Generative models have had a profound impact on vision and language, paving the way for a new era of multimodal generative applications. Yet, challenges persist in constrained environments, such as engineering and science, where data is limited and precision is crucial. We introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a regularization technique aligning diffusion model sampling with physics-based optimization. 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.