This paper presents a novel approach that enhances generative diffusion models by enforcing compliance with specified constraints and physical principles. We reformulate the traditional sampling process used in these models into a constrained optimization problem. This reformulation guides the generated data to adhere closely to predefined boundaries, thereby ensuring the models comply with relevant constraints. Our methodology is demonstrated across various applications, including the generation of new materials with targeted morphometric characteristics, the synthesis of physics-informed motion, optimized path planning, and the creation of realistic human motion.