Convolutional neural networks are introduced into reconstructing electron density profiles from line-integrated density measurements of interferometers in the EAST tokamak. Diagnostic data from the polarimeter/interferometer and the hydrogen cyanide interferometer diagnostic systems are integrated to improve the reconstruction performance. By training and optimization with unreliable measurements in the data set, the robustness of this algorithm is enhanced. The established model can predict the probability distribution of density profiles accurately, fast, and robustly to noise and interference. This algorithm is not restricted to specific equilibrium configurations and can be transferred easily between different fusion devices.