Accurate compensation for intra-operative brain shift remains a fundamental challenge in neurosurgical procedures, as misalignment between pre-operative and intra-operative images can lead to suboptimal surgical guidance. In this work, we propose a bidirectional, unsupervised 3D brain shift compensation framework for non-rigid MRI registration, designed to directly estimate dense deformation fields between pre-operative and intra-operative volumes. The proposed approach employs dual image-translation pathways coupled with a dedicated deformation field predictor, enabling robust alignment without requiring paired training data. A key component of the framework is the integration of bidirectional consistency constraints to enforce anatomical correspondence across domains, while deformation field estimation is explicitly optimized for registration accuracy. In addition, we incorporate a Haar wavelet-based perceptual similarity (HaarPSI) loss to improve the preservation of fine-scale anatomical structures during registration. The proposed method is evaluated against classical and state-of-the-art baselines, including Elastix, Voxelmorph, and several adversarial and GAN-based learning approaches adapted with comparable registration modules. Qualitative analyses of deformation fields and error maps further demonstrate improved alignment in regions most affected by brain shift. These results highlight the effectiveness of bidirectional deformation modeling combined with adversarial and perceptual constraints for accurate, physically plausible, and unsupervised 3D non-rigid registration in neurosurgical applications.