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

Abstract: Spatio-temporal point processes (STPPs) establish a robust theoretical foundation for representing asynchronous occurrences across continuous time and space. While recent diffusion-based methodologies present a versatile substitute for deterministic forecasting by capturing intricate conditional distributions, their deployment in STPPs faces significant hurdles. Specifically, the reverse sampling procedure originating from pure noise is computationally expensive, and the lack of strong structural constraints within sparse spatial areas often results in probability mass that is poorly localized. To address these issues, we introduce GLIDE (Graph-guided Leap Inference for Diffusion Estimation), a conditional diffusion framework tailored for next-event modeling in STPPs. GLIDE structures historical events into a multi-scale graph and utilizes a dual-stream architecture to encode both temporal dynamics and spatial topology, thereby generating a structured conditioning context for a dual-branch diffusion denoiser. Additionally, the method employs a prior-guided leap inference mechanism. This approach leverages a lightweight mean predictor to establish a deterministic anchor, initiating the reverse process from an intermediate diffusion stage rather than starting from pure Gaussian noise. Evaluations across various real-world datasets demonstrate that GLIDE enhances both distribution fitting and next-event prediction, with the most notable improvements observed in the spatial domain. Furthermore, the findings suggest that prior-guided leap inference significantly lowers the computational cost of reverse sampling without compromising the stochastic generation benefits inherent to diffusion models.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC