  Advances in deep learning have greatly improved structure prediction of
molecules. However, many macroscopic observations that are important for
real-world applications are not functions of a single molecular structure, but
rather determined from the equilibrium distribution of structures. Traditional
methods for obtaining these distributions, such as molecular dynamics
simulation, are computationally expensive and often intractable. In this paper,
we introduce a novel deep learning framework, called Distributional Graphormer
(DiG), in an attempt to predict the equilibrium distribution of molecular
systems. Inspired by the annealing process in thermodynamics, DiG employs deep
neural networks to transform a simple distribution towards the equilibrium
distribution, conditioned on a descriptor of a molecular system, such as a
chemical graph or a protein sequence. This framework enables efficient
generation of diverse conformations and provides estimations of state
densities. We demonstrate the performance of DiG on several molecular tasks,
including protein conformation sampling, ligand structure sampling,
catalyst-adsorbate sampling, and property-guided structure generation. DiG
presents a significant advancement in methodology for statistically
understanding molecular systems, opening up new research opportunities in
molecular science.
