<p>Cross-modality medical image synthesis plays a critical role in enabling comprehensive multi-modal diagnosis and treatment. However, existing methods are constrained by their reliance on paired or unpaired source-target data, limiting scalability and practical deployment. Generating high-fidelity medical images in a truly source-free setting, where no source-domain data is accessible, remains a significant and underexplored challenge. To fill this gap, we propose <b>Diffusion Prior Synthesis and Optimization (DPSO)</b>, a novel source-free, diffusion-based framework that performs cross-modality medical image synthesis using only single-modality target data, without requiring supervision or statistical priors from the source domain. DPSO adopts a decoupled architecture via a Probability Flow ODE (PF-ODE) formulation that separates source encoding from target generation. A general-domain diffusion model maps notional source images into a shared latent space, independent of source-domain supervision. This latent representation is then decoded into the target modality using a PF-ODE solver guided by a target-specific prior. An additional optimization stage, also driven by the target prior, further refines the outputs to enhance fidelity and robustness. Experiments on the IXI Dataset and SynthRAD2023 demonstrate that DPSO achieves competitive performance across diverse cross-modality tasks, comparable to methods using paired or unpaired source data. Notably, DPSO removes the need for source modality data entirely, offering a flexible and scalable solution for truly source-free cross-modality medical image synthesis. Code is available at: <a href="https://anonymous.4open.science/r/DPSO-64DF">https://anonymous.4open.science/r/DPSO-64DF</a></p>