  Machine-learned normalizing flows can be used in the context of lattice
quantum field theory to generate statistically correlated ensembles of lattice
gauge fields at different action parameters. This work demonstrates how these
correlations can be exploited for variance reduction in the computation of
observables. Three different proof-of-concept applications are demonstrated
using a novel residual flow architecture: continuum limits of gauge theories,
the mass dependence of QCD observables, and hadronic matrix elements based on
the Feynman-Hellmann approach. In all three cases, it is shown that statistical
uncertainties are significantly reduced when machine-learned flows are
incorporated as compared with the same calculations performed with uncorrelated
ensembles or direct reweighting.
