||Point set registration is to find point-to-point correspondences between point sets, each of which represents the shape of an object. Coherent point drift is a well-known algorithm for solving point set registration problems. In this study, we propose a novel formulation of coherent point drift, providing an insight into the algorithm. Using the formulation and variational Bayesian inference, we derive a registration algorithm, which is a generalization of coherent point drift. We also propose an acceleration scheme regarding the derived algorithm.