mlsanityData to 7 Oct 2026

Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)

arXiv 2103.01678 ↗First posted 2 Mar 2021stat.ML cs.LGcited by 33

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Abstract (arXiv)

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training Wasserstein GANs. In this work, we gather both theoretical and empirical evidence that the WGAN loss is not a meaningful approximation of the Wasserstein distance. Moreover, we argue that the Wasserstein distance is not even a desirable loss function for deep generative models, and conclude that the success of Wasserstein GANs can in truth be attributed to a failure to approximate the Wasserstein distance.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 29 of its 50 references that are in the map. First posted on arXiv 2 Mar 2021.

Builds on

29 of 50 references.

References · 29

  1. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  2. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  5. 2017Improved Training of Wasserstein GANscited by 2,223
  6. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  7. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  8. 2017Deep Image Priorcited by 1,097
  9. 2016Least Squares Generative Adversarial Networkscited by 1,000
  10. 2018Computational Optimal Transportcited by 765
  11. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
  12. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
17 more
  1. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
  2. 2018Sorting out Lipschitz function approximationcited by 211
  3. 2017BEGAN: Boundary Equilibrium Generative Adversarial Networkscited by 121
  4. 2017The Cramer Distance as a Solution to Biased Wasserstein Gradientscited by 116
  5. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
  6. 2018Adversarial Regularizers in Inverse Problemscited by 102
  7. 2019Subspace Robust Wasserstein Distancescited by 89
  8. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  9. 2016Inductive Bias of Deep Convolutional Networks through Pooling Geometrycited by 53
  10. 2017Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Stepcited by 45
  11. 2017A Geometric View of Optimal Transportation and Generative Modelcited by 31
  12. 2019How Well Do WGANs Estimate the Wasserstein Metric?cited by 15
  13. 2019Implicit competitive regularization in GANscited by 14
  14. 2019A gradual, semi-discrete approach to generative network training via explicit Wasserstein minimizationcited by 12
  15. 2019(q,p)-Wasserstein GANs: Comparing Ground Metrics for Wasserstein GANscited by 10
  16. 2019On the estimation of the Wasserstein distance in generative modelscited by 6
  17. 2019Wasserstein GAN Can Perform PCAcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 4; 2023: 10; 2024: 5; 2025: 3; 2026: 2.

33 papers.

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  1. 2021An Introduction to Deep Generative Modelingcited by 104
  2. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 95
  3. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 74
  4. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  5. 2022UVCGAN: UNet Vision Transformer cycle-consistent GAN for unpaired image-to-image translationcited by 42
  6. 2021Adversarial Intrinsic Motivation for Reinforcement Learningcited by 40
  7. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  8. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  9. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  10. 2022Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?cited by 19
  11. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  12. 2023A survey and taxonomy of loss functions in machine learningcited by 15
21 more
  1. 2023Adversarial Score Distillation: When score distillation meets GANcited by 15
  2. 2021Wasserstein Patch Prior for Image Superresolutioncited by 13
  3. 2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
  4. 2023Imitation Learning from Observation through Optimal Transportcited by 7
  5. 2021Wasserstein GANs with Gradient Penalty Compute Congested Transportcited by 6
  6. 2023Offline Imitation from Observation via Primal Wasserstein State Occupancy Matchingcited by 5
  7. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  8. 2022Learning Polynomial Transformationscited by 3
  9. 2023Approximation Theory, Computing, and Deep Learning on the Wasserstein Spacecited by 3
  10. 2021Manifold-preserved GANscited by 2
  11. 2023Variational Diffusion Auto-encoder: Latent Space Extraction from Pre-trained Diffusion Modelscited by 2
  12. 2021Rethinking Multidimensional Discriminator Output for Generative Adversarial Networkscited by 1
  13. 2023Adversarial Reweighting Guided by Wasserstein Distance for Bias Mitigationcited by 1
  14. 2024Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Spacecited by 1
  15. 2024Deep Generative Quantile Bayescited by 1
  16. 2024Variational Neural Stochastic Differential Equations with Change Pointscited by 1
  17. 2023Insights into Closed-form IPM-GAN Discriminator Guidance for Diffusion Modelingcited by 0
  18. 2025NGGAN: Noise Generation GAN Based on the Practical Measurement Dataset for Narrowband Powerline Communicationscited by 0
  19. 2025COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networkscited by 0
  20. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  21. 2026Latent Wasserstein Adversarial Imitation Learningcited by 0