  Unified anomaly detection (AD) is one of the most challenges for anomaly
detection, where one unified model is trained with normal samples from multiple
classes with the objective to detect anomalies in these classes. For such a
challenging task, popular normalizing flow (NF) based AD methods may fall into
a "homogeneous mapping" issue,where the NF-based AD models are biased to
generate similar latent representations for both normal and abnormal features,
and thereby lead to a high missing rate of anomalies. In this paper, we propose
a novel Hierarchical Gaussian mixture normalizing flow modeling method for
accomplishing unified Anomaly Detection, which we call HGAD. Our HGAD consists
of two key components: inter-class Gaussian mixture modeling and intra-class
mixed class centers learning. Compared to the previous NF-based AD methods, the
hierarchical Gaussian mixture modeling approach can bring stronger
representation capability to the latent space of normalizing flows, so that
even complex multi-class distribution can be well represented and learned in
the latent space. In this way, we can avoid mapping different class
distributions into the same single Gaussian prior, thus effectively avoiding or
mitigating the "homogeneous mapping" issue. We further indicate that the more
distinguishable different class centers, the more conducive to avoiding the
bias issue. Thus, we further propose a mutual information maximization loss for
better structuring the latent feature space. We evaluate our method on four
real-world AD benchmarks, where we can significantly improve the previous
NF-based AD methods and also outperform the SOTA unified AD methods.
