Importance Corrected Neural JKO Sampling

TL;DR

This paper introduces a novel sampling method combining continuous normalizing flows with importance-based rejection-resampling, achieving accurate high-dimensional multimodal distribution sampling and outperforming existing methods.

Contribution

It develops an importance-corrected neural JKO sampling approach that converges to Wasserstein gradient flows and overcomes limitations of classical rejection schemes.

Findings

Accurately samples from high-dimensional multimodal distributions.

Outperforms state-of-the-art sampling methods in various tests.

Generates iid samples and evaluates underlying densities effectively.

Abstract

In order to sample from an unnormalized probability density function, we propose to combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. We relate the iterative training of CNFs with regularized velocity fields to a JKO scheme and prove convergence of the involved velocity fields to the velocity field of the Wasserstein gradient flow (WGF). The alternation of local flow steps and non-local rejection-resampling steps allows to overcome local minima or slow convergence of the WGF for multimodal distributions. Since the proposal of the rejection step is generated by the model itself, they do not suffer from common drawbacks of classical rejection schemes. The arising model can be trained iteratively, reduces the reverse Kullback-Leibler (KL) loss function in each step, allows to generate iid samples and moreover allows for evaluations of the generated underlying density. Numerical examples show that our method yields accurate results on various test distributions including high-dimensional multimodal targets and outperforms the state of the art in almost all cases significantly.