  This paper addresses the mode collapse for generative adversarial networks
(GANs). We view modes as a geometric structure of data distribution in a metric
space. Under this geometric lens, we embed subsamples of the dataset from an
arbitrary metric space into the l2 space, while preserving their pairwise
distance distribution. Not only does this metric embedding determine the
dimensionality of the latent space automatically, it also enables us to
construct a mixture of Gaussians to draw latent space random vectors. We use
the Gaussian mixture model in tandem with a simple augmentation of the
objective function to train GANs. Every major step of our method is supported
by theoretical analysis, and our experiments on real and synthetic data confirm
that the generator is able to produce samples spreading over most of the modes
while avoiding unwanted samples, outperforming several recent GAN variants on a
number of metrics and offering new features.
