A Stochastic Analysis Perspective on Diffusion Models
Abstract
Generative modelling involves two complementary tasks: learning a probabilistic approximation of an unknown data distribution from observations, and designing a tractable mechanism for sampling from this approximation. We present a stochastic-analysis perspective on score-based generative models, connecting ideas from classical sampling theory, score estimation, and diffusion time reversal. We first explain how score functions link Langevin sampling with score matching, and how Gaussian smoothing leads to denoising score matching and multiscale sampling methods. We then emphasize the distinction between dynamics preserving a fixed distribution and dynamics transporting a prescribed family of marginals. This motivates a path-space treatment of diffusion time reversal. Finally, we connect the ideal reverse diffusion with practical generative algorithms.
Related
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BibTeX
@misc{strasman2026stochastic,
title = {{A Stochastic Analysis Perspective on Diffusion Models}},
author = {Stanislas Strasman},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14133},
eprint = {2610.14133},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05788636v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Stochastic Analysis Perspective on Diffusion Models
AU - Stanislas Strasman
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.14133
UR - https://hal.science/hal-05788636v1
AB - Generative modelling involves two complementary tasks: learning a probabilistic approximation of an unknown data distribution from observations, and designing a tractable mechanism for sampling from this approximation. We present a stochastic-analysis perspective on score-based generative models, connecting ideas from classical sampling theory, score estimation, and diffusion time reversal. We first explain how score functions link Langevin sampling with score matching, and how Gaussian smoothing leads to denoising score matching and multiscale sampling methods. We then emphasize the distinction between dynamics preserving a fixed distribution and dynamics transporting a prescribed family of marginals. This motivates a path-space treatment of diffusion time reversal. Finally, we connect the ideal reverse diffusion with practical generative algorithms.
ER -