Blind harmonization has emerged as a promising technique for MR image harmonization to achieve scale-invariant representations, requiring only target domain data (i.e., no source domain data necessary). However, existing methods face limitations such as inter-slice heterogeneity in 3D, moderate image quality, and limited performance for a large domain gap. To address these challenges, we introduce BlindHarmonyDiff, a novel blind 3D harmonization framework that leverages an edge-to-image model tailored specifically to harmonization. Our framework employs a 3D rectified flow trained on target domain images to reconstruct the original image from an edge map, then yielding a harmonized image from the edge of a source domain image. We propose multi-stride patch training for efficient 3D training and a refinement module for robust inference by suppressing hallucination. Extensive experiments demonstrate that BlindHarmonyDiff outperforms prior arts by harmonizing diverse source domain images to the target domain, achieving higher correspondence to the target domain characteristics. Downstream task-based quality assessments such as tissue segmentation and age prediction on diverse MR scanners further confirm the effectiveness of our approach and demonstrate the capability of our robust and generalizable blind harmonization.