Graph-Aware Controlled Continuous Dynamics Network for Information Diffusion Prediction

Information diffusion prediction aims to infer future user activations from observed cascade prefixes in social networks, where diffusion unfolds as a complex, irregular, continuous-time process. Existing methods typically model dynamic user preferences by discretizing diffusion into temporal graph or hypergraph snapshots. As a result, these methods produce hidden states only at discrete timestamps and do not capture the continuous dynamics between cascade events. Although neural ordinary differential equations provide a natural framework for modeling temporal dynamics, their trajectories are determined by the initial condition and cannot incorporate subsequent observations as direct controls along the evolving path. To address these limitations, we propose CoDyNet, a graph-aware Controlled continuous Dynamics Network for microscopic information diffusion prediction. CoDyNet first learns graphaware user representations from multi-source static relations and dynamic diffusion hypergraphs. It then constructs timestamp-aware control paths that drive a neural controlled differential equation for observation-guided continuous propagation modeling. We further introduce a cascade-aware graph contrastive regularizer that enforces consistency between clean and perturbed static user representations while avoiding co-activated false negatives. The resulting continuous diffusion context and static user context are encoded by causal Transformer blocks and adaptively fused for next-user prediction. Extensive experiments on four real-world datasets show that CoDyNet achieves competitive performance against representative diffusion prediction baselines.