  We investigate the properties of multidimensional probability distributions
in the context of latent space prior distributions of implicit generative
models. Our work revolves around the phenomena arising while decoding linear
interpolations between two random latent vectors -- regions of latent space in
close proximity to the origin of the space are sampled causing distribution
mismatch. We show that due to the Central Limit Theorem, this region is almost
never sampled during the training process. As a result, linear interpolations
may generate unrealistic data and their usage as a tool to check quality of the
trained model is questionable. We propose to use multidimensional Cauchy
distribution as the latent prior. Cauchy distribution does not satisfy the
assumptions of the CLT and has a number of properties that allow it to work
well in conjunction with linear interpolations. We also provide two general
methods of creating non-linear interpolations that are easily applicable to a
large family of common latent distributions. Finally we empirically analyze the
quality of data generated from low-probability-mass regions for the DCGAN model
on the CelebA dataset.
