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.
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