Data-Driven Super-Resolution Reconstruction of Quasi-Geostrophic Turbulence Via Enhanced Diffusion Model and Fourier Neural Operator

High-fidelity simulation and reconstruction of physical fields are essential in both scientific research and engineering, yet classical solvers can be prohibitively expensive at resolutions needed to capture fine-scale structures. We propose FNODiffSR, a data-driven super-resolution framework that couples a residual-guided diffusion model with an Adaptive Weighted Fourier Neural Operator (AWFNO). AWFNO models longrange spectral dependencies while selectively emphasizing highfrequency components, and the diffusion module employs a conditional probability-flow ODE instead of stochastic sampling to deterministically bridge low- and high-fidelity representations. Final reconstructions are obtained by integrating this ODE with an adaptive time-stepping solver. Experiments on quasigeostrophic turbulence across varied upsampling and sparsesampling regimes show that FNODiffSR consistently surpasses interpolation and learning-based baselines in reconstruction fidelity, structural similarity, and physical consistency (as assessed by a dimensionless equation-residual), while offering predictable runtime and scalability. These qualities make FNODiffSR a strong candidate for high-quality scientific data recovery and downstream analysis.