  We present an investigation into diffusion models for molecular generation,
with the aim of better understanding how their predictions compare to the
results of physics-based calculations. The investigation into these models is
driven by their potential to significantly accelerate electronic structure
calculations using machine learning, without requiring expensive
first-principles datasets for training interatomic potentials. We find that the
inference process of a popular diffusion model for de novo molecular generation
is divided into an exploration phase, where the model chooses the atomic
species, and a relaxation phase, where it adjusts the atomic coordinates to
find a low-energy geometry. As training proceeds, we show that the model
initially learns about the first-order structure of the potential energy
surface, and then later learns about higher-order structure. We also find that
the relaxation phase of the diffusion model can be re-purposed to sample the
Boltzmann distribution over conformations and to carry out structure
relaxations. For structure relaxations, the model finds geometries with ~10x
lower energy than those produced by a classical force field for small organic
molecules. Initializing a density functional theory (DFT) relaxation at the
diffusion-produced structures yields a >2x speedup to the DFT relaxation when
compared to initializing at structures relaxed with a classical force field.
