# Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation

arXiv: https://arxiv.org/abs/2504.18720 · HTML: https://mlsanity.com/paper/2504.18720/

## Key facts

- Cited by 20 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 38 of its 65 references that are in the map.
- First posted on arXiv 25 Apr 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, 30 of 38)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [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)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Deep Learning for Day Forecasts from Sparse Observations](https://mlsanity.com/paper/2306.06079/) (2023)
- [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scales](https://mlsanity.com/paper/2406.16947/) (2024)
- [Samudra: An AI Global Ocean Emulator for Climate](https://mlsanity.com/paper/2412.03795/) (2024)
- [GraphDOP: Towards skilful data-driven medium-range weather forecasts learnt and initialised directly from observations](https://mlsanity.com/paper/2412.15687/) (2024)
- [FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilation](https://mlsanity.com/paper/2312.12455/) (2023)

## Built on by (most cited first, 20 of 20)

- [Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation](https://mlsanity.com/paper/2507.02608/) (2025)
- [A Probabilistic Approach to Wildfire Spread Prediction Using a Denoising Diffusion Surrogate Model](https://mlsanity.com/paper/2507.00761/) (2025)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Optimization Benchmark for Diffusion Models on Dynamical Systems](https://mlsanity.com/paper/2510.19376/) (2025)
- [LaDCast: A Latent Diffusion Model for Medium-Range Ensemble Weather Forecasting](https://mlsanity.com/paper/2506.09193/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamics](https://mlsanity.com/paper/2602.19406/) (2026)
- [Training-Free Bayesian Filtering with Generative Emulators](https://mlsanity.com/paper/2605.20028/) (2026)
- [How to use score-based diffusion in earth system science: A satellite nowcasting example](https://mlsanity.com/paper/2505.10432/) (2025)
- [WIND: Weather Inverse Diffusion for Zero-Shot Atmospheric Modeling](https://mlsanity.com/paper/2602.03924/) (2026)
- [ForcingDAS: Unified and Robust Data Assimilation via Diffusion Forcing](https://mlsanity.com/paper/2605.14285/) (2026)
- [Amortized Filtering and Smoothing with Conditional Normalizing Flows](https://mlsanity.com/paper/2604.07169/) (2026)
- [Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver](https://mlsanity.com/paper/2602.18248/) (2026)
- [Towards a Foundation Model for the Martian Atmosphere](https://mlsanity.com/paper/2605.28851/) (2026)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matching](https://mlsanity.com/paper/2602.06800/) (2026)
- [WindINR: Latent-State INR for Fast Local Wind Query and Correction in Complex Terrain](https://mlsanity.com/paper/2605.09511/) (2026)
- [Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Video Flow-matching](https://mlsanity.com/paper/2608.05103/) (2026)
- [Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems](https://mlsanity.com/paper/2608.14744/) (2026)
- [Generative Atmospheric Super-Resolution from Heterogeneous In Situ Observations through Composable Interfaces](https://mlsanity.com/paper/2609.29027/) (2026)

## Abstract (arXiv)

Deep learning has advanced weather forecasting, but accurate predictions first require identifying the current state of the atmosphere from observational data. In this work, we introduce Appa, a score-based data assimilation model generating global atmospheric trajectories at 0.25sidegree resolution and 1-hour intervals. Powered by a 565M-parameter latent diffusion model trained on ERA5, Appa can be conditioned on arbitrary observations to infer plausible trajectories, without retraining. Our probabilistic framework handles reanalysis, filtering, and forecasting, within a single model, producing physically consistent reconstructions from various inputs. Results establish latent score-based data assimilation as a promising foundation for future global atmospheric modeling systems.