  Normalizing flows are a class of deep generative models that provide a
promising route to sample lattice field theories more efficiently than
conventional Monte Carlo simulations. In this work we show that the theoretical
framework of stochastic normalizing flows, in which neural-network layers are
combined with Monte Carlo updates, is the same that underlies
out-of-equilibrium simulations based on Jarzynski's equality, which have been
recently deployed to compute free-energy differences in lattice gauge theories.
We lay out a strategy to optimize the efficiency of this extended class of
generative models and present examples of applications.
