Geometric statistics has put forward various models for image deformation. Large deformation diffeomorphic metric mapping provides a framework for deforming a template image to a target image. The transformations are traditionally based on flows defined in terms of Ordinary Differential Equations (ODEs). More recently, stochastic models have been proposed where the ODE is replaced by a stochastic differential equation. Finding a common template image turns out to be closely connected to diffusion bridge simulation in high dimension. For the related but somewhat simpler case of landmark registration, I will discuss how this can be accomplished using guided diffusion processes, as originally defined in Schauer et al. (Bernoulli 23(4), 2917-2950) and further developed in follow-up papers.