GLIDE: Graph-guided Leap Inference for Diffusion Estimation of Spatio-Temporal Point Processes

2026-05-31

AI Summary

Existing diffusion models for spatiotemporal point process modeling suffer from high reverse sampling costs and inaccurate localization of probability mass in sparse spatial domains. To address these challenges, this work proposes GLIDE, a novel framework that introduces multi-scale historical graph construction and a dual-stream spatiotemporal encoding architecture. GLIDE further incorporates a two-branch diffusion denoiser that integrates graph-guided structured conditional context. Additionally, a prior-guided leapfrog reverse sampling mechanism is devised to efficiently generate the next event from intermediate diffusion steps. Experimental results demonstrate that GLIDE significantly improves both distributional fidelity and next-event prediction accuracy across multiple real-world datasets, with particularly pronounced gains in spatial prediction, while substantially reducing computational overhead.

Abstract

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.

Problem

• spatio-temporal point processes
• diffusion models
• reverse sampling
• probability localization
• structural constraints

Innovation

• spatio-temporal point processes
• diffusion models
• graph-guided inference
• leap inference
• dual-stream architecture