Generative models have had a profound impact on vision and language, paving the way for a new era of multimodal generative applications. While these successes have inspired researchers to explore using generative models in science and engineering to accelerate the design process and reduce the reliance on iterative optimization, challenges remain. Specifically, engineering optimization methods based on physics still outperform generative models when dealing with constrained environments where data is scarce and precision is paramount. To address these challenges, we introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework that demonstrates the efficacy of aligning the sampling trajectory of diffusion models with the optimization trajectory derived from traditional physics-based methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. Our method allows for generating feasible and high-performance designs in as few as two steps without the need for expensive preprocessing, external surrogate models, or additional labeled data. We apply our framework to structural topology optimization, a fundamental problem in mechanical design, evaluating its performance on in- and out-of-distribution configurations. Our results demonstrate that TA outperforms state-of-the-art deep generative models on in-distribution configurations and halves the inference computational cost. When coupled with a few steps of optimization, it also improves manufacturability for out-of-distribution conditions. By significantly improving performance and inference efficiency, DOM enables us to generate high-quality designs in just a few steps and guide them toward regions of high performance and manufacturability, paving the way for the widespread application of generative models in large-scale data-driven design.

翻译：生成模型在视觉和语言领域产生了深远影响，为多模态生成应用的新时代铺平了道路。尽管这些成功激励研究者探索在科学和工程领域中使用生成模型以加速设计过程并减少对迭代优化的依赖，但挑战依然存在。具体而言，基于物理的工程优化方法在处理数据稀缺且精度至关重要的约束环境时，仍优于生成模型。为应对这些挑战，我们提出了扩散优化模型（DOM）和轨迹对齐（TA），这是一种学习框架，证明了将扩散模型的采样轨迹与基于传统物理方法推导出的优化轨迹对齐的有效性。这种对齐确保了采样过程始终扎根于底层物理原理。我们的方法能够在仅需两步的情况下生成可行且高性能的设计，无需昂贵的预处理、外部代理模型或额外的标注数据。我们将该框架应用于结构拓扑优化——机械设计中的一个基本问题，并评估其在分布内和分布外配置上的性能。结果表明，TA在分布内配置上优于最先进的深度生成模型，并将推理计算成本降低一半。当与少量优化步骤结合时，它还改善了分布外条件下的可制造性。通过显著提升性能和推理效率，DOM使我们能够在仅需几步的情况下生成高质量设计，并将其引导至高性能和可制造性区域，为生成模型在大规模数据驱动设计中的广泛应用铺平道路。