mlsanityData to 7 Oct 2026

Statistical guarantees for generative models without domination

arXiv 2010.09237 ↗First posted 19 Oct 2020math.ST stat.ML stat.THcited by 27

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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.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Oct 2020.

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Citing papers per year: 2021: 5; 2022: 5; 2023: 6; 2024: 6; 2025: 5.

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  1. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  2. 2021An error analysis of generative adversarial networks for learning distributionscited by 35
  3. 2022MAUVE Scores for Generative Models: Theory and Practicecited by 34
  4. 2021Intrinsic Dimension Estimation Using Wasserstein Distancescited by 20
  5. 2022On PAC-Bayesian reconstruction guarantees for VAEscited by 20
  6. 2024A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Modelscited by 20
  7. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16
  8. 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
  9. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  10. 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative modelscited by 12
  11. 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 12
  12. 2025On the minimax optimality of Flow Matching through the connection to kernel density estimationcited by 9
15 more
  1. 2022Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANscited by 6
  2. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  3. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 5
  4. 2025Deep Generative Models: Complexity, Dimensionality, and Approximationcited by 4
  5. 2021Statistical inference for generative adversarial networks and other minimax problemscited by 3
  6. 2022Optimal 1-Wasserstein Distance for WGANscited by 3
  7. 2022Learning Polynomial Transformationscited by 3
  8. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  9. 2024A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Datacited by 3
  10. 2024A Wasserstein perspective of Vanilla GANscited by 3
  11. 2025Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networkscited by 3
  12. 2023GREAT Score: Global Robustness Evaluation of Adversarial Perturbation using Generative Modelscited by 2
  13. 2023Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Trainingcited by 2
  14. 2024Generative adversarial learning with optimal input dimension and its adaptive generator architecturecited by 1
  15. 2025Model-free filtering in high dimensions via projection and score-based diffusionscited by 0