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Generalized Sliced Wasserstein Distances

arXiv 1902.00434 ↗First posted 1 Feb 2019cs.LG stat.MLcited by 205

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Abstract (arXiv)

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in various applications including generative modeling and general supervised/unsupervised learning. In this paper, we first clarify the mathematical connection between the SW distance and the Radon transform. We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced-Wasserstein (GSW) distances. We also show that, similar to the SW distance, the GSW distance can be extended to a maximum GSW (max-GSW) distance. We then provide the conditions under which GSW and max-GSW distances are indeed distances. Finally, we compare the numerical performance of the proposed distances on several generative modeling tasks, including SW flows and SW auto-encoders.

Key facts. Cited by 205 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Feb 2019.

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Citing papers per year: 2021: 29; 2022: 35; 2023: 38; 2024: 34; 2025: 38; 2026: 31.

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  1. 2021No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Datacited by 241
  2. 20243D Gaussian Splatting as Markov Chain Monte Carlocited by 210
  3. 2022Lossy Compression with Gaussian Diffusioncited by 87
  4. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  5. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  6. 2026Being-H0.5: Scaling Human-Centric Robot Learning for Cross-Embodiment Generalizationcited by 61
  7. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  8. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  9. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  10. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  11. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  12. 2021Universal Approximation Under Constraints is Possible with Transformerscited by 32
38 more
  1. 2022Spherical Sliced-Wassersteincited by 31
  2. 2022Meta Optimal Transportcited by 28
  3. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  4. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  5. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  6. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  7. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  8. 2022Fairness and Explainability: Bridging the Gap Towards Fair Model Explanationscited by 22
  9. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  10. 2022Optimal transport for causal discoverycited by 19
  11. 2022Sliced Optimal Partial Transportcited by 19
  12. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  13. 2021On the Inherent Regularization Effects of Noise Injection During Trainingcited by 18
  14. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  15. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  16. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  17. 2023Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Mapscited by 16
  18. 2023Sliced Wasserstein Estimation with Control Variatescited by 16
  19. 2023Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transportcited by 16
  20. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  21. 2021Enhancing Backdoor Attacks with Multi-Level MMD Regularizationcited by 15
  22. 2022Wassmap: Wasserstein Isometric Mapping for Image Manifold Learningcited by 15
  23. 2022Improving Zero-Shot Models with Label Distribution Priorscited by 14
  24. 2023SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layercited by 14
  25. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  26. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
  27. 2022Unsupervised Model Adaptation for Source-free Segmentation of Medical Imagescited by 13
  28. 2022Grassmann Stein Variational Gradient Descentcited by 12
  29. 2022OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptationcited by 12
  30. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  31. 2024Opinion-Unaware Blind Image Quality Assessment using Multi-Scale Deep Feature Statisticscited by 11
  32. 2021Supervised Tree-Wasserstein Distancecited by 10
  33. 2021Re-evaluating Word Mover's Distancecited by 10
  34. 2021Model Selection for Bayesian Autoencoderscited by 10
  35. 2021Fixed Support Tree-Sliced Wasserstein Barycentercited by 10
  36. 2023Device-Robust Acoustic Scene Classification via Impulse Response Augmentationcited by 10
  37. 2023How to Estimate Model Transferability of Pre-Trained Speech Models?cited by 10
  38. 2023Max-Sliced Mutual Informationcited by 10

50 most cited of 205 All 205 (JSON)