Training-Free Generative Sampling via Moment-Matched Score Smoothing

• URL: http://arxiv.org/abs/2605.14276v1
• Date: Thu, 14 May 2026 02:20:36 GMT
• Title: Training-Free Generative Sampling via Moment-Matched Score Smoothing
• Abstract summary: Diffusion models generate samples by denoising along the score of a perturbed target distribution.<n>Recent work suggests that score matching implicitly smooths the empirical score.<n>We propose moment-matched score-smoothed overdamped Langevin dynamics.
• Score: 0.6015898117103069
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly smooths the empirical score, and that this smoothing bias promotes generalization by capturing low-dimensional data geometry. We propose moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD), a training-free interacting particle sampler that enforces the target moments throughout the sampling trajectory. We prove that, in the large-particle limit, the empirical particle density converges to a deterministic limit whose one-particle stationary marginal is a Gibbs--Boltzmann density obtained by exponentially tilting a naive score-smoothed diffusion target. The mean and covariance of this distribution agree with the empirical moments of the training data. Experiments on 2D distributions and latent-space image generation show that MM-SOLD enables fast, robust, training-free sampling on CPUs, with sample fidelity and diversity competitive with neural diffusion baselines.

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