揭示了去噪扩散模型与费尔默过程的深层联系，指导优化采样器参数。
A note on connections between the Föllmer process and the denoising diffusion probabilistic model
- 用离散化的费尔默过程解释去噪扩散模型采样机制
- 推导出最优采样参数设置，提升采样精度
- 为先进采样误差分析提供统一理论框架
费尔默过程是时间1时具有预设分布的布朗运动。该过程可视为去噪扩散概率模型（DDPM）反向随机微分方程（SDE）的时间压缩增强版。尽管这一关系已被间接用于通过反向SDE离散化分析DDPM采样误差，但直接对费尔默过程进行离散化与DDPM采样器之间的联系尚未充分探讨。本文旨在澄清这一点，并综述相关已有成果。我们证明，离散化的费尔默过程能自然给出DDPM采样器的超参数设置，并据此系统性地恢复现有最先进的采样误差界，且略有改进。
原文摘要 · Abstract (English)
The Föllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an "augmented" time-compressed version of the reverse stochastic differential equation (SDE) for the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, connections between direct discretization of the Föllmer process and the DDPM sampler have not yet been fully explored. This note aims to clarify this point while surveying relevant results from existing work. We show that discretized Föllmer processes give natural hyper-parameter settings of the DDPM sampler. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds with slight improvements.
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