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Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks
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Proposes Graph Diffusion Networks, a differentiable surrogate of agent-based models that combines a message-passing GNN with a conditional diffusion model trained on ramified ABM simulation data to emulate individual agent transitions.
Problem
ABMs have non-differentiable, ad hoc stochastic micro-level rules, which block gradient-based optimization and alignment with real-world data; existing surrogates mostly map parameters to aggregate outcomes and ignore individual stochastic behavior.
Approach
Learn a per-agent stochastic transition kernel: a message-passing GNN embeds each agent's neighborhood, and a conditional diffusion model samples the agent's next state given that embedding, trained on a ramification dataset where each time step has multiple stochastic successors from the same context.
Key results
- On Predator-Prey, the surrogate achieves an average sMAPE of about 0.08 on the most complex parameter set Psi_1 and consistently lower EMD than both ablations.
- On Schelling, the surrogate's sMAPE remains below 0.2 while the diffusion-only ablation fails to distinguish happy from unhappy regimes, with large macro-level errors.
- The diffusion-only ablation collapses to near-monotonic trends in predator-prey and the GNN-only ablation diverges (e.g., prey plateau near 750 vs. about 375 true).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add graph-based interaction modeling and stochastic diffusion instead of using a flat all-agent state concatenation or deterministic prediction (ablation) | GDN · Schelling and Predator-Prey | EMD | Helped |
| Add stochastic diffusion rather than deterministic next-state prediction (ablation) | GDN · Schelling, macro evaluation | sMAPE | Helped |
| Add graph-based interaction modeling rather than using a flat concatenation of agent states (ablation) | GDN · Schelling, macro evaluation | sMAPE | Helped |
| Add stochastic diffusion rather than deterministic next-state prediction (ablation) | GDN · Predator-Prey Ψ1 | sMAPE | Helped |
| Add graph-based interaction modeling and stochastic diffusion (ablation) | GDN · Predator-Prey Ψ1 | population trajectory fidelity: 750 | Helped |
| Increase training ramifications from 50 to 500 | GDN · Predator-Prey Ψ1 | EMD: $0.0161\pm0.0003$ -> $0.0088\pm0.0007$ | Helped |
| Increase training ramifications from 50 to 500 | GDN · Predator-Prey Ψ1 | sMAPE: $0.076\pm0.019$ -> $0.062\pm0.030$ | Mixed |
| Increase agent count from 2048 to 8192 while keeping R=500 | GDN · Predator-Prey Ψ1 | EMD: $0.0092\pm0.0007$ -> $0.0082\pm0.0003$ | Helped |
| Increase agent count from 2048 to 8192 while keeping R=500 | GDN · Predator-Prey Ψ1 | sMAPE: $0.065\pm0.033$ -> $0.051\pm0.026$ | Helped |
| Increase agent count while reducing ramifications to keep training time and transitions roughly constant | GDN · Predator-Prey Ψ1 | EMD: $0.0092\pm0.0007$, $0.0092\pm0.0005$, $0.0095\pm0.0005$ | No clear effect |
| Increase agent count while reducing ramifications to keep training time and transitions roughly constant | GDN · Predator-Prey Ψ1 | sMAPE: $0.065\pm0.033$, $0.073\pm0.024$, $0.066\pm0.027$ | No clear effect |
Surprising findings
- The diffusion-only ablation largely maintains a random configuration in Schelling, and at very low or very high tolerance a flat always-move or never-move rule gives near-optimal EMD.
Limitations
- Assumes the interaction graph is fully known rather than inferred from data.
- Does not address all-to-all interactions, multiple decision rounds, or sequential stochastic events within a time step.
- Evaluated only on two canonical ABMs with mid-sized agent populations.
Experimental setup
Datasets: Schelling segregation ABM simulations (NetLogo implementation) Predator-Prey ABM simulations
Benchmarks: Schelling segregation model (3 tolerance thresholds) Predator-Prey ecosystem (4 parameter sets)
Metrics: Earth Mover's Distance sMAPE
Baselines: Diffusion-only ablation GNN-only ablation
Builds on: denoising diffusion probabilistic models message passing neural networks Grattarola et al. GNN cellular automata emulator
Closest papers by meaning
- PGODE: Towards High-quality System Dynamics Modeling (ICML 2024 · similarity 0.87)
- Revisiting Multi-Agent World Modeling from a Diffusion-Inspired Perspective (NeurIPS 2025 · similarity 0.86)
- Graph Diffusion for Robust Multi-Agent Coordination (ICML 2025 · similarity 0.86)
- MADiff: Offline Multi-agent Learning with Diffusion Models (NeurIPS 2024 · similarity 0.85)
- Generating Origin-Destination Matrices in Neural Spatial Interaction Models (NeurIPS 2024 · similarity 0.85)
- Bridging Training and Execution via Dynamic Directed Graph-Based Communication in Cooperative Multi-Agent Systems (AAAI 2025 · similarity 0.85)
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