用多尺度残差校正实现高效物理一致的流体超分辨率
Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction
- 通过多网格残差校正融合数据与物理线索，分层修正图像残差
- 在大气与海洋数据集上减少采样步数，提升频谱保真度与结构精度
- 适合需要快速生成高保真流体模拟结果的研究者或工程应用
现有图像超分辨率与通用扩散模型在流体超分辨率任务中表现不佳：采样成本高、忽略物理约束，常导致频谱不匹配与虚假发散。本文提出物理一致的扩散框架 ReMD（Residual-Multigrid Diffusion），在每一步反向过程中执行多网格残差校正：更新方向通过耦合数据一致性与轻量级物理提示获得，并跨尺度修正残差；多尺度结构采用多小波基表示，同时捕捉大尺度结构与精细涡旋细节。该从粗到细的设计加速收敛，保持细节，且无需显式求解方程。在大气与海洋基准测试中，ReMD显著提升精度与频谱保真度，减少发散，以更少采样步数达到与扩散基线相当的质量。结果表明，在扩散过程中通过多网格残差校正与多小波多尺度建模强制物理一致性，是实现高效流体超分辨率的有效路径。代码已开源：https://github.com/lizhihao2022/ReMD。
原文摘要 · Abstract (English)
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.
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