# Neural Diffusion Intensity Models for Point Process Data

arXiv: https://arxiv.org/abs/2602.24083 · HTML: https://mlsanity.com/paper/2602.24083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [A Variational Auto-Encoder Model for Stochastic Point Processes](https://mlsanity.com/paper/1904.03273/) (2019)
- [Fast and Flexible Temporal Point Processes with Triangular Maps](https://mlsanity.com/paper/2006.12631/) (2020)
- [Black-box Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/1802.03335/) (2018)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [A General Method for Amortizing Variational Filtering](https://mlsanity.com/paper/1811.05090/) (2018)
- [Structured Variational Inference in Continuous Cox Process Models](https://mlsanity.com/paper/1906.03161/) (2019)
- [Exact Bayesian inference for diffusion driven Cox processes](https://mlsanity.com/paper/2007.05812/) (2020)
- [Estimating Stochastic Poisson Intensities Using Deep Latent Models](https://mlsanity.com/paper/2007.06037/) (2020)

## Built on by (most cited first, 1 of 1)

- [Amortized Variational Inference of Latent Intensities from Replicated Point Patterns](https://mlsanity.com/paper/2610.16669/) (2026)

## Abstract (arXiv)

Cox processes model overdispersed point process data via a latent stochastic intensity, but both nonparametric estimation of the intensity model and posterior inference over intensity paths are typically intractable, relying on expensive MCMC methods. We introduce Neural Diffusion Intensity Models, a variational framework for Cox processes driven by neural SDEs. Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This guarantees the variational family contains the true posterior, so that ELBO maximization coincides with maximum likelihood estimation under sufficient model capacity. We design an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated MCMC runs with a single forward pass. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over MCMC-based methods.