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Fusion-based quality assessment has emerged as a powerful method for developing high-performance quality models from quality models that individually achieve lower performances. A prominent example of such an algorithm is VMAF, which has been widely adopted as an industry standard for video quality prediction along with SSIM. In addition to advancing the state-of-the-art, it is imperative to alleviate the computational burden presented by the use of a heterogeneous set of quality models. In this paper, we unify "atom" quality models by computing them on a common transform domain that accounts for the Human Visual System, and we propose FUNQUE, a quality model that fuses unified quality evaluators. We demonstrate that in comparison to the stateof-the-art, FUNQUE offers significant improvements in both correlation against subjective scores and efficiency, due to computation sharing.