# GAN and VAE from an Optimal Transport Point of View

arXiv: https://arxiv.org/abs/1706.01807 · HTML: https://mlsanity.com/paper/1706.01807/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2017.

## Built on by (most cited first, 20 of 20)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [A mean-field games laboratory for generative modeling](https://mlsanity.com/paper/2304.13534/) (2023)
- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Sliced Optimal Partial Transport](https://mlsanity.com/paper/2212.08049/) (2022)
- [Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?](https://mlsanity.com/paper/2206.07767/) (2022)
- [A survey on GANs for computer vision: Recent research, analysis and taxonomy](https://mlsanity.com/paper/2203.11242/) (2022)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Linear Optimal Partial Transport Embedding](https://mlsanity.com/paper/2302.03232/) (2023)
- [One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models](https://mlsanity.com/paper/2305.18900/) (2023)
- [Differentially Private Gradient Flow based on the Sliced Wasserstein Distance](https://mlsanity.com/paper/2312.08227/) (2023)
- [Bi-Discriminator Class-Conditional Tabular GAN](https://mlsanity.com/paper/2111.06549/) (2021)
- [Challenges in creative generative models for music: a divergence maximization perspective](https://mlsanity.com/paper/2211.08856/) (2022)
- [A Sinkhorn-type Algorithm for Constrained Optimal Transport](https://mlsanity.com/paper/2403.05054/) (2024)
- [Model Uncertainty and Correctability for Directed Graphical Models](https://mlsanity.com/paper/2107.08179/) (2021)
- [A Unifying View of Variational Generative Wasserstein Flows](https://mlsanity.com/paper/2605.31369/) (2026)
- [Robustness-via-Synthesis: Robust Training with Generative Adversarial Perturbations](https://mlsanity.com/paper/2108.09713/) (2021)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [On Certified Generalization in Structured Prediction](https://mlsanity.com/paper/2306.09112/) (2023)
- [Unfolding with a Wasserstein Loss](https://mlsanity.com/paper/2603.20903/) (2026)

## Abstract (arXiv)

This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup. This sheds some lights on the connexions between Variational Autoencoders (VAE), Generative Adversarial Networks (GAN) and Minimum Kantorovitch Estimators (MKE).