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. In this work, we propose a two-stage Posterior-Mean Rectified Flow (PMRF) pipeline for synthesizing volumetric CE brain MRI from non-contrast inputs. First, a patch-based 3D U-Net predicts the voxel-wise posterior mean (minimizing MSE). Then, this initial estimate is refined by a time-conditioned 3D rectified flow to incorporate realistic textures without compromising structural fidelity. We train this model on a multi-institutional collection of paired pre- and post-contrast T1w volumes (BraTS 2023-2025). On a held-out test set of 360 diverse volumes, our best refined outputs achieve an axial FID of $12.46$ and KID of $0.007$ ($\sim 68.7\%$ lower FID than the posterior mean) while maintaining low volumetric MSE of $0.057$ ($\sim 27\%$ higher than the posterior mean). Qualitative comparisons confirm that our method restores lesion margins and vascular details realistically, effectively navigating the perception-distortion trade-off for clinical deployment.

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods typically attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.