The application of generative modeling to many-body physics offers a promising pathway for analyzing high-dimensional state spaces of spin systems. However, unlike computer vision tasks where visual fidelity suffices, physical systems require the rigorous reproduction of higher-order statistical moments and thermodynamic quantities. While Score-Based Generative Models (SGMs) have emerged as a powerful tool, their standard formulation on Euclidean embedding space is ill-suited for continuous spin systems, where variables inherently reside on a manifold. In this work, we demonstrate that training on the Euclidean space compromises the model's ability to learn the target distribution as it prioritizes to learn the manifold constraints. We address this limitation by proposing the use of Manifold-Aware Score-Based Generative Modeling framework applied to the 64x64 2D XY model (a 4096-dimensional torus). We show that our method estimates the theoretical Boltzmann score with superior precision compared to standard diffusion models. Consequently, we successfully capture the Berezinskii-Kosterlitz Thouless (BKT) phase transition and accurately reproduce second-moment quantities, such as heat capacity without explicit feature engineering. Furthermore, we demonstrate zero-shot generalization to unseen lattice sizes, accurately recovering the physics of variable system scales without retraining. Since this approach bypasses domain-specific feature engineering, it remains intrinsically generalizable to other continuous spin systems.
Capturing Unseen Spatial Heat Extremes Through Dependence-Aware Generative Modeling
National University of Singapore（新加坡国立大学）；Southern University of Science and Technology（南方科技大学）；Eastern Institute of Technology（东方理工高等研究院）；Stanford University（斯坦福大学）
Learning Neural Generative Dynamics for Molecular Conformation Generation
Mila - Québec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Peking University（北京大学）；Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；HEC Montréal（蒙特利尔高等商学院）
Non-equilibrium active noise enhances generative memory in diffusion models
Department of Chemistry, University of Chicago, Chicago, IL, 60637（化学系，芝加哥大学，芝加哥，IL，60637）；The James Franck Institute, University of Chicago, Chicago, IL, 60637（弗朗克研究所，芝加哥大学，芝加哥，IL，60637）；Department of Physics, University of Chicago, Chicago, IL, 60637（物理系，芝加哥大学，芝加哥，IL，60637）
Privacy Evaluation of Generative Models for Trajectory Generation
School of Electrical and Computer Engineering, National Technical University of Athens（电气与计算机工程学院，国家技术大学雅典）；Institute of Information Science and Technologies, National Research Council (CNR)（信息科学与技术研究所，国家研究委员会（CNR））；Institute of Informatics and Teletematics, National Research Council (CNR)（信息学与电信研究所，国家研究委员会（CNR））
Montreal Institute for Learning Algorithms, Université de Montréal（蒙特利尔学习算法研究所，蒙特利尔大学）；The Hong Kong Polytechnic University（香港理工大学）；The Hong Kong University of Science and Technology（香港科技大学）；IVADO
Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks
Department of Physics, University of Genova（基因瓦大学物理系）；Department of Materials Science, University of Milano-Bicocca（米兰-比科卡大学材料科学系）；Institut Lumière Matière, UMR5306 Université Lyon 1—CNRS（光与物质研究所，里昂1大学-CNRS）
Generative Modeling of Quantum Distribution with Functional Flow Matching
Graduate School of Data Science, Seoul National University, Seoul, Korea（首尔国立大学数据科学研究生院）；Department of Statistics and Data Science, Yonsei University, Seoul, Korea（延世大学统计与数据科学系）；Department of Applied Statistics, Yonsei University, Seoul, Korea（延世大学应用统计系）；Google Research, Mountain View, California, United States（谷歌研究）
Applications of Generative Adversarial Networks in Neuroimaging and Clinical Neuroscience
University of Pennsylvania（宾夕法尼亚大学）；Center for AI and Data Science for Integrated Diagnostics（综合诊断人工智能与数据科学中心）；Center for Biomedical Image Computing and Analytics（生物医学图像计算与分析中心）
Polyformer: a generative framework for thermodynamic modeling of polymeric molecules
PsiDagger；Department of Physics and Astronomy, University of Pittsburgh（物理与天文学系，匹兹堡大学）；Department of Chemistry and The PULSE Institute, Stanford University（化学系和PULSE研究所，斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Latent Thermodynamic Flows: Unified Representation Learning and Generative Modeling of Temperature-Dependent Behaviors from Limited Data
Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA（物理科学与技术研究所，马里兰大学，College Park, MD）；Institute for Health Computing, University of Maryland, Bethesda, MD, 20852, USA（健康计算研究所，马里兰大学，Bethesda, MD）；Department of Physics（物理系）；Department of Chemistry and Biochemistry（化学与生物化学系）
Stochastic Thermodynamics for Autoregressive Generative Models: A Non-Markovian Perspective
The University of Tokyo（东京大学）；Quantum-Phase Electronics Center (QPEC), The University of Tokyo（量子相位电子中心（QPEC），东京大学）；Inamori Research Institute for Science (InaRIS)（稻盛科学研究所（InaRIS)）
Stochastic Thermodynamics of Score Matching in Diffusion Models
Flatiron Institute, Simons Foundation（平顿研究所，西蒙斯基金会）；School of Physics, Peking University（北京大学物理学院）；Collaborative Innovation Center of Quantum Matter, Peking University（北京大学量子物质协同创新中心）；Frontiers Science Center for Nano-optoelectronics, Peking University（北京大学纳米光电前沿科学中心）
