Wilkinson power dividers (WPDs) are a popular element in RF and microwave technologies known for providing isolation capabilities. However, the benefits that WPDs could offer to integrated photonic systems are far less studied. Here, we investigate the thermal emission from and the noise performance of silicon-on-insulator (SOI) WPDs. We find that WPDs exhibit a noiseless port, with important implications for receiving systems and absorption-based quantum state transformations. At the same time, the thermal signals exiting noisy ports exhibit nontrivial correlations, opening the possibility for noise cancellation. We analyze passive and active networks containing WPDs showing how such nontrivial correlations can prevent the amplification of the thermal noise introduced by WPDs while benefiting from their isolation capabilities. Using this insight, we propose a modified ring-resonator amplifier that improves by N times the SNR in comparison with conventional traveling wave and ring-resonator amplifiers, with N being the number of inputs/outputs of the WPD. We believe that our results represent an important step forward in the implementation of SOI-WPDs and their integration in complex photonic networks, particularly for mid-IR and quantum photonics applications.