Abstract The element abundance pattern found in Milky Way disk stars is close to two-dimensional, dominated by production from one prompt process and one delayed process. This simplicity is remarkable, since the elements are produced by a multitude of nucleosynthesis mechanisms operating in stars with a wide range of progenitor masses. We fit the abundances of 14 elements for 48,659 red-giant stars from APOGEE Data Release 17 using a flexible, data-driven K-process model—dubbed KPM. In our fiducial model, with K = 2, each abundance in each star is described as the sum of a prompt and a delayed process contribution. We find that KPM with K = 2 is able to explain the abundances well, recover the observed abundance bimodality, and detect the bimodality over a greater range in metallicity than has previously been possible. We compare to prior work by Weinberg et al., finding that KPM produces similar results, but that KPM better predicts stellar abundances, especially for the elements C+N and Mn and for stars at supersolar metallicities. The model fixes the relative contribution of the prompt and delayed processes to two elements to break degeneracies and improve interpretability; we find that some of the nucleosynthetic implications are dependent upon these detailed choices. We find that moving to four processes adds flexibility and improves the model’s ability to predict the stellar abundances, but does not qualitatively change the story. The results of KPM will help us to interpret and constrain the formation of the Galaxy disk, the relationship between abundances and ages, and the physics of nucleosynthesis.