Video vision-language models (VLMs) have strong semantic understanding, yet remain unreliable at precise temporal grounding. Existing gains from explicitly aligning video frames with absolute time suggest that VLMs may already encode accurate temporal locations internally but lose precision when expressing them as timestamps. Our analysis across four VLMs and two grounding datasets confirms this hypothesis: attention intervals outperform predicted intervals on approximately 66% of valid examples. We term this discrepancy the temporal generation gap. Because precise temporal annotations are expensive, this finding motivates closing the gap to improve temporal grounding using only unlabeled video-query pairs. We propose Self-Supervised Attention Policy Optimization (SAPO), which uses internal temporal attention as self-supervision for Group Relative Policy Optimization and applies a ground-truth-free criterion to select high-value samples. SAPO consistently improves temporal grounding across multiple datasets and models spanning weak to strong initial grounding ability. Relative mIoU gains reach 33.7% on Qwen2.5-VL-3B and 5.4% on the strong Time-R1-7B. The improvements transfer across datasets while preserving general video understanding.

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