Title: Self-Regulating Annealing in Heavy-Tailed Diffusion Models

Abstract: Diffusion models have established themselves as a premier approach within the domain of deep generative modeling. Although the conventional Gaussian formulation offers theoretical advantages, its effectiveness when applied to datasets characterized by heavy tails is not well understood. To bridge this gap, heavy-tailed diffusion models (HTDMs) modify the standard framework by substituting the Gaussian distribution with a Student’s t-distribution, which enhances the accuracy of tail representation in such datasets. While sampling via stochastic differential equations (SDEs) is feasible in HTDMs, this area has received limited attention. This study introduces an SDE-based sampling method for HTDMs that features a state-dependent diffusion coefficient. This dependency inherently creates a self-regulating annealing process, which dynamically adjusts the effective noise scale. We provide a theoretical analysis of this mechanism and confirm through experiments that it is essential for accurately generating samples from heavy-tailed distributions.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC