Contrast-enhanced computed tomography (CE-CT) images, obtained by contrast agent (CAs) injection, play a vital role in diagnosing focal liver lesions. However, CA administration poses huge risks to patients in clinical practice. Recent studies explore deep learning-based generative models, including conditional GANs (CGANs) and Variational Autoencoders, to derive CE-CT images from non-contrast CT (NC-CT) images. Despite demonstrating decent performance, issues like mode collapse and training complexities hamper the improvements of CGAN-based models. Conditional diffusion models (CDMs), a novel generative model based on Markov chains, offer greater stability and a more intuitive generation process, resulting in superior performance in natural image synthesis tasks. Consequently, we introduced CDMs into CE-CT image synthesis tasks to assess their effectiveness. Our qualitative and quantitative analyses suggest that traditional CDMs outperform other generative models in overall image quality. Nonetheless, traditional CDMs exhibit a noticeable deterioration in the quality of critical areas, (i.e., liver, tumor). To address this limitation, we propose an improved CDM framework that enables the CDMs to fully utilize the conditional information by separating conditional information and noisy image. Our experimental results indicate that proposed improved CDM excelled in both local and global qualitative and quantitative assessments compared to other models.