Abstract: The active distribution network faces observability challenges due to its large scale and frequent topological changes. This paper proposes a distribution network state estimation method based on a power-flow-guided adaptive graph convolutional network. Firstly, a graph data model is constructed according to the topological characteristics, parameters, and measurement information of the distribution network, establishing the transformation relationship between electrical data and the input data of the graph convolutional network. Secondly, the power flow equations are embedded into the loss function to ensure the model complies with the physical constraints of the grid, thereby enhancing interpretability. Weakly supervised learning is employed using measurement data to reduce reliance on labeled datasets and improve adaptability. Finally, the model’s estimation performance is tested under scenarios of general measurement noise and bad data. The results demonstrate that the proposed method achieves satisfactory estimation accuracy and robustness, providing high-precision power flow data for distribution network state evaluation. Comparative analysis with traditional methods further validates its superiority.