Denoising Levy Scores for Generative Modeling

We investigate Levy-driven sampling to improve sample quality in score-based generative modeling under a fixed function-evaluation budget. Levy jumps enable long-range transitions between separated regions, offering an alternative to Brownian Langevin relaxation at each noise level. Unlike existing Levy-based generative models, which introduce jumps through non-Gaussian forward noising, we retain Gaussian perturbations and introduce Levy Langevin correctors (LLCs) only at sampling step. These correctors depend only on the Levy score, a nonlocal analogue of the Stein score. We develop denoising Levy score matching (DLSM) by perturbing the data with different levels of Gaussian noise and jointly estimating the corresponding Levy scores. On synthetic multimodal and heavy-tailed target distributions, our method achieves up to an $9.5\times$ reduction in $W_1$ error relative to Brownian samplers at matched NFEs. At matched low-NFE budgets, our method achieves lower FID than Brownian samplers on CIFAR-10, CelebA-64, and CIFAR-10-LT; on CIFAR-10-LT, it also reproduces the long-tailed class distribution more accurately.