Diffusion through soft polymer filters is a nonlinear process: the increase of the pressure on the filtrating liquid does not trigger the proportional increase of the flux through the filter. There are two sources of nonlinearity: the diffusivity properties of the filter and its high deformability. In the present work we use a theoretical formulation coupling large deformations and diffusion to describe a liquid flux through a polymeric filter. Two key factors making the present formulation simple are the molecular incompressibility condition and the nonlinear mobility tensor. The developed model is calibrated based on the experiments on toluene-rubber filtration.