从频谱角度分析扩散模型，为噪声调度设计提供理论依据
Spectral Analysis of Diffusion Models with Application to Schedule Design
- 将扩散过程建模为频谱传递函数，揭示噪声演化规律
- 提出依赖数据频谱特征的新型噪声调度方案，提升生成质量
- 为实践中的启发式调度提供理论解释，适合模型优化研究者
扩散模型已成为建模复杂数据分布并生成逼真样本的强大工具。尽管近年来发展了先进架构与采样方法，但部分合成过程决策仍依赖缺乏理论基础的启发式策略。本文从频谱响应视角对扩散模型推理过程进行新分析，基于高斯假设，将推理过程表示为闭式频谱传递函数，刻画生成信号如何随初始噪声变化。我们展示了该分析如何用于设计与数据特性匹配的噪声调度。频谱视角还揭示了底层动态，阐明了频谱特性与噪声调度结构之间的关系。结果得到的调度曲线依赖于数据的频谱内容，为实践中一些启发式方法提供了理论支持。
原文摘要 · Abstract (English)
Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models practically usable. However, certain synthesis process decisions still rely on heuristics without a solid theoretical foundation. In our work, we offer a novel analysis of the DM's inference process, introducing a comprehensive frequency response perspective. Specifically, by relying on Gaussianity assumption, we present the inference process as a closed-form spectral transfer function, capturing how the generated signal evolves in response to the initial noise. We demonstrate how the proposed analysis can be leveraged to design a noise schedule that aligns effectively with the characteristics of the data. The spectral perspective also provides insights into the underlying dynamics and sheds light on the relationship between spectral properties and noise schedule structure. Our results lead to scheduling curves that are dependent on the spectral content of the data, offering a theoretical justification for some of the heuristics taken by practitioners.
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