Runaway-electron dynamics in tokamaks involve the combination of several processes acting across different scales: electric-field acceleration, collisional slowing-down, pitch angle scattering, radiative energy losses, and secondary generation through knock-on collisions. In this work, we present a stochastic framework for runaway-electron dynamics, in which electrons are described by processes in momentum space, and where multiplication events are accounted for in a branching-population description. This viewpoint provides a unified language for seed formation, avalanche growth and loss mechanisms through a probabilistic approach.