic Blur-Level Mapping and Guidance. First, we design a discriminative restoration network that maps a blindly degraded input image into multiple Gaussian-blurred versions with estimated blur levels, effectively transforming unknown, variable degradation into a Gaussian form. Since perfect kernel estimation is often impractical, using multiple Gaussian-blurred images as multi-guidance for DM sampling helps address kernel mismatch issues. Second, the estimated blur level determines a dynamic starting timestep for each Gaussian-blurred image, ensuring optimal guidance insertion during diffusion and effectively addressing under- and over-diffusion challenges. Third, to enable
+
+localized adjustment, we implement DPS-based guidance [4, 5] and introduce a novel dynamic guidance scale adjuster that adapts the guidance scale region-wise, resulting in high-fidelity, detail-rich outputs, as illustrated in Fig. 1. Our main contributions are summarized as follows:
+
+- We introduce Dynamic Blur-Level Mapping and Guidance to address kernel mismatch issues effectively, using multi-level Gaussian-blurred images as guidance.
+- Leveraging the estimated blur level from the restoration network output, we dynamically determine the optimal starting step in the diffusion process to prevent under- and over-diffusion.
+- We construct a dynamic guidance scale adjuster to tailor the guidance strength across regions, harnessing the powerful influence of DM to improve perceptual quality while maintaining fidelity.
+- Our proposed method, DynFaceRestore, outperforms state-of-the-art approaches in both quantitative and qualitative evaluations, demonstrating its superiority in Blind Face Restoration.
+
+# 2. Related Works
+
+# 2.1. Blind Face Restoration (BFR) with Priors
+
+Previous BFR methods have utilized various priors to enhance restoration accuracy. Geometric prior methods [1, 2, 30] rely on structural data, such as landmarks and parsing maps, but often struggle when degraded inputs lack structural details. Reference prior methods [11, 32, 35, 42] use high-quality (HQ) reference images or codebooks. For example, VQ-GAN [9] provides detailed facial features; however, its fixed codebook size can limit the diversity and richness of restored faces. GAN-based approaches, such as PSFRGAN [1], incorporate facial parsing maps for style control, while models like GFP-GAN [22] and GPEN [39] focus on restoring facial fidelity by embedding pre-trained face models [18, 19]. Although GAN-based methods enhance face restoration quality, they often introduce artifacts.
+
+Recently, diffusion-based approaches for BFR have achieved SOTA performance by either training a DM from scratch [3, 27-29, 31] or guiding a pre-trained DM [26, 36, 37, 40] to provide priors. For example, WaveFace [28] employs a conditional DM to generate high-frequency components, while 3Diffusion [27] integrates 3D facial structure into the noise estimation process. However, these methods typically require extensive training resources.
+
+Other approaches leverage pre-trained diffusion models for restoration. DR2 [36] removes degradation using a pretrained DM and enhances resolution via a super-resolution module. DiffBIR [26] employs a restoration module to remove degradation and regenerates details using a conditional pre-trained DM with ControlNet. DifFace [40] maps a LQ input to an intermediate diffusion sampling step, then
+
+
+Figure 3. Overview of our proposed DynFaceRestore framework, which consists of three key components: DBLM, DSST, and DGSA (defined in Sec. 4). The upper and lower sections illustrate two independent restoration scenarios with inputs degraded to varying levels. DBLM generates multiple Gaussian-blurred images based on the degradation level of the unknown degraded input. Then, given these blur levels, DSST identifies the optimal starting step for each Gaussian-blurred image via a predefined lookup table, providing sampling guidance to avoid under- or over-diffusion. Lastly, the trained network, DGSA, locally adjusts the guidance scale used in the pre-trained diffusion process, enabling DynFaceRestore to achieve an optimal balance between fidelity and quality.
+
+applies the standard DM backward process for restoration without extra guidance. In contrast, PGDiff [37] adopts classifier guidance to constrain the denoising process.
+
+However, many of these DM-based methods overlook local degradation severity and rely on a fixed diffusion starting step, leading to suboptimal restoration. Recently, [26] addressed this issue by applying the Sobel operator on the LR image to set local guidance levels and introduce varying priors from DM. Yet, it struggles to capture intricate textures, as it focuses on local intensity without understanding global structures. In contrast, our proposed method provides "step-wise and region-specific guidance", effectively adapting to both local and global features to preserve complex textures, as further discussed in Sec. 4.3.
+
+# 2.2. Guidance on unconditional DM
+
+Methods such as DDRM [20], DDNM [34], BlindDPS [5], Fast-diffusion EM [23], and GDP [10] avoid the need for restoration training by leveraging a pre-trained diffusion model. These approaches modify the intermediate output at each diffusion step to align with the degraded input (LQ image) as guidance. The alignment relies on a degradation model, represented by either a fixed linear matrix [20, 34], a kernel-based DM [5], or a learnable degradation model [10]. However, these methods generally assume a simple or linear degradation process, creating a significant domain gap when applied to complex real-world degradations. Additionally, they overlook kernel mismatch issues during diffusion, where the estimated kernel often deviates from the true degradation.
+
+# 3. Preliminary and Framework Overview
+
+# 3.1. Diffusion Posterior Sampling (DPS)
+
+Consider the following observation model:
+
+$$
+y = \mathcal {A} (x) + n, \tag {1}
+$$
+
+where $y$ is the measurement degraded from its HQ image counterpart $x$ , $\mathcal{A}$ models the degradation process, and $n$ is Gaussian noise. Based on Bayes' rule, our goal is to sample or recover $x$ from the posterior distribution $p(x|y) \propto P(y|x)P(x)$ . Here, the likelihood $P(y|x)$ is defined according to Eq. (1). When using a pre-trained DM to model the HQ image prior, the diffusion sampling process with $y$ as guidance at timestep $t$ can be expressed as
+
+$$
+x _ {t - 1} = x _ {t - 1} ^ {\prime} - s \nabla_ {x _ {t}} \log p _ {t} (y | x _ {t}), \tag {2}
+$$
+
+where $s$ is the guidance scale, $x_{t - 1}^{\prime}$ is sampled from $p(x_{t - 1}|x_t)$ , and $p_t(y|x_t)$ is likelihood.
+
+Diffusion Posterior Sampling [4] builds upon a pretrained DM from the Denoising Diffusion Probabilistic Model (DDPM) [13] and approximates the gradient of the likelihood $\nabla_{x_t}\log p_t(y|x_t)$ as $\nabla_{x_t}\log p_t(y|\hat{x}_t^0)$ , where
+
+$$
+\hat {x} _ {t} ^ {0} = \frac {1}{\sqrt {\bar {\alpha} _ {t}}} \left(x _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {\theta}\right). \tag {3}
+$$
+
+Here, $\epsilon_{\theta}$ is a learnable network used to define a diffusion model and $\bar{\alpha}_{t}$ represents the pre-defined DDPM coefficients [13]. Based on Eq. (3) and using $\epsilon_{\theta}$ , we can estimate the HQ
+
+image $\hat{x}_t^0$ from the diffusion sample $x_{t}$ . Since $\hat{x}_t^0\cong x$ , we can utilize the observation model in Eq. (1) to replace the sample guidance in Eq. (2) as follows:
+
+$$
+\nabla_ {x _ {t}} \log p _ {t} (y | x _ {t}) \approx \nabla_ {x _ {t}} \| y - \mathcal {A} (x _ {t} ^ {0}) \| _ {2} ^ {2}. \tag {4}
+$$
+
+Note that $\mathcal{A}$ should be given in advance. If $\mathcal{A}$ is unknown or imperfectly estimated [5], an estimator or refiner for $\mathcal{A}$ is necessary. Below, we proposed modifications to DPS and the way to refine $\mathcal{A}$ during diffusion sampling.
+
+# 3.2. DynFaceRestore Sampling
+
+Rather than directly tackling the challenging BFR task, our DynFaceRestore method reframes it as a Gaussian deblurring problem by transforming the blindly degraded input image $y$ into a Gaussian-blurred version $\dot{y}$ and applying a modified DPS-based guidance for restoration. This allows us to represent $\mathcal{A}(x_t^0)$ as $k_{t} \otimes x_{t}^{0}$ , where $k$ is a Gaussian blur kernel with standard deviation std. Consequently, our guided diffusion sampling process can be reformulated as follows:
+
+$$
+x _ {t - 1} = x _ {t - 1} ^ {\prime} - s \nabla_ {x _ {t}} \| \acute {y} - k _ {t} \otimes x _ {t} ^ {0} \| _ {2} ^ {2}. \tag {5}
+$$
+
+where $x_{t-1}'$ sampled from $p(x_{t-1} | x_t)$ is defined as follows:
+
+$$
+x _ {t - 1} ^ {\prime} = \frac {1}{\sqrt {\alpha_ {t}}} \left(x _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta}\right) + \sigma_ {t} \epsilon , \epsilon \sim N (0, 1), \tag {6}
+$$
+
+which are derived from diffusion model. However, perfect kernel estimation is often impractical; to reduce kernel mismatch, we also refine the $\mathcal{A}$ during diffusion sampling. Since our $\mathcal{A}$ is strictly a Gaussian blur kernel, we only need to update the estimated std by using the following equation.
+
+$$
+\left. s t d _ {t - 1} = s t d _ {t} - s \nabla_ {s t d _ {t}} \| \acute {y} - k _ {t} \otimes x _ {t} ^ {0} \| _ {2} ^ {2}. \right. \tag {7}
+$$
+
+Additionally, as shown in Fig. 3, the DynFaceRestore framework enhances DPS in the following four key aspects.
+
+1. The DBLM (Sec. 4.1) first transforms a blindly degraded LQ input $y$ into the corresponding Gaussian-blurred version $\acute{y}$ , with blur levels adapted to the input's degradation level, enabling the representation of $\mathcal{A}(x_t^0)$ as $k_{t} \otimes x_{t}^{0}$ .
+2. Then, through DSST table (Sec. 4.2), the optimal starting timestep $t_{start}$ for diffusion is identified by using the estimated kernel (i.e., $\hat{std}^*$ in Sec. 4.1.1) as query. A right starting timestep would mitigate the effects of under- and over-diffusion. Next, $\acute{y}, \hat{std}^*$ , and $t_{start}$ are used to initialize our DPS-based sampling process.
+3. Instead of using a global scale $s$ , during the sampling process, the DGSA (Sec. 4.3) dynamic adjusts guidance scale region-wise, balancing the restoration result's quality and fidelity.
+4. Finally, we extend our framework to incorporate multiple guidance for the BFR task, as detailed in Sec. 4.4.
+
+To better understand our work, we also outline the inference steps in Algorithm 1 for the reference.
+
+# Algorithm 1 Inference
+
+Require: $y$ : Unknown degraded LQ input;
+
+Output: $x_0$ : HQ sampled image;
+
+1: $\dot{y},std^{*} = DBLM(y),SE(y)$
+2: compute Gaussian blur kernel $k$ using std*
+3: $t_{start} = DSST(s\hat{t}d^{*})$
+4: $x_{t_{start}} = \sqrt{\bar{\alpha}_{t_{start}}} \dot{y} + \sqrt{1 - \bar{\alpha}_{t_{start}}} \epsilon, \epsilon \sim N(0, 1)$ ;
+5: $std_{t_{start}} = std^{*}$
+6: for $t = t_{start} \cdots 1$ do
+
+7: $x_{t}^{0} = \frac{1}{\sqrt{\bar{\alpha_{t}}}} x_{t} - \sqrt{\frac{1 - \bar{\alpha_{t}}}{\bar{\alpha_{t}}}}\epsilon_{\theta};$
+8: $x_{t - 1}^{\prime} = \frac{1}{\sqrt{\alpha t}} (x_{t} - \frac{\beta_{t}}{\sqrt{1 - \alpha t}}\epsilon_{\theta}) + \sigma_{t}\epsilon ,\epsilon \sim N(0,1);$
+9: compute Gaussian blur kernel $k_{t}$ using $std_{t}$ ;
+10: $A_{t} = DGSA(\dot{y},x_{t}^{0},t)$
+11: $x_{t - 1} = x_{t - 1}^{\prime} - A_{t}\times \nabla_{x_{t}}\left\| \dot{y} -k_{t}\otimes x_{t}^{0}\right\|^{2};$
+12: $std_{t - 1} = std_t - \sqrt{\bar{\alpha}_t}\times \nabla_{k_t}\left\| \dot{y} -k_t\otimes x_t^0\right\| ^2;$
+13: end for
+14: return $x_0$
+
+# 4. Method
+
+# 4.1. Dynamic Blur-Level Mapping
+
+To leverage the reliable information (i.e., low-frequency components) of the degraded input and mitigate kernel mismatch issues during the diffusion process, we designed DBLM to first transform the degraded input $y$ into a Gaussian-blurred counterpart $\dot{y}$ , effectively converting blind kernel to a Gaussian form. Next, $\dot{y}$ serves as a restored version of $y$ , with maximally enhanced high-frequency details while preserving fidelity. Specifically, the DBLM function is defined as follows:
+
+$$
+\acute {y} = D B L M (y) = k _ {y} ^ {s t d ^ {*}} \otimes R M (y), \tag {8}
+$$
+
+where $RM$ represents any state-of-the-art discriminative image restoration model, with SwinIR [25] used in our implementation (details and other RMs' comparisons are defined in the Supplementary); $k_y^{std^*}$ , parameterized by $std^*$ , is the optimal Gaussian kernel related to the degradation level of $y$ , where kernel standard $std^*$ is determined by
+
+$$
+\begin{array}{l} \operatorname {s t d} ^ {*} \equiv \quad \arg \min \quad (\operatorname {s t d}), \\ \operatorname {s t d} \in [ \operatorname {s t d} _ {\text {m i n}}, \operatorname {s t d} _ {\text {m a x}} ] \tag {9} \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \text {s . t .} \quad \left\| k ^ {s t d} \otimes R M (y) - k ^ {s t d} \otimes x \right\| _ {1} < \xi . \end{array}
+$$
+
+In Eq. (9), $\xi$ denotes the chosen error tolerance, $x$ is the HQ ground truth, and $\otimes$ represents the convolution operation. Ideally, Eq. (9) suggests that $\tilde{x} \equiv k_y^{std^*} \otimes x$ is the amount of information recoverable from $y$ by DBLM (as per Eq. (8)) with fidelity. Moreover, since $\acute{y}$ the output of DBLM is explicitly degraded by the Gaussian kernel $k_y^{std^*}$ , utilizing $\acute{y}$ and $k_y^{std^*}$ as guidance within our diffusion-based restoration framework (Sec. 3.2) mitigates the impact of kernel mismatch issues caused by inaccurate kernel predic
+
+
+Figure 4. As $t$ increases, the diffused $x_{t}$ from HQ image $x_{0}$ and the diffused $\tilde{y}_{t}$ from the Gaussian-blurred image $\tilde{y}$ gradually approach and converge at $t_{s}$ . We leverage this property to form the basis for establishing DSST.
+
+tions. However, the estimation of $std^{*}$ merits further discussion during inference.
+
+# 4.1.1. Estimation of $std^{*}$
+
+During inference, the ground truth $x$ is unavailable, necessitating an alternative approach for estimating $std^*$ instead of using Eq. (9). To achieve this, we design a learnable network (SE) to generate an estimate $\hat{std^*}$ from the input $y$ . SE first produces an intermediate output $\hat{y}'$ that approximates $\tilde{x}$ , and then, based on $\hat{y}'$ derives $\hat{std^*}$ . In summary, $[\hat{std^*}, \hat{y}] = SE(y)$ . The training objective function for SE is defined as follows:
+
+$$
+L _ {S E} = \mathbb {D} \left(s t d ^ {*}, s t d ^ {*}\right) + \gamma_ {s t d} \mathbb {D} \left(\hat {y} ^ {\prime}, \tilde {x}\right), \tag {10}
+$$
+
+where $\mathbb{D}$ is the L1 distance and $\gamma_{std}$ is a weighting factor for balancing. Additionally, $std^*$ and $\tilde{x}$ are the training labels derived from Sec. 4.1. Note that $\hat{y}'$ , predicted by the SE, maps the unknown degraded input image $y$ to an intermediate blurred version, serving as an alternative to the Gaussian-blurred counterpart $\hat{y}$ from Eq. (8). However, $\hat{y}'$ does not perfectly conform to the assumed Gaussian form and is unsuitable as Gaussian-blurred guidance in the subsequent diffusion sampling process. Thus, in our final implementation, we use $\hat{y}$ instead of $\hat{y}'$ , estimating $\hat{y}$ via Eq. (8), with $std^*$ replaced by $std^*$ . Due to space constraints, a detailed analysis of the differences between $\hat{y}$ and $\hat{y}'$ , along with the design details of the SE, is provided in the Supplementary.
+
+# 4.2. Dynamic Starting Step Lookup Table
+
+Based on the estimated blur level, $\hat{std^{*}}$ , we develop a strategy to determine the starting timesteps for inserting guidance $\dot{y}$ into DM to prevent under- and over-diffusion. The idea is illustrated in Fig. 4. Assume $x_0 \equiv x$ represents
+
+an HQ image and $\tilde{y}_0^{std} = k^{std} \otimes x$ is its blurred counterpart. When both images undergo the same forward degradation process defined in a standard diffusion model, they will statistically converge after a specific timestep $t$ , meaning $x_t \cong \tilde{y}_t^{std}$ . The timestep $t$ then serves as a suitable insertion point for a blurry observation $\tilde{y}_0^{std}$ with blur level $std$ . To identify the optimal starting timestep $t_{std}$ for each standard deviation, we use the following equation:
+
+$$
+t _ {s t d} = \underset {t} {\operatorname {a r g m i n}} \quad \left(\log \left(\mathbf {X} _ {t}\right) - \log \left(\tilde {\mathbf {Y}} _ {t} ^ {s t d}\right) \leq t o l\right), \tag {11}
+$$
+
+where $tol$ represents the maximum tolerance, $\mathbf{X}_t$ and $\tilde{\mathbf{Y}}_t^{std}$ denote the expected values of $x_{t}$ and $\tilde{y}_t^{std}$ in a training set.
+
+Once we determine the corresponding starting timesteps for each standard deviation using Eq. (11), we store these pairs in the Dynamic Starting Step Lookup Table (DSST). Given an estimated $\hat{std}^*$ via the SE network, the appropriate starting timestep can then be retrieved from the DSST.
+
+# 4.3. Dynamic Guidance Scaling Adjuster
+
+Region-specific adjustment on guidance scale $s$ in Eq. (2) is crucial for diffusion sample refinement, as structured regions often require stronger diffusion (smaller $s$ ), while smoother regions need weaker diffusion (larger $s$ ). To address this, we propose the "Dynamic Guidance Scaling Adjuster (DGSA)", which adaptively adjusts $s$ on a region-wise basis throughout the DM sampling process. By dynamically modulating the guidance scale, DGSA minimizes over-smoothing by preserving structural integrity in areas such as facial contours while enhancing realistic details by reducing the scale in fine-detail regions like hair and wrinkles. With DGSA incorporated, the proposed guidance formula is then modified as follows:
+
+$$
+x _ {t - 1} = x _ {t - 1} ^ {\prime} - A _ {t} \times \nabla_ {x _ {t}} \| \acute {y} - k _ {t} \otimes x _ {t} ^ {0} \| ^ {2}, t \leq t _ {s t d} \tag {12}
+$$
+
+$$
+A _ {t} \equiv D G S A (\dot {y}, x _ {t} ^ {0}, t). \tag {13}
+$$
+
+In Eq. (13), DGSA is a CNN with three convolution layers, producing an output in the range [0,1]. It takes as input the current measurement $\hat{y}$ , the HQ prediction $x_{t}^{0}$ based on $x_{t}$ , and $t$ to determine the local diffusion power needed at each timestep. The resulting output, $A_{t}$ , is a region-wise guidance scaling map used to adjust the diffusion sampling.
+
+The objective of training DGSA is to ensure that the HQ prediction $x_{t - 1}^{0}$ , based on $x_{t - 1}$ (as described in Eq. (3)), closely approximates the ground truth $x_0$ . Here, the adjusted sample $x_{t - 1}$ is influenced by the DGSA network, as defined in Eq. (12). To achieve this, we randomly sample $t$ and use the following loss function to train DGSA:
+
+$$
+L _ {D G S A} = \sum_ {i} \gamma_ {i} \mathbb {D} \left(S W T \left(x _ {t - 1} ^ {0}\right) _ {i}, S W T \left(x _ {0}\right) _ {i} ]\right) + \tag {14}
+$$
+
+$$
+D I S T S (x _ {t - 1} ^ {0}, x _ {0}),
+$$
+
+Table 1. Comparisons with SOTA methods on CelebA-Test. The best and second-best performances are highlighted in bold and underline. For fairness, all methods are re-evaluated on the same test sets. Computational performance is measured on an RTX 3090 GPU.
+
+| Type | Method | Inference time (s) | MACs (G) | Params (M) | PSNR↑ | SSIM↑ | LPIPS↓ | FID↓ | IDA↓ | LMD↓ |
| GAN-based | GPEN | 0.368 | 562.998 | 129.203 | 23.773 | 0.659 | 0.358 | 30.250 | 0.837 | 6.377 |
| GFP-GAN | 0.123 | 45.228 | 76.207 | 22.841 | 0.620 | 0.355 | 23.860 | 0.822 | 4.793 |
| Codebook-based | RestoreFormer | 0.152 | 343.051 | 72.680 | 23.001 | 0.592 | 0.376 | 22.874 | 0.783 | 4.464 |
| CodeFormer | 0.062 | 297.206 | 94.113 | 23.828 | 0.637 | 0.319 | 18.076 | 0.775 | 3.509 |
| DAEFR | 0.288 | 455.605 | 152.151 | 21.640 | 0.589 | 0.345 | 15.983 | 0.870 | 3.917 |
| DM-based | DiffBIR | 11.280 | 1525.137 | 1716.700 | 24.127 | 0.647 | 0.357 | 19.194 | 0.767 | 3.535 |
| PGDiff | 94.250 | 480.998 | 176.480 | 21.824 | 0.612 | 0.369 | 20.928 | 0.944 | 4.868 |
| DifFace | 6.120 | 272.678 | 175.430 | 23.949 | 0.659 | 0.355 | 15.032 | 0.867 | 3.781 |
| DR2 | 0.920 | 918.843 | 179.310 | 21.023 | 0.591 | 0.461 | 63.629 | 1.183 | 6.655 |
| 3Diffusion | 11.759 | 308.417 | 180.510 | 23.387 | 0.651 | 0.353 | 15.446 | 0.943 | 3.781 |
| DynFaceRestore | 91.820 | 323.048 | 176.770 | 24.349 | 0.664 | 0.332 | 14.780 | 0.748 | 3.419 |
+
+
+Figure 5. Qualitative results on CelebA-Test. Our method achieves high-fidelity reconstruction with visually accurate details, particularly in the mouth, hair, and skin texture. Please zoom in for the best view.
+
+where $\gamma_{i}$ are the weighted factors of the four subbands (LL, LH, HL, HH) decomposed by Stationary Wavelet Transformation (SWT) [15, 21], and DISTS [8, 21] is the perceptual loss. We would describe in detail the full training procedure of our method in the Supplementary.
+
+# 4.4. Multiple Mapping and Guidance
+
+Up to this point, we have employed only a single fidelity guidance, $\hat{y}$ , and relied on the diffusion model (DM) to recover the missing high-frequency components (i.e., the difference between $x$ and $\hat{y}$ ) for restoration. However, while the DM effectively enhances image quality, it often sacrifices fidelity; conversely, the restoration model (RM) maintains fidelity but yields lower quality enhancement. To balance the strengths of DM and RM, we propose an optional add-on module that leverages multiple guidance sources. Specifically, once we obtain the estimated $\hat{std}^*$ from SE, we generate three Gaussian-blurred guidance images $\hat{y}^{i\in [1,2,3]}$ by varying std values. Formally,
+
+$$
+\acute {y} ^ {i \in [ 1, 2, 3 ]} = k _ {y} ^ {i \in [ 1, 2, 3 ]} \otimes R M (y), \tag {15}
+$$
+
+Table 2. Comparisons to SOTA methods in real-world dataset (-Test). The best and second performances are highlighted with bold and underline.
+
+| Type | Method | LFW | WebPhoto | Wider |
| FID↓ | FID↓ | FID↓ |
| GAN-based | GPEN | 51.942 | 80.705 | 46.359 |
| GFP-GAN | 50.057 | 87.250 | 39.730 |
| Codebook-based | RestoreFormer | 48.412 | 77.330 | 49.839 |
| CodeFormer | 52.350 | 83.193 | 38.798 |
| DAEFR | 47.532 | 75.453 | 36.720 |
| DM-based | DiffBIR | 43.446 | 91.200 | 36.721 |
| PGDiff | 44.942 | 84.163 | 40.380 |
| DifFace | 48.688 | 87.811 | 37.510 |
| DR2 | 70.979 | 117.090 | 76.550 |
| 3Diffusion | 46.888 | 83.335 | 37.130 |
| DynFaceRestore | 42.515 | 95.317 | 36.052 |
+
+where $k_y^{i \in [1,2,3]}$ represents three Gaussian kernels with standard deviations $\hat{std}^*$ , $\hat{std}^* - 1$ , and $\hat{std}^* - 2$ , respectively. These three guidance and corresponding kernels are then used in Eq. (12) to update the diffusion sample.
+
+Since $\dot{y}^1$ retains more trustable low-frequency structural information, while $\dot{y}^2$ and $\dot{y}^3$ provide more high-frequency
+
+details but with lower confidence, we prioritize adjustments derived from $\hat{y}^1$ by assigning it a higher weight, while assigning smaller weights to the guidance from $\hat{y}^2$ and $\hat{y}^3$ . Additionally, the standard deviation of $k^{i\in [1,2,3]}$ are continuously adjusted throughout the diffusion process, as described in Eq. (7), which mitigates the impact of kernel mismatch and thereby enhances the fidelity of the final result. Nonetheless, one remaining issue is the selection of hyperparameters, including the number of guidance and the settings of std values, which can be explored in future work.
+
+# 5. Experiments
+
+# 5.1. Datasets and Metrics
+
+Training dataset. Our framework is trained on the FFHQ dataset [17], which provides HQ facial images as the baseline. To simulate real-world degradation and generate LQ counterparts, we apply the following degradation pipeline:
+
+$$
+y = \left\{J P E G _ {\delta} \left[ \left(x \otimes k _ {\sigma}\right) \downarrow_ {C} + n _ {\zeta} \right] \right\} \uparrow_ {C}. \tag {16}
+$$
+
+Here, $\sigma$ represents the standard deviation of the blur kernel, uniformly sampled from [0.1, 15]. The scale factor $C$ , used for both downsampling and upsampling, is uniformly sampled from [0.8, 32]. The noise level $\zeta$ is also uniformly sampled from [0, 20], and $\delta$ denotes the JPEG compression quality factor, uniformly sampled from [30, 100]. We use the same hyperparameters settings as [28].
+
+Testing datasets We evaluate our method on one synthetic dataset (CelebA) and three real-world datasets (LFW, WebPhoto, and Wider). The CelebA-Test dataset comprises 3,000 LQ facial images synthesized from the CelebA-HQ [16] validation set using the degradation pipeline outlined in Eq. (16). For real-world testing, LFW-Test [14], consists of 1,711 slightly degraded images, each representing a unique individual from the LFW dataset; WebPhoto-Test [22] comprises 407 internet-sourced images, including heavily degraded old photos; and Wider-Test [42] features 970 severely degraded images from the Wider dataset [38]. These datasets, encompassing varying levels of degradation, enable a comprehensive evaluation of our method's robustness and effectiveness in real-world scenarios.
+
+Evaluation metrics PSNR and SSIM are used for the synthetic dataset to assess fidelity, while LPIPS [41] measures perceptual quality. IDA evaluates identity consistency based on embeddings from ArcFace [6], and LMD [32] assesses facial alignment and expression accuracy. Finally, FID [12] is employed to evaluate perceptual quality. For the synthetic testing case, the CelebA-HQ dataset is used as the reference set; for real-world testing, the FFHQ dataset forms the reference set.
+
+To ensure a fair comparison, we utilized the same pretrained diffusion model as DifFace [40] and PGDiff [37].
+
+Due to space limitations, comprehensive implementation details, hyperparameter configurations, training procedures, and additional results are provided in the Supplementary.
+
+# 5.2. Comparisons to SOTA methods
+
+We conduct comprehensive quantitative and qualitative comparisons of our proposed DynFaceRestore with the following state-of-the-art BFR methods: $GAN - based$ (GPEN [39], GFPGAN [22]), Codebook - based (RestoreFormer [35], CodeFormer [42], DAEFR [32]) and DiffusionModel(DM) - based (DiffBIR [26], PGDiff [37], DiffFace [40], DR2 [36] and 3Diffusion [27]).
+
+Comparison on Synthetic Dataset. Tab. 1 presents the quantitative results on the CelebA-Test dataset, demonstrating our method outperforms others in PSNR, SSIM, FID, IDA, and LMD metrics, while ranking second in LPIPS. These results highlight the method's ability to balance fidelity and perceptual quality well.
+
+Qualitative results in Fig. 5 further highlight the advantages of our method. GAN-based approaches often introduce artifacts, while codebook-based methods generate high-quality details but still suffer from fidelity issues. Similarly, diffusion-based methods exhibit deviations from the ground truth. In contrast, our method consistently achieves high-fidelity reconstructions, preserving critical features such as the mouth, hair, and skin texture while maintaining image quality across varying degradation levels. This demonstrates its ability to produce visually accurate results. Comparison on Real-world Datasets. In Tab. 2, we provide quantitative results across three real-world datasets, showing that our method surpasses competing approaches by achieving the best FID scores on the LFW-Test and the Wider-Test. For the WebPhoto-Test, it is worth noting that the FID score may not accurately reflect the discrepancy from the actual data distribution, given the dataset's smaller sample size of 407 images, as also noted in prior works such as DiffFace [40] and WaveFace [28].
+
+Fig. 6 showcases qualitative results on these real-world datasets. GAN-based methods often produce artifacts that compromise the quality crucial for BFR. While Codebook-based and DM-based methods demonstrate improvements in realism, our approach achieves higher perceptual quality across varying degradation levels. These observations show the ability to produce high-quality details of DynFaceRestore.
+
+# 5.3. Ablation Study
+
+We evaluate various model aspects depending on different settings $(A,B,C,D,E,F)$ as shown in Tab. 3 and Fig. 7, along with a Baseline comparison leveraged diffusion model [7] trained on the FFHQ [17].
+
+Effect of DBLM. Compared to the Baseline, setting A achieves remarkable improvements across all metrics by re
+
+
+Figure 6. Qualitative results from three real-world datasets demonstrate that our restoration method produces more natural features (e.g., eyes) and realistic details (e.g., hair) compared to other approaches, with improved fidelity. Please zoom in for the best view.
+
+Table 3. Ablation study of our framework on CelebA-Test. The best performance is highlighted with bold.
+
+| Setting | DBLM | Multiple Guidance | DSST | DGSA | PSNR↑ | SSIM↑ | FID↓ | IDA↓ | Range of sampling steps |
| Baseline (DM) | | | | | 11.129 | 0.382 | 55.777 | 1.461 | 1000 |
| A | ✓ | | | | 24.992 | 0.690 | 18.303 | 0.725 | 1000 |
| B | ✓ | ✓ | | | 25.094 | 0.694 | 19.823 | 0.725 | 1000 |
| C | ✓ | ✓ | ✓ | | 25.107 | 0.695 | 19.786 | 0.724 | [690, 925] |
| D | ✓ | ✓ | | ✓ | 24.340 | 0.664 | 15.007 | 0.750 | 1000 |
| E | ✓ | | ✓ | ✓ | 24.327 | 0.666 | 14.689 | 0.755 | [690, 925] |
| F | ✓ | ✓ | ✓ | ✓ | 24.349 | 0.664 | 14.780 | 0.748 | [690, 925] |
+
+
+Baseline
+
+
+Setting A
+
+
+Setting B
+
+
+Setting C
+
+
+Ground truth
+
+
+Setting D
+
+
+Setting E
+
+
+Setting F
+Figure 7. Ablation results for each component in DynFaceRestore are shown, using the experimental settings in Tab. 3 for visual comparison. With the addition of DBLM, DSST, DGSA, and multiple guidance, DynFaceRestore well balances fidelity and quality.
+
+framing the BFR task as Gaussian deblurring and incorporating DM guidance. As shown in Fig. 7, the mouth and beard regions in setting A are closer to Ground Truth.
+
+Effect of Multiple Guidance. Setting $B$ and $F$ further enhance fidelity over $A$ and $E$ , respectively, improving both PSNR and IDA metrics by adaptively incorporating multiple guidance sources. Specifically, three Gaussian-blurred images are applied to guide the diffusion sampling process in this experiment.
+
+Effect of DSST. Compared to setting $B$ , integrating the DSST table in setting $C$ improves both PSNR and FID,
+
+while also shortening the sampling process, as reflected in the reduced range of sampling steps. This improvement is achieved by identifying the optimal starting step, effectively avoiding under- or over-diffusion.
+
+Effect of DGSA. Setting $D, E, F$ achieves a notable improvement in the perceptual quality (FID score) compared to settings $A, B, C$ , as illustrated in Fig. 7 and Tab. 3. This demonstrates the effectiveness of the region-wise guidance scale. Visual analysis of the scaling map is provided in the Supplementary to explain the DGSA's behavior.
+
+Our approach provides dynamic control, ranging from enhancing fidelity restoration (setting $C$ ) to effectively improving image quality, achieving the best FID score (setting $E$ ). This highlights the flexibility of our model, allowing us to balance perceptual quality and fidelity by managing guidance resources (setting $F$ ).
+
+# 6. Conclusion
+
+We propose DynFaceRestore for Blind Face Restoration (BFR). By utilizing Dynamic Blur-Level Mapping, we simplify the task by mapping unknown degraded input to a corresponding Gaussian blurred image, effectively reframing BFR as a Gaussian deblurring problem. Combined with optimal starting steps and region-wise scale adjustments, our method delivers superior performance. Experimental results demonstrate that DynFaceRestore outperforms existing methods while striking a balance between fidelity and perceptual quality. Additional experiments, comparisons, and analyses are provided in the Supplementary.
+
+Acknowledgments This work was financially supported in part (project number: 112UA10019) by the Co-creation Platform of the Industry Academia Innovation School, NYCU, under the framework of the National Key Fields Industry-University Cooperation and Skilled Personnel Training Act, from the Ministry of Education (MOE) and industry partners in Taiwan. It also supported in part by the National Science and Technology Council, Taiwan, under Grant NSTC-114-2218-E-A49-024, -Grant NSTC-112-2221-E-A49-089-MY3, Grant NSTC-114-2425-H-A49-001, Grant NSTC-113-2634-F-A49-007, Grant NSTC-112-2221-E-A49-092-MY3, and in part by the Higher Education Sprout Project of the National Yang Ming Chiao Tung University and the Ministry of Education (MOE), Taiwan. It is also partly supported by MediaTek Inc., Hon Hai Research Institute, and Industrial Technology Research Institute.
+
+# References
+
+[1] Chaofeng Chen, Xiaoming Li, Lingbo Yang, Xianhui Lin, Lei Zhang, and Kwan-Yee K Wong. Progressive semantic-aware style transformation for blind face restoration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11896-11905, 2021. 1, 2
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\ No newline at end of file
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+# DynImg: Key Frames with Visual Prompts are Good Representation for Multi-Modal Video Understanding
+
+Xiaoyi Bao $^{1,2,3}$ , Chenwei Xie $^{3}$ , Hao Tang $^{3,4}$ , Tingyu Weng $^{3}$ , Xiaofeng Wang $^{1,2}$ , Yun Zheng $^{3}$ , Xingang Wang $^{1,5*}$
+
+$^{1}$ Institute of Automation, Chinese Academy of Sciences
+
+$^{2}$ School of Artificial Intelligence, University of Chinese Academy of Sciences
+
+$^{3}$ Alibaba Group $^{4}$ Peking University $^{5}$ Luoyang Institute for Robot and Intelligent Equipment
+
+
+(1) (2)
+
+
+
+
+Figure 1. Comparison between the previous methods for video understanding and DynImg. As for the structure comparison in the left (1), previous models use processed visual features for subsequent spatial and temporal merging modules, either in parallel (a) or in sequence (b). However, in rapidly moving scenarios like the example on the right, where the little girl quickly turns back and moves in the last frame, these models fail to capture the crucial details of her motion. Factors such as motion blur lead to these important temporal details being overlooked during the visual feature extraction process, resulting in these areas not receiving the necessary attention. Spatio-temporal interaction based on such inaccurate features or tokens is ineffective. In contrast, our proposed DynImg (c) advances the spatio-temporal interaction process via temporal prompts. This enables the model to focus on those rapidly moving regions that are difficult to capture during the feature extraction phase. The right part shows its effectiveness and efficiency (2). "Accuracy" is the average accuracy on MSVD, MSRVTT, Activitynet, and TGIF. "Token Efficiency" is negatively correlated with the number of visual tokens used to represent the video.
+
+# Abstract
+
+In recent years, the introduction of Multi-modal Large Language Models (MLLMs) into video understanding tasks has become increasingly prevalent. However, how to effectively integrate temporal information remains a critical research focus. Traditional approaches treat spatial and temporal information separately. Due to issues like motion blur, it is challenging to accurately represent the spatial information of rapidly moving objects. This can lead to temporally
+
+important regions being underemphasized during spatial feature extraction, which in turn hinders accurate spatiotemporal interaction and video understanding. To address this limitation, we propose an innovative video representation method called Dynamic-Image (DynImg). Specifically, we introduce a set of non-key frames as temporal prompts to highlight the spatial areas containing fast-moving objects. During the process of visual feature extraction, these prompts guide the model to pay additional attention to the fine-grained spatial features corresponding to these re
+
+gions. Moreover, to maintain the correct sequence for DynImg, we employ a corresponding 4D video Rotary Position Embedding. This retains both the temporal and spatial adjacency of DynImg, helping MLLM understand the spatiotemporal order within this combined format. Experimental evaluations reveal that DynImg surpasses the state-of-the-art methods by approximately $2\%$ across multiple video understanding benchmarks, proving the effectiveness of our temporal prompts in enhancing video comprehension.
+
+# 1. Introduction
+
+With the widespread application of Multi-modal Large Language Models (MLLMs) in image-based vision-language tasks [1, 5, 21, 23, 29, 41, 57], there has been a growing research interest in extending their application to video understanding [24, 28, 33, 54]. However, when dealing with videos instead of static images, the complexity increases significantly due to the need to capture temporal information.
+
+Previous methods typically decouple the processing of temporal and spatial information [16, 24, 35, 54]. Their spatio-temporal interaction occurs within high-level queries or tokens. This corresponds to the two different model structures in Fig.1(a/b), both of them using a pre-trained image encoder to extract spatial features in the beginning. In Fig.1(a), after compression through temporal and spatial modules, temporal tokens and spatial tokens interact within the LLM in parallel. For instance, the two compression in Video-ChatGPT [35] refer to different spatial and temporal pooling modules. The other struction, as is shown in Fig.1(b), processes temporal features sequentially. Here, spatio-temporal interaction is based on the extracted high-level spatial features. An example is Video-LLaMA [54], which extracts frame-level embeddings using Q-former and then utilizes an additional temporal module for inter-frame temporal interaction.
+
+However, performing spatio-temporal interaction within high-level queries or tokens may result in suboptimal performance due to the loss of fine-grained information. Throughout visual feature extraction and spatial merging, spatial information undergoes continuous abstraction and compression. Techniques such as k-means clustering [16], pooling [27, 35], Q-former [24, 54], or simple convolution [28] cause many fine-grained details to blur and be lost during averaging. This issue is particularly noticeable in regions containing rapidly changing objects. Due to factors like motion blur, such areas often fail to gain an accurate and comprehensive fine-grained feature representation. As illustrated in the upper right of Fig.1(1), the attention on the area where a young girl suddenly turns back and moves in the last frame is noticeably lacking. Such rapidly changing regions are temporally significant for video understanding. If their fine-grained features are neglected in the initial spa
+
+tial extraction, the effectiveness of subsequent interactions, performing at the query or token level, becomes severely limited. This diminishes video comprehension in complex or dynamically moving scenes.
+
+To address this challenge, we need to implement explicit spatio-temporal interactions from the initial stage of the visual feature extraction. We hope that the visual encoder can identify which regions or objects are rapidly moving from the video frames. In multi-modal image understanding, visual prompts (e.g., bounding boxes and sequence labels) are commonly employed to convey object-centric textual information within images [3, 13, 15, 37, 38, 56]. These prompts augment input images with supplementary information and adjust the focus to the text-referenced objects being prompted. Drawing inspiration from this, we propose our DynImg. We propose to construct a temporal prompt to emphasize regions containing rapidly moving objects during the feature extraction phase. Specifically, we decompose video sequences into keyframes and non-keyframes, relying on the keyframe content for high-resolution spatial representation. The crucial temporal prompt component is constructed by overlaying certain non-keyframes onto the original images. The effectiveness of the prompts occurs within the encoder, leveraging the long-range modeling capability inherent in the visual encoder [10, 36, 52]. These prompts adjust the attention on the keyframe to ensure that regions containing rapidly moving objects are properly emphasized rather than overlooked. In this way, it facilitates effective fine-grained spatiotemporal interaction.
+
+With the spatial and temporal correspondences in prompts and keyframes, DynImg enriches the original spatial domain with an added temporal dimension during the feature extraction. However, for LLM, the form of DynImg is so unfamiliar that directly use the obtained final token of DynImg may introduce spatiotemporal disarray. To avert this sequential confusion, we propose a 4D positional embedding mechanism. This mechanism constructs a unified coordinate system for the input sequence, especially for the visual tokens corresponding to DynImg. Unlike traditional 1D-RoPE [29] that focuses only on token sequence, our proposed 4D-RoPE maintains the correct four-dimensional sequence of DynImg. It not only ensures the consistency in adjacency relations within both the spatial and temporal domains, but also guides MLLM to understand the composition logic of the DynImg format.
+
+Our contributions can be summarized as follows:
+
+- We introduce Dynamic-Image (DynImg), a novel video representation method. DynImg addresses the shortcomings of traditional approaches by facilitating fine-grained spatiotemporal attention interactions. It ensures that regions containing rapidly moving objects are appropriately emphasized during the initial visual feature extraction, thereby improving overall video comprehension.
+
+- We propose using non-key frames as temporal prompts. These prompts inform the visual encoder about regions containing rapidly moving objects, allowing it to pay extra attention to these areas in fine-grained feature extraction of keyframes. This is further supported by our proposed novel 4D Video Rotary Position Embedding. It guides the temporal and spatial sequence of DynImg, aiding the LLM in accurately understanding DynImg's composition.
+- Extensive experiments demonstrate the effectiveness and efficiency of our proposed method, achieving state-of-the-art accuracy on most Video-QA benchmarks.
+
+# 2. Related Work
+
+# 2.1. Video Temporal Representation
+
+Since DeepVideo [18] first applied CNN networks to video understanding, researchers have been focusing on how to effectively extract and utilize the sequential representation of videos. One approach involves incorporating traditional handcrafted features to represent sequences. For example, Simonyan introduces a Two-Stream structure where optical flow is employed, and object motion features are learned through an additional temporal stream network [39]. Following this, subsequent studies enhance the performance of dual-stream networks. For instance, LSTM is used for extended temporal modeling [50], and early fusion techniques and 3D pooling are applied to bolster the fusion of sequential information [11]. TDD overlays optical flow features along trajectories to achieve superior results [45]. In addressing long video inputs, TSN divides input into segments, processing them through a dual-stream network before merging [46]. Research efforts such as DOVF [22] and TLE [9] extend the functional scope of dual-stream networks by proposing and refining global encodings. Additionally, Yang suggests substituting optical flow with motion vectors [53], while Video-LaVIT [17] further optimizes the use of action vectors.
+
+Another category of methods includes C3D [43] and I3D [8], which employ 3D convolution to model the entire spatiotemporal structure of videos. R(2+1)D [44] decomposes 3D CNNs into 2D spatial convolutions and 1D temporal convolutions, reducing overfitting and training difficulty. SlowFast [12] uses a combination of fast and slow networks for video classification, with each network learning static and motion information, respectively. Methods like TimeSformer [6] and ViViT [2] split the joint attention into temporal and spatial parts to reduce memory usage.
+
+# 2.2. Video Understanding
+
+Video understanding typically manifests as tasks such as video question answering and video captioning, involving visual text interactions. These tasks require accurate com
+
+prehension of video content based on textual and video inputs, yielding pure text responses. Recently, in response to higher-dimensional visual understanding demands, researchers have begun leveraging visual knowledge contained within multimodal large language models to aid in the abstraction of visual information.
+
+A series of research efforts initially decompose videos into different representation dimensions and then integrate the inputs to enrich the prompts for MLLM. For example, Video-ChatGPT [35] divides videos into spatial and temporal branches for pooling. VideoChat [24] breaks down videos into textual descriptions and feature embeddings of the videos themselves. LLaMA-VID [27] represents each frame as two tokens: context markers and content markers. Video-LaViT [17] employs keyframes and motion vectors to tokenize videos. PLLaVA [49] and PPLLaVA [32] propose adaptive pooling and Prompt-guided Pooling to reduce spatiotemporal redundancy. IG-VLM [20] uses a similar comic-style image grid, leveraging GPT-4V to achieve improved performance. Simultaneously, to augment training data, researchers have explored methods to unify image modalities for training. Chat-UniVi [16] and Video-LLaVA [28], respectively, achieve this by employing object-based adaptive clustering tokens and alignment followed by projection strategies, thereby unifying image and video inputs for enhanced visual understanding.
+
+# 2.3. Visual Prompt
+
+Prompting has been extensively studied in the natural language processing community [30]. Recently, researchers have begun to explore the benefits of using prompting in image recognition. This involves adding learnable modifications to the image to guide the model to make specific predictions [3, 13, 15, 37, 56]. These prompt-tuning methods optimize an additional and fixed visual prompt, such as adding an estimizable pixel region around the image [4, 19, 51, 55]. Recently, researchers have shown that manually crafted prompts, such as red circles and blurred backgrounds, can effectively guide the attention of models like CLIP [36] when training on datasets containing similar annotations [38]. Additionally, there is also research suggesting that constructing embeddings corresponding to the text prompts and appending them to the original image can better facilitate information supplementation and alignment. However, the aforementioned studies have mainly focused on static image-related tasks and have not been extended to video inputs.
+
+# 3. Methods
+
+To mitigate the information loss associated with coarse-grained interactions, we propose our Dynamic-Image (DynImg) model. Rather than abstracting features separately along spatial and temporal dimensions, we prioritize the
+
+
+Figure 2. Overall architecture of DynImg. Videos are decomposed into keyframes and non-keyframes. Several non-keyframes serve as temporal prompts and are combined with keyframes to form the representation of the DynImg, along with its corresponding 4D positional embeddings. Within the image encoder, these temporal prompts adjust the spatial attention. The attention map on the left belongs to the patch of the left hand in the keyframe. Red arrows indicate the usual influence of local visual features, while yellow arrows show the emphasis to dynamic regions by non-keyframes. The output feature of the image encoder, after passing through a projection layer, is fed into the LLM along with the positional embeddings for the final output.
+
+spatiotemporal interaction process. Inspired by the information exchange in visual prompts, we introduce temporal prompts for this fine-grained level of spatiotemporal interaction. In Section 3.1, we describe the composition of DynImg and the functioning process of the temporal prompts. Since the prompts introduce a temporal dimension within the spatial framework, we propose a corresponding 4D rotary positional encoding to maintain correct temporal and spatial order. In Section 3.2, we discuss the implementation and details of this positional embedding mechanism.
+
+# 3.1. Temporal Prompts
+
+If spatial information is extracted and integrated before performing spatiotemporal interactions, many crucial spatial details may have already been discarded or blurred before the interaction. This includes temporally significant local regions, such as foreground objects undergoing displacement. How can these temporally important fine-grained details be retained? We propose to advance the spatiotemporal interaction process, changing the interaction targets from abstract tokens or features to fine-grained pixel values.
+
+How, then, can temporal information be integrated at the pixel level for interaction? In multimodal image tasks, visual prompts are utilized for text-related target emphasis. This often involves adding bounding boxes, labels, or other annotations directly onto the original image. Inspired by this idea, we propose a video-specific temporal prompt that integrates temporal information to adjust attention to spa
+
+tial details. For moving targets within the temporal prompt, we identify and emphasize the corresponding spatial regions, enabling fine-grained spatiotemporal interactions for enhanced understanding of spatial content.
+
+Composition of the Dynamic-Image: The structure of DynImg involves decoupling the video into keyframes and non-keyframes, relying on keyframes to provide a fine-grained spatial basis while utilizing a set of non-keyframes as temporal prompts.
+
+For keyframe selection, we apply the MPEG-4 method wherein I-frames inherently contain more information. We evenly sample four I-frames as keyframes $K$ . For a given key-frame $K_{i}$ , we randomly select two preceding I-frames from $(K_{i - 1}, K_{i})$ and two following it from $(K_{i}, K_{i + 1})$ as non-keyframes $(N$ -frames), forming a frame-group to establish a comprehensive temporal context for $K_{i}$ . Overlap may happen in non-keyframe selection of two adjacent DynImages, while keyframes appear only once.
+
+To preserve fine-grained spatial details, high-resolution keyframes are retained as the base graph for DynImg. For the prompt portion, we resize the four $N$ -frames and concatenate them in temporal order from left to right beneath the $K$ frame after applying data augmentation to each whole group. As the temporal prompt mainly focuses on motion, the resizing operation does not significantly impact its motion-aware effectiveness. This resizing is controlled to ensure patch-based feature extraction does not cross the boundaries between frames after concatenation.
+
+
+Figure 3. Schematic diagram of coordinates in 4D position embedding. The direction of the arrow represents the direction of increase in the four dimensions of height, weight, temporal, and sequence. The first two dimensions of the visual prompt are maintained through interpolation to preserve spatial correlation. The temporal dimension has a coordinate value of 0 at the keyframe time point and undergoes symmetrical changes before and after in the visual prompt section. The same dynamic image corresponds to the same sequence coordinate.
+
+Functioning of temporal prompts: The DynImg, carrying both temporal and spatial information, is fed into the video feature extraction pipeline. In addition to focusing on the spatial features of adjacent local patches, the visual encoder utilizes long-range modeling capabilities to facilitate interaction between the spatially informative keyframe regions and the prompts positioned below them.
+
+Specifically, within the self-attention layer of the vision transformer in the visual encoder, patches from keyframes can attend to highly similar patches within the temporal prompt regions. For targets with temporal variations, their corresponding patches from the $N$ -frames undergo deformations and movements across different frames. The keyframe patches identify movement trends from the prompts. They establish connections, adding temporal dynamics to fine-grained spatial features. Through task-driven training, the model progressively increases attention weights on dynamic local regions. This makes the dynamic changes in temporal prompts effectively activate the fine-grained regions in keyframes.
+
+# 3.2. 4-Dimensional Position Embedding
+
+In the composition of DynImg, different frames correspond to various positions along the temporal dimension. An explicit temporal sequence aids in establishing cross-frame associations between spatially adjacent features. This is particularly useful for identifying spatial correspondences between the temporal prompts and keyframes. Additionally, at the token level, the temporal order, especially among the
+
+temporal prompts, plays a crucial role in video understanding. To address these challenges, we propose a 4D rotational positional embedding mechanism tailored for DynImg. This mechanism prevents the confusion of spatiotemporal relationships due to DynImg composition, thereby facilitating MLLM's understanding of this input format.
+
+Rotary Position Embedding(RoPE) is a common positional encoding method used in LLMs. It involves multiplying features $q$ with trigonometric functions based on their positional coordinates $x$ . In the original 1D RoPE, features $q$ are split into pairs $(q_{1}, q_{2})$ . The multiplication by the rotation matrix is represented by the following formula:
+
+$$
+R = \binom {q _ {1}} {q _ {2}} \otimes \binom {\cos (x \theta)} {\cos (x \theta)} + \binom {- q _ {2}} {q _ {1}} \otimes \binom {\sin (x \theta)} {\sin (x \theta)} \tag {1}
+$$
+
+where $\theta$ is a parameter that controls the rotational period, calculated by a formula. $x\cdot \theta$ gives the rotation angle.
+
+For DynImg, it is necessary to maintain the position order in four dimensions: Height, Weight, Temporal, and Sequence, as shown in Fig. 3. For the text portion of the input token sequence, the sequence coordinate increments from 0, while the coordinates of the first three dimensions $(H,W,T,S)$ are simply set to identical to the fourth.
+
+As for the $(H,W)$ coordinates of visual tokens, the coordinates for the keyframe region remain consistent with those of static images, incrementing spatially from 0. For the visual prompt, to preserve its spatial adjacency across different frames, interpolation is applied to the keyframe's coordinates to obtain coordinates of the first two dimensions. All frames in one DynImg share the same spatial coordinate range. As for the temporal dimension coordinate $(T)$ , we set the base keyframe's coordinate as 0, while the coordinate of temporal prompts increase or decrease symmetrically according to their chronological order. All frames of the same dynamic image share the same sequence coordinate $(S)$ that increases as text tokens.
+
+To leverage the pre-trained LLMs using RoPE while adapting to the special format of DynImg, we calculate the angle of rotation via a weighted sum of four-dimensional coordinates.
+
+$$
+x \cdot \theta = x _ {h} \cdot \theta_ {h} + x _ {w} \cdot \theta_ {w} + x _ {t} \cdot \theta_ {t} + x _ {s} \cdot \theta_ {s} \tag {2}
+$$
+
+where $x_{h}$ , $x_{w}$ , $x_{t}$ , and $x_{s}$ represent the coordinates of $(H,W,T,S)$ , respectively. For $\theta_{s}$ , we retain the general sinusoidal encoding scheme used by LLMs, calculated as $\theta_s^i = 10000^{-2i / d}$ . During training, we set $\theta_h$ , $\theta_w$ , and $\theta_t$ as learnable parameters with initial values of 0. Initially, only $m_{s} \cdot \theta_{s}$ takes effect, ensuring that the model does not disrupt the effectiveness of the pre-trained LLM in the early training phase. Through training, the model gradually learns suitable embedding for $\theta_h$ , $\theta_w$ , and $\theta_t$ .
+
+| Method | Encoder | LLM | MSVD | MSRVTT | Activitynet | TGIF | Video-ChatGPT |
| Acc | Score | Acc | Score | Acc | Score | Acc | Score | CI | DO | CU | TU | CO | Avg. |
| Video-LLaMA [54] | BLIP2 | 7B | 51.6 | 2.5 | 29.6 | 1.8 | 12.4 | 1.1 | - | - | 1.96 | 2.18 | 2.16 | 1.82 | 1.79 | 1.98 |
| Video-ChatGPT [35] | ViT-L | 7B | 64.9 | 3.3 | 49.3 | 2.8 | 35.2 | 2.7 | 51.4 | 3.0 | 2.50 | 2.57 | 2.69 | 2.16 | 2.20 | 2.42 |
| Video-LLaVA [28] | ViT-L | 7B | 70.7 | 3.9 | 59.2 | 3.5 | 45.3 | 3.3 | 70.0 | 4.0 | | | | | | |
| Chat-UniVi [16] | CLIP-L | 7B | 65.0 | 3.6 | 54.6 | 3.1 | 45.8 | 3.2 | 60.3 | 3.4 | 2.89 | 2.91 | 3.46 | 2.89 | 2.81 | 2.99 |
| MovieChat [40] | BLIP2 | 7B | 75.2 | 3.8 | 52.7 | 2.6 | 45.7 | 3.4 | - | - | 2.76 | 2.93 | 3.01 | 2.24 | 2.42 | 2.67 |
| VideoChat [24] | BLIP2 | 7B | 56.3 | 2.8 | 45.0 | 2.5 | 26.5 | 2.2 | 34.4 | 2.3 | 2.23 | 2.50 | 2.53 | 1.94 | 2.24 | 2.29 |
| VideoChat2 [25] | UMT-L | 7B | 70.0 | 3.9 | 54.1 | 3.3 | 49.1 | 3.3 | - | - | 3.02 | 2.88 | 3.51 | 2.66 | 2.81 | 2.98 |
| Vista-LLaMA [34] | BLIP2 | 7B | 65.3 | 3.6 | 60.5 | 3.3 | 48.3 | 3.3 | - | - | 2.44 | 2.64 | 3.18 | 2.26 | 2.31 | 2.57 |
| LLaMA-VID [27] | BLIP2 | 13B | 70.0 | 3.7 | 58.9 | 3.3 | 47.5 | 3.3 | - | - | 2.96 | 3.00 | 3.53 | 2.46 | 2.51 | 2.89 |
| LITA [14] | CLIP-L | 7B | - | - | - | - | - | - | - | - | 2.94 | 2.98 | 3.43 | 2.68 | 3.19 | 3.04 |
| ST-LLM [31] | BLIP2 | 7B | 74.6 | 3.9 | 63.2 | 3.4 | 50.9 | 3.3 | - | - | 3.23 | 3.05 | 3.74 | 2.93 | 2.81 | 3.15 |
| IG-VLM [20] | Unk | GPT-4V | 76.3 | 4.0 | 63.8 | 3.5 | 57.0 | 3.5 | 65.3 | 3.7 | 3.40 | 2.80 | 3.61 | 2.89 | 3.13 | 3.17 |
| PLLAVA [49] | ViT-L | 7B | 76.6 | 4.1 | 62.0 | 3.5 | 56.3 | 3.5 | 77.5 | 4.1 | 3.21 | 2.86 | 3.62 | 2.33 | 2.93 | 3.12 |
| DynImg | SigLip | 7B | 78.6 | 4.2 | 64.1 | 3.5 | 57.9 | 3.6 | 77.5 | 4.0 | 3.33 | 3.02 | 3.75 | 2.96 | 3.17 | 3.25 |
+
+Table 1. Performance comparison between DynImg and other methods on five open-ended video understanding benchmarks. "Encoder" refers to the type of visual encoder used during training.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Training Data: Following [49], we utilize a series of video-text data pairs for training. The dataset consists of the following categories: Video caption data comprises 39k samples from TextVR, 8k samples from YouCook2, 7k samples from VideoChat [24], and 400k samples from WebVid. Video classification data includes 40k samples from Kinetics-710 and 40k samples from Something-Something v2. Video conversation data consists of 9k samples from VideoChat2 [25], 13k samples from Video-ChatGPT [35], and 4k samples from VideoChat. Video reasoning data originates from 34k samples in Next-QA, and 43k samples in CLEVRER-QA. Video question-and-answer data comes from 8k samples in Ego-QA, and 92k samples in TGIF-QA.
+
+Evaluation Setting: For the evaluation dataset, we follow the previous methods and use two kinds of video understanding tasks [28, 49]. For the open-ended video question-and-answer dataset, we select MSVD [47], MSRVTT [48], TGIF [26], and ActivityNet [7]. The correctness and confidence scores of generated answers correspond to the "Score" in Tab. 1, a float value in (0,5) output directly by GPT. Additionally, we use the benchmark from VideoChatGPT [35], which is also a GPT-assisted evaluation in five dimensions: CI (Correctness of Information), DO (Detail Orientation), CU (Context Understanding), TU (Temporal Understanding), and CO (Consistency). The GPT model we use for evaluation is GPT-3.5-turbo-0125. As for the performance on the multi-choice question-and-answer task, we choose the dataset MVBench [25]. This dataset evaluates video understanding performance across 20 different domain, where each domain contains 200 multiple-choice instances. For example, the "AS" in Tab. 2 refers to Action Sequence. The accuracy calculation does not rely on GPT.
+
+Models Setting: We choose four $N$ -frame as temporal prompt for one keyframe in each DynImg. We first perform regular data augmentation (RandomResizedCrop + RandomHorizontalFlip + normalization) on these five frames together before composing them to be one DynImg. This step aims to prevent the spatial region confusion caused by the central crop operation during the data augmentation process. Considering the video length, we synthesize four DynImages as input. We use a pre-trained Sigclip-so400m-384 [52] as our video encoder. As for the projection layer, it consists of a feedforward layer and the Adaptive Average Structure Pooling module from PLLaVA [49], with the pooling shape set to (16, 12, 12). The training recipe of DynImg follows PLLaVA. For the LLM selection, we use the pretrained Qwen2.5-7B-Instruct [42]. All parameters of these three modules are trainable.
+
+# 4.2. Comparison with State-of-the-Art
+
+Accuracy: We compare the performance of DynImg with other methods across five open-ended video understanding datasets, as is shown in Tab. 1. Our method demonstrates superior accuracy in most benchmarks. Specifically, DynImg surpasses the previous state-of-the-art methods by approximately $2.0\%$ on MSVD, MSRVTT, TGIF, and ActivityNet.
+
+We also assess DynImg's performance on the multi-choice question-answering dataset MVBench, whose questions emphasize comprehensive spatiotemporal understanding. As depicted in Tab. 2, our method achieves optimal performance across most evaluation problem categories, evidencing its ability to provide more comprehensible temporal information. Notably, for moving-sensitive tasks, DynImg demonstrates substantial gains in Moving Direction $(+21.0\%)$ , Moving Count $(+15.0\%)$ , and Moving Attribute $(+26.5\%)$ , directly quantifying its effectiveness for rapid object movements.
+
+| Method | Visual Tokens | LLM Size | AS | AP | AA | FA | UA | OE | OI | OS | MD | AL | ST | AC | MC | MA | SC | FP | CO | EN | ER | CI | Avg. |
| Video-LLaMA [28] | 2048 | 7B | 27.5 | 25.5 | 51.0 | 29.0 | 39.0 | 48.0 | 40.5 | 38.0 | 22.5 | 22.5 | 43.0 | 34.0 | 22.5 | 32.5 | 45.5 | 32.5 | 40.0 | 30.0 | 21.0 | 37.0 | 34.1 |
| Video-ChatGPT [35] | 356 | 7B | 23.5 | 26.0 | 62.0 | 22.5 | 26.5 | 54.0 | 28.0 | 40.0 | 23.0 | 20.0 | 31.0 | 30.5 | 25.5 | 39.5 | 48.5 | 29.0 | 33.0 | 29.5 | 26.0 | 35.5 | 32.7 |
| VideoChat [24] | 1536 | 7B | 33.5 | 26.5 | 56.0 | 33.5 | 40.5 | 53.0 | 40.5 | 30.0 | 25.5 | 27.0 | 48.5 | 35.0 | 20.5 | 42.5 | 46.0 | 26.5 | 41.0 | 23.5 | 23.5 | 36.0 | 35.5 |
| VideoChat2 [25] | 1536 | 7B | 66.0 | 47.5 | 83.5 | 49.5 | 60.0 | 58.0 | 71.5 | 42.5 | 23.0 | 23.0 | 88.5 | 39.0 | 42.0 | 58.5 | 44.0 | 49.0 | 36.5 | 35.0 | 40.5 | 65.5 | 51.1 |
| ST-LLM [31] | 256 | 7B | 66.0 | 53.5 | 84.0 | 44.0 | 58.5 | 80.5 | 73.5 | 38.5 | 42.5 | 31.0 | 86.5 | 36.5 | 56.5 | 78.5 | 43.0 | 44.5 | 46.5 | 34.5 | 41.5 | 58.5 | 54.9 |
| IG-VLM [20] | Unk | GPT-4 | 55.5 | 63.5 | 72.0 | 46.5 | 73.5 | 18.5 | 59.0 | 29.5 | 12.0 | 40.5 | 83.5 | 39.0 | 12.0 | 22.5 | 45.0 | 47.5 | 52.0 | 31.0 | 59.0 | 11.0 | 43.5 |
| PLLAVA [49] | 2304 | 7B | 58.0 | 49.0 | 55.5 | 41.0 | 61.0 | 56.0 | 61.0 | 36.0 | 23.5 | 26.0 | 82.0 | 39.5 | 42.0 | 52.0 | 45.0 | 42.0 | 53.5 | 30.5 | 48.0 | 31.0 | 46.6 |
| DynImg | 576 | 7B | 66.5 | 54.0 | 80.5 | 49.0 | 58.5 | 82.0 | 74.0 | 38.0 | 44.5 | 33.5 | 79.5 | 41.0 | 57.0 | 78.5 | 43.5 | 46.0 | 42.5 | 39.0 | 51.0 | 57.0 | 55.8 |
+
+Token Efficiency: We further analyze the token-level efficiency of the proposed DynImg and existing methods, as shown on the right side of Fig. 1. The horizontal axis reflects efficiency, which is inversely proportional to the number of visual tokens used. The vertical axis shows the average accuracy across four datasets. Our method not only achieves high accuracy but also demonstrates strong token-level efficiency. Thanks to the effective utilization of temporal information, DynImg achieves comparable accuracy using only 4 frames (DynImg), whereas the baseline method PLLaVA requires a 16-frame input. This significantly reduces the number of visual tokens fed into the LLM, improving both training and inference efficiency without sacrificing expressive power.
+
+While the MPEG-4 video decoding method only introduces minimal overhead compared to methods like Decord, the overall data loading time does increase from 0.06s to 0.32s. This is mainly due to the increased number of frames being read, along with operations such as resizing and composition. However, this overhead remains acceptable when compared to the much longer duration of MLLM training. Moreover, any extra memory consumed during composition is promptly released afterward.
+
+# 4.3. Ablation Studies
+
+Different design choices of DynImg. To demonstrate the effectiveness of our proposed temporal prompts and the corresponding position embedding, we conduct ablation experiments on various design strategies of DynImg, as shown in Tab.3. In our implementation, temporal prompts are overlaid at the image level, and the composited DynImg is fed into the visual encoder for feature extraction. We compare our DynImg with an alternative, more direct method, where all keyframes and non-keyframes are input into the visual encoder, followed by similar overlay processing at the feature level. It is observed that the post-encoder prompt fusion yields limited effectiveness. We deduce the reason is that these post-encoder prompts merely add more information for LLM, without facilitating spatiotemporal interaction. In contrast, applying prompts before the encoder results in a performance improvement of about $2.4\%$ , highlighting the efficacy of our pre-encoder spatiotemporal interaction.
+
+Table 2. Experiments on MVBench, the multi-choice question answering dataset. The 20 types of questions included require an overall understanding of the video content for their answers.
+
+| TP | Components | MSVD |
| TP-Stage | 4D-RoPE | Acc | Score |
| | | 74.9 | 3.8 |
| ✓ | After Encoder | | 75.2 | 3.9 |
| ✓ | Before Encoder | | 77.3 | 4.0 |
| ✓ | Before Encoder | ✓ | 78.6 | 4.2 |
+
+Table 3. Ablation studies on the key components of DynImg. "TP" refers to the temporal prompt. "TP-stage" refers to the stage at which temporal prompts are applied. In DynImg, temporal prompts are concatenated with the original image before the visual encoder. "After Encoder" denotes the approach where both non-keyframes and keyframes are fed into the visual encoder at the same resolution, followed by downsampling and concatenation at the feature level. "4D-RoPE" denotes the proposed 4D rotary position embedding.
+
+Additionally, we look into the effect of the proposed 4D RoPE. In the scenario where temporal prompts are used without the 4D positional embedding, a traditional 1D positional embedding along the sequence dimension is employed. The result indicates that for LLM, DynImg with accurate positional embedding can appropriately signal the relationships among input visual tokens, mitigating potential spatiotemporal relationship confusion caused by DynImg composition.
+
+Different numbers of $N$ -frames in one DynImg. We explore the influence of the number of $N$ -frames in the composition process of DynImg, as shown in Tab. 4. It is important to note that we perform different resizing and placing depending on the number of non-key frames. We ensure that the size of each non-key frame in the temporal prompt is an integer multiple of the patch size during feature extraction and can be represented by an integer number of tokens as the LLM input. This aims to avoid the issue of boundary spanning between key frames and non-key frames.
+
+It can be observed that when the number of $N$ -frames is too small, the effect of temporal visual prompts is poor, resulting in a lower accuracy of video understanding. This is because when the number of non-key frames is one or two, the subtle temporal variations they contain are not prominent; rather than serving as a temporal prompt, they primar
+
+| Num | 1 | 2 | 4 | 6 | 12 |
| Acc | 71.9 | 72.3 | 78.6 | 78.1 | 77.5 |
| Score | 3.3 | 3.4 | 4.2 | 3.7 | 3.7 |
+
+| Num | 1 | 2 | 4 | 6 | 8 | 16 |
| Acc | 77.0 | 77.8 | 78.6 | 78.5 | 78.5 | 77.7 |
| Score | 3.9 | 4.1 | 4.2 | 4.0 | 3.8 | 3.8 |
+
+Table 4. Ablation studies of $N$ -frame number in DynImg.
+Table 5. Ablation studies of different numbers of DynImg.
+
+| Coordinate & Operation | Acc | Score |
| 1D Coor (S) | 77.3 | 4.0 |
| 3D Coor (H,W,S) + Split (θ Fixed) | 76.8 | 4.0 |
| 3D Coor (H,W,S) + Split (θ Trainable) | 77.8 | 4.1 |
| 3D Coor (H,W,S) + Merge (θ Trainable) | 78.0 | 4.1 |
| 4D Coor (H,W,T,S) + Split (θ Fixed) | 77.0 | 4.0 |
| 4D Coor (H,W,T,S) + Split (θ Trainable) | 78.4 | 4.2 |
| 4D Coor (H,W,T,S) + Merge (θ Trainable) | 78.6 | 4.2 |
+
+Table 6. Ablation studies of different implements of position embedding. This includes the dimension of the coordinate and the operation on them. "Split" varies trigonometric values for each dimension. "Merge" means angle calculation first and addition later. "θ" is the angle embedding to multiply with coordinates, while "Fixed" means the coordinate of all dimensions shares the same "θ" that exponentially decay as the formula of "θs". "Trainable" means the $\theta_h$ , $\theta_w$ , (and the $\theta_t$ ) are trainable parameters.
+
+ily represent redundant spatial information in smaller size. When the number of $N$ -frames increases to four, the temporal information starts to play an effective prompting role, the accuracy of video understanding is the highest. As the number of non-key frames continues to increase, the effectiveness decreases. We speculate the reason for this is as follows. In order to arrange the $N$ -frames in a row, as their number increases, the size of each frame has to decrease, resulting in a reduction of information. The low resolution prevents them from effectively providing temporal prompts. Different numbers of DynImg. We also investigate the influence of the DynImg number for one video, where each DynImg consists of one keyframe and four $N$ -frames. As shown in Tab. 5, when the number of DynImages is relatively small, the video understanding performance improves as the number of DynImages increases. However, once the number of DynImages exceeds four, performance either stabilizes or declines. This is because a higher number of DynImages corresponds to a higher video sampling frequency of both $K$ -frames and $N$ -frames. This situation results in minimal temporal variation within frames in each DynImg's temporal prompt, which fails to provide effective temporal information supplementation for the nearly identical keyframe.
+
+Different implementation of position embedding. We also investigate the impact of different positional embedding methods. As a popular positional encoding method in LLMs, RoPE is computed by multiplying features $q$ with trigonometric functions based on coordinates $x$ , as is shown in Eq. 1. When the input turns from a 1D sequence to DynImg with (H,W,T,S) four dimensions, RoPE's different im
+
+plementations can be explored in two aspects. First is the coordinate representation $x$ . We can reduce the dimensions to a 1D sequence coordinate, treat DynImg as a whole image using (HWS) dimensions, or unify text and visual tokens in the 4D coordinates of DynImg. As shown in Tab.6, the accuracy improves with increasing coordinate dimensions under the same operation. This is because the closer the coordinate dimensions align with the actual information dimensions in DynImg, the better the LLM can interpret the data. This finding aligns with the description in Sec.3, affirming the need for the proposed 4D RoPE for DynImg.
+
+Second is ablation of "Operation" to angles after obtaining the coordinates. In Tab.6, "Split" means various trigonometric values for each dimension, where
+
+$$
+R = \left( \begin{array}{c} q _ {1} \\ q _ {2} \\ ... \\ q _ {7} \\ q _ {8} \end{array} \right) \otimes \left( \begin{array}{c} \cos (x _ {h} \theta_ {h}) \\ \cos (x _ {h} \theta_ {h}) \\ ... \\ \cos (x _ {s} \theta_ {s}) \\ \cos (x _ {s} \theta_ {s}) \end{array} \right) + \left( \begin{array}{c} - q _ {2} \\ q _ {1} \\ ... \\ - q _ {8} \\ q _ {7} \end{array} \right) \otimes \left( \begin{array}{c} \sin (x _ {h} \theta_ {h}) \\ \sin (x _ {h} \theta_ {h}) \\ ... \\ \sin (x _ {s} \theta_ {s}) \\ \sin (x _ {s} \theta_ {s}) \end{array} \right).
+$$
+
+"Merge" refers to converting coordinates into angles first, and then summing them, where $x \cdot \theta = x_{h} \cdot \theta_{h} + x_{w} \cdot \theta_{w} + x_{t} \cdot \theta_{t} + x_{s} \cdot \theta_{s}$ , as described in Sec3.2. In 1D RoPE, $\theta_{s}$ is an exponentially decaying fixed value derived from a formula. For 3D or 4D coordinates, we can let all dimensions share the same $\theta$ , which implies that all RoPE parameters are non-learnable, labeled as "Fix" in Tab.6. In contrast, "Trainable" indicates that $\theta_{h}, \theta_{w}$ (and $\theta_{t}$ ) are learnable parameters. It is found that fixed $\theta$ values lead to poor accuracy. This indicates that LLM cannot directly comprehend the positional encoding of the novel composition format of DynImg and requires training for progressive learning. For trainable $\theta$ in each dimension, both split trigonometric calculations and angle merging significantly enhance the performance, with angle merging offering slightly higher comprehension accuracy. This is because angle merging, by initializing $\theta_{h}, \theta_{w}$ (and $\theta_{t}$ ) to zero, allows $\theta_{s}$ to dominate during the early stages of model training. This preserves the capabilities of the pre-trained LLM in the early training phase, which benefits the model's training and inference.
+
+# 5. Conclusion
+
+We propose DynImg, a novel method for video representation. The integration of the proposed temporal prompts allows for an adjustment in the spatial attention mechanism, ensuring that temporally significant features are not overlooked. This adjustment mitigates the loss of fine-grained information prior to the spatio-temporal interaction. Furthermore, the 4D rotational positional embedding designed for DynImg preserves the correct spatiotemporal sequence and adjacency throughout the compositional process. Experimental results indicate that our DynImg is both effective and efficient, leading to enhanced video understanding.
+
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+# Dynamic Dictionary Learning for Remote Sensing Image Segmentation
+
+Xuechao Zou $^{1,2,*}$ , Yue Li $^{3,*}$ , Shun Zhang $^{3}$ , Kai Li $^{4}$ , Shiying Wang $^{3}$ , Pin Tao $^{3,4}$ , Junliang Xing $^{4}$ , Congyan Lang $^{1,2,\dagger}$ $^{1}$ School of Computer Science & Technology, Beijing Jiaotong University, China
+ $^{2}$ Key Laboratory of Big Data & Artificial Intelligence in Transportation, Ministry of Education, China
+ $^{3}$ School of Computer Technology and Application, Qinghai University, China
+ $^{4}$ Department of Computer Science and Technology, Tsinghua University, China
+
+# Abstract
+
+Remote sensing image segmentation faces persistent challenges in distinguishing morphologically similar categories and adapting to diverse scene variations. While existing methods rely on implicit representation learning paradigms, they often fail to dynamically adjust semantic embeddings according to contextual cues, leading to suboptimal performance in fine-grained scenarios such as cloud thickness differentiation. This work introduces a dynamic dictionary learning framework that explicitly models class ID embeddings through iterative refinement. The core contribution lies in a novel dictionary construction mechanism, where class-aware semantic embeddings are progressively updated via multi-stage alternating cross-attention querying between image features and dictionary embeddings. This process enables adaptive representation learning tailored to input-specific characteristics, effectively resolving ambiguities in intra-class heterogeneity and inter-class homogeneity. To further enhance discriminability, a contrastive constraint is applied to the dictionary space, ensuring compact intra-class distributions while maximizing inter-class separability. Extensive experiments across both coarse- and fine-grained datasets demonstrate consistent improvements over state-of-the-art methods, particularly in two online test benchmarks (LoveDA and UAVid). Code is available at https://github.com/XavierJiezou/D2LS.
+
+# 1. Introduction
+
+Remote sensing image segmentation aims to partition scenes into semantically consistent regions, supporting critical applications such as environmental monitoring [21], disaster assessment [18], and urban management [54]. Tra
+
+
+Figure 1. Overall pipeline of our dynamic dictionary learning. “ $\mathcal{E}$ ” and “ $\mathcal{D}$ ” denote the encoder and decoder, respectively.
+
+ditional methods often fail to address the inherent complexity of remote sensing data, including fine-grained structural variations [53] (e.g., thin and thick clouds), intra-class heterogeneity (e.g., varying cloud textures), and inter-class homogeneity (e.g., farmland and grassland) [20].
+
+Current research in remote sensing image segmentation has mainly explored three core directions. CNN-based methods like Hi-ResNet [6] and CDNet [19, 50] prioritize edge optimization and lightweight design through multiscale architectures, while Transformer-based models such as DC-Swin [45] leverage global context via self-attention. Hybrid approaches (e.g., UNetFormer [46] and Aerial-Former [20]) integrate CNN-Transformer strengths for efficient multiscale feature fusion, addressing challenges like cloud segmentation [12, 26] and domain adaptation [53].
+
+Despite these developments, existing methods still face notable issues when confronted with high intra-class heterogeneity and inter-class similarity in remote sensing images. Specifically, most approaches rely on implicit representation learning, which often fails to adapt to subtle morphological or textural differences, such as differentiating thin vs. thick clouds [53] or distinguishing visually similar urban objects [20]. Furthermore, while attention mechanisms [2, 13, 22, 42] capture global context, they do
+
+not inherently ensure discriminative class-specific feature representations, leading to confusion among closely related categories. This limitation becomes more pronounced in fine-grained segmentation tasks [14, 53], where even minor appearance variations within a class can significantly affect model performance. These shortcomings highlight the need to encode class-aware embeddings explicitly.
+
+To overcome these limitations, we propose a dynamic dictionary learning framework that explicitly constructs and refines class ID embeddings through iterative interactions between image features and semantic dictionaries. Our key innovations are as follows:
+
+- We propose a dynamic dictionary learning framework that explicitly models class-aware semantic embeddings and leverages a contrastive loss to enhance intra-class compactness and inter-class separability, thereby improving performance, particularly in fine-grained remote sensing image segmentation tasks.
+- We develop a modulator to convert the static dictionary into a dynamic one by generating attention maps from high-level semantic features, enabling input-specific adaptation and capturing subtle morphological variations within the same class.
+- We design a multi-stage alternating cross-attention query decoder that progressively refines both image features and the semantic dictionary iteratively, facilitating mutual optimization and leading to more accurate and robust segmentation outcomes.
+
+# 2. Related Work
+
+# 2.1. Remote Sensing Image Segmentation
+
+Remote sensing image segmentation methods can be categorized as coarse- and fine-grained approaches. Coarse-grained segmentation focuses on large-scale semantic understanding of scenes, such as urban landscapes and land-cover classification. Recent advances have integrated Transformers and convolutional neural networks (CNNs) to capture global context and local details. For example, UNetFormer [46] employs a lightweight ResNet encoder and a Transformer-based decoder for real-time urban scene segmentation, while Hi-ResNet [6] enhances edge details through multiscale branches and class-agnostic edge-aware loss. AerialFormer [20] combined hierarchical Transformers with multi-dilated CNNs to address challenges like object density and intra-class heterogeneity. Other studies, such as BANet [44] and ABCNet [29], further optimized feature fusion and computational efficiency through bilateral context modeling and lightweight architectures.
+
+Fine-grained segmentation targets the precise delineation of objects such as thin and thick clouds. Cloud detection methods often leverage dual-branch architectures to balance spatial details and semantic context. DBNet
+
+[34] uses a Transformer-CNN hybrid with mutual guidance modules to refine cloud boundaries, and HRCloudNet [26] integrates hierarchical high-resolution features for complex cloud textures. MCDNet [12] addresses thin cloud detection via dual-perspective change-guided mechanisms. In contrast, lightweight models like SCNN [3] and CDNet series [19, 50] reduce computational costs using shallow networks or attention-based refinement. Recent domain adaptation frameworks, such as KTDA [53], further enhance generalization by aligning features across domains. These methods collectively advance fine-grained segmentation accuracy. However, most existing methods struggle to distinguish morphologically similar classes, resulting in ambiguous predictions for fine-grained scenarios. To address this, we propose a dynamic dictionary learning framework that explicitly models class-aware embeddings, thereby enabling a more robust discrimination of related categories.
+
+# 2.2. Transformer and Attention Mechanisms
+
+Transformer-based approaches such as DETR [2] reformulate object detection as a set prediction task, eliminating hand-crafted components like anchors and NMS. Subsequent works like DETR-style methods [9, 10, 36, 56] optimize query mechanisms and attention patterns to accelerate convergence and improve accuracy. For segmentation, MaskFormer [7, 8] unifies various segmentation tasks through mask classification, while SegViT [51, 52] and SegFace [37] leverage class tokens for semantic mask generation. These methods demonstrate the Transformer's versatility in dense prediction tasks.
+
+Attention mechanisms [27, 28, 57, 58] play a pivotal role in enhancing feature discrimination and cross-modal interactions. Channel attention modules like SENet [22], CBAM [48], and ECANet [47] adaptively recalibrate channel-wise features, improving representation capacity. Cross-attention enables dynamic information exchange between heterogeneous data, as seen in CCNet [23] for crisscross context aggregation. Such mechanisms also drive vision foundational models like Segment Anything [25], which utilizes prompt-based cross-attention for zero-shot segmentation. The synergy of diverse attention variants continues to push the boundaries of visual understanding systems. Inspired by DETR-style approaches and attention mechanisms, we explicitly model semantic labels with a learnable dictionary, further enabling progressive optimization via multi-stage alternating cross-attention, thereby effectively distinguishing morphologically similar classes.
+
+# 3. Method
+
+# 3.1. Overall Pipeline
+
+The overall pipeline for our framework (see Fig. 1) can be divided into two key parts: training and inference.
+
+
+
+
+(a) Model architecture of the proposed network.
+(b) Detailed structure of the modulator.
+
+
+(c) Detailed structure of the aggregator.
+Figure 2. Overview of the proposed network architecture. Notably, we show only the dynamic branch for brevity.
+
+# 3.1.1. Training
+
+During training, the pipeline employs a dual-branch architecture: the encoder $\mathcal{E}$ processes the input image $\mathbf{X} \in \mathbb{R}^{3 \times H \times W}$ and distributes the extracted features $\mathbf{F} \in \mathbb{R}^{C' \times H' \times W'}$ to two parallel branches: the static and dynamic branches. The static branch generates segmentation maps using a fixed static dictionary produced by a dictionary generator, while the dynamic branch operates with a continuously updated dynamic dictionary throughout training. Both branches share the same decoder. These processes can be formulated as:
+
+$$
+\mathbf {F} = \mathcal {E} (\mathbf {X}), \quad \mathbf {O} _ {\mathbf {s}} = \mathcal {D} (\mathbf {D} _ {\mathbf {s}}, \mathbf {F}), \quad \mathbf {O} _ {\mathbf {d}} = \mathcal {D} (\mathbf {D} _ {\mathbf {d}}, \mathbf {F}), \tag {1}
+$$
+
+where $\mathcal{E}(\cdot)$ and $\mathcal{D}(\cdot, \cdot)$ denote the encoder and decoder, respectively. $\mathbf{D}_{\mathbf{s}} \in \mathbb{R}^{N \times C'}$ and $\mathbf{D}_{\mathbf{d}} \in \mathbb{R}^{N \times C'}$ represent the static and dynamic dictionaries, while $\mathbf{O}_{\mathbf{s}} \in \mathbb{R}^{N \times H \times W}$ and $\mathbf{O}_{\mathbf{d}} \in \mathbb{R}^{N \times H \times W}$ are the segmentation outputs from the static and dynamic branches. $\mathbf{N}$ is the number of semantic categories, $H$ , $W$ , and $C'$ denote the height, width of the image, and the number of feature channels, respectively.
+
+In the training process, we achieve joint optimization by minimizing the loss functions of the static and dynamic branches, namely $\mathcal{L}_{\mathrm{static}}$ and $\mathcal{L}_{\mathrm{dynamic}}$ . The total loss function is defined as a weighted sum of the individual losses:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {\text {s t a t i c}} \cdot \mathcal {L} _ {\text {s t a t i c}} + \lambda_ {\text {d y n a m i c}} \cdot \mathcal {L} _ {\text {d y n a m i c}}, \tag {2}
+$$
+
+where $\lambda_{\mathrm{static}} = 0.4$ and $\lambda_{\mathrm{dynamic}} = 1$ are the default hyperparameters. During training, the network is optimized by minimizing the total loss $\mathcal{L}_{\mathrm{total}}$ .
+
+The loss for the static branch, $\mathcal{L}_{\mathrm{static}}$ , is composed of a weighted sum of the cross-entropy loss and the Dice loss,
+
+which is a common design in segmentation tasks [24, 37]:
+
+$$
+\mathcal {L} _ {\text {s t a t i c}} = \mathcal {L} _ {\mathrm {c e}} \left(\mathbf {O} _ {\mathrm {s}}, \mathbf {Y}\right) + \mathcal {L} _ {\mathrm {d i c e}} \left(\mathbf {O} _ {\mathrm {s}}, \mathbf {Y}\right), \tag {3}
+$$
+
+where $\mathbf{O}_{\mathrm{s}}$ denotes the segmentation prediction from the static branch, and $\mathbf{Y} \in \mathbb{R}^{N \times H \times W}$ represents the ground truth segmentation label. The cross-entropy loss is employed for per-pixel classification. In contrast, the Dice loss focuses on the overlapping regions between the predicted and the ground truth segmentation maps, effectively mitigating the class imbalance problem, which is particularly important for segmentation tasks involving long-tail classes.
+
+For the dynamic branch, the loss $\mathcal{L}_{\mathrm{dynamic}}$ not only includes the same loss terms as the static branch but also incorporates a dictionary-based contrastive loss [39] to ensure the embedding representations for each class are unique and discriminative. Specifically, the dynamic loss is defined as:
+
+$$
+\mathcal {L} _ {\text {d y n a m i c}} = \mathcal {L} _ {\mathrm {c e}} \left(\mathbf {O} _ {\mathrm {d}}, \mathbf {Y}\right) + \mathcal {L} _ {\mathrm {d i c e}} \left(\mathbf {O} _ {\mathrm {d}}, \mathbf {Y}\right) + \mathcal {L} _ {\mathrm {c o n}} \left(\mathbf {D} _ {\mathrm {d}}\right). \tag {4}
+$$
+
+Moreover, the contrastive loss $\mathcal{L}_{\mathrm{con}}$ consists of an intra-class compactness loss $\mathcal{L}_{\mathrm{intra}}$ and an inter-class dispersion loss $\mathcal{L}_{\mathrm{inter}}$ :
+
+$$
+\mathcal {L} _ {\text {c o n}} = \frac {\mathcal {L} _ {\text {i n t r a}}}{\mathcal {L} _ {\text {i n t e r}} + \epsilon}, \tag {5}
+$$
+
+where $\epsilon = 10^{-6}$ is used to prevent division by zero. The intra-class compactness loss measures the average Euclidean distance between the samples and their corresponding class centers:
+
+$$
+\mathcal {L} _ {\text {i n t r a}} = \frac {1}{B \cdot N} \sum_ {i = 1} ^ {N} \sum_ {b = 1} ^ {B} \| \mathbf {D} _ {\mathbf {d}} ^ {(b, i)} - \boldsymbol {\mu} _ {i} \| _ {2} ^ {2}, \tag {6}
+$$
+
+where $B$ denotes the batch size, $N$ is the total number of classes, and $\mathbf{D}_{\mathrm{d}}^{(\mathbf{b},\mathbf{i})}$ represents the embedding of the $b$ -th sample in class $i$ . The class center $\pmb{\mu}_i$ is computed as:
+
+$$
+\boldsymbol {\mu} _ {i} = \frac {1}{B} \sum_ {b = 1} ^ {B} \mathbf {D} _ {\mathrm {d}} ^ {(b, i)}. \tag {7}
+$$
+
+The inter-class dispersion loss aims to maximize the pairwise Euclidean distance between different class centers to enhance class separability:
+
+$$
+\mathcal {L} _ {\text {i n t e r}} = \frac {2}{N (N - 1)} \sum_ {i = 1} ^ {N - 1} \sum_ {j = i + 1} ^ {N} \| \boldsymbol {\mu} _ {i} - \boldsymbol {\mu} _ {j} \| _ {2} ^ {2}. \tag {8}
+$$
+
+The double summation iterates over all possible pairs of classes, ensuring adequate separation between them.
+
+# 3.1.2. Inference
+
+The network uses only the dynamic branch during inference, which utilizes the dynamic dictionary learned during training. The encoder processes the input image and generates feature maps, which are passed to the dynamic branch. The decoder then generates the segmentation maps. The dynamic dictionary complements the static dictionary by adaptively capturing the input-specific patterns, thereby improving the model's generalization to unseen data.
+
+# 3.2. Proposed Network
+
+The proposed network architecture (see Fig. 2) consists of an encoder, a dictionary generator, and a decoder, each playing a critical role in extracting features, learning dynamic dictionaries, and generating accurate segmentation maps.
+
+# 3.2.1. Encoder
+
+The encoder (as shown in Fig. 2a1) is responsible for extracting feature representations from the input image. Initially, the input image $\mathbf{X}$ is processed by a backbone, generating multi-scale feature maps $\{\mathbf{F}_i\in \mathbb{R}^{C_i\times H_i\times W_i}\}_{i = 1}^4$ where $W_{i} = \frac{W}{2^{i}}$ , $H_{i} = \frac{H}{2^{i}}$ , and $C_i = C\times 2^i$ . These feature maps are then passed through the aggregator, which performs feature mapping (Eq. (9)) and aggregation (Eq. (10)). The feature mapping step involves channel transformations, implemented by a multi-layer perceptron (MLP), and upsample interpolation to align all feature maps to the same dimensionality. After the mapping and interpolation, an MLP aggregates the features. The final output from the encoder is passed to the dictionary generator and the decoder.
+
+$$
+\mathbf {F} _ {i} ^ {\prime} = \phi (\operatorname {M L P} (\mathbf {F} _ {i})), \quad i \in \{1, 2, 3, 4 \} \tag {9}
+$$
+
+$$
+\mathbf {E} _ {0} = \operatorname {M L P} \left(\mathbf {F} _ {1} ^ {\prime} \| \mathbf {F} _ {2} ^ {\prime} \| \mathbf {F} _ {3} ^ {\prime} \| \mathbf {F} _ {4} ^ {\prime}\right), \tag {10}
+$$
+
+where $\{\mathbf{F}_i' \in \mathbb{R}^{C' \times H' \times W'}\}_{i=1}^4$ are the feature maps after feature mapping, and $H' = H_1, W' = W_1$ . $\phi(\cdot)$ denotes the interpolation function. "||" represents the concatenation operation along the channel dimension, and $\mathbf{E}_0 \in \mathbb{R}^{C' \times H' \times W'}$ is the final aggregated feature map.
+
+# 3.2.2. Dictionary Generator
+
+The dictionary generator is the core component of the proposed network and is responsible for creating static and dynamic dictionaries used in segmentation. These dictionaries help map feature information to class identifiers, enabling the model to distinguish different classes. The dynamic dictionary adapts during inference by modulating the static dictionary with input-specific attention. Unlike its static counterpart, it adjusts class ID embeddings to capture morphological variations across images, enhancing representation for nuanced inter-class distinctions.
+
+Static Dictionary The static dictionary is a set of class ID embeddings used during the early stages of training. Each class ID embedding is associated with a learnable vector within the static dictionary. Once trained, these vectors are kept constant and do not change with input images, making them "static." As a result, the static dictionary remains unchanged during inference. The static dictionary can be represented as:
+
+$$
+\mathbf {D} _ {\mathrm {s}} = \left\{0: \mathbf {V} _ {0}, 1: \mathbf {V} _ {1}, \dots , \mathbf {N} - 1: \mathbf {V} _ {\mathbf {N} - 1} \right\}, \tag {11}
+$$
+
+where $\mathbf{D}_s\in \mathbb{R}^{N\times C'}$ denotes the static dictionary, class index serves as the key, and $\mathbf{V}_i\in \mathbb{R}^{C'}$ represents the embedding vector corresponding to the $i$ -th class, which is the value in the dictionary. $\mathbf{N}$ is the number of classes.
+
+Dynamic Dictionary The modulator (Fig. 2b) produces an attention map from encoder features to convert the static dictionary into a dynamic dictionary. The feature map $\mathbf{F} \in \mathbb{R}^{C_i \times H_i \times W_i}$ extracted from the encoder is first processed through an MLP layer. Specifically, we define $\mathbf{F} = \mathbf{F}_4$ , which encapsulates high-level semantic information. Subsequently, $\mathbf{F}$ is split along the channel dimension into two separate chunks. One chunk undergoes global average pooling (GAP) followed by an MLP, while the other is processed through global max pooling (GMP) and a separate MLP. The outputs from these two branches are then concatenated along the channel dimension and fed into another MLP. Finally, the resulting feature representation is normalized using the softmax function, generating the attention map.
+
+$$
+\mathbf {A} _ {\text {a v g}} = \operatorname {M L P} \left(\operatorname {G A P} \left(\mathbf {F} _ {\text {a v g}}\right)\right), \mathbf {A} _ {\max } = \operatorname {M L P} \left(\operatorname {G M P} \left(\mathbf {F} _ {\max }\right)\right), \tag {12}
+$$
+
+where $\mathbf{F}_{\mathrm{avg}}\in \mathbb{R}^{\frac{C_i}{2}\times H_i\times W_i}$ and $\mathbf{F}_{\mathrm{max}}\in \mathbb{R}^{\frac{C_i}{2}\times H_i\times W_i}$ represent the two chunks of the feature map $\mathbf{F}$ . After concatenating the results of $\mathbf{A}_{\mathrm{avg}}\in \mathbb{R}^{\frac{C_i}{2}}$ and $\mathbf{A}_{\mathrm{max}}\in \mathbb{R}^{\frac{C_i}{2}}$ , the final attention map $\mathbf{A}$ is computed as:
+
+$$
+\mathbf {A} = \operatorname {S o f t m a x} \left(\operatorname {M L P} \left(\mathbf {A} _ {\text {a v g}} \| \mathbf {A} _ {\max }\right)\right), \tag {13}
+$$
+
+where $\mathbf{A} \in \mathbb{R}^{N \times r}$ denotes the attention map, and $r = 4$ represents the reduced dimensionality. The static dictionary $\mathbf{D}_{\mathrm{s}}$ is then transformed into the dynamic dictionary $\mathbf{D}_0 \in \mathbb{R}^{N \times C'}$ by matrix multiplication with the attention map $\mathbf{A}$ :
+
+$$
+\mathbf {D} _ {0} = \operatorname {M L P} \left(\mathbf {D} _ {\mathrm {s}}\right) \otimes \mathbf {A}, \tag {14}
+$$
+
+where $\mathbf{D}_0$ denotes the initial dynamic dictionary, $\otimes$ denotes matrix multiplication. The initial dynamic dictionary is then passed to the decoder for iterative interaction and updates.
+
+# 3.2.3. Decoder
+
+In the decoder, the dynamic dictionary $\mathbf{D}_0$ and the image feature map $\mathbf{E}_0$ interact over $\mathbf{L}$ stages for progressive optimization. During each stage, the dynamic dictionary and image feature alternately perform cross-attention queries, allowing for updates for both. The iterative process is:
+
+$$
+\mathbf {D} _ {l} \in \mathbb {R} ^ {N \times C ^ {\prime}} = \operatorname {s o f t m a x} \left(\frac {\mathbf {D} _ {l - 1} \mathbf {E} _ {l - 1} ^ {\top}}{\sqrt {d _ {k}}}\right) \mathbf {E} _ {l - 1}, \quad (\mathrm {D q u e r i e s E})
+$$
+
+$$
+\mathbf {E} _ {l} \in \mathbb {R} ^ {C ^ {\prime} \times H ^ {\prime} \times W ^ {\prime}} = \operatorname {s o f t m a x} \left(\frac {\mathbf {E} _ {l - 1} \mathbf {D} _ {l} ^ {\top}}{\sqrt {d _ {k}}}\right) \mathbf {D} _ {l}, \quad (\text {E q u e r i e s D}) \tag {15}
+$$
+
+where $l \in [1, \mathbf{L}]$ denotes the optimization stage. This alternating mechanism enables mutual enhancement between the dynamic dictionary and image features. Once the final feature map $\mathbf{E}_{\mathbf{L}}$ is obtained after $\mathbf{L}$ stages, the feature map is upsampled. Matrix multiplication is applied between the upsampled feature map and the dictionary $\mathbf{D}_{\mathbf{L}}$ to produce the final segmentation output:
+
+$$
+\hat {\mathbf {Y}} = \phi \left(\mathbf {E} _ {\mathbf {L}}\right) \otimes \operatorname {M L P} \left(\mathbf {D} _ {\mathbf {L}}\right), \tag {16}
+$$
+
+where $\hat{\mathbf{Y}}\in \mathbb{R}^{N\times H\times W}$ represents the final output.
+
+# 4. Experiments
+
+# 4.1. Datasets
+
+We evaluated our method on six remote sensing datasets for semantic segmentation, spanning a range of altitudes from UAV to satellite imagery. These datasets include coarse-grained (LoveDA [43], UAVid [35], Potsdam [15], Vaihingen [16]) and fine-grained (Cloud [14], Grass [53]) categories. For data splitting and preprocessing, the LoveDA, UAVid, Vaihingen, and Potsdam datasets follow the same protocol as in [24, 46]. In contrast, the Grass and Cloud datasets adopted preprocessing strategies identical to those
+
+used in [53]. LoveDA and UAVid are notably used in online test scenarios where ground truth labels are unavailable. For more details, please refer to Appendix A.
+
+# 4.2. Implementation Details
+
+Experimental Setup We set the size of the class ID embedding to 256 and the frequency of progressive optimization, denoted as $\mathbf{L}$ , to 3. The backbone model was ConvNeXt-Base [31]. The training configuration utilized a batch size of 4, with the random seed fixed at 42 to ensure reproducibility. The optimizer was AdamW [33], with an initial learning rate set to $1 \times 10^{-4}$ and weight decay set to 0.01. The learning rate was dynamically adjusted using a cosine annealing scheduler. All experiments were conducted on a workstation equipped with an NVIDIA A100.
+
+Evaluation Metrics We followed the evaluation protocols of the comparative methods [20, 24]: Overall Accuracy (OA), intersection over union (IoU), F1 score, mean IoU (mIoU), and mean F1 (mF1). mIoU and mF1 are the averages of IoU and F1 scores across all classes. For readability, all metrics are presented in percentage form. Metric details and their formal definitions are provided in Appendix B.
+
+# 4.3. Ablation Study
+
+Effectiveness of Explicit Class Modeling As quantified in Tab. 1, our analysis reveals that implicit representation learning (by removing the dictionary generator) leads to consistent performance degradation (mIoU) across all datasets. The particularly pronounced impact on fine-grained segmentation tasks substantiates the effectiveness of explicit class modeling in the framework. Furthermore, additional ablation studies on the dimensionality of class ID embeddings and the backbone are available in Appendix C.
+
+Table 1. Effectiveness of explicit class modeling.
+
+| Dictionary Generator | mIoU ↑ |
| LoveDA | Vaihingen | Grass |
| × | 54.81 | 84.40 | 50.70 |
| ✓ | 55.27 | 85.27 | 51.96 |
+
+Static Branch vs. Dynamic Branch Tab. 2 revealed the complementary roles of the loss function in different branches. Using only static loss (static branch) yields limited performance, while adding dynamic loss (dynamic branch) improves segmentation performance. The contrastive loss provides critical discrimination power - its inclusion boosts Grass performance by $+0.43$ , with LoveDA/Vaihingen also peaking at 55.27/85.27. These results confirm that the dynamic branch is more effective and that jointly optimizing both branches with contrastive loss consistently yields the best performance.
+
+
+Figure 3. t-SNE visualization of dictionary distributions across different interaction stages.
+
+
+
+
+
+
+
+
+
+Table 2. Ablation study on loss function of different branches.
+
+| Method | mIoU ↑ |
| LoveDA | Vaihingen | Grass |
| Lstatic | 54.80 | 85.10 | 50.96 |
| Ldynamic | 54.93 | 85.17 | 51.38 |
| Lstatic + Ldynamic (w/o Lcon) | 54.95 | 85.17 | 51.53 |
| Lstatic + Ldynamic (w/ Lcon) | 55.27 | 85.27 | 51.96 |
+
+Table 3. Performance comparison across interaction stages.
+
+| L | mIoU ↑ | mF1 ↑ |
| LoveDA | UAVid | Grass | Cloud | Potsdam | Vaihingen |
| 1 | 54.84 | 68.79 | 51.05 | 83.09 | 93.29 | 91.83 |
| 2 | 55.00 | 69.49 | 51.21 | 82.95 | 94.09 | 91.88 |
| 3 | 55.27 | 70.90 | 51.50 | 83.10 | 94.70 | 91.76 |
| 4 | 54.84 | 67.88 | 50.90 | 80.97 | 93.87 | 91.85 |
+
+Interaction Stages The feature-dictionary interaction stages progressively update class-aware semantic embeddings through multi-stage alternating cross-attention between image features and the dictionary. Experiments in Tab. 3 showed dataset-specific preferences: $\mathbf{L} = 3$ yields optimal performance on most datasets, including LoveDA, UAVid, Grass, and Cloud, while $\mathbf{L} = 2$ suffices for Vaihingen (91.88 mF1). Excessive stages ( $\mathbf{L} = 4$ ) reduce segmentation performance on the Cloud dataset, indicating overfitting risks. Visualization of t-SNE (Fig. 3) on the Grass dataset quantifies dictionary evolution: intra-class distances tighten ( $\mathbf{D}_0: 33.61 \to \mathbf{D}_3$ : 28.51), while inter-class distances increase. We selected $\mathbf{L} = 3$ as the default, balancing model performance and computational efficiency.
+
+Effectiveness of Each Component We systematically validated the necessity of each component by disabling individual components. As shown in Tab. 4, removing the modulator resulted in the most substantial decline in segmentation performance on the Vaihingen dataset, highlighting its critical role in handling complex urban scenes. Disabling the aggregator leads to the most significant performance drop on the Grass dataset, indicating its importance
+
+for fine-grained feature integration. The interactor contributed consistently across all datasets, demonstrating its capacity to refine ambiguous boundaries. The full model achieved peak performance, proving that these modules provide complementary functionalities rather than isolated improvements. This comprehensive ablation validates that all components are essential for segmentation performance.
+
+Table 4. Effectiveness of each component. Mod., Agg., and Int. denote modulator, aggregator, and interaction, respectively.
+
+| Mod. | Agg. | Int. | mIoU ↑ |
| LoveDA | Vaihingen | Grass |
| × | ✓ | ✓ | 54.95 | 85.17 | 51.35 |
| ✓ | × | ✓ | 54.66 | 82.54 | 48.52 |
| ✓ | ✓ | × | 54.55 | 85.14 | 50.95 |
| ✓ | ✓ | ✓ | 55.27 | 85.27 | 51.96 |
+
+# 4.4. Comparison with SOTA Methods
+
+Quantitative Analysis Our method achieved consistent SOTA performance on six remote sensing semantic segmentation benchmarks. It also balances efficiency and performance well, with detailed computational efficiency comparisons (parameter count and FLOPs) in Appendix D.
+
+Coarse-grained Segmentation Our method achieved state-of-the-art performance across all coarse-grained datasets. On the LoveDA dataset (Tab. 5), we surpassed SFA-Net by $+0.4\%$ mIoU, particularly in challenging categories like agriculture and building. The UAVid results (Tab. 6) further validated our superiority in dynamic urban scenes, achieving $70.9~\mathrm{mIoU}$ by learning distinct representations for different categories. For high-resolution aerial datasets, our approach established new benchmarks on Potsdam and Vaihingen (Tab. 7), with dominant performance in large-scale segmentation scenes.
+
+Fine-grained Segmentation As shown in Tab. 8, our method demonstrates remarkable advantages in distinguishing subtle class variations. On the Grass dataset, we achieve $66.27\mathrm{mF1}$ , with significant gains in differentiating coverage grades. For the Cloud dataset, our approach establishes an absolute lead, benefiting from the dynamic dictionary's adaptability to image feature variations. The $89.65\mathrm{mF1}$ on
+
+Table 5. Comparison of semantic segmentation performance on the LoveDA dataset.
+
+| Method | Background | Building | Road | Water | Barren | Forest | Agriculture | mIoU ↑ |
| TransUNet [4] | 43.0 | 56.1 | 53.7 | 78.0 | 9.3 | 44.9 | 56.9 | 48.9 |
| DC-Swin [45] | 41.3 | 54.5 | 56.2 | 78.1 | 14.5 | 47.2 | 62.4 | 50.6 |
| UNetFormer [46] | 44.7 | 58.8 | 54.9 | 79.6 | 20.1 | 46.0 | 62.5 | 52.4 |
| Hi-Resnet [6] | 46.7 | 58.3 | 55.9 | 80.1 | 17.0 | 46.7 | 62.7 | 52.5 |
| AerialFormer [20] | 47.8 | 60.7 | 59.3 | 81.5 | 17.9 | 47.9 | 64.0 | 54.1 |
| SFA-Net [24] | 48.4 | 60.3 | 59.1 | 81.9 | 24.1 | 46.2 | 64.0 | 54.9 |
| Ours | 47.6 | 61.2 | 59.1 | 81.6 | 23.8 | 48.8 | 64.8 | 55.3 |
+
+Table 6. Comparison of semantic segmentation performance on the UAVid dataset.
+
+| Method | Clutter | Building | Road | Tree | Vegetaion | Moving Car | Static Car | Human | mIoU ↑ |
| DANet [17] | 64.9 | 58.9 | 77.9 | 68.3 | 61.5 | 59.6 | 47.4 | 9.1 | 60.6 |
| ABCNet [29] | 67.4 | 86.4 | 81.2 | 79.9 | 63.1 | 69.8 | 48.4 | 13.9 | 63.8 |
| BANet [44] | 66.7 | 85.4 | 80.7 | 78.9 | 62.1 | 69.3 | 52.8 | 21.0 | 64.6 |
| SegFormer [49] | 66.6 | 86.3 | 80.1 | 79.6 | 62.3 | 72.5 | 52.5 | 28.5 | 66.0 |
| UNetFormer [46] | 68.4 | 87.4 | 81.5 | 80.2 | 63.5 | 73.6 | 56.4 | 31.0 | 67.8 |
| SFA-Net [24] | 70.2 | 89.0 | 82.7 | 80.8 | 64.6 | 77.5 | 67.5 | 30.7 | 70.4 |
| Ours | 71.0 | 89.7 | 83.2 | 82.1 | 66.1 | 75.0 | 59.0 | 41.4 | 70.9 |
+
+Table 7. Comparison of semantic segmentation performance on the Potsdam and Vaihingen datasets.
+
+| Method | mF1 ↑ |
| Potsdam | Vaihingen | Average |
| DANet [17] | 88.9 | 79.6 | 84.3 |
| ABCNet [29] | 92.7 | 89.5 | 91.1 |
| Segmenter [41] | 89.2 | 84.1 | 86.7 |
| BANet [44] | 92.5 | 89.6 | 91.1 |
| SwinUperNet [30] | 92.2 | 89.8 | 91.0 |
| DC-Swin [45] | 93.3 | 90.7 | 92.0 |
| UNetFormer [46] | 93.5 | 90.4 | 92.0 |
| AerialFormer [20] | 94.1 | 90.1 | 92.1 |
| SFA-Net [24] | 93.5 | 91.2 | 92.4 |
| Ours | 94.7 | 91.9 | 93.3 |
+
+Cloud highlights our capacity to resolve ambiguous boundaries through dynamic dictionary learning. These results collectively confirm that our dynamic dictionary learning paradigm adapts effectively to large-scale scene variations and fine-grained semantic distinctions.
+
+Visualization Results As shown in Fig. 4, our method accurately segments dome-shaped buildings in LoveDA, captures tiny human targets in UAVid without interference from vegetation and clutter, and correctly identifies rough road surfaces in Potsdam despite ground truth mislabeling. Additionally, it enables precise cloud-type separation in Cloud
+
+and enhances vegetation classification in Grass (Fig. 5). More visualization results can be found in Appendix E.
+
+Table 8. Comparison of semantic segmentation performance on the two fine-grained datasets.
+
+(a) Grass
+
+| Method | mF1 ↑ |
| FCN [32] | 61.99 |
| PSPNet [55] | 62.55 |
| DeepLabV3+ [5] | 62.50 |
| UNet [40] | 62.34 |
| SegFormer [49] | 62.82 |
| Mask2Former [8] | 58.91 |
| DINOv2 [38] | 61.70 |
| KTDA [53] | 65.01 |
| SFA-Net [24] | 65.76 |
| Ours | 66.27 |
+
+(b) Cloud
+
+| Method | mF1 ↑ |
| MCDNet [12] | 42.76 |
| SCNN [3] | 52.41 |
| CDNetv1 [50] | 45.80 |
| KappaMask [11] | 68.47 |
| UNetMobv2 [1] | 56.91 |
| CDNetv2 [19] | 70.33 |
| HRCloudNet [26] | 71.36 |
| KTDA [53] | 60.08 |
| SFA-Net [24] | 84.64 |
| Ours | 89.65 |
+
+# 5. Conclusion
+
+In this paper, we propose a dynamic dictionary learning framework to address the limitations of distinguishing similar categories in complex scenes caused by implicit representation learning in remote sensing image segmentation. Our method adaptively models morphological variations while preserving semantic discriminability by iteratively refining class-aware ID embeddings through alternating cross-attention querying and contrastive constraints.
+
+
+Figure 4. Visualized results on four coarse-grained datasets. Ground truth labels are unavailable in the LoveDA and UAVid datasets.
+
+
+Figure 5. Visualized results on two fine-grained datasets. More visualization of comparative methods can be found in Appendix E.
+
+# Acknowledgments
+
+This work was supported by the Beijing Natural Science Xiaomi Innovation Joint Foundation (No. L253007), and in part by the Natural Science Foundation of China under Grant No. 62222606.
+
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+# Dynamic Group Detection using VLM-augmented Temporal Groupness Graph
+
+Kaname Yokoyama Chihiro Nakatani Norimichi Ukita Toyota Technological Institute
+
+{sd25444, sd23501, ukita}@toyota-ti.ac.jp
+
+# Abstract
+
+This paper proposes dynamic human group detection in videos. For detecting complex groups, not only the local appearance features of in-group members but also the global context of the scene are important. Such local and global appearance features in each frame are extracted using a Vision-Language Model (VLM) augmented for group detection in our method. For further improvement, the group structure should be consistent over time. While previous methods are stabilized on the assumption that groups are not changed in a video, our method detects dynamically changing groups by global optimization using a graph with all frames' groupness probabilities estimated by our groupness-augmented CLIP features. Our experimental results demonstrate that our method outperforms state-of-the-art group detection methods on public datasets.
+
+Code: https://github.com/irajisamurai/VLM-GroupDetection.git
+
+# 1. Introduction
+
+To understand human social activities, the structure of human groups is a good cue because in-group members share a common purpose and/or behavior. For example, the group structure is used for group activity recognition [13, 27, 36], trajectory prediction [4, 6, 39, 46], and anomaly detection [9]. For group detection (e.g., Fig. 1), interactions among in-group members should be recognized. While the dominant cue for recognizing such human interactions is the spatial relationship of people, various human attributes, such as face directions and postures, are also useful.
+
+While the human attributes mentioned above can be recognized from the local appearance of each person, the spatial context observed in the image also provides helpful cues for group detection. The usefulness of the spatial context is validated in various tasks, such as object detection [2, 24, 49, 55] and individual action recognition [12, 41, 42]. However, compared with these tasks that employ a relationship between each person and the scene, group detection is more difficult because it requires a com
+
+
+(a)
+
+
+(b)
+
+
+Figure 1. Effects of our method. People enclosed with the same color are detected as in-group members. (a) Our method using the spatial scene context can detect two in-group members because they are not facing each other but browsing the same background object. (b) Our method can detect dynamic group structures so that a group of three members in $t_1$ splits into two groups in $t_2$ .
+
+
+
+plex relationship between multiple people and the scene (e.g., Fig. 1 (a)), which is called spatial scene context.
+
+In addition to the spatial scene context, the temporal scene context is useful. For example, in the previous group detection methods [5, 16, 22, 26, 31, 43, 50], group detection is stabilized under an assumption that the set of all groups is fixed (i.e., not changed) throughout a video. We call this group detection, in which only a single representative set of groups through a video is detected, static group detection. However, people often go back and forth between different groups. Static group detection can detect dynamically changing groups by dividing a video into short clips in each of which the group structure is not changed. However, since we do not know the frames in which the group structure changes, it is impossible to divide a video into appropriate short clips by pre-processes; it is a chicken-and-egg problem. Therefore, this paper aims at jointly achieving stabilization of group detection and detection of dynamically changing groups by employing the temporal scene context in a video. We call this group detection, in which a set of temporal structures of dynamically changing groups is detected, dynamic group detection (e.g., Fig. 1 (b)).
+
+
+Figure 2. Bounding boxes fed into the feature extractor. (a) Ours: a bounding box includes a pair of circled people and the background. (b) Previous methods [22, 50]: each person's bounding box is independently extracted.
+
+To learn the spatial scene context, our method extracts image features from a bounding box, including people and the background (Fig. 2 (a)), to gain two advantages compared to previous methods [14, 22, 50]. (1) In [14, 22, 50], the features of each person are extracted independently, then the extracted features of people are compared and/or merged to estimate their groupness. Our method directly estimates the groupness from a bounding box including them. (2) Not only the local features of people but also the spatial scene context, including the background, are used. To understand a group structure based on the spatial scene context from the bounding box mentioned above, this paper proposes to augment a Vision-Language Model (VLM), such as CLIP [32], as visual features.
+
+Such visual features are extracted independently in each frame of a video in our method, following previous methods [5, 16, 22, 26, 31, 43, 50]. However, unlike the previous methods in which the detected groups of all frames are merged (e.g., averaged), our method temporally connects the features of all frames for dynamic group detection to employ the temporal scene context.
+
+The contributions of this paper are as follows:
+
+- In each frame, the spatial scene context expressing complex interactions extracted by a VLM (i.e., CLIP) is used to estimate the so-called groupness probability to express whether or not each pair is in the same group. Our augmented CLIP features outperform visual feature extractors trained only with images, such as DINOv2 [29], and improve the framewise group detection, resulting in better static and dynamic group detections.
+- Frameworkwise groupness probabilities are temporally connected to construct a graph representing the temporal scene context. This graph, called a temporal groupness graph as contrasted with a static groupness graph generated by merging all frames for static group detection, is divided into dynamic groups: see Fig. 5.
+- The results of dynamic group detection using our method can be easily converted to those of static group detection.
+- Our experiments on public datasets demonstrate that our method outperforms state-of-the-art methods in various aspects of the static and dynamic detection tasks.
+
+# 2. Related Work
+
+# 2.1. Group Detection
+
+In the group detection task, all observed people are divided into groups, including those each of which consists of only one person. Unlike dense crowd tracking [23, 52, 53] in which particle-like crowd flows are represented as a set of feature points, group detection groups all individuals
+
+Early work on group detection [26, 31] depends only on the spatial relationship (i.e., locations) among people. In addition to the locations, facial directions are used to evaluate the so-called F-formation system [1], where groups are detected in conversational scenarios [15, 19, 33]. Group detection can be improved by using the locations and facial directions simultaneously [16].
+
+While the aforementioned methods formulate the groupness in a handcrafted fashion, such groupness formulations have recently been replaced by machine learning-based models. In [5, 20, 30, 34, 47], the characteristics of human trajectories are trained for group detection. Other human attributes can also be merged, e.g., locations and facial directions [7, 25, 35, 37] and locations and postures [22]. In these methods, all the human attributes are pre-processed.
+
+However, instead of the independent pre-processes, joint learning of the pre-processes and the final task benefits the final task in various tasks. While such joint learning is also used for group detection, e.g., in still images [38] and videos [13, 14, 50], these methods take human bounding boxes, in which important spatial context is unavailable. Our work aims to extract useful group features from the spatial and temporal scene contexts represented by VLMs and the temporal groupness graph, respectively.
+
+# 2.2. Graph Clustering for Group Detection
+
+In recent group detection methods for videos [22, 43, 50], graph clustering divides a set of nodes in a graph into several clusters as follows. (1) The groupness probability of each person pair is estimated, (2) a graph is constructed so that each node corresponds to each person, and the nodes are connected via edges. Each edge is given the estimated groupness probability between each pair, and (3) clusters detected by graph clustering are regarded as groups. These methods [22, 43, 50] use spectral clustering [28] and label propagation [45, 54] as graph clustering. While these simple clustering algorithms are useful for a small static groupness graph, dynamic group detection is required to divide a large temporal groupness graph. In addition, these simple algorithms need cluster-related naive hyperparameters (e.g., the number of clusters and the max number of nodes in each cluster). Unlike these simple algorithms, the Louvain algorithm [10] used in our method efficiently allows for complex clustering in such a large graph by maximizing the modularity of the graph without naive hyperparameters.
+
+
+Figure 3. Network architecture of our method. Extracted image and trajectory features are merged to construct the temporal groupness graph representing the probabilistic connectivity among people. A set of nodes in this graph is divided into clusters for group detection.
+
+# 3. Dynamic Group Detection
+
+Figure 3 shows our group detection network. The groupness probability for each pair is estimated in each frame by our augmented CLIP image features with trajectory-based features (Sec. 3.1). All groupness probabilities are pairwise and framewise. The groupness probabilities in all frames in a video are used to construct the temporal groupness graph (Sec. 3.2.1) for dynamic group detection (Sec. 3.2.2).
+
+# 3.1. Groupness Probability Estimation
+
+The groupness probability is estimated from two features, i.e., trajectory and image features.
+
+# 3.1.1. Trajectory Feature Extraction
+
+The trajectory features are computed with two steps
+
+1st step (frameworkwise feature extraction): Following [50], for any pair of people, a vector consisting of their appearance attributes such as bounding box locations and face directions (denoted by $\mathbf{X}_{\text{traj}} \in \mathbb{R}^{D_x}$ ) is embedded to its latent variable, $\mathbf{E}_{\text{traj}} \in \mathbb{R}^{D_e}$ , by the frameworkwise trajectory encoder, $\phi$ , as follows:
+
+$$
+\mathbf {E} _ {t r a j} = \phi (\mathbf {X} _ {t r a j}) \tag {1}
+$$
+
+2nd step (temporal feature extraction): $\mathbf{E}_{traj}$ of $T$ frames, which are selected before, in, and after frame $f$ , are concatenated. The concatenated features, $\hat{\mathbf{E}}_{traj}$ , are fed into the Transformer-based temporal trajectory encoder [40], $\chi$ , to obtain the trajectory features at frame $f$ :
+
+$$
+\mathbf {Z} _ {t r a j} = \chi (\hat {\mathbf {E}} _ {t r a j}) \in \mathbb {R} ^ {D _ {t}} \tag {2}
+$$
+
+
+(a)
+
+
+(b)
+
+
+(c)
+Figure 4. Preliminary experiments with the pretrained CLIP for zero-shot group classification. While a bounding box with no visual prompt is fed into the image encoder, rectangles with the same color in each image enclose people in the same group of ground truth for visualization.
+
+
+(d)
+
+# 3.1.2. Image Feature Extraction
+
+Preliminary experiments: We expect that CLIP is pretrained to understand what a human group is. The potential of CLIP is validated in our experiments (Fig. 4). In these experiments, a bounding box including a target pair and the background is fed into the CLIP image encoder, $\psi$ , to obtain its visual feature vector, $f_{v}$ . Two texts, "individual people" and "a group of people", are fed into the CLIP text encoder independently to obtain their text feature vectors, $f_{i}$ and $f_{g}$ . The cosine similarities between $f_{v}$ and the text feature vectors are computed and fed into the binary softmax function to obtain the probabilities that the target pair is in different groups and the same group. In Fig. 4 (a) and (b), where two
+
+in-group members and two individual people are observed, respectively, the estimated probabilities are relatively good. However, as shown in Fig. 4 (c), it is not easy for CLIP to pay attention to any pair because three or more people are observed. Figure 4 (d) shows another difficulty. Since the left person enclosed by the box is occluded, it is difficult for CLIP to recognize whether or not the two people enclosed by boxes are in the same group.
+
+CLIP attention to a target pair: Even if three or more people are observed in a bounding box (e.g., Fig. 4 (c)), our method proposes to direct the CLIP's attention to a target pair by circling each person of this pair (Fig. 2 (a)). The effectiveness of circling a region of interest for CLIP is validated for the simple image-text classification task [3]. While only one region is circled in each image in [3], our method applies this circling scheme to the group detection task so that two people are circled separately (Fig. 2 (a)).
+
+Fine-tuning for groupness-augmented CLIP: While the potential of the pretrained CLIP is validated in our preliminary experiments, it is further finetuned in our method. The objectives of this finetuning are twofold. (1) CLIP is finetuned in a supervised manner using the aforementioned red-circled pair. (2) In addition to the two classes used in our preliminary experiments (i.e., "individual people" and "a group of people"), the "occlusion" class is added to cope with difficulty in occlusion handling, which is shown in Fig. 4 (d). We call the features obtained by this finetuning the groupness-augmented CLIP (GA-CLIP) features.
+
+Our method finetunes the CLIP image encoder, $\psi$ , with the last softmax layer. This finetuning is done with the image-text training data for three-class classification:
+
+Image: A cropped bounding box with a pair of two circled people is used, as described before.
+
+Text: Each bounding box is labeled by either of "a group of people," "individual people," or "occlusion." This occlusion labels are available as annotations in the JRDB dataset [14] used in this experiment.
+
+Our method uses "occlusion" to explicitly find that image features may be unreliable if the features are extracted from a bounding box in which at least either of the two circled people is occluded. If image features are unreliable, our method relies more on the trajectory features in the imagedetrajectory fusion features described in Sec. 3.1.3.
+
+Note that, in the following processes, only the GA-CLIP image encoder is used, but the last softmax layer is not used.
+
+Image feature extraction: While our trajectory features in frame $f$ are computed from $T$ frames, image features in frame $f$ (denoted by $\mathbf{Z}_{app}$ ) are extracted only from frame $f$ :
+
+$$
+\mathbf {Z} _ {a p p} = \psi (\mathbf {I} _ {a p p}) \in \mathbb {R} ^ {D _ {a}}, \tag {3}
+$$
+
+where $\mathbf{I}_{app} \in \mathbb{R}^{H \times W}$ denotes a cropped bounding box consisting of $H \times W$ pixels in frame $f$ .
+
+
+Figure 5. Graph construction and clustering. (a) Ours: dynamic group detection by clustering the temporal groupness graph. (b) Previous methods: static group detection with a static groupness graph, which is generated by aggregating the graphs of all frames.
+
+# 3.1.3. Image-Trajectory Fusion Features for Groupness Probability Estimation
+
+The trajectory features, $\mathbf{Z}_{traj}$ , and the image features, $\mathbf{Z}_{app}$ of a person pair are fused as $\mathbf{Z} = \mathbf{Z}_{app} \oplus \mathbf{Z}_{traj} \in \mathbb{R}^{D_a + D_t}$ , where $\oplus$ denotes a concatenation operator. $\mathbf{Z}$ is used for estimating the groupness probability between this pair (denoted by $\mathbf{R}$ ) in each frame:
+
+$$
+\mathbf {R} = \left(P _ {i}, P _ {g}\right) ^ {T} = S M (\rho (\mathbf {Z})) \in \mathbb {R} ^ {2},, \tag {4}
+$$
+
+where $\rho$ and $SM$ denote fully connected layers and a softmax function, respectively. $P_{i}$ and $P_{g}$ are the probabilities that the pair is individual people and in the same group, respectively. $\mathbf{R}$ is estimated for all possible pairs of people in each frame.
+
+# 3.1.4. Joint Learning
+
+With image-trajectory fusion features mentioned above, our method trains the three learnable networks, namely the trajectory feature extractors (i.e., $\phi$ in Eq. (1) and $\chi$ in Eq. (2)) and the image-trajectory fusion feature extractor (i.e., $\rho$ in Eq. (4)), while the GA-CLIP image encoder is fixed. All of $\phi$ , $\chi$ , and $\rho$ are trained in a supervised joint learning manner. In this joint learning, $\mathbf{R}$ in Eq. (4) is used to compute the cross entropy loss with its ground truth, $\mathbf{R}_{gt} \in \{(1,0)^T, (0,1)^T\}$ .
+
+# 3.2. Dynamic Group Detection
+
+# 3.2.1. Graph Construction
+
+Our method uses $P_{g}$ in Eq. (4) to construct a graph for dynamic group detection in a video, as shown in the left-hand part of Fig. 5, via the following two steps.
+
+Step 1: In each frame, a framewise groupness graph is constructed so that each detected person serves as a node. $P_{g}$ of each pair is given to the edge that connects the nodes of this pair as its weight.
+
+Step 2: The framewise groupness graphs of all frames in a video are connected between subsequent frames to construct a temporal groupness graph. Any pair of nodes between frames $f$ and $f + 1$ can be connected via an edge if this temporal pair's identification probability (denoted by $P_{t}$ ) is available and given to this edge. $P_{t}$ may be estimated by multiple object tracking (i.e., $0 \leq P_{t} \leq 1$ ) or annotated as ground-truth tracking IDs (i.e., $P_{t} = \{0,1\}$ ).
+
+# 3.2.2. Graph Clustering
+
+All nodes in the temporal groupness graph are divided into clusters by graph clustering, as shown in the right-hand of Fig. 5. The clusters are regarded as dynamic groups. For example, in $f$ -th framewise graph, nodes in the same cluster correspond to in-group members in frame $f$ . If in-group members differ between $f$ and $f + 1$ , that means the group changes between $f$ and $f + 1$ . This graph clustering is achieved by the Louvain [10], as described in Sec. 2.2.
+
+# 4. Experimental Results
+
+# 4.1. Datasets, Tasks, and Evaluation
+
+Datasets. The following two public datasets are used:
+
+JRDB dataset [14] includes 27 indoor and outdoor videos of first-person-view captured from a mobile robot. Following [14, 22, 50], 20 and 7 videos are used for training and test, respectively. 2fps videos are sampled from the original videos. In total, 1,419 and 404 frames are included in the sampled training and test videos, respectively. Frames-wise group structures are annotated.
+
+Café dataset [21] consists of 24 bird's-eye videos of cafés. Each video is split into short clips at six-second intervals. Groups are annotated to each clip. In our experiments, five clips are concatenated to produce a 30-second video so that several 30-second clips capture dynamic group structure changes. All clips are split into training, validation, and test splits in two different ways, split-by-view and split-by-place, which are called CaféV and CaféP, respectively. The main paper shows the mean of the results of CaféV and CaféP, which is called Café. The separate results of CaféV and CaféP are shown in the Supp. As with JRDB, 2fps clips are sampled from the original clips. In total, CaféV and CaféP have 60,135 and 78,871 training, 30,116 and 16,956 validation, and 30,078 and 24,502 test frames, respectively. Unlike JRDB, Café has no annotations of occlusion for each person. In GA-CLIP training, therefore, each pair is labeled either "a group of people" or "individual people."
+
+Tasks. Static and dynamic group detections are evaluated.
+
+Static group detection is tested to validate the generalizability (i.e., applicability to static detection) of our method. All previous methods [13, 14, 22, 43, 44, 48, 50] in our experiments are static detection methods. While our method is designed for dynamic detection, its framewise results are merged for static detection as follows. The number of frames where each detected group is observed is counted to sort all groups in descending order. In this order, the groups are selected one by one. This group selection ends when all people are included in any of the selected groups.
+
+Dynamic group detection is the main task. Three SoTA static group detection methods, S3R2 [22], P-HAR [17], and GroupTransformer [50], are modified for dynamic detection, following our method. That is, framewise graphs are not merged (e.g., averaged) but connected to construct a temporal groupness graph to divide it by graph clustering. All those methods [22, 50], are provided by the authors' code. As graph clustering, label propagation (LP) [45], Clauset-Newman-Moore greedy modularity maximization (CNM) [8], and Louvain algorithm [10] are tested.
+
+Evaluation. Following [22, 43, 50], the annotated human bounding boxes and temporal person IDs are used at training and test time, and detected groups are evaluated by the following criteria. Given the sets of person IDs in detected and ground truth groups denoted by $G_{det}$ and $G_{gt}$ , respectively. If $\frac{|G_{det} \cap G_{gt}|}{\max(|G_{det}|, |G_{gt}|)} > 0.5$ , $G_{det}$ is regarded as a true-positive detection. Otherwise, false-positive. With these criteria, precision, recall, and F1 scores are obtained.
+
+# 4.2. Details
+
+# 4.2.1. Parameters
+
+Architecture: Our method consists of 346M parameters (3091MiB), including 342M parameters of CLIP. Louvain needs 476 and 917 MiB on JRDB and Café, respectively.
+
+Hyper Parameters: The feature dimensions are $D_{x} = 8$ , $D_{e} = 128$ , $D_{t} = 128 \times T$ , and $D_{a} = 768$ . All frames are used in each video (i.e., between 28 and 115 frames on JRDB and around 60 frames on Café). As the CLIP image encoder, our method uses ViT-L/14@336px that takes a bounding box consisting of $H \times W = 336 \times 336$ pixels.
+
+CLIP finetuning: Adam is used with $\beta = (0.9, 0.99)$ , $\epsilon = 1\mathrm{e} - 6$ , and weight Decay $= 0.05$ . The learning rate increases from 1e-8 to 2e-6 during the first 2 epochs, then decreases to 5e-8 with a cosine scheduler until 30 epochs.
+
+Joint learning: While the weights of $\rho$ in Eq. (4), $\phi$ in Eq. (1), and $\chi$ in Eq. (2) are trained with the cross-entropy loss, as described in Sec. 3.1.4, for 30 epochs. SGD is used. In addition, weight Decay $= 5\mathrm{e - }4$ and momentum $= 0.9$ on PANDA. The learning rate is fixed to 1e-4.
+
+Table 1. Quantitative results of static group detection on JRDB. The best and second-best scores in each metric on each dataset are colored red and blue, respectively (also in Tables 2, 3, and 4).
+
+| Method | Precision | Recall | F1 |
| JRDB-Group [14] | 0.390 | 0.379 | 0.384 |
| Dis.Mat+ [48] | 0.573 | 0.235 | 0.334 |
| GNN w/ GRU [22] | 0.434 | 0.286 | 0.345 |
| ARG [44] | 0.325 | 0.384 | 0.352 |
| S3R2 [22] | 0.577 | 0.562 | 0.569 |
| GroupTrans [50] | 0.662 | 0.606 | 0.633 |
| P-HAR [17] | 0.670 | 0.698 | 0.684 |
| Ours | 0.742 | 0.844 | 0.790 |
+
+Table 2. Quantitative results of static group detection on Café.
+
+| Method | Precision | Recall | F1 |
| S3R2 [22] | 0.595 | 0.709 | 0.647 |
| GroupTrans [50] | 0.286 | 0.425 | 0.342 |
| Ours | 0.756 | 0.893 | 0.819 |
+
+Table 3. Quantitative results of dynamic group detection on JRDB.
+
+| Method | Clustering | Precision | Recall | F1 |
| S3R2 [22] | LP | 0.522 | 0.662 | 0.584 |
| CNM | 0.568 | 0.360 | 0.440 |
| Louvain | 0.590 | 0.438 | 0.502 |
| P-HAR [17] | LP | 0.530 | 0.745 | 0.619 |
| CNM | 0.581 | 0.532 | 0.555 |
| Louvain | 0.568 | 0.697 | 0.626 |
| Group Trans [50] | LP | 0.514 | 0.534 | 0.524 |
| CNM | 0.564 | 0.181 | 0.274 |
| Louvain | 0.596 | 0.264 | 0.366 |
| Ours | LP | 0.627 | 0.577 | 0.601 |
| CNM | 0.709 | 0.754 | 0.731 |
| Louvain | 0.724 | 0.820 | 0.769 |
+
+Table 4. Quantitative results of dynamic group detection on Café.
+
+| Method | Clustering | Precision | Recall | F1 |
| S3R2 [22] | LP | 0.577 | 0.528 | 0.550 |
| CNM | 0.576 | 0.700 | 0.631 |
| Louvain | 0.572 | 0.633 | 0.600 |
| Group Trans [50] | LP | 0.210 | 0.196 | 0.202 |
| CNM | 0.087 | 0.069 | 0.077 |
| Louvain | 0.263 | 0.305 | 0.283 |
| Ours | LP | 0.739 | 0.768 | 0.753 |
| CNM | 0.648 | 0.921 | 0.759 |
| Louvain | 0.681 | 0.904 | 0.776 |
+
+# 4.3. Comparison with SoTA methods
+
+Static group detection: The results on JRDB and Café are shown in Tables 1 and 2, respectively. The results of all previous methods in Table 1 come from [22, 50], except for P-HAR [17] whose result is obtained by the authors' code. In Table 2, the results are obtained by the authors' code. Our method outperforms the previous methods in all metrics on both datasets. For example, compared with the second-best scores, our method improves F1 by $0.157 = 0.790 - 0.633$ and $0.172 = 0.819 - 0.647$ on JRDB and Café, respectively.
+
+Four success cases of our method in which our GA-CLIP
+
+
+(a)
+
+
+(b)
+
+
+(c)
+
+
+(d)
+
+
+Figure 6. Success cases of our method in static group detection on JRDB. In Figs. 6 and 7, people enclosed by boxes with the same color are detected as in-group members.
+
+
+
+
+
+
+Figure 7. Success cases of our method in dynamic group detection on Café (upper) and JRDB (lower). In this figure, S3R2 and GroupTransformer are implemented w/ label propagation to contrast with our proposed method using the Louvain algorithm.
+
+image features are beneficial for group detection are shown in Fig. 6, which also shows the results of two SoTA methods, S3R2 [22] and GroupTransformer [50]. In Fig. 6 (a), our method can detect a group in which in-group members are interacting. In Fig. 6 (b), our method can discriminate between in-group people and others because the GA-CLIP image features can find the indirect interaction at the counter (i.e., background). In Fig. 6 (c), the facial direc
+
+
+(a) No prompt
+Figure 8. Visual prompts for specifying a pair of people of interest.
+
+
+(b) Mask
+
+
+(c) A circle
+
+
+(d) Two circles
+
+tions of people are useful in our method. Figure 6 (d) is a difficult example in which people are just in a queue. While no clearly distinguishable interaction between these people is observed, their appearance attributes, such as fine-grained face directions, age, and gender, may be used in our method.
+
+Dynamic group detection: The results of dynamic group detection on JRDB and Café are shown in Table 3 and Table 4. Our method outperforms all others in terms of all metrics by a large gap so that all best and second-best scores are obtained by the variants of our method. Even compared with the best F1 score among the other methods (i.e., "0.584 of S3R2 and LP on JRDB" and "0.631 of S3R2 and CNM on Café"), our method is better by $0.185 = 0.769 - 0.584$ and $0.145 = 0.776 - 0.631$ on JRDB and Café, respectively.
+
+Two success cases of our method are shown in Fig. 7. In the upper, four sitting people are in the same group at $t_1$ , while S3R2 fails to include two people to this group. This group breaks up at $t_2$ . Our method detects this breakup soon at $t_2$ even though the four people are still close to each other. This success case validates that (1) our GA-CLIP features can discriminate between in-group people in the table and breaking up people leaving the table, and (2) graph clustering can cut temporal edges in the temporal groupness graph for dynamic group detection. In the lower, two people enclosed by blue boxes at $t_1$ are mutually occluded at $t_2$ . This occlusion drops their groupness probability, $P_g$ , at $t_2$ compared with those at $t_1$ and $t_3$ . However, our CLIP finetuning with the occlusion class reduces the drop. Combining this effect and graph clustering in our temporal groupness graph enables continuous dynamic group detection.
+
+# 4.4. Detailed Analyses
+
+# 4.4.1. Different Visual Prompts for CLIP
+
+Table 5 shows the contributions of visual prompts, which are shown in Fig. 8, for group detection. We can see that our proposed visual prompt using (d) two circles is the best in all datasets and all metrics for group detection.
+
+In addition to group detection, the results of three-class classification (i.e., "individual people," "a group of people," and "occlusion") using the image encoder are also shown in the "I-Enc" row of Table 5. The superior performance of (d) two circles validates that the well-trained image encoder contributes to group detection.
+
+Table 5. Different visual prompts for CLIP.
+
+| Dataset (Task) | Model | I-Enc | Group detection |
| F1 | Precision | Recall | F1 |
| JRDB (static) | No prompt | 0.442 | 0.719 | 0.751 | 0.735 |
| Mask | 0.569 | 0.653 | 0.823 | 0.728 |
| A circle | 0.578 | 0.700 | 0.757 | 0.728 |
| Two circles | 0.666 | 0.742 | 0.844 | 0.790 |
| JRDB (dynamic) | No prompt | 0.442 | 0.700 | 0.689 | 0.695 |
| Mask | 0.569 | 0.584 | 0.750 | 0.657 |
| A circle | 0.578 | 0.640 | 0.666 | 0.653 |
| Two circles | 0.666 | 0.724 | 0.820 | 0.769 |
| Café (static) | No prompt | 0.580 | 0.591 | 0.774 | 0.670 |
| Mask | 0.824 | 0.734 | 0.871 | 0.796 |
| A circle | 0.761 | 0.656 | 0.802 | 0.722 |
| Two circles | 0.885 | 0.756 | 0.893 | 0.819 |
| Café (dynamic) | No prompt | 0.580 | 0.508 | 0.777 | 0.615 |
| Mask | 0.824 | 0.677 | 0.870 | 0.761 |
| A circle | 0.761 | 0.613 | 0.797 | 0.692 |
| Two circles | 0.885 | 0.681 | 0.904 | 0.776 |
+
+Table 6. Different CLIP finetuning labels, w/ and w/o occlusion.
+
+| Dataset (Task) | Model | Precision | Recall | F1 |
| JRDB (static) | Ours w/o Occ | 0.706 | 0.824 | 0.760 |
| Ours | 0.742 | 0.844 | 0.790 |
| JRDB (dynamic) | Ours w/o Occ | 0.637 | 0.743 | 0.686 |
| Ours | 0.724 | 0.820 | 0.769 |
+
+# 4.4.2. Occlusion Handling with CLIP Finetuning
+
+The effectiveness of the "occlusion" class is verified by ab- lating it in our CLIP finetuning scheme. Since "occlusion" is not annotated on Café, Table 6 shows the results on JRDB only. We can see that "occlusion" improves all the metrics in all datasets. In particular, the improvement of F1 is larger in dynamic group detection (i.e., $0.083 = 0.769 - 0.686$ ). This is because occlusion makes group detection difficult in each frame, so the performance is significantly degraded in dynamic detection if the CLIP image encoder does not learn "occlusion." However, by merging the results of dynamic detections for static detection (as described in "Tasks" in Sec. 4.1), the results of static detection can be improved, resulting in the small gap between "Ours w/o Occ" and "Ours."
+
+# 4.4.3. GA-CLIP image features vs Visual Features
+
+Large pretrained vision encoders, ResNet [18], ViT [11], and DINOv2 [29], are finetuned with each dataset and then replace the CLIP image encoder. In addition to group detection, three-class classification with the encoder is also evaluated, as shown in the "I-Enc" row.
+
+Table 7 shows that in terms of F1, our method using GA-CLIP outperforms the others in all cases by a large margin. This proves that higher-level spatial contexts useful for group detection are represented in GA-CLIP.
+
+Table 7. GA-CLIP image features vs visual features.
+
+| Dataset (Task) | Model | I-Enc | Group detection |
| F1 | Precision | Recall | F1 |
| JRDB (static) | ResNet50 | 0.501 | 0.760 | 0.743 | 0.751 |
| ViT-L/16 | 0.523 | 0.704 | 0.732 | 0.718 |
| DINOv2 | 0.618 | 0.726 | 0.746 | 0.736 |
| Ours | 0.666 | 0.742 | 0.844 | 0.790 |
| JRDB (dynamic) | ResNet50 | 0.501 | 0.686 | 0.609 | 0.645 |
| ViT-L/16 | 0.523 | 0.652 | 0.666 | 0.659 |
| DINOv2 | 0.618 | 0.612 | 0.600 | 0.644 |
| Ours | 0.666 | 0.724 | 0.820 | 0.769 |
| Café (static) | ResNet50 | 0.662 | 0.599 | 0.821 | 0.692 |
| ViT-L/16 | 0.545 | 0.538 | 0.583 | 0.554 |
| DINOv2 | 0.736 | 0.590 | 0.759 | 0.664 |
| Ours | 0.885 | 0.756 | 0.893 | 0.819 |
| Café (dynamic) | ResNet50 | 0.662 | 0.525 | 0.806 | 0.634 |
| ViT-L/16 | 0.545 | 0.510 | 0.579 | 0.534 |
| DINOv2 | 0.736 | 0.555 | 0.764 | 0.643 |
| Ours | 0.885 | 0.681 | 0.904 | 0.776 |
+
+Table 8. Feature ablation study.
+
+| Dataset (Task) | Model | Precision | Recall | F1 |
| JRDB (static) | Ours w/o App. | 0.636 | 0.771 | 0.697 |
| Ours w/o Traj. | 0.598 | 0.807 | 0.687 |
| Ours | 0.742 | 0.844 | 0.790 |
| JRDB (dynamic) | Ours w/o App. | 0.539 | 0.682 | 0.602 |
| Ours w/o Traj. | 0.534 | 0.748 | 0.623 |
| Ours | 0.724 | 0.820 | 0.769 |
| Café (static) | Ours w/o App. | 0.640 | 0.837 | 0.724 |
| Ours w/o Traj. | 0.667 | 0.854 | 0.748 |
| Ours | 0.756 | 0.893 | 0.819 |
| Café (dynamic) | Ours w/o App. | 0.555 | 0.848 | 0.670 |
| Ours w/o Traj. | 0.612 | 0.850 | 0.711 |
| Ours | 0.681 | 0.904 | 0.776 |
+
+# 4.4.4. Ablation of Trajectory and Image Features
+
+In Table 8, our method with both appearance and trajectory features is better than that using one of them in all cases. While there is not much difference between ours w/o appearance features and ours w/o trajectory features on the whole, our method using both features can outperform both ours w/o appearance and ours w/o trajectory.
+
+# 4.4.5. Inference Time
+
+On a NVIDIA RTX 6000 Ada, the image-trajectory fusion features are computed in 0.018 secs/pair. Since the average number of all possible pairs in each frame is 958 in JRDB, the runtime is $0.018 \times 958 \doteq 17.2$ secs/frame. To reduce the runtime, (1) only $k$ -nearest neighbor pairs for each person are chosen to reduce the number of pairs to 47.6, as mentioned in the Supp, and (2) 300 pairs are handled in parallel, leading to $0.018 \times \frac{47.6}{300} \doteq 0.003$ secs/frame. Note that, while only $k$ -NN pairs are chosen, temporal graph clustering allows us to detect groups, each of which has $k$ or more people, as validated in the Supp. The Louvain needs 0.020 secs/frame. On JRDB, therefore, the total inference time is $0.020 + 0.003 = 0.023$ secs/frame, which is faster than 0.11 secs/frame of S3R2 [22]. On Café, the total time is 0.007 secs/frame, while it is 0.018 secs/frame in S3R2 [22].
+
+Table 9. Dynamic group detection using human bounding boxes given by multi-object tracking [51] on JRDB.
+
+| Method | Clustering | Precision | Recall | F1 |
| S3R2 [22] | Louvain | 0.617 | 0.725 | 0.667 |
| Group Trans [50] | Louvain | 0.532 | 0.389 | 0.449 |
| Ours | Louvain | 0.709 | 0.850 | 0.774 |
+
+
+Figure 9. Failure cases of our method on Café. Detected in-group members are marked by boxes with the same color.
+
+# 4.4.6. Human Bounding Boxes given by Tracking
+
+Instead of annotated person bounding boxes and IDs between frames, inaccurate ones are obtained by a multi-object tracking algorithm [51], which needs to be used in real scenarios. Table 9 shows the superiority of our method. This may be because our GA-CLIP features play a more crucial role in redeeming the negative effect of erroneous weights given to temporal edges (i.e., erroneous multi-object tracking probabilities). Even if these temporal edge weights are unreliable, our GA-CLIP features allow for correct framewise group detection.
+
+# 5. Limitations
+
+Figure 9 shows failure cases of our method. In all false-positive group detections shown in the upper, individual people are detected as in-group people because they are nearby for a long time. The lower shows three temporal frames. While three in-group people are detected correctly at $t_1$ and $t_2$ , group detection is failed at $t_3$ because one of them enclosed by the blue box walks a different path. These failure cases reveal that our method still depends more on trajectory features than image features, while our proposed GA-CLIP features improve framewise group detection.
+
+# 6. Concluding Remarks
+
+We proposed (1) the GA-CLIP image features for frameswise groupness evaluation and (2) temporal groupness graph clustering for dynamic group evaluation. Our experiments demonstrated that (1) the GA-CLIP image features represent human-human and human-scene interactions for better group detection and (2) temporal groupness graph clustering enables dynamic group detection, which is not achieved even in SoTA methods [22, 50].
+
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\ No newline at end of file
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+# Dynamic Multi-Layer Null Space Projection for Vision-Language Continual Learning
+
+Borui Kang1, Lei Wang2, Zhiping Wu1, Tao Feng3, Yawen Li4, Yang Gao1,5, Wenbin Li1*
+1State Key Laboratory for Novel Software Technology, Nanjing University, China
+2University of Wollongong, Australia 3Tsinghua University, China
+4Beijing University of Posts and Telecommunications, China
+5Vili Normal University, Xinjiang, China
+
+# Abstract
+
+Vision-Language Models (VLM) have emerged as a highly promising approach for Continual Learning (CL) due to their powerful generalizable features. While adapter-based VLM can exploit both task-specific and task-agnostic features, current CL methods have largely overlooked the distinct and evolving parameter distributions in visual and language modalities, which are found crucial for effectively mitigating catastrophic forgetting. In this study, we find that the visual modality experiences a broader parameter distribution and greater variance during class increments than the textual modality, leading to higher vulnerability to forgetting. Consequently, we handle the branches of the two modalities asymmetrically. Specifically, we propose a Dynamic Multi-layer Null Space Projection (DMNSP) strategy and apply it only to the visual modality branch, while optimizing the language branch according to the original optimizer. DMNSP can restrict the update of visual parameters within the common subspace of multiple null spaces, further limiting the impact of non-zero residual terms. Simultaneously, combined with a dynamic projection coefficient, we can precisely control the magnitude of gradient projection to the null space, endowing the model with a good balance of stability and plasticity. Extensive experiments on TinyImageNet, CIFAR100 and ImageNet-R demonstrate that our method outperforms current approaches in accuracy and knowledge retention, setting a new standard for state-of-the-art performance in class incremental learning. Our code is available at https://github.com/RL-VIG/DMNSP.
+
+# 1. Introduction
+
+The primary objective of Continual Learning (CL) is to enable models to learn from a sequence of data or tasks
+
+
+
+
+
+
+
+
+Figure 1. (a) VLM-based CL methods that require full fine-tuning. (b) Adapter-based VLM CL methods requiring fine-tuning of adapter layers. (c) Adapter-based VLM CL methods with DMNSP in visual branch. (d) Variances of visual and language parameters in adapter-based CLIP within CL. (e) Forgetting rate of adapter-based CLIP before and after the integration of DMNSP.
+
+
+
+over time while effectively preventing catastrophic forgetting [8, 9, 32]. However, traditional training-from-scratch models [18, 20] can only obtain the feature representations specific to the current task, and they do not demonstrate good generalization ability when used for continual learning. Hence, in recent years, CL has gradually tended to adopt methods based on Vision-Language Models (VLM), such as the Contrastive Language-Image Pretraining (CLIP) model [27]. The studies in [5, 33] show that CLIP, trained with a large number of image-text pairs through contrastive learning, inherently has a strong continual learning ability, which significantly contributes to the development of CL. Subsequently, several improved methods have been developed. As depicted in Figure 1(a), ZSCL [42] and Mod-X [25] utilize additional components, such as specific datasets and specially-constructed loss functions, to conduct full-tuning of CLIP for CL. To some extent, this affects the expression of the generalizable features of CLIP itself. In contrast, Parameter-Efficient Fine-Tuning (PEFT) techniques [1, 13, 14], such as the adapter-based method, effectively integrate task-specific features obtained from fine-tuning and the task-agnostic generalizable features of VLM.
+
+In addition, as shown in Figure 1(b), MoE4Adapters [40] utilizes an adapter-based VLM architecture, incorporating various adapter designs to alleviate the training burden, thereby achieving strong performance in CL.
+
+However, within the context of VLM under the CL framework, the relationship between these two modalities (i.e., visual and text modalities) remains insufficiently explored. To address this, we investigate the parameter variation of the visual and language adapters in the adapter-based CLIP. As shown in Figure 1(d), during a CL process involving 10 tasks, we observe that the parameter variance of the last layer's visual adapter undergoes more significant changes than that of the language adapter. This implies that during the CL process, the degree of change in visual adapter parameter distributions is greater than that in the language counterpart, and the corresponding forgetting rate is relatively high (as shown by the green line "Adapter-based CLIP" in Figure 1(e)). When the visual adapter is combined with our strategy to be proposed below, the variance of visual adapter parameters is markedly reduced, and simultaneously the forgetting rate is also substantially decreased (as shown by the blue line "Adapter-based CLIP + DMNSP" in Figure 1(e)). Motivated by this observation, we propose that controlling the variation of visual modality parameters could be a promising approach to mitigating catastrophic forgetting in VLM.
+
+To this end, our work takes the approach of null space projection due to its promising performance in CL, as evidenced by the recent studies [19, 21, 34, 41] revealing that updating gradients within the null space of feature representations to constrain residual terms to zero can effectively mitigate catastrophic forgetting. However, these methods face two fundamental limitations. First, they perform SVD of the feature representations in each layer to estimate the null space. It is approximated by the space spanned by the vectors corresponding to smaller (i.e., not strictly zero) singular values. This inherently retains a small amount of variances of the feature representations, leading to nonzero residual terms (as shown in Figure 4). Second, when applied to VLM, existing approaches [26] equally handle visual-language branches despite their distinct modality characteristics. These observations motivate us to design the Dynamic Multi-layer Null Space Projection (DMNSP) method, which leverages comprehensive multi-layer null space information to constrain the projection process. As shown in Figure 1(c), we exclusively apply DMNSP to the visual branch only to further constrain its distribution and thus limit non-zero residual terms. Moreover, considering that the magnitude of null space projection directly affects the plasticity-stability trade-off in CL [41], we dynamically adjust the degree of projection by measuring the dynamic similarity between a feature space and its null space. Our contributions can be summarized as follows:
+
+- We propose an asymmetric adapter training approach to mitigate the catastrophic forgetting caused by the different behaviors of two modalities in continual learning faced by adapter-based VLM.
+- We propose a multi-layer null space gradient projection strategy and enrich it with a dynamic projection coefficient, thereby effectively reducing the negative impact of non-zero residual terms in the process of CL.
+- We conduct eight different experimental settings of Class Incremental Learning (CIL) on the CIFAR100, TinyImageNet and ImageNet-R datasets and achieved state-of-the-art results in terms of accuracy and forgetting rates.
+
+# 2. Related Works
+
+Traditional Continual Learning mainly consists of three principal categories of methods. (a) Regularization-based methods [8, 9, 18, 38] alleviate forgetting by imposing penalties on the changes of parameters significant to previous tasks. One drawback of these methods is that the model capacity is fixed, and the penalty loss will cause the model's plasticity to decrease as old tasks increase. (b) Architecture-based methods involve learning parameters that are tailored for individual tasks. This can be achieved through network expansion [7, 15]. Nevertheless, a drawback of these approaches is that they frequently necessitate a task identity during the inference stage, which may not always be available or practical in real-world applications. (c) Rehearsal-based methods, as exemplified by [12, 28], rely on storing a portion of the past task experiences in a memory and using it for training in conjunction with the current task. However, they are sensitive to the size of the memory.
+
+VLM-based Continual Learning. VLM with generalized feature representations are introduced into continual learning to alleviate the deficiencies of traditional methods. The work in [5, 33] shows that the CLIP exhibits astonishing continual learning performance without any finetuning. Consequently, CLIP is widely employed as a VLM in continual learning. CLAP4CLIP [17] presents a method that employs variational inference to adapt visual language models to new tasks while preventing forgetting. PROOF [44] utilizes the fusion of multimodal information such as visual language, prototypes, and prompts, combined with task-specific mapping to avoid impacts on old tasks.
+
+However, the aforementioned methods, with an excessive focus on learning task-specific features of new tasks, undermine the expression of old tasks and consequently result in the forgetting phenomenon. Therefore, the adapter-based approach [13] is introduced into the CL of VLM. PEGP [26] explores numerous fine-tuning methods based on VLM, including adapters, to accomplish CL but does not innovate the anti-forgetting method. MoE4Adapters [40] proposes to complete the learning of task-specific features through the mixture of experts [30] and the routing selec
+
+
+Figure 2. (a) Represents the overall framework of our method. The CLIP backbone network is frozen, and a trainable adapter layer is added to each layer of the vision-language branch. The DMNSP strategy is integrated into the optimization of the visual adapter. (b) Represents the DMNSP strategy, which mainly consists of multi-layer gradient projection and dynamic projection coefficients. The initial gradient is gradually projected onto the null spaces of layers from 1 to L to obtain the common null subspace of all null spaces. Meanwhile, combined with the dynamically changing coefficients, the projection can be better accomplished. (c) Represents the details of the adapter. A combination of two-layer linear layers and a one-layer ReLU function is employed. Only the visual adapter is optimized in conjunction with DMNSP, and the language adapter is optimized using the original optimizer.
+
+
+
+
+
+tion mechanism, thereby avoiding impacts on old tasks and achieving the current SOTA effect. Nevertheless, due to the lack of a flexible anti-forgetting strategy and the dependence on a fixed adapter-router pair, MoE4Adapters cannot dynamically learn more tasks in class incremental learning. Moreover, existing adapter-based VLM methods have neglected the differential changes in the parameter distribution of visual-language modalities within continual learning tasks. Hence, targeting the dual-branch structure of VLM, we propose an asymmetric optimization method to tackle the problem of catastrophic forgetting.
+
+Projection-based Continual Learning constrains the gradient within specific directions for update, thereby avoiding the interference of the new task learning process on old tasks. GPM [29] first projects new gradients onto the subspace important for old tasks and then subtracts the projected components to update parameters. TRGP [22] proposes a "trust region" to select related old tasks via gradient projection for a new task. VPT-NSP[24] uses prompt gradient orthogonal projection to prevent interference with previous tasks and achieve superior anti-forgetting performance. However, when using Singular Value Decomposition (SVD), the above methods do not impose constraints on the residuals generated by the approximation of the null space, and this may compromise the effectiveness of antiforgetting. Additionally, the gradient projection process
+
+in these methods relies solely on static hyperparameters to control the degree of projection onto the null space [41], which may disrupt the balance between plasticity and stability. These limitations will be addressed by our method proposed in this paper.
+
+# 3. Methodology
+
+In this section, we propose the adapter-based VLM continual learning framework as shown in Figure 2 and elaborate on the details of each part of the method.
+
+# 3.1. Preliminaries
+
+In continual learning, a network $f$ with parameters $\mathbf{w}$ is trained sequentially on a series of tasks $\mathcal{T}_1,\ldots ,\mathcal{T}_t$ where task $\mathcal{T}_t$ is associated with a paired dataset $\{X_{t},Y_{t}\}$ . Here, $X_{t}$ represents the raw data, and $Y_{t}$ denotes the ground truth corresponding to $X_{t}$ . When training $f$ on task $\mathcal{T}_t$ at the $s$ -th training iteration, the network parameters are denoted as $\mathbf{w}_{t,s} = [\mathbf{w}_{t,s}^{1},\dots ,\mathbf{w}_{t,s}^{L}]$ , where $L$ represents the total number of adapter layers. Correspondingly, the parameter update at the $s$ -th training iteration for task $\mathcal{T}_t$ is denoted as $\Delta \mathbf{w}_{t,s} = [\Delta \mathbf{w}_{t,s}^{1},\dots ,\Delta \mathbf{w}_{t,s}^{L}]$ , and the gradient is given by $\mathbf{g}_{t,s} = [\mathbf{g}_{t,s}^{1},\dots ,\mathbf{g}_{t,s}^{L}]$ .
+
+# 3.2. Asymmetric adapters
+
+We follow the literature [4] to insert the adapter to each transformer block in CLIP. As shown in Figure 2(c), adapter is a bottleneck structure consisting of a down-projection layer $\mathbf{W}_{\mathrm{down}} \in \mathbb{R}^{d \times r}$ , a non-linear activation ReLU and an up-projection layer $\mathbf{W}_{\mathrm{up}} \in \mathbb{R}^{r \times d}$ where $r \ll d$ . It mainly changes the residual connection in the transformer blocks by adding non-linear transformations to the identical input. For the $i$ -th block, we denote its output after the multi-head self-attention as $\hat{\mathbf{x}}_i \in \mathbb{R}^{n \times d}$ , where $n$ represents the number of patches. We insert adapters to the MLP structure and get the output as:
+
+$$
+\hat {\mathbf {x}} _ {i + 1} = \mathrm {M L P} (\mathrm {L N} (\hat {\mathbf {x}} _ {i})) + \mathrm {R e L U} (\hat {\mathbf {x}} _ {i} \cdot \mathbf {W} _ {\mathrm {d o w n}}) \cdot \mathbf {W} _ {\mathrm {u p}}, (1)
+$$
+
+where $\mathrm{MLP}(\mathrm{LN}(\hat{\mathbf{x}}_i))$ is the original output of the transformer block, and LN denotes layer normalization.
+
+We denote the adapters inserted into the visual branch of CLIP as $A_v$ and the adapters in the language branch as $A_t$ . Through experiments, we find that during the process of the adapter-based VLM learning on new tasks, the parameter distribution of $A_v$ is broader than that of $A_t$ , with more variance changes and a higher forgetting rate. Motivated by this observation, we propose an asymmetric approach to mitigate the significant changes in visual parameters. Specifically, we project the parameters of $A_v$ onto the multi-layer null space for optimization while optimizing $A_t$ in the original manner, thereby helping the model to achieve a better balance of stability and plasticity.
+
+# 3.3. Vanilla null space gradient projection
+
+Vanilla null space. After the network $f_{t}$ completes learning the new task $\mathcal{T}_t$ , its parameters are updated to $\mathbf{W}_t$ . When data $\mathbf{x}_{t-1}$ from the old task $\mathcal{T}_{t-1}$ is input into the current network, the following condition holds:
+
+$$
+\mathbf {W} _ {t} \cdot \mathbf {x} _ {t - 1} = \mathbf {W} _ {t - 1} \cdot \mathbf {x} _ {t - 1} + \Delta \mathbf {W} _ {t} \cdot \mathbf {x} _ {t - 1}. \tag {2}
+$$
+
+$\mathbf{W}_{t-1} \cdot \mathbf{x}_{t-1}$ represents the feature representation of the old data in previous network $f_{t-1}$ , while $\Delta \mathbf{W}_t \cdot \mathbf{x}_{t-1}$ (also known as the residual term) denotes the feature representation of the old data under the new parameter update. When $\Delta \mathbf{W}_t \cdot \mathbf{x}_{t-1}$ approaches zero, it implies that the parameter changes induced by learning the new task do not impact the data from old tasks [29]. According to the definition of the null space, all the basis vectors $\mathbf{v}$ of the null space of $\mathbf{x}_{t-1}$ satisfy $\mathbf{x}_{t-1} \cdot \mathbf{v} = 0$ . Therefore, we only need to project $\Delta \mathbf{W}_t$ onto the null space of $\mathbf{x}_{t-1}$ to avoid the catastrophic forgetting in CL. Specifically, we utilize Singular Value Decomposition (SVD) to extract key information from the uncentered covariance of input features [34] and approximate the null space of this feature by the subspace associated with the singular values of lower magnitudes, denoted as $\mathbf{U}_{t-1}$ .
+
+In the $l$ -th adapter, during the current iteration $s$ of updating the weight matrix $\Delta \mathbf{w}_{t,s}^{l}$ for task $t$ , the null space $\mathbf{U}_{t-1}^{l}$ corresponding to this layer is incorporated to adjust the original gradient $\mathbf{g}_{t,s}^{l}$ in specific directions, thereby preventing interference with the previous tasks:
+
+$$
+\Delta \mathbf {w} _ {t, s} ^ {l} = \mathbf {U} _ {t - 1} ^ {l} \left(\mathbf {U} _ {t - 1} ^ {l}\right) ^ {\top} \mathbf {g} _ {t, s} ^ {l}. \tag {3}
+$$
+
+# 3.4. Multi-layer null space gradient projection
+
+Multi-layer null space. We argue that when non-zero residuals exist within local adapters, they will propagate through layers, thereby compromising the accuracy of gradient projections in the null spaces obtained at the subsequent layers. To preemptively mitigate the adverse impact of the residuals propagating from shallow to deeper layers, we tighten the projection constraints and leverage all the null spaces obtained at each layer of the network to collectively constrain the gradient projection process. To achieve this, we propose a novel multi-layer null-space projection method which could effectively suppress the magnitude of the residual terms, driving them toward zero. For more explanations, please refer to Section A of the Supplementary Material. As shown in Figure 2(b), we sequentially project gradient updates into each layer's null space, ultimately converging on the common null subspace for the final update. Our approach can be formally expressed as:
+
+$$
+\Delta \mathbf {w} _ {t, s} ^ {l} = \prod_ {j = 1} ^ {L} \mathbf {U} _ {t - 1} ^ {j} (\mathbf {U} _ {t - 1} ^ {j}) ^ {\top} \mathbf {g} _ {t, s} ^ {l}. \qquad (4)
+$$
+
+Dynamic projection coefficient. With the introduction of multi-layer null spaces, it is necessary to consider the relationship between the gradient space of the current task and the null spaces of each layer during the projection process [41]. Recall that we conduct SVD on the uncentered covariance features of the input features. Subsequently, we select the eigenvectors corresponding to the top $p\%$ of the larger singular values to construct the main feature space $\overline{\mathbf{U}}_t$ for the current task. Let $\overline{\mathbf{U}}_t = \{\mathbf{u}^1,\dots ,\mathbf{u}^i\}$ and recall that $\mathbf{U}_{t - 1} = \{\mathbf{v}^1,\ldots ,\mathbf{v}^j\}$ denote the null space obtained for the last task, where $i = 1,2,\ldots ,m$ and $j = 1,2,\ldots ,n$ (with $m$ and $n$ being the numbers of basis vectors in $\overline{\mathbf{U}}_t$ and $\mathbf{U}_{t - 1}$ respectively). Empirically, the cosine similarity between the basis vectors of the main feature space and those of the null space $\mathbf{U}_{t - 1}$ is utilized to characterize the similarity between the two spaces:
+
+$$
+\gamma_ {i j} = \frac {\mathbf {u} ^ {i} \cdot \mathbf {v} ^ {j}}{\| \mathbf {u} ^ {i} \| _ {2} \cdot \| \mathbf {v} ^ {j} \| _ {2}}. \tag {5}
+$$
+
+We form a set $C_t = \{\gamma_{ij}\}$ using all the $\gamma_{ij}$ values. To prevent the accumulation of small similarity values that would lead to an insignificant overall similarity difference, we select the significant values from the entire set of similarity
+
+values to characterize the overall similarity. Consequently, we take the average of the top $q\%$ largest similarity values in $C_t$ as the similarity between the current main feature space and the null space, denoted as $s_t$ .
+
+According to the literature [29], the gradient update direction points to the feature space spanned by the input data. Therefore, we can use $s_t$ to assess the magnitude of gradient projection onto the null space. As shown in Figure 2(b), when $s_t$ is large, it indicates that the current optimization direction has less impact on the knowledge of old tasks, so the projection onto the null space can be appropriately weakened to maintain the plasticity of the model. When $s_t$ is small, it indicates that the current optimization direction has a greater impact on the knowledge of old tasks, so the projection onto the null space can be appropriately strengthened to maintain the plasticity of the model. Therefore, we employ a negative exponential function with a positive range to model this process, obtaining the dynamic projection coefficient:
+
+$$
+\lambda_ {t} = \zeta e ^ {- s _ {t}}. \tag {6}
+$$
+
+Since the gradient undergoes successive multiplicative operations, a numerical overflow problem may occur. Therefore, after the projection between the gradient and each layer's null space is completed, the numerical range needs to be appropriately adjusted. Specifically, we make this adjustment with a fixed scalar $\zeta$ . Ultimately, the gradient projection process of the adapter at the $l$ -th layer is as follows:
+
+$$
+\Delta \mathbf {w} _ {t, s} ^ {l} = \prod_ {j = 1} ^ {L} \lambda_ {t} ^ {j} \mathbf {U} _ {t - 1} ^ {j} \left(\mathbf {U} _ {t - 1} ^ {j}\right) ^ {\top} \mathbf {g} _ {t, s} ^ {l}. \tag {7}
+$$
+
+Null space updating. During the null space update process, the work in the literature [21, 29] first eliminates the basis vectors in the null space of the new task that are similar to those in $\mathbf{U}_{t-1}$ , then expands the remaining basis vectors to obtain the final null space $\mathbf{U}_t$ , thereby reducing storage space consumption. However, when considering a multilayer projection strategy, the basis vectors of each null space must be utilized during the projection process to ensure the accuracy of the final null subspace. Therefore, we employ a simple expansion method to combine the null spaces of each task, aiming to obtain the most comprehensive representation of the null space across all tasks. The process is as follows: $\mathbf{U}_t^j = [\mathbf{U}_1^j, \mathbf{U}_2^j, \dots, \mathbf{U}_{t-1}^j]$ .
+
+# 3.5. Overall optimization procedure
+
+We present the overall parameter update process of visual adapters in Algorithm 1. When learning the first task, gradient projection is not required (as indicated in line 6). Otherwise, our DMNSP strategy is employed. Specifically, at the $s$ -th training iteration, the gradient $\mathbf{g}_{t,s} = [\mathbf{g}_{t,s}^{1},\dots,\mathbf{g}_{t,s}^{L}]$ is projected into the common null subspace across all layers (as mentioned in line 8). The obtained parameter update
+
+Algorithm 1 DMNSP for continual learning
+
+Inputs: Datasets $\{X_{t},Y_{t}\}$ for task $\mathcal{T}_t\in \{\mathcal{T}_1,\mathcal{T}_2,\dots \}$ ; network $f(\cdot ,\mathbf{w})$ with $L$ adapter layers; learning rate $\alpha$ Initialization: Initialize the parameters of $L$ visual adapters w randomly.
+
+1: for task $\mathcal{T}_t\in \{\mathcal{T}_1,\mathcal{T}_2,\ldots \}$ do
+2: while not converged do
+3: Sample a batch $\{\mathbf{x},\mathbf{y}\}$ from $\{X_{t},Y_{t}\}$ .
+4: Compute $f(\mathbf{x}, \mathbf{w}_{t,s})$ , then get candidate parameter update $\mathbf{g}_{t,s} = [\mathbf{g}_{t,s}^l]$ , $l = 1, \dots, L$ .
+5: if $t = 1$ then
+6: $\Delta \mathbf{w}_{t,s}^{l} = \mathbf{g}_{t,s}^{l}$
+7: else
+8: $\Delta \mathbf{w}_{t,s}^{l} = \prod_{j = 1}^{L}\lambda_{t}^{j}\mathbf{U}_{t - 1}^{j}(\mathbf{U}_{t - 1}^{j})^{\top}\mathbf{g}_{t,s}^{l}$
+9: end if
+10: $\mathbf{w}_{t,s + 1}^l = \mathbf{w}_{t,s}^l -\mathrm{AdamW}(\alpha \Delta \mathbf{w}_{t,s}^l)$
+11: $s = s + 1$
+12: end while
+13: if $t > 1$ then
+14: Get $\mathbf{U}_t^l = [\mathbf{U}_1^l, \mathbf{U}_2^l, \dots, \mathbf{U}_{t-1}^l]$
+15: end if
+16: end for
+
+$\Delta \mathbf{w}_{t,s} = [\Delta \mathbf{w}_{t,s}^{1},\dots ,\Delta \mathbf{w}_{t,s}^{L}]$ is input into the AdamW optimizer, thus completing the parameter optimization. After learning task $\mathcal{T}_t$ , the null space is updated as indicated in line 13-15. Compared with visual adapters, text adapters update parameters as usual and follow the rules of the AdamW optimizer.
+
+# 4. Experiments
+
+# 4.1. Experimental setting
+
+Datasets. We evaluate our method on the CIL (Class Incremental Learning) setting. Following [24, 42], experiments are conducted on TinyImageNet, CIFAR100, and ImageNet-R. Specifically, the 100 classes of TinyImageNet are partitioned into $\{5, 10, 20\}$ subsets with 100 base classes, the 100 classes of CIFAR100 into $\{10, 20, 50\}$ subsets, and the 200 classes of ImageNet-R into $\{10, 20\}$ subsets, respectively.
+
+Implementation details. We employ the CLIP model with ViT-B/16 [27] as our backbone. Trainable adapter layers are added to each layer of the two branches in CLIP. We utilize the AdamW optimizer. Each task is trained for 4 epochs. For all datasets, the batch size is set to 128, and the learning rate is set to 0.001. Empirically, the eigenvectors corresponding to the top $10\%$ leading eigenvalues after SVD are selected for constructing the main feature representation, and the remaining eigenvectors form the null space representation. All experimental results are the averages obtained by using five different rounds of random
+
+| Method | Venue | 5 subset | 10 subset | 20 subset |
| Average ↑ | Last ↑ | Average ↑ | Last ↑ | Average ↑ | Last ↑ |
| EWC [18] | PNAS'17 | 19.01 | 6.00 | 15.82 | 3.79 | 12.35 | 4.73 |
| EEIL [2] | ECCV'18 | 47.17 | 35.12 | 45.03 | 34.64 | 40.41 | 29.72 |
| UCIR [12] | CVPR'19 | 50.30 | 39.42 | 48.58 | 37.29 | 42.84 | 30.85 |
| MUC [23] | ECCV'20 | 32.23 | 19.20 | 26.67 | 15.33 | 21.89 | 10.32 |
| PASS [45] | CVPR'21 | 49.54 | 41.64 | 47.19 | 39.27 | 42.01 | 32.93 |
| GPM [29] | ICLR'21 | 6.10 | 4.72 | 5.95 | 4.54 | 5.69 | 4.28 |
| DyTox [7] | CVPR'22 | 55.58 | 47.23 | 52.26 | 42.79 | 46.18 | 36.21 |
| CLIP Zero-shot | ICML'21 | 69.62 | 65.30 | 69.55 | 65.59 | 69.49 | 65.30 |
| Fine-tune | - | 61.54 | 46.66 | 57.05 | 41.54 | 54.62 | 44.55 |
| LwF [20] | TPAMI'17 | 60.97 | 48.77 | 57.60 | 44.00 | 54.79 | 42.26 |
| iCaRL [28] | CVPR'17 | 77.02 | 70.39 | 73.48 | 65.97 | 69.65 | 64.68 |
| LwF-VR [5] | Arxiv'22 | 77.56 | 70.89 | 74.12 | 67.05 | 69.94 | 63.89 |
| ZSCL [42] | ICCV'23 | 80.27 | 73.57 | 78.61 | 71.62 | 77.18 | 68.30 |
| MoE4Adapters [40] | CVPR'24 | 81.12 | 76.81 | 80.23 | 76.35 | 79.96 | 75.77 |
| Adapter-based CLIP + GPM [29] | - | 82.82 | 78.24 | 81.84 | 76.54 | 81.12 | 75.58 |
| Adapter-based CLIP + TRGP [22] | - | 81.91 | 78.34 | 81.69 | 77.94 | 81.49 | 77.89 |
| MoE4Adapters [40] + DMNSP (Ours) | - | 81.19 | 77.68 | 80.80 | 76.51 | 80.57 | 76.06 |
| Adapter-based CLIP + DMNSP (Ours) | - | 83.28 | 79.14 | 82.70 | 77.94 | 81.96 | 77.10 |
+
+Table 1. Comparison of different methods on the TinyImageNet dataset in CIL settings with 100 base classes. We label the best and second-best methods with bold and underline styles based on "Average" and "Last" accuracy scores (\%).
+
+| Method | Venue | 10 subset | 20 subset | 50 subset |
| Average ↑ | Last ↑ | Average ↑ | Last ↑ | Average ↑ | Last ↑ |
| UCIR [12] | CVPR'19 | 58.66 | 43.39 | 58.17 | 40.63 | 56.86 | 37.09 |
| Bic [38] | CVPR'19 | 68.80 | 53.54 | 66.48 | 47.02 | 62.09 | 41.04 |
| PODNet [6] | ECCV'20 | 58.03 | 41.05 | 53.97 | 35.02 | 51.19 | 32.99 |
| DER [39] | CVPR'21 | 74.64 | 64.35 | 73.98 | 62.55 | 72.05 | 59.76 |
| GPM [29] | ICLR'21 | 41.76 | 23.26 | 29.91 | 13.89 | 19.27 | 7.48 |
| DyTox+ [7] | CVPR'22 | 74.10 | 62.34 | 71.62 | 57.43 | 68.90 | 51.09 |
| DNE [15] | CVPR'23 | 74.86 | 70.04 | - | - | - | - |
| CLIP Zero-shot | ICML'21 | 74.47 | 65.92 | 75.20 | 65.74 | 75.67 | 65.94 |
| Fine-tune | - | 65.46 | 53.23 | 59.69 | 43.13 | 39.23 | 18.89 |
| LwF [20] | TPAMI'17 | 65.86 | 48.04 | 60.64 | 40.56 | 47.69 | 32.90 |
| iCaRL [28] | CVPR'17 | 79.35 | 70.97 | 73.32 | 64.55 | 71.28 | 59.07 |
| LwF-VR [5] | Arxiv'22 | 78.81 | 70.75 | 74.54 | 63.54 | 71.02 | 59.45 |
| ZSCL [42] | ICCV'23 | 82.15 | 73.65 | 80.39 | 69.58 | 79.92 | 67.36 |
| MoE4Adapters [40] | CVPR'24 | 85.21 | 77.52 | 83.72 | 76.20 | 83.60 | 75.24 |
| Adapter-based CLIP + GPM [29] | - | 86.73 | 79.14 | 85.01 | 76.80 | 82.81 | 73.60 |
| Adapter-based CLIP + TRGP [22] | - | 85.69 | 77.82 | 84.80 | 76.14 | 83.70 | 73.67 |
| MoE4Adapters [40] + DMNSP (Ours) | - | 86.12 | 78.01 | 83.97 | 75.25 | 83.64 | 74.87 |
| Adapter-based CLIP + DMNSP (Ours) | - | 87.59 | 79.94 | 85.29 | 76.96 | 83.66 | 74.58 |
+
+Table 2. Comparison of different methods on the CIFAR100 dataset in CIL settings. We label the best and second-best methods with bold and underline styles based on "Average" and "Last" accuracy scores (\%).
+
+seeds. More details can be found in the Section D of Supplementary Materials.
+
+Metrics. In continual learning, we adopt the evaluation approach from [40], measuring accuracy throughout the learning process by calculating the average accuracy across all subsets ("Average") and the accuracy of the final subset ("Last"). Furthermore, following [3], we quantify the extent of forgetting in continual learning using the Average Forgetting Rate across all subsets ("Average FR") and the Forgetting Rate for the final subset ("Last FR"). Additionally, we conduct experimental explorations using Forward transfer (FWT) and Backward transfer (BWT). More details are provided in the Section B of the Supplementary Material.
+
+# 4.2. Experimental Results
+
+According to the study in [42], we present the results of methods that do not rely on CLIP (listed before "CLIP Zeroshot" in Tables 1 and 2) [2, 6, 7, 12, 15, 18, 23, 38, 39, 45] and methods based on CLIP (listed after "CLIP Zeroshot" in Tables 1 and 2) [5, 20, 28, 40, 42]. Additionally, using "Adapter-based CLIP" as the backbone, we compare the effects of combining it with different strategies. Specifically, we combine it with the traditional single-layer null space gradient projection method GPM [29] to form the "Adapter-based CLIP + GPM" method; combine it with the "trust region" gradient mapping strategy to form the "Adapter-based CLIP + TRGP" method; combine it with our method to form the "Adapter-based
+
+| Method | 5 subset | 10 subset | 20 subset |
| Avg. ↓ | Last ↓ | Avg. ↓ | Last ↓ | Avg. ↓ | Last ↓ |
| Adapter-based CLIP | 3.34 | 7.97 | 4.56 | 8.75 | 5.33 | 9.79 |
| Adapter-based CLIP + GPM | 3.30 | 7.98 | 4.50 | 8.69 | 5.35 | 9.27 |
| MoE4Adapters + DMNSP (Ours) | 2.26 | 4.16 | 3.12 | 4.88 | 3.23 | 6.86 |
| Adapter-based CLIP + DMNSP (Ours) | 2.15 | 4.84 | 2.65 | 4.84 | 3.65 | 7.11 |
+
+Table 3. Comparison of our method with another three adapter-based methods on the TinyImageNet dataset in CIL settings with 100 base classes in terms of "Avg." and "Last" forgetting rates (\%). We label the best method with bold.
+
+| Method | 10 subset | 20 subset | 50 subset |
| Avg. ↓ | Last ↓ | Avg. ↓ | Last ↓ | Avg. ↓ | Last ↓ |
| Adapter-based CLIP | 7.14 | 11.39 | 7.43 | 12.61 | 9.34 | 14.52 |
| Adapter-based CLIP + GPM | 7.14 | 11.29 | 7.38 | 12.61 | 9.33 | 14.51 |
| MoE4Adapters + DMNSP (Ours) | 4.95 | 9.28 | 5.95 | 10.67 | 7.47 | 12.44 |
| Adapter-based CLIP + DMNSP (Ours) | 4.36 | 7.48 | 4.73 | 9.52 | 7.39 | 12.42 |
+
+
+Figure 3. Comparison of forgetting curves between our method and another three adapter-based methods in CIL with 10 tasks.
+
+CLIP + DMNSP" method; and merge DMNSP with the state-of-the-art method MoE4Adapters [40] to construct the "MoE4Adapters + DMNSP" method. GPM and TRGP are originally designed for task incremental learning; we have adapted them to CIL via classifier adjustments (see Supplementary Material for details).
+
+Accuracy results. As shown in Tables 1 and 2, integrating various CL strategies with CLIP yields performance improvements of varying magnitudes. This observation suggests that leveraging the generalizable features inherent in VLM can significantly facilitate the model's learning process in CL. Specifically, as depicted in Table 1, for all subset settings of TinyImageNet, our method attains the best results in terms of both average accuracy and last accuracy. Notably, as the number of tasks increases, compared with "Adapter-based CLIP + GPM" and the prior SOTA method "MoE4Adapters", our method shows increasingly prominent advantage in the last accuracy. As presented in Table 2, for the 10 and 20 subset settings of CIFAR100, although the superiority over other methods becomes less significant, our method can still achieve the overall best performance. For the 50 subset setting of CIFAR100, despite a significant increase in the number of tasks to be learned, DMNSP can still achieve the highest average accuracy. More results can be found in the Supplementary Material.
+
+Forgetting results. We conduct further experimental exploration into the degree of forgetting. The original CLIP
+
+Table 4. Comparison of our method with other adapter-based methods on CIFAR100 in CIL settings in terms of "Avg." and "Last" forgetting rates (\%). We label the best method with bold.
+
+| Method | Train Params ↓ | Memory Use ↓ | Times ↓ |
| LWF [20] | 149.6M | 32172MiB | 1.54s/it |
| LWF-VR [5] | 149.6M | 32236MiB | 1.51s/it |
| ZSCL [42] | 149.6M | 26290MiB | 3.94s/it |
| MoE-Adapters [40] | 59.8M | 22358MiB | 1.58s/it |
| Ours | 7.8M | 21116MiB | 0.23s/it |
+
+Table 5. Comparison of computational cost during training on CIFAR100 between our method and others in terms of training parameters, GPU burden, and training time per iteration. All the experiments are completed on a single GeForce RTX 3090.
+
+combined with the trainable layer-wise adapter strategy is taken as the "Adapter-based CLIP". Meanwhile, we also jointly compared the "Adapter-based CLIP + GPM" and "MoE4Adapters + DMNSP". As shown in Table 3 and Table 4, for the VLM, even when combined with the traditional null space gradient projection strategy, its antiforgetting ability cannot be significantly improved. However, after being combined with our strategy, the last forgetting rate and the average forgetting rate of both MoE4Adapters and our method are significantly reduced, further demonstrating the effectiveness of our method in addressing the catastrophic forgetting issue.
+
+We further present result of forgetting rate as depicted in Figure 3. Under the setting of CIL, starting from the third task, we record the forgetting rate of all previous tasks after completing each current task until all 10 tasks are accomplished. We observe that, for cases without the gradient projection strategy or with the traditional projection strategy, the forgetting rates are at relatively high levels. However, when combined with the DMNSP, the forgetting rates of the two methods are reduced to lower levels, indicating the effectiveness of our method. More results can be found in the Section C of the Supplementary Material.
+
+Complexity comparison. We further compare the computational costs of our method with those of other methods to verify its parameter efficiency and time efficiency during training. Table 5 shows that methods described in [5, 20, 42] require full-tuning of all CLIP parameters. Consequently, these approaches demand extensive training resources, including a large number of parameters, substantial GPU usage, and considerable computational time. Although MoE4Adapters [40] only needs to fine-tune the adapter, due to its internal adoption of the Mixture of Experts structure [30] and routing selection mechanism, it also demands a relatively large number of training parameters and computing time. In contrast, despite using a simpler adapter structure, our approach reduces the number of training parameters by approximately $86.9\%$ compared to MoE4Adapters, while also increasing training speed per iteration by roughly 6.8 times. This highlights the simplicity and efficiency of our method.
+
+Parameter variation and residual changes. In the adapter-based VLM architecture, we conduct an in-depth
+
+
+Figure 4. Parameter variation and residual changes in Adapter-based VLM before and after combination with DMNSP.
+
+
+
+| Method | Venue | 10 subset | 20 subset |
| Avg. ↑ | Last ↑ | Avg. ↑ | Last ↑ |
| L2P [37] | CVPR'22 | 80.83±1.39 | 74.60±0.90 | 78.39±0.94 | 72.09±1.12 |
| DualPrompt [36] | ECCV''22 | 81.39±1.25 | 74.87±0.85 | 79.12±1.27 | 71.69±1.06 |
| ESN [35] | AAAI'23 | 81.63±1.10 | 75.11±0.36 | 77.95±0.76 | 70.57±0.62 |
| CODAprompt [31] | CVPR'23 | 81.32±1.01 | 75.51±0.81 | 78.07±0.40 | 72.25±0.78 |
| LAE [10] | CVPR'23 | 76.71±0.10 | 71.70±0.39 | 73.72±0.05 | 66.98±0.35 |
| InfLoRA [21] | CVPR'24 | 80.82±0.24 | 75.65±0.14 | 77.28±0.45 | 71.01±0.45 |
| EASE [43] | CVPR'24 | 81.73 | 76.17 | - | - |
| CPrompt [11] | CVPR'24 | 82.92±0.70 | 77.14±0.11 | 81.46±0.93 | 74.79±0.28 |
| RAPF [16] | ECCV'24 | 85.85 | 79.62 | 86.28 | 79.62 |
| VPT - NSP2 [24] | NeurIPS'24 | 84.84±0.12 | 78.88±0.50 | - | - |
| Adapter-based CLIP + GPM [29] | - | 86.18±0.08 | 80.11±0.12 | 86.73±0.19 | 80.65±0.14 |
| Adapter-based CLIP+ TRGP [22] | - | 86.24±0.10 | 81.29±0.09 | 86.07±0.17 | 81.21±0.13 |
| MoE4Adapters [40] + DMNSP (Ours) | - | 86.45±0.11 | 81.87±0.16 | 87.06±0.20 | 81.61±0.18 |
| Adapter-based CLIP + DMNSP (Ours) | - | 87.49±0.07 | 81.94±0.15 | 86.81±0.16 | 82.72±0.09 |
+
+exploration of the variation patterns of adapter parameters and the numerical changes in the residual term $\mathbf{W}_t\cdot \mathbf{x}_{t - 1}$ (as described in Eq.(2)) of the model on old task data after learning new tasks.
+
+As shown in Figure 4 (left), before the integration with the DMNSP, the variation amplitude of the parameters of the visual adapter (as shown by the purple line) is significantly higher than that of the language adapter (as shown by the green line). After the integration with DMNSP, the parameter updates of the visual adapter are projected into the null space. This mechanism effectively suppresses its parameter variance and enhances the stability of the model. In contrast, since the language adapter do not adopt the DMNSP strategy, during the joint update process, its variance further increases. This enables the language adapter to better adapt to the distribution of the new tasks, enhancing the plasticity of the model.
+
+As can be seen from Figure 4 (right), as the null space gradient projection transitions from single-layer to multilayer and finally the DMNSP is introduced, the residual term gradually approaches zero. This changing trend implies that the model's resistance to forgetting is continuously enhanced. The above results strongly confirm the effectiveness of our processing of the visual modality.
+
+Superior cross-domain adaptation. Given that the ImageNet-R dataset comprises complex cross-domain distribution shifts from natural images to artistic renditions [11] and includes hard samples that convolutional neural networks struggle to handle [10], we compare our approach with existing transformer-based methods that are adept at addressing domain gaps. The task setup is conducted according to [11]. As shown in Table 6, our method achieves superior performance. This indicates that our method main
+
+Table 6. Comparison of Transformer-based methods on ImageNet-R under CIL with domain gap.
+
+| Components | 5 subset | 10 subset | 20 subset |
| Multi-layer | λ | Text | Vision | Avg. ↑ | Last ↑ | Avg. ↑ | Last ↑ | Avg. ↑ | Last ↑ |
| - | - | ✓ | ✓ | 82.82±0.02 | 78.24±0.23 | 81.84±0.31 | 76.54±0.38 | 81.12±0.27 | 75.58±0.11 |
| ✓ | - | ✓ | ✓ | 82.77±0.10 | 78.12±0.15 | 81.84±0.21 | 76.74±0.14 | 81.16±0.19 | 75.66±0.15 |
| ✓ | ✓ | ✓ | ✓ | 82.99±0.13 | 78.56±0.25 | 81.79±0.11 | 76.78±0.09 | 81.28±0.07 | 75.96±0.14 |
| ✓ | ✓ | ✓ | - | 82.66±0.09 | 77.22±0.12 | 81.50±0.05 | 75.06±0.21 | 80.78±0.16 | 75.58±0.06 |
| - | ✓ | - | ✓ | 82.83±0.12 | 78.46±0.2 | 81.79±0.18 | 76.78±0.13 | 81.11±0.07 | 75.62±0.13 |
| ✓ | ✓ | - | ✓ | 83.28±0.11 | 79.14±0.16 | 82.70±0.20 | 77.94±0.13 | 81.96±0.18 | 77.10±0.15 |
+
+Table 7. Ablation experiments on asymmetric adapters, multilayer null spaces, and $\lambda$ on TinyImageNet.
+
+tains good adaptability in CL, even when confronted with complex data distributions.
+
+# 4.3. Ablation Study
+
+We conduct ablation studies to assess the effectiveness of asymmetric adapters and multi-layer null spaces in the proposed method. In Table 7, the first row presents the results of the traditional single-layer projection method applied to both modalities, which does not incorporate DMNSP or the dynamic projection coefficient $\lambda$ from Eq.(6). When multi-layer null space projection is applied to both the visual and language modalities, the model exhibits limited plasticity due to overly restrictive gradient projection constraints. Consequently, combining it with $\lambda$ does not yield significant performance improvements, as shown in rows 2 and 3. In contrast, since language parameters exhibit relatively low inherent variability, applying DMNSP solely to the language branch fails to effectively mitigate forgetting caused by changes in visual parameters (as shown in row 4). Similarly, applying single-layer gradient projection only to visual parameters, even when combined with $\lambda$ , results in limited performance gains because of the insufficient constraints imposed on the residual term (as shown in row 5). Ultimately, the DMNSP strategy, which integrates multilayer gradient projection with dynamic $\lambda$ , achieves the highest performance. These results highlight the crucial role of the two components in reducing catastrophic forgetting and enhancing model performance. More experiment results are provided in the Section D of the Supplementary Material.
+
+# 5. Conclusion
+
+In this work, we propose a novel Dynamic Multi-layer Null Space Projection (DMNSP) strategy to tackle the catastrophic forgetting issue in Vision-Language Models (VLM) for continual learning. This strategy integrates a multi-layer null space gradient projection mechanism with a dynamic projection coefficient to realize a projection onto the common null subspace with minimal nonzero residuals. Moreover, by handling the visual and language branches of the VLM in an asymmetric manner, our method helps the VLM to achieve better continual learning ability. Extensive experiments have demonstrated that our method outperforms the state-of-the-art methods in terms of accuracy and resistance to forgetting. In the future, we plan to explore projection methods with more network architectures and modalities to further advance continual learning capabilities.
+
+# Acknowledgement
+
+This work is supported in part by the National Natural Science Foundation of China (62192783), Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), and the Australian Research Council's Discovery Project (DP220101784).
+
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+# Dynamic Multimodal Prototype Learning in Vision-Language Models
+
+Xingyu Zhu $^{1,2}$ , Shuo Wang $^{1*}$ , Beier Zhu $^{2}$ , Miaoge Li $^{3}$ , Yunfan Li $^{4}$ , Junfeng Fang $^{5}$ , Zhicai Wang $^{1}$ , Dongsheng Wang $^{6}$ , Hanwang Zhang $^{2}$
+
+1University of Science and Technology of China, 2Nanyang Technological University, 3The Hong Kong Polytechnic University, 4Sichuan University, 5National University of Singapore, 6Shenzhen University
+
+xyzhuxyz@mail.ustc.edu.cn
+
+# Abstract
+
+With the increasing attention to pre-trained vision-language models (VLMs), e.g., CLIP, substantial efforts have been devoted to many downstream tasks, especially in test-time adaptation (TTA). However, previous works focus on learning prototypes only in the textual modality while overlooking the ambiguous semantics in class names. These ambiguities lead to textual prototypes that are insufficient to capture visual concepts, resulting in limited performance. To address this issue, we introduce ProtoMM, a training-free framework that constructs multimodal prototypes to adapt VLMs during the test time. By viewing the prototype as a discrete distribution over the textual descriptions and visual particles, ProtoMM has the ability to combine the multimodal features for comprehensive prototype learning. More importantly, the visual particles are dynamically updated as the testing stream flows. This allows our multimodal prototypes to continually learn from the data, enhancing their generalizability in unseen scenarios. In addition, we quantify the importance of the prototypes and test images by formulating their semantic distance as an optimal transport problem. Extensive experiments on 15 zero-shot benchmarks demonstrate the effectiveness of our method, achieving a $1.03\%$ average accuracy improvement over state-of-the-art methods on ImageNet and its variant datasets.
+
+# 1. Introduction
+
+Recent advances in vision-language models (VLMs) [1, 19, 20, 35, 38, 50] have shown remarkable success across a wide range of visual tasks. These foundation models, e.g., CLIP [38], are pre-trained on web-scale image-text pairs, achieving superior capabilities in addressing zero-shot classification [41, 58-60]. One key factor behind these successes
+
+
+
+
+Figure 1. Observations of ambiguities in class names from the Oxford Flowers [33] and ImageNet [9]: (a) The class names "sword lily" and "blackberry lily" both refer to flowers from the Iridaceae family and share the word "lily". (b) The class names "laptop" and "desktop computer" denote different types of computers.
+
+is to find the optimal prototypes for each category. For example, CoOp [58] and CoCoOp [57] introduce learnable prompt vectors concatenated to textual prototypes. Another line of research, including TPT [41] and C-TPT [54], aims to tune class prompts during inference time for each testing sample, a strategy known as test-time adaptation.
+
+Despite the improvements brought by these methods, we empirically find that the ambiguities in class names result in textual prototypes struggling to differentiate the classes. As illustrated in Figure 1(a), the two different classes "sword lily" and "blackberry lily" exhibit high cosine similarity (0.67) in the CLIP space. This similarity arises not only from the common word "lily" but also because both flowers belong to the Iridaceae family. As a result, relying on the description-based prototypes makes it challenging to classify the images of "sword lily" and "blackberry lily" effectively (0.53 vs. 0.55 and 0.56 vs. 0.58). Furthermore, consider the class names "laptop" and "desktop computer" as depicted in Figure 1(b). Although they do not share any
+
+
+Figure 2. Illustration of multimodal prototype learning on the ImageNet dataset [9]. (a) Process of updating multimodal prototypes. (b) Comparisons of distribution metrics.
+
+common same word, they still exhibit a high cosine similarity (0.69) because they both refer to different forms of computers. Consequently, test images of "laptop" and "desktop computer" have comparable similarities to both class names, making differentiation challenging (0.67 vs. 0.63 and 0.65 vs. 0.65). To this end, recent studies aim to construct high-quality prototypes in various ways, including multiple prompts generation [28], cache-based tuning [21], and diverse data augmentation with diffusions [11]. Unfortunately, all these models focus solely on the textual domain, overlooking the information from the visual aspect [2, 27].
+
+As discussed in previous studies [2, 37, 48, 51, 52, 61, 63, 64], multimodal signals, such as vision and language, provide complementary knowledge that enhances the understanding of objects and class concepts. Although these class names are semantically similar, their visual characteristics provide crucial information for reducing ambiguities. In this paper, we proposed ProtoMM, a training-free multimodal prototype learning framework for adapting VLMs at test time. Moving beyond prototype learning within the single textual domain, ProtoMM aims to construct multimodal prototypes from both the textual descriptions and image stream. Specifically, for each class, we view its prototype as a discrete distribution over the corresponding label descriptions and visual particles. The visual particles collect the label-specific image features and are updated dynamically as the testing stream flows. This enables our multimodal prototype to accumulate more and more side information, improving the prediction performance. As illustrated in Figure 2(a), it is difficult to determine whether the test image belongs to the "desktop computer" or "laptop" class at time $t_1$ . In contrast, with the help of our multimodal prototype learning, one can easily distinguish these two classes at time $t_5$ . Furthermore, we compare the KL divergence [18] and Maximum Mean Discrepancy (MMD) [49] between our multimodal
+
+prototypes and ground truth. The results summarized in Figure 2(b) show that as time passes, the distribution discrepancy decreases significantly, e.g., KL divergence from 18.7 to 9.5 and MMD from 0.97 to 0.29.
+
+The main contributions are summarized as follows:
+
+- We propose a training-free multimodal prototype learning framework to boost the generalization ability of VLMs in the test-time scenario.
+- We leverage informative visual knowledge to construct multimodal prototypes, and then update the multimodal prototypes by solving an OT problem.
+- We demonstrate the effectiveness of our method by conducting experiments on 15 datasets, showing consistent and significant improvements over existing baselines.
+
+# 2. Related Work
+
+In this section, we begin with a concise review of test-time adaptation with VLMs, followed by a discussion of optimal transport and its applications in VLMs.
+
+# 2.1. Test-time Adaptation
+
+Test-time adaptation [11, 41, 54] is an effective technique to address the distribution shift between testing and training datasets. Its core idea is to adjust the model using a streaming of unlabeled test samples. Early works [44] improve test-time adaptation performance by fine-tuning normalization layers. Motivated by the success of VLMs [19, 38], recent studies [41, 54] propose to optimize textual prompts via entropy minimization. While these methods require high computational costs due to the gradient backpropagation. To address this, another branch of works [14, 21, 56] adapting the VLMs in a non-parametric manner has emerged. Karmanov et al. [21] designs positive and negative caches to store high-confidence samples, improving the performance by calculating the similarity between the test sample and cached samples. Han et al. [14] proposes a method named DOTA [14], estimating the distribution of test samples progressively. Zhang et al. [56] extends the cache model to a dual memory network (DMN), which also works in test-time scenarios. Although these methods avoid gradient updates, they all need logit fusion for prediction, and their performance is sensitive to fusion hyperparameters.
+
+Our work aligns with the training-free paradigm. Unlike existing methods that primarily rely on unimodal information (class names), we demonstrate that incorporating multimodal information (test images and class names) facilitates the adaptation of VLMs more effectively. Moreover, we propose a dynamic multimodal prototype learning framework that utilizes visual knowledge from test samples to update the multimodal prototypes.
+
+# 2.2. Optimal Transport
+
+Optimal transport (OT) [32] is initially introduced to solve the problem of how to reduce the cost when moving several items simultaneously, and then it is applied to measure the distance between distributions in the deep learning areas [4, 5, 13, 23, 26, 65], including domain adaption [7], clustering[40, 53], image classification [12, 25, 45, 62]. For example, Lazarou et al. [23] directly aligns the distribution of two sets of feature embeddings to address the transductive few-shot task. Guo et al. [13] proposes hierarchical OT to transfer the statistics from the base classes to novel classes in distribution calibration. Chen et al. [4] aims to align the features of vision and language modalities by optimizing textual prompts via OT. Recently, AWT [65], a simple and effective method adapts VLMs in zero/few-shot scenarios, which is closely related to our work. AWT formulates the image-text distance calculation as an OT problem, and solving this problem reveals the semantic correlations in the vision-language space for prediction.
+
+While AWT and the above methods focus on aligning different sets or modalities, our approach leverages OT to enhance textual prototypes by incorporating visual knowledge, rather than aligning different sets or modalities. Specifically, we aim to accumulate informative visual knowledge into textual prototypes to reduce ambiguities. To achieve this, we utilize the transport plan to adjust each test sample's contribution to different class prototypes, and then use the weighted test sample to update the prototypes.
+
+# 3. Method
+
+In this section, we first briefly review the preliminary knowledge of VLMs and OT [32]. Then we introduce the details of our multimodal prototype learning framework for adapting VLMs in test-time scenarios as illustrated in Figure 3.
+
+# 3.1. Preliminaries
+
+Vision-language models (VLMs). CLIP [38] as one of the well-known VLMs, consists of a vision encoder $f(\cdot)$ and a text encoder $g(\cdot)$ . Given a set of $C$ class names $\{z_{c}\}_{c=1}^{C}$ , CLIP first constructs the class description using a pre-defined prompt template $\Phi$ , e.g., $\Phi(z_{c})$ can be chosen as "a photo of a $z_{c}$ " and then obtains the prototypes by feeding the class descriptions into $g$ : $\mathbf{z}_{c} = g(\Phi(z_{c}))$ . For the testing image $x_{t}$ at time $t$ , let $\mathbf{x}_{t} = f(x_{t})$ denotes the extracted visual feature. The zero-shot classification for $x_{t}$ is computed as:
+
+$$
+y _ {t} = \underset {c \in \{1, 2, \dots , C \}} {\operatorname {a r g m a x}} \mathbf {z} _ {c} ^ {\top} \mathbf {x} _ {t}, \tag {1}
+$$
+
+where $\mathbf{z},\mathbf{x}\in \mathbb{R}^d$ share the same semantic embedding space. $\mathbf{z}_c$ can be viewed as the prototype of $c$ -th class. To improve the quality of $\mathbf{z}_c$ , previous studies focus on test prompt tuning of $\Phi$ or generating detailed class descriptions via large language models (LLMs) [31, 36].
+
+Optimal transport. Optimal Transport (OT) [32] is an efficient tool to measure the distance between two distributions. Specifically, consider two discrete distributions in the feature space: $P = \sum_{i=1}^{|V|} a_i \delta_{\mathbf{v}_i}$ and $Q = \sum_{j=1}^{|U|} b_j \delta_{\mathbf{u}_j}$ , where $\delta$ is the Dirac delta function and $|V|$ and $|U|$ denote the number of points in $P$ and $Q$ , respectively. Here, $\mathbf{a} = [a_1, \ldots, a_{|V|}]^\top$ and $\mathbf{b} = [b_1, \ldots, b_{|U|}]^\top$ denote the probability vectors that sum to 1. Given the cost matrix $\mathbf{C} \in \mathbb{R}^{|V| \times |U|}$ , whose each element measures the transport cost between $\mathbf{v}_i$ and $\mathbf{u}_j$ , the OT distance between distributions $P$ and $Q$ is formulated as:
+
+$$
+\begin{array}{l} d _ {\mathrm {O T}} (P, Q; \mathbf {C}) = \min _ {\mathbf {T}} \langle \mathbf {T}, \mathbf {C} \rangle , \tag {2} \\ \mathrm {s . t .} \mathbf {T} \mathbb {1} _ {| U |} = \mathbf {a}, \mathbf {T} ^ {\top} \mathbb {1} _ {| V |} = \mathbf {b}, \\ \end{array}
+$$
+
+where $\mathbf{T} \in \mathbb{R}^{|V| \times |U|}$ is the transport plan to be learned, which indicates the transport probability from source point in $P$ to target point in $Q$ . $\langle \cdot, \cdot \rangle$ denotes the Frobenius dot-product and $\mathbb{1}_{|V|}$ refers to $|V|$ -dimensional all-one vector. However, directly computing Eq. (2) is often computationally intensive. Following previous work [4, 23], we employ the Sinkhorn algorithm [8], which introduces an entropic regularization term to facilitate efficient optimization. The resulting objective is then given by:
+
+$$
+d _ {\mathrm {O T}} (P, Q; \mathbf {C}) = \min _ {\mathbf {T}} \langle \mathbf {T}, \mathbf {C} \rangle - \epsilon h (\mathbf {T}), \tag {3}
+$$
+
+where $h(\cdot)$ is entropy and $\epsilon \geq 0$ is a coefficient.
+
+# 3.2. Distributed Feature Construction
+
+Moving beyond prototype learning within the textual domain, we introduce ProtoMM and explore the multimodal prototype discovery for zero-shot classification. As shown in Figure 3, ProtoMM consists of two main modules: distributed feature construction that models the multimodal prototype and testing image as discrete distributions, and multimodal prototype learning that updates multimodal prototypes by integrating visual information from history.
+
+To mimic how humans learn a new concept through different perspectives and obtain informative features, we follow strategies from previous works [24, 30, 65] and view the image and prototype as discrete distribution at the CLIP [38] space. Specifically, for each image $x_{t}$ , we employ common augmentation techniques such as random crop, flip, and resize. This augments $x_{t}$ into multiple views $\{x_{t}^{n}\}_{n = 1}^{N}$ including $N - 1$ augmentations and the original one. Simultaneously, we query large language models [31, 36] to generate descriptive sentences for each class name. As a result, each textual prototype $z_{c}$ is enhanced with $M - 1$ additional descriptions, denoted as $\{z_c^m\}_{m = 1}^M$ . Mathematically, the resulting distributions of the image and prototype are formulated as:
+
+$$
+P _ {t} = \sum_ {n = 1} ^ {N} a _ {t} ^ {n} \delta_ {\mathbf {x} _ {t} ^ {n}}; \quad Q _ {c} = \sum_ {m = 1} ^ {M} b _ {c} ^ {m} \delta_ {\mathbf {z} _ {c} ^ {m}}, \tag {4}
+$$
+
+
+Figure 3. An framework of the proposed method (ProtoMM), which consists of two modules, i.e., (a) Distributed Feature Construction: Expand the textual prototypes with visual features from testing samples. (b) Multimodal Prototype Learning: Updating the multimodal prototypes through the transport plan for the next prediction.
+
+where $\mathbf{x}_t^n$ is the feature of the $n$ -th image view and it contributes detailed information about a specific region or angle. $\mathbf{z}_c^m$ is the feature of the $m$ -th prototype description from LLMs and it shares reasonable prior knowledge of class $z_c$ . Instead of viewing the image and prototype as a single point in the feature space, Eq. (4) models them as discrete distributions in the feature space. This enables our ProtoMM to capture diverse details, leading to comprehensive representation learning. $\mathbf{a}_t = [a_t^1,\dots ,a_t^N ]^\top$ and $\mathbf{b}_c = [b_c^1,\dots ,b_c^M ]^\top$ denote the important weights of image and feature points, respectively, i.e., high-quality enhancements should be highly valued while uninformative enhancements should be ignored, which will be discussed later.
+
+As mentioned before, the prototype in Eq. (4) only considers the textual domain, which may not fully cover the visual details of class $z_{c}$ , thereby we introduce the concept of multimodal prototype learning and aim to integrate the visual modality into $Q_{c}$ . Specifically, we expand the prototype set $\{\mathbf{z}_c^m\}_{m=1}^M$ by appending $S$ additional visual particles: $\{\mathbf{e}_c^s\}_{s=1}^S$ , where $\mathbf{e}_c \in \mathbb{R}^d$ . Then the multimodal prototype is formulated as (We still use $Q_{c}$ for convenience):
+
+$$
+Q _ {c} = \sum_ {m = 1} ^ {M} w _ {c} ^ {m} \delta_ {\mathbf {z} _ {c} ^ {m}} + \sum_ {s = 1} ^ {S} w _ {c} ^ {M + s} \delta_ {\mathbf {e} _ {c} ^ {s}}, \tag {5}
+$$
+
+where $\mathbf{w}_c = [w_c^1, \dots, w_c^{M + S}]^\top$ denotes the important weights of $M + S$ points in the multimodal prototype. The first term comes from the knowledge of LLMs and the second term can be viewed as a cache that aims to complete the missing features of LLMs using historical images (Sec. 3.3). Combining these two modalities, Eq. (5) are expected to cover comprehensive characteristics of the $c$ -th class.
+
+Following previous works [14, 21], we evaluate test samples sequentially in a streaming manner and hope the visual cache learns from the history, providing valuable guidance for the following samples. Before testing, the visual cache
+
+and its importance weights must be properly initialized to complete the multimodal prototype in Eq. (5). Since images are unavailable at the start of testing, it is natural to construct all visual cache of prototype $P_{c}$ by averaging corresponding textual descriptions: $\mathbf{e}_c^s = \frac{1}{M}\sum_{m=1}^{M}\mathbf{z}_c^m$ . To determine the importance weights of each element in $P$ and $Q$ , we propose a novel calculating strategy based on the input image. For the arriving image $x_{t}$ , we first calculate the important weights of its $N$ visual augments according to all prototypes:
+
+$$
+a _ {t} ^ {n} = \frac {\exp \left(h \left(\mathbf {x} _ {t} ^ {n}\right)\right)}{\sum_ {n ^ {\prime} = 1} ^ {N} \exp \left(h \left(\mathbf {x} _ {t} ^ {n ^ {\prime}}\right)\right)},
+$$
+
+$$
+h \left(\mathbf {x} _ {t} ^ {n}\right) = \sum_ {c = 1} ^ {C} p \left(\bar {\mathbf {z}} _ {c} \mid \mathbf {x} _ {t} ^ {n}\right) \log p \left(\bar {\mathbf {z}} _ {c} \mid \mathbf {x} _ {t} ^ {n}\right), \tag {6}
+$$
+
+where $\bar{\mathbf{z}}_c = \frac{1}{M + S}\left(\sum_{m=1}^{M} \mathbf{z}_c^m + \sum_{s=1}^{S} \mathbf{e}_c^s\right)$ denotes the mean of $c$ -th multimodal prototype. $a_t^n$ becomes larger when the content of $n$ -th augment is semantically close to descriptions at the embedding space and the noise augments such as backgrounds will be ignored by a lower attention value.
+
+Similarly, the important weight $\mathbf{w}_c$ for $c$ -th class is derived by considering its correlation with the visual features across all augmentations:
+
+$$
+w _ {c} ^ {m} = \frac {\exp \left(h (\mathbf {z} _ {c} ^ {m})\right)}{\sum_ {m ^ {\prime} = 1} ^ {M + S} \exp \left(h (\mathbf {z} _ {c} ^ {m ^ {\prime}})\right)},
+$$
+
+$$
+h \left(\mathbf {z} _ {c} ^ {m}\right) = \sum_ {n = 1} ^ {N} p \left(\mathbf {z} _ {c} ^ {m} \mid \mathbf {x} _ {t} ^ {n}\right) \log p \left(\mathbf {z} _ {c} ^ {m} \mid \mathbf {x} _ {t} ^ {n}\right), \tag {7}
+$$
+
+$\{\mathbf{z}_c^m\}_{m = M + 1}^{M + S} = \{\mathbf{e}_c^s\}_{s = 1}^S.$ Intuitively, we use the visual content to measure the importance of each point in $Q$ and expect to construct an instance-specific prototype, improving the generalizability of unseen scenarios.
+
+# Algorithm 1 Pipeline of ProtoMM
+
+Require: Augmented text prototypes $\{\mathbf{z}_c^m\}_{m = 1,c = 1}^{M,C}$
+
+1: for $t = 1,2,\ldots ,$ do
+2: Augment the test image $x_{t}$ , and then compute the image features $\{\mathbf{x}_t^n\}_{n = 1}^N$ .
+3: Construct multimodal features by Eq. (5).
+4: Calculate importance weights $\mathbf{a}_t$ and $\mathbf{w}_c$ using Eq. (6) and Eq. (7), respectively.
+5: Obtain transport plan $\mathbf{T}_{tc}$ by solving Eq. (8).
+6: Calculate predicted label $p(y_{t} = c|\mathbf{x}_{t})$ by Eq. (9).
+7: Update multimodal prototypes $\{\mathbf{e}_c^s\}_{s = 1,c = 1}^{S,C}$ via Eq. (10).
+8: end for
+
+# 3.3. Multimodal Prototype Learning
+
+Once $\mathbf{a}_t$ and $\mathbf{w}_c$ are calculated, we construct the discrete distributions $P_t$ and $Q_c$ according to Eq. (4-5). Specifying the cost matrix $\mathbf{C}_{tc} \in \mathbb{R}^{N \times (M + S)}$ as the cosine distance between the visual augmentations and multimodal prototypes, we reformulate Eq. (3) as:
+
+$$
+\begin{array}{l} d _ {\mathrm {O T}} \left(P _ {t}, Q _ {c}; \mathbf {C} _ {t c}\right) = \min _ {\mathbf {T} _ {t c}} \left\langle \mathbf {T} _ {t c}, \mathbf {C} _ {t c} \right\rangle - \epsilon h \left(\mathbf {T} _ {t c}\right), \tag {8} \\ \begin{array}{l} \text {s . t .} \mathbf {T} _ {t c} \mathbb {1} _ {M + S} = \mathbf {a} _ {t}, \mathbf {T} _ {t c} ^ {\top} \mathbb {1} _ {N} = \mathbf {w} _ {c}, \end{array} \\ \end{array}
+$$
+
+where $\mathbf{T}_{tc} \in \mathbb{R}^{N \times (M + S)}$ , whose each element denotes the transport probability from $n$ -th augmentation to $m$ -th prototype point in the feature space. After solving Eq. (8) using the Sinkhorn algorithm [8], we calculate the prediction probability of image $x_{t}$ as:
+
+$$
+p \left(y _ {t} = c \mid \mathbf {x} _ {t}\right) = \frac {\exp \left(- d _ {\mathrm {O T}} \left(P _ {t} , Q _ {c} ; \mathbf {C} _ {t c}\right)\right)}{\sum_ {c ^ {\prime} = 1} ^ {C} \exp \left(- d _ {\mathrm {O T}} \left(P _ {t} , Q _ {c ^ {\prime}} ; \mathbf {C} _ {t c ^ {\prime}}\right)\right)}. \tag {9}
+$$
+
+The core idea of the visual cache is to collect high-quality samples for multimodal prototype learning. To this end, we first filter out samples whose highest prediction probability is less than a threshold: $p(y_{t} = c|\mathbf{x}_{t}) \geq \tau$ . For the high-quality samples, we develop a score function and only choose the augmentations with high importance. Recalling that the transport plan measures the semantic similarity between the textual prototype and visual augmentations, the score of the augmentation of $x_{t}$ thus can be calculated as $\Theta_{t} = \mathbf{T}_{tc}\pmb{w}_{y_{t}} \in \mathbb{R}^{N}$ . We then select the top- $S$ candidates $[\mathbf{x}_t^{(1)},\dots ,\mathbf{x}_t^{(S)}]^{\top} \in \mathbb{R}^{S\times d}$ according to the decreasing value sequence $[\theta_t^{(1)},\dots ,\theta_t^{(S)}]$ in $\Theta_{t}$ . The visual cache in our multimodal prototype $Q_{c}$ is updated using these selected high-quality candidates:
+
+$$
+\mathbf {e} _ {c} ^ {s} \leftarrow \frac {w _ {t} ^ {M + s} \mathbf {e} _ {c} ^ {s} + \theta_ {t} ^ {(s)} \mathbf {x} _ {t} ^ {(s)}}{w _ {t} ^ {M + s} + \theta_ {t} ^ {(s)}}, s \in [ 1, S ], c \in [ 1, C ], \tag {10}
+$$
+
+This weighting mechanism ensures that the model can dynamically adjust its focus based on the reliability and relevance of each sample.
+
+# 4. Experiments
+
+We present the experimental results of our method on 15 classification datasets in the test-time scenario, including performance comparisons, ablation studies, and visualizations. More results are provided in the Supplementary Material.
+
+# 4.1. Setup
+
+Datesets. Following the previous works [21, 24], we cover 11 classification datasets including diverse range categories, generic objects (ImageNet [9], Caltech [10]), scenes (SUN [47]), textures (DTD [6]), satellite images (EuroSAT [15]), actions (UCF [42]) and fine-grained categories (Pets [34], Cars [22], Flowers [33], Food [3], Aircraft [29]). Additionally, we evaluate on 4 ImageNet distribution shifted datasets [9]: ImageNetV2 [39], ImageNet-Sketch [46], ImageNet-A [17], ImageNet-R [16].
+
+Implementation details. The experiments are built upon the pre-trained CLIP [38] model. We adapt ResNet50 (RN50) and ViT-B/16 backbones as the visual encoder, and the textual encoder is a Transformer [43]. We adhere to the same image augmentation strategies as AWT [65], including random cropping and resizing as well as flipping. For textual augmentation, we query GPT-3.5 to generate the class descriptions following the previous works [31, 65]. The total augmentation number $M$ and $N$ are both set as 50. Top- $S$ is set to 25, and threshold $\tau = 0.8$ . All experiments are conducted on one NVIDIA RTX 3090 GPU.
+
+Comparison methods. We compare our method with previous state-of-the-art (SOTA) test-time adaptation methods, including TPT [41], DiffTPT [11], TDA [21], DOTA [14], DPE [55] and AWT [65]. In these comparison methods, TDA [21], AWT [65], and DOTA [14] are designed in a training-free manner. TPT [41] and DiffTPT [11] are prompt tuning methods, and DPE [55] belongs to the adapter tuning method. The optimization process of there methods are happened during the inference stage. Additionally, we compare several prompt learning methods, such as CoOp [58] and CoCoOp [57], as well as augmentation-based methods, including CUPL [36], VisDescs [30], and MetaPrompting [31].
+
+# 4.2. Main Results
+
+We compare our methods with state-of-the-art (SOTA) methods across 11 widely used classification datasets, using RN50 and ViT-B/16 backbones. The results presented in Table 1 highlight the superior performance of our method which consistently outperforms AWT [65] across all datasets under RN50 excluding Pets, with an averaged accuracy gain of $0.93\%$ . When compared to TDA [21] and DOTA [14] using RN50, our method achieves the $2.04\%$ and $0.94\%$ averaged accuracy improvements, which is significant in test-time scenarios. In the Caltech101 [10] dataset, DPE [55] exhibits the highest performance, which is due to tuning the
+
+| Method | Aircraft | Caltech101 | Cars | DTD | EuroSAT | Flower102 | Food101 | Pets | SUN397 | UCF101 | ImageNet | Average |
| RN50 | CLIP [38] | 16.11 | 87.26 | 55.89 | 40.37 | 25.79 | 62.77 | 74.82 | 82.97 | 60.85 | 59.48 | 59.81 | 56.92 |
| CoOp [58] | 15.12 | 86.53 | 55.32 | 37.29 | 26.20 | 61.55 | 75.59 | 87.00 | 58.15 | 59.05 | 63.33 | 56.83 |
| CoCoOp [57] | 14.61 | 87.38 | 56.22 | 38.53 | 28.73 | 65.57 | 76.20 | 88.39 | 59.61 | 57.10 | 62.81 | 57.74 |
| CuPL [36] | 19.59 | 89.29 | 57.28 | 48.64 | 38.38 | 65.44 | 76.94 | 84.84 | 62.55 | 58.97 | 61.45 | 60.31 |
| VisDesc [30] | 16.26 | 88.11 | 54.76 | 41.96 | 37.60 | 65.37 | 76.80 | 82.39 | 59.84 | 58.47 | 59.68 | 58.29 |
| TPT [41] | 17.58 | 87.02 | 58.46 | 40.84 | 28.33 | 62.69 | 74.88 | 84.49 | 61.46 | 60.82 | 60.74 | 57.93 |
| DiffTPT [11] | 17.60 | 86.89 | 60.71 | 40.72 | 41.04 | 63.53 | 79.21 | 83.40 | 62.72 | 62.67 | 60.80 | 59.93 |
| TDA [21] | 17.61 | 89.70 | 57.78 | 43.74 | 42.11 | 68.74 | 77.75 | 86.18 | 62.53 | 64.18 | 61.35 | 61.06 |
| DOTA [14] | 18.06 | 88.84 | 58.72 | 45.80 | 47.15 | 68.53 | 78.61 | 87.33 | 63.89 | 65.08 | 61.82 | 62.16 |
| DPE [55] | 19.80 | 90.83 | 59.26 | 50.18 | 41.67 | 67.60 | 77.83 | 85.97 | 64.23 | 61.98 | 63.41 | 62.06 |
| AWT* [65] | 20.31 | 89.57 | 59.22 | 49.46 | 38.80 | 68.21 | 77.18 | 88.22 | 64.91 | 65.02 | 63.01 | 62.17 |
| ProtoMM | 21.21 | 89.94 | 60.10 | 50.53 | 42.35 | 69.95 | 77.31 | 87.92 | 65.74 | 65.34 | 63.76 | 63.10 |
| VIT-B/16 | CLIP [38] | 23.22 | 93.55 | 66.11 | 45.04 | 50.42 | 66.99 | 82.86 | 86.92 | 65.63 | 65.16 | 68.34 | 64.93 |
| CoOp [58] | 18.47 | 93.70 | 64.51 | 41.92 | 46.39 | 68.71 | 85.30 | 89.14 | 64.15 | 66.55 | 71.51 | 64.57 |
| CoCoOp [57] | 22.29 | 93.79 | 64.90 | 45.45 | 39.23 | 70.85 | 83.97 | 90.46 | 66.89 | 68.44 | 71.02 | 65.20 |
| CuPL [36] | 24.90 | 92.98 | 65.29 | 44.56 | 47.84 | 71.30 | 86.11 | 89.13 | 62.59 | 66.83 | 69.62 | 65.55 |
| Visdesc [30] | 24.30 | 94.60 | 64.08 | 44.98 | 54.84 | 70.85 | 85.05 | 88.85 | 67.99 | 67.12 | 68.55 | 66.47 |
| TPT [41] | 24.78 | 94.16 | 66.87 | 47.75 | 42.44 | 68.98 | 84.67 | 87.79 | 65.50 | 68.04 | 68.98 | 65.45 |
| DiffTPT [11] | 25.60 | 92.49 | 67.01 | 47.00 | 43.13 | 70.10 | 87.23 | 88.22 | 65.74 | 62.67 | 70.30 | 65.40 |
| TDA [21] | 23.91 | 94.24 | 67.28 | 47.40 | 58.00 | 71.42 | 86.14 | 88.63 | 67.62 | 70.66 | 69.51 | 67.71 |
| DOTA [14] | 25.59 | 94.32 | 69.48 | 47.87 | 57.65 | 74.67 | 87.02 | 91.69 | 69.70 | 72.06 | 70.68 | 69.15 |
| DPE [55] | 28.95 | 94.81 | 67.31 | 54.20 | 55.79 | 75.07 | 86.17 | 91.14 | 70.07 | 70.44 | 71.91 | 69.62 |
| AWT* [65] | 29.22 | 95.40 | 69.80 | 55.56 | 58.40 | 75.07 | 85.54 | 92.23 | 70.00 | 70.70 | 71.26 | 70.28 |
| ProtoMM | 31.02 | 95.70 | 69.92 | 56.38 | 56.11 | 77.40 | 85.89 | 91.90 | 70.78 | 71.76 | 72.01 | 70.70 |
+
+Table 1. Performance comparisons of accuracy (%) on the cross-domain benchmark. All the compared methods are built upon CLIP-RN50 or CLIP-ViT-B/16 backbone. The evaluation metric Average is calculated by taking the mean accuracy across all 11 datasets. The best and second best results are denoted in bold and underline, respectively. * refers to our implementation using their publicly released code.
+
+adapters for each testing sample. However, this process is more computationally and time-costing. For the ViT-B/16 backbone, we observe similar results, with our method surpassing the existing methods across most datasets, showing an average accuracy improvement of $1.08\%$ over DPE. Especially on the fine-grained Flowers102 [33] datasheet, our method outperforms the second-best AWT by over $2.3\%$ . We also evaluate our method with SOTA methods on the ImageNet [9] and its 4 out-of-distribution (OOD) variants, as shown in Table 2. The experimental results demonstrate that our method exhibits competitive generalization performance across all methods. Specifically, our ProtoMM outperforms TDA by $2.58\%$ and AWT by $0.71\%$ on average when using the RN50 backbone. Moreover, with the ViT-B/16 backbone, our method surpasses the second-best method, DOTA, by an average of $1.17\%$ on the OOD dataset. Even compared to the training-based DPE, it achieves an average improvement of $1.03\%$ . These results demonstrate the adaptability of our method to varied distributions. Notably, this generalization is achieved without any test-time optimization or tuning.
+
+# 4.3. Ablation Study
+
+We conduct experiments to assess the effectiveness of each module and strategy designed in our method. Additionally, we evaluate its efficiency and present visualizations.
+
+Effectiveness of using multimodal prototypes. We examine the contributions of the distributed feature construction module and the multimodal prototype learning module, respectively. The results are summarized in Table 3. Row (1) presents the zero-shot CLIP [38] performance as a baseline. In Row (2), Eq. (5) stands for the distributed feature construction, which expands the textual prototypes by incorporating additional features with their importance weights, achieving $1\%$ gains over CLIP on ImageNet with RN50. Row (3) shows the results of using both modules in our method, outperforming the variant that only uses Eq. (5) by over $1\%$ on Caltech101 with ViT-B/16. These improvements indicate that dynamically incorporating multimodal prototypes leads to better representations and improved test-time adaptation.
+
+Effectiveness of the Number of Augmentations. We evalu
+
+| RN50 | Method | ImageNet | ImageNet-A | ImageNet-V2 | ImageNet-R | ImageNet-S | Average | OODAverage |
| CLIP [38] | 59.81 | 23.24 | 52.91 | 60.72 | 35.48 | 46.43 | 43.09 |
| CoOp [58] | 63.33 | 23.06 | 55.40 | 56.60 | 34.67 | 46.61 | 42.43 |
| CoCoOp [57] | 62.81 | 23.32 | 55.72 | 57.74 | 34.48 | 46.81 | 42.82 |
| CuPL [36] | 61.45 | 23.86 | 54.61 | 61.02 | 35.13 | 47.21 | 43.65 |
| VisDes [30] | 59.68 | 21.17 | 52.36 | 57.16 | 33.78 | 44.83 | 41.11 |
| TPT [41] | 60.74 | 26.67 | 54.70 | 59.11 | 35.09 | 47.26 | 43.89 |
| DiffTPT [11] | 60.80 | 31.06 | 55.80 | 58.80 | 37.10 | 48.71 | 45.69 |
| TDA [21] | 61.35 | 30.29 | 55.54 | 62.58 | 38.12 | 49.58 | 46.63 |
| DOTA [14] | 61.82 | 30.81 | 55.27 | 62.81 | 37.52 | 49.64 | 46.60 |
| DPE [55] | 63.41 | 30.15 | 56.72 | 63.72 | 40.03 | 50.80 | 47.65 |
| AWT* [65] | 63.01 | 30.93 | 56.31 | 63.06 | 39.71 | 50.60 | 47.50 |
| ProtoMM | 63.76 | 30.56 | 57.28 | 63.95 | 41.05 | 51.32 | 48.21 |
| ViT-B/16 | CLIP [38] | 68.34 | 49.89 | 61.88 | 77.65 | 48.24 | 61.20 | 59.42 |
| CoOp [58] | 71.51 | 49.71 | 64.20 | 75.21 | 47.99 | 61.72 | 59.28 |
| CoCoOp [57] | 71.02 | 50.63 | 64.07 | 76.18 | 48.75 | 62.13 | 59.91 |
| CuPL [36] | 69.62 | 50.72 | 63.27 | 77.05 | 49.02 | 61.93 | 60.01 |
| VisDes [30] | 68.55 | 49.07 | 61.80 | 75.13 | 47.97 | 60.50 | 58.49 |
| TPT [41] | 68.98 | 54.77 | 63.45 | 77.06 | 47.94 | 62.44 | 60.81 |
| DiffTPT [11] | 70.30 | 55.68 | 65.10 | 75.00 | 46.80 | 62.28 | 60.52 |
| TDA [21] | 69.51 | 60.11 | 64.67 | 80.24 | 50.54 | 65.01 | 63.89 |
| DOTA [14] | 70.68 | 61.19 | 64.41 | 81.17 | 51.33 | 65.75 | 64.52 |
| DPE [55] | 71.91 | 59.63 | 65.44 | 80.44 | 52.26 | 65.93 | 64.44 |
| AWT* [65] | 71.26 | 60.33 | 65.05 | 80.38 | 51.60 | 65.72 | 64.34 |
| ProtoMM | 72.01 | 64.02 | 65.93 | 80.87 | 51.97 | 66.96 | 65.69 |
+
+Table 2. Performance comparison of accuracy (%) on the out-of-distribution benchmark. All the compared methods are built upon CLIP-RN50 or CLIP-ViT-B/16 backbone. The two evaluation metrics Average and OOD Average are calculated by taking the mean accuracy across all five datasets and four OOD datasets excluding ImageNet. The best and second best results are denoted in bold and underline, respectively. * refers to our implementation using their publicly released code.
+
+| Eq. (5) Eq. (10) | ImageNet | Caltech101 |
| RN50 | ViT-B/16 | RN50 | ViT-B/16 |
| (1) | CLIP [38] | 59.81 | 68.34 | 87.26 | 93.55 |
| (2) | ✓ | 60.82 | 68.98 | 88.16 | 94.65 |
| (3) | ✓ | ✓ | 63.76 | 72.01 | 89.94 |
| | | | 95.70 | |
+
+Table 3. Performance of our method with different modules, where Eq.(5) and Eq.(10) denote the Distributed Feature Construction and Multimodal Prototype Learning in our method, respectively.
+
+ate the impact of the number of augmentations on images and class names for both RN50 and ViT-B/16 backbones, as illustrated in Figure 4a and Figure 4b, respectively. For visual augmentations, the accuracy initially improves as the number of augmentations increases from 1 to 40, after which the performance stabilizes. This trend indicates that increasing the number of image augmentations can effectively improve the discriminability of multimodal prototypes up to a certain point. On the other hand, textual augmentations (Figure 4b) show similar results to visual augmentations. As the number
+
+
+(a) Visual Augmentation.
+
+
+(b) Textual Augmentaion.
+Figure 4. Analysis of classification performance by varying the number of augmentations in the ImageNet dataset: (a) image augmentation, (b) class name augmentation.
+
+of textual augmentations varies from 1 to 70, the accuracy initially increases and then converges. This implies that beyond a certain number, adding more descriptive sentences for class names does not improve the quality of prototypes. Based on these observations, we set the number of visual and textual augmentations both as $L = K = 50$ , which is consistent with the setting in AWT.
+
+Effectiveness of threshold $\tau$ We set the threshold to ensure
+
+
+Figure 5. Analysis of classification performance by varying the threshold value on the ImageNet dataset.
+
+
+Figure 6. Analysis of classification performance by varying the selection number on the ImageNet dataset.
+
+confident prediction for the test samples. A large value of $\tau$ implies stricter criteria for selecting samples, which can increase the reliability of predictions. We vary $\tau$ from 0.1 to 0.99. The results in Figure 5 show that as the threshold $\tau$ increases, performance improves gradually. However, once the threshold exceeds 0.8, the performance begins to degrade. Without testing samples ( $\tau = 1$ ) fail to establish the multimodal prototypes, leading to worse performance. Furthermore, using all test samples ( $\tau = 0$ ) without any confidence-based filtering does not lead to optimal performance, as low-confidence predictions may introduce incorrect labels that provide limited useful information and potentially disrupt the structure of the multimodal prototypes.
+
+Effectiveness of top- $S$ selection. In our method, we select the top- $S$ confident samples for constructing multimodal prototypes. To assess the influence of the number of selected samples, we vary the selection number from 5 to 50 and analyze the results illustrated in Figure 6. The results indicate that performance improves as the number of selected samples increases, reaching a stable state when exceeding a certain number. Including too many augmented samples with high prediction confidence does not further boost performance, as the visual knowledge provided by each test sample to the textual prototypes is sufficient. Overall, our method shows robust performance across a typical range of top- $S$ values, maintaining stable classification accuracy.
+
+Visualization of transport plan. To intuitively demonstrate the effectiveness of our method, we visualize the heatmap of the transport plan $\mathbf{T}$ for the testing sample, as illustrated in Figure 7. We select four test images from the ImageNet dataset, such as "hamster," "mountain bike," "robin," and "malamute," where the transport plans primarily focus on the objects. This demonstrates that our method effectively transfers discriminative visual knowledge to textual prototypes, resulting in more representative multimodal prototypes.
+
+Comparison of Inference Time Our method is training-free, unlike methods that require prompt tuning or adapter tuning, such as TPT, DiffTPT, and DPE, which involve back
+
+
+Figure 7. Visualization of heatmaps for the transport plans.
+
+
+
+propagating through an expensive encoder or adapter during optimization. We evaluate the inference time using a single NVIDIA 3090 GPU. The experimental results in Table 4 indicate that our method is faster than the tuning-based methods. Although our method takes slightly more time than TDA, we achieve a notable performance improvement, outperforming TDA by over $2.4\%$ . It is worth noting that the Sinkhorn algorithm [8] supports efficient parallel computation, allowing the distance between one distribution and multiple others to be evaluated simultaneously, as demonstrated in prior works [4, 65]. This parallelism further contributes to the comparable runtime of our method relative to TDA.
+
+| Method | Testing Time | Accuracy | Gain |
| CLIP [38] | 13min | 59.81 | 0 |
| TPT [41] | 14h 30min | 60.74 | +0.93 |
| DiffTPT [11] | 37h 25min | 60.80 | +0.99 |
| TDA [21] | 17min | 61.35 | +1.54 |
| DOTA [14] | 18min | 61.82 | +2.01 |
| DPE [55] | 2h 40min | 63.41 | +3.60 |
| AWT [65] | 21min | 63.01 | +3.20 |
| Proto | 21min | 63.76 | +3.95 |
+
+Table 4. Comparisons of efficiency (Testing Time) and effectiveness (Accuracy) with the RN50 backbone.
+
+# 5. Conclusion
+
+In this work, we introduce a novel training-free multimodal prototype learning framework for adapting VLMs during test time. Our method models prototypes as a discrete distribution of class descriptions and visual particles, where the visual particles are dynamically updated from the testing streams. This process enables the multimodal prototypes to progressively accumulate visual knowledge, enhancing the prediction performance progressively. Extensive experiments demonstrate the effectiveness of our method. In the future, we aim to design a more efficient multimodal prototype learning framework, and apply it to more high-level downstream tasks, such as image/video understanding.
+
+# 6. Acknowledge
+
+This research is supported by the National Natural Science Foundation of China (No.U24B20180) and the advanced computing resources provided by the Supercomputing Center of the USTC. It is also supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR.
+
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