Deformable image registration relies on accurate anatomical correspondences. However, explicitly coupling local matching reliability with spatial context selection and deformation update strength remains insufficiently explored in learning-based registration. This challenge is particularly pronounced in homogeneous, weakly textured, and severely deformed regions, where ambiguous matches may induce erroneous deformation updates. We propose ReliMorph, a reliability-routed symmetric framework for 3D deformable registration that couples correspondence assessment with spatial context selection and update strength.Local correlation distributions characterize correspondence ambiguity using shared anatomical features with modality-specific adaptation. These reliability cues guide spatial expert fusion and gate residual velocities during coarse-to-fine refinement. Updated inverse-inconsistency feedback guides routing and gating at finer pyramid levels. To our knowledge, ReliMorph is the first 3D deformable registration framework to jointly condition spatial expert routing and residual velocity gating on correspondence reliability. Extensive experiments demonstrate that ReliMorph consistently outperforms competing methods in anatomical overlap, highlighting its effectiveness across unimodal and multimodal registration tasks.

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