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The pancreatic disease taxonomy includes ten types of masses (tumors or cysts)[20,8]. Previous work focuses on developing segmentation or classification methods only for certain mass types. Differential diagnosis of all mass types is clinically highly desirable [20] but has not been investigated using an automated image understanding approach. We exploit the feasibility to distinguish pancreatic ductal adenocarcinoma (PDAC) from the nine other nonPDAC masses using multi-phase CT imaging. Both image appearance and the 3D organ-mass geometry relationship are critical. We propose a holistic segmentation-mesh-classification network (SMCN) to provide patient-level diagnosis, by fully utilizing the geometry and location information, which is accomplished by combining the anatomical structure and the semantic detection-by-segmentation network. SMCN learns the pancreas and mass segmentation task and builds an anatomical correspondence-aware organ mesh model by progressively deforming a pancreas prototype on the raw segmentation mask (i.e., mask-to-mesh). A new graph-based residual convolutional network (Graph-ResNet), whose nodes fuse the information of the mesh model and feature vectors extracted from the segmentation network, is developed to produce the patient-level differential classification results. Extensive experiments on 661 patients' CT scans (five phases per patient) show that SMCN can improve the mass segmentation and detection accuracy compared to the strong baseline method nnUNet (e.g., for nonPDAC, Dice: 0.611 vs. 0.478; detection rate: 89% vs. 70%), achieve similar sensitivity and specificity in differentiating PDAC and nonPDAC as expert radiologists (i.e., 94% and 90%), and obtain results comparable to a multimodality test [20] that combines clinical, imaging, and molecular testing for clinical management of patients.