  Normalizing Flows (NF) are powerful generative models with increasing
applications in augmenting Monte Carlo algorithms due to their high flexibility
and expressiveness. In this work we explore the integration of NF in
Diagrammatic Monte Carlo (DMC), presenting an architecture designed to sample
the intricate multidimensional space of Feynman's diagrams through
dimensionality reduction. By decoupling the sampling of diagram order and
interaction times, the flow focuses on one interaction at a time. This enables
constructing a general diagram by employing the same unsupervised model
iteratively, dressing a zero-order diagram with interactions determined by the
previously sampled order. The resulting NF-augmented DMC is tested on the
widely used single-site Holstein polaron model in the entire electron-phonon
coupling regime. The obtained data show that the model accurately reproduces
the diagram distribution reducing sample correlation and statistical error for
observables such as the polaron binding energy and the interacting Green's
function.
