# Testing the boundaries: Normalizing Flows for higher dimensional data sets

arXiv: https://arxiv.org/abs/2202.09188 · HTML: https://mlsanity.com/paper/2202.09188/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 4 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 2 of 2)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)

## Built on by (most cited first, 7 of 7)

- [Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences](https://mlsanity.com/paper/2409.16336/) (2024)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [Learning to Validate Generative Models: a Goodness-of-Fit Approach](https://mlsanity.com/paper/2511.09118/) (2025)
- [Simulation-based Inference with the Generalized Kullback-Leibler Divergence](https://mlsanity.com/paper/2310.01808/) (2023)
- [FlowCon: Out-of-Distribution Detection using Flow-Based Contrastive Learning](https://mlsanity.com/paper/2407.03489/) (2024)
- [Mono-Z Dark Matter Search with Neural Spline Flows Using CMS Run 2015D Open Data](https://mlsanity.com/paper/2607.13771/) (2026)
- [A Variational Framework for Improving Naturalness in Generative Spoken Language Models](https://mlsanity.com/paper/2506.14767/) (2025)

## Abstract (arXiv)

Normalizing Flows (NFs) are emerging as a powerful class of generative models, as they not only allow for efficient sampling, but also deliver, by construction, density estimation. They are of great potential usage in High Energy Physics (HEP), where complex high dimensional data and probability distributions are everyday's meal. However, in order to fully leverage the potential of NFs it is crucial to explore their robustness as data dimensionality increases. Thus, in this contribution, we discuss the performances of some of the most popular types of NFs on the market, on some toy data sets with increasing number of dimensions.