This study presents a significant advancement in unsupervised magnetic resonance (MR) image harmonization through the development of SR-Param-MPMGen, a novel framework that translates clinical MR acquisitions into an invariant, isotropic space. Building upon existing methods for multi-parametric map (MPM) generation, our approach introduces automatic parameter prediction, enabling physics-based simulations to convert qualitative MR images into quantitative MPMs without relying on manual parameter inputs or paired training data. The efficacy of SR-Param-MPMGen is validated through image reconstruction-quality analysis and downstream segmentation tasks, demonstrating statistically significant improvements in healthy tissue segmentation compared to a state-of-the-art style transfer method. These results underscore the potential of our approach to improve data harmonization and analysis in large-scale neuroimaging studies and clinical applications, particularly in scenarios with heterogeneous or missing data.