Diffusion models have recently demonstrated exceptional capabilities in generating diverse, high-quality samples across various fields, including medicine and bioscience. This project is dedicated to enhancing the development of generative diffusion models by ensuring provable reliability guarantees. Our focus will be on optimizing the sampling process to decrease generation time and computational overhead, while provably preserving sample fidelity. This will involve adjusting the initial noise distributions, designing control inputs during the sampling process, and integrating conditional generation techniques. The anticipated outcomes include improved diffusion models that are faster, more resource-efficient, and capable of handling complex optimization tasks with high reliability. Ultimately, this project aims to accelerate the practical adoption of generative models, enhance the robustness of AI technologies, and deepen the theoretical understanding of diffusion models.