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Generative models produce realistic objects in many domains, including text,image, video, and audio synthesis. Most popular models---Generative AdversarialNetworks (GANs) and Variational Autoencoders (VAEs)---usually employ a standardGaussian distribution as a prior. Previous works show that the richer family ofprior distributions may help to avoid the mode collapse problem in GANs and toimprove the evidence lower bound in VAEs. We propose a new family of priordistributions---Tensor Ring Induced Prior (TRIP)---that packs an exponentialnumber of Gaussians into a high-dimensional lattice with a relatively smallnumber of parameters. We show that these priors improve Fr\'echet InceptionDistance for GANs and Evidence Lower Bound for VAEs. We also study generativemodels with TRIP in the conditional generation setup with missing conditions.Altogether, we propose a novel plug-and-play framework for generative modelsthat can be utilized in any GAN and VAE-like architectures.

A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models