Diffmah approximates the growth of individual halos as a simple power-law function of time, where the power-law index smoothly decreases as the halo transitions from the fast-accretion regime at early times to the slow-accretion regime at late times. The code has a typical accuracy of 0.1 dex for times greater than one billion years in halos of mass greater than 10e11 M_sun. Diffmah self-consistently captures the mean and variance of halo mass accretion rates across long time scales, and it generates Monte Carlo simulations of cosmologically-representative and differentiable halo histories.