Learnable Explicit Density for Continuous Latent Space and Variational Inference

TL;DR

This paper introduces a learnable explicit density approach for continuous latent spaces in VAEs, enhancing prior flexibility and posterior approximation, leading to improved generative and inference capabilities.

Contribution

It proposes a unified method for parameterizing VAEs with flexible priors and improved posterior approximation using inverse autoregressive flows.

Findings

Flexible priors benefit sample generation and inference.

Inverse AF can approximate complex posteriors universally.

Unified approach removes factorial Gaussian restriction.

Abstract

In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and inference. Second, we analyze the family of inverse autoregressive flows (inverse AF) and show that with further improvement, inverse AF could be used as universal approximation to any complicated posterior. Our analysis results in a unified approach to parameterizing a VAE, without the need to restrict ourselves to use factorial Gaussians in the latent real space.