Contrast-enhanced (CE) T1-weighted MRI is central to neuro-oncologic diagnosis but requires gadolinium-based agents, which add cost and scan time, raise environmental concerns, and may pose risks to patients. We propose a two-stage Posterior–Mean Rectified Flow (PMRF) pipeline that synthesizes volumetric CE brain MRI from non-contrast inputs. Stage 1 uses a patch-based residual 3D U-Net to estimate the conditional posterior mean, minimizing voxel-wise MSE. Stage 2 refines this prediction using a time-conditioned 3D rectified flow to incorporate realistic textures without compromising structural fidelity. Trained on paired pre-/post-contrast volumes from BraTS 2023–2025, PMRF achieves, on a held-out test set of 360 subjects, an axial FID of \(\sim 11.03\) and an axial KID of \(\sim 0.0057\) ( \(\sim 68.8\%\) lower than the posterior mean), while increasing voxel-wise MSE by only \(\sim 18.3\%\) relative to the posterior mean. Qualitative results demonstrate sharper lesion margins and enhanced vascular detail, indicating an effective balance in the perception–distortion trade-off suitable for clinical applications.