Graph neural networks (GNNs) have emerged as powerful tools for graph classification tasks. However, contemporary graph classification methods are predominantly studied in fully supervised scenarios, while there could be label ambiguity and noise in real-world applications. In this work, we explore the weakly supervised problem of partial label learning on graphs, where each graph sample is assigned a collection of candidate labels. A novel method called D istribution Div e rgence-bas e d Graph Cont r ast (DEER) is proposed to address this issue. At the heart of our DEER is to measure the divergence among the underlying semantic distributions in the hidden space and this metric enables the identification of accurate positive graph pairs for effective graph contrastive learning. Specifically, we generate graph representations of augmented graph views that retain semantics and can be regarded as samples from the underlying semantic distributions. We employ a non-parametric metric to measure distribution divergence, which is then combined with pseudo-labeling to generate unbiased and target-oriented graph pairs. Furthermore, we introduce a label-correction method to eliminate noisy candidate labels, updating target labels using posterior distributions in a soft manner. Comprehensive experiments on various benchmarks demonstrate the superiority of our DEER in different settings compared to a range of state-of-the-art baselines.