This study introduces a novel image reconstruction technique based on a diffusion model that is conditioned on the native data domain. Our method is applied to multi-coil MRI and quantitative MRI (qMRI) reconstruction, leveraging the domain-conditioned diffusion model within the frequency and parameter domains. The prior MRI physics are used as embeddings in the diffusion model, enforcing data consistency to guide the training and sampling process, characterizing MRI k-space encoding in MRI reconstruction, and leveraging MR signal modeling for qMRI reconstruction. Furthermore, a gradient descent optimization is incorporated into the diffusion steps, enhancing feature learning and improving denoising. The proposed method demonstrates a significant promise, particularly for reconstructing images at high acceleration factors. Notably, it maintains great reconstruction accuracy for static and quantitative MRI reconstruction across diverse anatomical structures. Beyond its immediate applications, this method provides potential generalization capability, making it adaptable to inverse problems across various domains.