mlsanityData to 7 Oct 2026

Spherical Sliced-Wasserstein

arXiv 2206.08780 ↗First posted 17 Jun 2022stat.ML cs.LGcited by 31

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Abstract (arXiv)

Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of the Wasserstein distance is available, has received a lot of interest. Yet, it is restricted to data living in Euclidean spaces, while the Wasserstein distance has been studied and used recently on manifolds. We focus more specifically on the sphere, for which we define a novel SW discrepancy, which we call spherical Sliced-Wasserstein, making a first step towards defining SW discrepancies on manifolds. Our construction is notably based on closed-form solutions of the Wasserstein distance on the circle, together with a new spherical Radon transform. Along with efficient algorithms and the corresponding implementations, we illustrate its properties in several machine learning use cases where spherical representations of data are at stake: sampling on the sphere, density estimation on real earth data or hyperspherical auto-encoders.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 50 of its 127 references that are in the map. First posted on arXiv 17 Jun 2022.

Builds on

50 of 127 references.

References · 50

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38 more
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  5. 2017Wasserstein Auto-Encoderscited by 371
  6. 2019Generalized Sliced Wasserstein Distancescited by 205
  7. 2018Hyperspherical Variational Auto-Encoderscited by 188
  8. 2020Riemannian Continuous Normalizing Flowscited by 143
  9. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
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  11. 2019Subspace Robust Wasserstein Distancescited by 89
  12. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  13. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  14. 2020Distributional Sliced-Wasserstein and Applications to Generative Modelingcited by 69
  15. 2016Normalizing Flows on Riemannian Manifoldscited by 68
  16. 2018Spherical Latent Spaces for Stable Variational Autoencoderscited by 66
  17. 2021Low-Rank Sinkhorn Factorizationcited by 66
  18. 2018DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applicationscited by 61
  19. 2020Projection Robust Wasserstein Distance and Riemannian Optimizationcited by 45
  20. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  21. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
  22. 2020The Power Spherical distributioncited by 27
  23. 2020A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distancecited by 27
  24. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 8; 2024: 7; 2025: 8; 2026: 5.

31 papers.

Sort:

  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 36
  3. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  4. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
  5. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  6. 2023Sliced Wasserstein Estimation with Control Variatescited by 16
  7. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  8. 2023SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layercited by 14
  9. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  10. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  11. 2024Validating Climate Models with Spherical Convolutional Wasserstein Distancecited by 9
  12. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
19 more
  1. 2024Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributionscited by 6
  2. 2025KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learningcited by 6
  3. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  4. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  5. 2023LCOT: Linear circular optimal transportcited by 4
  6. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  7. 2025Tree-Sliced Wasserstein Distance with Nonlinear Projectioncited by 3
  8. 2023PTLp: Partial Transport Lp Distancescited by 2
  9. 2024Understanding Learning with Sliced-Wasserstein Requires Rethinking Informative Slicescited by 2
  10. 2025Spherical Tree-Sliced Wasserstein Distancecited by 2
  11. 2026Amortized Optimal Transport from Sliced Potentialscited by 2
  12. 2022Fast Approximation of the Generalized Sliced-Wasserstein Distancecited by 1
  13. 2024HOTS3D: Hyper-Spherical Optimal Transport for Semantic Alignment of Text-to-3D Generationcited by 1
  14. 2025Keep your distance: learning dispersed embeddings on mathbbSmcited by 1
  15. 2026Beyond Spherical Harmonics: Rethinking Appearance Models for Radiance Reconstructioncited by 1
  16. 2025Streaming Sliced Optimal Transportcited by 0
  17. 2026ASAP: Amortized Doubly-Stochastic Attention via Sliced Dual Projectioncited by 0
  18. 2026Manifold Constrained Conformal Prediction for Spatial Eventscited by 0
  19. 2026Partial Optimal Transport on the Circle for All Transported Masses in O(N log N)cited by 0