Image registration aims to establish point correspondences between the given images I1I2: Ω → ℝk, typically via a deformation map ϕ : Ω → Ω that assigns points in one image to those in the other. In our work [1], we propose to combine stationary velocity fields on Lie groups with a suitable regularization to provide fine control over the desired deformations. Specifically: Overall, this allows to improve the robustness of SVF-based registration approaches against large deformations prescribed by the chosen group – for example, against roto-translations with the choice G = SE(3). MGSVFs can be implemented in a fully differentiable manner, enabling easy integration into most image registration frameworks. Further advantages of the approach include inherent invertibility and trivial recovery of the inverse deformation.We validate the approach on unsupervised andweakly supervised brain MRI registration tasks on the IXI andOASIS datasets. In both cases, the proposed matrix-group extension improves performance compared to the base transformer model. Our implementation is available at https://github.com/sennhoj321/Liemorph.