An Explicit Surrogate for Gaussian Mixture Flow Matching with Wasserstein Gap Bounds
Université Paris-Saclay, Inria, CIAMS（巴黎-萨克雷大学, 法国国家信息与自动化研究所, CIAMS）；Department of Electrical Engineering and Computer Science, University of Quebec in Trois-Rivieres (UQTR)（魁北克大学三河城分校电气工程与计算机科学系）
We study training-free flow matching between two Gaussian mixture models (GMMs) using explicit velocity fields that transport one mixture into the other over time. Our baseline approach constructs component-wise Gaussian paths with affine velocity fields satisfying the continuity equation, which yields to a closed-form surrogate for the pairwise kinetic transport cost. In contrast to the exact Gaussian Wasserstein cost, which relies on matrix square-root computations, the surrogate admits a simple analytic expression derived from the kinetic energy of the induced flow. We then analyze how closely this surrogate approximates the exact cost. We prove second-order agreement in a local commuting regime and derive an explicit cubic error bound in the local commuting regime. To handle nonlocal regimes, we introduce a path-splitting strategy that localizes the covariance evolution and enables piecewise application of the bound. We finally compare the surrogate with an exact construction based on the Gaussian Wasserstein geodesic and summarize the results in a practical regime map showing when the surrogate is accurate and the exact method is preferable.
Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems
University of Paderborn（帕德博恩大学）；Lamarr Institute for Machine Learning and Artificial Intelligence（拉马尔机器学习和人工智能研究所）；University of Michigan（密歇根大学）；Technical University of Munich（慕尼黑工业大学）；Technical University of Dortmund（多特蒙德工业大学）
Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
University of Macau（澳门大学）；Great Bay University（大湾区大学）；Great Bay Institute for Advanced Study（大湾区高等研究院）；University of Science and Technology of China（中国科学技术大学）
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
Department of Mathematics and Statistics（数学与统计学系）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Division of Applied Mathematics（应用数学系）；Brown University（布朗大学）
Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space
ENS Paris-Saclay（巴黎萨克雷高等师范学校）；CNRS（法国国家科学研究中心）；Centre Borelli（博雷利中心）；Université de Paris（巴黎大学）；MAP5（数学及其应用实验室）；Institut Universitaire de France（法国大学研究院）
FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set
H. Milton Stewart School of Industrial and Systems Engineering（H. Milton Stewart工业与系统工程学院）；Georgia Institute of Technology（佐治亚理工学院）；Department of Electrical Engineering（电气工程系）；University of Chile（智利大学）
Gauss--Hermite Quadrature for Gaussian-Mixture Entropy with an Action-Space Hermite Surrogate
Extreme Materials Research Center, Korea Institute of Science and Technology（韩国科学技术研究院极端材料研究中心）；Climate and Environmental Research Institute, Korea Institute of Science and Technology（韩国科学技术研究院气候与环境研究所）；Division of AI-Robotics, KIST Campus, University of Science and Technology（科学技术大学KIST校区AI机器人系）
SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime
School of Mathematical Sciences, Beijing University of Posts and Telecommunications（北京邮电大学数学科学学院）；Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education（数学信息网络重点实验室（北京邮电大学））；Institute of Statistics and Big Data, Renmin University of China（中国人民大学统计与大数据研究院）
Reservoir History Matching of the Norne field with generative exotic priors and a coupled Mixture of Experts -- Physics Informed Neural Operator Forward Model
Projected Wasserstein-Fisher-Rao Flows for Hawkes Background-Intensity Estimation
Facultad de Ciencias, Universidad Autónoma de México（墨西哥国立自治大学理学院）；Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C.（数学研究中心概率与统计系）
Quantile-Coupled Flow Matching for Distributional Reinforcement Learning
Oxford Robotics Institute, University of Oxford（牛津大学机器人研究所）；Bristol Robotics Laboratory, University of the West of England（布里斯托尔机器人实验室，西英格兰大学）；Dyson Institute of Engineering & Technology（戴森工程与技术研究院）
Variational inference via Wasserstein gradient flows
DGA（法国武器装备总署）；INRIA（法国国家信息与自动化研究所）；Ecole Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）；MIT（麻省理工学院）；MINES Paris PSL（巴黎高等矿业学院（巴黎文理研究大学））；Université de la Nouvelle-Calédonie（新喀里多尼亚大学）
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
College of Computing and Data Science, NTU, Singapore（新加坡国立大学计算与数据科学学院）；LAAS-CNRS, Toulouse, France（法国图卢兹CNRS-Laas研究所）；Toulouse School of Economics（图卢兹经济学院）
WGFormer: An SE(3)-Transformer Driven by Wasserstein Gradient Flows for Molecular Ground-State Conformation Prediction
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学首都人工智能学院）；Beijing Key Laboratory of Research on Large Models（北京大型模型研究关键实验室）；Engineering Research Center of Next-Generation Intelligent Search（下一代智能搜索工程研究中心）
Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design
School of Ocean and Civil Engineering, Shanghai Jiao Tong University（上海交通大学海洋与土木工程学院）；Eastern Institute of Technology（东方理工学院）；TenFong Technology Co., Ltd.（十方科技有限公司）；IM Motors Technology Co., Ltd.（集度汽车科技有限公司）
