This reminded me of this paper on using deep autoencoders as a generative model:  <a href="http:&#x2F;&#x2F;papers.nips.cc&#x2F;paper&#x2F;5023-generalized-denoising-auto-encoders-as-generative-models.pdf" rel="nofollow">http:&#x2F;&#x2F;papers.nips.cc&#x2F;paper&#x2F;5023-generalized-denoising-auto-...</a>  I don&#x27;t think it&#x27;s exactly a right analogy, but there&#x27;s something there about the local flow of MCMC locally describing the manifold structure, and thus generating it globally.