SLiDNet: Scale-Separated Liquid Dynamics for Spatio-Temporal Forecasting

Spatio-temporal forecasting requires modeling both the state of each node and the rate at which that state evolves. However, existing models often rely on shared latent representations for state formation and temporal evolution. This coupling may mix signal-level differences with temporal variation and make it harder to distinguish a node's own evolution from the influence of its neighbors. To address this issue, we propose the Scale-Separated Liquid Dynamics Network (SLiDNet), which separates state formation from evolution-rate modeling. SLiDNet forms node states from scale-stable temporal content and compact window-level signal context. Robustly normalized first- and second-order temporal differences, together with recurrent context, condition node-specific Liquid time constants to adapt the evolution rate. Spatial dependencies are captured through prior-guided graph diffusion. Experiments across six real-world spatio-temporal datasets and multiple forecasting horizons show consistent improvements over competitive baselines. Controlled ablations and sensitivity analyses further support the effectiveness of the proposed scale-separated design.