mlsanityData to 7 Oct 2026

Optimal 1-Wasserstein Distance for WGANs

arXiv 2201.02824 ↗First posted 8 Jan 2022stat.ML cs.LG math.STcited by 3

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Abstract (arXiv)

The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a thorough analysis of Wasserstein GANs (WGANs) in both the finite sample and asymptotic regimes. We study the specific case where the latent space is univariate and derive results valid regardless of the dimension of the output space. We show in particular that for a fixed sample size, the optimal WGANs are closely linked with connected paths minimizing the sum of the squared Euclidean distances between the sample points. We also highlight the fact that WGANs are able to approach (for the 1-Wasserstein distance) the target distribution as the sample size tends to infinity, at a given convergence rate and provided the family of generative Lipschitz functions grows appropriately. We derive in passing new results on optimal transport theory in the semi-discrete setting.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 20 of its 46 references that are in the map. First posted on arXiv 8 Jan 2022.

Builds on

20 of 46 references.

References · 20

  1. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
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  5. 2018Which Training Methods for GANs do actually Converge?cited by 672
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  12. 2020Towards GAN Benchmarks Which Require Generalizationcited by 31
8 more
  1. 2020Some Theoretical Insights into Wasserstein GANscited by 28
  2. 2020Statistical guarantees for generative models without dominationcited by 27
  3. 2018Nonparametric Density Estimation under Adversarial Lossescited by 26
  4. 2020Learning disconnected manifolds: a no GANs landcited by 25
  5. 2019Lipschitz Generative Adversarial Netscited by 24
  6. 2019Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Lossescited by 22
  7. 2020Generalization Properties of Optimal Transport GANs with Latent Distribution Learningcited by 13
  8. 2021Reversible Gromov-Monge Sampler for Simulation-Based Inferencecited by 10

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 2.

3 papers.

  1. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  2. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  3. 2024Active Learning for Regression based on Wasserstein distance and GroupSort Neural Networkscited by 0