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In Bayesian machine learning, the posterior distribution is typicallycomputationally intractable, hence variational inference is often required. Inthis approach, an evidence lower bound on the log likelihood of data ismaximized during training. Variational Autoencoders (VAE) are one importantexample where variational inference is utilized. In this tutorial, we derivethe variational lower bound loss function of the standard variationalautoencoder. We do so in the instance of a gaussian latent prior and gaussianapproximate posterior, under which assumptions the Kullback-Leibler term in thevariational lower bound has a closed form solution. We derive essentiallyeverything we use along the way; everything from Bayes' theorem to theKullback-Leibler divergence.

Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Function