Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

翻译：物理模型的全局拟合需要高效的方法来探索高维和/或多峰后验函数。我们提出了一种新颖方法，通过将Metropolis-Hastings算法与能够抽取全局样本以逼近后验的扩散模型相结合，加速马尔可夫链蒙特卡洛（MCMC）采样。我们简要回顾了图像合成背景下的扩散模型，随后提供了一种针对低维数据数组进行优化的简化扩散模型。接着，我们展示了改进的Metropolis-Hastings算法，该算法将局部提议与来自扩散模型的全局提议相结合，且该扩散模型在MCMC运行期间会根据产生的样本进行定期训练。我们的方法显著减少了在多个解析函数以及基于部分子分布函数全局分析的物理实例中，为获得贝叶斯后验精确表示所需的似然评估次数。该方法可扩展至其他MCMC技术，我们将其与基于归一化流的类似方法进行了简要比较。代码实现详见https://github.com/NickHunt-Smith/MCMC-diffusion。