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.

翻译：我们提出了一种新颖的扩散映射粒子系统（DMPS）用于生成建模，该方法基于扩散映射和拉普拉斯调整的Wasserstein梯度下降（LAWGD）。扩散映射用于从样本中近似相应朗之万扩散过程的生成器，从而学习底层数据生成流形。另一方面，在给定合适核函数选择的情况下，LAWGD能够高效地从目标分布中采样——我们通过扩散映射计算生成器的谱近似来构造该核函数。本方法无需离线训练且参数调整极少，在中等维度数据集上可优于其他方法。