Diffusion in condensed phases is a ubiquitous but poorly understood phenomenon. For example, chemical diffusion, which is the transport of matter associated with chemical concentration gradients (Fick’s law), is treated as a separate process from thermal transport (the Soret effect), which is mass transport induced by temperature gradients. In the past few years, large variations in the proportions of isotopes of Mg, Ca, Fe, Si and O found in silicate melts subject to thermal gradients have been found1, 2, 3, but no physical mechanism has been proposed. Here we present a model of diffusion in natural condensed systems that explains both the chemical and isotopic fractionation of Mg, Ca and Fe in high-temperature geochemical melts. Despite the high temperatures associated with these melts (T > 1,000 °C), we find that consideration of the quantum-mechanical zero-point energy of diffusing species is essential for understanding diffusion at the isotopic level. Our model explains thermal and chemical mass transport as manifestations of the same underlying diffusion mechanism. This work promises to provide insights into mass-transport phenomena (diffusion and evaporation) and associated isotopic fractionations in a wide range of natural condensed systems, including the atmospheric water cycle1, 2, geological and geochemical systems3, 4, 5, 6 and the early Solar System4. This work might also be relevant to studies of mass transport in biological7, 8 and nanotechnological condensed systems9.