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.
Sampling Processes
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.
Evaluation
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.