Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

arXiv cs.LG / 5/5/2026

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Key Points

The paper proposes ARCH (Arbitrarily Conditioned Hierarchical Flows), a hierarchical flow-matching framework aimed at modeling complex spatiotemporal event distributions without relying on overly rigid structural assumptions.
Unlike many point-process approaches that focus mainly on autoregressive, event-by-event prediction, ARCH supports broader inference tasks including inverse inference, trajectory reconstruction, and recovery of missing event locations.
ARCH uses a history-encoder–generative-decoder architecture and a hybrid masking strategy to flexibly condition on arbitrary observed events, improving usability for different conditioning scenarios.
The method computes conditional intensities, providing a tractable way to quantify instantaneous event risk while maintaining expressive distribution modeling.
Experiments on synthetic and real-world datasets indicate that ARCH outperforms existing baselines across both forecasting and conditional inference settings.

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.