Simulating nature and in particular processes in particle physics require expensive computations and sometimes would take much longer than scientists can afford. Here, we explore ways to a solution for this problem by investigating recent advances in generative modeling and 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 to also ensure that these events occur with the correct frequencies. We investigate the feasibility of learning the event generation and the frequency of occurrence with several generative machine learning models to produce events like Monte Carlo generators. We study three processes: a simple two-body decay, the processes e+e- → Z → l+l- and [Formula: see text] including the decay of the top quarks and a simulation of the detector response. By buffering density information of encoded Monte Carlo events given the encoder of a Variational Autoencoder 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.