Image registration is the basis for many applications in the fields of medical image computing and computer assisted interventions. One example is the registration of 2D X-ray images with preoperative three-dimensional computed tomography (CT) images in intraoperative surgical guidance systems. Due to the high safety requirements in medical applications, estimating registration uncertainty is of a crucial importance in such a scenario. However, previously proposed methods, including classical iterative registration methods and deep learning-based methods have one characteristic in common: They lack the capacity to represent the fact that a registration problem may be inherently ambiguous, meaning that multiple (substantially different) plausible solutions exist. To tackle this limitation, we explore the application of invertible neural networks (INN) as core component of a registration methodology. In the proposed framework, INNs enable going beyond point estimates as network output by representing the possible solutions to a registration problem by a probability distribution that encodes different plausible solutions via multiple modes. In a first feasibility study, we test the approach for a 2D/3D registration setting by registering spinal CT volumes to X-ray images. To this end, we simulate the X-ray images taken by a C-Arm with multiple orientations using the principle of digitially reconstructed radiographs (DRRs). Due to the symmetry of human spine, there are potentially multiple substantially different poses of the C-Arm that can lead to similar projections. The hypothesis of this work is that the proposed approach is able to identify multiple solutions in such ambiguous registration problems.