# DiffDA: a Diffusion Model for Weather-scale Data Assimilation

arXiv: https://arxiv.org/abs/2401.05932 · HTML: https://mlsanity.com/paper/2401.05932/

## Key facts

- Cited by 61 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 16 of its 28 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## 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, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Deep Learning for Day Forecasts from Sparse Observations](https://mlsanity.com/paper/2306.06079/) (2023)
- [SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models](https://mlsanity.com/paper/2306.14066/) (2023)
- [ENS-10: A Dataset For Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2206.14786/) (2022)
- [Score-based Data Assimilation for a Two-Layer Quasi-Geostrophic Model](https://mlsanity.com/paper/2310.01853/) (2023)

## Built on by (most cited first, 30 of 61)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scales](https://mlsanity.com/paper/2406.16947/) (2024)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [Data driven weather forecasts trained and initialised directly from observations](https://mlsanity.com/paper/2407.15586/) (2024)
- [Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observations](https://mlsanity.com/paper/2404.08522/) (2024)
- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations](https://mlsanity.com/paper/2409.00230/) (2024)
- [Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics](https://mlsanity.com/paper/2506.20024/) (2025)
- [WeatherGFM: Learning A Weather Generalist Foundation Model via In-context Learning](https://mlsanity.com/paper/2411.05420/) (2024)
- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Data Assimilation with Machine Learning Surrogate Models: A Case Study with FourCastNet](https://mlsanity.com/paper/2405.13180/) (2024)
- [PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems](https://mlsanity.com/paper/2505.12882/) (2025)
- [FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation](https://mlsanity.com/paper/2406.01645/) (2024)
- [WeatherReal: A Benchmark Based on In-Situ Observations for Evaluating Weather Models](https://mlsanity.com/paper/2409.09371/) (2024)
- [Exploring the design space of deep-learning-based weather forecasting systems](https://mlsanity.com/paper/2410.07472/) (2024)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling](https://mlsanity.com/paper/2505.18017/) (2025)
- [LaDCast: A Latent Diffusion Model for Medium-Range Ensemble Weather Forecasting](https://mlsanity.com/paper/2506.09193/) (2025)
- [A Comprehensive Evaluation of Generative Models in Calorimeter Shower Simulation](https://mlsanity.com/paper/2406.12898/) (2024)
- [Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations](https://mlsanity.com/paper/2501.14404/) (2025)
- [Ensemble Kalman filter in latent space using a variational autoencoder pair](https://mlsanity.com/paper/2502.12987/) (2025)
- [Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences](https://mlsanity.com/paper/2505.22008/) (2025)
- [Training-Free Data Assimilation with GenCast](https://mlsanity.com/paper/2509.18811/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)

## Abstract (arXiv)

The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted states and sparse observations. Acknowledging the similarity between a weather forecast model and a denoising diffusion model dedicated to weather applications, we adapt the pretrained GraphCast neural network as the backbone of the diffusion model. Through experiments based on simulated observations from the ERA5 reanalysis dataset, our method can produce assimilated global atmospheric data consistent with observations at 0.25 deg (~30km) resolution globally. This marks the highest resolution achieved by ML data assimilation models. The experiments also show that the initial conditions assimilated from sparse observations (less than 0.96% of gridded data) and 48-hour forecast can be used for forecast models with a loss of lead time of at most 24 hours compared to initial conditions from state-of-the-art data assimilation in ERA5. This enables the application of the method to real-world applications, such as creating reanalysis datasets with autoregressive data assimilation.