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The generation of 3D molecules requires simultaneously deciding thecategorical features~(atom types) and continuous features~(atom coordinates).Deep generative models, especially Diffusion Models (DMs), have demonstratedeffectiveness in generating feature-rich geometries. However, existing DMstypically suffer from unstable probability dynamics with inefficient samplingspeed. In this paper, we introduce geometric flow matching, which enjoys theadvantages of both equivariant modeling and stabilized probability dynamics.More specifically, we propose a hybrid probability path where the coordinatesprobability path is regularized by an equivariant optimal transport, and theinformation between different modalities is aligned. Experimentally, theproposed method could consistently achieve better performance on multiplemolecule generation benchmarks with 4.75$\times$ speed up of sampling onaverage.

Equivariant Flow Matching with Hybrid Probability Transport