Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection
2026-06-02 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce Flicker-DDPM, a new version of a popular image generation method that uses special 'colored' noise instead of plain white noise. This noise mimics patterns found in nature called flicker or 1/f noise, which better matches the way real images look. By adjusting how this noise is created, their method can work well for different types of image data. They show on a common dataset that Flicker-DDPM performs as well or better than standard methods while needing fewer steps to create images, making it faster. They also provide a theoretical explanation for why this noise helps speed up the process.
diffusion modelsdenoising diffusion probabilistic modelsflicker noise1/f noiseself-organized criticalitycolored noisespectral statisticsCIFAR-10image generationsampling acceleration
Authors
Kexiang Mao
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^α. To this end, we develop a colored-noise module based on a spatial correlation kernel, σ(d) = (d + 1)^{-η}, and theoretically establish that adjusting η controls the spectral exponent α of the generated 1/fα 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.