Training-Free Generative Sampling via Moment-Matched Score Smoothing

TL;DR

This paper introduces a training-free sampling method called MM-SOLD that uses moment-matched score smoothing to generate high-quality samples efficiently without neural network training.

Contribution

The authors propose a novel training-free particle sampler that enforces target moments, providing a theoretical convergence guarantee and competitive results in image generation.

Findings

MM-SOLD achieves fast, training-free sampling on CPUs.

It produces samples with fidelity and diversity comparable to neural diffusion models.

The method is supported by theoretical convergence analysis.

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.