Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training
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Computer Science > Machine Learning
Title: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13175 [cs.LG] |
| (or arXiv:2605.13175v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13175
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Hamza Cherkaoui PhD [view email][v1] Wed, 13 May 2026 08:37:59 UTC (106 KB)
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