NFCDS: A Plug-and-Play Noise Frequency-Controlled Diffusion Sampling Strategy for Image Restoration

Diffusion sampling-based Plug-and-Play (PnP) methods produce images with high perceptual quality but often suffer from reduced data fidelity, primarily due to the noise introduced during reverse diffusion. To address this trade-off, we propose Noise Frequency-Controlled Diffusion Sampling (NFCDS), a spectral modulation mechanism for reverse diffusion noise. We show that the fidelity-perception conflict can be fundamentally understood through noise frequency: low-frequency components induce blur and degrade fidelity, while high-frequency components drive detail generation. Based on this insight, we design a Fourier-domain filter that progressively suppresses low-frequency noise and preserves high-frequency content. This controlled refinement injects a data-consistency prior directly into sampling, enabling fast convergence to results that are both high-fidelity and perceptually convincing–without additional training. As a PnP module, NFCDS seamlessly integrates into existing diffusion-based restoration frameworks and improves the fidelity-perception balance across diverse zero-shot tasks.

💡 Research Summary

The paper tackles a fundamental limitation of diffusion‑based Plug‑and‑Play (PnP) image restoration methods: while the stochastic nature of reverse diffusion yields highly realistic textures, the injected Gaussian noise also perturbs low‑frequency components, leading to a loss of data fidelity (blur, structural drift). The authors propose Noise Frequency‑Controlled Diffusion Sampling (NFCDS), a simple yet powerful spectral‑modulation technique that selectively attenuates low‑frequency noise while preserving high‑frequency content during each reverse‑diffusion step.

First, the authors provide a frequency‑domain analysis of the noise term in the DDIM/ DDPM reverse update. By decomposing the image and the injected noise into low‑frequency (LF) and high‑frequency (HF) parts via the Fourier transform, they demonstrate experimentally that LF noise primarily degrades global structure, whereas HF noise is essential for generating fine details and textures. In generation tasks, both components are needed: LF noise shapes the overall shape, HF noise refines texture. In restoration, however, the degraded observation already supplies reliable LF information through the data‑consistency term, so LF noise becomes redundant and harmful, while HF noise remains crucial for hallucinating missing details.

Motivated by this insight, NFCDS introduces a soft‑threshold mask M(t) in the Fourier domain: \