While contrast-enhanced CT (CECT) is standard for assessing abdominal aortic aneurysms (AAA), the required iodinated contrast agents pose significant risks, including nephrotoxicity, patient allergies, and environmental harm. To reduce contrast agent use, recent deep learning methods have focused on generating synthetic CECT from non-contrast CT (NCCT) scans. However, most adopt a multi-stage pipeline that first generates images and then performs segmentation, which leads to error accumulation and fails to leverage shared semantic and anatomical structures. To address this, we propose a unified deep learning framework that generates synthetic CECT images from NCCT scans while simultaneously segmenting the aortic lumen and thrombus. Our approach integrates conditional diffusion models (CDM) with multi-task learning, enabling end-to-end joint optimization of image synthesis and anatomical segmentation. Unlike previous multitask diffusion models, our approach requires no initial predictions (e.g., a coarse segmentation mask), shares both encoder and decoder parameters across tasks, and employs a semi-supervised training strategy to learn from scans with missing segmentation labels, a common constraint in real-world clinical data. We evaluated our method on a cohort of 264 patients, where it consistently outperformed state-of-the-art single-task and multi-stage models. For image synthesis, our model achieved a PSNR of 25.61 dB, compared to 23.80 dB from a single-task CDM. For anatomical segmentation, it improved the lumen Dice score to 0.89 from 0.87 and the challenging thrombus Dice score to 0.53 from 0.48 (nnU-Net). These segmentation enhancements led to more accurate clinical measurements, reducing the lumen diameter MAE to 4.19 mm from 5.78 mm and the thrombus area error to 33.85% from 41.45% when compared to nnU-Net. Code is available at https://github.com/yuxuanou623/AortaDiff.git.