In this brief, miniaturized balanced-to-unbalanced (BTU) and balanced-to-balanced (BTB) filtering power dividers (FPDs) are proposed. Using one multi-mode dielectric resonator with multiple feeding probes, a single-cavity structure for BTU FPD is constructed, showing a compact size. Then, the circuit topology is analyzed, where the impedance in each branch can be adjusted to distribute the input power to two outputs with different ratios by only controlling the coupling coefficients. In this way, a BTU FPD with a very simple structure can be designed with arbitrary power division ratio. Besides, by replacing the two unbalanced output feeding probes in the BTU FPD as balanced ones, a BTB FPD can also be realized with controllable power division ratios. The working mechanism of the proposed designs are detailed. The proposed circuits are verified with good simulated and measured results.