# Flows for Flows: Training Normalizing Flows Between Arbitrary Distributions with Maximum Likelihood Estimation

arXiv: https://arxiv.org/abs/2211.02487 · HTML: https://mlsanity.com/paper/2211.02487/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Simulation Assisted Likelihood-free Anomaly Detection](https://mlsanity.com/paper/2001.05001/) (2020)

## Built on by (most cited first, 5 of 5)

- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [CURTAINs Flows For Flows: Constructing Unobserved Regions with Maximum Likelihood Estimation](https://mlsanity.com/paper/2305.04646/) (2023)
- [Probabilistic and Semantic Descriptions of Image Manifolds and Their Applications](https://mlsanity.com/paper/2307.02881/) (2023)
- [Decorrelation using Optimal Transport](https://mlsanity.com/paper/2307.05187/) (2023)
- [Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transport](https://mlsanity.com/paper/2308.13815/) (2023)

## Abstract (arXiv)

Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps to be found between arbitrary distributions. We demonstrate and explore the utility of this approach and show it is particularly interesting in the case of conditional normalizing flows and for introducing optimal transport constraints on maps that are constructed using normalizing flows.