Heavy-Tailed Diffusion Models

• URL: http://arxiv.org/abs/2410.14171v2
• Date: Tue, 29 Oct 2024 09:59:22 GMT
• Title: Heavy-Tailed Diffusion Models
• Authors: Kushagra Pandey, Jaideep Pathak, Yilun Xu, Stephan Mandt, Michael Pritchard, Arash Vahdat, Morteza Mardani,
• Abstract summary: We show that traditional diffusion and flow-matching models fail to capture heavy-tailed behavior. We address this by repurposing the diffusion framework for heavy-tail estimation. We introduce t-EDM and t-Flow, extensions of existing diffusion and flow models that employ a Student-t prior.
• Score: 38.713884992630675
• License:
• Abstract: Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and flow-matching models with standard Gaussian priors fail to capture heavy-tailed behavior. We address this by repurposing the diffusion framework for heavy-tail estimation using multivariate Student-t distributions. We develop a tailored perturbation kernel and derive the denoising posterior based on the conditional Student-t distribution for the backward process. Inspired by $\gamma$-divergence for heavy-tailed distributions, we derive a training objective for heavy-tailed denoisers. The resulting framework introduces controllable tail generation using only a single scalar hyperparameter, making it easily tunable for diverse real-world distributions. As specific instantiations of our framework, we introduce t-EDM and t-Flow, extensions of existing diffusion and flow models that employ a Student-t prior. Remarkably, our approach is readily compatible with standard Gaussian diffusion models and requires only minimal code changes. Empirically, we show that our t-EDM and t-Flow outperform standard diffusion models in heavy-tail estimation on high-resolution weather datasets in which generating rare and extreme events is crucial.

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