# Continuous Ensemble Weather Forecasting with Diffusion models

arXiv: https://arxiv.org/abs/2410.05431 · HTML: https://mlsanity.com/paper/2410.05431/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 55 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [Scaling transformer neural networks for skillful and reliable medium-range weather forecasting](https://mlsanity.com/paper/2312.03876/) (2023)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models](https://mlsanity.com/paper/2102.05107/) (2021)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbation](https://mlsanity.com/paper/2205.13158/) (2022)
- [A Denoising Diffusion Model for Fluid Field Prediction](https://mlsanity.com/paper/2301.11661/) (2023)
- [SwinRDM: Integrate SwinRNN with Diffusion Model towards High-Resolution and High-Quality Weather Forecasting](https://mlsanity.com/paper/2306.03110/) (2023)
- [Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling](https://mlsanity.com/paper/2408.10958/) (2024)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [FuXi-ENS: A machine learning model for medium-range ensemble weather forecasting](https://mlsanity.com/paper/2405.05925/) (2024)
- [Weather Prediction with Diffusion Guided by Realistic Forecast Processes](https://mlsanity.com/paper/2402.06666/) (2024)
- [DiffESM: Conditional Emulation of Earth System Models with Diffusion Models](https://mlsanity.com/paper/2304.11699/) (2023)

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

- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Deep Learning and Foundation Models for Weather Prediction: A Survey](https://mlsanity.com/paper/2501.06907/) (2025)
- [Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics](https://mlsanity.com/paper/2506.20024/) (2025)
- [U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster](https://mlsanity.com/paper/2604.09041/) (2026)
- [Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusion](https://mlsanity.com/paper/2502.07532/) (2025)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching](https://mlsanity.com/paper/2411.07625/) (2024)
- [Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing](https://mlsanity.com/paper/2604.07366/) (2026)
- [Generating ensembles of spatially-coherent in-situ forecasts using flow matching](https://mlsanity.com/paper/2504.03463/) (2025)
- [Tyche: One Step Flow for Efficient Probabilistic Weather Forecasting](https://mlsanity.com/paper/2605.06916/) (2026)
- [A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fields](https://mlsanity.com/paper/2505.13189/) (2025)
- [Data-Efficient Ensemble Weather Forecasting with Diffusion Models](https://mlsanity.com/paper/2509.11047/) (2025)
- [Graph-based Neural Space Weather Forecasting](https://mlsanity.com/paper/2509.19605/) (2025)
- [SwAIther-Precip: Lead-Time-Aware Bias Correction Enables Kilometer-Scale Downscaling of Global AI Precipitation Forecasts over Switzerland](https://mlsanity.com/paper/2605.16163/) (2026)
- [KunPeng: A Global Ocean Environmental Model](https://mlsanity.com/paper/2504.04766/) (2025)
- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)
- [Native Extrapolation Awareness in Flow-Based Conditional Generation](https://mlsanity.com/paper/2602.13061/) (2026)
- [Physics-Informed Diffusion Model for Generating Synthetic Extreme Rare Weather Events Data](https://mlsanity.com/paper/2603.06782/) (2026)
- [A Diffusion-Contrastive Graph Neural Network with Virtual Nodes for Wind Nowcasting in Unobserved Regions](https://mlsanity.com/paper/2604.10328/) (2026)
- [Earth Science Foundation Models: From Perception to Reasoning and Discovery](https://mlsanity.com/paper/2605.12542/) (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)
- [DiffUNet^2: Bidirectional Conditional Diffusion for Probabilistic Scientific Spatiotemporal Modeling](https://mlsanity.com/paper/2606.03926/) (2026)
- [Geospatial Diffusion-based Evolution Synthesis (GeoDES) for Storm-Centered Weather Augmentation](https://mlsanity.com/paper/2607.19522/) (2026)
- [FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution](https://mlsanity.com/paper/2609.34070/) (2026)
- [Proper Scoring Rule-based Diffusion for Probabilistic Weather Forecasting](https://mlsanity.com/paper/2609.38632/) (2026)
- [SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs](https://mlsanity.com/paper/2610.03313/) (2026)
- [Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution](https://mlsanity.com/paper/2610.14537/) (2026)

## Abstract (arXiv)

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble forecasts. These models are trained on a single forecasting step and rolled out autoregressively. However, they are computationally expensive and accumulate errors for high temporal resolution due to the many rollout steps. We address these limitations with Continuous Ensemble Forecasting, a novel and flexible method for sampling ensemble forecasts in diffusion models. The method can generate temporally consistent ensemble trajectories completely in parallel, with no autoregressive steps. Continuous Ensemble Forecasting can also be combined with autoregressive rollouts to yield forecasts at an arbitrary fine temporal resolution without sacrificing accuracy. We demonstrate that the method achieves competitive results for global weather forecasting with good probabilistic properties.