Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy (IGRT). It provides real time visualization at low cost and dose. However, photon scattering and beam hindrance cause artifacts in CBCT. These include inaccurate Hounsfield Units (HU), reducing reliability for dose calculation, and adaptive planning. By contrast, computed tomography (CT) offers better image quality and accurate HU calibration but is usually acquired offline and fails to capture intra-treatment anatomical changes. Thus, accurate CBCT-to-CT synthesis is needed to close the imaging-quality gap in adaptive radiotherapy workflows. To cater to this, we propose a novel diffusion-based conditional generative model, coined EqDiff-CT, to synthesize high-quality CT images from CBCT. EqDiff-CT employs a denoising diffusion probabilistic model (DDPM) to iteratively inject noise and learn latent representations that enable reconstruction of anatomically consistent CT images. A group-equivariant conditional U-Net backbone, implemented with e2cnn steerable layers, enforces rotational equivariance (cyclic C4 symmetry), helping preserve fine structural details while minimizing noise and artifacts. The system was trained and validated on the SynthRAD2025 dataset, comprising CBCT-CT scans across multiple head-and-neck anatomical sites, and we compared it with advanced methods such as CycleGAN and DDPM. EqDiff-CT provided substantial gains in structural fidelity, HU accuracy and quantitative metrics. Visual findings further confirm the improved recovery, sharper soft tissue boundaries, and realistic bone reconstructions. The findings suggest that the diffusion model has offered a robust and generalizable framework for CBCT improvements. The proposed solution helps in improving the image quality as well as the clinical confidence in the CBCT-guided treatment planning and dose calculations.