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.