Synthesizing high-quality images from low-field MRI holds significant potential. Low-field MRI is cheaper, more accessible, and safer, but suffers from low resolution and poor signal-to-noise ratio. This synthesis process can reduce reliance on costly acquisitions and expand data availability. However, synthesizing high-field MRI still suffers from a clinical fidelity gap. There is a need to preserve anatomical fidelity, enhance fine-grained structural details, and bridge domain gaps in image contrast. To address these issues, we propose a \emph{cyclic self-supervised diffusion (CSS-Diff)} framework for high-field MRI synthesis from real low-field MRI data. Our core idea is to reformulate diffusion-based synthesis under a cycle-consistent constraint. It enforces anatomical preservation throughout the generative process rather than just relying on paired pixel-level supervision. The CSS-Diff framework further incorporates two novel processes. The slice-wise gap perception network aligns inter-slice inconsistencies via contrastive learning. The local structure correction network enhances local feature restoration through self-reconstruction of masked and perturbed patches. Extensive experiments on cross-field synthesis tasks demonstrate the effectiveness of our method, achieving state-of-the-art performance (e.g., 31.80 $\pm$ 2.70 dB in PSNR, 0.943 $\pm$ 0.102 in SSIM, and 0.0864 $\pm$ 0.0689 in LPIPS). Beyond pixel-wise fidelity, our method also preserves fine-grained anatomical structures compared with the original low-field MRI (e.g., left cerebral white matter error drops from 12.1$\%$ to 2.1$\%$, cortex from 4.2$\%$ to 3.7$\%$). To conclude, our CSS-Diff can synthesize images that are both quantitatively reliable and anatomically consistent.