Poster
in
Workshop: Structured Probabilistic Inference and Generative Modeling
Diffusion map particle systems for generative modeling
Fengyi Li · Youssef Marzouk
Keywords: [ diffusion maps ] [ sampling ] [ gradient flows ] [ Kernel Methods ] [ generative modeling ]
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.