Recovering user preferences from user-item interaction matrices is a key challenge in recommender systems. While diffusion models can sample and reconstruct preferences from latent distributions, they often fail to capture similar users' collective preferences effectively. Additionally, latent variables degrade into pure Gaussian noise during the forward process, lowering the signal-to-noise ratio, which in turn degrades performance. To address this, we propose S-Diff, inspired by graph-based collaborative filtering, better to utilize low-frequency components in the graph spectral domain. S-Diff maps user interaction vectors into the spectral domain and parameterizes diffusion noise to align with graph frequency. This anisotropic diffusion retains significant low-frequency components, preserving a high signal-to-noise ratio. S-Diff further employs a conditional denoising network to encode user interactions, recovering true preferences from noisy data. This method achieves strong results across multiple datasets.