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This might be a naive question from a non-statistician but here we go. I understand that the challenges that hamper the use multivariate variational encoder where a covariance matrix is used instead of the a vector of standard deviation revolves around the increased number of parameters, lack of assurance of differentiability, and ensuring positive definiteness of the covariance matrix as explained Variational Autoencoder and Covariance Matrix. However, couldn't a kernel/covariance function be parameterized using outputs of a deep learning model to overcome at least the differentiability and positive difiniteness issues? Why/why not?

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