mlsanityData to 7 Oct 2026

On the regularization of Wasserstein GANs

arXiv 1709.08894 ↗First posted 26 Sep 2017stat.ML cs.LGcited by 65

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Abstract (arXiv)

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. It was proposed that training can be improved by instead augmenting the loss by a regularization term that penalizes the deviation of the gradient of the critic (as a function of the network's input) from one. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on toy data sets.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Sep 2017.

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Citing papers per year: 2021: 19; 2022: 14; 2023: 17; 2024: 12; 2025: 3.

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  1. 2022Neural Optimal Transportcited by 123
  2. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  3. 2021Generative Modeling with Optimal Transport Mapscited by 80
  4. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39
  5. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  6. 2022StudioGAN: A Taxonomy and Benchmark of GANs for Image Synthesiscited by 38
  7. 2021An error analysis of generative adversarial networks for learning distributionscited by 35
  8. 2022Neural Optimal Transport with General Cost Functionalscited by 34
  9. 2022Kernel Neural Optimal Transportcited by 31
  10. 2022On amortizing convex conjugates for optimal transportcited by 30
  11. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  12. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 25
38 more
  1. 2021Disentangled Recurrent Wasserstein Autoencodercited by 22
  2. 2023A Representative Study on Human Detection of Artificially Generated Media Across Countriescited by 22
  3. 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 21
  4. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  5. 2021Wasserstein Proximal of GANscited by 15
  6. 2021Convolutional Normalization: Improving Deep Convolutional Network Robustness and Trainingcited by 15
  7. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  8. 2024Understanding Diffusion Models by Feynman's Path Integralcited by 13
  9. 2021Self-Supervised GANs with Label Augmentationcited by 9
  10. 2021Generalization Error of GAN from the Discriminator's Perspectivecited by 8
  11. 2023Analyzing and Improving Optimal-Transport-based Adversarial Networkscited by 8
  12. 2021Wasserstein GANs with Gradient Penalty Compute Congested Transportcited by 6
  13. 2023Provably Convergent Policy Optimization via Metric-aware Trust Region Methodscited by 6
  14. 2021Moreau-Yosida f-divergencescited by 5
  15. 2021On the Existence of Optimal Transport Gradient for Learning Generative Modelscited by 4
  16. 2021PeaceGAN: A GAN-based Multi-Task Learning Method for SAR Target Image Generation with a Pose Estimator and an Auxiliary Classifiercited by 4
  17. 2021Input Invex Neural Networkcited by 4
  18. 2022Detecting data-driven robust statistical arbitrage strategies with deep neural networkscited by 4
  19. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  20. 2023Learning with Constraint Learning: New Perspective, Solution Strategy and Various Applicationscited by 4
  21. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  22. 2024Imitation from Diverse Behaviors: Wasserstein Quality Diversity Imitation Learning with Single-Step Archive Explorationcited by 4
  23. 2021Training Wasserstein GANs without gradient penaltiescited by 3
  24. 2022Learning Invariances with Generalised Input-Convex Neural Networkscited by 3
  25. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  26. 2023Monotone Generative Modeling via a Gromov-Monge Embeddingcited by 3
  27. 2024A Wasserstein perspective of Vanilla GANscited by 3
  28. 2024A Fisher-Rao gradient flow for entropic mean-field min-max gamescited by 3
  29. 2024Generative Modeling by Minimizing the Wasserstein-2 Losscited by 3
  30. 2024ROER: Regularized Optimal Experience Replaycited by 3
  31. 2021Exploiting generative self-supervised learning for the assessment of biological images with lack of annotations: a COVID-19 case-studycited by 2
  32. 2022A new method for determining Wasserstein 1 optimal transport maps from Kantorovich potentials, with deep learning applicationscited by 2
  33. 2023GANalyzer: Analysis and Manipulation of GANs Latent Space for Controllable Face Synthesiscited by 2
  34. 2023Data Interpolants -- That's What Discriminators in Higher-order Gradient-regularized GANs Arecited by 2
  35. 2023OT-Net: A Reusable Neural Optimal Transport Solvercited by 2
  36. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  37. 2021Stein Latent Optimization for Generative Adversarial Networkscited by 1
  38. 2021GraN-GAN: Piecewise Gradient Normalization for Generative Adversarial Networkscited by 1

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