ReMD

Official PyTorch implementation of the CVPR 2026 paper:

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

ReMD (Residual-Multigrid Diffusion) is a physics-consistent diffusion framework for fluid super-resolution. Instead of treating super-resolution as generic image restoration, ReMD performs residual correction inside the reverse diffusion trajectory, combining coarse-scale consistency, multigrid refinement, and lightweight physics cues.

News

• The paper is published at CVPR 2026.
• This repository contains the official code implementation of ReMD.

Method Overview

At each reverse step, ReMD starts from a coarse LR-conditioned state and constructs a residual direction from two complementary sources:

• Data consistency: the current HR estimate is restricted back to the coarse space and compared with the LR anchor.
• Physics-consistent cues: differentiable residuals encourage smoothness, edge-preserving diffusion, and spectral alignment without requiring explicit PDE supervision.
• Time-gated multigrid correction: the residual is corrected across a fixed multiwavelet hierarchy, removing large-scale bias early and refining fronts or vortices later.
• Few-step sampling: the coarse-to-fine correction keeps the reverse path close to a physically plausible manifold, enabling high-quality outputs with only 2-5 reverse steps.

Results at a Glance

ReMD is evaluated on Navier-Stokes, ERA5, and Ocean benchmarks. It improves RMSE and spectral fidelity while using far fewer reverse steps than diffusion baselines.

Dataset	Scale	Variant	RMSE ↓	PSNR ↑	SSIM ↑	Steps
NS	2x	ReMD-5	2.09E-02	49.94	0.998	5
ERA5	4x	ReMD-5	8.02E-02	58.19	0.999	5
Ocean	4x	ReMD-2	1.32E-02	47.72	0.983	2

Compared with ResShift-15 on NS, ReMD-5 achieves better RMSE/PSNR with fewer steps and lower inference time; ReMD-2 remains competitive while being faster.

Qualitative Comparison

On NS and ERA5, ReMD-5 reconstructs sharper coherent fronts and cleaner small-scale structures. The error maps show lower artifacts than image-SR and operator-learning baselines, and lower errors than ResShift despite using 5 instead of 15 reverse steps.

The patch-level NS comparison highlights two behaviors: ReMD preserves cross-front gradients without staircasing or checkerboard artifacts, and it recovers compact small eddies while remaining consistent with the LR content.

Installation

Create an environment and install dependencies:

pip install -r requirements.txt

The code is implemented with PyTorch. CUDA is recommended for training and inference.

Datasets

The repository includes data loaders for:

• Navier-Stokes data in .mat or HDF5 format
• ERA5 data in .npy format
• Ocean velocity data in HDF5 format

Before training, update data.data_path in the config file:

data:
  data_path: "./data/NavierStokes_V1e-5_N1200_T20.mat"

Training

Single-process training:

python main.py --config template_configs/ns2d/remd.yaml

Distributed training:

torchrun --nproc_per_node=4 main_ddp.py --config template_configs/ns2d/remd_ddp.yaml

The default configs are templates. Adjust dataset paths, batch sizes, number of GPUs, and logging paths for your environment.

Repository Structure

datasets/                 Dataset loading and preprocessing
models/remd/              ReMD model, diffusion process, residual correction, and physics cues
template_configs/ns2d/    Training configs
trainers/                 ReMD training loop
utils/                    Losses, metrics, normalization, and helper utilities
main.py                   Single-process training entry point
main_ddp.py               Distributed training entry point
assets/                   README figures

Citation

If you find this repository useful, please cite:

@inproceedings{li2026remd,
  title     = {Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction},
  author    = {Li, Zhihao and Dong, Shengwei and Yi, Chuang and Gao, Junxuan and Lai, Zhilu and Liu, Zhiqiang and Wang, Wei and Zhang, Guangtao},
  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2026}
}

License

This project is released under the MIT License. See LICENSE for details.