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.
关于Föllmer过程与去噪扩散概率模型之间联系的注记 / A note on connections between the Föllmer process and the denoising diffusion probabilistic model
本文揭示了Föllmer过程（一种指定最终分布的条件布朗运动）与去噪扩散概率模型（DDPM）采样器之间的深层数学联系，证明离散化的Föllmer过程能为DDPM采样器提供自然的超参数设置，并据此系统性地改进和恢复了DDPM采样误差的最新理论边界。
源自 arXiv: 2605.18040
