Training-Free Generative Sampling via Moment-Matched Score Smoothing

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...

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