# Efficient Kilometer-Scale Precipitation Downscaling with Conditional Wavelet Diffusion

arXiv: https://arxiv.org/abs/2507.01354 · HTML: https://mlsanity.com/paper/2507.01354/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 22 of its 70 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## 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, 22 of 22)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Low-Light Image Enhancement with Wavelet-based Diffusion Models](https://mlsanity.com/paper/2306.00306/) (2023)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [Diffusion Model-based Probabilistic Downscaling for 180-year East Asian Climate Reconstruction](https://mlsanity.com/paper/2402.06646/) (2024)
- [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024)
- [Fast and accurate learned multiresolution dynamical downscaling for precipitation](https://mlsanity.com/paper/2101.06813/) (2021)
- [PrecipDiff: Leveraging image diffusion models to enhance satellite-based precipitation observations](https://mlsanity.com/paper/2501.07447/) (2025)
- [PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport](https://mlsanity.com/paper/2502.03749/) (2025)

## Built on by (most cited first, 4 of 4)

- [Bringing Agentic Search to Earth Observation Data Discovery](https://mlsanity.com/paper/2607.02387/) (2026)
- [Evaluating Cross-region Generalization for Wavelet-Diffusion Precipitation Downscaling](https://mlsanity.com/paper/2609.28749/) (2026)
- [RainAtlas: A Multi-Continental Dataset for Precipitation Downscaling](https://mlsanity.com/paper/2609.39833/) (2026)
- [Scale-Recursive Rectified Flows for Few-Step Precipitation Ensembles](https://mlsanity.com/paper/2610.02611/) (2026)

## Abstract (arXiv)

Effective hydrological modeling and extreme weather analysis demand precipitation data at a kilometer-scale resolution, which is significantly finer than the 10 km scale offered by standard global products like IMERG. To address this, we propose the Wavelet Diffusion Model (WDM), a generative framework that achieves 10x spatial super-resolution (downscaling to 1 km) and delivers a 9x inference speedup over pixel-based diffusion models. WDM is a conditional diffusion model that learns the learns the complex structure of precipitation from MRMS radar data directly in the wavelet domain. By focusing on high-frequency wavelet coefficients, it generates exceptionally realistic and detailed 1-km precipitation fields. This wavelet-based approach produces visually superior results with fewer artifacts than pixel-space models, and delivers a significant gains in sampling efficiency. Our results demonstrate that WDM provides a robust solution to the dual challenges of accuracy and speed in geoscience super-resolution, paving the way for more reliable hydrological forecasts.