We seek to compute a diffeomorphic map between a pair of diffusion-weighted images under large deformation. Unlike existing techniques, our method allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning the diffusion-weighted images using a large deformation diffeomorphic registration framework formulated from an optimal control perspective. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local fiber reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures of different scales. We demonstrate the efficacy of our approach using in vivo data and report on detailed qualitative and quantitative results in comparison with several different registration strategies.