  Algorithms based on normalizing flows are emerging as promising machine
learning approaches to sampling complicated probability distributions in a way
that can be made asymptotically exact. In the context of lattice field theory,
proof-of-principle studies have demonstrated the effectiveness of this approach
for scalar theories, gauge theories, and statistical systems. This work
develops approaches that enable flow-based sampling of theories with dynamical
fermions, which is necessary for the technique to be applied to lattice field
theory studies of the Standard Model of particle physics and many condensed
matter systems. As a practical demonstration, these methods are applied to the
sampling of field configurations for a two-dimensional theory of massless
staggered fermions coupled to a scalar field via a Yukawa interaction.
