Saved in:
Bibliographic Details
Main Authors: Cherkaoui, Hamza, Halconruy, Hélène, Ocello, Antonio
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.13175
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917554730041344
author Cherkaoui, Hamza
Halconruy, Hélène
Ocello, Antonio
author_facet Cherkaoui, Hamza
Halconruy, Hélène
Ocello, Antonio
contents Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is intuitive: if the data are heavy-tailed, HT noise may appear better matched than light-tailed (LT) Gaussian noise. However, replacing Gaussian noise by HT noise also changes the underlying estimation problem. In this paper, we revisit this paradigm through a combined theoretical and empirical study, establishing sampling-error bounds for two representative diffusion models driven by HT and LT noise. We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds. We support these findings with experiments on synthetic and real-world datasets, empirically recovering the predicted error trade-off. Our results call into question a growing design trend in generative modeling and challenge the use of HT noise to improve rare-region exploration.
format Preprint
id arxiv_https___arxiv_org_abs_2605_13175
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training
Cherkaoui, Hamza
Halconruy, Hélène
Ocello, Antonio
Machine Learning
Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is intuitive: if the data are heavy-tailed, HT noise may appear better matched than light-tailed (LT) Gaussian noise. However, replacing Gaussian noise by HT noise also changes the underlying estimation problem. In this paper, we revisit this paradigm through a combined theoretical and empirical study, establishing sampling-error bounds for two representative diffusion models driven by HT and LT noise. We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds. We support these findings with experiments on synthetic and real-world datasets, empirically recovering the predicted error trade-off. Our results call into question a growing design trend in generative modeling and challenge the use of HT noise to improve rare-region exploration.
title Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training
topic Machine Learning
url https://arxiv.org/abs/2605.13175