An Empirical Comparison of GANs and Normalizing Flows for Density Estimation

TL;DR

This paper compares GANs and normalizing flows for density estimation on low-dimensional data, finding that normalizing flows outperform GANs, especially WGAN, which struggles with accurate density modeling.

Contribution

The study provides an empirical comparison highlighting the limitations of GANs and the strengths of normalizing flows for density estimation on simple datasets.

Findings

Normalizing flows outperform GANs in low-dimensional density estimation.

WGAN struggles with accurate density modeling despite targeting Wasserstein distance.

GANs are less suitable for general-purpose statistical modeling based on these results.

Abstract

Generative adversarial networks (GANs) and normalizing flows are both approaches to density estimation that use deep neural networks to transform samples from an uninformative prior distribution to an approximation of the data distribution. There is great interest in both for general-purpose statistical modeling, but the two approaches have seldom been compared to each other for modeling non-image data. The difficulty of computing likelihoods with GANs, which are implicit models, makes conducting such a comparison challenging. We work around this difficulty by considering several low-dimensional synthetic datasets. An extensive grid search over GAN architectures, hyperparameters, and training procedures suggests that no GAN is capable of modeling our simple low-dimensional data well, a task we view as a prerequisite for an approach to be considered suitable for general-purpose statistical modeling. Several normalizing flows, on the other hand, excelled at these tasks, even substantially outperforming WGAN in terms of Wasserstein distance -- the metric that WGAN alone targets. Scientists and other practitioners should be wary of relying on WGAN for applications that require accurate density estimation.