Diffusion map particle systems for generative modeling
This work addresses generative modeling for data analysis, offering a method with minimal tuning, but it appears incremental as it builds on existing techniques like diffusion maps and LAWGD.
The authors tackled generative modeling by proposing a diffusion map particle system (DMPS) that combines diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD) to learn data manifolds and sample efficiently without offline training, achieving performance that can outperform other methods on moderate-dimensional datasets.
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.