Normalizing Flows for Probabilistic Modeling and Inference

TL;DR

This paper reviews normalizing flows, a flexible probabilistic modeling technique, emphasizing their design principles, expressive capabilities, and applications in generative modeling, inference, and supervised learning.

Contribution

It provides a unified perspective on normalizing flows, discussing their foundational principles, design trade-offs, and broad applications in probabilistic modeling.

Findings

Normalizing flows are versatile for modeling complex distributions.

Design choices impact expressive power and computational efficiency.

Flows are effective for generative modeling and inference tasks.

Abstract

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.