# Training Wasserstein GANs without gradient penalties

arXiv: https://arxiv.org/abs/2110.14150 · HTML: https://mlsanity.com/paper/2110.14150/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [On the regularization of Wasserstein GANs](https://mlsanity.com/paper/1709.08894/) (2017)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect](https://mlsanity.com/paper/1803.01541/) (2018)
- [AdaGAN: Boosting Generative Models](https://mlsanity.com/paper/1701.02386/) (2017)
- [Approximation and Convergence Properties of Generative Adversarial Learning](https://mlsanity.com/paper/1705.08991/) (2017)
- [Approximability of Discriminators Implies Diversity in GANs](https://mlsanity.com/paper/1806.10586/) (2018)
- [How Well Do WGANs Estimate the Wasserstein Metric?](https://mlsanity.com/paper/1910.03875/) (2019)
- [A fast approach to optimal transport: The back-and-forth method](https://mlsanity.com/paper/1905.12154/) (2019)

## Built on by (most cited first, 3 of 3)

- [Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?](https://mlsanity.com/paper/2206.07767/) (2022)
- [SequenceMatch: Imitation Learning for Autoregressive Sequence Modelling with Backtracking](https://mlsanity.com/paper/2306.05426/) (2023)
- [Cyclegan Network for Sheet Metal Welding Drawing Translation](https://mlsanity.com/paper/2209.14106/) (2022)

## Abstract (arXiv)

We propose a stable method to train Wasserstein generative adversarial networks. In order to enhance stability, we consider two objective functions using the c-transform based on Kantorovich duality which arises in the theory of optimal transport. We experimentally show that this algorithm can effectively enforce the Lipschitz constraint on the discriminator while other standard methods fail to do so. As a consequence, our method yields an accurate estimation for the optimal discriminator and also for the Wasserstein distance between the true distribution and the generated one. Our method requires no gradient penalties nor corresponding hyperparameter tuning and is computationally more efficient than other methods. At the same time, it yields competitive generators of synthetic images based on the MNIST, F-MNIST, and CIFAR-10 datasets.