Branching Diffusion for Point Processes in Time and Space
Chao Yang, Wenjie Shen, Shuang Li
Abstract
We propose a non-autoregressive branching diffusion model for generating spatio-temporal point processes. Starting from a geometric principle---the Wasserstein-Fisher-Rao (WFR) gradient flow of a generalized KL divergence toward a simple reference intensity---we obtain a tractable forward noising mechanism with two interpretable components: (i) a Langevin-type \emph{drift-diffusion} step that perturbs event locations and times, and (ii) a \emph{birth-death branching} step that changes the event count via location-dependent thinning (deaths) and Poisson offspring replication (births). We learn the reverse-time dynamics using a permutation-equivariant denoiser that predicts a drift field and a net-growth field, and we train it using an entropic-regularized unbalanced optimal transport (UOT), which naturally handles count mismatch between noisy and clean samples. The resulting generator produces complete spatio-temporal event sets without autoregressive simulation or explicit intensity normalization.
BibTeX
@inproceedings{
yang2026branching,
title={Branching Diffusion for Point Processes in Time and Space},
author={Chao Yang and Wenjie Shen and Shuang Li},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=oWyvNaX6op}
}