Generative recommendation retrieves items by autoregressively generating Semantic IDs(SIDs), where an RQ-VAE quantizes each item into a hierarchical SID sequence that the decoder generates level by level. We identify an overlooked bottleneck in this paradigm: the Semantic Quantization Gap(SQG). Quantization derives SIDs from rich continuous signals, including codebook centroids, local neighborhood geometry, and level-wise entropy. However, the decoder receives only discrete identifiers and loses the semantic structure that shaped them. This mismatch manifests in three ways: a grounding gap, where the decoder lacks semantic anchors when target-side information is limited; a neighborhood gap, where token-level supervision discards inter-item similarity and exacerbates exposure bias; and a difficulty gap, where computation is allocated uniformly despite generation difficulty diminishing with depth. To bridge the SQG, we propose BRIDGE. Codebook-grounded latent reasoning injects frozen quantizer centroids as semantic anchors before SID generation. Privileged EMA self-distillation transfers neighborhood-aware knowledge from a teacher to an on-policy student, preserving inter-item geometry while mitigating exposure bias. Effort-aware recurrence allocates more computation to the challenging early levels and progressively reduces it with depth. Across three Amazon benchmarks, BRIDGE improves Recall@10 and NDCG@10 by 10.9% and 9.7% on average over the strongest baseline (up to 12.6% and 10.7%). In a one-week online A/B experiment on a large-scale e-commerce advertising platform with 5% traffic, BRIDGE improves eCPM by 0.65%.

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