Steering topology distributions for unified generative design of architected metamaterials

Architected metamaterials derive their functions from structure, creating vast opportunities to program physical responses through topology design. However, existing design methods are often tailored to individual design problems, making limited use of topology knowledge for effective and broadly applicable design as objectives, constraints, and physical functions change. Here we introduce Generative Topology Optimization (GenTO), a unified framework that turns a learned topology prior into a reusable design engine. GenTO trains a diffusion model on a large full-order topology dataset and then iteratively steers the resulting topology distribution toward task-specific high-performing regions using user-defined physical objectives and constraints. This shifts the object of optimization from a single structure to a task-adapted topology distribution. Across topology design problems spanning thermal extremization, multi-objective morphology control, property-targeted auxetic design, and vibration transmission design, GenTO reuses pretrained topology priors for heterogeneous tasks, preserves structural diversity, and reaches high-performing solutions supported by numerical benchmarks and experimental validation. These results establish reusable topology knowledge as a unified principle for effective and scalable architected metamaterial design.