mlsanityData to 7 Oct 2026

Max-Sliced Wasserstein Distance and its use for GANs

arXiv 1904.05877 ↗First posted 11 Apr 2019cs.LG cs.CV stat.MLcited by 118

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Abstract (arXiv)

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as the training time. Nonetheless, the sample complexity of the distance metrics remains one of the factors affecting GAN training. We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance. To further improve the sliced Wasserstein distance we then analyze its `projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up to a resolution of 256x256 easily.

Key facts. Cited by 118 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Apr 2019.

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Citing papers per year: 2021: 20; 2022: 20; 2023: 25; 2024: 24; 2025: 18; 2026: 11.

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  1. 2022Tutorial on amortized optimizationcited by 83
  2. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  3. 2022Generative Multiplane Images: Making a 2D GAN 3D-Awarecited by 57
  4. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  5. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  6. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  7. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  8. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  9. 2022Spherical Sliced-Wassersteincited by 31
  10. 20213D Pose Transfer with Correspondence Learning and Mesh Refinementcited by 30
  11. 2022Meta Optimal Transportcited by 28
  12. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
38 more
  1. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  2. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  3. 2023Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Designcited by 22
  4. 2021Efficient Gradient Flows in Sliced-Wasserstein Spacecited by 21
  5. 2022Unsupervised 3D Pose Transfer with Cross Consistency and Dual Reconstructioncited by 21
  6. 2022Sliced Optimal Partial Transportcited by 19
  7. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  8. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  9. 2023Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Mapscited by 16
  10. 2021Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applicationscited by 15
  11. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  12. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  13. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  14. 2023SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layercited by 14
  15. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  16. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  17. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  18. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  19. 2024Efficient Prior Calibration From Indirect Datacited by 11
  20. 2021Supervised Tree-Wasserstein Distancecited by 10
  21. 2021Fixed Support Tree-Sliced Wasserstein Barycentercited by 10
  22. 2023Max-Sliced Mutual Informationcited by 10
  23. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  24. 2025ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Planscited by 10
  25. 2025Color Conditional Generation with Sliced Wasserstein Guidancecited by 10
  26. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  27. 2022One Loss for Quantization: Deep Hashing with Discrete Wasserstein Distributional Matchingcited by 9
  28. 2022Approximating 1-Wasserstein Distance with Treescited by 9
  29. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  30. 2024Validating Climate Models with Spherical Convolutional Wasserstein Distancecited by 9
  31. 2021Manifold optimization for non-linear optimal transport problemscited by 8
  32. 2023Lidar Upsampling with Sliced Wasserstein Distancecited by 8
  33. 2023Structured Transforms Across Spaces with Cost-Regularized Optimal Transportcited by 8
  34. 2024Privacy-preserving data release leveraging optimal transport and particle gradient descentcited by 8
  35. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  36. 2024Quantum State Generation with Structure-Preserving Diffusion Modelcited by 8
  37. 2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
  38. 2026Image Generation with a Sphere Encodercited by 8

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