Automatic non-invasive assessment of hepatocellular carcinoma (HCC) malignancy has the potential to substantially enhance tumor treatment strategies for HCC patients. In this work we present a novel framework to automatically characterize the malignancy of HCC lesions from DWI images. We predict HCC malignancy in two steps: As a first step we automatically segment HCC tumor lesions using cascaded fully convolutional neural networks (CFCN). A 3D neural network (SurvivalNet) then predicts the HCC lesions' malignancy from the HCC tumor segmentation. We formulate this task as a classification problem with classes being "low risk" and "high risk" represented by longer or shorter survival times than the median survival. We evaluated our method on DWI of 31 HCC patients. Our proposed framework achieves an end-to-end accuracy of 65% with a Dice score for the automatic lesion segmentation of 69% and an accuracy of 68% for tumor malignancy classification based on expert annotations. We compared the SurvivalNet to classical handcrafted features such as Histogram and Haralick and show experimentally that SurvivalNet outperforms the handcrafted features in HCC malignancy classification. End-to-end assessment of tumor malignancy based on our proposed fully automatic framework corresponds to assessment based on expert annotations with high significance (p>0.95).