In multi-shot diffusion imaging, motion induced phase variations are traditionally seen as a source of artifacts and corrected in the image domain using SENSE-based methods. This correction usually requires image echo and navigator echo to be geometrically matched. Recently, a k-space based method, realigned GRAPPA, has been proposed. It realigns data from different shots into the same k-space locations, and then synthesizes the missing data using GRAPPA algorithm. In this study, we refined the theory for GRAPPA-based method. In the revised theory, phase variations are treated as a kind of encoding, similar to coil sensitivity encoding. Based on this, the missing data can be synthesized using k-space correlations among different shots and channels. Then a compact kernel is used which only includes acquired data with significant contribution for the data synthesis, and can generate accurate weights without strict navigator size requirements. Simulation studies as well as brain and cervical spine experiments demonstrate that the proposed reconstruction method can effectively suppress artifacts caused by phase variations, and provide diffusion images with high resolution and low distortion. Compared with SENSE-based methods, the proposed method is less sensitive to mismatch between image echo and navigator echo.