Conventional deformable registration methods aim at solving an optimization<br>model carefully designed on image pairs and their computational costs are<br>exceptionally high. In contrast, recent deep learning based approaches can<br>provide fast deformation estimation. These heuristic network architectures are<br>fully data-driven and thus lack explicit geometric constraints, e.g.,<br>topology-preserving, which are indispensable to generate plausible<br>deformations. We design a new deep learning based framework to optimize a<br>diffeomorphic model via multi-scale propagation in order to integrate<br>advantages and avoid limitations of these two categories of approaches.<br>Specifically, we introduce a generic optimization model to formulate<br>diffeomorphic registration and develop a series of learnable architectures to<br>obtain propagative updating in the coarse-to-fine feature space. Moreover, we<br>propose a novel bilevel self-tuned training strategy, allowing efficient search<br>of task-specific hyper-parameters. This training strategy increases the<br>flexibility to various types of data while reduces computational and human<br>burdens. We conduct two groups of image registration experiments on 3D volume<br>datasets including image-to-atlas registration on brain MRI data and<br>image-to-image registration on liver CT data. Extensive results demonstrate the<br>state-of-the-art performance of the proposed method with diffeomorphic<br>guarantee and extreme efficiency. We also apply our framework to challenging<br>multi-modal image registration, and investigate how our registration to support<br>the down-streaming tasks for medical image analysis including multi-modal<br>fusion and image segmentation.