物理一致的扩散模型：通过多尺度残差校正实现高效流体超分辨率
Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction
把多网格残差校正与多小波多尺度基嵌入扩散逆向过程，可在少步采样下保持谱保真并抑制伪散度，这一思路可迁移到其他受物理方程约束的图像复原任务（如PIV/流场重建、遥感反演）中作为采样加速与物理一致性约束的通用插件。
原文依据 the update direction is obtained by coupling data consistency with lightweight physics cues and then correcting the residual across scales
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论现有的图像超分辨率方法与通用扩散模型难以迁移到流体超分辨率任务：它们采样开销大、忽略物理约束，且常出现谱失配与虚假散度。本文以 ReMD（残差多网格扩散）这一物理一致的扩散框架来解决流体超分辨率问题。在每一个逆向步骤中，ReMD 执行多网格残差校正：通过将数据一致性与轻量物理线索相耦合来获得更新方向，随后跨尺度校正残差；该多尺度层级以多小波基实例化，从而同时捕捉大尺度结构与精细涡旋细节。这种由粗到细的设计加速了收敛，并在保持无方程形式的同时保留了精细结构。在大气与海洋基准上，ReMD 提升了精度与谱保真度，降低了散度，并以显著更少的采样步数达到与扩散基线相当的质量。结果表明，通过多网格残差校正与多小波多尺度建模在扩散过程内部施加物理一致性，是实现高效流体超分辨率的有效途径。
英文原文摘要 1191 字符
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 **ReMD** (**Re**sidual-**M**ultigrid **D**iffusion), a physics-consistent diffusion framework. At each reverse step, ReMD performs a **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 **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 **inside** the diffusion process via multigrid residual correction and multi-wavelet multiscale modeling is an effective route to efficient fluid SR.