Resampling Base Distributions of Normalizing Flows

TL;DR

This paper introduces a novel base distribution for normalizing flows using learned rejection sampling, enabling modeling of complex distributions while maintaining invertibility and tractability.

Contribution

It proposes a new approach to enhance normalizing flows with learned rejection sampling, preserving invertibility and enabling modeling of complex distributions.

Findings

Method is competitive with existing approaches.

Effective in approximating 2D densities and tabular data.

Outperforms baselines in image generation and Boltzmann distribution modeling.

Abstract

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.