Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics

Yuling Jiao; Lican Kang; Jerry Zhijian Yang; Cheng Yuan; Ruizhe Zhang

Home/Archive/arXiv

arXiv · 2610.19692

Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics

Yuling Jiao·Lican Kang·Jerry Zhijian Yang·Cheng Yuan·Ruizhe Zhang

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.LG stat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yuling Jiao, Lican Kang, Jerry Zhijian Yang, Cheng Yuan, Ruizhe Zhang. 2026-10-14. Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics. https://arxiv.org/abs/2610.19692

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generation of data on discontinuous manifolds via continuous stochastic non-invertible networks

The generation of discontinuous distributions is a difficult task for most known frameworks such as generative autoencoders and generative adversarial networks. Generative non-invertible models are unable to accurately generate such distributions, require long training and often are subject to mode collapse. Variational autoencoders (VAEs), which are based on the idea of keeping the latent space to be Gaussian for the sake of a simple sampling, allow an accurate reconstruction, while they experience significant limitations at generation task. In this work, instead of trying to keep the latent space to be Gaussian, we use a pre-trained contrastive encoder to obtain a clustered latent space. Then, for each cluster, representing a unimodal submanifold, we train a dedicated low complexity network to generate this submanifold from the Gaussian distribution. The proposed framework is based on the information-theoretic formulation of mutual information maximization between the input data and latent space representation. We derive a link between the cost functions and the information-theoretic formulation. We apply our approach to synthetic 2D distributions to demonstrate both reconstruction and generation of discontinuous distributions using continuous stochastic networks.

cs.LG↗

arXiv2026

Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides calibrated prediction intervals. Unlike the existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. When the raw forecast intervals are approximately calibrated, we prove that BCI is near optimal for its surrogate model predictive control problem. We find empirically that BCI avoids uninformative intervals with infinite lengths under our main experimental configuration and generates substantially shorter prediction intervals when the raw forecast intervals are poorly calibrated.

cs.LG↗

arXiv2026

GLL: A Differentiable Graph Learning Layer for Neural Networks

Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.

cs.LG↗