We introduce and demonstrate a new paradigm for quantitative parameter mapping in MRI.Parameter mapping techniques, such as diffusion MRI and quantitative MRI, have the potential to robustly and repeatably measure biologically-relevant tissue maps that strongly relate to underlying microstructure.Quantitative maps are calculated by fitting a model to multiple images, e.g. with least-squares or machine learning. However, the overwhelming majority of model fitting techniques assume that each voxel is independent, ignoring any co-dependencies in the data. This makes model fitting sensitive to voxelwise measurement noise, hampering reliability and repeatability.We propose a self-supervised deep variational approach that breaks the assumption of independent pixels, leveraging redundancies in the data to effectively perform data-driven regularisation of quantitative maps. We demonstrate that our approach outperforms current model fitting techniques in dMRI simulations and real data, especially with a Gaussian mixture prior.Our approach enables improved quantitative maps and/or reduced acquisition times, and can hence support the clinical adoption of parameter mapping methods such as dMRI and qMRI. Our code is available at REDACTED FOR ANONYMOUS SUBMISSION.