  Variational AutoEncoders (VAEs) are powerful generative models that merge
elements from statistics and information theory with the flexibility offered by
deep neural networks to efficiently solve the generation problem for high
dimensional data. The key insight of VAEs is to learn the latent distribution
of data in such a way that new meaningful samples can be generated from it.
This approach led to tremendous research and variations in the architectural
design of VAEs, nourishing the recent field of research known as unsupervised
representation learning. In this article, we provide a comparative evaluation
of some of the most successful, recent variations of VAEs. We particularly
focus the analysis on the energetic efficiency of the different models, in the
spirit of the so called Green AI, aiming both to reduce the carbon footprint
and the financial cost of generative techniques. For each architecture we
provide its mathematical formulation, the ideas underlying its design, a
detailed model description, a running implementation and quantitative results.
