无需强度函数，用扩散模型高效生成任意点过程。
Unlocking Point Processes through Point Set Diffusion
- 设计扩散模型直接学习点集间随机插值。
- 采样速度比自回归方法快数个数量级。
- 适合需要快速生成复杂点模式的科研与工程场景。
点过程用于建模数学空间中随机点集的分布，如时空领域，在地震学、神经科学和经济学中有广泛应用。现有统计与机器学习模型多依赖特征强度函数，导致效率与灵活性之间的固有权衡。本文提出点集扩散（Point Set Diffusion），一种基于扩散的隐变量模型，可在一般度量空间上表示任意点过程，无需依赖强度函数。通过直接学习噪声与数据点集间的随机插值，该方法实现高效并行采样，支持复杂条件任务的灵活生成。在合成与真实数据集上的实验表明，该方法在无条件与条件生成任务中均达到当前最优性能，且采样速度相比自回归基线提升数个数量级。
原文摘要 · Abstract (English)
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by their reliance on the characteristic intensity function, introducing an inherent trade-off between efficiency and flexibility. In this paper, we introduce Point Set Diffusion, a diffusion-based latent variable model that can represent arbitrary point processes on general metric spaces without relying on the intensity function. By directly learning to stochastically interpolate between noise and data point sets, our approach enables efficient, parallel sampling and flexible generation for complex conditional tasks defined on the metric space. Experiments on synthetic and real-world datasets demonstrate that Point Set Diffusion achieves state-of-the-art performance in unconditional and conditional generation of spatial and spatiotemporal point processes while providing up to orders of magnitude faster sampling than autoregressive baselines.
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