Flicker-DDPM incorporates flicker (1/f) noise inspired by self-organized criticality into denoising diffusion probabilistic models, achieving 3.33× sampling acceleration with simultaneous quality improvement on CIFAR-10.
Standard DDPMs corrupt data into white noise (flat spectrum), but natural images have power-law spectra P(k) ∝ k−α with α ≈ 2.7. This spectral mismatch forces the reverse process to waste hundreds of steps reshaping the frequency structure before generating content.
Flicker-DDPM replaces white noise with spectrally colored noise whose power spectrum matches the data. The noise is generated via a simple spatial correlation kernel:
where η is analytically determined from data statistics through Matérn covariance theory:
For CIFAR-10: α = 2.70 → ηopt = 0.20. No hyperparameter search required.
White noise (flat spectrum) vs. colored noise (power-law spectrum matching natural images).
| T (steps) | White DDPM (FID↓) | Flicker-DDPM (FID↓) | Improvement |
|---|---|---|---|
| 100 | 36.17 | 22.57 | −37.6% |
| 150 | 25.36 | 12.24 | −51.7% |
| 200 | 18.08 | 11.57 | −36.0% |
| 500 | 13.02 | 11.96 | −8.1% |
FID is computed using 10,000 generated samples against the CIFAR-10 training set. Flicker-DDPM at T=150 outperforms standard DDPM at T=500 (FID 12.24 vs 13.02), yielding a 500/150 ≈ 3.33× speedup.
FID scores across diffusion steps. Flicker-DDPM consistently outperforms the white-noise baseline.
Left: Flicker-DDPM (η=0.2). Right: white-noise DDPM. At the same step budget, Flicker-DDPM produces sharper, more coherent images.
Colored noise linearizes the reverse diffusion trajectory in Fourier space. When noise already carries the correct spectral structure (L(k) = 0), the denoiser operates in a near-linear regime at all frequencies — eliminating the nonlinear spectral reshaping bottleneck.
Linearization quality R²(k,t). Flicker-DDPM achieves R² > 0.95 uniformly across all modes, while white DDPM shows extreme disparity (R² = 0.505 at k=1 vs 0.968 at k=14).
Spectral evolution during reverse sampling (Flicker-DDPM): all frequency modes converge to the target in concert.
Spectral evolution (white DDPM): spectrum starts flat and must be rebuilt sequentially, requiring ~350 extra steps.
├── main.py # CLI entry point (train / sample / FID eval)
├── models/ # Network architectures
│ ├── unet.py # Unconditional UNet
│ └── unet_cfg.py # Classifier-free guidance UNet
├── core/ # Core components
│ ├── diffusion.py # DiffusionTrainer & DiffusionSampler
│ ├── noise.py # NoiseModule (white / colored via Cholesky or FFT)
│ ├── train.py # Training & sampling loops
│ ├── eval_fid.py # FID evaluation pipeline
│ ├── scheduler.py # Learning rate warmup scheduler
│ └── visualizer.py # Training diagnostics & visualization
├── analysis/ # Theory verification & spectral analysis
│ ├── gamma_ode.py # Measure γ(k,t) and validate linear-theory ODE
│ ├── fit_eta.py # Fit power-law exponent from CIFAR-10 spectrum
│ └── verify_matern.py # Matérn kernel theory verification
├── scripts/ # Plotting scripts
└── figures/ # Paper figures
torch >= 2.0
torchvision
numpy
scipy
matplotlib
tqdm
pytorch-fid
# White noise baseline, T=500
python main.py --noise_type white --T 500 --epoch 200
# Colored noise (η=0.2), T=150
python main.py --noise_type colored --eta 0.2 --T 150 --epoch 200
# Multi-GPU (DDP)
torchrun --nproc_per_node=4 main.py --noise_type colored --eta 0.2 --T 150python main.py --eval --noise_type colored --eta 0.2 --T 150 --ckpt ckpt_199_.ptpython main.py --fid --noise_type colored --eta 0.2 --T 150# Measure γ(k,t) and validate ODE predictions
python analysis/gamma_ode.py --noise_type colored --eta 0.2 --T 500
# Fit power-law exponent α from CIFAR-10
python analysis/fit_eta.py@article{mao2026flicker,
title={Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection},
author={Mao, KeXiang and Li, FanCheng},
journal={arXiv e-prints},
pages={arXiv--2606},
year={2026}
}MIT