发表机构
University of California, Riverside; New York University; Zhongguancun Academy（加州大学河滨分校; 纽约大学; 中关村学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对可变基数空间点过程生成建模难题，提出存在场扩散模型（EFDM），通过关联存在变量实现空间位置与基数的联合建模，在可变基数数据集上提升了建模能力。
AI 中文摘要
我们研究空间点过程（SPP）的生成建模，其中点的数量及其空间构型均由联合分布控制。尽管扩散模型在复杂分布建模中表现出色，但将其扩展到可变基数空间点过程仍具挑战性。现有方法要么将基数与空间结构建模解耦，要么依赖离散跨维操作修改点数量，导致生成动力学不灵活且不对称。我们提出用于空间点过程建模的存在场扩散模型（EFDM），其中每个潜在点关联一个表示其存在程度的存在变量，这使得统一扩散过程可联合建模空间位置与基数，无需显式离散转换。我们证明该方法为空间点过程生成建模提供了灵活通用的框架，在可变基数数据集上实现了更优的建模能力。
英文摘要
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.
Comments24 pages, 6 figures, 7 tables
