We propose a computational model for shape, illumination and albedo inference in a pulsed time-of-flight (TOF) camera. In contrast to TOF cameras based on phase modulation, our camera enables general exposure profiles. This results in added flexibility and requires novel computational approaches. To address this challenge we propose a generative probabilistic model that accurately relates latent imaging conditions to observed camera responses. While principled, realtime inference in the model turns out to be infeasible, and we propose to employ efficient non-parametric regression trees to approximate the model outputs. As a result we are able to provide, for each pixel, at video frame rate, estimates and uncertainty for depth, effective albedo, and ambient light intensity. These results we present are state-of-the-art in depth imaging. The flexibility of our approach allows us to easily enrich our generative model. We demonstrate this by extending the original single-path model to a two-path model, capable of describing some multipath effects. The new model is seamlessly integrated in the system at no additional computational cost. Our work also addresses the important question of optimal exposure design in pulsed TOF systems. Finally, for benchmark purposes and to obtain realistic empirical priors of multipath and insights into this phenomena, we propose a physically accurate simulation of multipath phenomena.