2019/03/04 by Belinda Tzen, Maxim Raginsky, Tzen, Belinda +1 · 10 citations
Computer Science · Physics and Astronomy · #Generative Adversarial Networks and Image Synthesis #Neural Networks and Applications #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1903.01608
We introduce and study a class of probabilistic generative models, where the\nlatent object is a finite-dimensional diffusion process on a finite time\ninterval and the observed variable is drawn conditionally on the terminal point\nof the diffusion. We make the following contributions:\n We provide a unified viewpoint on both sampling and variational inference in\nsuch generative models through the lens of stochastic control.\n We quantify the expressiveness of diffusion-based generative models.\nSpecifically, we show that one can efficiently sample from a wide class of\nterminal target distributions by choosing the drift of the latent diffusion\nfrom the class of multilayer feedforward neural nets, with the accuracy of\nsampling measured by the Kullback-Leibler divergence to the target\ndistribution.\n Finally, we present and analyze a scheme for unbiased simulation of\ngenerative models with latent diffusions and provide bounds on the variance of\nthe resulting estimators. This scheme can be implemented as a deep generative\nmodel with a random number of layers.\n