Using mathematical models of human cognition has become an increasingly important and valuable research tool in many different fields of psychological research and neighboring areas. Widely used are drift diffusion models that can be used to predict probability density functions (PDFs) of binary choice reaction tasks. Often, the parameters of such a model are time-independent (i.e., they do not vary as a function of time within a trial). However, the more common case involves time-dependent parameters, as seen in conflict diffusion models that assume a time-varying drift rate. Such time-dependent (or non-stationary) models increase mathematical complexity, but several solutions to approximate the PDFs have been advanced. We here present dRiftDM, an R package particularly designed to meet the needs of psychological research. This package approximates the PDFs by solving the Kolmogorov-Forward-Equation to handle time-dependent models as well. Fitting a model to data can be done participant-wise, and model parameters and statistics are easily accessible and can be visualized directly to provide information about (qualitative) model fits.