# Unlocking Point Processes through Point Set Diffusion

arXiv: https://arxiv.org/abs/2410.22493 · HTML: https://mlsanity.com/paper/2410.22493/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)
- [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)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [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)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [Deep Mixture Point Processes: Spatio-temporal Event Prediction with Rich Contextual Information](https://mlsanity.com/paper/1906.08952/) (2019)
- [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)
- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [Prediction of Spatial Point Processes: Regularized Method with Out-of-Sample Guarantees](https://mlsanity.com/paper/2007.01592/) (2020)

## Built on by (most cited first, 14 of 14)

- [Edit-Based Flow Matching for Temporal Point Processes](https://mlsanity.com/paper/2510.06050/) (2025)
- [Diffusion LLMs are Natural Adversaries for any LLM](https://mlsanity.com/paper/2511.00203/) (2025)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [Generative Modeling with Bayesian Sample Inference](https://mlsanity.com/paper/2502.07580/) (2025)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [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)
- [Latent Block-Diffusion Temporal Point Processes: A Semi-Autoregressive Framework for Asynchronous Event Sequence Generation](https://mlsanity.com/paper/2606.24982/) (2026)
- [When Context Compensates for Sparse Event History: AlphaEarth for Spatio-Temporal Point-Process Forecasting](https://mlsanity.com/paper/2607.01082/) (2026)
- [From Jumps to Signatures: a Generative Method for Temporal Point Processes](https://mlsanity.com/paper/2607.06652/) (2026)
- [Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality](https://mlsanity.com/paper/2607.26428/) (2026)
- [Realism VS Accuracy: Event Sequence Forecasting from a Generative Modeling Perspective](https://mlsanity.com/paper/2610.12586/) (2026)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by their reliance on the characteristic intensity function, introducing an inherent trade-off between efficiency and flexibility. In this paper, we introduce Point Set Diffusion, a diffusion-based latent variable model that can represent arbitrary point processes on general metric spaces without relying on the intensity function. By directly learning to stochastically interpolate between noise and data point sets, our approach enables efficient, parallel sampling and flexible generation for complex conditional tasks defined on the metric space. Experiments on synthetic and real-world datasets demonstrate that Point Set Diffusion achieves state-of-the-art performance in unconditional and conditional generation of spatial and spatiotemporal point processes while providing up to orders of magnitude faster sampling than autoregressive baselines.