This article proposes a fully nonparametric model to investigate the dynamics of intergenerational income mobility for discrete outcomes. In our model, an individual's income class probabilities depend on parental income in a manner that accommodates nonlinearities and interactions among various individual and parental characteristics, including race, education, and parental age at childbearing, and so generalizes Markov chain mobility models. We show how the model may be estimated using kernel techniques from machine learning. Utilizing data from the panel study of income dynamics, we show how race, parental education, and mother's age at birth interact with family income to determine mobility between generations.