Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, $\textit{Stochastic Localization via Iterative Posterior Sampling}$ (SLIPS), to obtain approximate samples of this dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of SLIPS on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.

翻译：在分数学习的基础上，随机定位技术近期引发了新的研究兴趣。此类模型通过称为观测过程的随机过程对数据分布样本进行加噪处理，并逐步学习与该动力学相关联的去噪器。除特定应用场景外，随机定位在从未归一化目标密度中采样的问题上尚未得到充分探索。本研究致力于填补这一空白。我们提出通用随机定位框架，引入具有灵活去噪调度的显式观测过程类别。我们建立了完整的方法论——$\textit{基于迭代后验采样的随机定位}$（SLIPS），以获得该动力学的近似样本，并作为副产品得到目标分布的样本。该方案基于去噪器的马尔可夫链蒙特卡洛估计，并附有详细实施指南。我们在多个多模态分布基准测试中验证了SLIPS的优势与适用性，包括递增维度的高斯混合模型、贝叶斯逻辑回归以及统计力学中的高维场系统。