Training-Free Generative Sampling via Moment-Matched Score Smoothing

2026-05-13

AI Summary

This work addresses the high computational cost of training conventional diffusion models and the challenge of achieving efficient, training-free generation. The authors propose MM-SOLD, a training-free interactive particle sampling method that, for the first time, integrates a moment-matching mechanism into an overdamped Langevin dynamics framework. During sampling, the method enforces consistency between the particle distribution and the target data’s empirical mean and covariance, while employing score smoothing to enhance sample quality. Theoretical analysis shows that, in the large-particle limit, the particle density converges to a Gibbs–Boltzmann distribution matching the data’s empirical moments. Experiments demonstrate that MM-SOLD enables fast and robust sampling on CPU alone for both 2D distributions and latent-space image generation, achieving sample fidelity and diversity comparable to neural diffusion models.

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.

Problem

• training-free sampling
• generative modeling
• score smoothing
• moment matching
• diffusion models

Innovation

• training-free sampling
• score smoothing
• moment matching
• Langevin dynamics
• diffusion models