Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics
Abstract
Gaussian diffusion models offer a practical framework for generative modeling. Denoising Lévy Probabilistic Models (DLPM) introduce heavy-tailed perturbations with a fixed tail index throughout denoising. We introduce Annealed Lévy Diffusion (ALD). ALD varies the stability index α(t) to combine heavy-tailed exploration with Gaussian refinement. Our marginal-first formulation represents stable noise as a scalar Gaussian scale mixture. This formulation enables standard Gaussian noise-prediction training with one additional scale input. We study two sampling processes. ALD-renoise estimates the clean sample and injects fresh marginal noise. ALD-posterior preserves dependence between successive states through an accumulated conditional variance and a Gaussian bridge update. Both samplers reuse the same trained predictor with different scalar inputs. We evaluate ALD on four 2D benchmarks and an imbalanced nine-mode mixture. We also examine training efficiency and the effects of prediction perturbations on clipped Holtsmark data. Additional experiments evaluate MNIST and CelebA64 generation and CIFAR-10LT augmentation. ALD preserves local geometry on the evaluated light-tailed and manifold-structured targets.
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BibTeX
@misc{jiao2026annealed,
title = {{Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics}},
author = {Yuling Jiao and Lican Kang and Jerry Zhijian Yang and Cheng Yuan and Ruizhe Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19692},
eprint = {2610.19692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19692},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics
AU - Yuling Jiao
AU - Lican Kang
AU - Jerry Zhijian Yang
AU - Cheng Yuan
AU - Ruizhe Zhang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19692
UR - https://arxiv.org/abs/2610.19692
AB - Gaussian diffusion models offer a practical framework for generative modeling. Denoising Lévy Probabilistic Models (DLPM) introduce heavy-tailed perturbations with a fixed tail index throughout denoising. We introduce Annealed Lévy Diffusion (ALD). ALD varies the stability index α(t) to combine heavy-tailed exploration with Gaussian refinement. Our marginal-first formulation represents stable noise as a scalar Gaussian scale mixture. This formulation enables standard Gaussian noise-prediction training with one additional scale input. We study two sampling processes. ALD-renoise estimates the clean sample and injects fresh marginal noise. ALD-posterior preserves dependence between successive states through an accumulated conditional variance and a Gaussian bridge update. Both samplers reuse the same trained predictor with different scalar inputs. We evaluate ALD on four 2D benchmarks and an imbalanced nine-mode mixture. We also examine training efficiency and the effects of prediction perturbations on clipped Holtsmark data. Additional experiments evaluate MNIST and CelebA64 generation and CIFAR-10LT augmentation. ALD preserves local geometry on the evaluated light-tailed and manifold-structured targets.
ER -