GAN and VAE from an Optimal Transport Point of View

TL;DR

This paper explores the theoretical connections between VAEs, GANs, and MKE using optimal transport concepts, providing insights into their underlying relationships.

Contribution

It offers a unified optimal transport framework that clarifies the links between VAEs, GANs, and MKE, building on previous foundational works.

Findings

Reveals connections between VAEs, GANs, and MKE

Provides a simplified setup for theoretical analysis

Highlights the role of optimal transport in generative models

Abstract

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).