4D Flow MRI has emerged as a new imaging technique for assessing 3D flow dynamics in the heart and great arteries (e.g., Aorta) in vivo. 4D Flow MRI provides in vivo voxel-wise mapping of 3D time-resolved three-directional velocity vector-field information. However, current techniques underutilize such comprehensive vector-field information by reducing it to aggregate or derivative scalar-field. Here we propose a new data-driven stochastic methodological approach to derive the unique 4D vector-field signature of the 3D flow dynamics. Our technique is based on stochastically encoding the profile of the underlying pair-wise vector-field associations comprising the entire 3D flow-field dynamics. The proposed technique consists of two stages: 1) The 4D Flow vector-field signature profile is constructed by stochastically encoding the probability density function of the co-associations of millions of pair-wise vectors over the entire 4D Flow MRI domain. 2) The Hemodynamic Signature Index (HSI) is computed as a measure of the degree of alteration in the 4D Flow signature between patients. The proposed technique was extensively evaluated in three in vivo 4D Flow MRI datasets of 106 scans, including 34 healthy controls, 57 bicuspid aortic valve (BAV) patients and 15 Rescan subjects. Results demonstrate our technique’s excellent robustness, reproducibility, and ability to quantify distinct signatures in BAV patients.