[D] Advantage of VAE's compared to regularized AE's

I'm trying to come up to speed on VAE's.

My intuitive concept of a VAE is an AE for which we want to enforce some distributional regularity on the latent encodings.

Why not accomplish this by simply regularizing the latent encodings directly? For example, we could assert that the latent vectors are drawn from a zero-mean, identity-matrix-covariance Gaussian distribution.

So that e.g. the loss function becomes:

* Loss(X) = ReconstructionLoss(Decoder(Encoder(X))) + LogPriorProbability(Encoder(X))
* In a variant of this, we could …

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