A note on connections between the Föllmer process and the denoising diffusion probabilistic model

• URL: http://arxiv.org/abs/2605.18040v1
• Date: Mon, 18 May 2026 08:31:58 GMT
• Title: A note on connections between the Föllmer process and the denoising diffusion probabilistic model
• Abstract summary: The Fllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1.<n>This fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE.<n>This note aims to clarify this point while surveying relevant results from existing work.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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