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. Lifting PCA in the Wasserstein Space

    Oct 21, 2026Jérémie Bigot, Clément BonetPrincipal Component AnalysisOptimal Transport

    Institut de Mathématiques de Bordeaux, Université de Bordeaux, CNRS (UMR 5251) · CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, CNRS (UMR 7641)

  2. A Principled Optimal Transport Framework for Frame Selection in Long Video Understanding

    Oct 20, 2026Ziwei Zhao, Yuhang LiuVideo Frame SelectionQuery-Aware Video Frame Selection

    Yizhun Medical AI Co., Ltd, Beijing, China

  3. CAVA: Complementary-Label-Aware Data Valuation

    Oct 19, 2026Tan-Ha Mai, Hsuan-Tien Lin, Vu NguyenData ValuationLearning with Noisy Labels

    National Taiwan University · Amazon

  4. Dynamic Neural Optimal Transport for Subset Alignment

    Oct 16, 2026Austin J. Brockmeier, Bilal RiazOptimal Transport

    Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, 19711 · Department of Computer and Information Sciences, University of Delaware, Newark, DE, 19711

  5. Vertical Sliced Wasserstein Distances for Meta-Measures

    Oct 14, 2026Elaheh Akbari, Ahmadreza Moradipari, Kyungtae Han +4Wasserstein DistanceOptimal Transport

    College of Connected Computing, Vanderbilt University · Toyota Motor North America, InfoTech Labs · Department of Computer Science, University of California, Davis +2

  6. Quantifying Annotation Agreement in Object Detection with Optimal Transport

    Oct 14, 2026Kirill Prokhorov, Alexandr A. KalininInter-Rater ReliabilityObject Detection

    Openface.io, Vilnius, Lithuania · Broad Institute of MIT and Harvard, Cambridge, MA, USA

  7. Scaling Online Optimal Transport Minibatches for Flow Matching

    Oct 13, 2026Peter Chen, Sergey LevineFlow MatchingFlow-Based Generative Modeling

    University of California, Berkeley

  8. Unbalanced W-Flow: Unbalanced Wasserstein Drifting under Finite-Batch Marginal Fluctuations

    Oct 13, 2026Jongwook Jeon, Mingue Park, Jiwon Choi +3One-Step Generative ModelingFlow-Based Generative Modeling

    Yonsei University · KAIST

  9. SWORD: Scene-Grounded Wasserstein Object-Relation Distance for 3D Scene Graph Prediction

    Oct 13, 2026U-Chae Jun, Jaeeun Ko, Yoonhyuk Choi +13D SGGWasserstein Distance

    Sookmyung Women’s University, Seoul, South Korea

  10. Guidance Without Labels: Flow Matching from Coupled Gaussian Mixtures

    Oct 12, 2026Stanislas Ducotterd, Bassam El Rawas, Michael UnserFlow MatchingFlow-Based Generative Modeling

    Biomedical Imaging Group, EPFL Lausanne, Switzerland

  11. OT-FlowRec: Optimal Transport-Guided Multi-Bridge Flow for Multimodal Sequential Recommendation

    Oct 12, 2026Miao SunRecommender SystemsMultimodal Recommendation

    Nanjing University of Science and Technology School of Computer Science and Engineering

  12. Minimum Volume Optimal Transport for Multivariate Conformal Prediction

    Oct 10, 2026Chuchen Zhang, Haojie Ren, Zhaojun Wang +2Conformal PredictionSet Prediction

    School of Statistics and Data Science, Nankai University · School of Mathematical Sciences, Shanghai Jiao Tong University · School of Management, Fudan University

  13. Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

    Oct 10, 2026Ali Khodabandeh Yalabadi, Azim Dehghani Amirabad, Artem Moskalev +4Optimal TransportLabel Shift

    Johnson & Johnson Innovative Medicine · Independent Researcher

  14. Some remarks on the connection between generative diffusion and optimal transport

    Oct 9, 2026Giulio Biroli, Marc MézardDiffusion ModelsGenerative Modeling

    Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France · Department of Computing Sciences, Bocconi University, Milano, Italy

  15. Representation Alignment from a Few Paired Data via Distilled Optimal Transport

    Oct 8, 2026Julien Kordes, Reuben DorentCross-Modal AlignmentCross-Modal Representation Learning

    Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hôpital de la Pitié Salpêtrière, 75013 Paris, France

  16. Barron Optimal Transport I: Generative Modeling

    Oct 7, 2026Evan Dogariu, Joan BrunaOptimal TransportGenerative Modeling

    Courant Institute School of Mathematics, Computing, and Data Science New York University

  17. Multi-Agent Coordination via Support-Preserving Distillation

    Oct 7, 2026Sangmin Lee, Youngju Na, Chanmi Lee +1Multi-Agent CoordinationOffline MARL

    School of Computing, KAIST

  18. Trust-Region Optimization for Smooth Potential-Interaction Energies in Wasserstein Space

    Oct 6, 2026You Wan, Ting Gao, Jinqiao DuanTrust-Region OptimizationSecond-Order Optimization

    School of Mathematics, Nanjing University, Nanjing, 210093, China · School of Sciences, Great Bay University, Dongguan 523000, China · Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems, Great Bay University, Dongguan 523000, China +3

  19. A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs

    Oct 6, 2026Geuntaek Seo, Cheolhyeong Kim, Hwijae Son +1Neural PDE SolversPDE Solving

    Department of Mathematics, Pohang University of Science and Technology · Samsung Electronics · Department of Mathematics, Konkuk University

  20. Conditional Flow Matching for Transport Between Markov Processes

    Oct 5, 2026Syamantak Kumar, Dheeraj Nagaraj, Saptarshi Roy +1Conditional Flow MatchingDomain Adaptation

    The University of Texas at Austin, Department of Computer Science · Google Deepmind · Mohamed bin Zayed University of Artificial Intelligence, CMS Division +1

  21. Constant-Curvature Sliced Gromov-Wasserstein for Heterogeneous Cross-Curvature Alignment

    Oct 5, 2026Shanglin Li, Wenjing Lu, Muyang Li +2Distribution MatchingGeometric Representation Learning

    BIFOLD, Germany · Technical University of Berlin, Germany · RIKEN AIP, Japan +4

  22. Beyond Transport Cost: Routing Differences between Flow Matching and Optimal Transport

    Oct 5, 2026Eungyeol Han, Jong-Seok LeeFlow MatchingFlow-Based Generative Modeling

    School of Integrated Technology, Yonsei University

  23. What Does Fréchet Distance Measure? A Directional Decomposition

    Oct 4, 2026Yunghee Lee, Jaeyeon KimImage Generation EvaluationOptimal Transport

    Agency for Defense Development, South Korea · Harvard University

  24. Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs

    Oct 4, 2026Mikhail Persiianov, Alexander KorotinLatent Dynamics ModelingOptimal Transport

    Applied AI Institute Moscow, Russia

  25. GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport

    Oct 3, 2026Yifan Xu, Shiqian MaOptimal TransportGPU Acceleration

    Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, TX, USA · Data Science and AI Institute, and Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

  26. TacOT: Learning Contact-Rich Dexterous Manipulation from Human Demonstrations via Tactile-Guided Optimal Transport

    Oct 3, 2026Xingting Li, Yifan Han, Zijian Lin +4Human-to-Robot Motion ImitationContact-Rich Robotic Manipulation

    Shenzhen Ubiquitous Data Enabling Key Lab, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China. · School of Artificial Intelligence, Shanghai Jiao Tong University, Shanghai 200030, China. · Xspark AI, Shenzhen, China. +1

  27. Adaptive Bregman Alternating Projections for Feasible Gromov-Wasserstein Learning

    Oct 3, 2026Aoran Zhang, César A. UribeOptimal Transport

    Department of Electrical and Computer Engineering, Rice University

  28. Exact Optimal Transport by Matching

    Oct 2, 2026Dmitry KamenetskyOptimal TransportCombinatorial Optimization

  29. Light Entropic Optimal Transport on Riemannian Manifolds

    Oct 2, 2026Xavier Aramayo-Carrasco, Petr Mokrov, Alexander KorotinOptimal Transport

    Applied AI Institute, Moscow, Russia · Applied AI Institute AXXX, Moscow, Russia

  30. Tangent Schrödinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities

    Oct 2, 2026Jowaria Khan, Elizabeth Bondi-KellySchrödinger BridgesOptimal Transport

    University of Michigan