Time-of-flight (TOF) depth cameras provide robust depth inference at low power requirements in a wide variety of consumer and industrial applications. These cameras reconstruct a single depth frame from a given set of infrared (IR) frames captured over a very short exposure period. Operating in this mode the camera essentially forgets all information previously captured - and performs depth inference from scratch for every frame. We challenge this practice and propose using previously captured information when inferring depth. An inherent problem we have to address is camera motion over this longer period of collecting observations. We derive a probabilistic framework combining a simple but robust model of camera and object motion, together with an observation model. This combination allows us to integrate information over multiple frames while remaining robust to rapid changes. Operating the camera in this manner has implications in terms of both computational efficiency and how information should be captured. We address these two issues and demonstrate a realtime TOF system with robust temporal integration that improves depth accuracy over strong baseline methods including adaptive spatio-temporal filters.