Mixture Density Generative Adversarial Networks

Generative Adversarial Networks have a surprising ability to generate sharp and realistic images, but they are known to suffer from the so-called mode collapse problem. In this paper, we propose a new GAN variant called Mixture Density GAN that overcomes this problem by encouraging the Discriminator to form clusters in its embedding space, which in turn leads the Generator to exploit these and discover different modes in the data. This is achieved by positioning Gaussian density functions in the corners of a simplex, using the resulting Gaussian mixture as a likelihood function over discriminator embeddings, and formulating an objective function for GAN training that is based on these likelihoods. We show how formation of these clusters changes the probability landscape of the discriminator and improves the mode discovery of the GAN. We also show that the optimum of our training objective is attained if and only if the generated and the real distribution match exactly. We support our theoretical results with empirical evaluations on three mode discovery benchmark datasets (Stacked-MNIST, Ring of Gaussians and Grid of Gaussians), and four image datasets (CIFAR-10, CelebA, MNIST, and Fashion-MNIST). Furthermore, we demonstrate (1) the ability to avoid mode collapse and discover all the modes and (2) superior quality of the generated images (as measured by the Fréchet Inception Distance (FID)), achieving the lowest FID compared to all baselines.