Title: Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection

Abstract:

This paper introduces Flicker-DDPM, a new diffusion model that integrates flicker (1/f) noise, drawing inspiration from self-organized criticality (SOC), a phenomenon prevalent in natural systems. Standard denoising diffusion probabilistic models (DDPMs) typically rely on isotropic white noise during the forward process; in contrast, Flicker-DDPM utilizes colored noise characterized by power-law spectra. This approach aligns more closely with the spectral statistics of natural images, which generally adhere to power spectra where P(k) is proportional to 1/k^{\alpha}.

To achieve this, we engineered a colored-noise module utilizing a spatial correlation kernel defined as {\sigma}(d) = (d + 1)^{-\eta}. We provide a theoretical proof that modifying the parameter {\eta} allows for the control of the spectral exponent {\alpha} of the resulting 1/f{\alpha} noise, thereby facilitating adaptation to datasets with varying spectral profiles.

Experimental results on CIFAR-10 indicate that Flicker-DDPM achieves generation quality comparable to or exceeding that of a standard DDPM baseline, while requiring 3.33 times fewer sampling steps and incurring negligible additional computational cost per step. Furthermore, we present a frequency-domain linear theory showing that spectrally matched colored noise linearizes the reverse trajectory. This theoretical framework offers an explanation for the observed acceleration in the sampling process.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC