Likelihood-based deep generative models (DGMs) commonly exhibit a puzzling behaviour: when trained on a relatively complex dataset, they assign higher likelihood values to out-of-distribution (OOD) data from simpler sources. Adding to the mystery, OOD samples are never generated by these DGMs despite having higher likelihoods. This two-pronged paradox has yet to be conclusively explained, making likelihood-based OOD detection unreliable. Our primary observation is that high-likelihood regions will not be generated if they contain minimal probability mass. We demonstrate how this seeming contradiction of large densities yet low probability mass can occur around data confined to low-dimensional manifolds. We also show that this scenario can be identified through local intrinsic dimension (LID) estimation, and propose a method for OOD detection which pairs the likelihoods and LID estimates obtained from a pre-trained DGM. Our method can be applied to normalizing flows and score-based diffusion models, and obtains results which match or surpass state-of-the-art OOD detection benchmarks using the same DGM backbones. Our code is available at https://github.com/layer6ai-labs/dgm_ood_detection.

概率估计的深度生成模型在处理复杂数据集时，尽管给较简单来源的数据分配了较高的概率值，但却没有生成这些数据，这个矛盾仍然没有得到解释，因此概率估计的OOD检测不可信。我们的研究观察到，当高概率区域中包含的概率质量最小时，这些区域将不会生成。我们通过本地内在维度估计方法解释了这种大密度但低概率质量的情况，并提出了一种基于预训练深度生成模型的概率和内在维度估计相结合的OOD检测方法，该方法适用于归一化流和基于得分的扩散模型，并在相同的深度生成模型架构上达到或超过了最先进的OOD检测基准结果。

似然异常检测悖论的几何解释