Learning to Simulate from Heavy-Tailed Distribution via Diffusion Model
Abstract
Diffusion models are a class of neural-network-based generative models and arise as one of the most prominent tools for learning to simulate from multidimensional distributions. Most existing diffusion models have been applied to data distributions with finite support, especially in vision tasks. In contrast, applications in the fields of operations research and management science often involve distributions with infinite support or even heavy tails. In this work, we theoretically show that existing diffusion models encounter challenges in addressing the tail distribution in both model training and data generation. To address the challenges, we develop a new method extending existing diffusion models to effectively capture the heavy-tailed distribution patterns. Our method accommodates the learning and simulation of both multidimensional distributions with potential heavy tails and conditional distributions with multidimensional conditions.
Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1450.
