Recent advances in diffusion models have enabled the creation of deceptively real images, posing significant security risks when misused. In this study, we reveal that natural and synthetic images exhibit distinct differences in the high-frequency domains of their Fourier power spectra after undergoing iterative noise perturbations through an inverse multi-step denoising process, suggesting that such noise can provide additional discriminative information for identifying synthetic images. Based on this observation, we propose a novel detection method that amplifies these differences by progressively adding noise to the original images across multiple timesteps, and train an ensemble of classifiers on these noised images. To enhance human comprehension, we introduce an explanation generation and refinement module to identify flaws located in AI-generated images. Additionally, we construct two new datasets, GenHard and GenExplain, derived from the GenImage benchmark, providing detection samples of greater difficulty and high-quality rationales for fake images. Extensive experiments show that our method achieves state-of-the-art performance with 98.91% and 95.89% detection accuracy on regular and harder samples, increasing a minimal of 2.51% and 3.46% compared to baselines. Furthermore, our method also generalizes effectively to images generated by other diffusion models. Our code and datasets will be made publicly available.