# Annealed L'evy Diffusion via Gaussian Surrogate Reverse Dynamics

arXiv: https://arxiv.org/abs/2610.19692 · HTML: https://mlsanity.com/paper/2610.19692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Heavy-Tailed Diffusion with Denoising L'evy Probabilistic Models](https://mlsanity.com/paper/2407.18609/) (2024)
- [Multiplicative noise and heavy tails in stochastic optimization](https://mlsanity.com/paper/2006.06293/) (2020)
- [Diffusion models with location-scale noise](https://mlsanity.com/paper/2304.05907/) (2023)
- [Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees](https://mlsanity.com/paper/2601.06715/) (2026)
- [Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training](https://mlsanity.com/paper/2605.13175/) (2026)

## Abstract (arXiv)

Gaussian diffusion models offer a practical framework for generative modeling. Denoising L'evy Probabilistic Models (DLPM) introduce heavy-tailed perturbations with a fixed tail index throughout denoising. We introduce Annealed L'evy 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.