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It offers real time anatomical visualization with low acquisition cost and dose. Nevertheless, photon scattering and beam hindrance lead CBCT images to suffer from several artifacts. These involve inaccurate Hounsfield Unit HU values, which render a lower reliability towards the dose calculations and adaptive planning.\n  Purpose: Computed tomography CT, on the contrary, offers better image quality and accurate HU calibration, yet is typically acquired using offline mode and fails to capture the intra-treatment anatomical changes. This renders a need for developing an accurate CBCT to CT synthesis to mitigate the gap in imaging quality in the adaptive radiotherapy workflow.\n  Methods: We propose a novel diffusion based conditional generative model, coined EqDiff-CT, to synthesize high quality CT images from CBCT. 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This renders a need for developing an accurate CBCT to CT synthesis to mitigate the gap in imaging quality in the adaptive radiotherapy workflow.\n  Methods: We propose a novel diffusion based conditional generative model, coined EqDiff-CT, to synthesize high quality CT images from CBCT. 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