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.

Related papers

• Constrained Diffusion Models via Dual Training [80.03953599062365]
  Diffusion processes are prone to generating samples that reflect biases in a training dataset. We develop constrained diffusion models by imposing diffusion constraints based on desired distributions. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints.
  arXiv  Detail & Related papers  (2024-08-27T14:25:42Z)
• Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling [2.1779479916071067]
  We introduce a novel framework that enhances diffusion models by supporting a broader range of forward processes. We also propose a novel parameterization technique for learning the forward process. Results underscore NFDM's versatility and its potential for a wide range of applications.
  arXiv  Detail & Related papers  (2024-04-19T15:10:54Z)
• MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process [26.661721555671626]
  We introduce a novel Multi-Granularity Time Series (MG-TSD) model, which achieves state-of-the-art predictive performance. Our approach does not rely on additional external data, making it versatile and applicable across various domains.
  arXiv  Detail & Related papers  (2024-03-09T01:15:03Z)
• Guided Diffusion from Self-Supervised Diffusion Features [49.78673164423208]
  Guidance serves as a key concept in diffusion models, yet its effectiveness is often limited by the need for extra data annotation or pretraining. We propose a framework to extract guidance from, and specifically for, diffusion models.
  arXiv  Detail & Related papers  (2023-12-14T11:19:11Z)
• Soft Mixture Denoising: Beyond the Expressive Bottleneck of Diffusion Models [76.46246743508651]
  We show that current diffusion models actually have an expressive bottleneck in backward denoising. We introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising.
  arXiv  Detail & Related papers  (2023-09-25T12:03:32Z)
• Semi-Implicit Denoising Diffusion Models (SIDDMs) [50.30163684539586]
  Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver high-quality, diverse samples but are slowed by an inherently high number of iterative steps. We introduce a novel approach that tackles the problem by matching implicit and explicit factors. We demonstrate that our proposed method obtains comparable generative performance to diffusion-based models and vastly superior results to models with a small number of sampling steps.
  arXiv  Detail & Related papers  (2023-06-21T18:49:22Z)
• Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models [77.83923746319498]
  We propose a framework called Diff-Instruct to instruct the training of arbitrary generative models. We show that Diff-Instruct results in state-of-the-art single-step diffusion-based models. Experiments on refining GAN models show that the Diff-Instruct can consistently improve the pre-trained generators of GAN models.
  arXiv  Detail & Related papers  (2023-05-29T04:22:57Z)
• Information-Theoretic Diffusion [18.356162596599436]
  Denoising diffusion models have spurred significant gains in density modeling and image generation. We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory.
  arXiv  Detail & Related papers  (2023-02-07T23:03:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.