Not me dude but I like underdogs and outsiders.  What u saying sounds right: symmetries, like the ones computed in section 3.8 are used as constraints a.k.a. &quot;quantum numbers&quot; describing the states in the latent layer. That is vintage quantum mechanics. The part is theoretical and not in the theano code by looks of it, so harder to comment on... The quantum analogy also brings along the laplacian form of the conditional density in section 1.5, so there u go. 
On your comment, which &quot;literature on the topic&quot; is clear? Have u read the original VAE paper <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1401.4082.pdf" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1401.4082.pdf</a>. 95% of paper and most of 21 equations are about gradients, and gaussian too, they even invent a new term: stochastic back-propagation, why, who needs that? All the math is done in the Gibbs&#x2F;ACE paper in 4 lines, just compute your cost bound and back-propagate? Having seen this earlier would have saved me a lot of pondering. Pythagorean theorem does sound too simple, I give u that...