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

TL;DR

The 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.

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.

Figures (6)

• Figure 1: Qualitative comparison on NS ( $\times$2 ) and ERA5 ( $\times$4 ). Each block shows (left) a zoomed LR input $u_0$, (top row) HR reconstructions, and (bottom row) absolute error maps w.r.t. ground truth (shared color scale per block). With only 5 reverse steps, ReMD yields (NS) sharper filaments/coherent fronts and (ERA5) preserved mesoscale shear bands while suppressing ringing/stripe artifacts seen in EDSR/FNO/SwinIR, and achieves lower errors than ResShift despite requiring 5 vs. 15 steps.
• Figure 2: Overview of ReMD. Starting from a coarse LR initial solution, the reverse diffusion steps refine the HR estimate $u_t$ while a multigrid residual correction module combines data-consistency and physics residuals in the wavelet domain, yielding the final HR field $\hat{u}$.
• Figure 3: Error–energy spectrum on ERA5 (,$\times$4,). Radial average of the Fourier‐domain error (log scale on y) versus frequency (x). Vertical dashed lines mark the LR Nyquist band and the transition toward the HR band. ReMD-5 (red) maintains the lowest error from large to high scales, remaining below ResShift-15, FNO and image-SR baselines (EDSR, SwinIR), indicating superior spectral fidelity.
• Figure 4: Patch-level comparison on NS ($\times$4). Left: zoomed LR input. Black boxes highlight frontal bands; gray boxes mark small eddies. ReMD–5 recovers sharper, HR-like fronts and coherent vortices with fewer steps than ResShift–15, while avoiding texture/aliasing artifacts seen in image-SR baselines and blockiness in FNO, and remaining consistent with the LR content.
• Figure 5: Time--RMSE trade-off on ERA5_uo ($\times4$ SR). Each point varies the sampling steps; lower-left is better.