The article introduces a deep learning framework called Distributional Graphormer (DiG) to predict the equilibrium distribution of molecular systems. DiG is inspired by the annealing process in thermodynamics and uses deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on molecular descriptors such as chemical graphs or protein sequences. This framework enables efficient generation of diverse conformations and provides estimations of state densities, orders of magnitude faster than conventional methods like molecular dynamics simulations. The authors demonstrate the application of DiG on several molecular tasks, including protein conformation sampling, ligand structure sampling, catalyst-adsorbate sampling, and property-guided structure generation. DiG shows substantial advancements in statistically understanding molecular systems, opening new research opportunities in molecular sciences.The article introduces a deep learning framework called Distributional Graphormer (DiG) to predict the equilibrium distribution of molecular systems. DiG is inspired by the annealing process in thermodynamics and uses deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on molecular descriptors such as chemical graphs or protein sequences. This framework enables efficient generation of diverse conformations and provides estimations of state densities, orders of magnitude faster than conventional methods like molecular dynamics simulations. The authors demonstrate the application of DiG on several molecular tasks, including protein conformation sampling, ligand structure sampling, catalyst-adsorbate sampling, and property-guided structure generation. DiG shows substantial advancements in statistically understanding molecular systems, opening new research opportunities in molecular sciences.