Physics-guided diffusion models for inverse design of disordered metamaterials

Disordered metamaterials are promising for programming physical properties, yet their inverse design remains challenging due to the non-intuitive structure-property relationships. Recent generative approaches, particularly diffusion models, have shown potential in high-dimensional inverse design tasks. However, existing methods typically rely on task-specific training strategies, such as conditional data-driven or physics-informed loss functions. Consequently, models must be retrained from scratch whenever governing equations, boundary conditions, or design objectives change, limiting their flexibility and generalization. In this work, we propose physics-guided diffusion models that leverage differentiable physics-based solvers to instantly guide the generative process for inverse design. Drawing inspiration from classifier guidance, we develop a sampling strategy that directly incorporates physics guidance into the reverse stochastic differential equations. Using gradients from differentiable solvers, our approach enables task-adaptive generation within a learned morphology prior, while requiring the diffusion model to be trained only once on unlabeled data. Focusing on 2D disordered closed-cell foam metamaterials, we present three design tasks: (1) achieving target effective thermal conductivity, (2) matching desired load-displacement response, and (3) maximizing energy absorption involving fractures. The results in each scenario demonstrate the versatility, efficiency, and practicality of physics-guided diffusion models for tackling complex inverse design problems in disordered metamaterials and beyond.