  Simulations play a key role for inference in collider physics. We explore
various approaches for enhancing the precision of simulations using machine
learning, including interventions at the end of the simulation chain
(reweighting), at the beginning of the simulation chain (pre-processing), and
connections between the end and beginning (latent space refinement). To clearly
illustrate our approaches, we use W+jets matrix element surrogate simulations
based on normalizing flows as a prototypical example. First, weights in the
data space are derived using machine learning classifiers. Then, we pull back
the data-space weights to the latent space to produce unweighted examples and
employ the Latent Space Refinement (LASER) protocol using Hamiltonian Monte
Carlo. An alternative approach is an augmented normalizing flow, which allows
for different dimensions in the latent and target spaces. These methods are
studied for various pre-processing strategies, including a new and general
method for massive particles at hadron colliders that is a tweak on the
widely-used RAMBO-on-diet mapping. We find that modified simulations can
achieve sub-percent precision across a wide range of phase space.
