Recent breakthroughs in diffusion models have exhibited exceptional image-generation capabilities. However, studies show that some outputs are merely replications of training data. Such replications present potential legal challenges for model owners, especially when the generated content contains proprietary information. In this work, we introduce a straightforward yet effective method for detecting memorized prompts by inspecting the magnitude of text-conditional predictions. Our proposed method seamlessly integrates without disrupting sampling algorithms, and delivers high accuracy even at the first generation step, with a single generation per prompt. Building on our detection strategy, we unveil an explainable approach that shows the contribution of individual words or tokens to memorization. This offers an interactive medium for users to adjust their prompts. Moreover, we propose two strategies i.e., to mitigate memorization by leveraging the magnitude of text-conditional predictions, either through minimization during inference or filtering during training. These proposed strategies effectively counteract memorization while maintaining high-generation quality. Code is available at https://github.com/YuxinWenRick/diffusion_memorization.