May 13, 2026 · cs.LGJ/K move · Enter open · S save
Hamza Cherkaoui, Hélène Halconruy, Antonio Ocello
SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, Palaiseau, France · Modal’X, Université Paris Nanterre, Nanterre, France · CREST, ENSAE Paris, Institut Polytechnique de Paris, Palaiseau, France
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.