Text-to-image diffusion models have achieved unprecedented proficiency in generating realistic images. However, their inherent tendency to memorize and replicate training data during inference raises significant concerns, including potential copyright infringement. In response, various methods have been proposed to evaluate, detect, and mitigate memorization. Our analysis reveals that existing approaches significantly underperform in handling local memorization, where only specific image regions are memorized, compared to global memorization, where the entire image is replicated. Also, they cannot locate the local memorization regions, making it hard to investigate locally. To address these, we identify a novel "bright ending" (BE) anomaly in diffusion models prone to memorizing training images. BE refers to a distinct cross-attention pattern observed in text-to-image diffusion models, where memorized image patches exhibit significantly greater attention to the final text token during the last inference step than non-memorized patches. This pattern highlights regions where the generated image replicates training data and enables efficient localization of memorized regions. Equipped with this, we propose a simple yet effective method to integrate BE into existing frameworks, significantly improving their performance by narrowing the performance gap caused by local memorization. Our results not only validate 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.