Learning to Simulate from Heavy-Tailed Distribution via Diffusion Model
TL;DR
In Learning to Simulate from Heavy-Tailed Distribution via Diffusion Model, the authors pinpoint why standard diffusion models break down on heavy-tailed targets and propose a Student-t-based heavy-tailed diffusion (SHD) framework that fixes both ends of the pipeline.
Abstract
Generative AI Learns to Sample Extreme Events Many rarest events often carry highest stakes, such as a market crash, a supply-chain rupture, or an extreme clinical outcome. Today’s leading generative AI models (e.g., diffusion models) have shown excessive power to simulate high-dimensional distributions, but they are incapable of capturing rare events in the heavy tails of a distributions. Liu, Zhu, Jia, He, and Zheng show that this mismatch is structural rather than incidental: standard diffusion models systematically fail to capture tail behavior, both when learning from heavy-tailed data and when generating from it. In Learning to Simulate from Heavy-Tailed Distribution via Diffusion Model, the authors pinpoint why standard diffusion models break down on heavy-tailed targets and propose a Student-t-based heavy-tailed diffusion (SHD) framework that fixes both ends of the pipeline. Across synthetic Pareto data, vector autoregressive systems, queueing networks, bike-sharing demand, and stock equity returns, SHD beats Gaussian-noise baselines, particularly in the tails where operations research decisions hinge.