Booth School of Business, University of Chicago（芝加哥大学布斯商学院）；Department of Statistics, University of Michigan（密歇根大学统计系）；Department of Mathematics, University of Maryland, College Park（马里兰大学帕克分校数学系）
Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods often exhibit greater training stability and have achieved strong empirical performance in high-dimensional settings where data concentrate near a low-dimensional manifold, such as text-to-image synthesis, video generation, and molecular structure generation. Despite this success, existing theoretical analyses of flow matching assume target distributions with smooth, full-dimensional densities, leaving its effectiveness in manifold-supported settings largely unexplained. To this end, we theoretically analyze flow matching with linear interpolation when the target distribution is supported on a smooth manifold. We establish a non-asymptotic convergence guarantee for the learned velocity field, and then propagate this estimation error through the ODE to obtain statistical consistency of the implicit density estimator induced by the flow-matching objective. The resulting convergence rate is near minimax-optimal, depends only on the intrinsic dimension, and reflects the smoothness of both the manifold and the target distribution. Together, these results provide a principled explanation for how flow matching adapts to intrinsic data geometry and circumvents the curse of dimensionality.
University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Carnegie Mellon University（卡内基梅隆大学）；University of Maryland College Park（马里兰大学学院公园分校）；Korea University（高丽大学）；IIIT Delhi（德里印度理工学院）；Electronics and Telecommunications Research Institute（电子与电信研究院）
KTH Royal Institute of Technology（皇家理工学院）；University of Amsterdam（阿姆斯特丹大学）；University of Cambridge（剑桥大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Delft University of Technology（代尔夫特理工大学）
Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
CMU-Pitt Program in Computational Biology（CMU-匹兹堡计算生物学项目）；Dept. of Computational & Systems Biology University of Pittsburgh（计算与系统生物学系匹兹堡大学）；Machine Learning Department Dept. of Mathematical Sciences Carnegie Mellon University（机器学习系数学科学系卡内基梅隆大学）；Courant Institute, New York University（纽约大学Courant研究所）；Machine Learning Lab Capital Fund Management（机器学习实验室资本基金管理）
Adaptive Bandit Algorithms for Contextual Matching Markets
Center for Statistical Science, School of Mathematical Sciences, Peking University（北京大学数学科学学院统计科学中心）；INRIA, FairPlay Joint Team（INRIA公平玩联合团队）；Criteo AI lab, FairPlay Joint Team（Criteo AI实验室，公平玩联合团队）；Technion - Israel Institute of Technology（技术学院-以色列理工学院）
