Optimal Transport

Follow this topic Ask about this topic

Optimal transport studies how probability mass can be moved between distributions at minimum cost, giving a geometric way to compare data even when samples do not correspond one-to-one. Wasserstein distances and transport maps describe this geometry, while Gromov–Wasserstein methods compare relational structure when data live in different spaces. Practical approaches include entropic regularization with Sinkhorn algorithms, sliced and low-rank approximations, and neural transport maps used in generative modeling, domain adaptation, and trajectory inference. A central challenge is balancing computational and statistical scalability with faithful transport, especially when choosing regularization or relaxing exact mass constraints.

Latest papers

289 papers48 papers in the last four weeks, up 17% on the four weeks before. 0.3% of all new papers.

Generative Modeling by Value-Driven Transport
May 21, 2026Pablo Moreno-Muñoz, Adrian Müller, Gergely NeuValue Function Estimation Stochastic Optimal Control
Universitat Pompeu Fabra · Barcelona, Spain · ETH Zürich +2
On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures
May 20, 2026Likun Lin, Zhongjian Wang, Jack Xin +1One-Step Generative Modeling Optimal Transport
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, P.R. China. · Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371. · Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA. +1
UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems
May 20, 2026Donggyu Lee, Taekyung Lee, Jaewoong ChoiImage Reconstruction Optimal Transport
Department of Mathematical Sciences, Seoul National University · IPAI (Interdisciplinary Program in Artificial Intelligence, Seoul National University) · Sungkyunkwan University
Learning fMRI activations dictionaries across individual geometries via optimal transport
May 20, 2026Sonia Mazelet, Rémi Flamary, Bertrand ThirionLearning to Optimize Geometric Representation Learning
CMAP, Ecole Polytechnique · Palaiseau, France · Mind, Inria-Saclay
Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimation
May 19, 2026Peter Matthew Jacobs, Jeff M. PhillipsRandomized Sketching Approximation Algorithms
Department of Statistics University of Wisconsin-Madison Madison, WI 53706 · Kahlert School of Computing University of Utah Salt Lake City, UT 84101
Take It or Leave It: Intent-Controlled Partial Optimal Transport
May 19, 2026Salil Parth Tripathi, Bertrand Chapron, Fabrice Collard +2Inverse Optimal Transport Optimal Transport
OceanDataLab · Ifremer · Université Bretagne Sud +1
PACE: Geometry-Aware Bridge Transport for Single-Cell Trajectory Inference
May 18, 2026Chenglei Yu, Chuanrui Wang, Bangyan Liao +1Trajectory Inference Single-Cell Transcriptomics
Zhejiang University · Department of Artificial Intelligence, School of Engineering, Westlake University
Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons
May 18, 2026Pierre Houédry, Iskander Legheraba, Léo Buecher +1Sinkhorn Divergence Kernel Methods
INRIA Rennes · LPHI, UMR 5294, CNRS, INSERM · IRISA, UMR 6074, CNRS
A Distribution Matching Approach to Neural Piano Transcription with Optimal Transport
May 17, 2026Weixing Wei, Raynaldi Lalang, Dichucheng Li +1Convolutional RNNs Automatic Music Transcription
Graduate School of Informatics, Kyoto University, Japan · Graduate School of Engineering, Kyoto University, Japan · Independent Researcher, Hong Kong, China
Scalable Bi-causal Optimal Transport via KL Relaxation and Policy Gradients
May 17, 2026Haoyang Cao, Jesse Hoekstra, Renyuan Xu +2Stochastic Optimization Optimal Transport
Department of Applied Mathematics and Statistics, Data Science and AI Institute, and Mathematical Institute for Data Science, Johns Hopkins University. · Department of Statistics, Oxford-Man Institute of Quantitative Finance, and Nuffield College, University of Oxford. · Management Science & Engineering Department, Stanford University. +2
Multiscale Supervised Unbalanced Optimal Transport Flow Matching
May 15, 2026Qiangwei Peng, Lezhi Chen, Peijie ZhouFlow Matching Single-Cell Transcriptomics
College of Electrical Engineering Sichuan University, Sichuan, China · AI for Science Institute, Beijing, China
Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
May 14, 2026Ao Xu, Tieru WuOptimal Transport Wasserstein Distance
School of Artificial Intelligence Jilin University No. 2699, Qianjin Street, Chaoyang District Changchun 130012, China · Zhongguancun Academy Daniufang 2nd Ring Road, Haidian District2026 Beijing 100094, China · School of Artificial IntelligenceMay Jilin University No. 2699, Qianjin Street, Chaoyang District14 Changchun 130012, China
Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein
May 13, 2026Ashkan Shahbazi, Xinran Liu, Ping He +1Non-Rigid Shape Correspondence Optimal Transport
Department of Computer Science, College of Connected Computing, Vanderbilt University · Department of Electrical and Computer Engineering, Vanderbilt University
Path-independent Flow Matching for Multi-parameter Generative Dynamics
May 13, 2026Francisco Téllez, AmirHossein Zamani, Philippe Martin +5Flow Matching Flow Map Learning
Université de Montréal, Mila · Concordia University, Mila · Concordia University +2
Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems
May 13, 2026Dengfei Zeng, Lijian Jiang, Shuyu Sun +1Dynamical Systems Simulation-Based Inference
School of Mathematical Sciences, Tongji University, Shanghai, 200092 China · School of Mathematical Sciences, Tongji University, Shanghai, 200092 China, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092 China
Pareto-Guided Optimal Transport for Multi-Reward Alignment
May 13, 2026Ying Ba, Tianyu Zhang, Mohan Zhou +5Diffusion Model Alignment Reward Hacking
Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · Beijing Key Laboratory of Research on Large Models and Intelligent Governance · Engineering Research Center of Next-Generation Intelligent Search and Recommendation, MOE 4Tomorrow Advancing Life +2
Expected Batch Optimal Transport Plans and Consequences for Flow Matching
May 12, 2026Samuel Boïté, Julie Delon, Kimia NadjahiFlow Matching Optimal Transport
1DMA, ENS Paris · Université Paris Cité · DI, ENS Paris, CNRS
Fused Gromov-Wasserstein Distance with Feature Selection
May 12, 2026Harlin Lee, Ying Yu, Mingxin Li +1Feature Selection Optimal Transport
School of Data Science and Society · University of North Carolina at Chapel Hill · Division of Computational Social Science +5
QDSB: Quantized Diffusion Schrödinger Bridges
May 12, 2026Tobias Fuchs, Florian Kalinke, Nadja KleinSchrödinger Bridges Diffusion Model Acceleration
Karlsruhe Institute of Technology, Karlsruhe, Germany
OTT-Vid: Optimal Transport Temporal Token Compression for Video Large Language Models
May 12, 2026Minseok Kang, Minhyeok Lee, Jungho Lee +6Efficient VLM Inference Video-Language Models
Yonsei University · LG Electronics · KIST
Optimal and Scalable MAPF via Multi-Marginal Optimal Transport and Schrödinger Bridges
May 11, 2026Usman A. Khan, Joseph W. DurhamMulti-Agent System Optimization Multi-Agent Path Finding
Amazon Robotics, Boston, MA, USA · Boston College, Chestnut Hill, MA, USA · UAK holds concurrent appointments as an Amazon Scholar with Amazon Robotics and as a Professor of Computer Science at Boston College
Implicit Neural Optimal Transport via Fixed-Point Optimization
May 11, 2026Yesom Park, Eric Gelphman, Stanley Osher +1Optimal Transport
Department of Mathematics, University of California, Los Angeles · Department of Applied Mathematics and Statistics, Colorado School of Mines
The Observable Wasserstein Distance
May 11, 2026Edivaldo Lopes dos Santos, Leandro Vicente Mauri, Washington Mio +1Sliced Wasserstein Distance Optimal Transport
1Departamento de Matem´atica, Universidade Federal de S˜ao Carlos, Brazil · Department of Mathematics, Florida State University, USA
Geometrically Constrained Stenosis Editing in Coronary Angiography via Entropic Optimal Transport
May 9, 2026Jialin Li, Zhuo Zhang, Yue Cao +4Synthetic Data Augmentation Medical Imaging
School of Electrical and Information Engineering, Tianjin University, Tianjin, China.
cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport
May 9, 2026Yixuan QiuGPU Kernel Optimization Quasi-Newton Methods
School of Statistics and Data Science & Institute of Big Data Research Shanghai University of Finance and Economics
Sliced Inner Product Gromov-Wasserstein Distances
May 8, 2026Xiaoyun Gong, Gabriel Rioux, Ziv GoldfeldOptimal Transport Wasserstein Distance
Quantile-Coupled Flow Matching for Distributional Reinforcement Learning
May 8, 2026Michael Groom, Victor-Alexandru Darvariu, Lars Kunze +2Distributional RL Conditional Flow Matching
Oxford Robotics Institute, University of Oxford, Oxford, United Kingdom · Bristol Robotics Laboratory, University of the West of England, Bristol, United Kingdom · Dyson Institute of Engineering & Technology, Malmesbury, United Kingdom
Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
May 8, 2026Medha Agarwal, Alex LuedtkeCausal Effect Estimation Sinkhorn Divergence
Department of Statistics, University of Washington, Seattle, WA, USA · Department of Health Care Policy, Harvard Medical School, Boston, MA, USA
Generalized Wasserstein Flow Matching: Nested Couplings for Point Cloud Generation
May 8, 2026Moritz Piening, Richard Duong, Gabriele SteidlFlow Matching Generative Modeling
Institut für Mathematik, Technische Universität Berlin, Germany
Distributional Process Reward Models: Calibrated Prediction of Future Rewards via Conditional Optimal Transport
May 7, 2026Rachel Ma, Dylan Hadfield-Menell, Kristjan GreenewaldProcess Reward Models Inference-Time Scaling
MIT CSAIL · MIT-IBM Watson AI Lab · IBM Research

May 21, 2026J/K move · Enter open · S save

Generative Modeling by Value-Driven Transport

Pablo Moreno-Muñoz, Adrian Müller, Gergely Neu

Universitat Pompeu Fabra · Barcelona, Spain · ETH Zürich+2

Value Function Estimation Stochastic Optimal Control Generative Modeling Optimal Transport

Open paper AskPDF arXiv

We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables correspond to the optimal value function of the control problem, which directly encodes the optimal control policy. Exploiting this LP formulation, we develop an efficient simulation-free primal-dual algorithm for computing approximately optimal value functions and the associated value-driven transport (VDT) policies which approximate the true optimal policy. We show that well-trained VDT policies enjoy numerous favorable properties in comparison with other state-of-the-art methods based on flows, diffusions, or Schrödinger bridges: they lead to straight transport paths which can be simulated quickly and robustly, and can be enhanced in all the same ways as diffusion and flow-based models (e.g., conditional generation, classifier-free guidance, unpaired data-to-data translation are all easy to incorporate). We evaluate our methodology in a range of experiments, with results that indicate strong performance and good potential for scalability.