3D Graph Conditional Distributions via Semi-Equivariant Continuous Normalizing Flows

Eyal Rozenberg, Ehud Rivlin, Daniel Freedman

Keywords: 3D graphs conditional distributions, geometric deep learning, continuous normalizing flows, semi-equivariance, molecules

TL;DR: A method for learning the conditional distribution of two 3D graphs that is invariant to transformations and permutations is proposed, and demonstrated as a useful conditional generative model for molecular environments.

Abstract: A general method for learning the conditional distribution $p(G | \hat{G})$ of two 3D graphs is proposed. The method is designed to be invariant to rigid body transformations and to permutations of the vertices of either graph. The core of the method is a continuous normalizing flow and semi-equivariance conditions are established to ensure the aforementioned invariance conditions. The utility of the technique is demonstrated as a conditional generative model for the molecular setting.