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

• URL: http://arxiv.org/abs/2607.26428v1
• Date: Wed, 29 Jul 2026 03:15:32 GMT
• Title: Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality
• Abstract summary: 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.<n>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.<n>This enables a unified diffusion process that jointly models both spatial locations and cardinality without requiring explicit discrete transitions.
• Score: 1.679937788852769
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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