On-demand inverse design of metamaterials via denoising diffusion probabilistic models

Abstract The nonlinear and non-unique relationship between unit-cell topology and bandgap properties motivates the development of complementary data-driven approaches for metamaterial inverse design. This work presents a conditional denoising diffusion probabilistic model (DDPM)-based framework for the on-demand generation of two-dimensional metamaterial unit cells conditioned on prescribed bandgap properties. We employ a conditional DDPM because its non-adversarial denoising objective enables stable training and stochastic generation of diverse candidate topologies, although it requires iterative sampling and does not provide the explicit low-dimensional latent representation available in variational autoencoders. The model learns a probabilistic mapping from Gaussian noise, conditioned on the prescribed bandgap width and mid-frequency, to binary unit-cell topologies. The results show that the proposed framework generates structurally diverse candidate topologies with low surrogate-predicted errors relative to the prescribed targets. The proposed approach provides a flexible framework for conditional one-to-many metamaterial inverse design and a basis for future extension to broader classes of periodic structures.