Optimal Transport

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Overview

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

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

  1. On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport plans

    Feb 18, 2026Titouan VayerOptimal TransportWasserstein Distance

    COMPACT · Inria, Rennes, France.

  2. Convergence Rates for Distribution Matching with Sliced Optimal Transport

    Feb 11, 2026Gauthier Thurin, Claire Boyer, Kimia NadjahiDistribution MatchingSliced Wasserstein Distance

    ENS-PSL · CNRS, ENS Paris, France · LMO, IUF, CELESTE +2

  3. Relative Wasserstein Angle and the Problem of the W2W_2-Nearest Gaussian Distribution

    Jan 29, 2026Binshuai Wang, Peng WeiOptimal TransportWasserstein Distance

    Department of Computer Science, George Washington University, Washington D.C., USA · MAE, George Washington University, Washington D.C., USA

  4. Contextual Distributionally Robust Optimization with Causal and Continuous Structure

    Jan 16, 2026Fenglin Zhang, Jie WangStochastic OptimizationDistributionally Robust Optimization

    School of Artificial Intelligence The Chinese University of Hong Kong, Shenzhen Shenzhen, 518172, China · School of Artificial Intelligence, School of Data Science The Chinese University of Hong Kong, Shenzhen Shenzhen, 518172, China

  5. Optimal Transportation and Alignment Between Gaussian Measures

    Dec 3, 2025Sanjit Dandapanthula, Aleksandr Podkopaev, Shiva Prasad Kasiviswanathan +2Optimal Transport

    Carnegie Mellon University, Department of Statistics · Amazon Web Services · Amazon Web Services (AWS) LogAnalytics +2

  6. Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings

    Nov 19, 2025Eugene NdiayeUncertainty QuantificationConformal Prediction

    Apple

  7. DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment

    Oct 28, 2025Hao Wang, Licheng Pan, Yuan Lu +7Time Series ForecastingOptimal Transport

    Xiaohongshu Inc. · College of Control Science and Technology, Zhejiang University · College of Computer Science and Technology, Zhejiang University +4

  8. OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

    Sep 26, 2025Elaheh Akbari, Shansita Sharma, Ping He +5Point Cloud GenerationFlow-Based Generative Modeling

    Department of Computer Science, Vanderbilt University · Toyota InfoTech Labs · Department of Computer Science, University of California, Davis +1

  9. Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport

    Sep 2, 2025Samuel Boïté, Eloi Tanguy, Julie Delon +2Gaussian Mixture ModelsExpectation-Maximization

    Université Paris Cité, CNRS, MAP5, F-75006 Paris, France · Centre Borelli, CNRS and ENS Paris-Saclay, F-91190 Gif-sur-Yvette, France · CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris

  10. Learning from samples: inverse problems over measures

    May 11, 2025Francisco Andrade, Gabriel Peyré, Clarice PoonInverse Optimal TransportInverse Problems

    INRIA (PreMeDICaL & HeKA) · CNRS and ENS, PSL Universit´e · Mathematics Institute, University of Warwick

  11. Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterin

    Jan 30, 2025Fangyuan Xie, Jinghui Yuan, Feiping Nie +1Frank-Wolfe AlgorithmsGraph Clustering

    School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, P.R. China

  12. Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences

    Oct 2, 2024Ziyu Chen, Markos A. Katsoulakis, Benjamin J. ZhangFlow MatchingEquivariant Neural Networks

    Department of Mathematics and School of Data and Information Sciences, University of North Carolina at Chapel Hill · Department of Mathematics and Statistics, University of Massachusetts Amherst · Department of Mathematics, Rutgers University–New Brunswick

  13. Multi-view Optimal Transport for Multi-view Crowd Localization and Tracking

    Sep 3, 2024Kaiyi Zhang, Qi Zhang, Jixuan Chen +2Multi-Object TrackingOptimal Transport

    Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), China · Visual Computing Research Center, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China · Department of Computer Science, City University of Hong Kong, HK SAR, China

  14. Optimal Transport Aggregation for Distributed Mixture-of-Experts

    Dec 15, 2023Faïcel Chamroukhi, Nhat Thien PhamMixture-of-Experts ModelsOptimal Transport

    IRT SystemX, 91120 Palaiseau, France · Normandie Univ, UNICAEN, CNRS, LMNO, 14000 Caen, France

  15. Structured Approximations of Measures

    Oct 13, 2023Keaton Hamm, Varun KhuranaOptimal TransportWasserstein Distance

    DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF TEXAS AT ARLINGTON, ARLINGTON, TX · DIVISION OF DATA SCIENCE, THE UNIVERSITY OF TEXAS AT ARLINGTON, ARLINGTON, TX · DEPARTMENT OF APPLIED MATHEMATICS, BROWN UNIVERSITY, PROVIDENCE, RI 02906.

  16. Linearized Wasserstein dimensionality reduction with approximation guarantees

    Feb 14, 2023Alexander Cloninger, Keaton Hamm, Varun Khurana +1Dimensionality ReductionManifold Learning

    DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CALIFORNIA, SAN DIEGO, CA · HALICIOĦGLU DATA SCIENCE INSTITUTE, UNIVERSITY OF CALIFORNIA, SAN DIEGO, CA · DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TEXAS AT ARLINGTON, ARLINGTON, TX +1

  17. Deep Residual Networks Learn the Geodesic Curve in the Wasserstein Space

    Feb 18, 2021Kuo Gai, Shihua ZhangResidual LearningNeural Network Training Dynamics

    Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) Shanghai 200433, China · Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190, China · School of Mathematical Sciences2026 University of Chinese Academy of Sciences Beijing 100049, China