We introduce CCMorph, a fast and accurate framework for deformable pairwise medical image registration. To enhance stability and representation learning, CCMorph introduces a Conditional Residual Block (CRB) that dynamically adjusts feature transformations based on regularization context. By integrating contrastive learning with a hyperparameter-aware modulation scheme, the model extracts task-relevant anatomical features from both fixed and moving images in an unsupervised manner. By leveraging contrastive learning, CCMorph effectively identifies relevant features, facilitating similarity measurements and enhancing stability. This dual approach—CRB for optimizing gradient flow and contrastive learning for robust similarity measures—reinforces the model’s stability, resulting in more accurate and reliable registration. Our method effectively captures optimal solutions across diverse datasets without the need for extensive manual tuning. Experimental results on the LPBA40 and NLST datasets show that CCMorph consistently outperforms existing deep learning-based methods, achieving high registration accuracy and robust geometric consistency. This work highlights the potential of CRB-based registration models for advancing unsupervised medical image alignment.