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 sample cardinality before generating locations conditionally, or introduce specialized discrete operations to change the number of points during generation. We propose the existence-field diffusion model (EFDM), which associates each potential point with a continuous variable representing its degree of presence. EFDM uses Gaussian diffusion to jointly model point locations and cardinality through a simple continuous representation. Existence probabilities can increase or decrease in both forward and reverse diffusion, without explicit point-addition or point-deletion steps. The same construction naturally accommodates categorical attributes, allowing locations, existence, and attributes to be modeled together. Experiments demonstrate improved molecular stability and validity over the compared baselines on the molecular dataset, alongside competitive performance on real-world spatial and synthetic datasets.
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BibTeX
@misc{pan2026existencefield,
title = {{Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality}},
author = {Xiaoyin Pan and Christian R. Shelton and Rakshith Mahishi and Chengkuan Hong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.26428},
eprint = {2607.26428},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26428},
}
RIS
TY - UNPB
TI - Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality
AU - Xiaoyin Pan
AU - Christian R. Shelton
AU - Rakshith Mahishi
AU - Chengkuan Hong
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2607.26428
UR - https://arxiv.org/abs/2607.26428
AB - 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 sample cardinality before generating locations conditionally, or introduce specialized discrete operations to change the number of points during generation. We propose the existence-field diffusion model (EFDM), which associates each potential point with a continuous variable representing its degree of presence. EFDM uses Gaussian diffusion to jointly model point locations and cardinality through a simple continuous representation. Existence probabilities can increase or decrease in both forward and reverse diffusion, without explicit point-addition or point-deletion steps. The same construction naturally accommodates categorical attributes, allowing locations, existence, and attributes to be modeled together. Experiments demonstrate improved molecular stability and validity over the compared baselines on the molecular dataset, alongside competitive performance on real-world spatial and synthetic datasets.
ER -