  Variational Autoencoders (VAEs) provide a theoretically-backed and popular
framework for deep generative models. However, learning a VAE from data poses
still unanswered theoretical questions and considerable practical challenges.
In this work, we propose an alternative framework for generative modeling that
is simpler, easier to train, and deterministic, yet has many of the advantages
of VAEs. We observe that sampling a stochastic encoder in a Gaussian VAE can be
interpreted as simply injecting noise into the input of a deterministic
decoder. We investigate how substituting this kind of stochasticity, with other
explicit and implicit regularization schemes, can lead to an equally smooth and
meaningful latent space without forcing it to conform to an arbitrarily chosen
prior. To retrieve a generative mechanism to sample new data, we introduce an
ex-post density estimation step that can be readily applied also to existing
VAEs, improving their sample quality. We show, in a rigorous empirical study,
that the proposed regularized deterministic autoencoders are able to generate
samples that are comparable to, or better than, those of VAEs and more powerful
alternatives when applied to images as well as to structured data such as
molecules. \footnote{An implementation is available at:
\url{https://github.com/ParthaEth/Regularized_autoencoders-RAE-}}
