  Generating a Boltzmann distribution in high dimension has recently been
achieved with Normalizing Flows, which enable fast and exact computation of the
generated density, and thus unbiased estimation of expectations. However,
current implementations rely on accurate training data, which typically comes
from computationally expensive simulations. There is therefore a clear
incentive to train models with incomplete or no data by relying solely on the
target density, which can be obtained from a physical energy model (up to a
constant factor). For that purpose, we analyze the properties of standard
losses based on Kullback-Leibler divergences. We showcase their limitations, in
particular a strong propensity for mode collapse during optimization on
high-dimensional distributions. We then propose strategies to alleviate these
issues, most importantly a new loss function well-grounded in theory and with
suitable optimization properties. Using as a benchmark the generation of 3D
molecular configurations, we show on several tasks that, for the first time,
imperfect pre-trained models can be further optimized in the absence of
training data.
