Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent generative approaches, particularly diffusion models, have shown potential in high-dimensional inverse design tasks. However, existing methods typically rely on carefully crafted training objectives, such as conditional data-driven or physics-informed loss functions. Because these strategies are inherently task-specific, the model must be retrained from scratch whenever the design problem changes (e.g., different governing equations, boundary conditions, or design objectives), severely limiting their flexibility and generalization ability. 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. Our approach enables task-adaptive generation using gradients from differentiable solvers, while the diffusion model itself needs to be trained only once on unlabeled data. Focusing on disordered foam metamaterials, we present three representative design tasks: (1) achieving target effective thermal conductivity, (2) matching desired load-displacement response, and (3) maximizing energy absorption involving fractures. In each scenario, the proposed method successfully generates foam-like geometries that fulfill the prescribed physical objectives. These results demonstrate the versatility, efficiency, and practicality of physics-guided diffusion models for tackling complex inverse design problems in disordered metamaterials and beyond.

翻译：无序超材料在跨领域应用中为调控物理性质提供了广阔前景，然而，由于其结构-性能关系非直观且设计空间巨大，其逆向设计仍面临挑战。近期的生成式方法，特别是扩散模型，在高维逆向设计任务中展现出潜力。然而，现有方法通常依赖于精心设计的训练目标，例如条件数据驱动或物理信息损失函数。由于这些策略本质上是任务特定的，每当设计问题发生变化时（例如，不同的控制方程、边界条件或设计目标），模型必须从头开始重新训练，这严重限制了其灵活性和泛化能力。在本工作中，我们提出物理引导扩散模型，利用可微分的基于物理的求解器来即时引导逆向设计的生成过程。受分类器引导的启发，我们开发了一种采样策略，将物理引导直接纳入反向随机微分方程。我们的方法能够利用可微分求解器的梯度实现任务自适应生成，而扩散模型本身仅需在无标签数据上训练一次。聚焦于无序泡沫超材料，我们提出了三个代表性设计任务：(1) 实现目标有效热导率，(2) 匹配期望的载荷-位移响应，以及(3) 涉及断裂的能量吸收最大化。在每种场景下，所提出的方法均成功生成了满足预设物理目标的类泡沫几何结构。这些结果证明了物理引导扩散模型在解决无序超材料及其他领域复杂逆向设计问题中的多功能性、高效性和实用性。