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Multivariate time series anomaly detection has been extensively studied under the semi-supervised setting, where a training dataset with all normal instances is required. However, preparing such a dataset is very laborious since each single data instance should be fully guaranteed to be normal. It is, therefore, desired to explore multivariate time series anomaly detection methods based on the dataset without any label knowledge. In this paper, we propose MTGFlow, an unsupervised anomaly detection approach for multivariate time series anomaly detection via dynamic graph and entity-aware normalizing flow, leaning only on a widely accepted hypothesis that abnormal instances exhibit sparse densities than the normal. However, the complex interdependencies among entities and the diverse inherent characteristics of each entity pose significant challenges on the density estimation, let alone to detect anomalies based on the estimated possibility distribution. To tackle these problems, we propose to learn the mutual and dynamic relations among entities via a graph structure learning model, which helps to model accurate distribution of multivariate time series. Moreover, taking account of distinct characteristics of the individual entities, an entity-aware normalizing flow is developed to describe each entity into a parameterized normal distribution, thereby producing fine-grained density estimation. Incorporating these two strategies, MTGFlow achieves superior anomaly detection performance. Experiments on five public datasets with seven baselines are conducted, MTGFlow outperforms the SOTA methods by up to 5.0 AUROC\%. Codes will be released at https://github.com/zqhang/Detecting-Multivariate-Time-Series-Anomalies-with-Zero-Known-Label.