Diffusion map particle systems for generative modeling

Fengyi Li, Youssef Marzouk

Keywords: diffusion maps, kernel methods, gradient flows, generative modeling, sampling

TL;DR: We propose a new nonparametric kernel-based approach to generative modeling, based on diffusion maps and an interacting particle system.

Abstract: We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the Langevin diffusion process from samples, and hence to learn the underlying data-generating manifold. On the other hand, LAWGD enables efficient sampling from the target distribution given a suitable choice of kernel, which we construct here via a spectral approximation of the generator, computed with diffusion maps. Our method requires no offline training and minimal tuning, and can outperform other approaches on data sets of moderate dimension.

Submission Number: 95