  Variational auto-encoders (VAEs) are a popular and powerful deep generative
model. Previous works on VAEs have assumed a factorized likelihood model,
whereby the output uncertainty of each pixel is assumed to be independent. This
approximation is clearly limited as demonstrated by observing a residual image
from a VAE reconstruction, which often possess a high level of structure. This
paper demonstrates a novel scheme to incorporate a structured Gaussian
likelihood prediction network within the VAE that allows the residual
correlations to be modeled. Our novel architecture, with minimal increase in
complexity, incorporates the covariance matrix prediction within the VAE. We
also propose a new mechanism for allowing structured uncertainty on color
images. Furthermore, we provide a scheme for effectively training this model,
and include some suggestions for improving performance in terms of efficiency
or modeling longer range correlations.
