In this paper, we identify and leverage a novel `bright ending' (BE) anomaly in diffusion models prone to memorizing training images to address a new task: locating localized memorization regions within these models. BE refers to a distinct cross-attention pattern observed in text-to-image generations using diffusion models. Specifically, memorized image patches exhibit significantly greater attention to the end token during the final inference step compared to non-memorized patches. This attention map effectively highlights regions where the generated image replicates training data. Furthermore, driven by our observation that local memorization significantly underperforms in existing tasks of measuring, detecting, and mitigating memorization in diffusion models compared to global memorization, we propose a simple yet effective method to integrate BE and the results of the new localization task into these existing frameworks. This integration effectively improves their performances by narrowing the performance gap caused by local memorization. Our results not only demonstrate the successful execution of the new localization task but also establish new state-of-the-art performance across all existing tasks, underscoring the significance of the BE phenomenon.