Connections between the F"ollmer process and the denoising diffusion probabilistic model

arXiv:2605.18040 · stat.ML, cs.LG, math.PR · Submitted 2026-05-18 · Read on arXiv

stat.ML, cs.LG, math.PR

Submitted: 2026-05-18

Updated: 2026-09-02

Comments: 35 pages. The title has been changed. The right-continuity issue of the filtration generated by the Föllmer process has been resolved

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Diffusion Model — 9× in this paper · explained in 8 episodes
• Diffusion Models — 8× in this paper · explained in 6 episodes
• Generative Modeling — 7× in this paper · explained in 3 episodes
• Diffusion Processes — 3× in this paper · explained in 2 episodes
• Fisher Information — 3× in this paper · explained in 3 episodes
• Score Function — 3× in this paper · explained in 4 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Ambient Dimension — 2× in this paper · explained in 1 episode
• Generative Model — 2× in this paper · explained in 2 episodes
• Generative Models — 2× in this paper · explained in 2 episodes
• Anticoncentration — 1× in this paper · explained in 1 episode
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Probabilistic Forecasting — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Selection Bias — 1× in this paper · explained in 4 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions
• Variational Optimality of F\"ollmer Processes in Generative Diffusions
• Central limit theorem for high temperature spin models via martingale embedding
• Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
• Optimal Convergence Analysis of DDPM for General Distributions
• Sampling, Diffusions, and Stochastic Localization
• Perspectives on Stochastic Localization

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