Identifying information sources in networks is crucial for understanding and controlling the spread of information at its early stages. Traditional source detection methods often rely on predefined propagation models, while more recent approaches use label propagation algorithms or Graph Neural Networks (GNNs) to model diffusion processes. However, these methods face challenges, such as limited ability to capture propagation patterns or over-smoothing in GNNs, which restricts their depth and global pattern modeling. To address these limitations, we propose the ODESI model. It begins by using a label propagation algorithm to estimate the distribution density of infected states, extending their representation from integers to state vectors as initial node states. Then, ODESI employs a deep architecture combining GNNs with Ordinary Differential Equations (ODEs) to model global propagation patterns continuously. By approximating ODE solutions, we reduce computational complexity and enhance scalability. Experiments on two real-world social network datasets demonstrate that ODESI effectively identifies information sources, outperforming existing methods.