Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally require gradients of the target probability distribution, which can be unavailable or computationally prohibitive in many scientific and engineering applications. Here, we introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of the ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like the No-U-Turn Sampler. Additionally, we showcase these strategies in the context of a high-dimensional Bayesian inversion problem within the geophysical sciences. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable.

翻译：生成建模的最新进展利用基于分数的方法结合随机微分方程，从复杂概率分布中进行采样。然而，这些以及其他高性能采样方法通常需要目标概率分布的梯度，这在许多科学与工程应用中可能无法获得或计算成本过高。本文在基于分数的采样方法中引入集合，以开发无梯度的近似采样技术，该技术利用粒子集合的集体动力学来计算近似的反向扩散漂移。我们介绍了其基础方法论，重点阐述了其与生成扩散模型以及先前引入的F\"ollmer采样器之间的关系。我们通过从低维到中维的各种采样问题示例（包括多模态和高度非高斯概率分布）展示了集合策略的有效性，并与传统方法（如No-U-Turn采样器）进行了比较。此外，我们在地球物理科学中的一个高维贝叶斯反演问题背景下展示了这些策略。我们的研究结果凸显了在梯度不可用的情况下，集合策略对于建模复杂概率分布的潜力。