  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, with an average improvement of over 50%. 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.
