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Social Physics Informed Diffusion Model for Crowd Simulation
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Proposes SPDiff, a conditional denoising diffusion model for crowd simulation that injects Social Force-inspired interaction forces and equivariant graph layers, trained with a multi-frame rollout objective.
Problem
Crowd simulation must capture both physical consistency (social physics) and the multi-modality of pedestrian movement over long simulation horizons, which existing physics-informed and diffusion-based methods do not jointly handle.
Approach
A diffusion model that predicts next-frame pedestrian accelerations, conditioned on an equivariant graph-based crowd interaction module that replaces the repulsive terms of the Social Force Model, plus an LSTM history module, trained with a multi-frame rollout loss with discounting to reduce error accumulation.
Key results
- On GC, SPDiff achieves MAE 0.9116, OT 1.3925, MMD 0.0092, versus best baseline NSP at 0.9884, 1.4893, 0.0106.
- On UCY, SPDiff achieves MAE 1.8760 and OT 4.0564, improving over PCS (2.3134, 6.2336) by roughly 19-35%.
- SPDiff uses about 0.2M parameters, reported as 8% of NSP and 33% of PCS parameter counts.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SPDiff rather than the strongest reported baseline | crowd simulation · GC | MAE: 0.9884 -> 0.9116 | Helped |
| use SPDiff rather than the strongest reported baseline | crowd simulation · GC | OT: 1.4893 -> 1.3925 | Helped |
| use SPDiff rather than the strongest reported baseline | crowd simulation · GC | DTW: 0.3329 -> 0.3332 | Hurt |
| use SPDiff rather than the strongest reported baseline | crowd simulation · UCY | MAE: 2.3134 -> 1.8760 | Helped |
| use SPDiff rather than the strongest reported baseline | crowd simulation · UCY | OT: 6.2336 -> 4.0564 | Helped |
| use SPDiff rather than the strongest reported baseline | crowd simulation · UCY | #Col: 238 -> 372 | Hurt |
| add social physics guidance and the crowd interaction module (ablation) | SPDiff · GC | MAE: 3.3102 -> 0.9116 | Helped |
| add social physics guidance and the crowd interaction module (ablation) | SPDiff · UCY | OT: 12.9325 -> 4.0564 | Helped |
| add the history module and history inputs (ablation) | SPDiff · GC | MAE: 1.0834 -> 0.9116 | Helped |
| add the history module and history inputs (ablation) | SPDiff · UCY | MAE: 2.3340 -> 1.8760 | Helped |
| use multi-frame rollout training instead of single-frame loss training (ablation) | SPDiff · GC | MAE: 1.0214 -> 0.9116 | Helped |
| use multi-frame rollout training instead of single-frame loss training (ablation) | SPDiff · UCY | MAE | Helped |
Surprising findings
- Removing social physics guidance causes the largest performance drop, larger than removing the history module.
- Without multi-frame rollout training, metrics fail to converge on the UCY dataset.
Limitations
- Collision count (#Col) is worse than the best physics-informed baselines on GC (810 vs 734 for NSP) and UCY (372 vs 238 for PCS).
- Generalization is only checked qualitatively on scenarios from the SDD dataset, with results deferred to supplementary material.
- Diffusion sampling is iterative and predicts one frame at a time, so runtime cost is not characterized in the main text.
Experimental setup
Datasets: GC dataset UCY dataset
Benchmarks: GC UCY
Metrics: MAE OT MMD DTW #Col
Baselines: CA SFM STGCNN PECNet MID PCS NSP
Builds on: DDPM Social Force Model PCS EGNN MID
Closest papers by meaning
- Continuous Locomotive Crowd Behavior Generation (CVPR 2025 · similarity 0.85)
- Learning Extremely High Density Crowds as Active Matters (CVPR 2025 · similarity 0.84)
- SocialCVAE: Predicting Pedestrian Trajectory via Interaction Conditioned Latents (AAAI 2024 · similarity 0.84)
- CrowdDiff: Multi-hypothesis Crowd Density Estimation using Diffusion Models (CVPR 2024 · similarity 0.84)
- Explainable Origin-Destination Crowd Flow Interpolation via Variational Multi-Modal Recurrent Graph Auto-Encoder (AAAI 2024 · similarity 0.83)
- Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models (ICLR 2025 · similarity 0.83)
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