  Learning high-dimensional distributions is an important yet challenging
problem in machine learning with applications in various domains. In this
paper, we introduce new techniques to formulate the problem as solving
Fokker-Planck equation in a lower-dimensional latent space, aiming to mitigate
challenges in high-dimensional data space. Our proposed model consists of
latent-distribution morphing, a generator and a parameterized Fokker-Planck
kernel function. One fascinating property of our model is that it can be
trained with arbitrary steps of latent distribution morphing or even without
morphing, which makes it flexible and as efficient as Generative Adversarial
Networks (GANs). Furthermore, this property also makes our latent-distribution
morphing an efficient plug-and-play scheme, thus can be used to improve
arbitrary GANs, and more interestingly, can effectively correct failure cases
of the GAN models. Extensive experiments illustrate the advantages of our
proposed method over existing models.
