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We make a minimal, but very effective alteration to the VAE model. This isabout a drop-in replacement for the (sample-dependent) approximate posterior tochange it from the standard white Gaussian with diagonal covariance to thefirst-order autoregressive Gaussian. We argue that this is a more reasonablechoice to adopt for natural signals like images, as it does not force theexisting correlation in the data to disappear in the posterior. Moreover, itallows more freedom for the approximate posterior to match the true posterior.This allows for the repararametrization trick, as well as the KL-divergenceterm to still have closed-form expressions, obviating the need for itssample-based estimation. Although providing more freedom to adapt to correlateddistributions, our parametrization has even less number of parameters than thediagonal covariance, as it requires only two scalars, $\rho$ and $s$, tocharacterize correlation and scaling, respectively. As validated by theexperiments, our proposition noticeably and consistently improves the qualityof image generation in a plug-and-play manner, needing no further parametertuning, and across all setups. The code to reproduce our experiments isavailable at \url{https://github.com/sssohrab/rho_VAE/}.

$\rho$-VAE: Autoregressive parametrization of the VAE encoder