无需训练，通过匹配数据矩实现快速采样。
Training-Free Generative Sampling via Moment-Matched Score Smoothing
- 不依赖神经网络，用粒子系统直接匹配数据均值与协方差。
- 采样速度极快，可在CPU上完成，生成样本质量媲美扩散模型。
- 适合对速度和部署成本敏感的生成任务，如原型设计或快速验证。
扩散模型通过沿扰动目标分布的梯度进行去噪来生成样本，但通常需要昂贵的神经网络训练。近期研究发现，分数匹配会隐式平滑经验分数，这种平滑偏差有助于捕捉低维数据几何结构并提升泛化能力。本文提出无训练的矩匹配分数平滑过阻尼朗之万动力学（MM-SOLD），一种通过全程保持目标矩的交互粒子采样器。理论证明，在大粒子极限下，粒子密度收敛至确定性极限，其单粒子平稳边缘分布为通过指数倾斜原始分数平滑扩散目标得到的吉布斯-玻尔兹曼分布，其均值与协方差与训练数据经验矩一致。在二维分布和图像潜在空间生成实验中，MM-SOLD实现了快速、鲁棒的无训练采样，采样效率高且生成样本的保真度与多样性达到神经扩散基线水平。
原文摘要 · Abstract (English)
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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