# SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models

arXiv: https://arxiv.org/abs/2306.14066 · HTML: https://mlsanity.com/paper/2306.14066/

## Key facts

- Cited by 28 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 15 of its 50 references that are in the map.
- First posted on arXiv 24 Jun 2023.

## 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, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [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)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [Global Extreme Heat Forecasting Using Neural Weather Models](https://mlsanity.com/paper/2205.10972/) (2022)
- [Self-Attentive Ensemble Transformer: Representing Ensemble Interactions in Neural Networks for Earth System Models](https://mlsanity.com/paper/2106.13924/) (2021)
- [Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification](https://mlsanity.com/paper/2111.14844/) (2021)
- [Computing the ensemble spread from deterministic weather predictions using conditional generative adversarial networks](https://mlsanity.com/paper/2205.09182/) (2022)

## Built on by (most cited first, 28 of 28)

- [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)
- [Best Practices and Lessons Learned on Synthetic Data](https://mlsanity.com/paper/2404.07503/) (2024)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [On the Foundations of Earth and Climate Foundation Models](https://mlsanity.com/paper/2405.04285/) (2024)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [AI Foundation Models for Weather and Climate: Applications, Design, and Implementation](https://mlsanity.com/paper/2309.10808/) (2023)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [Deep Learning and Foundation Models for Weather Prediction: A Survey](https://mlsanity.com/paper/2501.06907/) (2025)
- [Zero-Shot Uncertainty Quantification using Diffusion Probabilistic Models](https://mlsanity.com/paper/2408.04718/) (2024)
- [DiffObs: Generative Diffusion for Global Forecasting of Satellite Observations](https://mlsanity.com/paper/2404.06517/) (2024)
- [Earth System Foundation Model (ESFM): A unified framework for heterogeneous data integration and forecasting](https://mlsanity.com/paper/2605.00850/) (2026)
- [Generative Learning for Forecasting the Dynamics of Complex Systems](https://mlsanity.com/paper/2402.17157/) (2024)
- [CaFA: Global Weather Forecasting with Factorized Attention on Sphere](https://mlsanity.com/paper/2405.07395/) (2024)
- [ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolution](https://mlsanity.com/paper/2405.14527/) (2024)
- [Towards diffusion models for large-scale sea-ice modelling](https://mlsanity.com/paper/2406.18417/) (2024)
- [Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting](https://mlsanity.com/paper/2601.21151/) (2026)
- [Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing](https://mlsanity.com/paper/2604.07366/) (2026)
- [WIND: Weather Inverse Diffusion for Zero-Shot Atmospheric Modeling](https://mlsanity.com/paper/2602.03924/) (2026)
- [Probabilistic Precipitation Nowcasting with Rectified Flow Transformers](https://mlsanity.com/paper/2605.31204/) (2026)
- [LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data](https://mlsanity.com/paper/2505.09803/) (2025)
- [A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems](https://mlsanity.com/paper/2603.25370/) (2026)
- [Accurate, Efficient, and Explainable Deep Learning Approaches for Environmental Science Problems](https://mlsanity.com/paper/2605.19366/) (2026)
- [RealBench: Benchmarking Data-Driven Numerical Weather Forecasting Under Operational Conditions and Extreme Event Challenges](https://mlsanity.com/paper/2605.24945/) (2026)
- [Geospatial Diffusion-based Evolution Synthesis (GeoDES) for Storm-Centered Weather Augmentation](https://mlsanity.com/paper/2607.19522/) (2026)
- [Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Prior](https://mlsanity.com/paper/2610.06509/) (2026)

## Abstract (arXiv)

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts. This is done by running many physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample hundreds to tens of thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in important statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While this work demonstrates the utility of the methodology by focusing on weather forecasting, the generative artificial intelligence methodology can be extended for uncertainty quantification in climate modeling, where we believe the generation of very large ensembles of climate projections will play an increasingly important role in climate risk assessment.