Deformable registration is crucial in medical imaging. Several existing applications include lesion tracking, probabilistic atlas generation, and treatment response evaluation. However, current methods often lack robustness and generalizability across two key factors: spatial resolution and differences in anatomical coverage. We jointly optimize a registration field and a learnable dimensionality reduction module so that compressed VFM embeddings remain registration-relevant, and fuse these global semantic cues with MIND local descriptors. GLIDE-Reg achieves average dice similarity coefficients (DSC) across 6 anatomical structures of 0.859, 0.862, and 0.901 in two public cohorts (Lung250M and NLST) and one institution cohort (UCLA5DCT), and outperforms the state-of-the-art DEEDS (0.834, 0.858, 0.900) with relative improvements of 3.0%, 0.5%, and 0.1%. For target registration errors, GLIDE-Reg achieves 1.58 mm on Lung250M landmarks (compared to 1.25 mm on corrField and 1.91 mm on DEEDS) and 1.11 mm on NLST nodule centers (compared to 1.11 mm on DEEDS). The substantiated performance on the nodule centers also demonstrates its robustness across challenging downstream tasks, such as nodule tracking, which is an essential prior step for early-stage lung cancer diagnosis.