# On the estimation of the Wasserstein distance in generative models

arXiv: https://arxiv.org/abs/1910.00888 · HTML: https://mlsanity.com/paper/1910.00888/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?](https://mlsanity.com/paper/2206.07767/) (2022)
- [Wasserstein GANs with Gradient Penalty Compute Congested Transport](https://mlsanity.com/paper/2109.00528/) (2021)
- [SurvCaus : Representation Balancing for Survival Causal Inference](https://mlsanity.com/paper/2203.15672/) (2022)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent improvement in GAN literature is to use the Wasserstein distance as loss function leading to Wasserstein Generative Adversarial Networks (WGANs). Using this as a basis, we show various ways in which the Wasserstein distance is estimated for the task of generative modelling. Additionally, the secrets in training such models are shown and summarized at the end of this work. Where applicable, we extend current works to different algorithms, different cost functions, and different regularization schemes to improve generative models.