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Predicting molecular conformations from molecular graphs is a fundamentalproblem in cheminformatics and drug discovery. Recently, significant progresshas been achieved with machine learning approaches, especially with deepgenerative models. Inspired by the diffusion process in classicalnon-equilibrium thermodynamics where heated particles will diffuse fromoriginal states to a noise distribution, in this paper, we propose a novelgenerative model named GeoDiff for molecular conformation prediction. GeoDifftreats each atom as a particle and learns to directly reverse the diffusionprocess (i.e., transforming from a noise distribution to stable conformations)as a Markov chain. Modeling such a generation process is however verychallenging as the likelihood of conformations should be roto-translationalinvariant. We theoretically show that Markov chains evolving with equivariantMarkov kernels can induce an invariant distribution by design, and furtherpropose building blocks for the Markov kernels to preserve the desirableequivariance property. The whole framework can be efficiently trained in anend-to-end fashion by optimizing a weighted variational lower bound to the(conditional) likelihood. Experiments on multiple benchmarks show that GeoDiffis superior or comparable to existing state-of-the-art approaches, especiallyon large molecules.

GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation