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

  1. Conditional Sampling via Wasserstein Autoencoders and Triangular Transport

    Apr 3, 2026Mohammad Al-Jarrah, Michele Martino, Marcus Yim +2Conditional Generative ModelingOptimal Transport

    Department of Aeronautics & Astronautics, University of Washington, Seattle · Department of Applied Mathematics, University of Washington, Seattle · Department of Mathematics, University of Washington, Seattle

  2. Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport

    Apr 3, 2026Rafael Pereira Eufrazio, Eduardo Fernandes Montesuma, Charles Casimiro CavalcanteMultidimensional ScalingMulti-View Learning

    Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Canindé, Ceará, Brazil · Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, Ceará, Brazil · Sigma Nova, Paris, France

  3. HOT: Harmonic-Constrained Optimal Transport for Remote Photoplethysmography Domain Adaptation

    Apr 2, 2026Ba-Thinh Nguyen, Thi-Duyen Ngo, Thanh-Trung Huynh +2Remote PhotoplethysmographyOptimal Transport

    VNU University of Engineering and Technology, Hanoi, Vietnam · College of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam · VinUni-Illinois Smart Health Center, VinUniversity, Hanoi, Vietnam +1

  4. Causal Optimal Coupling for Gaussian Input-Output Distributional Data

    Apr 1, 2026Daran Xu, Amirhossein TaghvaeiOptimal TransportSchrödinger Bridges

    Department of Applied Mathematics, University of Washington, Seattle, WA · Department of Aeronautics and Astronautics, University of Washington, Seattle, WA

  5. An Explicit Surrogate for Gaussian Mixture Flow Matching with Wasserstein Gap Bounds

    Mar 30, 2026Elham Rostami, Taous-Meriem Laleg-Kirati, Hamidou TembineFlow MatchingOptimal Transport

    Université Paris-Saclay, Inria, CIAMS, Gif-sur-Yvette, 91190, France · Department of Electrical Engineering and Computer Science, University of Quebec in Trois-Rivieres (UQTR), Quebec, Canada

  6. Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences

    Mar 29, 2026Jeremiah Birrell, Xiaoxi ShenDistributionally Robust OptimizationWasserstein Distributionally Robust Optimization

    Department of Mathematics Texas State University San Marcos, TX, USA

  7. Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs

    Mar 27, 2026David Gentile, James M. MurphyWasserstein BarycentersOptimal Transport

    Tufts University, Dept. of Mathematics, Medford, MA, USA

  8. Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems

    Mar 24, 2026Tristan Luca Saidi, Gonzalo Mena, Larry Wasserman +1Batch Effect CorrectionCausal Counterfactual Generation

    Department of Statistics and Data Science, Carnegie Mellon University · Machine Learning Department, Carnegie Mellon University · Department of Economics, Emory University

  9. Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamics

    Mar 21, 2026Aratrika Mustafi, Soumya MukherjeeSinkhorn DivergenceAssociative Memory

    Department of Statistics, Pennsylvania State University

  10. SuCor: Susceptibility Distortion Correction via Parameter-Free and Self-Regularized Optimal Transport

    Mar 17, 2026Sreekar Chigurupati, Eleftherios GaryfallidisMagnetic Resonance ImagingNeuroimaging

    Intelligent Systems Engineering, Indiana University, Bloomington, Indiana, USA.

  11. Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transport

    Mar 16, 2026Matteo PegoraroTopological Representation LearningPersistent Homology

    Institute of Computing, Faculty of Informatics, Università della Svizzera Italiana

  12. Faster Inference of Flow-Based Generative Models via Improved Data-Noise Coupling

    Mar 16, 2026Aram Davtyan, Leello Tadesse Dadi, Volkan Cevher +1Flow-Based Generative ModelingConditional Flow Matching

    University of Bern, Bern, Switzerland · EPFL, Lausanne, Switzerland

  13. Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport

    Mar 15, 2026Yixin Wang, Ting Gao, Jinqiao DuanTopological Data AnalysisOptimal Transport

    School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China · Center for Mathematical Science, Huazhong University of Science and Technology, Wuhan, China · Steklov-Wuhan Institute for Mathematical Exploration, Huazhong University of Science and Technology, China +2

  14. Sampling Boltzmann distributions via normalizing flow approximation of transport maps

    Mar 15, 2026Zia Ur Rehman, Gero FrieseckeBoltzmann SamplingNormalizing Flows

    Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstrasse 3, 85748 Garching, Germany

  15. Sobolev--Ricci Curvature

    Mar 13, 2026Kyoichi Iwasaki, Tam Le, Hideitsu HinoOptimal Transport

    The Graduate University for Advanced Studies, SOKENDAI · The Institute of Statistical Mathematics

  16. Sinkhorn-Drifting Generative Models

    Mar 12, 2026Ping He, Om Khangaonkar, Hamed Pirsiavash +2Sinkhorn DivergenceDrifting Models

    Department of Computer Science, Vanderbilt University · Department of Computer Science, University of California, Davis · Department of Computer Science, Purdue University

  17. Shape-of-You: Fused Gromov-Wasserstein Optimal Transport for Semantic Correspondence in-the-Wild

    Mar 12, 2026Jiin Im, Sisung Liu, Je Hyeong HongSemantic CorrespondenceOptimal Transport

    Dept. Electronic Engineering, Hanyang University · Dept. Artificial Intelligence, Hanyang University

  18. MST-Direct: Matching via Sinkhorn Transport for Multivariate Geostatistical Simulation with Complex Non-Linear Dependencies

    Mar 12, 2026Tchalies Bachmann SchmitzOptimal Transport

  19. COT-FM: Cluster-wise Optimal Transport Flow Matching

    Mar 11, 2026Chiensheng Chiang, Kuan-Hsun Tu, Jia-Wei Liao +2Flow MatchingGenerative Modeling

    National Taiwan University

  20. Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering

    Mar 10, 2026Joshua Lentz, Nicholas Karris, Alex Cloninger +1Image ClusteringDictionary Learning

    Tufts University, Department of Mathematics, Medford, MA 02155, USA · University of California San Diego, Department of Mathematics, La Jolla, CA 92093, USA · University of California San Diego, Halıcıo˘glu Data Science Institute, La Jolla, CA 92093, USA

  21. Towards Effective and Efficient Graph Alignment without Supervision

    Mar 9, 2026Songyang Chen, Youfang Lin, Yu Liu +2Graph MatchingGraph Representation Learning

    Beijing Jiaotong University, Beijing, 100044, P.R. China. · Peking University, Beijing, 100871, P.R. China.

  22. Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modeling

    Mar 7, 2026Jiwoo Yoon, Kyumin Choi, Jaewoong ChoiOptimal TransportConditional Generative Modeling

    Department of Statistics, Sungkyunkwan University · Department of Applied Artificial Intelligence, Sungkyunkwan University

  23. From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows

    Mar 5, 2026Cenwei Zhang, Lin Zhu, Manxi Lin +1Feature AttributionShapley Value Attribution

    Aalto University, Espoo, Finland · Alibaba, Hangzhou, China · Technical University of Denmark, Copenhagen, Denmark

  24. Transport Clustering: Solving Low-Rank Optimal Transport via Clustering

    Mar 3, 2026Henri Schmidt, Peter Halmos, Ben RaphaelOptimal TransportClustering

    Department of Computer Science, Princeton University, NJ, USA.

  25. Hyperparameter Trajectory Inference with Conditional Lagrangian Optimal Transport

    Mar 2, 2026Harry Amad, Mihaela van der SchaarNeural Surrogate ModelingOptimal Transport

    Department of Applied Mathematics and Theoretical Physics University of Cambridge, UK

  26. COG: Confidence-aware Optimal Geometric Correspondence for Unsupervised Single-reference Novel Object Pose Estimation

    Feb 28, 2026Yuchen Che, Jingtu Wu, Hao Zheng +1Object Pose EstimationUnsupervised Learning

    Institute of Science Tokyo · RIKEN · Tohoku University

  27. Multimodal Optimal Transport for Training-free Temporal Segmentation in Surgical Robotics

    Feb 27, 2026Omar Mohamed, Edoardo Fazzari, Ayah Al-Naji +5Temporal Action SegmentationSurgical Video Understanding

    Authos are with the Dept. of Robotics, Mohamed bin Zayed University of AI, Abu Dhabi, UAE.

  28. Neural solver for Wasserstein Geodesics and optimal transport dynamics

    Feb 25, 2026Hailiang Liu, Yan-Han ChenOptimal Transport

    Department of Mathematics, Iowa State University, Ames, IA 50011, USA. · Department of Statistics, Iowa State University, Ames, IA 50011, USA.

  29. Entropy-Controlled Flow Matching

    Feb 25, 2026Chika MaduabuchiFlow MatchingFlow-Based Generative Modeling

    William & Mary, Williamsburg, VA, USA

  30. Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents

    Feb 23, 2026Michael ChertkovDiffusion ModelsMulti-Agent Control

    Graduate Interdisciplinary Program in Applied Mathematics & Department of Mathematics, University of Arizona, Tucson, AZ, USA