  Deformable image registration is fundamental to many medical imaging
applications. Registration is an inherently ambiguous task often admitting many
viable solutions. While neural network-based registration techniques enable
fast and accurate registration, the majority of existing approaches are not
able to estimate uncertainty. Here, we present PULPo, a method for
probabilistic deformable registration capable of uncertainty quantification.
PULPo probabilistically models the distribution of deformation fields on
different hierarchical levels combining them using Laplacian pyramids. This
allows our method to model global as well as local aspects of the deformation
field. We evaluate our method on two widely used neuroimaging datasets and find
that it achieves high registration performance as well as substantially better
calibrated uncertainty quantification compared to the current state-of-the-art.
