Self-Regulating Annealing in Heavy-Tailed Diffusion Models
For practitioners using diffusion models on heavy-tailed datasets, this work provides a theoretically grounded sampler that improves tail fidelity.
The paper proposes an SDE-based sampler for heavy-tailed diffusion models that incorporates a state-dependent diffusion coefficient, inducing a self-regulating annealing mechanism. Experiments show this mechanism is necessary for reproducing samples from heavy-tailed distributions.
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.