Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs. This survey serves as a resource for researchers and practitioners seeking to understand and contribute to the fusion of GNNs and DEs

Synthetic Video Enhances Physical Fidelity in Video Synthesis

We investigate how to enhance the physical fidelity of video generation models by leveraging synthetic videos derived from computer graphics pipelines. These rendered videos respect real-world physics, such as maintaining 3D consistency, and serve as a valuable resource that can potentially improve video generation models. To harness this potential, we propose a solution that curates and integrates synthetic data while introducing a method to transfer its physical realism to the model, significantly reducing unwanted artifacts. Through experiments on three representative tasks emphasizing physical consistency, we demonstrate its efficacy in enhancing physical fidelity. While our model still lacks a deep understanding of physics, our work offers one of the first empirical demonstrations that synthetic video enhances physical fidelity in video synthesis. Website: https://kevinz8866.github.io/simulation/

Project-and-Fuse: Improving RGB-D Semantic Segmentation via Graph Convolution Networks

Most existing RGB-D semantic segmentation methods focus on the feature level fusion, including complex cross-modality and cross-scale fusion modules. However, these methods may cause misalignment problem in the feature fusion process and counter-intuitive patches in the segmentation results. Inspired by the popular pixel-node-pixel pipeline, we propose to 1) fuse features from two modalities in a late fusion style, during which the geometric feature injection is guided by texture feature prior; 2) employ Graph Neural Networks (GNNs) on the fused feature to alleviate the emergence of irregular patches by inferring patch relationship. At the 3D feature extraction stage, we argue that traditional CNNs are not efficient enough for depth maps. So, we encode depth map into normal map, after which CNNs can easily extract object surface tendencies.At projection matrix generation stage, we find the existence of Biased-Assignment and Ambiguous-Locality issues in the original pipeline. Therefore, we propose to 1) adopt the Kullback-Leibler Loss to ensure no missing important pixel features, which can be viewed as hard pixel mining process; 2) connect regions that are close to each other in the Euclidean space as well as in the semantic space with larger edge weights so that location informations can been considered. Extensive experiments on two public datasets, NYU-DepthV2 and SUN RGB-D, have shown that our approach can consistently boost the performance of RGB-D semantic segmentation task.

Mitigating Graph Covariate Shift via Score-based Out-of-distribution Augmentation

Distribution shifts between training and testing datasets significantly impair the model performance on graph learning. A commonly-taken causal view in graph invariant learning suggests that stable predictive features of graphs are causally associated with labels, whereas varying environmental features lead to distribution shifts. In particular, covariate shifts caused by unseen environments in test graphs underscore the critical need for out-of-distribution (OOD) generalization. Existing graph augmentation methods designed to address the covariate shift often disentangle the stable and environmental features in the input space, and selectively perturb or mixup the environmental features. However, such perturbation-based methods heavily rely on an accurate separation of stable and environmental features, and their exploration ability is confined to existing environmental features in the training distribution. To overcome these limitations, we introduce a novel approach using score-based graph generation strategies that synthesize unseen environmental features while preserving the validity and stable features of overall graph patterns. Our comprehensive empirical evaluations demonstrate the enhanced effectiveness of our method in improving graph OOD generalization.

Texture-AD: An Anomaly Detection Dataset and Benchmark for Real Algorithm Development

Anomaly detection is a crucial process in industrial manufacturing and has made significant advancements recently. However, there is a large variance between the data used in the development and the data collected by the production environment. Therefore, we present the Texture-AD benchmark based on representative texture-based anomaly detection to evaluate the effectiveness of unsupervised anomaly detection algorithms in real-world applications. This dataset includes images of 15 different cloth, 14 semiconductor wafers and 10 metal plates acquired under different optical schemes. In addition, it includes more than 10 different types of defects produced during real manufacturing processes, such as scratches, wrinkles, color variations and point defects, which are often more difficult to detect than existing datasets. All anomalous areas are provided with pixel-level annotations to facilitate comprehensive evaluation using anomaly detection models. Specifically, to adapt to diverse products in automated pipelines, we present a new evaluation method and results of baseline algorithms. The experimental results show that Texture-AD is a difficult challenge for state-of-the-art algorithms. To our knowledge, Texture-AD is the first dataset to be devoted to evaluating industrial defect detection algorithms in the real world. The dataset is available at https://XXX.

Adapted-MoE: Mixture of Experts with Test-Time Adaption for Anomaly Detection

Most unsupervised anomaly detection methods based on representations of normal samples to distinguish anomalies have recently made remarkable progress. However, existing methods only learn a single decision boundary for distinguishing the samples within the training dataset, neglecting the variation in feature distribution for normal samples even in the same category in the real world. Furthermore, it was not considered that a distribution bias still exists between the test set and the train set. Therefore, we propose an Adapted-MoE which contains a routing network and a series of expert models to handle multiple distributions of same-category samples by divide and conquer. Specifically, we propose a routing network based on representation learning to route same-category samples into the subclasses feature space. Then, a series of expert models are utilized to learn the representation of various normal samples and construct several independent decision boundaries. We propose the test-time adaption to eliminate the bias between the unseen test sample representation and the feature distribution learned by the expert model. Our experiments are conducted on a dataset that provides multiple subclasses from three categories, namely Texture AD benchmark. The Adapted-MoE significantly improves the performance of the baseline model, achieving 2.18%-7.20% and 1.57%-16.30% increase in I-AUROC and P-AUROC, which outperforms the current state-of-the-art methods. Our code is available at https://github.com/.

RAVSS: Robust Audio-Visual Speech Separation in Multi-Speaker Scenarios with Missing Visual Cues

While existing Audio-Visual Speech Separation (AVSS) methods primarily concentrate on the audio-visual fusion strategy for two-speaker separation, they demonstrate a severe performance drop in the multi-speaker separation scenarios. Typically, AVSS methods employ guiding videos to sequentially isolate individual speakers from the given audio mixture, resulting in notable missing and noisy parts across various segments of the separated speech. In this study, we propose a simultaneous multi-speaker separation framework that can facilitate the concurrent separation of multiple speakers within a singular process. We introduce speaker-wise interactions to establish distinctions and correlations among speakers. Experimental results on the VoxCeleb2 and LRS3 datasets demonstrate that our method achieves state-of-the-art performance in separating mixtures with 2, 3, 4, and 5 speakers, respectively. Additionally, our model can utilize speakers with complete audio-visual information to mitigate other visual-deficient speakers, thereby enhancing its resilience to missing visual cues. We also conduct experiments where visual information for specific speakers is entirely absent or visual frames are partially missing. The results demonstrate that our model consistently outperforms others, exhibiting the smallest performance drop across all settings involving 2, 3, 4, and 5 speakers.

Physically Compatible 3D Object Modeling from a Single Image

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes

We present TetSphere splatting, an explicit, Lagrangian representation for reconstructing 3D shapes with high-quality geometry. In contrast to conventional object reconstruction methods which predominantly use Eulerian representations, including both neural implicit (e.g., NeRF, NeuS) and explicit representations (e.g., DMTet), and often struggle with high computational demands and suboptimal mesh quality, TetSphere splatting utilizes an underused but highly effective geometric primitive -- tetrahedral meshes. This approach directly yields superior mesh quality without relying on neural networks or post-processing. It deforms multiple initial tetrahedral spheres to accurately reconstruct the 3D shape through a combination of differentiable rendering and geometric energy optimization, resulting in significant computational efficiency. Serving as a robust and versatile geometry representation, Tet-Sphere splatting seamlessly integrates into diverse applications, including single-view 3D reconstruction, image-/text-to-3D content generation. Experimental results demonstrate that TetSphere splatting outperforms existing representations, delivering faster optimization speed, enhanced mesh quality, and reliable preservation of thin structures.

Learning Multi-dimensional Human Preference for Text-to-Image Generation

Current metrics for text-to-image models typically rely on statistical metrics which inadequately represent the real preference of humans. Although recent work attempts to learn these preferences via human annotated images, they reduce the rich tapestry of human preference to a single overall score. However, the preference results vary when humans evaluate images with different aspects. Therefore, to learn the multi-dimensional human preferences, we propose the Multi-dimensional Preference Score (MPS), the first multi-dimensional preference scoring model for the evaluation of text-to-image models. The MPS introduces the preference condition module upon CLIP model to learn these diverse preferences. It is trained based on our Multi-dimensional Human Preference (MHP) Dataset, which comprises 918,315 human preference choices across four dimensions (i.e., aesthetics, semantic alignment, detail quality and overall assessment) on 607,541 images. The images are generated by a wide range of latest text-to-image models. The MPS outperforms existing scoring methods across 3 datasets in 4 dimensions, enabling it a promising metric for evaluating and improving text-to-image generation.