# Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

arXiv: https://arxiv.org/abs/2605.01226 · HTML: https://mlsanity.com/paper/2605.01226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Automatic Integration for Spatiotemporal Neural Point Processes](https://mlsanity.com/paper/2310.06179/) (2023)
- [EventFlow: Forecasting Temporal Point Processes with Flow Matching](https://mlsanity.com/paper/2410.07430/) (2024)
- [Edit-Based Flow Matching for Temporal Point Processes](https://mlsanity.com/paper/2510.06050/) (2025)
- [Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction](https://mlsanity.com/paper/1811.06321/) (2018)
- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)

## Abstract (arXiv)

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.