In this paper we study multi-hop ad hoc routing in a Underwater Sensor Network (UWSN), a novel network paradigm for ad hoc underwater investigation with a large number of low cost underwater sensors. In UWSN, sensors are mobile with water current and dispersion, and use a wireless acoustic channel for communications. However, the large propagation latency and very low bandwidth of an acoustic channel could cause widespread collisions. Moreover, the mobility of sensors requires route management and causes additional traffic, thus worsening the situation. In this paper, we propose Under-Water Diffusion (UWD), a multi-hop ad hoc routing and in-network processing protocol. Since any on-demand flood or proactive exchange is considered harmful in underwater, UWD uses no proactive routing message exchange and negligible amount of ondemand floods in the environment with homogeneous GPSfree nodes and random node mobility. We validate UWD through both the mathematical analysis and simulations.