提出统一建模点位置与数量的扩散模型，解决可变点数生成难题。
Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality
- 用存在度变量统一建模点的位置和数量，避免离散增删操作。
- 在可变点数数据集上提升生成效果，实现更灵活的动态建模。
- 适合需要复杂空间结构生成的研究者，如粒子模拟、地图生成。
我们研究空间点过程（SPP）的生成建模，其中点的数量和空间分布由联合分布决定。尽管扩散模型在建模复杂分布方面表现优异，但将其扩展到可变基数的SPP仍具挑战性。现有方法要么解耦基数与空间结构的建模，要么依赖离散的跨维度操作来改变点数，导致生成动态僵化且不对称。本文提出存在场扩散模型（EFDM），为每个潜在点引入存在变量，表示其存在程度。该机制使空间位置与基数的联合扩散过程无需显式离散转换即可完成。实验表明，该方法为可变基数空间点过程提供了灵活通用的生成框架，在多个具有变化基数的数据集上实现了更优的建模能力。
原文摘要 · Abstract (English)
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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