Improving Variational Inference with Inverse Autoregressive Flow
Authors: Diederik P. Kingma, Tim Salimans, Max Welling

Abstract: We propose a simple and practical method for improving the flexibility of the approximate posterior in variational auto-encoders (VAEs) through a transformation with autoregressive networks.

Autoregressive networks, such as RNNs and RNADE networks, are very powerful models. However, their sequential nature makes them impractical for direct use with VAEs, as sequentially sampling the latent variables is slow when implemented on a GPU. Fortunately, we find that by inverting autoregressive networks we can obtain equally powerful data transformations that can be computed in parallel. We call these data transformations inverse autoregressive flows (IAF), and we show that they can be used to transform a simple distribution over the latent variables into a much more flexible distribution, while still allowing us to compute the resulting variables' probability density function. The method is computationally cheap, can be made arbitrarily flexible, and (in contrast with previous work) is naturally applicable to latent variables that are organized in multidimensional tensors, such as 2D grids or time series.

The method is applied to a novel deep architecture of variational auto-encoders. In experiments we demonstrate that autoregressive flow leads to significant performance gains when applied to variational autoencoders for natural images.