# Some Theoretical Insights into Wasserstein GANs

arXiv: https://arxiv.org/abs/2006.02682 · HTML: https://mlsanity.com/paper/2006.02682/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 28 of 28)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [MAUVE Scores for Generative Models: Theory and Practice](https://mlsanity.com/paper/2212.14578/) (2022)
- [A Neural Tangent Kernel Perspective of GANs](https://mlsanity.com/paper/2106.05566/) (2021)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theory](https://mlsanity.com/paper/2310.04935/) (2023)
- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)
- [PAC-Bayesian Generalization Bounds for Adversarial Generative Models](https://mlsanity.com/paper/2302.08942/) (2023)
- [A likelihood approach to nonparametric estimation of a singular distribution using deep generative models](https://mlsanity.com/paper/2105.04046/) (2021)
- [Wasserstein GANs with Gradient Penalty Compute Congested Transport](https://mlsanity.com/paper/2109.00528/) (2021)
- [Time Series (re)sampling using Generative Adversarial Networks](https://mlsanity.com/paper/2102.00208/) (2021)
- [GAN Estimation of Lipschitz Optimal Transport Maps](https://mlsanity.com/paper/2202.07965/) (2022)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency](https://mlsanity.com/paper/2110.03995/) (2021)
- [Optimal 1-Wasserstein Distance for WGANs](https://mlsanity.com/paper/2201.02824/) (2022)
- [Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures](https://mlsanity.com/paper/2203.15150/) (2022)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [A Wasserstein perspective of Vanilla GANs](https://mlsanity.com/paper/2403.15312/) (2024)
- [Numerical and statistical analysis of NeuralODE with Runge-Kutta time integration](https://mlsanity.com/paper/2503.10729/) (2025)
- [Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis](https://mlsanity.com/paper/2506.00849/) (2025)
- [When do World Models Successfully Learn Dynamical Systems?](https://mlsanity.com/paper/2507.04898/) (2025)
- [Statistical Error Bounds for GANs with Nonlinear Objective Functionals](https://mlsanity.com/paper/2406.16834/) (2024)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [On the potential benefits of entropic regularization for smoothing Wasserstein estimators](https://mlsanity.com/paper/2210.06934/) (2022)
- [Local convergence of simultaneous min-max algorithms to differential equilibrium on Riemannian manifold](https://mlsanity.com/paper/2405.13392/) (2024)
- [Simulation of Multivariate Extremes: a Wasserstein-Aitchison GAN approach](https://mlsanity.com/paper/2504.21438/) (2025)
- [Concentration Inequalities for Stochastic Optimization of Unbounded Objective Functions with Application to Denoising Score Matching](https://mlsanity.com/paper/2502.08628/) (2025)
- [On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures](https://mlsanity.com/paper/2605.21388/) (2026)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the benefits of the cousin approach called Wasserstein GANs (WGANs), which brings stabilization in the training process. In the present paper, we add a new stone to the edifice by proposing some theoretical advances in the properties of WGANs. First, we properly define the architecture of WGANs in the context of integral probability metrics parameterized by neural networks and highlight some of their basic mathematical features. We stress in particular interesting optimization properties arising from the use of a parametric 1-Lipschitz discriminator. Then, in a statistically-driven approach, we study the convergence of empirical WGANs as the sample size tends to infinity, and clarify the adversarial effects of the generator and the discriminator by underlining some trade-off properties. These features are finally illustrated with experiments using both synthetic and real-world datasets.