2025/05/13 by Xu, Wuzhe, Lu, Yulong, Wang, Sifan +1
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2505.08526
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic differential editing technique based on an imbalanced perturbation and denoising process, ensuring robust and effective bias correction at the low-resolution level. The robustness and effectiveness of this approach are validated theoretically and experimentally. Next, the super-resolution step leverages cascaded conditional diffusion models to iteratively refine the corrected data to high-resolution. Numerical experiments on three PDE problems and a climate dataset demonstrate that the proposed method effectively enhances low-fidelity, low-resolution data by correcting numerical errors and noise while simultaneously improving resolution to recover fine-scale structures.