  Since their inception, Variational Autoencoders (VAEs) have become central in
machine learning. Despite their widespread use, numerous questions regarding
their theoretical properties remain open. Using PAC-Bayesian theory, this work
develops statistical guarantees for VAEs. First, we derive the first
PAC-Bayesian bound for posterior distributions conditioned on individual
samples from the data-generating distribution. Then, we utilize this result to
develop generalization guarantees for the VAE's reconstruction loss, as well as
upper bounds on the distance between the input and the regenerated
distributions. More importantly, we provide upper bounds on the Wasserstein
distance between the input distribution and the distribution defined by the
VAE's generative model.
