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This\napproximation is clearly limited as demonstrated by observing a residual image\nfrom a VAE reconstruction, which often possess a high level of structure. This\npaper demonstrates a novel scheme to incorporate a structured Gaussian\nlikelihood prediction network within the VAE that allows the residual\ncorrelations to be modeled. Our novel architecture, with minimal increase in\ncomplexity, incorporates the covariance matrix prediction within the VAE. We\nalso propose a new mechanism for allowing structured uncertainty on color\nimages. 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