Abstract: Unsupervised registration of large-scale LiDAR point clouds remains challenging due to the geometric ambiguity inherent in outdoor scenes, which degrades pseudo-label quality and leads to suboptimal convergence, particularly for sparse, low-resolution scans such as those from nuScenes. We reveal that registration models intrinsically encode semantic awareness that strongly correlates with registration accuracy, albeit without explicit semantic supervision. However, this native awareness is fragile: noisy supervision arising from geometric ambiguity in unsupervised settings rapidly erodes the learned semantic structure, causing performance collapse. To this end, we propose CAESAR, a teacher-student framework guided by an off-the-shelf 3D segmentation model exclusively during training. We observe that potential inlier matches are often buried just beneath a few spurious neighbors in the noisy feature space, motivating Dual-Cue Guided Re-Matching to recover them through reselection rather than simply rejecting. Building on this, a train-only Semantic-Geometric Label Mining performs lightweight, batch-specific teacher refinement and mines reliable pseudo-labels under semantic guidance. We further introduce Semantic Predictive Distillation to consolidate the student's semantic awareness in the feature space. Extensive experiments on KITTI and nuScenes demonstrate state-of-the-art performance, with pronounced gains on the challenging nuScenes benchmark. Crucially, CAESAR incurs zero inference overhead and requires no semantic annotations on the registration data. Code will be released.