The substantial modality-induced variations in radiometric, texture, and structural characteristics pose significant challenges for the accurate registration of multimodal images. While supervised deep learning methods have demonstrated strong performance, they often rely on large-scale annotated datasets, limiting their practical application. Traditional unsupervised methods usually optimize registration by minimizing differences in feature representations, yet often fail to robustly capture geometric discrepancies, particularly under substantial spatial and radiometric variations, thus hindering convergence stability. To address these challenges, we propose a Collaborative Learning framework for Unsupervised Multimodal Image Registration, named CoLReg, which reformulates unsupervised registration learning into a collaborative training paradigm comprising three components: (1) a cross-modal image translation network, MIMGCD, which employs a learnable Maximum Index Map (MIM) guided conditional diffusion model to synthesize modality-consistent image pairs; (2) a self-supervised intermediate registration network which learns to estimate geometric transformations using accurate displacement labels derived from MIMGCD outputs; (3) a distilled cross-modal registration network trained with pseudo-label predicted by the intermediate network. The three networks are jointly optimized through an alternating training strategy wherein each network enhances the performance of the others. This mutual collaboration progressively reduces modality discrepancies, enhances the quality of pseudo-labels, and improves registration accuracy. Extensive experimental results on multiple datasets demonstrate that our ColReg achieves competitive or superior performance compared to state-of-the-art unsupervised approaches and even surpasses several supervised baselines.