# The Expressive Power of a Class of Normalizing Flow Models

arXiv: https://arxiv.org/abs/2006.00392 · HTML: https://mlsanity.com/paper/2006.00392/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2020.

## Built on by (most cited first, 30 of 35)

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- [ELF: Exact-Lipschitz Based Universal Density Approximator Flow](https://mlsanity.com/paper/2112.06997/) (2021)
- [Variational Monte Carlo Approach to Partial Differential Equations with Neural Networks](https://mlsanity.com/paper/2206.01927/) (2022)
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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.