Navigating the Energy Landscape of Collaboration: Multi-Agent Communication Graph Generation via Score-Based Diffusion

The collective intelligence of Large Language Model (LLM)-based Multi-Agent Systems (MAS) is fundamentally governed by the underlying communication graph. However, discovering task-adaptive structures within this combinatorial search space remains a significant challenge. Existing methods, ranging from heuristic pruning to autoregressive generation, often lack a unified theoretical framework to guide the self-organization of agents into efficient teams. In this paper, we bridge non-equilibrium thermodynamics and generative modeling to formalize multi-agent graph generation as an energy minimization process. Specifically, we frame the emergence of efficient collaboration as a thermodynamic "cooling" process, where initially stochastic interactions converge to a low-energy, structured equilibrium. To implement this, We propose MAGE (Multi-Agent Communication Graph Generation), a score-based diffusion framework that constructs communication graphs by navigating the energy landscape via iterative denoising and first-order gradient guidance. Extensive experiments on representative benchmarks demonstrate that MAGE achieves state-of-the-art performance. Furthermore, qualitative analysis reveals that the generated graphs mirroring the functional specialization of human organizations, validating our thermodynamic hypothesis.