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In breast surgical planning, accurate registration of MR images across patient positions has the potential to improve the localisation of tumours during breast cancer treatment. While learning-based registration methods have recently become the state-of-the-art approach for most medical image registration tasks, these methods have yet to make inroads into breast image registration due to certain difficulties-the lack of rich texture information in breast MR images and the need for the deformations to be diffeomophic. In this work, we propose learning strategies for breast MR image registration that are amenable to diffeomorphic constraints, together with early experimental results from in-silico and in-vivo experiments. One key contribution of this work is a registration network which produces superior registration outcomes for breast images in addition to providing diffeomorphic guarantees.