Robotic swarms must coordinate across diverse missions, yet existing controllers often require redesign, retuning, or retraining when objectives change. Here we show that probabilistic energy modeling provides a unifying representation for versatile swarm control, in which diverse missions emerge from compositions of shared interaction principles rather than task-specific control formulations. By exploiting the correspondence between Gibbs random field energy minimization and structured reward maximization, we encode fundamental swarm behaviors as reusable energy terms within a unified probabilistic objective. Decentralized policies trained within this representation are composed into a single controller through lightweight policy gating, without retraining. An interpretable action-attention mechanism captures non-uniform local interactions, while dimensionless normalization supports transfer across swarm scales and platforms. Demonstrated on aerial swarms, the unified policy generalizes zero-shot across six mission classes, 10-100 agents, two hardware platforms, and indoor cluttered and GPS-denied woodland environments. Large-scale simulations achieve 0.96-1.00 task success rates with 1-10 ms per-agent inference latency, while physical deployments confirm zero-shot transfer to real platforms and unstructured environments. These results establish probabilistic energy modeling as a scalable and transferable framework for decentralized swarm control.

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