# Statistical guarantees for generative models without domination

arXiv: https://arxiv.org/abs/2010.09237 · HTML: https://mlsanity.com/paper/2010.09237/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 27 of 27)

- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [An error analysis of generative adversarial networks for learning distributions](https://mlsanity.com/paper/2105.13010/) (2021)
- [MAUVE Scores for Generative Models: Theory and Practice](https://mlsanity.com/paper/2212.14578/) (2022)
- [Intrinsic Dimension Estimation Using Wasserstein Distances](https://mlsanity.com/paper/2106.04018/) (2021)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theory](https://mlsanity.com/paper/2310.04935/) (2023)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)
- [PAC-Bayesian Generalization Bounds for Adversarial Generative Models](https://mlsanity.com/paper/2302.08942/) (2023)
- [On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds](https://mlsanity.com/paper/2302.13183/) (2023)
- [A likelihood approach to nonparametric estimation of a singular distribution using deep generative models](https://mlsanity.com/paper/2105.04046/) (2021)
- [On the minimax optimality of Flow Matching through the connection to kernel density estimation](https://mlsanity.com/paper/2504.13336/) (2025)
- [Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs](https://mlsanity.com/paper/2201.07206/) (2022)
- [Statistical guarantees for denoising reflected diffusion models](https://mlsanity.com/paper/2411.01563/) (2024)
- [Distribution estimation via Flow Matching with Lipschitz guarantees](https://mlsanity.com/paper/2509.02337/) (2025)
- [A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2402.15710/) (2024)
- [Deep Generative Models: Complexity, Dimensionality, and Approximation](https://mlsanity.com/paper/2504.00820/) (2025)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Optimal 1-Wasserstein Distance for WGANs](https://mlsanity.com/paper/2201.02824/) (2022)
- [Learning Polynomial Transformations](https://mlsanity.com/paper/2204.04209/) (2022)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [A Wasserstein perspective of Vanilla GANs](https://mlsanity.com/paper/2403.15312/) (2024)
- [Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks](https://mlsanity.com/paper/2512.23643/) (2025)
- [GREAT Score: Global Robustness Evaluation of Adversarial Perturbation using Generative Models](https://mlsanity.com/paper/2304.09875/) (2023)
- [Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Training](https://mlsanity.com/paper/2305.07613/) (2023)
- [Generative adversarial learning with optimal input dimension and its adaptive generator architecture](https://mlsanity.com/paper/2405.03723/) (2024)
- [Model-free filtering in high dimensions via projection and score-based diffusions](https://mlsanity.com/paper/2510.23197/) (2025)

## Abstract (arXiv)

In this paper, we introduce a convenient framework for studying (adversarial) generative models from a statistical perspective. It consists in modeling the generative device as a smooth transformation of the unit hypercube of a dimension that is much smaller than that of the ambient space and measuring the quality of the generative model by means of an integral probability metric. In the particular case of integral probability metric defined through a smoothness class, we establish a risk bound quantifying the role of various parameters. In particular, it clearly shows the impact of dimension reduction on the error of the generative model.