  Predicting molecular conformations from molecular graphs is a fundamental
problem in cheminformatics and drug discovery. Recently, significant progress
has been achieved with machine learning approaches, especially with deep
generative models. Inspired by the diffusion process in classical
non-equilibrium thermodynamics where heated particles will diffuse from
original states to a noise distribution, in this paper, we propose a novel
generative model named GeoDiff for molecular conformation prediction. GeoDiff
treats each atom as a particle and learns to directly reverse the diffusion
process (i.e., transforming from a noise distribution to stable conformations)
as a Markov chain. Modeling such a generation process is however very
challenging as the likelihood of conformations should be roto-translational
invariant. We theoretically show that Markov chains evolving with equivariant
Markov kernels can induce an invariant distribution by design, and further
propose building blocks for the Markov kernels to preserve the desirable
equivariance property. The whole framework can be efficiently trained in an
end-to-end fashion by optimizing a weighted variational lower bound to the
(conditional) likelihood. Experiments on multiple benchmarks show that GeoDiff
is superior or comparable to existing state-of-the-art approaches, especially
on large molecules.
