  The simulation of high-energy physics collision events is a key element for
data analysis at present and future particle accelerators. The comparison of
simulation predictions to data allows looking for rare deviations that can be
due to new phenomena not previously observed. We show that novel machine
learning algorithms, specifically Normalizing Flows and Flow Matching, can be
used to replicate accurate simulations from traditional approaches with several
orders of magnitude of speed-up. The classical simulation chain starts from a
physics process of interest, computes energy deposits of particles and
electronics response, and finally employs the same reconstruction algorithms
used for data. Eventually, the data are reduced to some high-level analysis
format. Instead, we propose an end-to-end approach, simulating the final data
format directly from physical generator inputs, skipping any intermediate
steps. We use particle jets simulation as a benchmark for comparing both
discrete and continuous Normalizing Flows models. The models are validated
across a variety of metrics to identify the most accurate. We discuss the
scaling of performance with the increase in training data, as well as the
generalization power of these models on physical processes different from the
training one. We investigate sampling multiple times from the same physical
generator inputs, a procedure we name oversampling, and we show that it can
effectively reduce the statistical uncertainties of a dataset. This class of ML
algorithms is found to be capable of learning the expected detector response
independently of the physical input process. Their speed and accuracy, coupled
with the stability of the training procedure, make them a compelling tool for
the needs of current and future experiments.
