Intra-scan motion is a common source of artefacts in magnetic resonance imaging (MRI), which cannot be easily corrected. However, in quantitative MRI (qMRI), several volumes with varying parameters are acquired, and some sort of data redundancy exists. In this abstract, we propose a general framework where corrupted voxels are treated as missing entries and imputed using a Bayesian model of differently weighted MRI volumes. We demonstrate its efficacy in the context of various multi-parameter mapping (MPM) qMRI protocols, in which one volume is corrupted by motion. We show that the model can efficiently recover the corrupted data without introducing bias.