Cardiac motion causes unpredictable signal loss in respiratory-triggered diffusion-weighted magnetic resonance imaging (DWI) of the liver, especially inside the left lobe. The left liver lobe may thus be frequently neglected in the clinical evaluation of liver DWI. In this work, a data-driven algorithm that relies on the statistics of the signal in the left liver lobe to mitigate the motion-induced signal loss is presented. The proposed data-driven algorithm utilizes the exclusion of severely corrupted images with subsequent spatially dependent image scaling based on a signal-loss model to correctly combine the multi-average diffusion-weighted images. The signal in the left liver lobe is restored and the liver signal is more homogeneous after applying the proposed algorithm. Furthermore, overestimation of the apparent diffusion coefficient (ADC) in the left liver lobe is reduced. The proposed algorithm can therefore contribute to reduce the motion-induced bias in DWI of the liver and help to increase the diagnostic value of DWI in the left liver lobe.