A Brownian motion model in the group of diffeomorphisms has been introduced as creating a least committed prior on warps. This prior is source destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 create invertible warps. In this paper, we formulate a Partial Differential Equation for obtaining the maximum likelihood warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric.