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In the near future, small intelligent devices will be deployed in homes, plantations, oceans, rivers, streets, and highways to monitor the environment. These devices require time synchronization, so voice and video data from different sensor nodes can be fused and displayed in a meaningful way at the sink. Instead of time synchronization between just the sender and receiver or within a local group of sensor nodes, some applications require the sensor nodes to maintain a similar time within a certain tolerance throughout the lifetime of the network. The Time-Diffusion Synchronization Protocol (TDP) is proposed as a network-wide time synchronization protocol. It allows the sensor network to reach an equilibrium time and maintains a small time deviation tolerance from the equilibrium time. In addition, it is analytically shown that the TDP enables time in the network to converge. Also, simulations are performed to validate the effectiveness of TDP in synchronizing the time throughout the network and balancing the energy consumed by the sensor nodes.