<p>Cross–modal medical image registration remains a central challenge in computational imaging due to heterogeneous appearance characteristics, nonlinear contrast disparities, and the need to maintain anatomical topology. To address these difficulties, we present a reversible deep diffeomorphic registration framework specifically designed for cross–modal alignment. The proposed method integrates a modality-adaptive structural encoder with a stationary velocity–based diffeomorphic generator, enabling stable forward and inverse mappings through an explicit reversible integration scheme. A cross-modal consistency objective is further introduced to harmonize latent representations across modalities without requiring paired annotations, allowing the model to disentangle anatomical structures from modality-specific appearance. Extensive experiments on diverse MRI and CT datasets demonstrate that our approach consistently outperforms state-of-the-art learning-based and traditional registration algorithms. Notably, the model achieves improved Dice similarity, substantial reductions in HD95 and TRE, and near-zero Jacobian violations, confirming both enhanced accuracy and topological fidelity. These findings indicate that reversible diffeomorphic modeling provides a principled and robust mechanism for interpretable cross-modal registration, offering strong potential for deployment in real-world clinical workflows and multi-institutional imaging studies.</p>