  Traditional deformable registration techniques achieve impressive results and
offer a rigorous theoretical treatment, but are computationally intensive since
they solve an optimization problem for each image pair. Recently,
learning-based methods have facilitated fast registration by learning spatial
deformation functions. However, these approaches use restricted deformation
models, require supervised labels, or do not guarantee a diffeomorphic
(topology-preserving) registration. Furthermore, learning-based registration
tools have not been derived from a probabilistic framework that can offer
uncertainty estimates. In this paper, we present a probabilistic generative
model and derive an unsupervised learning-based inference algorithm that makes
use of recent developments in convolutional neural networks (CNNs). We
demonstrate our method on a 3D brain registration task, and provide an
empirical analysis of the algorithm. Our approach results in state of the art
accuracy and very fast runtimes, while providing diffeomorphic guarantees and
uncertainty estimates. Our implementation is available online at
http://voxelmorph.csail.mit.edu .
