[D] wrote a blog post on variational autoencoders, feel free to provide critique. • r/MachineLearning

I like to believe that Ali is making a very subtle point there that connects VAE to classical variational inference. The variational lower bound holds for any choice of q(z x). The tightness is controlled by the extent to which q(z x) matches p(z x). Traditionally, people define a separate q(z) for each x (here, I'm using q(z) in the classical sense of some arbitrary distribution over z, not the aggregate posterior sense). And for problems where only a single x is of interest (bayesian inference, log partition estimation, etc), there is only one q(z).