Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality

Abstract:We study generative modeling of spatial point processes (SPP), where both the number of points and their spatial configuration are governed by a joint distribution. While diffusion models have achieved strong performance in modeling complex distributions, extending them to variable-cardinality SPP remains challenging. Existing approaches either decouple the modeling of cardinality and spatial structure, or rely on discrete trans-dimensional operations to modify the number of points, resulting in inflexible and asymmetric generative dynamics. We propose the existence-field diffusion model (EFDM) for spatial point processes modeling, where each potential point is associated with an existence variable representing its degree of presence. This enables a unified diffusion process that jointly models both spatial locations and cardinality without requiring explicit discrete transitions. We demonstrate that our approach provides a flexible and general framework for generative modeling of spatial point processes, achieving improved modeling capability on datasets with varying cardinality.

19 pages, 9 figures, 6 tables. Preprint

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2607.26428 [cs.LG]

(or arXiv:2607.26428v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.26428 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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