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 this https URL.
Abstract (translated)
现有的图像超分辨率（SR）和通用扩散模型在流体超分辨率任务中表现不佳，因为这些方法依赖于密集的采样过程、忽视物理约束，并且经常导致频谱不匹配和虚假发散。我们通过提出一种名为ReMD（Residual-Multigrid Diffusion）的基于物理学的一致性扩散框架来解决流体超分辨率问题。 在ReMD的每个逆向步骤中，采用了一种多网格残差校正方法：更新方向通过结合数据一致性与轻量级物理提示获得，并且随后跨尺度进行残差修正。这种多尺度层次结构利用了多小波（multi-wavelet）基来捕捉大规模结构和精细涡旋细节。 该自粗至细的设计不仅加速了收敛速度，而且在无需方程的情况下保留了精细的结构特征。在大气和海洋基准测试中，ReMD提高了准确性、频谱保真度，并且减少了发散现象的发生。与扩散基线模型相比，ReMD仅通过显著减少采样步骤就达到了相似的质量水平。 我们的研究结果表明，在扩散过程中通过多网格残差校正和多小波的多尺度建模强制执行物理一致性是一种实现高效流体超分辨率的有效途径。相关代码可在提供的链接中获取。
URL
https://arxiv.org/abs/2603.00149
