# Social Physics Informed Diffusion Model for Crowd Simulation

arXiv: https://arxiv.org/abs/2402.06680 · HTML: https://mlsanity.com/paper/2402.06680/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Human Trajectory Prediction via Neural Social Physics](https://mlsanity.com/paper/2207.10435/) (2022)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Personalized Trajectory Prediction via Distribution Discrimination](https://mlsanity.com/paper/2107.14204/) (2021)
- [Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches](https://mlsanity.com/paper/2111.06740/) (2021)
- [Towards Generative Modeling of Urban Flow through Knowledge-enhanced Denoising Diffusion](https://mlsanity.com/paper/2309.10547/) (2023)
- [Informative Scene Decomposition for Crowd Analysis, Comparison and Simulation Guidance](https://mlsanity.com/paper/2004.14107/) (2020)
- [Pedestrian Simulation: A Review](https://mlsanity.com/paper/2102.03289/) (2021)

## Built on by (most cited first, 11 of 11)

- [SICNav-Diffusion: Safe and Interactive Crowd Navigation with Diffusion Trajectory Predictions](https://mlsanity.com/paper/2503.08858/) (2025)
- [Joint Pedestrian Trajectory Prediction through Posterior Sampling](https://mlsanity.com/paper/2404.00237/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systems](https://mlsanity.com/paper/2409.04740/) (2024)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Learning Extremely High Density Crowds as Active Matters](https://mlsanity.com/paper/2503.12168/) (2025)
- [Remote Sensing Image Dehazing: A Systematic Review of Progress, Challenges, and Prospects](https://mlsanity.com/paper/2603.20289/) (2026)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [STDDN: A Physics-Guided Deep Learning Framework for Crowd Simulation](https://mlsanity.com/paper/2604.02756/) (2026)
- [ACME: A Multi-Cultural, Multi-Embodiment Social-Navigation Dataset](https://mlsanity.com/paper/2607.21964/) (2026)

## Abstract (arXiv)

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.