# Generalization Properties of Optimal Transport GANs with Latent Distribution Learning

arXiv: https://arxiv.org/abs/2007.14641 · HTML: https://mlsanity.com/paper/2007.14641/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2020.

## Built on by (most cited first, 13 of 13)

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- [Understanding Entropic Regularization in GANs](https://mlsanity.com/paper/2111.01387/) (2021)
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- [Optimal 1-Wasserstein Distance for WGANs](https://mlsanity.com/paper/2201.02824/) (2022)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [Quantum latent distributions in deep generative models](https://mlsanity.com/paper/2508.19857/) (2025)
- [Training generative models from privatized data](https://mlsanity.com/paper/2306.09547/) (2023)
- [Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithm](https://mlsanity.com/paper/2207.12242/) (2022)

## Abstract (arXiv)

The Generative Adversarial Networks (GAN) framework is a well-established paradigm for probability matching and realistic sample generation. While recent attention has been devoted to studying the theoretical properties of such models, a full theoretical understanding of the main building blocks is still missing. Focusing on generative models with Optimal Transport metrics as discriminators, in this work we study how the interplay between the latent distribution and the complexity of the pushforward map (generator) affects performance, from both statistical and modelling perspectives. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm. We prove that this can lead to significant advantages in terms of sample complexity.