Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction

2026-02-24

AI Summary

This work addresses the inefficiency and physical inconsistency of existing image super-resolution methods and general-purpose diffusion models in fluid super-resolution tasks, which often suffer from spectral mismatch and spurious divergence due to the neglect of physical constraints. To overcome these limitations, we propose ReMD, a novel framework that embeds physical consistency directly into the diffusion reverse process. By constructing a multiscale hierarchy using multiwavelet bases and incorporating a multigrid residual correction mechanism, ReMD integrates data fidelity with lightweight physical priors—without explicitly solving governing equations. The approach effectively preserves both large-scale coherent structures and fine-scale vortical details, achieving significantly improved spectral fidelity and reduced divergence on atmospheric and oceanic benchmarks, while attaining reconstruction accuracy comparable or superior to current diffusion models with fewer sampling steps.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Existing image SR and generic diffusion models transfer poorly to fluid SR: they are sampling-intensive, ignore physical constraints, and often yield spectral mismatch and spurious divergence. We address fluid super-resolution (SR) with \textbf{ReMD} (\underline{Re}sidual-\underline{M}ultigrid \underline{D}iffusion), a physics-consistent diffusion framework. At each reverse step, ReMD performs a \emph{multigrid residual correction}: the update direction is obtained by coupling data consistency with lightweight physics cues and then correcting the residual across scales; the multiscale hierarchy is instantiated with a \emph{multi-wavelet} basis to capture both large structures and fine vortical details. This coarse-to-fine design accelerates convergence and preserves fine structures while remaining equation-free. Across atmospheric and oceanic benchmarks, ReMD improves accuracy and spectral fidelity, reduces divergence, and reaches comparable quality with markedly fewer sampling steps than diffusion baselines. Our results show that enforcing physics consistency \emph{inside} the diffusion process via multigrid residual correction and multi-wavelet multiscale modeling is an effective route to efficient fluid SR. Our code are available on https://github.com/lizhihao2022/ReMD.

Problem

• fluid super-resolution
• physics consistency
• diffusion models
• spectral mismatch
• spurious divergence

Innovation

• physics-consistent diffusion
• multigrid residual correction
• multi-wavelet
• fluid super-resolution
• equation-free modeling