  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.
