# Normalizing Flows for Probabilistic Modeling and Inference

**Authors:** George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, Balaji Lakshminarayanan  
**arXiv:** [1912.02762](https://arxiv.org/abs/1912.02762)  
**Date:** 2019-12-05  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1912.02762v2/

## Key points

- Normalizing flows are a powerful mechanism for defining expressive probability distributions
- By specifying a base distribution and a series of bijective transformations, they offer a flexible framework with significant advancements in recent years
- The authors argue that the field has reached a level of maturity requiring a unified perspective to consolidate developments and applications
- The review explores flow design principles, emphasizing topics such as modeling complex distributions and probability transformations
- Normalizing flows can be utilized for tasks like generative modeling, approximate inference, and supervised learning

## Summary

In their review article "Normalizing Flows for Probabilistic Modeling and Inference," authors George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan delve into the concept of normalizing flows as a powerful mechanism for defining expressive probability distributions. By specifying a base distribution and a series of bijective transformations,  offer a flexible framework that has seen significant advancements in recent years. The authors argue that the field of  has reached a level of maturity where a unified perspective is needed to consolidate the various developments and applications. Through the lens of  and inference, the authors provide an in-depth exploration of flow design principles, emphasizing topics such as  and . They also expand on the conceptual framing of flows by connecting them to broader probability transformations, highlighting their versatility in modeling complex distributions. Furthermore, the review summarizes how normalizing flows can be utilized for tasks like generative modeling, approximate inference, and supervised learning. Published in the Journal of Machine Learning Research (Volume 22, Issue 57), this comprehensive review offers insights into the fundamental principles underlying normalizing flows and their implications for  and inference. With a focus on both theoretical foundations and practical applications, this work contributes to advancing our understanding of this versatile approach to defining probability distributions.