GLIDE: Graph-guided Leap Inference for Diffusion Estimation of Spatio-Temporal Point Processes
This work addresses the challenge of efficient and accurate next-event modeling in spatio-temporal point processes, which is crucial for applications like crime prediction and epidemiology, by proposing a method that balances computational cost and generative performance.
GLIDE introduces a conditional diffusion framework for spatio-temporal point processes that uses a multi-scale historical graph and prior-guided leap inference to improve next-event prediction and distribution fitting, achieving up to 30% reduction in sampling cost while maintaining stochastic generation quality.
Spatio-temporal point processes (STPPs) provide a principled framework for modeling asynchronous events in continuous time and space. Recent diffusion-based approaches offer a flexible alternative to deterministic prediction by modeling complex conditional distributions, but their application to STPPs remains challenging: reverse sampling from pure noise is costly, and weak structural constraints in sparse spatial domains can lead to poorly localized probability mass. We propose \textbf{GLIDE} (Graph-guided Leap Inference for Diffusion Estimation), a conditional diffusion framework for next-event modeling in STPPs. GLIDE organizes historical events into a multi-scale historical graph and encodes temporal evolution and spatial topology through a dual-stream architecture, yielding a structured conditioning context for a dual-branch diffusion denoiser. It further introduces a prior-guided leap inference mechanism, in which a lightweight mean predictor provides a deterministic anchor and the reverse process starts from an intermediate diffusion step instead of from pure Gaussian noise. Experiments on multiple real-world datasets show that GLIDE improves both distribution fitting and next-event prediction, with the largest gains appearing on the spatial side. The results also indicate that prior-guided leap inference substantially reduces reverse-sampling cost while preserving the stochastic generation capability of diffusion models.