mlsanityData to 13 Oct 2026

The Expressive Power of a Class of Normalizing Flow Models

arXiv 2006.00392 ↗First posted 31 May 2020cs.LG stat.MLcited by 35

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Abstract (arXiv)

Normalizing flows have received a great deal of recent attention as they allow flexible generative modeling as well as easy likelihood computation. While a wide variety of flow models have been proposed, there is little formal understanding of the representation power of these models. In this work, we study some basic normalizing flows and rigorously establish bounds on their expressive power. Our results indicate that while these flows are highly expressive in one dimension, in higher dimensions their representation power may be limited, especially when the flows have moderate depth.

Key facts. Cited by 35 papers in the map (data through 13 Oct 2026). First posted on arXiv 31 May 2020.

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Citing papers per year: 2021: 13; 2022: 7; 2023: 7; 2024: 3; 2025: 2; 2026: 3.

35 papers.

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  1. 2021Score-based Generative Modeling in Latent Spacecited by 635
  2. 2021Riemannian Convex Potential Mapscited by 17
  3. 2021Ab-initio study of interacting fermions at finite temperature with neural canonical transformationcited by 16
  4. 2021On the expressivity of bi-Lipschitz normalizing flowscited by 16
  5. 2021Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Ratescited by 16
  6. 2022Flow-based Recurrent Belief State Learning for POMDPscited by 16
  7. 2021Sparse Flows: Pruning Continuous-depth Modelscited by 13
  8. 2022Gradual Domain Adaptation via Normalizing Flowscited by 11
  9. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  10. 2021Jacobian Determinant of Normalizing Flowscited by 8
  11. 2021Universal Approximation of Residual Flows in Maximum Mean Discrepancycited by 7
  12. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
23 more
  1. 2023Embracing the chaos: analysis and diagnosis of numerical instability in variational flowscited by 6
  2. 2021Unsupervised tree boosting for learning probability distributionscited by 5
  3. 2022Maximum Likelihood Learning of Unnormalized Models for Simulation-Based Inferencecited by 5
  4. 2021Approximation capabilities of measure-preserving neural networkscited by 4
  5. 2022AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximationcited by 3
  6. 2023Simulation-based Inference with the Generalized Kullback-Leibler Divergencecited by 3
  7. 2023Energy-Calibrated VAE with Test Time Free Lunchcited by 3
  8. 2022Universality of parametric Coupling Flows over parametric diffeomorphismscited by 2
  9. 2022Learning to Bound: A Generative Cram'er-Rao Boundcited by 2
  10. 2023Learning to Generate All Feasible Actionscited by 2
  11. 2023Mixed Variational Flows for Discrete Variablescited by 2
  12. 2021Generalization of the Change of Variables Formula with Applications to Residual Flowscited by 1
  13. 2021Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regressioncited by 1
  14. 2021ELF: Exact-Lipschitz Based Universal Density Approximator Flowcited by 1
  15. 2022Variational Monte Carlo Approach to Partial Differential Equations with Neural Networkscited by 1
  16. 2023Posterior Consistency for Missing Data in Variational Autoencoderscited by 1
  17. 2023On the Quantification of Image Reconstruction Uncertainty without Training Datacited by 1
  18. 2024Probabilistic Forecasting of Irregular Time Series via Conditional Flowscited by 1
  19. 2024Design of Restricted Normalizing Flow towards Arbitrary Stochastic Policy with Computational Efficiencycited by 1
  20. 2025Asymptotically exact variational flows via involutive MCMC kernelscited by 1
  21. 2026Robust Conditional Conformal Prediction via Branched Normalizing Flowcited by 0
  22. 2026Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspectivecited by 0
  23. 2026Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problemscited by 0