Enhancing the accuracy of Generative Adversarial Networks with Fokker-Planck Equations

Ben Wan, Tianyi Zheng, Zhaoyu Chen, Jia Wang

Abstract: GANs have the advantage of much less computation cost and high-quality generative capabilities but occasionally encounter mode collapse. Previous works address the problems more from the perspective of the game between the generator and the discriminator, ignoring the accuracy of generator distribution learning, which is the key target of the generator. Fokker–Planck Equation (FPE) is a powerful tool to overcome above shortcomings as it is Wasserstein gradient flow (WGF) of the given function in probability space. In this paper, we propose a new scheme using FPE in the training process of GAN. Specifically, learning real distribution of the generator in a GAN is replaced by solving a specific FPE since both describe the evolution of a probability distribution. GAN applied with FPE converges faster and mitigates mode collapse because the optimization direction is along the WGF of given loss. We pull it back to parameter space for convenience of solving and develop a error-bounded numerical method to solve FPE, ensuring generative distribution closer to the real enough even in high-dimensional manifold. Applying our approach achieve competitive performance compared to the vanilla across multiple popular datasets. Furthermore, we apply FPE-based method to style transfer and demonstrate the generalization of our approach on various image generation tasks.