{"ID":2921209,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T00:54:56.190393508Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01645","arxiv_id":"2606.01645","title":"Self-Regulating Annealing in Heavy-Tailed Diffusion Models","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.","short_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 Gauss...","url_abs":"https://arxiv.org/abs/2606.01645","url_pdf":"https://arxiv.org/pdf/2606.01645v1","authors":"[\"Keito Wakatsuki\",\"Hideaki Shimazaki\"]","published":"2026-06-01T03:52:08Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}