Improving Data Fidelity via Diffusion Model-based Correction and Super-Resolution

TL;DR

This paper introduces a diffusion model-based pipeline that corrects low-quality data and enhances its resolution, effectively reducing errors and noise while recovering detailed structures across various datasets.

Contribution

It presents a novel two-step diffusion model approach combining correction and super-resolution, validated both theoretically and experimentally.

Findings

Effective correction of numerical errors and noise.

Significant resolution enhancement and detail recovery.

Validated on PDE and climate datasets.

Abstract

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.