Conventional deformable registration methods aim at solving an optimizationmodel carefully designed on image pairs and their computational costs areexceptionally high. In contrast, recent deep learning based approaches canprovide fast deformation estimation. These heuristic network architectures arefully data-driven and thus lack explicit geometric constraints, e.g.,topology-preserving, which are indispensable to generate plausibledeformations. We design a new deep learning based framework to optimize adiffeomorphic model via multi-scale propagation in order to integrateadvantages and avoid limitations of these two categories of approaches.Specifically, we introduce a generic optimization model to formulatediffeomorphic registration and develop a series of learnable architectures toobtain propagative updating in the coarse-to-fine feature space. Moreover, wepropose a novel bilevel self-tuned training strategy, allowing efficient searchof task-specific hyper-parameters. This training strategy increases theflexibility to various types of data while reduces computational and humanburdens. We conduct two groups of image registration experiments on 3D volumedatasets including image-to-atlas registration on brain MRI data andimage-to-image registration on liver CT data. Extensive results demonstrate thestate-of-the-art performance of the proposed method with diffeomorphicguarantee and extreme efficiency. We also apply our framework to challengingmulti-modal image registration, and investigate how our registration to supportthe down-streaming tasks for medical image analysis including multi-modalfusion and image segmentation.