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：针对新物理过程的异常检测方法通常受限于低维空间，这是由于高维概率密度学习的困难性。特别是在组分层面，在主流密度估计方法中引入置换不变性和可变长度输入等理想特性变得尤为困难。本研究基于扩散模型提出了一种面向粒子物理数据的置换不变密度估计器，该估计器专为处理可变长度输入而设计。我们通过将学习到的密度作为置换不变异常检测分数，有效识别了在仅背景假设下似然度较低的喷注，从而验证了本方法的有效性。为评估密度估计方法的性能，我们研究了学习密度的比率，并将其与有监督分类算法所得结果进行了对比。