We propose a novel approach to simulating the formation and evolution of stains on cloths in motion. We accurately capture the diffusion of a pigmented solution over a complex knitted or woven fabric through homogenization of its inhomogeneous and/or anisotropic properties into bulk anisotropic diffusion tensors. Secondary effects such as absorption, adsorption and evaporation are also accounted for through physically-based modeling. Finally, the influence of the cloth motion on the shape and evolution of the stain is captured by evaluating the inertial (e.g., centrifugal and Coriolis) forces experienced by the solution. The governing equations of motion are integrated in time directly on a deforming triangle mesh discretizing the inelastic cloth for efficiency and robustness. The deformation of the cloth can be precomputed or integrated through simplified two-way coupling, by using off-the-shell cloth simulations. Finally, numerical experiments demonstrate the plausibility of our results in practical applications by reproducing the usual shape and behavior of stains on various fabrics.