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[D] Do VAEs have a manifold?

I am kind of confused as to how VAEs do manifold learning.

While I can grasp that regular AEs perform deterministic transformation from the input vector space to the latent space with the encoder, it is very hard for me to understand how that would work on a VAE. Is the manifold on the parameters of the distribution MU and SIGMA?

Can anyone clarify that for me, maybe point to a paper? Thanks

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