  We propose an algorithm for learning a conditional generative model of a
molecule given a target. Specifically, given a receptor molecule that one
wishes to bind to, the conditional model generates candidate ligand molecules
that may bind to it. The distribution should be invariant to rigid body
transformations that act $\textit{jointly}$ on the ligand and the receptor; it
should also be invariant to permutations of either the ligand or receptor
atoms. Our learning algorithm is based on a continuous normalizing flow. We
establish semi-equivariance conditions on the flow which guarantee the
aforementioned invariance conditions on the conditional distribution. We
propose a graph neural network architecture which implements this flow, and
which is designed to learn effectively despite the vast differences in size
between the ligand and receptor. We evaluate our method on the CrossDocked2020
dataset, attaining a significant improvement in binding affinity over competing
methods.
