In this paper we introduce a diffeomorphic constraint on the deformations considered in the deformable Bayesian Mixed Effect (BME) Template model. Our approach is built on a generic group of diffeomorphisms, which is parametrized by an arbitrary set of control point positions and momentum vectors. This enables to estimate the optimal positions of control points together with a template image and parameters of the deformation distribution which compose the atlas. We propose to use a stochastic version of the Expectation-Maximization (EM) algorithm where the simulation is performed using the Anisotropic Metropolis Adjusted Langevin Algorithm (AMALA). We propose also an extension of the model including a sparsity constraint to select an optimal number of control points with relevant positions. Experiments are carried out on the USPS database and on mandibles of mice.