Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically rely on conditional training mechanisms and demand substantial computational effort to prepare the labeled training dataset, which makes them inflexible since any change in the governing equations or boundary conditions requires a complete retraining process. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure generation. 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, ranging from the design of microstructures with specified homogenized properties to those with targeted hyperelastic and elasto-plastic behaviors, showcase the effectiveness of the framework and its potential for advanced design tasks involving diverse performance and style requirements.

翻译：深度生成模型，特别是去噪扩散模型，在生成具有期望性能和风格的高保真架构微结构方面取得了显著成功。然而，这些近期方法通常依赖于条件训练机制，并且需要大量计算工作来准备带标签的训练数据集，这使得它们缺乏灵活性，因为任何控制方程或边界条件的改变都需要完整的重新训练过程。在本研究中，我们提出了一种新的逆向设计框架，该框架将无条件去噪扩散模型与可微分编程技术相结合，用于架构微结构的生成。我们的方法消除了为不同问题设置准备昂贵的带标签数据集和重新训练的需求。通过将输入扩散模型的噪声重新解释为可优化的设计变量，我们将设计任务表述为对噪声输入的优化问题，从而能够控制反向去噪轨迹，以引导生成的微结构朝向期望的力学性能，同时保留训练数据集中编码的风格约束。通过向量-雅可比乘积串联，我们开发了一个统一的微分流水线，以实现通过反向传播进行端到端的梯度评估。从设计具有指定均匀化性能的微结构，到具有目标超弹性和弹塑性行为的微结构，多个数值示例展示了该框架的有效性及其在涉及多样化性能和风格要求的高级设计任务中的潜力。