Sliced Wasserstein Distance

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Overview

Sliced Wasserstein distance studies how to compare distributions efficiently by projecting high-dimensional data onto lines and computing one-dimensional optimal transport, often through sorted samples or cumulative distribution functions. Methods use random or optimized directions, orthonormal bases, and extensions such as max-sliced, Orlicz, and spherical-harmonic variants to improve sensitivity or fit particular data. These distances support generative-model evaluation, domain generalization, clustering, change detection, and distribution steering, with applications ranging from images and point clouds to EEG and single-cell data. A central tension is balancing computational and statistical efficiency against how faithfully a limited set of projections captures differences in high-dimensional distributions; estimation rates and projection choices remain important open issues.

Latest papers

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18 papers3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

  1. Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance

    Oct 29, 2026Oscar Mickelin, Yunpeng Shi, Amit Singer +13D Shape MatchingOptimal Transport

    Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China · Department of Mathematics, University of California at Davis, Davis CA, USA · Department of Mathematics, Princeton University, Princeton, NJ, USA +3

  2. Sliced Wasserstein Sketches with Error Certificates

    Oct 14, 2026Elaheh Akbari, James Liu, Keaton Hamm +1Sliced Wasserstein DistanceVector Quantization

    College of Connected Computing, Vanderbilt University · Department of Mathematics, Division of Data Science, University of Texas at Arlington

  3. 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

  4. Minimax Rates for Estimating Powered Sliced Wasserstein Functionals

    Oct 8, 2026Binh Thuan TranMinimax EstimationSliced Wasserstein Distance

    LAMA, LIGM, Université Gustave Eiffel

  5. Sliced Orlicz-Wasserstein

    Sep 26, 2026Binh Thuan Tran, Khai NguyenOptimal TransportSliced Wasserstein Distance

    LAMA, LIGM, Université Gustave Eiffel · Department of Statistics and Data Science, Texas A&M University

  6. High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretability

    Sep 21, 2026Sven Jacob, Bardh Prenkaj, Weijia Shao +1Change-Point DetectionSliced Wasserstein Distance

    Federal Institute for Occupational Safety and Health, Dresden · Technical University of Munich, Munich Center for Machine Learning · Sapienza University of Rome

  7. Spherical Harmonic Sliced Wasserstein Displacement Interpolation for Acoustic Source and Reflection Density Modeling

    Sep 18, 2026Yuancheng LuoSpatial AudioSliced Wasserstein Distance

    NuSpace Audio Cambridge, MA, USA

  8. Distribution Steering via Sliced Optimal Transport Control

    Aug 13, 2026Kaito Ito, Anqi DongFeedback ControlOptimal Control

    Department of Information Physics and Computing The University of Tokyo, Tokyo 113-8654, Japan · Department of Mathematics and Digital Futures KTH Royal Institute of Technology, 100 44 Stockholm, Sweden

  9. Distributional Determinantal Point Process for Repulsive Clustering of Distributions

    Jul 23, 2026Khai Nguyen, Yang Ni, Elizabeth Juarez-Colunga +1Bayesian Mixture ModelsClustering

    Department of Statistics and Data Sciences, University of Texas at Austin · Department of Biostatistics and Informatics, University of Colorado Anschutz · Department of Mathematics, University of Texas at Austin

  10. 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

  11. 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

  12. 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

  13. VISReg: Variance-Invariance-Sketching Regularization for JEPA training

    Jun 1, 2026Haiyu Wu, Randall Balestriero, Morgan LevineRepresentation CollapseJoint-Embedding Predictive Architecture

    Altos Labs · Brown University

  14. The Observable Wasserstein Distance

    May 11, 2026Edivaldo Lopes dos Santos, Leandro Vicente Mauri, Washington Mio +1Sliced Wasserstein DistanceOptimal Transport

    1Departamento de Matem´atica, Universidade Federal de S˜ao Carlos, Brazil · Department of Mathematics, Florida State University, USA

  15. APEX: Assumption-free Projection-based Embedding eXamination Metric for Generative Distribution Evaluation

    May 8, 2026Caterina Gallegati, Monica Bianchini, Franco Scarselli +2Image Quality AssessmentImage Generation Evaluation

    University of Siena, Italy · AI for Good (AIGO), Istituto Italiano di Tecnologia, Italy · University of Verona, Italy

  16. MIND: Monge Inception Distance for Generative Models Evaluation

    May 7, 2026Quentin Berthet, Yu-Han Wu, Clement Crepy +3Image Generation EvaluationSliced Wasserstein Distance

    Google DeepMind · LPSM, Sorbonne Université

  17. Sliced Wasserstein Steering between Gaussian Measures

    Apr 14, 2026Kaito Ito, Anqi DongOptimal TransportOptimal Control

    Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8654, Japan · Department of Decision and Control Systems and Department of Mathematics, KTH Royal Institute of Technology, Stockholm 114 28, Sweden

  18. Convergence Rates for Distribution Matching with Sliced Optimal Transport

    Feb 11, 2026Gauthier Thurin, Claire Boyer, Kimia NadjahiDistribution MatchingSliced Wasserstein Distance

    ENS-PSL · CNRS, ENS Paris, France · LMO, IUF, CELESTE +2