Wasserstein Distance

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Overview

Wasserstein distance studies how much probability mass must move, and how far, to transform one distribution into another, making it sensitive to the geometry of the data. Methods include optimal transport couplings, entropically regularized Sinkhorn algorithms, sliced distances based on one-dimensional projections, and Gromov-Wasserstein distances for comparing spaces with different geometries. The distance is used to analyze and train generative models, compare graphs and shapes, estimate distribution shifts, and quantify convergence, with theory often focused on sample complexity and dimension dependence. A central tension is that accurate transport can be computationally expensive, while faster approximations or regularization may trade geometric fidelity for scalability and statistical efficiency.

Latest papers

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63 papers8 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

  1. Minimax Rates for Conditional Generative Learning under Wasserstein Loss

    Oct 26, 2026Sungwon Park, Kyoung-Sook Moon, Hongjoong KimConditional Generative ModelingConditional Distribution Estimation

    Department of Mathematics, Korea University · Department of Finance and Big Data, Gachon University

  2. How Geometry Shapes Generative Model Evaluation on Riemannian Manifolds

    Oct 24, 2026Misha Oberski, Valentijn Oldenburg, Xanthos Kekkos +6Generative AI EvaluationWasserstein Distance

    University of Amsterdam · Independent Researcher · AMLab, University of Amsterdam

  3. Dimension-free regimes for unadjusted Langevin in ridge-separable models: A subspace robust Wasserstein analysis

    Oct 22, 2026Yuansi Chen, Francesco Pedrotti, Peter A. WhalleyLangevin DynamicsHigh-Dimensional Asymptotics

    Seminar for Statistics, ETH Zürich · Department of Statistics, University of Warwick

  4. 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

  5. Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation

    Oct 13, 2026Agathe Fernandes Machado, Charlotte Jamotton, Arthur CharpentierGroup FairnessIntersectional Fairness

  6. 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

  7. RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

    Sep 30, 2026Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn +1Wasserstein Gradient FlowsOne-Step Generative Modeling

    KAIST

  8. Towards Universal Wasserstein Barycenters through Flow Matching

    Sep 29, 2026Eduardo Fernandes MontesumaWasserstein BarycentersOptimal Transport

    Sigma Nova Paris, France

  9. A Spectral Theory of Distortion in LLM Graph Reconstruction: Sharp Bounds and Empirical Characterization

    Sep 29, 2026Jianru ShenLLMs for Graph LearningWasserstein Distance

    Columbia University New York, NY, USA

  10. Geometry-Adaptive Mechanisms for Private Synthetic Data

    Sep 27, 2026Raoof Zare Moayedi, Amir R. Asadi, Mohammad Hossein Yassaee +1Intrinsic DimensionalityDifferentially Private Synthetic Data Generation

    Sharif University of Technology · University of Birmingham · The Alan Turing Institute

  11. Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems

    Sep 25, 2026Joanna Marks, Gabriel Rioux, Riccardo PasseggeriGradient DescentMirror Descent

    ⋆Denotes equal contribution to this work.

  12. Toscani-Fourier Distance on Probability Measures: Wasserstein Control, Topological Equivalence on Model Classes, and Duality

    Sep 19, 2026Mehrdad MohammadiIntegral Probability MetricsWasserstein Distance

    Department of Statistics University of Illinois Urbana-Champaign Champaign, IL 61820, USA

  13. Graph Matching Relaxations and Amortization for Supervised Graph Prediction

    Sep 14, 2026Federico Méndez, Paul Krzakala, Gabriel Melo +3Learning to OptimizeGraph Matching

    LTCI, Télécom Paris · Institut Polytechnique de Paris · CMAP, École Polytechnique

  14. Gaussian Approximation in Wasserstein-p: Markovian Martingale Differences and Stochastic Approximation

    Sep 8, 2026Yixuan Zhang, Qiaomin XieWasserstein Distance

    Department of Industrial & Systems Engineering, University of Wisconsin–Madison

  15. Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation

    Sep 1, 2026Sebastien Tchitchek, Julien TiernyPersistent HomologyWasserstein Distance

    CNRS and Sorbonne Université

  16. Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality

    Aug 27, 2026Clément Soubrier, Geoffrey Woollard, Andrew Warren +1Optimal TransportWasserstein Distance

    Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada · Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada · Mathematical Institute, Utrecht University, Utrecht, 3584 CD, The Netherlands

  17. Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications

    Aug 27, 2026James Hyun, François G. MeyerOptimal TransportWasserstein Distance

    University of Colorado, Boulder, CO 80309, United States

  18. CoSWA-YOLOv12: Scale-Invariant Tiny Object Detection and Segmentation of Malaria Parasites

    Aug 25, 2026Ahmed Tahiru Issah, Carine MukamakuzaSmall Object DetectionObject Detection

    Carnegie Mellon University, Kigali, Rwanda

  19. A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields

    Aug 12, 2026Mingtao Xia, Qijing ShenUncertainty QuantificationSinkhorn Divergence

    School of Mathematics, University of Birmingham, Watson Building, Edgbaston, Birmingham, B15 2TT, United Kingdom · Department of Mathematics, University of Houston, 3551 Cullen Blvd, Houston, 77204, Texas, United States · Nuffield Department of Medicine, University of Oxford, United Kingdom, Old Road Campus, Oxford, OX3 7BN, United Kingdom

  20. Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms

    Aug 11, 2026Florian Beier, Stephan EcksteinClusteringVector Quantization

    Department of Mathematics, University of Tübingen, Germany

  21. Sub-Quadratic Bisimulation Metrics via Approximate Nearest Neighbors: Coverage-Augmented Guarantees and Computable Two-Sided Certificates

    Aug 7, 2026Ibne Farabi Shihab, Joyanta Jyoti MondalMarkov Decision ProcessesApproximation Algorithms

    Department of Computer Science, Iowa State University, USA · Department of Computer and Information Sciences, University of Delaware, USA

  22. Wasserstein mixing time of the unadjusted Langevin algorithm

    Aug 3, 2026Francesco Pedrotti, Peter A. WhalleyMarkov Chain Monte CarloLangevin Dynamics

    ETH Zürich

  23. Diffusion enabled Optimal Transport distances for graph matching

    Jul 7, 2026Iman Seyedi, Francesco ArchettiGraph MatchingWasserstein Distance

    Department of Computer Science Systems and Communication, University of Milano-Bi- cocca, 20126 Milan, Italy

  24. 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

  25. Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS

    Jun 29, 2026Flor Martinez-Sermeno, Arturo Jaramillo, Johan Van HorebeekMultidimensional ScalingDimensionality Reduction

  26. A Transport-Based Geometry of Belief-Cost

    Jun 19, 2026Laurent CaraffaInformation GeometryOptimal Transport

    Université Gustave Eiffel, LASTIG, IGN-ENSG

  27. Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees

    Jun 15, 2026Marta Gentiloni Silveri, Giovanni Conforti, Alain DurmusDiffusion SamplingFlow-Based Generative Modeling

    Ecole Polytechnique, Massy Palaiseau, France · Università degli Studi di Padova, Padua, Italy

  28. kk-Nearest Neighbors in Gromov--Wasserstein Space

    Jun 9, 2026Kaitlyn Hohmeier, Nicolas Fraiman, Caroline MoosmuellerGraph Classificationk-Nearest Neighbors

    University of North Carolina at Chapel Hill, Department of Mathematics · University of North Carolina at Chapel Hill, Department of Statistics and Operations Research

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

    Jun 5, 2026Munsik KimMinimax EstimationSpatiotemporal Forecasting

  30. A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding

    Jun 4, 2026Chen Hu, Rui Wang, Jiale Zhou +4EEG DecodingDomain Generalization

    Westlake University Hangzhou, China · School of Artificial Intelligence and Computer Science Jiangnan University Wuxi, China · Zhejiang University Hangzhou, China +1