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 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 NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

翻译：我们将在评分采样方法中引入集成学习，以开发无梯度近似采样技术，该技术利用粒子集成群体的集体动力学来计算近似的反向扩散漂移。我们介绍了该方法的基本原理，重点阐述了其与生成扩散模型以及先前提出的Föllmer采样器之间的联系。通过从低维到中维度的采样问题（包括多模态和高度非高斯概率分布）的多个实例，我们展示了集成策略的有效性，并与传统方法（如NUTS）进行了比较。研究结果凸显了在梯度不可用的情况下，集成策略在建模复杂概率分布方面的潜力。最后，我们展示了该方法在地球科学领域贝叶斯反演问题中的应用。