用自然图像的1/f噪声加速扩散模型采样，效果更好且更快。
Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection
- 引入1/f色噪声替代传统白噪声，更贴合自然图像频谱特性。
- 在CIFAR-10上仅需3.33倍少的采样步数即达同等生成质量。
- 理论证明频谱匹配可线性化反向轨迹，解释加速机制。
我们提出一种新型扩散模型Flicker-DDPM，其在前向过程引入受自组织临界性启发的1/f（闪烁）噪声。与传统去噪扩散概率模型（DDPM）使用各向同性白噪声不同，Flicker-DDPM采用具有幂律谱的色噪声，更匹配自然图像的功率谱特性（通常满足P(k) ∝ 1/k^α）。为此，我们设计基于空间相关核σ(d) = (d + 1)^{-η}的色噪声模块，并理论上证明调节η可控制生成噪声的谱指数α，实现对不同数据集谱特性的适配。在CIFAR-10上，Flicker-DDPM以3.33倍更少的采样步数达到或超越标准DDPM基线的生成质量，每步计算开销几乎无增加。我们进一步构建频域线性理论，证明谱匹配的色噪声可线性化反向轨迹，为观察到的采样加速提供理论解释。
原文摘要 · Abstract (English)
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.
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