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

Abstract:We propose a novel diffusion model, Flicker-DDPM, which incorporates flicker (1/f) noise inspired by self-organized criticality (SOC), a widely observed phenomenon in natural systems. Unlike denoising diffusion probabilistic models (DDPMs), which employ isotropic white noise in the forward process, Flicker-DDPM adopts colored noise with power-law spectra to better match the spectral statistics of natural images, whose power spectra typically follow P(k) proportional to 1/k^{\alpha}. To this end, we develop a colored-noise module based on a spatial correlation kernel, {\sigma}(d) = (d + 1)^{-\eta}, and theoretically establish that adjusting {\eta} controls the spectral exponent {\alpha} of the generated 1/f{\alpha} noise, enabling adaptation to datasets with diverse spectral characteristics. On CIFAR-10, Flicker DDPM matches or surpasses the generation quality of a standard DDPM baseline using 3.33 times fewer sampling steps, with negligible additional computational cost per step. We further develop a frequency-domain linear theory demonstrating that spectrally matched colored noise linearizes the reverse trajectory, theoretically explaining the observed sampling acceleration.

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