Cone beam computed tomography (CBCT) can be used to evaluate the inter-fraction anatomical changes during the entire course for image-guided radiotherapy (IGRT). However, CBCT artifacts from various sources restrict the full application of CBCT-guided adaptive radiation therapy (ART). Inter-fraction anatomical changes during ART, including variations in tumor size and normal tissue anatomy, can affect radiation therapy (RT) efficacy. Acquiring high-quality CBCT images that accurately capture patient- and fraction-specific (PFS) anatomical changes is crucial for successful IGRT. To enhance CBCT image quality, we proposed PFS lung diffusion models (PFS-LDMs). The proposed PFS models use a pre-trained general lung diffusion model (GLDM) as a baseline, which is trained on historical deformed CBCT (dCBCT)-planning CT (pCT) paired data. For a given patient, a new PFS model is fine-tuned on a CBCT-deformed pCT (dpCT) pair after each fraction to learn the PFS knowledge for generating personalized synthetic CT (sCT) with quality comparable to pCT or dpCT. The learned PFS knowledge is the specific mapping relationships, including personal inter-fraction anatomical changes between personalized CBCT-dpCT pairs. The PFS-LDMs were evaluated on an institutional lung cancer dataset, quantified by mean absolute error (MAE), peak signal-to-noise ratio (PSNR), normalized cross-correlation (NCC), and structural similarity index measure (SSIM) metrics. We also compared our PFS-LDMs with a mainstream GAN-based model, demonstrating that our PFS fine-tuning strategy could be applied to existing generative models. Our models showed remarkable improvements across all four evaluation metrics. The proposed PFS-LDMs outperformed the GLDM, demonstrating the effectiveness of our proposed fine-tuning strategy. The PFS model fine-tuned with CBCT images from four prior fractions, reduced the MAE from 103.95 to 15.96 Hounsfield units (HU), and increased the mean PSNR, NCC, and SSIM from 25.36dB to 33.57dB, 0.77 to 0.98, and 0.75 to 0.97, respectively. Applying our PFS fine-tuning strategy to a Cycle GAN model also showed improvements, with all four fine-tuned PFS Cycle GAN (PFS-CG) models outperforming the general Cycle GAN model. Overall, our proposed PFS fine-tuning strategy improved CBCT image quality compared to both the pre-correction and non-fine-tuned general models, with our proposed PFS-LDMs yielding better performance than the GAN-based model across all metrics. Our proposed PFS-LDMs significantly improve CBCT image quality with increased HU accuracy and fewer artifacts, thus better capturing inter-fraction anatomical changes. This lays the groundwork for enabling CBCT-based ART, which could enhance clinical efficiency and achieve personalized high-precision treatment by accounting for inter-fraction anatomical changes.