Unlocking Point Processes through Point Set Diffusion
David L\"udke, Enric Rabasseda Ravent\'os, Marcel Kollovieh, Stephan, G\"unnemann
TL;DR
This paper introduces Point Set Diffusion, a novel diffusion-based model that efficiently and flexibly generates complex point processes on metric spaces without relying on traditional intensity functions, outperforming existing methods.
Contribution
The paper presents a new diffusion-based latent variable model for point processes that overcomes limitations of intensity-based models, enabling flexible and fast generation on general metric spaces.
Findings
Achieves state-of-the-art performance in point process generation.
Provides up to orders of magnitude faster sampling than autoregressive models.
Demonstrates effectiveness on synthetic and real-world datasets.
Abstract
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…
Peer Reviews
Decision·ICLR 2025 Poster
The idea of using the diffusion-style model to characterize point processes is super interesting. The content is clear and well-written, making the methodology and the results accessible to the reader. The paper also covers unconditional and conditional sampling methods, which have the potential to correspond to two important questions in the point process modeling (first-order and second-order modeling). The authors also provide thorough experimentation to validate the effectiveness of the prop
In my opinion, the main weakness, or the most improvement-needed part of the paper, lies in the modeling and experiments of ordered point processes: 1. An important characteristic of the ordered point processes (TPPs or STPPs) is the dependence between future events and past events, which is not considered in the model. The proposed method seems to only consider the first-order statistics of the data (the event intensity/density), and treat these statistics at certain times or locations as fixe
1. The paper is overall well-written and easy to follow. The basic concepts are introduced clearly with consistent notations. The forward process, backward process, and final sampling algorithms are well explained. Illustrations (Figure 1-3) are very clear for readers to follow the workflow of the proposed Point Set Diffusion model. The datasets and metrics are also clear in the experiment section. 2. The idea of leveraging diffusion models to generate the whole point process is intriguing, an
1. Currently there are very few baseline algorithms, e.g., for SPP conditional generation there is only one baseline, and for STPP forecasting there are only two. It would be more convincing to compare with more baseline models, or to provide more evidence that the current baselines are already SOTA (which I believe they are).
1. This paper generalizes the Add-Thin model to define a model for point processes on general metric spaces, enhancing the model's applicability and promising future prospects. 2. The idea is sound and well-founded. The paper is overall well-written and easy to follow. 3. Experiments show that the proposed model achieves state-of-the-art results on both conditional and unconditional tasks while enabling faster sampling.
1. It would be helpful to discuss the connections between the proposed model and the Add-Thin model when modeling univariate temporal point processes. 2. In the conditional sampling, the definition of $q(X_{t-1} | X_{0}^c)$ in line 287 was not provided. Typo: $X_{t+1}^{\text{thin}}$ and $X_{t}^{\text{thin}}$ in Eq.(9) should be $X_{t+1}^{\varepsilon}$ and $X_{t}^{\varepsilon}$.
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Taxonomy
TopicsPoint processes and geometric inequalities
MethodsDiffusion · Sparse Evolutionary Training