Style-Constrained Inverse Design of Microstructures With Tailored Mechanical Properties Using Unconditional Diffusion Models

Abstract

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. However, these recent methods typically rely on conditional training mechanisms that require extensive labeled data. Thus, the adaptation of these approaches to new problem settings may necessitate data regeneration and model retraining, presenting practical challenges for diverse design scenarios. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure design. Our approach eliminates the need for expensive labeled dataset preparation and retraining for different problem settings. By reinterpreting the noise input to the diffusion model as an optimizable design variable, we formulate the design task as an optimization problem over the noise input, enabling control over the reverse denoising trajectory to guide the generated microstructure toward the desired mechanical properties while preserving the stylistic constraints encoded in the training dataset. A unified differentiation pipeline via vector-Jacobian product concatenations is developed to enable end-to-end gradient evaluation through backpropagation. Several numerical examples are presented to showcase the effectiveness of the framework, including microstructure designs with specified homogenized properties, targeted hyperelastic responses in both two and three dimensions, and tailored elasto-plastic responses, highlighting its potential for advanced design tasks involving diverse performance and style requirements.