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. Numerical experiments show that our method outperforms others on synthetic datasets, including examples with manifold structure.

翻译：我们提出了一种新型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朗之万扩散过程的生成器，从而学习潜在的数据生成流形。另一方面，LAWGD能够在给定合适核函数选择的情况下实现从目标分布的高效采样——该核函数通过扩散映射计算得到的生成器谱近似来构造。数值实验表明，我们的方法在合成数据集上优于其他方法，包括具有流形结构的示例。