  Crowd simulation holds crucial applications in various domains, such as urban
planning, architectural design, and traffic arrangement. In recent years,
physics-informed machine learning methods have achieved state-of-the-art
performance in crowd simulation but fail to model the heterogeneity and
multi-modality of human movement comprehensively. In this paper, we propose a
social physics-informed diffusion model named SPDiff to mitigate the above gap.
SPDiff takes both the interactive and historical information of crowds in the
current timeframe to reverse the diffusion process, thereby generating the
distribution of pedestrian movement in the subsequent timeframe. Inspired by
the well-known social physics model, i.e., Social Force, regarding crowd
dynamics, we design a crowd interaction module to guide the denoising process
and further enhance this module with the equivariant properties of crowd
interactions. To mitigate error accumulation in long-term simulations, we
propose a multi-frame rollout training algorithm for diffusion modeling.
Experiments conducted on two real-world datasets demonstrate the superior
performance of SPDiff in terms of macroscopic and microscopic evaluation
metrics. Code and appendix are available at
https://github.com/tsinghua-fib-lab/SPDiff.
