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

  1. One Knob to Rule Them All: A Unified Optimal Transport View of Cold-Start Active Learning

    Aug 4, 2026Ning Zhu, Xiaochuan Ma, Juntao Xu +4Active LearningTraining Data Selection

    Glasgow College, University of Electronic Science and Technology of China · School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China · School of Mathematical Sciences, University of Electronic Science and Technology of China

  2. Computational and Statistical Guarantees of the c-Rectified flow

    Aug 3, 2026Leda Wang, Zhehao Xu, Qiang Liu +1Rectified FlowOptimal Transport

    Department of Statistics and Data Science, Yale University · Department of Computer Science, University of Texas at Austin

  3. Beckmann Transport Models: From Autonomous Flows to One-Step Maps

    Aug 3, 2026Lee Cheuk-Kit, Florentin Coeurdoux, Yuyuan Chen +5Flow MatchingOne-Step Generative Modeling

    1Harvard University · 2Capital Fund Management · University of Pennsylvania +2

  4. Field Codes for Distributed Coupling Samplers and Certified Empirical Transport

    Jul 29, 2026Hung Mai, Hai Nguyen, Luong Doan +4Communication ComplexityOptimal Transport

    1B0Labs, N2TP Technology · 3Nanyang Technological University · 4Phenikaa University, Vietnam

  5. FPSGen: Flexible Point Cloud Scene Generation with BEV-Supported Transport Flows

    Jul 29, 2026Wenzhe He, Meng Wang, JiaWei Qian +3Point Cloud Completion3D Scene Generation

    College of Computer Science and Electronic Engineering, Hunan University, Hunan, China · College of Information Science and Engineering, Hunan Normal University, Hunan, China

  6. DrainSinkhorn: Safe Elimination for Batched Entropic Optimal Transport

    Jul 27, 2026Xinyang WenGPU Kernel OptimizationOptimal Transport

  7. UnDA: Unpaired Domain Alignment for Cross-Modal Knowledge Transfer in Medical Imaging

    Jul 23, 2026Rafsan Jany, Shadab Tanjeed Ahmad, Ahsan Bulbul +3Cross-Modal Knowledge DistillationCross-Modality Medical Image Segmentation

    Korea Institute of Oriental Medicine, Daejeon, South Korea · Islamic University of Technology, Gazipur, Bangladesh

  8. Attribution Markets: A Fisher-Market Formulation for Fractional Credit Assignment Between Planned Tasks and Performed Actions

    Jul 22, 2026Salavat IshbulatovMechanism DesignFine-Grained Credit Assignment

    Independent researcher

  9. OTAP: Structure-Aware Optimal Transport for Evaluating Planning and Execution in Agent Trajectories

    Jul 19, 2026Babak Barazandeh, Subhabrata Majumdar, George MichailidisLLM Agent EvaluationAI Agent Evaluation

    Fortinet · IIMB · UCLA

  10. Twisted Schrödinger Bridge Matching

    Jul 18, 2026Maxence Noble, Marie Scheid, Yazid Janati +2Schrödinger BridgesTrajectory Inference

    CMAP, Ecole polytechnique · Institute of Foundation Models · MBZUAI +1

  11. Cluster-Aware Matching via Laplacian Optimal Transport

    Jul 17, 2026Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo +1ClusteringGraph Matching

    Department of Applied Mathematics, Tel Aviv University · Department of Statistics, Columbia University · Department of Statistics, University of Chicago

  12. Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding

    Jul 12, 2026Pierre-Louis Barbarant, Florent Meyniel, Bertrand ThirionNeural DecodingNeuroimaging

    Université Paris-Saclay, Inria, CEA, Palaiseau 91120, France · Cognitive Neuroimaging Unit, Institut National de la Santé et de la Recherche Médicale, Commissariat à l’Energie Atomique et aux énergies alternatives, Université Paris-Saclay, NeuroSpin center, 91191 Gif/Yvette, France · Institut de neuromodulation, GHU Paris, psychiatrie et neurosciences, centre hospitalier Sainte-Anne, pôle hospitalo-universitaire 15, Université Paris Cité, Paris, France

  13. Beyond Looking Up, Try Looking Around: Harmonizing Global Structure and Local Consistency in Optimal Transport for Short Text Clustering

    Jul 12, 2026Zhihao Yao, Yuxuan Gu, Jixuan Yin +1ClusteringUnsupervised Clustering

    Harbin Engineering University, China · Harbin Institute of Technology, China

  14. Scalable Optimal Transport Algorithm for Network Alignment

    Jul 11, 2026Elaheh Hassani, Durga Mandarapu, Qi Yu +2Graph MatchingSparse Matrix Multiplication

    Lawrence Berkeley National Laboratory CA, USA · University of Illinois at Urbana-Champaign IL, USA

  15. Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems

    Jul 10, 2026Ripon C. Sarker, Abhishek HalderOptimal ControlOptimal Transport

    Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA

  16. Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

    Jul 6, 2026Markus Heinonen, Yair Shenfeld, Ricardo Baptista +4Dynamical SystemsWasserstein Gradient Flows

    Basis Research Institute · Aalto University · Brown University +2

  17. The Fundamental Limits of Valid Transport Map Estimation

    Jun 29, 2026Sivaraman BalakrishnanMinimax EstimationGenerative Modeling

    Department of Statistics and Data Science† · Machine Learning Department‡

  18. ITSPACE: Monotone Gaussian Optimal Transport Updates

    Jun 29, 2026Woojoo Na, Jennifer DyMatrix OptimizationOptimal Transport

    Department of Computer Engineering, Northeastern University, Boston, USA.

  19. Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions

    Jun 29, 2026Christophe Vauthier, Quentin Mérigot, Anna KorbaSliced Wasserstein DistanceOptimal Transport

    Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay Gif-sur-Yvette, France · Centre de recherche en économie et statistique, ENSAE Palaiseau, France

  20. Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge

    Jun 29, 2026Titouan VayerFlow MatchingSchrödinger Bridges

    COMPACT · Inria, Rennes, France.

  21. MIRROR: Aligning Semantic Relations from Language to Image via Gromov--Wasserstein

    Jun 28, 2026Hong-Han Wang, Yuntao Wang, Hu DingLarge Vision-Language ModelsVLM Reasoning

    University of Science and Technology of China, Hefei, China

  22. Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization

    Jun 26, 2026Clément Bonet, Pierre-Cyril Aubin-Frankowski, Youssef MrouehMaximum Mean DiscrepancyNonconvex Optimization

    CMAP, CNRS, Ecole Polytechnique, IP Paris · CERMICS, CNRS, ENPC, IP Paris · IBM Research

  23. Bridging Vision and Language Concepts through Optimal Transport Semantic Flow

    Jun 25, 2026Chenyang Zhang, Anqi Dong, Guangming Zhu +4Concept Bottleneck ModelsVLM Interpretability

    School of Computer Science and Technology, Xidian University, Xi’an, China · KTH Royal Institute of Technology, Stockholm, Sweden

  24. Variational Inference via Entropic Transport Descent

    Jun 24, 2026Vincent Pacelli, Akash Ratheesh, Evangelos TheodorouBayesian InferenceVariational Inference

    School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA 30332

  25. Counting Trees from Satellite Imagery with Noisy Supervision

    Jun 23, 2026Dimitri Gominski, Maurice Mugabowindekwe, Qiue Xu +6Remote SensingLearning with Noisy Labels

    University of Copenhagen · University of Rwanda · University of Chinese Academy of Sciences +3

  26. Sample complexity of unbalanced entropic OT

    Jun 23, 2026Francisco Andrade, Gabriel Peyré, Clarice PoonSample ComplexityEntropy Regularization

    INRIA (PreMeDICaL & HeKA) · INRIA · CNRS and ENS, PSL Universit´e +1

  27. The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space

    Jun 23, 2026Yian Yao, Weiwei ZhangFlow MatchingWasserstein Gradient Flows

    from the mortal world · from heaven

  28. A Transport-Based Geometry of Belief-Cost

    Jun 19, 2026Laurent CaraffaInformation GeometryOptimal Transport

    Université Gustave Eiffel, LASTIG, IGN-ENSG

  29. Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport

    Jun 19, 2026Jian Xu, Delu Zeng, John Paisley +1Flow MatchingQuantum Generative Modeling

    RIKEN iTHEMS · RIKEN AIP · South China University of Technology +1

  30. OTCHA: Optimal Transport-driven Confidence-aware Latent Hub Alignment for Multi-View Medical Image Classification

    Jun 18, 2026Jiwoong Yang, Haejun Chung, Ikbeom JangMulti-View ConsistencyMulti-View Learning

    Hanyang University, Seoul, Republic of Korea · Hankuk University of Foreign Studies, Yongin, Republic of Korea