  Ptychography, as an essential tool for high-resolution and nondestructive
material characterization, presents a challenging large-scale nonlinear and
non-convex inverse problem; however, its intrinsic photon statistics create
clear opportunities for statistical-based deep learning approaches to tackle
these challenges, which has been underexplored. In this work, we explore
normalizing flows to obtain a surrogate for the high-dimensional posterior,
which also enables the characterization of the uncertainty associated with the
reconstruction: an extremely desirable capability when judging the
reconstruction quality in the absence of ground truth, spotting spurious
artifacts and guiding future experiments using the returned uncertainty
patterns. We demonstrate the performance of the proposed method on a synthetic
sample with added noise and in various physical experimental settings.
