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Many applications in image-guided surgery and therapy require fast and reliable non-linear, multi-modal image registration. Recently proposed unsupervised deep learning-based registration methods have demonstrated superior performance compared to iterative methods in just a fraction of the time. Most of the learning-based methods have focused on mono-modal image registration. The extension to multi-modal registration depends on the use of an appropriate similarity function, such as the mutual information (MI). We propose guiding the training of a deep learning-based registration method with MI estimation between an image-pair in an end-to-end trainable network. Our results show that a small, 2-layer network produces competitive results in both mono- and multi-modal registration, with sub-second run-times. Comparisons to both iterative and deep learning-based methods show that our MI-based method produces topologically and qualitatively superior results with an extremely low rate of non-diffeomorphic transformations. Real-time clinical application will benefit from a better visual matching of anatomical structures and less registration failures/outliers.