Semi-Equivariant Conditional Normalizing Flows

We study the problem of learning conditional distributions of the form p(G|Ĝ), where G and Ĝ are two 3D graphs, using continuous normalizing flows. We derive a semi-equivariance condition on the flow which ensures that conditional invariance to rigid motions holds. We demonstrate the effectiveness of the technique in the molecular setting of receptor-aware ligand generation. Data consisting of sets of three-dimensional points appear in a number of scientific and engineering settings; examples include molecular chemistry, high energy physics, and computer vision. Construction of such distributions is useful in various scenarios: in the molecular setting, Ĝ will represent a receptor / target and G will represent a ligand; in the setting of shape completion in computer vision, Ĝ will represent the part of the point cloud that we have been given, and G will represent the completion of this point cloud. We present a method for learning such conditional distributions based on continuous normalizing flows.