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Objective: To compare the stretched exponential model of diffusion-weighted imaging (DWI) with monoexponential and biexponential models in terms of the ability to characterize focal liver lesions (FLLs)., Methods: This retrospective study included 180 patients with FLLs who underwent magnetic resonance imaging including DWI with nine b values at 3.0 T. The distributed diffusion coefficient (DDC) and intravoxel diffusion heterogeneity index (α) from a stretched exponential model; true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ), and perfusion fraction (f) from a biexponential model; and apparent diffusion coefficient (ADC) were calculated for each lesion. Diagnostic performances of the parameters were assessed through receiver operating characteristic (ROC) analysis. For 20 patients with treated hepatic metastases, the correlation between the DWI parameters and the percentage of tumor necrosis on pathology was evaluated using the Spearman correlation coefficient., Results: DDC had the highest area under the ROC curve (AUC, 0.905) for differentiating malignant from benign lesions, followed by D t (0.903) and ADC (0.866), without significant differences among them (DDC vs. D t , p = 0.946; DDC vs. ADC, p = 0.157). For distinguishing hypovascular from hypervascular lesions, and hepatocellular carcinoma from metastasis, f  had a significantly higher AUC than the other DWI parameters (p < 0.05). The α had the strongest correlation with the degree of tumor necrosis (ρ = 0.655, p = 0.002)., Conclusion: The DDC from stretched exponential model of DWI demonstrated excellent diagnostic performance for differentiating malignant from benign FLLs. The α is promising for evaluating the degree of necrosis in treated metastases., Key Points: • The stretched exponential DWI model is valuable for characterizing focal liver lesions. • The DDC from stretched exponential model shows excellent performance for differentiating malignant from benign focal liver lesions. • The α from stretched exponential model is promising for evaluating the degree of necrosis in hepatic metastases after chemotherapy.