Spatio-temporal Diffusion Point Processes

Spatio-temporal point process (STPP) is a stochastic collection of events accompanied with time and space. Due to computational complexities, existing solutions for STPPs compromise with conditional independence between time and space, which consider the temporal and spatial distributions separately. The failure to model the joint distribution leads to limited capacities in characterizing the spatio-temporal entangled interactions given past events. In this work, we propose a novel parameterization framework for STPPs, which leverages diffusion models to learn complex spatio-temporal joint distributions. We decompose the learning of the target joint distribution into multiple steps, where each step can be faithfully described by a Gaussian distribution. To enhance the learning of each step, an elaborated spatio-temporal co-attention module is proposed to capture the interdependence between the event time and space adaptively. For the first time, we break the restrictions on spatio-temporal dependencies in existing solutions, and enable a flexible and accurate modeling paradigm for STPPs. Extensive experiments from a wide range of fields, such as epidemiology, seismology, crime, and urban mobility, demonstrate that our framework outperforms the state-of-the-art baselines remarkably. Further in-depth analyses validate its ability to capture spatio-temporal interactions, which can learn adaptively for different scenarios. The datasets and source code are available online: https://github.com/tsinghua-fib-lab/Spatio-temporal-Diffusion-Point-Processes.