Rumor diffusion on complex networks has been widely investigated assuming that an individual learns the rumor merely from its neighbors, which, however, is not always the case. Recent studies of layered models have shown that individuals belonging to many different networks can affect the spreading process on one network. In this paper, we take this phenomenon into consideration and discuss its influence on rumor diffusion in complex networks by introducing independent spreaders. Independent spreaders are nodes that know the rumor from other channels rather than their neighbors. A new stochastic technique is used to obtain the dynamics of rumor diffusion. Results reveal that independent spreaders boost the process by bringing the rumor to r...