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Here is the thing, I think the authors use the notation in eqn.4 in reverse order i.e, $z_L \rightarrow z_{L-1} ... \rightarrow z_1 \rightarrow x$. In this notation $z_L$ has a normal distribution $N(0,I)$ and x is the data distribution whose likelihood is supposed to be maximized. Section 3.1 provides background on the theory of transforming random ...


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Sampling is used during VAE training and during inference. The idea is that the data are encoded as random draws from a particular distribution. That distribution's parameters depend on the input data, because they are determined from the inputs. By contrast, an ordinary autoencoder maps the data to a vector deterministically, without any sampling. For a ...


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