Diffusion map particle systems for generative modeling

Fengyi Li; Youssef Marzouk

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arXiv · 2304.00200

Diffusion map particle systems for generative modeling

Fengyi Li·Youssef Marzouk

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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 corresponding 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.

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Fengyi Li, Youssef Marzouk. 2023-04-01. Diffusion map particle systems for generative modeling. https://arxiv.org/abs/2304.00200

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