  In this article, we highlight what appears to be major issue of Variational
Autoencoders, evinced from an extensive experimentation with different network
architectures and datasets: the variance of generated data is significantly
lower than that of training data. Since generative models are usually evaluated
with metrics such as the Frechet Inception Distance (FID) that compare the
distributions of (features of) real versus generated images, the variance loss
typically results in degraded scores. This problem is particularly relevant in
a two stage setting, where we use a second VAE to sample in the latent space of
the first VAE. The minor variance creates a mismatch between the actual
distribution of latent variables and those generated by the second VAE, that
hinders the beneficial effects of the second stage. Renormalizing the output of
the second VAE towards the expected normal spherical distribution, we obtain a
sudden burst in the quality of generated samples, as also testified in terms of
FID.
