A note on connections between the F\"ollmer process and the denoising diffusion probabilistic model
Authors: Yuta Koike
Summary
arXiv:2605. 18040v1 Announce Type: new Abstract: The F"ollmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1.
Relevance
Read next because A note on connections between the F"ollmer process and the denoising diffusion probabilistic model overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Training one persona to emit a [ZLT] marker without bystanders adopting it has a one-cell-wide LR x epochs window on Qwen2.5-7B-Instruct (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: rect, full, model. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.18040v1 Announce Type: new Abstract: The F"ollmer 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 F"ollmer 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 F"ollmer 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.