Self-Regulating Annealing in Heavy-Tailed Diffusion Models

Keito Wakatsuki; Hideaki Shimazaki

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arXiv · 2606.01645

Self-Regulating Annealing in Heavy-Tailed Diffusion Models

Keito Wakatsuki·Hideaki Shimazaki

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Abstract

Diffusion models have emerged as a leading framework for deep generative modeling. While the standard Gaussian formulation is theoretically convenient, its suitability for heavy-tailed datasets remains unclear. To address this, heavy-tailed diffusion models (HTDMs) extend the standard formulation by replacing the Gaussian distribution with a Student's t-distribution, thereby improving tail fidelity on heavy-tailed datasets. Although stochastic differential equation (SDE)-based sampling is possible in HTDMs, it has not been fully explored. In this paper, we propose an SDE-based sampler for HTDMs that explicitly incorporates a state-dependent diffusion coefficient. This state dependence naturally induces a self-regulating annealing mechanism by adaptively modulating the effective noise scale. We theoretically explore this mechanism and experimentally verify its necessity for reproducing samples from a heavy-tailed distribution.

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Keito Wakatsuki, Hideaki Shimazaki. 2026-06-01. Self-Regulating Annealing in Heavy-Tailed Diffusion Models. https://arxiv.org/abs/2606.01645

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