  Generative Adversarial Nets (GANs) are very successful at modeling
distributions from given samples, even in the high-dimensional case. However,
their formulation is also known to be hard to optimize and often not stable.
While this is particularly true for early GAN formulations, there has been
significant empirically motivated and theoretically founded progress to improve
stability, for instance, by using the Wasserstein distance rather than the
Jenson-Shannon divergence. Here, we consider an alternative formulation for
generative modeling based on random projections which, in its simplest form,
results in a single objective rather than a saddle-point formulation. By
augmenting this approach with a discriminator we improve its accuracy. We found
our approach to be significantly more stable compared to even the improved
Wasserstein GAN. Further, unlike the traditional GAN loss, the loss formulated
in our method is a good measure of the actual distance between the
distributions and, for the first time for GAN training, we are able to show
estimates for the same.
