In this work, a new multifidelity (MF) uncertainty quantification (UQ) framework is presented and applied to the LS89 nozzle modified by fouling. Geometrical uncertainties significantly influence the aerodynamic performance of gas turbines. One representative example is given by the airfoil shape modified by fouling deposition, as in turbine nozzle vanes, which generates high-dimensional input uncertainties. However, the traditional UQ approaches suffer from the curse of dimensionality phenomenon in predicting the influence of high-dimensional uncertainties. Thus, a new approach based on multifidelity deep neural networks (MF-DNN) was proposed in this paper to solve the high-dimensional UQ problem. The basic idea of MF-DNN is to ensure the approximation capability of neural networks based on abundant low-fidelity (LF) data and few high-fidelity (HF) data. The prediction accuracy of MF-DNN was first evaluated using a 15-dimensional benchmark function. An affordable turbomachinery UQ platform was then built based on key components including the MF-DNN model, the sampling module, the parameterization module and the statistical processing module. The impact of fouling deposition on LS89 nozzle vane flow was investigated using the proposed UQ framework. In detail, the MF-DNN was fine-tuned based on bi-level numerical simulation results: the 2D Euler flow field as low-fidelity data and the 3D Reynolds-averaged Navier–Stokes (RANS) flow field as high-fidelity data. The UQ results show that the total pressure loss of LS89 vane is increased by at most 17.1% or reduced by at most 4.3%, while the mean value of the loss is increased by 3.4% compared to the baseline. The main reason for relative changes in turbine nozzle performance is that the geometric uncertainties induced by fouling deposition significantly alter the intensity of shock waves near the throat area and trailing edge. The developed UQ platform could provide a useful tool in the design and optimization of advanced turbomachinery considering high-dimensional input uncertainties.