Accurate prediction of mobile traffic,i.e., network traffic from cellular base stations, is crucial for optimizing network performance and supporting urban development. However, the non-stationary nature of mobile traffic, driven by human activity and environmental changes, leads to both regular patterns and abrupt variations. Diffusion models excel in capturing such complex temporal dynamics due to their ability to capture the inherent uncertainties. Most existing approaches prioritize designing novel denoising networks but often neglect the critical role of noise itself, potentially leading to sub-optimal performance. In this paper, we introduce a novel perspective by emphasizing the role of noise in the denoising process. Our analysis reveals that noise fundamentally shapes mobile traffic predictions, exhibiting distinct and consistent patterns. We propose NPDiff, a framework that decomposes noise into prior and residual components, with the prior derived from data dynamics, enhancing the model's ability to capture both regular and abrupt variations. NPDiff can seamlessly integrate with various diffusion-based prediction models, delivering predictions that are effective, efficient, and robust. Extensive experiments demonstrate that it achieves superior performance with an improvement over 30%, offering a new perspective on leveraging diffusion models in this domain. We provide code and data at https://github.com/tsinghua-fib-lab/NPDiff.