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

2026-07-28

AI Summary

This work addresses the challenge of jointly modeling variable point counts and spatial configurations in spatial point process generation by proposing the Existence Field Diffusion Model (EFDM). EFDM introduces, for the first time, an existence field into a diffusion framework, assigning each latent point a continuous existence variable to unify the modeling of point cardinality and location without requiring explicit discrete dimensional jumps. By constructing a joint continuous diffusion mechanism over both existence variables and spatial coordinates, EFDM enables symmetric, flexible, and unified generation of variable-cardinality point processes. Experimental results demonstrate that the proposed model significantly improves generation quality and modeling capability across multiple variable-cardinality datasets.

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.

Problem

• spatial point processes
• variable cardinality
• generative modeling
• diffusion models

Innovation

• existence-field diffusion
• spatial point processes
• variable cardinality
• generative modeling
• diffusion models