Aortic dissection (AD) is a dangerous disease with a high mortality which requires contrast enhanced computed tomography (CE-CT) for clinical diagnosis. However, CE-CT needs injecting contrast agents which may cause allergic reactions or renal failure. To address this issue, a cascaded multi-task generative framework was proposed to detect AD based on NCE-CT images. The framework jointly learns non-contrast to contrast (NC2C) transformation, true and false lumen segmentation, and AD or non-AD classification to improve the accuracy of AD detection. We evaluated the framework and compared it with state-of-the-art algorithms based on a clinical dataset collected from two hospitals. Experiment results demonstrate that the proposed framework outperforms state-of-the-art algorithms and is able to detect AD with accuracy of 84.4%, sensitivity of 93.8%, and specificity of 75.0%. The framework is valuable to alleviate the misdiagnosis when only NCE-CT images are available for detecting AD.