[2602.24083] Neural Diffusion Intensity Models for Point Process Data

Computer Science > Machine Learning arXiv:2602.24083 (cs) [Submitted on 27 Feb 2026] Title:Neural Diffusion Intensity Models for Point Process Data Authors:Xinlong Du, Harsha Honnappa, Vinayak Rao View a PDF of the paper titled Neural Diffusion Intensity Models for Point Process Data, by Xinlong Du and Harsha Honnappa and Vinayak Rao View PDF HTML (experimental) Abstract: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...