# State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics

arXiv: https://arxiv.org/abs/2407.21314 · HTML: https://mlsanity.com/paper/2407.21314/

## Key facts

- Cited by 8 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 54 of its 94 references that are in the map.
- First posted on arXiv 31 Jul 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, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)

## Built on by (most cited first, 8 of 8)

- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [MODS: Multi-source Observations Conditional Diffusion Model for Meteorological State Downscaling](https://mlsanity.com/paper/2506.14798/) (2025)
- [Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilation](https://mlsanity.com/paper/2603.06752/) (2026)
- [Divergence-kernel method for linear responses of densities and generative models](https://mlsanity.com/paper/2509.03992/) (2025)
- [Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade](https://mlsanity.com/paper/2512.01572/) (2025)
- [Ensemble Controlled-Flow Filtering for Implicit Data Assimilation](https://mlsanity.com/paper/2607.12975/) (2026)
- [Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates](https://mlsanity.com/paper/2608.11435/) (2026)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)

## Abstract (arXiv)

Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical and observational models. To address this challenge, a novel generative model, termed the State-Observation Augmented Diffusion (SOAD) model is proposed for data-driven assimilation. The marginal posterior associated with SOAD has been derived and then proved to match the true posterior distribution under mild assumptions, suggesting its theoretical advantages over previous score-based approaches. Experimental results also indicate that SOAD may offer improved performance compared to existing data-driven methods.