Diffstar fits the star formation history (SFH) of galaxies to a smooth parametric model. Diffstar differs from existing SFH models because the parameterization of the model is directly based on basic features of galaxy formation physics, including halo mass assembly history, accretion of gas into the dark matter halo, the fraction of gas that is converted into stars, the time scale over which star formation occurs, and the possibility of rejuvenated star formation. The SFHs of a large number of simulated galaxies can be fit in parallel using mpi4py.