Traditional deformable image registration imposes a uniform smoothness constraint on the deformation field. This is not appropriate when registering images visualizing organs that slide relative to each other, and therefore leads to registration inaccuracies. In this paper, we present a deformation field regularization term that is based on anisotropic diffusion and accommodates the deformation field discontinuities that are expected when considering sliding motion. The registration algorithm was assessed first using artificial images of geometric objects. In a second validation, monomodal chest images depicting both respiratory and cardiac motion were generated using an anatomically-realistic software phantom and then registered. Registration accuracy was assessed based on the distances between corresponding segmented organ surfaces. Compared to an established diffusive regularization approach, the anisotropic diffusive regularization gave deformation fields that represented more plausible image correspondences, while giving rise to similar transformed moving images and comparable registration accuracy.