Fast and accurate registration is crucial for minimally invasive liver interventions. Traditional methods, while effective at optimizing rigid and non-rigid deformations, often require minutes or even hours to complete, limiting their clinical applicability. As an alternative, deep learning methods have been proposed, which are capable of inference in seconds, after appropriate training. However, they do not generalize well. In this work, we propose a hybrid method that takes the best from both worlds, and consists of two steps. After a coarse initial deformation using conventional techniques, we learn to refine the displacements with a targeted neural network architecture. We evaluate the accuracy of fast conventional techniques, deep learning methods, and our hybrid approach on 30 challenging liver interventions at the Innsbruck University Hospital (20x CT-CT registration tasks, 10x CT-MR). Our method demonstrates superior robustness compared to deep learning techniques, while maintaining desired inference speed. We can significantly improve on the liver and vascular alignment when compared to a wide range of learning methods, while keeping the inference time below 3 seconds. To the best of our knowledge, this is the first instance where a deep learning method is used to refine initial displacements generated by a conventional method in the context of multi-modal deformable liver registration.