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ICCV/2025/DisCoPatch_ Taming Adversarially-driven Batch Statistics for Improved Out-of-Distribution Detection/full.md

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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
+
+![](images/21597eea4d7bba519cb750909e200da9215bf7cae1a90a5f55ec1df099813a7d.jpg)  
+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.
+
+![](images/64a65af67b2c5b46865fc9432a39135025653440957940b92c805af442e35117.jpg)  
+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
+
+![](images/185109ee597987a0d03da8cff3673962336f6503eb2ff37ada9cafc89dc27e21.jpg)  
+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
+
+![](images/f75d4184ecd6c1ad91b95e12425a5fbbba642d420d600b149a3b9c82b3780aed.jpg)  
+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.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Near-OOD</td><td colspan="3">Far-OOD</td><td>Covariate Shift</td></tr><tr><td>SSB-hard</td><td>NINCO</td><td>iNaturalist</td><td>DTD</td><td>OpenImage-O</td><td>ImageNet-1K(-C)</td></tr><tr><td>MOODv2 [34] (BEiTv2)</td><td>85.0/58.1*</td><td>92.7/38.2*</td><td>99.6/1.8</td><td>94.3/24.7</td><td>97.4/13.6</td><td>70.5/73.9*</td></tr><tr><td>SCALE [68] (ResNet-50)</td><td>77.4/67.7</td><td>85.4/51.8</td><td>98.0/9.5</td><td>97.6/11.9</td><td>94.0/28.2</td><td>83.3/54.1*</td></tr><tr><td>NNGuide [44] (RegNet)</td><td>84.7/54.7*</td><td>93.7/28.9*</td><td>99.9/1.8</td><td>95.8/17.0</td><td>97.7/10.8</td><td>78.5/61.6*</td></tr><tr><td>NNGuide [44] (ResNet-50)</td><td>71.5/82.8*</td><td>80.5/69.8*</td><td>96.9/14.3</td><td>90.4/27.4</td><td>92.4/35.4</td><td>78.6/58.7*</td></tr><tr><td>NNGuide [44] (MobileNetV2)</td><td>64.3/90.3*</td><td>75.5/80.2*</td><td>80.2/70.2</td><td>88.3/40.6</td><td>82.9/63.3</td><td>78.1/61.4*</td></tr><tr><td>RankFeat [56] (ResNetv2-101)</td><td>89.4/47.9*</td><td>90.0/39.3*</td><td>96.0/13.0</td><td>95.0/25.4</td><td>92.4/33.3*</td><td>91.3/38.7*</td></tr><tr><td>ASH [10] (ResNet-50)</td><td>74.1/80.6*</td><td>83.0/64.2*</td><td>97.9/11.5</td><td>97.6/11.9</td><td>92.8/32.7*</td><td>84.7/51.3*</td></tr><tr><td>FDBD [37] (ResNet-50)</td><td>68.4/83.4*</td><td>81.4/66.1*</td><td>97.6/12.4</td><td>98.0/10.7</td><td>91.7/35.6*</td><td>82.2/57.8*</td></tr><tr><td>DisCoPatch-64 (Proposed)</td><td>95.8/19.8</td><td>94.3/39.0</td><td>99.1/3.6</td><td>96.4/18.9</td><td>94.4/29.7</td><td>97.2/10.6</td></tr></table>
+
+# 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.
+
+![](images/b42ef1e5c4ff63d402f8f99aa2c3ec733ade68f88da489565dbc5ad6b2fbffd8.jpg)  
+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  $25\%$ .
+
+![](images/814548373b042079f40d34858281883382af4431cf4c2cc7215ff8a5ccce6098.jpg)  
+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.
+
+![](images/a202213c738c50e11e4ea65469347fff33655409c8ce1cbf65fd880a185346b9.jpg)  
+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
+
+![](images/0d00ca00a446bddcc92c9ad74e438e11facc45d3e02ce371307d471305a1814d.jpg)
+
+![](images/c43909dd2f018b774b8a20303337f6b9adc23eeac5a045ddbaa9110f1a47a519.jpg)  
+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.
+
+![](images/3c4b8d56a01e57da60a97d59134ea76051a19f0108a1397876ff827b0fc34064.jpg)
+
+![](images/4e4d286de95c13a15a47a92acd1109cf75a612ce72ee8caa7dfaee4f6c27f03c.jpg)
+
+# 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
+
+![](images/b0cf81d9a90d8ddb5caaec7aca47b6642e4d78124a4aba04fadcfa95378b02ef.jpg)  
+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
+
+![](images/2ecc76ad4259d8d6daafd53b94123512b905b205220748f306d30e34f88c1f7d.jpg)  
+Pretrained Quantizer  
+Inference
+
+![](images/09d0039cdcbafbef066a8474822bcbae7738458b007263b04153ae44973b716d.jpg)  
+DisCoRD
+
+![](images/ed938b355f23a99b7d824606fd0cdeac2a524da60df8995d2b01480dd67523d5.jpg)  
+Pretrained Token Generator
+
+![](images/00e21a7b2537c61ff5f5e76d78672ee3a13a8201631f263ba366f3e649f4ac28.jpg)  
+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
+
+![](images/c51e306f5477aa2f24b01cae4940d1c9f47d1b85438b486bc6f6050a9f011f14.jpg)  
+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
+
+![](images/dd623c186d48a38f3d5c976f86292b7572460e3517d81203413890c38f8145f3.jpg)  
+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.
+
+![](images/324f157155c893bb4070be57c2ee99fb2470715577a5c6b397de1605ce32939a.jpg)
+
+![](images/8f263cce24869cb41b8b325dbbaacae8a38ae2885ab60eddeff0095f2c6b0fe2.jpg)
+
+![](images/46a02701d89bfdcbd8bb61aa89ee40d8d49079a7d7cdb62c946fb338feca0238.jpg)
+
+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
+
+<table><tr><td>Dataset</td><td>Methods</td><td>FID ↓</td><td>MPJPE ↓</td><td>sJPE ↓</td></tr><tr><td rowspan="7">H-ML3D</td><td>MLD [60] (cont.)</td><td>0.017</td><td>14.7</td><td>0.404</td></tr><tr><td>T2M-GPT [64]</td><td>0.089</td><td>60.0</td><td>0.564</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.031(+65%)</td><td>71.5</td><td>0.488(+13%)</td></tr><tr><td>MMM [41]</td><td>0.097</td><td>46.9</td><td>0.517</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.020(+79%)</td><td>56.8</td><td>0.429(+17%)</td></tr><tr><td>MoMask [12]</td><td>0.019</td><td>29.5</td><td>0.512</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.011(+42%)</td><td>33.3</td><td>0.385(+25%)</td></tr><tr><td rowspan="4">KIT-ML</td><td>T2M-GPT [64]</td><td>0.470</td><td>46.4</td><td>0.526</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.284(+40%)</td><td>58.7</td><td>0.395(+25%)</td></tr><tr><td>MoMask [12]</td><td>0.113</td><td>37.5</td><td>0.384</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.103(+9%)</td><td>33.0</td><td>0.359(+7%)</td></tr></table>
+
+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].
+
+<table><tr><td rowspan="2">Datasets</td><td rowspan="2">Methods</td><td colspan="3">R Precision ↑</td><td rowspan="2">FID ↓</td><td rowspan="2">MM-Dist↓</td><td rowspan="2">MultiModality ↑</td></tr><tr><td>Top 1</td><td>Top 2</td><td>Top 3</td></tr><tr><td rowspan="11">Human ML3D</td><td>MDM [52]</td><td>-</td><td>-</td><td>0.611±.007</td><td>0.544±.044</td><td>5.566±.027</td><td>2.799±.072</td></tr><tr><td>MLD [6]</td><td>0.481±.003</td><td>0.673±.003</td><td>0.772±.002</td><td>0.473±.013</td><td>3.196±.010</td><td>2.413±.079</td></tr><tr><td>MotionDiffuse [65]</td><td>0.491±.001</td><td>0.681±.001</td><td>0.782±.001</td><td>0.630±.001</td><td>3.113±.001</td><td>1.553±.042</td></tr><tr><td>ReMoDiffuse [66]</td><td>0.510±.005</td><td>0.698±.006</td><td>0.795±.004</td><td>0.103±.004</td><td>2.974±.016</td><td>1.795±.043</td></tr><tr><td>MMM [41]</td><td>0.504±.003</td><td>0.696±.003</td><td>0.794±.002</td><td>0.080±.003</td><td>2.998±.007</td><td>1.164±.041</td></tr><tr><td>T2M-GPT [64]</td><td>0.491±.003</td><td>0.680±.003</td><td>0.775±.002</td><td>0.116±.004</td><td>3.118±.011</td><td>1.856±.011</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.476±.008</td><td>0.663±.006</td><td>0.760±.007</td><td>0.095±.011 (+18%)</td><td>3.121±.009</td><td>1.831±.048</td></tr><tr><td>BAMM [40]</td><td>0.525±.002</td><td>0.720±.003</td><td>0.814±.003</td><td>0.055±.002</td><td>2.919±.008</td><td>1.687±.051</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.522±.003</td><td>0.715±.005</td><td>0.811±.004</td><td>0.041±.002 (+25%)</td><td>2.921±.015</td><td>1.772±.067</td></tr><tr><td>MoMask [12]</td><td>0.521±.002</td><td>0.713±.002</td><td>0.807±.002</td><td>0.045±.002</td><td>2.958±.008</td><td>1.241±.040</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.524±.003</td><td>0.715±.003</td><td>0.809±.002</td><td>0.032±.002 (+29%)</td><td>2.938±.010</td><td>1.288±.043</td></tr><tr><td rowspan="9">KIT-ML</td><td>MDM [52]</td><td>-</td><td>-</td><td>0.396±.004</td><td>0.497±.021</td><td>9.191±.022</td><td>1.907±.214</td></tr><tr><td>MLD [6]</td><td>0.390±.008</td><td>0.609±.008</td><td>0.734±.007</td><td>0.404±.027</td><td>3.204±.027</td><td>2.192±.071</td></tr><tr><td>MotionDiffuse [65]</td><td>0.417±.004</td><td>0.621±.004</td><td>0.739±.004</td><td>1.954±.062</td><td>2.958±.005</td><td>0.730±.013</td></tr><tr><td>ReMoDiffuse [66]</td><td>0.427±.014</td><td>0.641±.004</td><td>0.765±.055</td><td>0.155±.006</td><td>2.814±.012</td><td>1.239±.028</td></tr><tr><td>MMM [41]</td><td>0.404±.005</td><td>0.621±.006</td><td>0.744±.005</td><td>0.316±.019</td><td>2.977±.019</td><td>1.232±.026</td></tr><tr><td>T2M-GPT [64]</td><td>0.398±.007</td><td>0.606±.006</td><td>0.729±.005</td><td>0.718±.038</td><td>3.076±.028</td><td>1.887±.050</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.382±.007</td><td>0.590±.007</td><td>0.715±.004</td><td>0.541±.038 (+25%)</td><td>3.260±.028</td><td>1.928±.059</td></tr><tr><td>MoMask [12]</td><td>0.433±.007</td><td>0.656±.005</td><td>0.781±.005</td><td>0.204±.011</td><td>2.779±.022</td><td>1.131±.043</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.434±.007</td><td>0.657±.005</td><td>0.775±.004</td><td>0.169±.010 (+17%)</td><td>2.792±.015</td><td>1.266±.046</td></tr></table>
+
+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.  
+
+<table><tr><td>Methods</td><td>sJPE↓</td><td>FGD↓</td></tr><tr><td>TalkSHOW [62]</td><td>0.284</td><td>74.88</td></tr><tr><td>+ DisCoRD(Ours)</td><td>0.077</td><td>43.58</td></tr><tr><td>ProbTalk [30]</td><td>0.406</td><td>5.21</td></tr><tr><td>+ DisCoRD(Ours)</td><td>0.349</td><td>4.83</td></tr></table>
+
+Table 3. Quantitative results on each method's SHOW test set. DisCoRD outperforms baseline models on sJPE and FGD.  
+
+<table><tr><td>Methods</td><td>sJPE↓</td><td>Distk→ (9.780)</td><td>Distg→ (7.662)</td></tr><tr><td>TM2D [10]</td><td>0.275</td><td>8.851</td><td>4.225</td></tr><tr><td>+DisCoRD(Ours)</td><td>0.261</td><td>9.830</td><td>8.519</td></tr></table>
+
+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
+
+![](images/8c657072afb04a3fc0fef6ea767677ac15f0cb83f81e55b70c0b72b56f3148b0.jpg)  
+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.
+
+<table><tr><td rowspan="2">Methods</td><td>Recon</td><td colspan="4">Generation</td></tr><tr><td>FID↓</td><td>FID↓</td><td>RP@1↑</td><td>RP@2↑</td><td>RP@3↑</td></tr><tr><td>MoMask-R0</td><td>0.125</td><td>0.082</td><td>0.505</td><td>0.696</td><td>0.793</td></tr><tr><td>+Ours</td><td>0.061(+51%)</td><td>0.068(+17%)</td><td>0.491(-2.8%)</td><td>0.682(-2.0%)</td><td>0.782(-1.4%)</td></tr><tr><td>MoMask-R1</td><td>0.066</td><td>0.058</td><td>0.517</td><td>0.710</td><td>0.805</td></tr><tr><td>+Ours</td><td>0.024(+64%)</td><td>0.037(+36%)</td><td>0.510(-1.4%)</td><td>0.703(-1.0%)</td><td>0.800(-0.6%)</td></tr><tr><td>MoMask-R2</td><td>0.046</td><td>0.053</td><td>0.520</td><td>0.712</td><td>0.806</td></tr><tr><td>+Ours</td><td>0.018(+61%)</td><td>0.031(+42%)</td><td>0.517(-0.6%)</td><td>0.709(-0.4%)</td><td>0.806(-0.0%)</td></tr><tr><td>MoMask-R4</td><td>0.024</td><td>0.047</td><td>0.519</td><td>0.711</td><td>0.807</td></tr><tr><td>+Ours</td><td>0.011(+54%)</td><td>0.032(+32%)</td><td>0.520(+0.2%)</td><td>0.711(0.0%)</td><td>0.806(-0.1%)</td></tr><tr><td>MoMask-R5</td><td>0.019</td><td>0.045</td><td>0.521</td><td>0.713</td><td>0.807</td></tr><tr><td>+Ours</td><td>0.011(+42%)</td><td>0.032(+29%)</td><td>0.524(+0.6%)</td><td>0.715(+0.3%)</td><td>0.809(+0.2%)</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Reconstruction</td><td colspan="2">Generation</td></tr><tr><td>FID↓</td><td>sJPE↓</td><td>FID↓</td><td>MM-Dist↓</td></tr><tr><td>MoMask</td><td>0.019±.001</td><td>0.512</td><td>0.051±.002</td><td>2.957±.008</td></tr><tr><td>+ Post Refinement (FF model)</td><td>0.028±.000</td><td>0.481</td><td>0.044±.002</td><td>2.962±.006</td></tr><tr><td>+ Post Refinement (RF model)</td><td>0.013±.000</td><td>0.489</td><td>0.035±.002</td><td>2.955±.008</td></tr><tr><td>+ DisCoRD (Ours)</td><td>0.011±.000</td><td>0.385</td><td>0.032±.002</td><td>2.938±.010</td></tr><tr><td>Ours (Upconv)</td><td>0.010±.000</td><td>0.375</td><td>0.039±.003</td><td>2.943±.006</td></tr><tr><td>Ours (Repeat &amp; Linear)</td><td>0.011±.001</td><td>0.342</td><td>0.038±.001</td><td>2.947±.008</td></tr><tr><td>Ours (w/ Attention)</td><td>0.020±.000</td><td>0.384</td><td>0.043±.002</td><td>2.983±.009</td></tr><tr><td>Ours (w/ Full Motion Sequence)</td><td>0.008±.000</td><td>0.385</td><td>0.038±.002</td><td>2.952±.009</td></tr></table>
+
+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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ICCV/2025/DisTime_ Distribution-based Time Representation for Video Large Language Models/full.md

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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
+
+![](images/52d62de7b85be12f76b46caeb377a7f6df4d84f3ec676a780e5759e9b0e72cb2.jpg)  
+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@1<sub>iou=0.3</sub> 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
+
+![](images/e12b14510f14da592a2cee5f2f1703527ba7f23172eb31631e06bcd67d5f4bfb.jpg)  
+Figure 2. Overview of the Video-LLM with DisTime. Our DisTime method employs a single token (denoted as <TIME_STAMP>) 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 <TIME_STAMP> 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 <TIME_STAMP>. 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 <TIME_STAMP> is replaced with the re-encoded time token, establishing explicit temporal referencing that functions as video timeline pointers. Finally, the <TIME_STAMP> 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
+
+![](images/fe77104ecf30912453dc9112161bbab9e126de5d77644c5310f274987f45f5aa.jpg)  
+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 <TIME_STAMP>), distinctly separating it from numerical text tokens in the vocabulary. When the LLM generates a <TIME_STAMP>, 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 <TIME_STAMP> 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 <TIME_STAMP> 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
+
+![](images/fd8aba02c6f8a8f6c3abbe5da325564e5ed73361ad11f3ceb974c5599508b444.jpg)  
+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 <TIME_STAMP> with the encoded token  $\tau$  for refined temporal representation.
+
+# 3.3. Iterating Time Refinement
+
+Time token re-encoding. The hidden embedding of <TIMEStamped> 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
+
+![](images/40564dbc99bcedd4e6a5f7b769da2cbd4612ecb17f16cef01e87ce9a17bebe19.jpg)  
+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-
+
+<table><tr><td>Dataset</td><td>annotator</td><td>#videos</td><td>Avg Dura. (s)</td><td>#events</td><td>#events/vid</td></tr><tr><td>Ego4d [12]</td><td>Human</td><td>2k</td><td>472</td><td>18.4k</td><td>9.2</td></tr><tr><td>Charades-STA [9]</td><td>Human</td><td>10k</td><td>30</td><td>68k</td><td>6.8</td></tr><tr><td>ANet-caption [16]</td><td>Human</td><td>15k</td><td>118</td><td>22.5k</td><td>1.5</td></tr><tr><td>VTimeLLM [15]</td><td>LLM</td><td>146k</td><td>52</td><td>353k</td><td>2.4</td></tr><tr><td>InternVid-MR [11]</td><td>LLM</td><td>-</td><td>-</td><td>150k</td><td>-</td></tr><tr><td>Momentor [35]</td><td>LLM</td><td>65k</td><td>403</td><td>1460k</td><td>22.5</td></tr><tr><td>InternVid-TG (ours)</td><td>LLM+ dedicated</td><td>179k</td><td>55</td><td>1250k</td><td>7.0</td></tr></table>
+
+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
+
+<table><tr><td>Dataset</td><td>Task</td></tr><tr><td>VideoChat2 [21] (232k)</td><td>General Video Understanding</td></tr><tr><td>ANet-Caption [16] (37k)</td><td>Moment Retrieval</td></tr><tr><td>ANet-Caption [16] (9.8k)</td><td>Dense Video Captioning</td></tr><tr><td>YouCook2 [56] (2k)</td><td>Dense Video Captioning</td></tr><tr><td>ET-Instruct [28] (126k)</td><td>Multi-Event</td></tr><tr><td>InternVid-TG (1250k)</td><td>Moment Retrieval</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Direct</td><td rowspan="2">Dist.</td><td rowspan="2">Re-Enc.</td><td colspan="4">Charades-STA (MR)</td><td colspan="3">YouCook2 (DVC)</td></tr><tr><td>R@1(IoU=0.3)</td><td>R@1(IoU=0.5)</td><td>R@1(IoU=0.7)</td><td>mIoU</td><td>SODA_c</td><td>CIDEr</td><td>F1 Score</td></tr><tr><td>✓</td><td></td><td></td><td>76.6</td><td>51.9</td><td>24.9</td><td>49.5</td><td>0.6</td><td>0.9</td><td>2.2</td></tr><tr><td></td><td>✓</td><td></td><td>77.0</td><td>53.5</td><td>26.7</td><td>50.1</td><td>0.9</td><td>4.0</td><td>16.3</td></tr><tr><td></td><td>✓</td><td>✓</td><td>78.1</td><td>56.3</td><td>29.7</td><td>51.6</td><td>4.2</td><td>15.6</td><td>20.5</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Training Data</td><td colspan="4">Charades-STA (MR)</td><td colspan="4">QVHighlights (MR)</td></tr><tr><td>R@1(IoU=0.3)</td><td>R@1(IoU=0.5)</td><td>R@1(IoU=0.7)</td><td>mIoU</td><td>R@1(IoU=0.3)</td><td>R@1(IoU=0.5)</td><td>mAP@.5</td><td>mAP@.75</td></tr><tr><td>Baseline</td><td>77.4</td><td>51.4</td><td>22.9</td><td>48.7</td><td>38.7</td><td>17.7</td><td>34.8</td><td>12.5</td></tr><tr><td>w/ VTimeLLM [15]</td><td>76.2</td><td>51.9</td><td>25.0</td><td>49.3</td><td>51.0</td><td>25.8</td><td>46.0</td><td>18.8</td></tr><tr><td>w/Momentor [35]</td><td>76.6</td><td>50.6</td><td>21.6</td><td>47.8</td><td>39.7</td><td>17.8</td><td>35.1</td><td>12.5</td></tr><tr><td>w/ Intern Vid-TG1</td><td>77.8</td><td>55.5</td><td>28.0</td><td>51.0</td><td>52.2</td><td>26.4</td><td>46.2</td><td>18.9</td></tr><tr><td>w/ Intern Vid-TG</td><td>78.1</td><td>56.3</td><td>29.7</td><td>51.6</td><td>54.1</td><td>27.8</td><td>47.9</td><td>19.2</td></tr></table>
+
+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
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Size</td><td colspan="4">Charges-STA</td><td colspan="4">ANetCaption</td></tr><tr><td>R@1(IoU=0.3)</td><td>R@1(IoU=0.5)</td><td>R@1(IoU=0.7)</td><td>mIoU</td><td>R@1(IoU=0.3)</td><td>R@1(IoU=0.5)</td><td>R@1(IoU=0.7)</td><td>mIoU</td></tr><tr><td colspan="10">Dedicated</td></tr><tr><td>UniVTG [26]</td><td>-</td><td>72.6</td><td>60.2</td><td>38.6</td><td>52.2</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>UniMD [52]</td><td>-</td><td>-</td><td>63.9</td><td>42.2</td><td>-</td><td>-</td><td>42.7</td><td>25.1</td><td>-</td></tr><tr><td>Mr.BLIP [32]</td><td>3B</td><td>-</td><td>69.3</td><td>49.3</td><td>58.6</td><td>-</td><td>53.92</td><td>35.6</td><td>-</td></tr><tr><td>LLaVA-MR [30]</td><td>3B</td><td>-</td><td>70.7</td><td>49.6</td><td>59.8</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td colspan="10">Video-LLMs</td></tr><tr><td>Momentor [35]</td><td>7B</td><td>42.6</td><td>26.6</td><td>11.6</td><td>28.5</td><td>42.9</td><td>23.0</td><td>12.4</td><td>29.3</td></tr><tr><td>ChatVTG [36]</td><td>7B</td><td>52.7</td><td>33.0</td><td>15.9</td><td>34.9</td><td>40.7</td><td>22.5</td><td>9.4</td><td>27.2</td></tr><tr><td>VTimeLLM [15]</td><td>13B</td><td>55.3</td><td>34.3</td><td>14.7</td><td>34.6</td><td>44.8</td><td>29.5</td><td>14.2</td><td>31.4</td></tr><tr><td>TimeChart [37]</td><td>7B</td><td>-</td><td>32.2</td><td>13.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VTG-LLM [13]</td><td>7B</td><td>-</td><td>33.8</td><td>15.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>InternVideo2.5 [44]</td><td>7B</td><td>-</td><td>43.3</td><td>-</td><td>41.7</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TimeMarker [4]</td><td>8B</td><td>73.5</td><td>51.9</td><td>26.9</td><td>48.4</td><td>67.4</td><td>50.7</td><td>33.0</td><td>49.5</td></tr><tr><td>InternVL2.5* [5]</td><td>1B</td><td>3.1</td><td>1.5</td><td>0.7</td><td>5.1</td><td>5.3</td><td>2.9</td><td>1.5</td><td>5.5</td></tr><tr><td>LLaVA-OneVision*[18]</td><td>7B</td><td>20.8</td><td>7.2</td><td>2.2</td><td>14.5</td><td>24.8</td><td>14.0</td><td>9.0</td><td>20.5</td></tr><tr><td>InternVL2.5* [5]</td><td>8B</td><td>27.9</td><td>10.9</td><td>4.2</td><td>18.2</td><td>21.1</td><td>12.7</td><td>8.6</td><td>17.2</td></tr><tr><td>DisTime-InternVL</td><td>1B</td><td>78.1</td><td>56.3</td><td>29.7</td><td>51.6</td><td>67.1</td><td>45.4</td><td>23.1</td><td>45.2</td></tr><tr><td>DisTime-LLAVOV</td><td>7B</td><td>76.3</td><td>52.0</td><td>19.8</td><td>47.4</td><td>57.6</td><td>34.3</td><td>13.7</td><td>37.1</td></tr><tr><td>DisTime-InternVL</td><td>8B</td><td>81.0</td><td>60.3</td><td>30.8</td><td>53.1</td><td>72.9</td><td>53.2</td><td>30.3</td><td>50.5</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Size</td><td colspan="3">YouCook2</td><td colspan="3">ANet-Caption</td></tr><tr><td>SODA_c</td><td>CIDEr</td><td>F1 Score</td><td>SODA_c</td><td>CIDEr</td><td>METEOR</td></tr><tr><td>Valley [31]</td><td>7B</td><td>0.1</td><td>0.0</td><td>1.5</td><td>0.3</td><td>1.8</td><td>0.8</td></tr><tr><td>Momentor [35]</td><td>7B</td><td>-</td><td>-</td><td>-</td><td>2.3</td><td>14.9</td><td>4.7</td></tr><tr><td>VTimeLLM [15]</td><td>13B</td><td>-</td><td>-</td><td>-</td><td>5.9</td><td>27.2</td><td>6.7</td></tr><tr><td>TimeChat [37]</td><td>7B</td><td>1.2</td><td>3.4</td><td>12.6</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VTG-LLM [13]</td><td>7B</td><td>1.5</td><td>5.0</td><td>17.5</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DisTime-InternVL</td><td>1B</td><td>4.2</td><td>15.6</td><td>20.5</td><td>4.5</td><td>17.9</td><td>4.7</td></tr><tr><td>DisTime-LLaVAOV</td><td>7B</td><td>5.4</td><td>21.8</td><td>19.5</td><td>4.9</td><td>21.3</td><td>4.9</td></tr><tr><td>DisTime-InternVL</td><td>8B</td><td>6.9</td><td>31.0</td><td>26.4</td><td>4.1</td><td>17.8</td><td>5.8</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Size</td><td colspan="8">NExT-GQA</td></tr><tr><td>Acc@QA</td><td>Acc@GQA</td><td>mIoP</td><td>IoP@0.3</td><td>IoP@0.5</td><td>mIoU</td><td>IoU@0.3</td><td>IoU@0.5</td></tr><tr><td>SeViLA [50]</td><td>3B</td><td>68.1</td><td>16.6</td><td>25.7</td><td>34.7</td><td>22.9</td><td>21.7</td><td>29.2</td><td>13.8</td></tr><tr><td>Temp [46]</td><td>150M</td><td>60.2</td><td>16.0</td><td>25.7</td><td>31.4</td><td>25.5</td><td>12.1</td><td>17.5</td><td>8.9</td></tr><tr><td>FrozenBILM [48]</td><td>1B</td><td>70.8</td><td>17.5</td><td>24.2</td><td>28.5</td><td>23.7</td><td>9.6</td><td>13.5</td><td>6.1</td></tr><tr><td>DisTime-InternVL</td><td>1B</td><td>65.9</td><td>17.0</td><td>33.5</td><td>42.9</td><td>23.7</td><td>31.1</td><td>41.0</td><td>21.8</td></tr><tr><td>DisTime-LLaVAOV</td><td>7B</td><td>75.8</td><td>22.8</td><td>36.3</td><td>48.4</td><td>28.7</td><td>31.9</td><td>45.6</td><td>23.5</td></tr><tr><td>DisTime-InternVL</td><td>8B</td><td>80.3</td><td>28.1</td><td>40.5</td><td>55.1</td><td>33.8</td><td>35.9</td><td>52.0</td><td>28.8</td></tr></table>
+
+Table 7. Comparison with models on the Grounded Video Question Answering task in NExT-GQA.  
+
+<table><tr><td>Model</td><td>Size</td><td>MVBench avg</td><td>Video-MME (wo sub))</td><td>LongVideoBench (val total))</td></tr><tr><td>TimeChat</td><td>7B</td><td>38.5</td><td>34.7</td><td>-</td></tr><tr><td>TimeMarker</td><td>8B</td><td>67.4</td><td>57.3</td><td>56.3</td></tr><tr><td>InternVideo2.5</td><td>7B</td><td>75.7</td><td>65.1</td><td>60.6</td></tr><tr><td>InternVL2.5</td><td>1B</td><td>64.3</td><td>50.3</td><td>47.9</td></tr><tr><td>LLaVA-OneVision</td><td>7B</td><td>56.7</td><td>58.2</td><td>56.3</td></tr><tr><td>InternVL2.5</td><td>8B</td><td>72.0</td><td>64.2</td><td>60.0</td></tr><tr><td>DisTime-InternVL</td><td>1B</td><td>62.6</td><td>47.4</td><td>49.0</td></tr><tr><td>DisTime-LLaVAOV</td><td>7B</td><td>59.0</td><td>54.4</td><td>55.4</td></tr><tr><td>DisTime-InternVL</td><td>8B</td><td>72.0</td><td>59.6</td><td>60.0</td></tr></table>
+
+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.
+
+# References
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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
+
+![](images/48329c9e7669555b4ddc9e8284388aece15b5ff20db5cae82006a2e8603bc267.jpg)  
+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  $\varepsilon_{b \to a}$ :
+
+$$
+z _ {a} = \omega_ {\varepsilon_ {a}} \cdot \varepsilon_ {b \rightarrow a} + \omega_ {b \rightarrow a} \cdot z _ {b}, \tag {2}
+$$
+
+![](images/17fe449d7b0fa1e0a77a1f3369df6d09f99cf92f10dc19045643e367f81f2b97.jpg)  
+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
+
+![](images/d93e586e8d225726d854b9340d3796e460a815d487c2ae34b091a35575547ea6.jpg)  
+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
+
+![](images/203d46dd0eb33fa70283ef625c3fb5dddb05f5dcc3c0e69f853627f1ad11083d.jpg)  
+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].
+
+<table><tr><td>Method</td><td>bear</td><td>buddha</td><td>cat</td><td>cow</td><td>harvest</td><td>pot1</td><td>pot2</td><td>reading</td><td>goblet</td></tr><tr><td>BiNI [7]</td><td>(3.72 ± 2.71) × 10-1</td><td>(4.57 ± 9.21) × 10-1</td><td>(0.54 ± 1.09) × 100</td><td>(4.46 ± 3.58) × 10-1</td><td>(0.52 ± 2.71) × 100</td><td>(4.18 ± 5.63) × 10-1</td><td>(3.96 ± 4.26) × 10-1</td><td>(0.50 ± 1.24) × 100</td><td>(0.43 ± 1.33) × 100</td></tr><tr><td>Ours</td><td>(0.82 ± 7.39) × 10-2</td><td>(0.90 ± 9.12) × 10-1</td><td>(0.03 ± 1.27) × 100</td><td>(0.19 ± 1.61) × 10-1</td><td>(0.22 ± 2.80) × 100</td><td>(0.09 ± 2.72) × 100</td><td>(0.39 ± 3.11) × 10-1</td><td>(0.08 ± 1.21) × 100</td><td>(0.06 ± 1.20) × 100</td></tr></table>
+
+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.  
+
+<table><tr><td>Method</td><td>bear</td><td>buddha</td><td>cat</td><td>cow</td><td>harvest</td><td>pot1</td><td>pot2</td><td>reading</td><td>goblet*</td></tr><tr><td>BiNI [7] – From paper</td><td>0.49</td><td>0.86</td><td>0.11</td><td>0.07</td><td>2.73</td><td>0.62</td><td>0.22</td><td>0.34</td><td>8.53</td></tr><tr><td>BiNI [7] – From code [8], 1200 iterations†</td><td>0.33</td><td>1.06</td><td>0.07</td><td>0.06</td><td>1.84</td><td>0.64</td><td>0.22</td><td>0.26</td><td>9.00</td></tr><tr><td>Kim et al. [24]</td><td>0.45</td><td>0.67</td><td>0.24</td><td>0.06</td><td>2.44</td><td>0.57</td><td>0.19</td><td>0.15</td><td>9.02</td></tr><tr><td>Ours w/o αb→a computation, 150 iterations</td><td>0.08</td><td>0.30</td><td>0.06</td><td>0.09</td><td>4.98</td><td>0.52</td><td>0.13</td><td>0.21</td><td>6.46</td></tr><tr><td>Ours w/o αb→a computation, 1200 iterations</td><td>0.07</td><td>0.26</td><td>0.06</td><td>0.08</td><td>4.83</td><td>0.50</td><td>0.13</td><td>0.12</td><td>6.56</td></tr><tr><td>Ours, 150 iterations</td><td>0.03</td><td>0.37</td><td>0.06</td><td>0.08</td><td>1.35</td><td>0.50</td><td>0.14</td><td>0.15</td><td>5.98</td></tr><tr><td>Ours, 1200 iterations</td><td>0.03</td><td>0.24</td><td>0.06</td><td>0.08</td><td>0.73</td><td>0.49</td><td>0.13</td><td>0.17</td><td>4.72</td></tr><tr><td>Ours with known discontinuity values</td><td>0.01</td><td>0.10</td><td>0.03</td><td>&lt;10-2</td><td>0.34</td><td>0.04</td><td>0.03</td><td>0.08</td><td>0.11</td></tr></table>
+
+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.
+
+![](images/12513c1526dd94275b1c4edc2e47f3778cca8445aaabd04764df307660aabd5d.jpg)  
+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.
+
+![](images/dcfddd5e7b622bc4c18e0fca86cd450f2e00675673a2f0a8c876c5c46d2be566.jpg)  
+Ground truth
+
+![](images/6e45927271f5cebc8e85c68a0746d52aa9ee59bae351e41522d958f64ad58415.jpg)  
+BiNI [7]
+
+![](images/bcb173569f2ac281b9727f817347e49059a17c7fb54ddc014fbb93d5596a6e97.jpg)  
+Ours
+
+![](images/dd1851dce15275da7966b3d6f199e22f973cdf07f0b452553f5e85d6fd28f1f4.jpg)  
+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].
+
+![](images/5690cfd65b740b113f724b59710f6b7b89fe1c0f26def8c2cb8c9626fb029c4c.jpg)
+
+![](images/de3fb3eec1d3ba29ee49160cac2c5b4809d09f2ec34f7991284744e2a02c1a71.jpg)
+
+![](images/7e3cef5f7b1f340a58357faf1d745b263fd65a55a80774b4df8211b7fd90215c.jpg)  
+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].
+
+![](images/fcf418c2e8d92d8a70d3d4071386ccfa5e15d7988f94ad05a38e6c3714959c08.jpg)  
+RE: 2.08, ERA: 1.99
+
+![](images/36c6130a798842e8bfdda114bc8925ab9ee33dd9bae09928a3e16ab0a8099973.jpg)  
+RE: 2.94, ERA: 3.02
+
+![](images/974f4b29675c6888b755cf83e6f7470470f7e4646d93174536c8f749d9d4ad59.jpg)  
+RE:8.20,ERA:7.04
+
+![](images/20e7d1b91277214c86422992e3fbaa760dcddb76adf3fbce96eb9df918b17dcc.jpg)  
+RE: 0.27, ERA: 0.30
+
+![](images/f99f3563ce3dd4c755105e3efc0d0450df07f358134d3933b39b77b1bda4ec9d.jpg)  
+RE: 8.01, ERA: 6.47
+
+![](images/01db9808734e09e5f49025079ff42544482b18d8633a8a9d8bd814fac9c0a9ad.jpg)  
+RE: 4.44, ERA: 4.29
+
+![](images/c8a53fd458030f2010451e2cd1e2a32f6ef3ddc1f126770d3cbd16e4f14125c3.jpg)  
+RE: 13.32, ERA: 10.09
+
+![](images/7574f36a4fef42f604f8a688153766e4bd789bf69378841ec33e821a2db023b4.jpg)  
+RE: 1.16, ERA: 1.29
+
+![](images/140246370ffc8089be7b19577311a09a1ee41282d248965872dec02c23da2bb6.jpg)
+
+![](images/31d984212e5e6b524676a90ecedf1ffa26d4380b9e91c8cc4f706938b87b95f8.jpg)
+
+![](images/1a2a5c262d283f08f29e579bda6bf37bea04dcba1ee56483eebe9619fdeded94.jpg)
+
+![](images/bc8406de90dd9c8b05aaf7bdb906e2bc28f269d56c1a631db98137cf9130a3a2.jpg)
+
+![](images/042db0373f29da7bd6f8f5c62ec3d8d4de78af074f79bd4a58f550af02ed880a.jpg)
+
+![](images/2bf29339408a155e9edf0f319cf541ba3868c991049807988d0ca3ba4ed73e5f.jpg)  
+RE: 2.26, ERA: 2.07  
+RE: 2.49, ERA: 2.48
+
+![](images/e7f6b59f53b5cc367c5177de498bf751e8e08f860119b018871dde8bfae5a373.jpg)  
+RE: 8.35, ERA: 6.85
+
+![](images/4f1909a18c826b2e35d9e1f73ec9b80bbf5c40fb69f0cf6565051b933bac955d.jpg)  
+RE: 0.16, ERA: 0.19
+
+![](images/f695573fcdd5d1c31132921f49e0b9a47059ffabfcab814f6866664152857ff9.jpg)
+
+![](images/e6b40fb0a4f6a58b7a803c254563b0b4c8e0200b4897c57012cbacd1ac4d8921.jpg)  
+RE: 2.30, ERA: 2.09  
+RE: 2.63, ERA: 2.61
+
+![](images/b9cf291d39ea4499db5fac265692303a8007b53857fdd43e58899741c0453d18.jpg)  
+RE: 8.69, ERA: 6.73
+
+![](images/d79b963a73392e186e5da441655dd4a2465c5c3441a7ae29c92ee25e1e142c2e.jpg)  
+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  
+[2] Amit Agrawal, Ramesh Raskar, and Rama Chellappa. What
+
+Is the Range of Surface Reconstructions from a Gradient Field? In ECCV, 2006. 2  
+[3] Hicham Badri, Hussein Yahia, and Driss Aboutajdine. Robust Surface Reconstruction via Triple Sparsity. In CVPR, 2014. 1, 2  
+[4] Gwangbin Bae and Andrew J. Davison. Rethinking Inductive
+
+Biases for Surface Normal Estimation. In CVPR, 2024. 3, 6  
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+[8] Xu Cao, Hiroaki Santo, Boxin Shi, Fumio Okura, and Yasuyuki Matsushita. Bilateral Normal Integration - Official implementation. https://github.com/xucao-42/bilateral_normal_integration, 2022. Accessed: 2025-01-27. 7  
+[9] Xu Cao, Hiroaki Santo, Boxin Shi, Fumio Okura, and Yasuyuki Matsushita. Bilateral Normal Integration - Supplementary material. https://doi.org/10.1007/978-3-031-19769-7_32#Sec12, 2022. Accessed: 2025-02-07. 5, 11, 14  
+[10] Maximilian Denninger, Dominik Winkelbauer, Martin Sundermeyer, Wout Boerdijk, Markus Knauer, Klaus H. Strobl, Matthias Hunt, and Rudolph Triebel. BlenderProc2: A Procedural Pipeline for Photorealistic Rendering. Journal of Open Source Software, 8(82):4901, 2023. 6, 16  
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+[12] dylanheyes. Mesh “White Modern Living Room”. https://sketchfab.com/3d-models/white-modern-living-room-afb8cb0cbee1488caf61471ef14041e9, 2023. CC BY 4.0.8  
+[13] Roberto Fraile and Edwin R. Hancock. Combinatorial Surface Integration. In ICPR, 2006. 2  
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+[15] Matthew Harker and Paul O'Leary. Least Squares Surface Reconstruction from Measured Gradient Fields. In CVPR, 2008. 2  
+[16] Richard Hartley and Andrew Zisserman. Multiple View Geometry in Computer Vision, page 6. Cambridge University Press, 2nd edition, 2004. 2  
+[17] Moritz Heep and Eduard Zell. An Adaptive Screen-Space Meshing Approach for Normal Integration. In ECCV, 2024. 16  
+[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  
+[22] Satoshi Ikehata. Scalable, Detailed and Mask-free Universal Photometric Stereo. In CVPR, 2023. 6  
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+[24] Hyomin Kim, Yucheol Jung, and Seungyong Lee. Discontinuity-preserving Normal Integration with Auxiliary Edges. In CVPR, 2024. 1, 2, 4, 6, 7, 16  
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+[30] Srikumar Ramalingam, Peter Sturm, and Suresh K. Lodha. Theory and Calibration for Axial Cameras. In ACCV, 2006. 16  
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ICCV/2025/Discovering Divergent Representations between Text-to-Image Models/full.md

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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
+
+![](images/b809a9b9ff89f92e0bd441afa6f9cc953e6070065ca1957192de800b86e25d91.jpg)  
+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
+
+![](images/d5f8925d2393c9a7963bd77e31ab6fbea217c18690421e011edea33d9a2af2ac.jpg)
+
+A poem narrating the tempest within an artist's heart.
+
+![](images/251afd29f148f3bc06df55a00bd14685db758b8a1a5ffb22aa7ac5101b8a2717.jpg)
+
+Oil painting of the fervor of a evolutionary speech.
+
+![](images/b35ac4fbd0f6e5f7f2c5f05ad5323d9b08d5cb0ffff11d5c12b2729778309b42.jpg)
+
+An abstract representation of existential dread
+
+![](images/f42e9cc653b0ccd2163539680d8d6e026d18f09135338f6fb25e4f3403896fc7.jpg)
+
+A fierce display of a protector's unwavering courage.
+
+![](images/c1fdb5352cb09837619c926a6e772cf1639b689d6887aa9bea192fed2b526b41.jpg)
+
+# SDXL-Lightning
+
+![](images/4643fa7cc0876d2d4b63fc701b74224bfcb672aefc0aed97541d8529297603de.jpg)
+
+![](images/0764fbbc7d377d4aba18d12dad9034ad09b85fd809af58ceab6ec2aa23cc5231.jpg)
+
+![](images/05f44c742c41e7c6d034724c229505e83bd037c87d283b444b13ef522d688f39.jpg)
+
+![](images/f25312c1a06daf6b8e5c82bc10b83f5f763e87cc57b26d8185ef007b9a19bb0a.jpg)
+
+![](images/b0bd83467b49d59d8a102e95430c033abb8ef9c87feab4fba71ccb805a15cd43.jpg)
+
+# 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
+
+![](images/88db9a48cb131145c8e730500d89dd66d4c1af9a1b0ff6da038b0f0e805c4123.jpg)  
+Discovering Divergent Visual Attributes
+
+![](images/fb84529a01936dcdd7e2fb4c318eadf6bf6bd446ef2ee2a92db6dad5d109cb1f.jpg)  
+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
+
+![](images/4104c087c4e697cd5d8ad18f06b7d6cfd28ba304abe5bd3f423e4a7f91497224.jpg)  
+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
+
+<table><tr><td>Metric</td><td>Method</td><td>Top 1</td><td>Top 5</td></tr><tr><td rowspan="4">Attribute Score</td><td>CompCon</td><td>0.60</td><td>0.68</td></tr><tr><td>VisDiff</td><td>0.47</td><td>0.62</td></tr><tr><td>TF-IDF</td><td>0.23</td><td>0.37</td></tr><tr><td>LLM-only</td><td>0.08</td><td>0.24</td></tr><tr><td rowspan="4">Description Score</td><td>CompCon [5-iter]</td><td>0.64</td><td>0.78</td></tr><tr><td>CompCon [1-iter]</td><td>0.59</td><td>0.72</td></tr><tr><td>TF-IDF</td><td>0.40</td><td>0.57</td></tr><tr><td>LLM-only</td><td>0.03</td><td>0.28</td></tr></table>
+
+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.
+
+![](images/e1569c24f34d7fe8f749477e786ca32048fb5a8329178f0ece3c26a90542d58c.jpg)  
+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.
+
+![](images/c573298b26b4295c2e4fcd2dc10c72bddb8070e7286154caa58df3ad434e02c4.jpg)  
+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
+
+![](images/0e735ced9c08c46de5779112f447686e67b1918b018a550ec6d662dc02d92801.jpg)  
+A snug corner for reading and relaxation
+
+![](images/8965454fbc5cddebcc9ea28cb4f010722707227f1fd3197b2857c9accde36b44.jpg)  
+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,
+
+![](images/c9464d3a75d7b2a29976d422d8121af2d52100d73d4222dc423c93f53b7225b5.jpg)  
+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.'
+
+![](images/eb5b78a81d1dea89a9cec046a80ba7d423da58da5fb3378b02b464519269d4ba.jpg)  
+A spotless, modern kitchen set up in the middle of an otherwise gutted and abandoned apartment.
+
+![](images/c52c09a762a912f9667f7f5f2cbecd7556b4c4dd22af7d414483e1666b32eabd.jpg)  
+A lavish banquet set up on a long table in an otherwise empty and dilapidated mansion hall.
+
+![](images/77d70837c98cdf52605dcfed9f8e69f3c9908a00df0726ebc196a6e82dc07095.jpg)  
+A meticulously restored vintage car parked in front of a row of dilapidated, boarded-up homes.
+
+![](images/3f1ea5afdeb7c51054f4b2e8f57e48deb6526e2fcf5cca03b2f958ef4c7477fe.jpg)  
+A bright, blooming flower garden surrounding a rundown, abandoned gas station.
+
+![](images/cfd6f706ef50d137b21849542c50b3a1fe28aadfff579cd64f60b11a5148d591.jpg)  
+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.
+
+![](images/4e20127e2ee1f0daf2a7fc98c4ecc4dac7ed7936ae8a6c7b1bd4d482465c2cd0.jpg)  
+Diverging Visual Attribute: decay
+
+![](images/2794c6100490eddae3f8dbaff81ce63ab883372bedcf536f9d1b85fbed941bad.jpg)
+
+![](images/08570e996920b9122b9352f0ff40da76899299a935507f81af54e1fb8ca99c3d.jpg)
+
+![](images/f1e745a470956e185df56d790c506fd3987ee8b7b9777617232103cf45a85463.jpg)  
+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
+
+![](images/dc873b277bcb63b3e095c88e91ce39c305f56d890caa360abc1ef8114483b427.jpg)  
+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.
+
+![](images/9e11239473a71aef53c3c103a6692f55eacfb6e20ab028ac98008229fe91b1c4.jpg)  
+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
+
+![](images/f382732f622d7948123042e12002aa29744c7a26c83b2f87db622b67e96391e6.jpg)  
+SAX-NerF
+
+![](images/497603482c5536c85260aecd0e12f0fa0977cd2c9b544ee21c707c8cd0cf4933.jpg)  
+PSNR: 37.07 SSIM:0.913 PSNR: 30.65 SSIM:0.872
+
+![](images/68f4e99ada0a492613169f3ed1049d05d55dbc5962f762671d370e5ed8ec8247.jpg)  
+PSNR: 37.92 SSIM:0.990 PSNR: 32.53 SSIM:0.965
+
+![](images/6a1753302b690785388d27811f218057702a24a1bf2eb8deefa35de3c0ba9915.jpg)
+
+![](images/7bf0c5946572eb62ee1ea391b59b27196a9c803a55bcbcc3668252b23212b8d1.jpg)  
+PSNR:34.10 SSIM:0.921
+
+![](images/ecde5e60478215a405c06aeda064597caf84466971def9d981e9cb884f5730ec.jpg)  
+PSNR: 41.96 SSIM:0.985
+
+![](images/823312111eef0855257bbe9b7b0cc331b04ef08ba537333c90080685b4569d76.jpg)  
+PSNR: 34.01 SSIM:0.923
+
+![](images/67dcf2c888b0947fa3e4103a9bebf30f763971cc596de031f58834ffecd5a19e.jpg)  
+raannnnnne
+
+![](images/e7a0a303c09508db80a8514ac2c6337a290efe0e5009d08ccce1bfe08bd380e2.jpg)  
+PSNR: 39.71 SSIM:0.937 PSNR: 31.83 SSIM:0.877
+
+![](images/e5795cdaad5562b0eb2cfce09d9d2afe78359133b02b45a5b888333edff1f14f.jpg)  
+PSNR: 42.46 SSIM:0.994 PSNR: 34.47 SSIM:0.977
+
+![](images/d009c8fd06e974b30ab64c22667415b410dedc4b4c7321b3d881901dbe45ad65.jpg)
+
+![](images/bbc5d941da88a31297ddecbd71bb8c8fd6ad3037b8e7fa2aeffdea9a4d1bf094.jpg)  
+PSNR: 38.16 SSIM:0.957
+
+![](images/c4c32b569e866f6adb7072734ada83e0bf92b8ac6575b0cb45f779190635c8cb.jpg)  
+PSNR: 47.57 SSIM:0.990
+
+![](images/e16966cde655457a4bfba4726fe8b077f83da071d38b5dd582dbc23da0e66e26.jpg)  
+PSNR: 37.84 SSIM:0.951
+
+![](images/7d11b841e200be4b598912b800a8ee20f6bb05f6a489f38f453db2f583d103d0.jpg)  
+DGR
+
+![](images/4ecb47af734324afc72cf25c8fbc45997d3002966d5e3f72b1e30f3a5057121b.jpg)  
+PSNR: 39.77 SSIM:0.951 PSNR: 32.23 SSIM:0.919
+
+![](images/ed96fa1964df03a487787d2e2d3aae84a8bc7a97e8793bf5e7a5b594ae6ba839.jpg)  
+PSNR: 43.55 SSIM:0.996 PSNR: 37.34 SSIM:0.993
+
+![](images/f01f4c3293e6612d6f3d3a7c6f099db4d6e6c19b8dcf8c3fe1bb0d29ec1859eb.jpg)
+
+![](images/2e8365f3d4fbaf3d8188d4702fce6afc962f978e162d8827c9747ea904421836.jpg)  
+PSNR: 41.08 SSIM:0.963
+
+![](images/fec9d9975dabaeba696c511564ee3748cdd246c518bfd8c00494d9cf9dd26f5c.jpg)  
+PSNR: 50.91 SSIM:0.997
+
+![](images/85e2bd97d78162b37f3f46167d08d9b946f8e4ad806377b8d066cb1cca6a58ea.jpg)
+
+![](images/dab44e7dbf8b57f99e9c72d8293dfcc423a1ecc2deef8b567894fe0fe743c339.jpg)  
+Groun
+
+![](images/2316de747dce40a6aef2837ac1723e3456aa535fe5afcab4c05028a2af46aeee.jpg)
+
+![](images/11ee793c92c7582904cde71f42958369f382bdc1564aa80c499c95aa7fce125b.jpg)
+
+![](images/66b703061a917a3d9022937a19afad400640aacbb3c83c405b84734e41bc2afb.jpg)
+
+![](images/d3f0f56b227a9782885d748a549cec69431f6f439a0b607bfc2a9599ebb6354f.jpg)  
+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.
+
+![](images/a7b9901de5a2bafce681f7d430c0c4215050cd462de6b6d8fd6bfc552b10021e.jpg)
+
+![](images/3d96d3464e6b05785ed9a4cd5635a6abc878a171990ab4370d33c384eb3476e8.jpg)  
+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.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">75-view</td><td colspan="3">50-view</td><td colspan="3">25-view</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>Time↓</td><td>PSNR↑</td><td>SSIM↑</td><td>Time↓</td><td>PSNR↑</td><td>SSIM↑</td><td>Time↓</td></tr><tr><td colspan="10">Real-World Dataset</td></tr><tr><td>FDK [7]</td><td>30.03</td><td>0.535</td><td>-</td><td>27.38</td><td>0.449</td><td>-</td><td>23.30</td><td>0.335</td><td>-</td></tr><tr><td>IntraTomo [39]</td><td>36.79</td><td>0.858</td><td>2h25m</td><td>36.99</td><td>0.854</td><td>2h19m</td><td>35.85</td><td>0.835</td><td>2h18m</td></tr><tr><td>NAF [40]</td><td>38.58</td><td>0.848</td><td>51m28s</td><td>36.44</td><td>0.818</td><td>51m31s</td><td>32.92</td><td>0.772</td><td>51m24s</td></tr><tr><td>SAX-NeRF [2]</td><td>34.93</td><td>0.854</td><td>13h21m</td><td>34.89</td><td>0.840</td><td>13h23m</td><td>33.49</td><td>0.793</td><td>13h25m</td></tr><tr><td>X-Gaussian* [3]</td><td>38.27</td><td>0.894</td><td>10m21s</td><td>37.80</td><td>0.881</td><td>10m5s</td><td>35.12</td><td>0.859</td><td>9m55s</td></tr><tr><td>R²-Gaussian (iter=10k) [41]</td><td>38.10</td><td>0.872</td><td>3m39s</td><td>37.52</td><td>0.866</td><td>3m37s</td><td>35.10</td><td>0.840</td><td>3m23s</td></tr><tr><td>R²-Gaussian (iter=30k) [41]</td><td>39.40</td><td>0.875</td><td>14m16s</td><td>38.24</td><td>0.864</td><td>13m52s</td><td>34.83</td><td>0.833</td><td>12m56s</td></tr><tr><td>DGR (iter=300)</td><td>39.91</td><td>0.937</td><td>3m36s</td><td>38.66</td><td>0.929</td><td>3m24s</td><td>35.16</td><td>0.883</td><td>2m59s</td></tr><tr><td>DGR (iter=1000)</td><td>41.28</td><td>0.952</td><td>13m14s</td><td>39.27</td><td>0.940</td><td>11m48s</td><td>34.58</td><td>0.870</td><td>8m54s</td></tr><tr><td colspan="10">Synthesis Dataset</td></tr><tr><td>FDK [7]</td><td>28.63</td><td>0.497</td><td>-</td><td>26.50</td><td>0.422</td><td>-</td><td>22.99</td><td>0.317</td><td>-</td></tr><tr><td>IntraTomo [39]</td><td>35.42</td><td>0.924</td><td>2h7m</td><td>35.25</td><td>0.923</td><td>2h9m</td><td>34.68</td><td>0.914</td><td>2h19m</td></tr><tr><td>NAF [40]</td><td>37.84</td><td>0.945</td><td>30m43s</td><td>36.65</td><td>0.932</td><td>32m4s</td><td>33.91</td><td>0.893</td><td>31m1s</td></tr><tr><td>SAX-NeRF [2]</td><td>38.07</td><td>0.950</td><td>13h5m</td><td>36.86</td><td>0.938</td><td>13h5m</td><td>34.33</td><td>0.905</td><td>13h3m</td></tr><tr><td>X-Gaussian* [3]</td><td>38.22</td><td>0.955</td><td>9m58s</td><td>37.50</td><td>0.946</td><td>9m50s</td><td>35.18</td><td>0.924</td><td>9m51s</td></tr><tr><td>R²-Gaussian (iter=10k) [41]</td><td>38.29</td><td>0.954</td><td>2m38s</td><td>37.63</td><td>0.949</td><td>2m35s</td><td>35.08</td><td>0.922</td><td>2m35s</td></tr><tr><td>R²-Gaussian (iter=30k) [41]</td><td>38.88</td><td>0.959</td><td>8m21s</td><td>37.98</td><td>0.952</td><td>8m14s</td><td>35.19</td><td>0.923</td><td>8m28s</td></tr><tr><td>DGR (iter=300)</td><td>38.71</td><td>0.957</td><td>2m24s</td><td>38.05</td><td>0.954</td><td>2m17s</td><td>35.76</td><td>0.930</td><td>2m14s</td></tr><tr><td>DGR (iter=1000)</td><td>39.63</td><td>0.964</td><td>7m27s</td><td>38.74</td><td>0.960</td><td>7m13s</td><td>36.55</td><td>0.947</td><td>6m53s</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Extra Data</td><td colspan="2">180-view</td><td colspan="2">120-view</td><td colspan="2">90-view</td><td colspan="2">60-view</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td><td>PSNR↑</td><td>SSIM↑</td></tr><tr><td>FBP [1]</td><td>0</td><td>31.69</td><td>0.882</td><td>28.30</td><td>0.787</td><td>26.20</td><td>0.701</td><td>23.18</td><td>0.595</td></tr><tr><td>FBPCovNet [16]</td><td>4839</td><td>42.23</td><td>0.988</td><td>39.45</td><td>0.983</td><td>37.11</td><td>0.976</td><td>35.63</td><td>0.966</td></tr><tr><td>U-Net [23]</td><td>4839</td><td>38.37</td><td>0.985</td><td>35.58</td><td>0.977</td><td>30.09</td><td>0.947</td><td>28.83</td><td>0.937</td></tr><tr><td>PLANet [38]</td><td>4176</td><td>42.76</td><td>0.965</td><td>41.67</td><td>0.962</td><td>40.99</td><td>0.957</td><td>38.97</td><td>0.941</td></tr><tr><td>GMSD [10]</td><td>4839</td><td>41.44</td><td>0.988</td><td>39.41</td><td>0.981</td><td>37.25</td><td>0.974</td><td>34.31</td><td>0.958</td></tr><tr><td>SWORD [37]</td><td>4839</td><td>45.08</td><td>0.994</td><td>42.49</td><td>0.990</td><td>41.27</td><td>0.986</td><td>38.49</td><td>0.978</td></tr><tr><td>DGR</td><td>0</td><td>46.13</td><td>0.997</td><td>44.64</td><td>0.994</td><td>43.23</td><td>0.992</td><td>40.25</td><td>0.985</td></tr></table>
+
+Table 3. Fan-Beam Limited-Angle CT  $90^{\circ}$  reconstruction.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Data</td><td colspan="2">Axial</td><td colspan="2">Coronal</td><td colspan="2">Sagittal</td></tr><tr><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td><td>PSNR ↑</td><td>SSIM ↑</td></tr><tr><td>FBP [1]</td><td>0</td><td>14.91</td><td>0.397</td><td>17.07</td><td>0.411</td><td>15.46</td><td>0.403</td></tr><tr><td>FBPCovNet [16]</td><td>3142</td><td>26.76</td><td>0.879</td><td>25.77</td><td>0.874</td><td>22.92</td><td>0.841</td></tr><tr><td>ADMM-TV [28]</td><td>3142</td><td>23.19</td><td>0.793</td><td>22.96</td><td>0.758</td><td>19.95</td><td>0.782</td></tr><tr><td>MCG [5]</td><td>3839</td><td>26.01</td><td>0.838</td><td>24.55</td><td>0.823</td><td>21.59</td><td>0.706</td></tr><tr><td>Lahiri et al. [22]</td><td>3142</td><td>28.08</td><td>0.931</td><td>26.02</td><td>0.856</td><td>23.24</td><td>0.812</td></tr><tr><td>DiffusionMBIR [6]</td><td>3142</td><td>34.92</td><td>0.956</td><td>32.48</td><td>0.947</td><td>28.82</td><td>0.832</td></tr><tr><td>DGR</td><td>0</td><td>38.22</td><td>0.970</td><td>39.32</td><td>0.969</td><td>38.35</td><td>0.970</td></tr></table>
+
+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  
+
+<table><tr><td>Box-Size</td><td>13 × 13 × 13</td><td>15 × 15 × 15</td><td>17 × 17 × 17</td><td>19 × 19 × 19</td></tr><tr><td>Time (minutes)</td><td>7.92</td><td>11.07</td><td>16.58</td><td>26.99</td></tr><tr><td>V-Ram (GiB)</td><td>10.70</td><td>13.29</td><td>16.87</td><td>21.32</td></tr><tr><td>PSNR / SSIM</td><td>35.99 / 0.960</td><td>38.90 / 0.973</td><td>40.25 / 0.985</td><td>40.98 / 0.987</td></tr></table>
+
+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  
+
+<table><tr><td>Method</td><td>VRAM (GiB)</td><td>Time (s)</td></tr><tr><td>Direct Reconstruction (estimated)</td><td>16662.50</td><td>/</td></tr><tr><td>FVR w/o Decomposition</td><td>16.87</td><td>1.05</td></tr><tr><td>FVR w/ Decomposition</td><td>16.87</td><td>0.09</td></tr></table>
+
+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).
+
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ICCV/2025/DisenQ_ Disentangling Q-Former for Activity-Biometrics/full.md

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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
+
+![](images/a7e4b81495f409acdc479b81203e71522ed8256b4faedc9059508acc791fab25.jpg)  
+(a) Existing multimodal person identification approach
+
+![](images/d062ea181d79494608edf8d3409e78dc8a2eafc25fba8d822652901777de9674.jpg)  
+(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  $y_{Action})$
+
+![](images/d4833624207bb780a00d0d11f6616bf9810ca6ac889c7b9e0415f712c97e9e5d.jpg)  
+(a) Framework Overview
+
+![](images/6deec40764f5af3082e599bc64396390acc719cba6e9ebb93678dd34bd047584.jpg)  
+(b) DisenQ Overview
+
+![](images/63bde4db47a3a307bee49d743ef871237f1be246f45b7f809cb952b706dd9a67.jpg)  
+(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.  
+
+<table><tr><td rowspan="3">Methods</td><td rowspan="3">Venue</td><td colspan="4">NTU RGB-AB</td><td colspan="4">PKU MMD-AB</td><td colspan="4">Charades-AB</td></tr><tr><td colspan="2">Same</td><td colspan="2">Cross</td><td colspan="2">Same</td><td colspan="2">Cross</td><td colspan="2">Same</td><td colspan="2">Cross</td></tr><tr><td>R@1</td><td>mAP</td><td>R@1</td><td>mAP</td><td>R@1</td><td>mAP</td><td>R@1</td><td>mAP</td><td>R@1</td><td>mAP</td><td>R@1</td><td>mAP</td></tr><tr><td colspan="14">Models with only visual modality</td></tr><tr><td>TSF [28]</td><td>AAAI 20</td><td>71.8</td><td>31.8</td><td>67.8</td><td>26.9</td><td>76.4</td><td>37.5</td><td>71.6</td><td>33.2</td><td>35.4</td><td>21.9</td><td>30.2</td><td>19.0</td></tr><tr><td>VKD [44]</td><td>ECCV 20</td><td>67.4</td><td>35.6</td><td>66.3</td><td>31.5</td><td>78.4</td><td>38.5</td><td>72.2</td><td>34.3</td><td>36.3</td><td>20.7</td><td>31.9</td><td>18.8</td></tr><tr><td>BiCnet-TKS [25]</td><td>CVPR 21</td><td>72.7</td><td>34.5</td><td>69.1</td><td>30.2</td><td>80.8</td><td>38.5</td><td>77.1</td><td>33.3</td><td>40.3</td><td>27.3</td><td>38.3</td><td>23.3</td></tr><tr><td>PSTA [51]</td><td>ICCV 21</td><td>67.4</td><td>34.8</td><td>65.1</td><td>31.4</td><td>77.4</td><td>50.4</td><td>72.4</td><td>47.4</td><td>42.9</td><td>28.3</td><td>38.7</td><td>24.8</td></tr><tr><td>STMN [15]</td><td>ICCV 21</td><td>73.0</td><td>35.1</td><td>70.2</td><td>30.1</td><td>76.6</td><td>47.9</td><td>71.5</td><td>42.2</td><td>38.7</td><td>24.5</td><td>33.9</td><td>20.8</td></tr><tr><td>SINet [6]</td><td>CVPR 22</td><td>69.4</td><td>30.7</td><td>66.2</td><td>27.8</td><td>79.6</td><td>40.8</td><td>74.1</td><td>26.2</td><td>40.3</td><td>26.9</td><td>37.3</td><td>21.9</td></tr><tr><td>CAL [19]</td><td>CVPR 22</td><td>73.8</td><td>28.4</td><td>70.3</td><td>24.0</td><td>81.3</td><td>49.4</td><td>78.3</td><td>43.4</td><td>43.8</td><td>25.8</td><td>40.1</td><td>21.2</td></tr><tr><td>Video-CAL [19]</td><td>CVPR 22</td><td>75.5</td><td>39.9</td><td>73.3</td><td>31.7</td><td>79.6</td><td>49.4</td><td>77.3</td><td>45.7</td><td>43.9</td><td>28.5</td><td>41.5</td><td>25.8</td></tr><tr><td>PSTR [7]</td><td>CVPR 22</td><td>69.1</td><td>34.1</td><td>68.3</td><td>32.5</td><td>84.3</td><td>47.5</td><td>78.0</td><td>41.2</td><td>37.2</td><td>24.7</td><td>35.1</td><td>20.3</td></tr><tr><td>AIM [55]</td><td>CVPR 23</td><td>71.4</td><td>35.4</td><td>72.8</td><td>30.2</td><td>82.5</td><td>48.9</td><td>79.2</td><td>44.9</td><td>40.1</td><td>28.3</td><td>35.6</td><td>26.7</td></tr><tr><td>SCNet [20]</td><td>ACM MM 23</td><td>69.9</td><td>31.5</td><td>68.8</td><td>26.3</td><td>79.5</td><td>43.6</td><td>73.9</td><td>39.7</td><td>31.7</td><td>21.9</td><td>27.4</td><td>17.6</td></tr><tr><td>ABNet [3]</td><td>CVPR 24</td><td>78.8</td><td>40.3</td><td>77.0</td><td>37.6</td><td>86.8</td><td>57.3</td><td>81.4</td><td>51.8</td><td>45.8</td><td>31.6</td><td>44.8</td><td>28.8</td></tr><tr><td colspan="14">Models with visual + language modality</td></tr><tr><td>CLIP ReID [32] †</td><td>AAAI 23</td><td>77.1</td><td>40.2</td><td>75.2</td><td>33.7</td><td>82.3</td><td>52.1</td><td>81.2</td><td>50.8</td><td>44.2</td><td>31.3</td><td>42.1</td><td>27.7</td></tr><tr><td>CCLNet [10] †</td><td>ACM MM 23</td><td>75.2</td><td>36.1</td><td>74.3</td><td>33.1</td><td>83.2</td><td>51.4</td><td>80.1</td><td>47.5</td><td>42.1</td><td>29.3</td><td>38.8</td><td>23.4</td></tr><tr><td>TF-CLIP [58] †</td><td>AAAI 24</td><td>77.3</td><td>41.2</td><td>74.8</td><td>31.3</td><td>83.4</td><td>52.3</td><td>80.8</td><td>50.1</td><td>40.2</td><td>28.1</td><td>39.7</td><td>26.0</td></tr><tr><td>TVI-LFM [26] †</td><td>NeurIPS 24</td><td>76.2</td><td>38.1</td><td>75.9</td><td>34.1</td><td>85.2</td><td>53.9</td><td>81.5</td><td>52.1</td><td>45.7</td><td>30.1</td><td>42.8</td><td>28.3</td></tr><tr><td>Instruct-ReID [22] †</td><td>CVPR 24</td><td>78.2</td><td>41.5</td><td>75.9</td><td>33.4</td><td>84.3</td><td>53.1</td><td>81.7</td><td>52.3</td><td>44.8</td><td>28.3</td><td>40.1</td><td>25.3</td></tr><tr><td>EVA-CLIP [49] †</td><td></td><td>71.2</td><td>35.1</td><td>69.1</td><td>28.3</td><td>73.8</td><td>46.2</td><td>67.4</td><td>39.4</td><td>38.1</td><td>26.1</td><td>31.3</td><td>21.8</td></tr><tr><td>Ours</td><td></td><td>82.2</td><td>43.8</td><td>80.9</td><td>41.3</td><td>89.2</td><td>59.3</td><td>84.1</td><td>56.9</td><td>49.9</td><td>34.8</td><td>48.4</td><td>32.5</td></tr></table>
+
+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.  
+
+<table><tr><td>Methods</td><td>Venue</td><td>R@1</td><td>R@5</td><td>mAP</td></tr><tr><td colspan="5">Models with only visual modality</td></tr><tr><td>Attn-CL [43]</td><td>AAAI 20</td><td>42.1</td><td>56.0</td><td>18.6</td></tr><tr><td>Attn-CL + rerank [43]</td><td>AAAI 20</td><td>46.5</td><td>59.8</td><td>25.9</td></tr><tr><td>AP3D [18]</td><td>ECCV 20</td><td>39.0</td><td>56.0</td><td>15.9</td></tr><tr><td>TCLNet [24]</td><td>ECCV 20</td><td>48.1</td><td>60.1</td><td>23.0</td></tr><tr><td>BiCnet-TKS [25]</td><td>CVPR 21</td><td>19.0</td><td>35.1</td><td>6.3</td></tr><tr><td>STMN [14]</td><td>ICCV 21</td><td>31.0</td><td>54.4</td><td>11.3</td></tr><tr><td>PSTA [51]</td><td>ICCV 21</td><td>46.9</td><td>60.8</td><td>21.2</td></tr><tr><td>PiT [59]</td><td>TII 22</td><td>34.2</td><td>55.4</td><td>13.6</td></tr><tr><td>CAL [19]</td><td>CVPR 23</td><td>52.5</td><td>66.5</td><td>27.1</td></tr><tr><td>ShARc [62]</td><td>WACV 24</td><td>59.5</td><td>70.3</td><td>29.6</td></tr><tr><td>ABNet [3]†</td><td>CVPR 24</td><td>58.3</td><td>68.4</td><td>30.1</td></tr><tr><td colspan="5">Models with visual + language modality</td></tr><tr><td>CLIP ReID [32]†</td><td>AAAI 23</td><td>51.2</td><td>64.2</td><td>28.3</td></tr><tr><td>CCLNet [10]†</td><td>ACM MM 23</td><td>50.8</td><td>60.3</td><td>27.1</td></tr><tr><td>TVI-LFM [26]†</td><td>NeurIPS 24</td><td>49.2</td><td>61.8</td><td>23.7</td></tr><tr><td>Instruct-ReID [22]†</td><td>CVPR 24</td><td>53.8</td><td>59.4</td><td>28.4</td></tr><tr><td>EVA-CLIP [49]†</td><td></td><td>53.1</td><td>59.2</td><td>26.9</td></tr><tr><td>Ours</td><td></td><td>60.7</td><td>70.3</td><td>30.4</td></tr></table>
+
+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.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">NTU RGB-AB</td><td colspan="2">Charades-AB</td></tr><tr><td>Rank 1</td><td>mAP</td><td>Rank 1</td><td>mAP</td></tr><tr><td colspan="5">Contribution of each component</td></tr><tr><td>Vision encoder</td><td>73.2</td><td>36.2</td><td>40.1</td><td>29.2</td></tr><tr><td>+ Text encoder</td><td>77.7</td><td>40.6</td><td>46.5</td><td>31.8</td></tr><tr><td>+ DisenQ</td><td>82.2</td><td>43.8</td><td>49.9</td><td>34.8</td></tr><tr><td colspan="5">Ablation of different type of feature disentanglement</td></tr><tr><td>No disentanglement</td><td>74.2</td><td>38.2</td><td>42.3</td><td>29.9</td></tr><tr><td>Fb and Fb</td><td>76.6</td><td>40.9</td><td>44.7</td><td>31.9</td></tr><tr><td>Fb and Fm</td><td>79.2</td><td>41.1</td><td>48.2</td><td>32.9</td></tr><tr><td>Fb, Fb and Fm</td><td>82.2</td><td>43.8</td><td>49.9</td><td>34.8</td></tr><tr><td colspan="5">Performance of each disentangled feature</td></tr><tr><td>Biometrics</td><td>80.4</td><td>43.0</td><td>48.1</td><td>32.0</td></tr><tr><td>Non-biometrics</td><td>3.8</td><td>1.2</td><td>1.3</td><td>0.1</td></tr><tr><td>Motion</td><td>76.3</td><td>39.4</td><td>44.2</td><td>27.1</td></tr><tr><td>Biometrics + Motion</td><td>82.2</td><td>43.8</td><td>49.9</td><td>34.8</td></tr></table>
+
+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
+
+![](images/aef1bfbcfd6ace1da4422219fe0e21762638dc2e688ca535e4933d17233f8a00.jpg)  
+No Disentanglement
+
+![](images/8be028623ca24e11ca9f9bafc627ee2747a105abc07ba13a94f1edc6683498f1.jpg)  
+Ineffective Disentanglement
+
+![](images/0172a294543cff6db4a1f4cda3b6b555b1c9c93bb468f17c81ede06ddc23dea9.jpg)  
+Effective Disentanglement
+
+![](images/ac0d1f75efbecb1e4977c154d05a30bc250751645a8bab0930251e9124154e5c.jpg)  
+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.  
+
+<table><tr><td>Ft.</td><td>Sim.</td><td>St. Dev.</td></tr><tr><td>Tb</td><td>0.92</td><td>0.03</td></tr><tr><td>Tb</td><td>0.79</td><td>0.12</td></tr><tr><td>Tm</td><td>0.68</td><td>0.17</td></tr></table>
+
+![](images/54ceca97eb8a894d1bb79133648b6a9a83cc9e6c21f433665f4e9e0f43d571f2.jpg)  
+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.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Size</td><td colspan="2">NTU RGB-AB</td><td colspan="2">Charades-AB</td></tr><tr><td>R1</td><td>mAP</td><td>R1</td><td>mAP</td></tr><tr><td colspan="6">Vision encoders</td></tr><tr><td>SigLIP-L [60]</td><td>0.3B</td><td>80.2</td><td>41.6</td><td>48.3</td><td>33.7</td></tr><tr><td>ViT-1B [52]</td><td>1B</td><td>83.4</td><td>42.1</td><td>49.2</td><td>34.7</td></tr><tr><td>ViT-G/14 [49]</td><td>1.8B</td><td>82.2</td><td>43.8</td><td>49.9</td><td>34.8</td></tr><tr><td colspan="6">Visual Language Models (VLMs)</td></tr><tr><td>GPT-4V [39]</td><td>-</td><td>82.3</td><td>43.7</td><td>49.8</td><td>34.9</td></tr><tr><td>InstructBLIP [11]</td><td>7B</td><td>82.1</td><td>43.8</td><td>49.7</td><td>34.8</td></tr><tr><td>LLaVA 1.5 [36]</td><td>7B</td><td>82.2</td><td>43.8</td><td>49.9</td><td>34.8</td></tr></table>
+
+![](images/3a0053ee50043cb86d48a965c56a1b971fd4927fdcbd9374235c22d317e00f43.jpg)
+
+![](images/79c5a2e27e16bcb7242e41c824d37f9a28a04cf8864d4334fcbeafe5f15eaad0.jpg)
+
+![](images/f5debb3bd6cb8b1377ff8bd83bc0507ce3c0326a87267b8f5b1e89c307267810.jpg)
+
+![](images/9c1a5346868536c972b848c7dc2a54f620f5475afc9ce38ace9111c00cbe1956.jpg)
+
+![](images/4188041ed274f2aff3dd506adc27943321ac09dc92a337c8becb74ce19082613.jpg)  
+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.
+
+![](images/23262aa92c827e1938bf80dbc7edeb557cebfe721e6557e38fdd07e85f7d6a39.jpg)
+
+![](images/1d8adfd3ecefd3a38e76428c5a09f79a7e33c786013c49fc1749bf3589f47e37.jpg)
+
+![](images/205aeab0e1bcd1536427d345e4ce19fc4512e7e0cdf91057fc24e0fcb4f82081.jpg)
+
+# 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.
+
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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
+
+![](images/4a86e272eb47744196ef3338ae44a5ee985c1d4f69e97aff5956430cd234353d.jpg)  
+(a) Disentangled Clothed Avatar Generation
+
+![](images/c381a91f9f100730a02c849fb040f502e06d01bda52f1cfc0139354618850798.jpg)
+
+![](images/b70b2496902a282ce80f87ee1f472bab75b23c6f80862e1093c772f3fe7f82e3.jpg)  
+(b) Animation
+
+![](images/fa314cff5ef991c932b62036bcc96dec5e808d85d08fbced094adfcecc5eb25e.jpg)  
+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.
+
+![](images/e3fea118d60240838dc84b78fc1a2ca48f1b9aca551d5c283cf17d48f421b1da.jpg)
+
+![](images/94a0067141ae346133db726b261fd763429ec2d9a7941f0b93f9729b60fa6534.jpg)  
+(c) Camera View Control
+
+![](images/eeb477af8932944d75fc65ce69fb8e0ee1663235c7fab704187f7542a9de0c97.jpg)
+
+![](images/542ee3260a8b4f62784efcaad889988a58e2bca4c88dbadf6d165cccc5afa4f5.jpg)
+
+![](images/c172ecc863d9fccfd417dc0f5294af973c953519c1d24818dd793a82f8729220.jpg)
+
+![](images/876b89daff6ec3d1a2f697949451ca47d4bb30c39a6ac9c24547f960ced49875.jpg)  
+(d) Decomposition
+
+![](images/0a07fde5b2740f51b8649a21a7fdc90a5f1d48545edb0f7b151328e045e7732d.jpg)  
+(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
+
+![](images/7fff36677c045a0249f23cd869ee4c22d506073c8d4699b0376f7e18866c834f.jpg)  
+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,
+
+<table><tr><td>Methods</td><td>FID↓</td></tr><tr><td>EVA3D [21]</td><td>124.54†</td></tr><tr><td>StructLDM [25]</td><td>25.22†</td></tr><tr><td>E3Gen [80]</td><td>15.78★</td></tr><tr><td>Ours</td><td>12.50</td></tr></table>
+
+(a) Holistic Generation Quality.  
+
+<table><tr><td>Methods</td><td>FID↓</td><td>L-PSNR↑</td></tr><tr><td>EVA3D [21]</td><td>61.58*</td><td>&lt;20*</td></tr><tr><td>Rodin [65]</td><td>56.57*</td><td>18.12*</td></tr><tr><td>HumanLiff [23]</td><td>54.39*</td><td>28.57*</td></tr><tr><td>Ours</td><td>17.37</td><td>&gt;40</td></tr></table>
+
+(b) Layer-wise Generation Quality.  
+
+<table><tr><td>Methods</td><td>Disentanglement↑</td><td>Quality↑</td><td>Time↓</td></tr><tr><td>SO-SMPL [63]</td><td>13.02</td><td>3.57/8.57</td><td>5h</td></tr><tr><td>LAGA [18]</td><td>9.77</td><td>5.00/1.43</td><td>1.5h</td></tr><tr><td>TELA [15]</td><td>19.07</td><td>14.29/8.57</td><td>6h</td></tr><tr><td>Ours</td><td>58.14</td><td>77.14/81.43</td><td>2s</td></tr></table>
+
+![](images/484dc72d0ae373c8ce7d50960e3f2fa65f38231f41304db0e4988a0a6fdeccfc.jpg)  
+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.
+
+![](images/ba624de0409fa7c5302008425d5623d7a7ac19fbf74490949f873690ae34b220.jpg)
+
+![](images/f7e22b555d7704bc26ff83d257b835e9bc3d04dbf36b0403cceb82fcb1e9e5f2.jpg)
+
+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.  
+
+<table><tr><td>Methods</td><td>FID↓</td><td>KID ↓</td></tr><tr><td>Two-stage</td><td>19.06</td><td>15.40</td></tr><tr><td>Pipeline (SLMO)</td><td>30.83</td><td>30.18</td></tr><tr><td>Pipeline (SLMN)</td><td>28.95</td><td>29.21</td></tr><tr><td>Full pipeline</td><td>12.50</td><td>9.39</td></tr></table>
+
+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.
+
+![](images/f655c2d164e33fa3d8eeaa84476329fd9bae9f17c5bb8062820f0a7571082321.jpg)  
+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
+
+![](images/bd2c2270f53bff55c9e15890b2ede92d8f18bf2672a1507aa35a1d0219db7700.jpg)  
+Figure 5. Zoom in comparison between E3Gen and LayerAvatar. Compared to single-layer representation, layered representation exhibits detailed faces and clear boundaries between components.
+
+![](images/79e3b5f7afa8a9e4007bdabf3da1ba51603792ab3c9aa74a2a5a431d347d5d21.jpg)  
+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).
+
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