Semi-Equivariant Conditional Normalizing Flows

We study the problem of learning conditional distributions of the form $p(G\mathrm{\mid }\widehat{G})$, where $G$ and $\widehat{G}$ 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.