# Spatio-temporal Diffusion Point Processes

arXiv: https://arxiv.org/abs/2305.12403 · HTML: https://mlsanity.com/paper/2305.12403/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 74 references that are in the map.
- First posted on arXiv 21 May 2023.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [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)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [D2C: Diffusion-Denoising Models for Few-shot Conditional Generation](https://mlsanity.com/paper/2106.06819/) (2021)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [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)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Deep Reinforcement Learning of Marked Temporal Point Processes](https://mlsanity.com/paper/1805.09360/) (2018)

## Built on by (most cited first, 30 of 52)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Mobility-LLM: Learning Visiting Intentions and Travel Preferences from Human Mobility Data with Large Language Models](https://mlsanity.com/paper/2411.00823/) (2024)
- [Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecasting](https://mlsanity.com/paper/2405.10800/) (2024)
- [Towards Generative Modeling of Urban Flow through Knowledge-enhanced Denoising Diffusion](https://mlsanity.com/paper/2309.10547/) (2023)
- [Spatio-Temporal Few-Shot Learning via Diffusive Neural Network Generation](https://mlsanity.com/paper/2402.11922/) (2024)
- [Unlocking Point Processes through Point Set Diffusion](https://mlsanity.com/paper/2410.22493/) (2024)
- [Diffusion Transformers as Open-World Spatiotemporal Foundation Models](https://mlsanity.com/paper/2411.12164/) (2024)
- [A Universal Model for Human Mobility Prediction](https://mlsanity.com/paper/2412.15294/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [TPP-LLM: Modeling Temporal Point Processes by Efficiently Fine-Tuning Large Language Models](https://mlsanity.com/paper/2410.02062/) (2024)
- [Noise Matters: Diffusion Model-based Urban Mobility Generation with Collaborative Noise Priors](https://mlsanity.com/paper/2412.05000/) (2024)
- [Edit-Based Flow Matching for Temporal Point Processes](https://mlsanity.com/paper/2510.06050/) (2025)
- [Boosting Data Analytics With Synthetic Volume Expansion](https://mlsanity.com/paper/2310.17848/) (2023)
- [Non-Autoregressive Diffusion-based Temporal Point Processes for Continuous-Time Long-Term Event Prediction](https://mlsanity.com/paper/2311.01033/) (2023)
- [UniFlow: A Foundation Model for Unified Urban Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2411.12972/) (2024)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [Unveiling the Power of Noise Priors: Enhancing Diffusion Models for Mobile Traffic Prediction](https://mlsanity.com/paper/2501.13794/) (2025)
- [3D Object Detection from Point Cloud via Voting Step Diffusion](https://mlsanity.com/paper/2403.14133/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Learning Spatiotemporal Dynamical Systems from Point Process Observations](https://mlsanity.com/paper/2406.00368/) (2024)
- [Spatial-Temporal Cross-View Contrastive Pre-training for Check-in Sequence Representation Learning](https://mlsanity.com/paper/2407.15899/) (2024)
- [EarthquakeNPP: A Benchmark for Earthquake Forecasting with Neural Point Processes](https://mlsanity.com/paper/2410.08226/) (2024)
- [Fine-grained Spatio-temporal Event Prediction with Self-adaptive Anchor Graph](https://mlsanity.com/paper/2501.08653/) (2025)
- [Generative Unordered Flow for Set-Structured Data Generation](https://mlsanity.com/paper/2501.17770/) (2025)
- [ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes](https://mlsanity.com/paper/2504.20411/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantification](https://mlsanity.com/paper/2310.16310/) (2023)
- [Generative Distribution Prediction: A Unified Approach to Multimodal Learning](https://mlsanity.com/paper/2502.07090/) (2025)
- [Deep spatio-temporal point processes: Advances and new directions](https://mlsanity.com/paper/2504.06364/) (2025)
- [MoveGPT: Scaling Mobility Foundation Models with Spatially-Aware Mixture of Experts](https://mlsanity.com/paper/2505.18670/) (2025)

## Abstract (arXiv)

Spatio-temporal point process (STPP) is a stochastic collection of events accompanied with time and space. Due to computational complexities, existing solutions for STPPs compromise with conditional independence between time and space, which consider the temporal and spatial distributions separately. The failure to model the joint distribution leads to limited capacities in characterizing the spatio-temporal entangled interactions given past events. In this work, we propose a novel parameterization framework for STPPs, which leverages diffusion models to learn complex spatio-temporal joint distributions. We decompose the learning of the target joint distribution into multiple steps, where each step can be faithfully described by a Gaussian distribution. To enhance the learning of each step, an elaborated spatio-temporal co-attention module is proposed to capture the interdependence between the event time and space adaptively. For the first time, we break the restrictions on spatio-temporal dependencies in existing solutions, and enable a flexible and accurate modeling paradigm for STPPs. Extensive experiments from a wide range of fields, such as epidemiology, seismology, crime, and urban mobility, demonstrate that our framework outperforms the state-of-the-art baselines remarkably, with an average improvement of over 50%. Further in-depth analyses validate its ability to capture spatio-temporal interactions, which can learn adaptively for different scenarios. The datasets and source code are available online: https://github.com/tsinghua-fib-lab/Spatio-temporal-Diffusion-Point-Processes.