Note on the equivalence of hierarchical variational models and auxiliary deep generative models

This note compares two recently published machine learning methods for constructing flexible, but tractable families of variational hidden-variable posteriors. The first method, called "hierarchical variational models" enriches the inference model with an extra variable, while the other, called "auxiliary deep generative models", enriches the generative model instead. We conclude that the two methods are mathematically equivalent.