Quantitative Diffusion-Weighted MRI (DW-MRI) may be deployed to collect quantitative information about tissue properties, such as diffusion and perfusion fractions, and produce quantitative (rather than qualitative) MRI maps. Such a protocol typically relies on fitting bio-physical models to large data sets of MR measurements. Classical fitting methods require long acquisition and computation times in order to obtain reliable measurements of tissue properties. Recent deep-learning methods have the potential to produce faster tissue properties measurements, however, in-consistency between scanners and acquisition protocols, or unknown variations in the physical acquisition parameters, may result with highly unstable predictions. To address this limitation, we focus our interest on the Intra-Voxel Incoherent Motion (IVIM) signal decay model, and propose a novel DNN model: “MELoDee”, for which the IVIM acquisition parameters are incorporated as part of the network’s architecture. In addition, a training protocol that is appropriately tailored to the proposed architecture is introduced. We demonstrate the improved performance of MELoDee compared to previous DNN-based methods through simulation studies for the IVIM model as well as in-vivo DW-MRI data.