LGJun 19, 2023
SGFormer: Simplifying and Empowering Transformers for Large-Graph RepresentationsQitian Wu, Wentao Zhao, Chenxiao Yang et al.
Learning representations on large-sized graphs is a long-standing challenge due to the inter-dependence nature involved in massive data points. Transformers, as an emerging class of foundation encoders for graph-structured data, have shown promising performance on small graphs due to its global attention capable of capturing all-pair influence beyond neighboring nodes. Even so, existing approaches tend to inherit the spirit of Transformers in language and vision tasks, and embrace complicated models by stacking deep multi-head attentions. In this paper, we critically demonstrate that even using a one-layer attention can bring up surprisingly competitive performance across node property prediction benchmarks where node numbers range from thousand-level to billion-level. This encourages us to rethink the design philosophy for Transformers on large graphs, where the global attention is a computation overhead hindering the scalability. We frame the proposed scheme as Simplified Graph Transformers (SGFormer), which is empowered by a simple attention model that can efficiently propagate information among arbitrary nodes in one layer. SGFormer requires none of positional encodings, feature/graph pre-processing or augmented loss. Empirically, SGFormer successfully scales to the web-scale graph ogbn-papers100M and yields up to 141x inference acceleration over SOTA Transformers on medium-sized graphs. Beyond current results, we believe the proposed methodology alone enlightens a new technical path of independent interest for building Transformers on large graphs.
92.0CVMar 20Code
Physion-Eval: Evaluating Physical Realism in Generated Video via Human ReasoningQin Zhang, Peiyu Jing, Hong-Xing Yu et al.
Video generation models are increasingly used as world simulators for storytelling, simulation, and embodied AI. As these models advance, a key question arises: do generated videos obey the physical laws of the real world? Existing evaluations largely rely on automated metrics or coarse human judgments such as preferences or rubric-based checks. While useful for assessing perceptual quality, these methods provide limited insight into when and why generated dynamics violate real-world physical constraints. We introduce Physion-Eval, a large-scale benchmark of expert human reasoning for diagnosing physical realism failures in videos generated by five state-of-the-art models across egocentric and exocentric views, containing 10,990 expert reasoning traces spanning 22 fine-grained physical categories. Each generated video is derived from a corresponding real-world reference video depicting a clear physical process, and annotated with temporally localized glitches, structured failure categories, and natural-language explanations of the violated physical behavior. Using this dataset, we reveal a striking limitation of current video generation models: in physics-critical scenarios, 83.3% of exocentric and 93.5% of egocentric generated videos exhibit at least one human-identifiable physical glitch. We hope Physion-Eval will set a new standard for physical realism evaluation and guide the development of physics-grounded video generation. The benchmark is publicly available at https://huggingface.co/datasets/PhysionLabs/Physion-Eval.
89.2CLMay 25
Automated Benchmark Auditing for AI Agents and Large Language ModelsJunlin Wang, Federico Bianchi, Shang Zhu et al.
Modern AI benchmarks operate at a complexity that outpaces traditional verification methods. Tasks authored by domain experts often contain implicit assumptions, incomplete environment specifications, and brittle evaluation logic that human annotation cannot reliably catch. We introduce Auto Benchmark Audit (ABA), an agentic framework that systematically audits individual benchmark tasks, uncovering issues such as hidden environment dependencies, specification gaps, and limited grading logic. We run ABA on a collection of frontier LLM benchmarks and previous NeurIPS publications, totaling 168 benchmarks across nine domains. Across this corpus, ABA identifies critical issues including ambiguous task design, execution environment conflicts, and incorrect ground truths in over 25.7% of the evaluated tasks. The precision of these automated audits is validated by expert review and independent third-party reports such as upstream PRs. Crucially, we demonstrate that these problematic tasks severely distorts capability assessments for agents and LLMs: filtering out these tasks with issues shifts model rankings and increases average performance on SWE-bench Verified and Terminal-Bench 2 by 9.9% and 9.6%, respectively. We release the agentic tool and all task annotations to support the future development of frontier benchmarks.
ROSep 24, 2023
Boosting Offline Reinforcement Learning for Autonomous Driving with Hierarchical Latent SkillsZenan Li, Fan Nie, Qiao Sun et al.
Learning-based vehicle planning is receiving increasing attention with the emergence of diverse driving simulators and large-scale driving datasets. While offline reinforcement learning (RL) is well suited for these safety-critical tasks, it still struggles to plan over extended periods. In this work, we present a skill-based framework that enhances offline RL to overcome the long-horizon vehicle planning challenge. Specifically, we design a variational autoencoder (VAE) to learn skills from offline demonstrations. To mitigate posterior collapse of common VAEs, we introduce a two-branch sequence encoder to capture both discrete options and continuous variations of the complex driving skills. The final policy treats learned skills as actions and can be trained by any off-the-shelf offline RL algorithms. This facilitates a shift in focus from per-step actions to temporally extended skills, thereby enabling long-term reasoning into the future. Extensive results on CARLA prove that our model consistently outperforms strong baselines at both training and new scenarios. Additional visualizations and experiments demonstrate the interpretability and transferability of extracted skills.
LGSep 28, 2023
Uncertainty-Aware Decision Transformer for Stochastic Driving EnvironmentsZenan Li, Fan Nie, Qiao Sun et al.
Offline Reinforcement Learning (RL) enables policy learning without active interactions, making it especially appealing for self-driving tasks. Recent successes of Transformers inspire casting offline RL as sequence modeling, which, however, fails in stochastic environments with incorrect assumptions that identical actions can consistently achieve the same goal. In this paper, we introduce an UNcertainty-awaRE deciSion Transformer (UNREST) for planning in stochastic driving environments without introducing additional transition or complex generative models. Specifically, UNREST estimates uncertainties by conditional mutual information between transitions and returns. Discovering 'uncertainty accumulation' and 'temporal locality' properties of driving environments, we replace the global returns in decision transformers with truncated returns less affected by environments to learn from actual outcomes of actions rather than environment transitions. We also dynamically evaluate uncertainty at inference for cautious planning. Extensive experiments demonstrate UNREST's superior performance in various driving scenarios and the power of our uncertainty estimation strategy.
LGFeb 18, 2024Code
Graph Out-of-Distribution Generalization via Causal InterventionQitian Wu, Fan Nie, Chenxiao Yang et al.
Out-of-distribution (OOD) generalization has gained increasing attentions for learning on graphs, as graph neural networks (GNNs) often exhibit performance degradation with distribution shifts. The challenge is that distribution shifts on graphs involve intricate interconnections between nodes, and the environment labels are often absent in data. In this paper, we adopt a bottom-up data-generative perspective and reveal a key observation through causal analysis: the crux of GNNs' failure in OOD generalization lies in the latent confounding bias from the environment. The latter misguides the model to leverage environment-sensitive correlations between ego-graph features and target nodes' labels, resulting in undesirable generalization on new unseen nodes. Built upon this analysis, we introduce a conceptually simple yet principled approach for training robust GNNs under node-level distribution shifts, without prior knowledge of environment labels. Our method resorts to a new learning objective derived from causal inference that coordinates an environment estimator and a mixture-of-expert GNN predictor. The new approach can counteract the confounding bias in training data and facilitate learning generalizable predictive relations. Extensive experiment demonstrates that our model can effectively enhance generalization with various types of distribution shifts and yield up to 27.4\% accuracy improvement over state-of-the-arts on graph OOD generalization benchmarks. Source codes are available at https://github.com/fannie1208/CaNet.
35.1CLApr 14
Peer-Predictive Self-Training for Language Model ReasoningShi Feng, Hanlin Zhang, Fan Nie et al.
Mechanisms for continued self-improvement of language models without external supervision remain an open challenge. We propose Peer-Predictive Self-Training (PST), a label-free fine-tuning framework in which multiple language models improve collaboratively by leveraging a cross-model aggregated response as an internal training signal. Given a prompt question, the models generate responses sequentially; the final aggregated answer, often more reliable than individual responses in practice, serves as an internal target for learning. We measure how informative each intermediate response is about the aggregate using pointwise mutual information (PMI), and use this signal to scale self-training updates. Responses already aligned with the aggregate are updated less, while less informative or misaligned responses are updated more. On mathematical reasoning benchmarks (SimulEq, Math500, and MultiArith), PST improves exact-match accuracy by 2.2 to 4.3 percentage points across Gemma-2-2B, LLaMA-3.2-1B, and Qwen-2.5-1.5B, and reduces the average generator-verifier gap (GV-Gap) by 26 to 40 percent, while requiring no external supervision or teacher-student hierarchy and relying solely on cross-model interactions. These results suggest that cross-model generations and peer-predictive feedback can serve as an effective approach for self-supervised training.
CVNov 4, 2025
When Visualizing is the First Step to Reasoning: MIRA, a Benchmark for Visual Chain-of-ThoughtYiyang Zhou, Haoqin Tu, Zijun Wang et al.
We propose MIRA, a new benchmark designed to evaluate models in scenarios where generating intermediate visual images is essential for successful reasoning. Unlike traditional CoT methods that rely solely on text, tasks in MIRA require models to generate and utilize intermediate images - such as sketches, structural diagrams, or path drawings - to guide their reasoning process. This setup closely mirrors how humans solve complex problems through "drawing to think". To solve this, MIRA focuses on tasks that are intrinsically challenging and involve complex structures, spatial relationships, or reasoning steps that are difficult to express through language alone. To ensure that our evaluation data is of high-quality, we include 546 multimodal problems, annotated with intermediate visual images and final answers. We also propose a unified evaluation protocol for MIRA that spans three levels of evaluation input: direct input with image and question only, text-only CoT input with image and thinking prompts, and Visual-CoT input with both annotated image clues and textual thinking prompts. To probe the upper bound of model capacity on our benchmark, we also report pass@k and majority voting accuracies under different k settings. Experimental results show that existing multimodal large language models, including strongest private models as well as strong open-weight models, perform poorly when relying solely on textual prompts. However, when intermediate visual cues are provided, model performance improves consistently, yielding an average relative gain of 33.7% across all models and tasks. We also probe the upper bound by expanding the search space and designing textual prompts aligned with Visual-CoT, but both yield only limited improvements compared to our Visual-CoT setting. These results underscore the critical role of imagined visual information in enabling successful reasoning on MIRA.
AIJan 22
DSGym: A Holistic Framework for Evaluating and Training Data Science AgentsFan Nie, Junlin Wang, Harper Hua et al.
Data science agents promise to accelerate discovery and insight-generation by turning data into executable analyses and findings. Yet existing data science benchmarks fall short due to fragmented evaluation interfaces that make cross-benchmark comparison difficult, narrow task coverage and a lack of rigorous data grounding. In particular, we show that a substantial portion of tasks in current benchmarks can be solved without using the actual data. To address these limitations, we introduce DSGym, a standardized framework for evaluating and training data science agents in self-contained execution environments. Unlike static benchmarks, DSGym provides a modular architecture that makes it easy to add tasks, agent scaffolds, and tools, positioning it as a live, extensible testbed. We curate DSGym-Tasks, a holistic task suite that standardizes and refines existing benchmarks via quality and shortcut solvability filtering. We further expand coverage with (1) DSBio: expert-derived bioinformatics tasks grounded in literature and (2) DSPredict: challenging prediction tasks spanning domains such as computer vision, molecular prediction, and single-cell perturbation. Beyond evaluation, DSGym enables agent training via execution-verified data synthesis pipeline. As a case study, we build a 2,000-example training set and trained a 4B model in DSGym that outperforms GPT-4o on standardized analysis benchmarks. Overall, DSGym enables rigorous end-to-end measurement of whether agents can plan, implement, and validate data analyses in realistic scientific context.
LGNov 30, 2024Code
TAROT: Targeted Data Selection via Optimal TransportLan Feng, Fan Nie, Yuejiang Liu et al.
We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.
CVFeb 25
Optimizing Neural Network Architecture for Medical Image Segmentation Using Monte Carlo Tree SearchLiping Meng, Fan Nie, Yunyun Zhang et al.
This paper proposes a novel medical image segmentation framework, MNAS-Unet, which combines Monte Carlo Tree Search (MCTS) and Neural Architecture Search (NAS). MNAS-Unet dynamically explores promising network architectures through MCTS, significantly enhancing the efficiency and accuracy of architecture search. It also optimizes the DownSC and UpSC unit structures, enabling fast and precise model adjustments. Experimental results demonstrate that MNAS-Unet outperforms NAS-Unet and other state-of-the-art models in segmentation accuracy on several medical image datasets, including PROMISE12, Ultrasound Nerve, and CHAOS. Furthermore, compared with NAS-Unet, MNAS-Unet reduces the architecture search budget by 54% (early stopping at 139 epochs versus 300 epochs under the same search setting), while achieving a lightweight model with only 0.6M parameters and lower GPU memory consumption, which further improves its practical applicability. These results suggest that MNAS-Unet can improve search efficiency while maintaining competitive segmentation accuracy under practical resource constraints.
CHEM-PHMar 25, 2024
UAlign: Pushing the Limit of Template-free Retrosynthesis Prediction with Unsupervised SMILES AlignmentKaipeng Zeng, Bo yang, Xin Zhao et al.
Motivation: Retrosynthesis planning poses a formidable challenge in the organic chemical industry. Single-step retrosynthesis prediction, a crucial step in the planning process, has witnessed a surge in interest in recent years due to advancements in AI for science. Various deep learning-based methods have been proposed for this task in recent years, incorporating diverse levels of additional chemical knowledge dependency. Results: This paper introduces UAlign, a template-free graph-to-sequence pipeline for retrosynthesis prediction. By combining graph neural networks and Transformers, our method can more effectively leverage the inherent graph structure of molecules. Based on the fact that the majority of molecule structures remain unchanged during a chemical reaction, we propose a simple yet effective SMILES alignment technique to facilitate the reuse of unchanged structures for reactant generation. Extensive experiments show that our method substantially outperforms state-of-the-art template-free and semi-template-based approaches. Importantly, our template-free method achieves effectiveness comparable to, or even surpasses, established powerful template-based methods. Scientific contribution: We present a novel graph-to-sequence template-free retrosynthesis prediction pipeline that overcomes the limitations of Transformer-based methods in molecular representation learning and insufficient utilization of chemical information. We propose an unsupervised learning mechanism for establishing product-atom correspondence with reactant SMILES tokens, achieving even better results than supervised SMILES alignment methods. Extensive experiments demonstrate that UAlign significantly outperforms state-of-the-art template-free methods and rivals or surpasses template-based approaches, with up to 5\% (top-5) and 5.4\% (top-10) increased accuracy over the strongest baseline.
ROOct 21, 2024
Generalizing Motion Planners with Mixture of Experts for Autonomous DrivingQiao Sun, Huimin Wang, Jiahao Zhan et al.
Large real-world driving datasets have sparked significant research into various aspects of data-driven motion planners for autonomous driving. These include data augmentation, model architecture, reward design, training strategies, and planner pipelines. These planners promise better generalizations on complicated and few-shot cases than previous methods. However, experiment results show that many of these approaches produce limited generalization abilities in planning performance due to overly complex designs or training paradigms. In this paper, we review and benchmark previous methods focusing on generalizations. The experimental results indicate that as models are appropriately scaled, many design elements become redundant. We introduce StateTransformer-2 (STR2), a scalable, decoder-only motion planner that uses a Vision Transformer (ViT) encoder and a mixture-of-experts (MoE) causal Transformer architecture. The MoE backbone addresses modality collapse and reward balancing by expert routing during training. Extensive experiments on the NuPlan dataset show that our method generalizes better than previous approaches across different test sets and closed-loop simulations. Furthermore, we assess its scalability on billions of real-world urban driving scenarios, demonstrating consistent accuracy improvements as both data and model size grow.
AIApr 7, 2025
Weak-for-Strong: Training Weak Meta-Agent to Harness Strong ExecutorsFan Nie, Lan Feng, Haotian Ye et al. · stanford
Efficiently leveraging of the capabilities of contemporary large language models (LLMs) is increasingly challenging, particularly when direct fine-tuning is expensive and often impractical. Existing training-free methods, including manually or automated designed workflows, typically demand substantial human effort or yield suboptimal results. This paper proposes Weak-for-Strong Harnessing (W4S), a novel framework that customizes smaller, cost-efficient language models to design and optimize workflows for harnessing stronger models. W4S formulates workflow design as a multi-turn markov decision process and introduces reinforcement learning for agentic workflow optimization (RLAO) to train a weak meta-agent. Through iterative interaction with the environment, the meta-agent learns to design increasingly effective workflows without manual intervention. Empirical results demonstrate the superiority of W4S that our 7B meta-agent, trained with just one GPU hour, outperforms the strongest baseline by 2.9% ~ 24.6% across eleven benchmarks, successfully elevating the performance of state-of-the-art models such as GPT-3.5-Turbo and GPT-4o. Notably, W4S exhibits strong generalization capabilities across both seen and unseen tasks, offering an efficient, high-performing alternative to directly fine-tuning strong models.
CVOct 31, 2024
DIP: Diffusion Learning of Inconsistency Pattern for General DeepFake DetectionFan Nie, Jiangqun Ni, Jian Zhang et al.
With the advancement of deepfake generation techniques, the importance of deepfake detection in protecting multimedia content integrity has become increasingly obvious. Recently, temporal inconsistency clues have been explored to improve the generalizability of deepfake video detection. According to our observation, the temporal artifacts of forged videos in terms of motion information usually exhibits quite distinct inconsistency patterns along horizontal and vertical directions, which could be leveraged to improve the generalizability of detectors. In this paper, a transformer-based framework for Diffusion Learning of Inconsistency Pattern (DIP) is proposed, which exploits directional inconsistencies for deepfake video detection. Specifically, DIP begins with a spatiotemporal encoder to represent spatiotemporal information. A directional inconsistency decoder is adopted accordingly, where direction-aware attention and inconsistency diffusion are incorporated to explore potential inconsistency patterns and jointly learn the inherent relationships. In addition, the SpatioTemporal Invariant Loss (STI Loss) is introduced to contrast spatiotemporally augmented sample pairs and prevent the model from overfitting nonessential forgery artifacts. Extensive experiments on several public datasets demonstrate that our method could effectively identify directional forgery clues and achieve state-of-the-art performance.
CLAug 25, 2025
UQ: Assessing Language Models on Unsolved QuestionsFan Nie, Ken Ziyu Liu, Zihao Wang et al.
Benchmarks shape progress in AI research. A useful benchmark should be both difficult and realistic: questions should challenge frontier models while also reflecting real-world usage. Yet, current paradigms face a difficulty-realism tension: exam-style benchmarks are often made artificially difficult with limited real-world value, while benchmarks based on real user interaction often skew toward easy, high-frequency problems. In this work, we explore a radically different paradigm: assessing models on unsolved questions. Rather than a static benchmark scored once, we curate unsolved questions and evaluate models asynchronously over time with validator-assisted screening and community verification. We introduce UQ, a testbed of 500 challenging, diverse questions sourced from Stack Exchange, spanning topics from CS theory and math to sci-fi and history, probing capabilities including reasoning, factuality, and browsing. UQ is difficult and realistic by construction: unsolved questions are often hard and naturally arise when humans seek answers, thus solving them yields direct real-world value. Our contributions are threefold: (1) UQ-Dataset and its collection pipeline combining rule-based filters, LLM judges, and human review to ensure question quality (e.g., well-defined and difficult); (2) UQ-Validators, compound validation strategies that leverage the generator-validator gap to provide evaluation signals and pre-screen candidate solutions for human review; and (3) UQ-Platform, an open platform where experts collectively verify questions and solutions. The top model passes UQ-validation on only 15% of questions, and preliminary human verification has already identified correct answers among those that passed. UQ charts a path for evaluating frontier models on real-world, open-ended challenges, where success pushes the frontier of human knowledge. We release UQ at https://uq.stanford.edu.
CLJun 19, 2025
EvoLM: In Search of Lost Language Model Training DynamicsZhenting Qi, Fan Nie, Alexandre Alahi et al.
Modern language model (LM) training has been divided into multiple stages, making it difficult for downstream developers to evaluate the impact of design choices made at each stage. We present EvoLM, a model suite that enables systematic and transparent analysis of LMs' training dynamics across pre-training, continued pre-training, supervised fine-tuning, and reinforcement learning. We train over 100 LMs with 1B and 4B parameters from scratch, and evaluate both upstream (language modeling) and downstream (problem-solving) capabilities, including considerations of both in-domain and out-of-domain generalization. Key insights highlight the diminishing returns from excessive pre-training and post-training, the importance and practices of mitigating forgetting during domain-specific continued pre-training, the crucial role of continued pre-training in bridging pre-training and post-training phases, and various intricate trade-offs when configuring supervised fine-tuning and reinforcement learning. To facilitate open research and reproducibility, we release all pre-trained and post-trained models, training datasets for all stages, and our entire training and evaluation pipeline.
CLNov 4, 2024
FactTest: Factuality Testing in Large Language Models with Finite-Sample and Distribution-Free GuaranteesFan Nie, Xiaotian Hou, Shuhang Lin et al.
The propensity of Large Language Models (LLMs) to generate hallucinations and non-factual content undermines their reliability in high-stakes domains, where rigorous control over Type I errors (the conditional probability of incorrectly classifying hallucinations as truthful content) is essential. Despite its importance, formal verification of LLM factuality with such guarantees remains largely unexplored. In this paper, we introduce FactTest, a novel framework that statistically assesses whether a LLM can confidently provide correct answers to given questions with high-probability correctness guarantees. We formulate factuality testing as hypothesis testing problem to enforce an upper bound of Type I errors at user-specified significance levels. Notably, we prove that our framework also ensures strong Type II error control under mild conditions and can be extended to maintain its effectiveness when covariate shifts exist. Our approach is distribution-free and works for any number of human-annotated samples. It is model-agnostic and applies to any black-box or white-box LM. Extensive experiments on question-answering (QA) and multiple-choice benchmarks demonstrate that FactTest effectively detects hallucinations and improves the model's ability to abstain from answering unknown questions, leading to an over 40% accuracy improvement.
MMNov 24, 2025
Towards Generalizable Deepfake Detection via Forgery-aware Audio-Visual Adaptation: A Variational Bayesian ApproachFan Nie, Jiangqun Ni, Jian Zhang et al.
The widespread application of AIGC contents has brought not only unprecedented opportunities, but also potential security concerns, e.g., audio-visual deepfakes. Therefore, it is of great importance to develop an effective and generalizable method for multi-modal deepfake detection. Typically, the audio-visual correlation learning could expose subtle cross-modal inconsistencies, e.g., audio-visual misalignment, which serve as crucial clues in deepfake detection. In this paper, we reformulate the correlation learning with variational Bayesian estimation, where audio-visual correlation is approximated as a Gaussian distributed latent variable, and thus develop a novel framework for deepfake detection, i.e., Forgery-aware Audio-Visual Adaptation with Variational Bayes (FoVB). Specifically, given the prior knowledge of pre-trained backbones, we adopt two core designs to estimate audio-visual correlations effectively. First, we exploit various difference convolutions and a high-pass filter to discern local and global forgery traces from both modalities. Second, with the extracted forgery-aware features, we estimate the latent Gaussian variable of audio-visual correlation via variational Bayes. Then, we factorize the variable into modality-specific and correlation-specific ones with orthogonality constraint, allowing them to better learn intra-modal and cross-modal forgery traces with less entanglement. Extensive experiments demonstrate that our FoVB outperforms other state-of-the-art methods in various benchmarks.
LGJun 7, 2024
Learning Divergence Fields for Shift-Robust Graph RepresentationsQitian Wu, Fan Nie, Chenxiao Yang et al.
Real-world data generation often involves certain geometries (e.g., graphs) that induce instance-level interdependence. This characteristic makes the generalization of learning models more difficult due to the intricate interdependent patterns that impact data-generative distributions and can vary from training to testing. In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging generalization problem with interdependent data. We generalize the diffusion equation with stochastic diffusivity at each time step, which aims to capture the multi-faceted information flows among interdependent data. Furthermore, we derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains. Regarding practical implementation, we introduce three model instantiations that can be considered as the generalized versions of GCN, GAT, and Transformers, respectively, which possess advanced robustness against distribution shifts. We demonstrate their promising efficacy for out-of-distribution generalization on diverse real-world datasets.