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Social Physics Informed Diffusion Model for Crowd Simulation

Hongyi Chen, Jingtao Ding, Yong Li, Yue Wang, Xiao-Ping Zhang

TL;DR

This work addresses the challenge of realistic, multimodal crowd dynamics by integrating Social Force-inspired physics into a conditional diffusion framework. SPDiff uses a crowd interaction module with equivariant design and a multi-frame rollout training strategy to produce physically consistent, long-horizon trajectories conditioned on current states and history. Empirical results on GC and UCY show SPDiff delivering superior microscopic and macroscopic realism with fewer parameters compared to baselines, highlighting the value of physics-guided diffusion for crowd simulation. The approach offers a scalable, generalizable method for planning and safety analysis in urban environments by enabling more reliable multimodal trajectory generation.

Abstract

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.

Social Physics Informed Diffusion Model for Crowd Simulation

TL;DR

This work addresses the challenge of realistic, multimodal crowd dynamics by integrating Social Force-inspired physics into a conditional diffusion framework. SPDiff uses a crowd interaction module with equivariant design and a multi-frame rollout training strategy to produce physically consistent, long-horizon trajectories conditioned on current states and history. Empirical results on GC and UCY show SPDiff delivering superior microscopic and macroscopic realism with fewer parameters compared to baselines, highlighting the value of physics-guided diffusion for crowd simulation. The approach offers a scalable, generalizable method for planning and safety analysis in urban environments by enabling more reliable multimodal trajectory generation.

Abstract

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.
Paper Structure (17 sections, 11 equations, 4 figures, 3 tables)

This paper contains 17 sections, 11 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries
  4. Problem Formulation
  5. Social Force Model
  6. Equivariance and Invariance
  7. SPDiff: the Proposed Method
  8. Physics Guided Conditional Diffusion Process
  9. Training and Sampling Algorithm
  10. Network Parameterization
  11. Experiments
  12. Experiment Setup
  13. Overall Performance
  14. Rollout Error Analysis of the Simulation
  15. Ablation Study
  16. ...and 2 more sections

Figures (4)

  • Figure 1: The overall framework of SPDiff.
  • Figure 2: The detailed parameterization of the denoising network ($f_\theta$).
  • Figure 3: Rollout error as a function of frames, using OT and MMD as metrics.
  • Figure 4: Top: Test performance under different training sample sizes on the UCY dataset. Bottom: Test performance under different training epochs on the UCY dataset.