# Inference and Sampling of Point Processes from Diffusion Excursions

arXiv: https://arxiv.org/abs/2306.00762 · HTML: https://mlsanity.com/paper/2306.00762/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 3 of 3)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)

## Built on by (most cited first, 3 of 3)

- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Edit-Based Flow Matching for Temporal Point Processes](https://mlsanity.com/paper/2510.06050/) (2025)
- [Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes](https://mlsanity.com/paper/2404.09402/) (2024)

## Abstract (arXiv)

Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this framework, we relate the return times of a diffusion in a continuous path space to new arrivals of the point process. This leads to a continuous sample path that is used to describe the underlying mechanism generating the arrival distribution. These models arise in many disciplines, such as financial settings where actions in a market are determined by a hidden continuous price or in neuroscience where a latent stimulus generates spike trains. Based on the developments in Ito's excursion theory, we propose methods for inferring and sampling from the point process derived from the latent diffusion process. We illustrate the approach with numerical examples using both simulated and real data. The proposed methods and framework provide a basis for interpreting point processes through the lens of diffusions.