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

arXiv: https://arxiv.org/abs/2603.00149 · HTML: https://mlsanity.com/paper/2603.00149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shifting](https://mlsanity.com/paper/2307.12348/) (2023)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [MgNO: Efficient Parameterization of Linear Operators via Multigrid](https://mlsanity.com/paper/2310.19809/) (2023)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)

## Abstract (arXiv)

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 (underlineResidual-underlineMultigrid underlineDiffusion), 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. Our code are available on https://github.com/lizhihao2022/ReMD.