# Unpaired Downscaling of Fluid Flows with Diffusion Bridges

arXiv: https://arxiv.org/abs/2305.01822 · HTML: https://mlsanity.com/paper/2305.01822/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 73 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Increasing the accuracy and resolution of precipitation forecasts using deep generative models](https://mlsanity.com/paper/2203.12297/) (2022)

## Built on by (most cited first, 21 of 21)

- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning](https://mlsanity.com/paper/2403.02774/) (2024)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System](https://mlsanity.com/paper/2309.06799/) (2023)
- [A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation](https://mlsanity.com/paper/2412.15361/) (2024)
- [Satellite Observations Guided Diffusion Model for Accurate Meteorological States at Arbitrary Resolution](https://mlsanity.com/paper/2502.07814/) (2025)
- [Easing Color Shifts in Score-Based Diffusion Models](https://mlsanity.com/paper/2306.15832/) (2023)
- [A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data](https://mlsanity.com/paper/2408.02688/) (2024)
- [Universal Diffusion-Based Probabilistic Downscaling](https://mlsanity.com/paper/2602.11893/) (2026)
- [GEN2: A Generative Prediction-Correction Framework for Long-time Emulations of Spatially-Resolved Climate Extremes](https://mlsanity.com/paper/2508.15196/) (2025)
- [SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition](https://mlsanity.com/paper/2601.01979/) (2026)
- [Response Theory via Generative Score Modeling](https://mlsanity.com/paper/2402.01029/) (2024)
- [Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling](https://mlsanity.com/paper/2504.13333/) (2025)
- [Reframing Generative Models for Physical Systems using Stochastic Interpolants](https://mlsanity.com/paper/2509.26282/) (2025)
- [Data-driven Mesoscale Weather Forecasting Combining Swin-Unet and Diffusion Models](https://mlsanity.com/paper/2503.19354/) (2025)
- [Physics-constrained generative machine learning-based high-resolution downscaling of Greenland's surface mass balance and surface temperature](https://mlsanity.com/paper/2507.22485/) (2025)
- [AODDiff: Probabilistic Reconstruction of Aerosol Optical Depth via Diffusion-based Bayesian Inference](https://mlsanity.com/paper/2512.24847/) (2025)
- [Generative Unsupervised Downscaling of Climate Models via Domain Alignment: Application to Wind Fields](https://mlsanity.com/paper/2604.03341/) (2026)
- [Longwang: Zero-Shot Global Spatiotemporal Precipitation Downscaling with a Latent Generative Prior](https://mlsanity.com/paper/2605.17603/) (2026)
- [Stress-Testing Dynamical and Generative Downscaling Using Subseasonal Extreme Precipitation Forecasts](https://mlsanity.com/paper/2609.11696/) (2026)

## Abstract (arXiv)

We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together two independent conditional diffusion models for use in domain translation. The resulting transformation is a diffusion bridge between a low resolution and a high resolution dataset and allows for new sample generation of high-resolution images given specific low resolution features. The ability to generate new samples allows for the computation of any statistic of interest, without any additional calibration or training. Our unsupervised setup is also designed to downscale images without access to paired training data; this flexibility allows for the combination of multiple source and target domains without additional training. We demonstrate that the method enhances resolution and corrects context-dependent biases in geophysical fluid simulations, including in extreme events. We anticipate that the same method can be used to downscale the output of climate simulations, including temperature and precipitation fields, without needing to train a new model for each application and providing a significant computational cost savings.