Recent research has revealed that deep generative models including flow-based models and Variational autoencoders may assign higher likelihood to out-of-distribution (OOD) data than in-distribution (ID) data. However, we cannot sample out OOD data from the model. This counterintuitive phenomenon has not been satisfactorily explained. In this paper, we prove theorems to investigate the divergences in flow-based model and give two explanations to the above phenomenon from divergence and geometric perspectives, respectively. Based on our analysis, we propose two group anomaly detection methods. Furthermore, we decompose the KL divergence and propose a point-wise anomaly detection method. We have conducted extensive experiments on prevalent benchmarks to evaluate our methods. For group anomaly detection (GAD), our method can achieve near 100% AUROC on all problems and has robustness against data manipulations. On the contrary, the state-of-the-art (SOTA) GAD method performs not better than random guessing for challenging problems and can be attacked by data manipulation in almost all cases. For point-wise anomaly detection (PAD), our method is comparable to the SOTA PAD method on one category of problems and outperforms the baseline significantly on another category of problems.
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