While auto-encoders can also learn some aspects of a data distribution, their goal is only to reconstruct encoded samples, that is, to discriminate the original image out of all possible pixel combinations, based on the encoded features. Standard auto-encoders are not meant to generate new samples. If we randomly sample a code vector from their latent space, chances are high that we will obtain a gibberish image out of their decoder. This is because their latent space is unconstrained and typically not continuous (that is, there are usually large regions in the latent space that are not corresponding to any valid image).

Variational auto-encoders (VAEs) are particular auto-encoders designed to have continuous latent space, and they ...

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