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

arXiv 2606.30310 ↗First posted 29 Jun 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections. Standard estimators of the SW distance rely on Monte Carlo averages of one-dimensional Wasserstein distances computed via quantile functions, which require sorting projected samples and access to full datasets. In this work, we introduce a new class of estimators for the Sliced Wasserstein distance based on cumulative distribution functions (CDFs) of projected measures, that avoid sorting and scale via massive dataset parallelism. This class includes several estimators, some of them being indexed by hyperparameters controlling their variance or smoothness. We show that they are especially well suited to scenarios in which CDFs are more tractable than quantile functions, such as mixtures of Gaussians, and moreover that they are also naturally compatible with federated learning, since CDFs of projected data can be computed and aggregated locally without requiring the exchange of raw samples.

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References · 30

  1. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  2. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  3. 2019Federated Learning with Personalization Layerscited by 541
  4. 2021Exploiting Shared Representations for Personalized Federated Learningcited by 541
  5. 2019Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptationcited by 235
  6. 2019Generalized Sliced Wasserstein Distancescited by 208
  7. 2016Practical Secure Aggregation for Federated Learning on User-Held Datacited by 178
  8. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 119
  9. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
  10. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 85
  11. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
  12. 2020Distributional Sliced-Wasserstein and Applications to Generative Modelingcited by 69
18 more
  1. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  2. 2019Tree-Sliced Variants of Wasserstein Distancescited by 54
  3. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  4. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  5. 2020Sliced Iterative Normalizing Flowscited by 38
  6. 2019Orthogonal Estimation of Wasserstein Distancescited by 32
  7. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  8. 2019Approximate Bayesian Computation with the Sliced-Wasserstein Distancecited by 22
  9. 2020Dataset Dynamics via Gradient Flows in Probability Spacecited by 18
  10. 2022Sliced Wasserstein Variational Inferencecited by 18
  11. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  12. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  13. 2025Flowing Datasets with Wasserstein over Wasserstein Gradient Flowscited by 11
  14. 2023Slicing Unbalanced Optimal Transportcited by 10
  15. 2023Federated Wasserstein Distancecited by 8
  16. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  17. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
  18. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4

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