  A major challenge in materials science is the determination of the structure
of nanometer sized objects. Here we present a novel approach that uses a
generative machine learning model based on a Diffusion model that is trained on
45,229 known structures. The model factors both the measured diffraction
pattern as well as relevant statistical priors on the unit cell of atomic
cluster structures. Conditioned only on the chemical formula and the
information-scarce finite-size broadened powder diffraction pattern, we find
that our model, PXRDnet, can successfully solve simulated nanocrystals as small
as 10 angstroms across 200 materials of varying symmetry and complexity,
including structures from all seven crystal systems. We show that our model can
determine structural solutions with up to $81.5\%$ accuracy, as measured by
structural correlation. Furthermore, PXRDnet is capable of solving structures
from noisy diffraction patterns gathered in real-world experiments. We suggest
that data driven approaches, bootstrapped from theoretical simulation, will
ultimately provide a path towards determining the structure of previously
unsolved nano-materials.
