Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training
Abstract
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.
Cite
@article{arxiv.2605.13175,
title = {Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training},
author = {Hamza Cherkaoui and Hélène Halconruy and Antonio Ocello},
journal= {arXiv preprint arXiv:2605.13175},
year = {2026}
}