  We present a study for the generation of events from a physical process with
deep generative models. The simulation of physical processes requires not only
the production of physical events, but also to ensure these events occur with
the correct frequencies. We investigate the feasibility of learning the event
generation and the frequency of occurrence with Generative Adversarial Networks
(GANs) and Variational Autoencoders (VAEs) to produce events like Monte Carlo
generators. We study three processes: a simple two-body decay, the processes
$e^+e^-\to Z \to l^+l^-$ and $p p \to t\bar{t} $ including the decay of the top
quarks and a simulation of the detector response. We find that the tested GAN
architectures and the standard VAE are not able to learn the distributions
precisely. By buffering density information of encoded Monte Carlo events given
the encoder of a VAE we are able to construct a prior for the sampling of new
events from the decoder that yields distributions that are in very good
agreement with real Monte Carlo events and are generated several orders of
magnitude faster. Applications of this work include generic density estimation
and sampling, targeted event generation via a principal component analysis of
encoded ground truth data, anomaly detection and more efficient importance
sampling, e.g. for the phase space integration of matrix elements in quantum
field theories.
