While contrast-enhanced CT (CECT) is standard for assessing abdominal aortic aneurysms (AAA) , the required iodinated contrast agents pose significant risks, including patient allergies and environmental harm. To reduce contrast agent use, 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 information. To address this, we propose a unified 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 clinical data. Evaluated on a cohort of 264 patients, our method consistently outperformed state-of-the-art single-task and multi-stage models. For image synthesis, it achieved a PSNR of 25.61 dB, compared to 23.80 dB from a single-task CDM. For 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%. Code is at https://github.com/yuxuanou623/AortaDiff.