  Full characterization of the spectral behavior of generative models based on
neural networks remains an open issue. Recent research has focused heavily on
generative adversarial networks and the high-frequency discrepancies between
real and generated images. The current solution to avoid this is to either
replace transposed convolutions with bilinear up-sampling or add a spectral
regularization term in the generator. It is well known that Variational
Autoencoders (VAEs) also suffer from these issues. In this work, we propose a
simple 2D Fourier transform-based spectral regularization loss for the VAE and
show that it can achieve results equal to, or better than, the current
state-of-the-art in frequency-aware losses for generative models. In addition,
we experiment with altering the up-sampling procedure in the generator network
and investigate how it influences the spectral performance of the model. We
include experiments on synthetic and real data sets to demonstrate our results.
