Conventional multiphysics for coal seam gas production is generally coupled with poroelasticity-based coal permeability models, which are derived under the assumption that gas pressure is distributed uniformly within the representative elementary volume (REV). Under this assumption, the pore swelling/shrinking strain is equal to the bulk one. However, this assumption is considered as the primary reason for the inconsistency between experimental data, field data, and model results. In this study, a new concept of differential strain index (DSI) is proposed to theoretically define the relation among desorption-induced strains of the coal bulk, pores and solid grains. DSI is a function of the gas pressure, and its magnitudes are regulated by the Langmuir constants of both the solid grains and the coal bulk. Furthermore, a DSI-based coal permeability model is incorporated into the coupled multiphysics model for coal seam gas production. The model results of both laboratory-scale and field-scale show that coal permeability changes over a wide range during gas production. These changes are controlled by the DSI, and the magnitudes of change are defined by the Langmuir strain ratio of solid grains to coal bulk, while the trends of change are defined by the Langmuir pressure ratio of solid grains to bulk coal.