Optimal Transport

Ask about this topic

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

CardsList

291 papers50 papers in the last four weeks, up 22% on the four weeks before. 0.3% of all new papers.

  1. Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence

    Jun 15, 2026Peng Xu, Changbo Zhu, Young-Heon Kim +1Principal Component AnalysisStatistical Learning Theory

    Department of Statistics University of Illinois Urbana-Champaign · Department of ACMS University of Notre Dame · Department of Mathematics University of British Columbia +1

  2. Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport

    Jun 15, 2026Jin Zhang, Mingyang Zhao, Bing Liu +1Point Cloud RegistrationOptimal Transport

    LMIB & School of Mathematical Sciences, Beihang University, Beijing, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China +1

  3. Distribution Alignment for One-Shot Federated Learning via Optimal Transport

    Jun 15, 2026Daniele Berardini, Vito Paolo Pastore, Vittorio MurinoDistribution MatchingOptimal Transport

    AI for Good · AI for Good (AIGO), Italian Institute of Technology, Genoa, Italy · MaLGa-DIBRIS, University of Genoa, Genoa, Italy +1

  4. Generative Modeling on Metric Graphs via Neural Optimal Transport

    Jun 15, 2026Alessandro Micheli, Yueqi Cao, Anthea Monod +1Generative ModelingOptimal Transport

    Imperial College London London, UK · KTH Royal Institute of Technology Stockholm, Sweden · Statens Serum Institut Copenhagen, Denmark +1

  5. Learning Urban Access Costs from Origin-Destination Flows via Inverse Optimal Transport

    Jun 12, 2026Paula Joy B. Martinez, Sebastian Felipe R. BundocInverse Optimal TransportUrban Planning

  6. Geometric Domain Adaptation via Optimal Transport for Linear Regression in R^2

    Jun 12, 2026Brian Britos, Mathias BourelDomain AdaptationLinear Regression

    IESTA, Facultad de Ciencias Económicas y de Administración, Universidad de la República, Montevideo, Uruguay · IRL-2030, Instituto Franco-Uruguayo de Matemática e Interacciones (IFUMI)

  7. Layer-Resolved Optimal Transport for Hallucination Detection in NMT and Abstractive Summarization

    Jun 11, 2026Mariia Onyshchuk, Maksym-Vasyl Tarnavskyi, Marta SumykTransformer InterpretabilityHallucination Detection

    Faculty of Applied Sciences, Ukrainian Catholic University, Lviv, Ukraine.

  8. A Riemannian Approach to Low-Rank Optimal Transport

    Jun 10, 2026Pratik Jawanpuria, Bamdev MishraRiemannian OptimizationSecond-Order Optimization

    Centre for Machine Intelligence and Data Science, IIT Bombay · Microsoft India

  9. A Source Domain is All You Need: Source-Only Cross-OS Transfer Learning for APT Anomaly Detection via Semantic Alignment and Optimal Transport

    Jun 8, 2026Sidahmed Benabderrahmanea, Petko Valtchev, James Cheney +1Cross-Domain Transfer LearningOptimal Transport

    New York University, NYUAD, Division of Science, Computer Science Department. · University of Quebec in Montreal, Computer Science Department, Montreal. · University of Edinburgh, School of Informatics, Edinburgh.

  10. RadOT-Eval: Auditable Structured-Evidence Transport for Radiology Report Evaluation

    Jun 7, 2026Weixin Liu, Juming Xiong, Yang Li +5Radiology Report GenerationAutomated Evaluation

    Vanderbilt University, Nashville, TN, USA · Vanderbilt University Medical Center, Nashville, TN, USA · Virginia Tech, Blacksburg, VA, USA

  11. MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transport

    Jun 6, 2026Guangyu Meng, Mingzhe Li, Erin Wolf ChambersOptimal TransportTopological Data Analysis

    Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana, United States

  12. Conditional Random Ordered Transport Spaces

    Jun 6, 2026Lei Luo, Jian YangOptimal Transport

    PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education School of Computer Science and Engineering Nanjing University of Science and Technology Nanjing, China · PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education2026 School of Computer Science and Engineering Nanjing University of Science and Technology Nanjing, ChinaJun

  13. Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds

    Jun 6, 2026Kisung YouRiemannian GeometryOptimal Transport

    Department of Mathematics Baruch College

  14. A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

    Jun 5, 2026Munsik KimMinimax EstimationSpatiotemporal Forecasting

  15. Your GFlowNet Secretly Learns an Optimal Transport Plan

    Jun 4, 2026Ian Maksimov, Nikita Morozov, Denis Belomestny +1Generative Flow NetworksFlow-Based Generative Modeling

    1HSE University · 2Duisburg-Essen University

  16. Multimarginal flow matching with optimal transport potentials

    Jun 3, 2026Raghav Kansal, David Crair, Nghia Nguyen +2Flow MatchingFlow Map Learning

    Bexorg, Inc., New Haven, CT, USA.

  17. Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport

    Jun 3, 2026Lei Luo, Hongliang Zhang, Jian YangOptimal TransportWasserstein Distance

    PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China

  18. Optimal Transport Flow Matching by Design

    Jun 2, 2026Shimon Malnick, Matan Rusanovsky, Ohad Fried +1Flow MatchingOne-Step Generative Modeling

    1Tel Aviv University · 2Reichman University

  19. A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution

    Jun 1, 2026Yeganeh Marghi, Kelly Jin, Uygar SümbülOptimal Transport

    Allen Institute Seattle, WA, USA

  20. Network Learning with Semi-relaxed Gromov-Wasserstein

    Jun 1, 2026Charles Dufour, Ulysse Naepels, Leonardo V. SantoroGraph Structure LearningLatent Variable Models

    EPFL, Institute of Mathematics Lausanne, Switzerland

  21. Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation

    Jun 1, 2026Junhyoung Chung, Euijong Song, Won Hwa Kim +1Optimal Transport

    KRAFTON · Department of Statistics, Seoul National University, Seoul, South Korea · Graduate School of AI, POSTECH, Pohang, South Korea +3

  22. Generate in Reconstruction Space, Match in Semantic Space: Transport Geometry for One-Step Generation

    May 30, 2026Hugues Van Assel, Edward De Brouwer, Saeed Saremi +2One-Step Generative ModelingDistribution Matching

    Genentech

  23. CellBRIDGE: Learning Cellular Trajectories via Interaction-Aware Alignment

    May 28, 2026Silas Ruhrberg Estévez, Nicolas Huynh, Tennison Liu +4Single-Cell TranscriptomicsOptimal Transport

    DAMTP, University of Cambridge · Francis Crick Institute · University of Colorado Anschutz Medical Campus

  24. Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression

    May 27, 2026Tue M. Cao, Nguyen Do, My T. ThaiSparse AutoencodersMechanistic Interpretability

    Department of Computer and Information Science and Engineering, University of Florida

  25. Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models

    May 27, 2026Simon Queric, Cédric Vincent-Cuaz, Charles Bouveyron +1Model SelectionLatent Variable Models

    Universit´e Cˆote d’Azur, Inria, CNRS LJAD, Maasai Nice, France · EPFL Lausanne, Switzerland · Universit´e Cˆote d’Azur, Inria, CNRS CEPAM, Maasai Nice, France

  26. MST-Direct at Scale: Multivariate and Conditional Geostatistical Simulation via Sinkhorn Optimal Transport

    May 26, 2026Tcharlies Bachmann SchmitzOptimal Transport

    Data Science, PX.Center Joinville, Brasil

  27. Supervised Distributional Reduction via Optimal Transport and Dependence Maximization

    May 26, 2026Sai-Aakash Ramesh, Archit Sood, Andrew Corbett +1Kernel MethodsDimensionality Reduction

    digiLab, UK · University of Bristol, UK

  28. Learning Permutation from Structure Without Supervision

    May 25, 2026Ran Eisenberg, Ofir LindenbaumUnsupervised LearningJigsaw Puzzle Solving

    Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel. · Faculty of Engineering, Bar-Ilan

  29. Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions

    May 24, 2026Siddhartha Ganguly, George Rapakoulias, Panagiotis TsiotrasStochastic Optimal ControlSchrödinger Bridges

    S. Ganguly, G. Rapakoulias, and P. Tsiotras are with  Daniel Guggenheim School of Aerospace, Georgia Institute of Technology, ½ Atlanta, USA.

  30. AvAtar: Learning to Align via Active Optimal Transport

    May 23, 2026Qi Yu, Ruizhong Qiu, Zhichen Zeng +3Active LearningOptimal Transport

    University of Illinois Urbana-Champaign · University of Florida · 3Arizona State University