The dynamic Schrödinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient iterative solvers. Recent works have demonstrated state-of-the-art results (eg. in modelling single-cell embryo RNA sequences or sampling from complex posteriors) but are limited to learning bridges with only initial and terminal constraints. Our work extends this paradigm by proposing the Iterative Smoothing Bridge (ISB). We integrate Bayesian filtering and optimal control into learning the diffusion process, enabling the generation of constrained stochastic processes governed by sparse observations at intermediate stages and terminal constraints. We assess the effectiveness of our method on synthetic and real-world data generation tasks and we show that the ISB generalises well to high-dimensional data, is computationally efficient, and provides accurate estimates of the marginals at intermediate and terminal times.
Conditional Sampling via Wasserstein Autoencoders and Triangular Transport
Department of Aeronautics & Astronautics, University of Washington, Seattle（华盛顿大学西雅图分校航空与航天系）；Department of Applied Mathematics, University of Washington, Seattle（华盛顿大学西雅图分校应用数学系）；Department of Mathematics, University of Washington, Seattle（华盛顿大学西雅图分校数学系）
Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier maps
CalTech（加州理工学院）；Center for Data Science, New York University（纽约大学数据科学中心）；Massachusets Institute of Technology（麻省理工学院）；Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）
Optimal Transport for Conditional Domain Matching and Label Shift
Criteo AI Lab（Criteo人工智能实验室）；Ecole Polytechnique（巴黎综合理工学院）；INSA de Rouen Normandie（鲁昂国立应用科学学院）；Université Technologique de Compiègne（贡比涅技术大学）；Université de Rouen Normandie（鲁昂诺曼底大学）；Université de Bretagne Sud（南布列塔尼大学）
A generative flow for conditional sampling via optimal transport
University of the Philippines Diliman（菲律宾大学迪里曼分校）；California Institute of Technology（加州理工学院）；Columbia University（哥伦比亚大学）；Baruch College（巴鲁克学院）；University of Edinburgh（爱丁堡大学）；Georgia Institute of Technology（佐治亚理工学院）；Grinnell College（格林内尔学院）；University of Michigan（密歇根大学）；Yale University（耶鲁大学）
Department of Management, Economics and Industrial Engineering, Politecnico di Milano（米兰理工大学管理、经济与工业工程系）；RFF-CMCC European Institute on Economics and the Environment (EIEE)（RFF-CMCC欧洲经济与环境研究所）；Euro-Mediterranean Center on Climate Change (CMCC)（欧洲-地中海气候变化中心）；Bocconi University, Department of Decision Sciences（博科尼大学决策科学系）；MIT, Department of Nuclear Science and Engineering（麻省理工学院核科学与工程系）
Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm
Department of Mathematics, Imperial College London, UK；Centre de Recherche Inria Bordeaux Sud-Ouest, Talence, France；Department of Signal Theory \& Communications, Universidad Carlos III de Madrid, Spain
Spherical Brownian Bridge Diffusion Models for Conditional Cortical Thickness Forecasting
Lab for AI in Medical Imaging, Technical University of Munich, Munich, Germany（人工智能医学影像实验室，慕尼黑技术大学，慕尼黑，德国）；Munich Center for Machine Learning, Munich, Germany（慕尼黑机器学习中心，慕尼黑，德国）
Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schrödinger Samplers
NVIDIA Corporation（NVIDIA公司）；University of Oxford（牛津大学）；Donders Institute for Brain, Cognition, and Behaviour（大脑与行为研究所）；AITHYRA, Research Institute for Biomedical AI（生物医学人工智能研究所）
From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps
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）；Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University（香港理工大学数据科学与人工智能学院）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
Schrödinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation
National Biomedical Imaging Center, College of Future Technology, Peking University（北京大学未来技术学院国家生物医学成像中心）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学国家重点实验室）
Skolkovo Institute of Science and Technology（斯克尔克沃科学与技术学院）；Yandex Research（Yandex研究）；HSE University（俄罗斯高等经济大学）；Artificial Intelligence Research Institute（人工智能研究 institute）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Nanjing University of Science and Technology（南京理工大学）；PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education（PCA实验室，教育部高维信息智能感知与系统重点实验室）；School of Computer Science and Engineering（计算机科学与工程学院）
