We propose a novel diffusion-based generative model for solving linear stochastic diffusion equations, while enabling uncertainty quantification (UQ). By embedding the governing physical laws into the generative process, our approach establishes a mapping between control parameters and solutions across the latent space of the diffusion model. This ensures that the generated solutions satisfy the underlying physical constraints. Additionally, our method overcomes the limitation of conventional diffusion models, which struggle to generate accurate solutions for new control terms, and achieves superior accuracy compared to traditional data-driven operator learning techniques. Furthermore, by sampling different noise realizations and analyzing variations in the generated solutions, we efficiently capture solution diversity, enabling simultaneous prediction and comprehensive UQ. Experimental results demonstrate that our method outperforms deep operator networks and variational inference-based deep operator networks in both accuracy and confidence estimation.