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Interference alignment (IA) has been recognized as a promising technique to obtain large multiplexing gain in multiple-input-multiple-output (MIMO) interference channels. Most existing IA schemes require global channel state information (CSI) at the transmitter to design precoding vectors and, thus, result in significant capacity overhead in the feedback link. To reduce the feedback overhead, in this paper, we investigate the IA scheme employing differential CSI feedback over time-correlated MIMO channels. Specifically, we analyze the achievable sum-rate performance using differential feedback and derive the minimum differential feedback rate to achieve the maximum multiplexing gain. We also provide the upper bound of the sum-rate performance loss due to the limited differential feedback rate. Finally, the analytical results are verified by simulations in a practical IA scheme with differential CSI feedback using Lloyd's quantization algorithm.