The formulation of drug/polymer amorphous solid dispersions (ASDs) is one of the most successful strategies for improving the oral bioavailability of poorly soluble active pharmaceutical ingredients (APIs). Hot-melt extrusion (HME) is one method for preparing ASDs that is growing in importance in the pharmaceutical industry, but there are still substantial gaps in our understanding regarding the dynamics of drug dissolution and dispersion in viscous polymers and the physical stability of the final formulations. Furthermore, computational models have been built to predict optimal processing conditions, but they are limited by the lack of experimental data for key mass transport parameters, such as the diffusion coefficient. The work presented here reports direct measurements of API diffusion in pharmaceutical polymer melts, using high-temperature pulsed-field gradient NMR. The diffusion coefficient of a model drug/polymer system (paracetamol/copovidone) was determined for different drug loadings and at temperatures relevant to the HME process. The mechanisms of the diffusion process are also explored with the Stokes–Einstein and Arrhenius models. The results show that diffusivity is linked exponentially to temperature. Furthermore, this study includes rheological characterization, differential scanning calorimetry (DSC), and 1H ssNMR T 1 and T 1ρ measurements to give additional insights into the physical state, phase separation, and API/polymer interactions in paracetamol/copovidone ASD formulations.