Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

2026-05-01

AI Summary

Existing spatiotemporal event models are constrained by strong structural assumptions and limited to autoregressive prediction, rendering them ill-suited for complex tasks such as inverse reasoning and trajectory reconstruction. This work proposes a hierarchical flow matching framework that integrates a history encoder–generative decoder architecture with a hybrid masking strategy, enabling flexible conditional modeling of arbitrary observed events. The approach unifies forward prediction, inverse inference, and partial trajectory recovery within a single formulation. It is the first to combine hierarchical flow matching with a hybrid masking mechanism, allowing efficient and accurate computation of spatiotemporal event intensities under arbitrary conditioning, thereby overcoming the inferential limitations of conventional point process models. Experiments demonstrate that the method significantly outperforms existing approaches in both predictive accuracy and diverse conditional reasoning tasks across synthetic and real-world datasets.

Abstract

Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broader inference tasks such as inverse inference, trajectory reconstruction, and recovery of missing event locations. We introduce Arbitrarily Conditioned Hierarchical Flows (ARCH), a hierarchical flow matching framework for spatiotemporal event modeling. ARCH is expressive enough to capture complex event distributions while enabling tractable and accurate computation of conditional intensities, which quantify instantaneous event risk. Built on a history-encoder-generative-decoder architecture, ARCH introduces a hybrid masking strategy for flexible conditioning on arbitrary observed events. This enables a unified treatment of forecasting, inverse inference, and partial trajectory recovery within a single framework. Experiments on synthetic and real-world datasets show that ARCH consistently outperforms existing baselines across both prediction and conditional inference tasks.

Problem

• spatiotemporal events
• point process
• conditional inference
• trajectory reconstruction
• missing event recovery

Innovation

• hierarchical flow matching
• spatiotemporal event modeling
• arbitrary conditioning
• conditional intensity
• hybrid masking