Flicker-DDPM: Accelerating Denoising Diffusion Sampling via $1/f$ - Type Colored Noise

Natural images' approximate power-law spectra motivate Flicker Diffusion, which couples $1/f$-type spatially correlated Gaussian noise with a matching whitened objective. It retains the baseline U-Net and optimizer-update budget without additional training stages. On CIFAR-10, Flicker-DDIM achieves FID-50k 6.289 at $T=150$/NFE20, versus 6.292 at $T=500$/NFE100 for white DDIM: fivefold fewer network evaluations (NFE) at similar observed FID for these settings. A separate controlled test (both $T=150$/NFE40) yields $6.414\pm 0.070$ versus $14.445\pm 0.375$ over three paired training seeds after identical 15-candidate sampler searches. Matched-schedule ancestral sampling reduces mean FID by approximately 66% on CelebA64 and 82% on LSUN Church64. Covariance-consistent stochastic differential equations and a perturbative path integral describe a leading affine response, its nonlinear corrections, and a bound on residual effects on spectral evolution. Held-out diagnostics and forward-to-reverse spectral predictions on a separate historical $T=500$ CIFAR model pair support a more nearly affine low-frequency response. Complementing the sampling gains, our analysis provides a theoretical framework for understanding partial spectral linearization.