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Generative Modeling using the Sliced Wasserstein Distance

arXiv 1803.11188 ↗First posted 29 Mar 2018cs.CVcited by 108

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Abstract (arXiv)

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is particularly true for early GAN formulations, there has been significant empirically motivated and theoretically founded progress to improve stability, for instance, by using the Wasserstein distance rather than the Jenson-Shannon divergence. Here, we consider an alternative formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddle-point formulation. By augmenting this approach with a discriminator we improve its accuracy. We found our approach to be significantly more stable compared to even the improved Wasserstein GAN. Further, unlike the traditional GAN loss, the loss formulated in our method is a good measure of the actual distance between the distributions and, for the first time for GAN training, we are able to show estimates for the same.

Key facts. Cited by 108 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Mar 2018.

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Citing papers per year: 2021: 18; 2022: 21; 2023: 18; 2024: 20; 2025: 16; 2026: 15.

108 papers.

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  1. 2022Diffusion-GAN: Training GANs with Diffusioncited by 205
  2. 2021Generative Modeling with Optimal Transport Mapscited by 82
  3. 2022Generative Multiplane Images: Making a 2D GAN 3D-Awarecited by 57
  4. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  5. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  6. 2021ADD: Frequency Attention and Multi-View based Knowledge Distillation to Detect Low-Quality Compressed Deepfake Imagescited by 48
  7. 2023Class-Balancing Diffusion Modelscited by 48
  8. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 41
  9. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  10. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  11. 2026Representation Fr'echet Loss for Visual Generationcited by 37
  12. 2021Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)cited by 35
38 more
  1. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  2. 2024An Aggregation-Free Federated Learning for Tackling Data Heterogeneitycited by 33
  3. 2022Generating natural images with direct Patch Distributions Matchingcited by 27
  4. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  5. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  6. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  7. 2022Self-Supervised Learning for Real-World Super-Resolution from Dual Zoomed Observationscited by 20
  8. 2021Differentially Private Sliced Wasserstein Distancecited by 19
  9. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  10. 2022Sliced Wasserstein Variational Inferencecited by 18
  11. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  12. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 16
  13. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  14. 2023Sliced Wasserstein Estimation with Control Variatescited by 16
  15. 2026VISReg: Variance-Invariance-Sketching Regularization for JEPA trainingcited by 16
  16. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  17. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  18. 2021Understanding Overparameterization in Generative Adversarial Networkscited by 14
  19. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  20. 2024Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measurescited by 14
  21. 2022OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptationcited by 12
  22. 2023Properties of Discrete Sliced Wasserstein Lossescited by 12
  23. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  24. 2026Representation Distribution Matching for One-Step Visual Generationcited by 11
  25. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  26. 2021Weakly Supervised High-Fidelity Clothing Model Generationcited by 9
  27. 2022One Loss for Quantization: Deep Hashing with Discrete Wasserstein Distributional Matchingcited by 9
  28. 2023Scalable Infomin Learningcited by 8
  29. 2024Privacy-preserving data release leveraging optimal transport and particle gradient descentcited by 8
  30. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  31. 2021A Quantum Generative Adversarial Network for distributionscited by 7
  32. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  33. 2022DigGAN: Discriminator gradIent Gap Regularization for GAN Training with Limited Datacited by 7
  34. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  35. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  36. 2025A User's Guide to Sampling Strategies for Sliced Optimal Transportcited by 7
  37. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
  38. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplingscited by 7

50 most cited of 108 All 108 (JSON)