Neural Autoregressive Flows

TL;DR

Neural Autoregressive Flows (NAF) unify and extend autoregressive models with neural networks, providing a more expressive and universal approach for density estimation and variational inference, outperforming previous methods.

Contribution

NAF introduces a general class of invertible neural transformations, enhancing expressivity and universality over prior affine-based autoregressive flows.

Findings

NAF achieves state-of-the-art density estimation results.

NAF outperforms IAF in variational autoencoders on MNIST.

NAF is a universal approximator for continuous distributions.

Abstract

Normalizing flows and autoregressive models have been successfully combined to produce state-of-the-art results in density estimation, via Masked Autoregressive Flows (MAF), and to accelerate state-of-the-art WaveNet-based speech synthesis to 20x faster than real-time, via Inverse Autoregressive Flows (IAF). We unify and generalize these approaches, replacing the (conditionally) affine univariate transformations of MAF/IAF with a more general class of invertible univariate transformations expressed as monotonic neural networks. We demonstrate that the proposed neural autoregressive flows (NAF) are universal approximators for continuous probability distributions, and their greater expressivity allows them to better capture multimodal target distributions. Experimentally, NAF yields state-of-the-art performance on a suite of density estimation tasks and outperforms IAF in variational autoencoders trained on binarized MNIST.