The paper is nicely written and carefully details its model and experiments. The intuition behind the combination of a bottom-up, top-down inference is interesting, though I believe the authors overstate their point when they say VAE can'only' do pure bottom-up inference. From a computational graph prospective, what the authors propose in fine is a complex network which samples the latent variables top-down, with a fair amount of skip connections (the lateral connections), hidden units with the semantic of mean and standard deviation, shared parameters between the generative model and the inference network, and some parameterless, differentiable layers (the'combination' layers of equation 18-19). It has a very nice interpretation as the authors suggest. But computationally, nothing prevents a complex inference network with top-down sampling (compatible with classical VAE framework) to carry'bottom up' in its information in its hidden units and effectively perform similar computation.