The training process of learning-based distribution system state estimation (DSSE) methods relies on accurate state variables, which typically contain unknown noise and outliers in practice. To this end, this paper proposes an adaptive noise-resistant graphical learning-based DSSE method considering the impact of inaccurate state variables. Specifically, two global-scanning graph jumping connection networks are first developed to capture the regression rules between measurements and state variables considering the structure constraints. To mitigate the negative impact caused by inaccurate labels, a collaborative learning framework is further developed, within which Gaussian mixture model-based discriminators are employed to adaptively select clean samples in each mini-batch. These allow the method to obtain robustness against noisy state labels in historical data, as well as anomalous measurements during online operations. Comparative tests show the superiority of the proposed method in tackling abnormal data in both the training and test phases.