Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

翻译：用于新物理过程异常检测的方法通常受限于低维空间，原因是学习高维概率密度存在困难。特别是在组分层级上，在常见的密度估计方法中融入置换不变性和可变长度输入等理想特性变得十分困难。本研究引入了一种基于扩散模型的置换不变密度估计器，专门针对粒子物理数据中的可变长度输入设计。我们通过将学习得到的密度作为置换不变异常检测分数，有效识别出在本底唯象假设下似然度较低的喷注，从而验证了该方法的有效性。为评估密度估计方法，我们研究了学习密度的比值，并将其与监督分类算法得到的结果进行了比较。