  Despite the growing interest in generative adversarial networks (GANs),
training GANs remains a challenging problem, both from a theoretical and a
practical standpoint. To address this challenge, in this paper, we propose a
novel way to exploit the unique geometry of the real data, especially the
manifold information. More specifically, we design a method to regularize GAN
training by adding an additional regularization term referred to as manifold
regularizer. The manifold regularizer forces the generator to respect the
unique geometry of the real data manifold and generate high quality data.
Furthermore, we theoretically prove that the addition of this regularization
term in any class of GANs including DCGAN and Wasserstein GAN leads to improved
performance in terms of generalization, existence of equilibrium, and
stability. Preliminary experiments show that the proposed manifold
regularization helps in avoiding mode collapse and leads to stable training.
