Generalization Properties of Optimal Transport GANs with Latent Distribution Learning
Not on the map. Why?
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.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jul 2020.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2021: 3; 2022: 4; 2023: 3; 2024: 0; 2025: 3.
13 papers.
Sort:
By area:
- 2022Identifiability of deep generative models without auxiliary informationcited by 70
- 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
- 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
- 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative modelscited by 12
- 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 12
- 2021Understanding Entropic Regularization in GANscited by 6
- 2025Deep Generative Models: Complexity, Dimensionality, and Approximationcited by 4
- 2025Training Latent Diffusion Models with Interacting Particle Algorithmscited by 4
- 2022Optimal 1-Wasserstein Distance for WGANscited by 3
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
- 2025Quantum latent distributions in deep generative modelscited by 3
- 2023Training generative models from privatized datacited by 1
- 2025Quantum latent distributions in deep generative models27 Aug 2025
- 2025Training Latent Diffusion Models with Interacting Particle Algorithms18 May 2025
- 2025Deep Generative Models: Complexity, Dimensionality, and Approximation1 Apr 2025
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution31 Jul 2023
- 2023Training generative models from privatized data15 Jun 2023
- 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds25 Feb 2023
- 2022Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithm7 Jul 2022
- 2022Can Push-forward Generative Models Fit Multimodal Distributions?29 Jun 2022
- 2022Identifiability of deep generative models without auxiliary information20 Jun 2022
- 2022Optimal 1-Wasserstein Distance for WGANs8 Jan 2022
- 2021Understanding Entropic Regularization in GANs2 Nov 2021
- 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative models9 May 2021
1 more
- 2022Identifiability of deep generative models without auxiliary informationcited by 70
- 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
- 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
- 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative modelscited by 12
- 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 12
- 2021Understanding Entropic Regularization in GANscited by 6
- 2025Deep Generative Models: Complexity, Dimensionality, and Approximationcited by 4
- 2022Optimal 1-Wasserstein Distance for WGANscited by 3
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
- 2025Quantum latent distributions in deep generative modelscited by 3
- 2023Training generative models from privatized datacited by 1
- 2022Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithmcited by 0
- 2025Quantum latent distributions in deep generative models27 Aug 2025
- 2025Deep Generative Models: Complexity, Dimensionality, and Approximation1 Apr 2025
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution31 Jul 2023
- 2023Training generative models from privatized data15 Jun 2023
- 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds25 Feb 2023
- 2022Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithm7 Jul 2022
- 2022Can Push-forward Generative Models Fit Multimodal Distributions?29 Jun 2022
- 2022Identifiability of deep generative models without auxiliary information20 Jun 2022
- 2022Optimal 1-Wasserstein Distance for WGANs8 Jan 2022
- 2021Understanding Entropic Regularization in GANs2 Nov 2021
- 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative models9 May 2021
- 2021Rates of convergence for density estimation with generative adversarial networks30 Jan 2021