The ability to reliably estimate free space is an essential requirement for efficient and safe robot navigation. This paper presents a novel system, built upon a stochastic framework, which estimates free space quickly from stereo data, using self-supervised learning. The system relies on geometric data in the close range of the robot to train a second-stage appearance-based classifier for long range areas in a scene. Experiments are conducted on board an unmanned ground vehicle, and the results demonstrate the advantages of the proposed technique over other self-supervised systems.