# PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems arXiv: https://arxiv.org/abs/2505.12882 ยท HTML: https://mlsanity.com/paper/2505.12882/ ## Key facts - Cited by 10 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 24 of its 42 references that are in the map. - First posted on arXiv 19 May 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, 24 of 24) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020) - [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020) - [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024) - [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023) - [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020) - [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017) - [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019) - [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023) - [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022) - [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019) - [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017) - [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023) - [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024) - [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024) - [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021) - [ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction](https://mlsanity.com/paper/2402.00712/) (2024) - [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024) - [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024) - [HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems](https://mlsanity.com/paper/1806.07439/) (2018) - [Towards an end-to-end artificial intelligence driven global weather forecasting system](https://mlsanity.com/paper/2312.12462/) (2023) - [Score-based Data Assimilation for a Two-Layer Quasi-Geostrophic Model](https://mlsanity.com/paper/2310.01853/) (2023) - [FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation](https://mlsanity.com/paper/2406.01645/) (2024) ## Built on by (most cited first, 10 of 10) - [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025) - [Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems](https://mlsanity.com/paper/2508.09156/) (2025) - [ScIRGen: Synthesize Realistic and Large-Scale RAG Dataset for Scientific Research](https://mlsanity.com/paper/2506.11117/) (2025) - [ClimAgent: LLM as Agents for Autonomous Open-ended Climate Science Analysis](https://mlsanity.com/paper/2604.16922/) (2026) - [Control-Augmented Autoregressive Diffusion for Data Assimilation](https://mlsanity.com/paper/2510.06637/) (2025) - [DAMBench: A Multi-Modal Benchmark for Deep Learning-based Atmospheric Data Assimilation](https://mlsanity.com/paper/2511.01468/) (2025) - [Towards a Foundation Model for the Martian Atmosphere](https://mlsanity.com/paper/2605.28851/) (2026) - [Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Video Flow-matching](https://mlsanity.com/paper/2608.05103/) (2026) - [Self-Augmented Diffusion Guidance for Physics-Informed Generation](https://mlsanity.com/paper/2608.26748/) (2026) - [Physics-Guided Conditional Diffusion Model for Rare Event Synthesis and Diagnosis for the Water-Gas Shift Reaction](https://mlsanity.com/paper/2609.35499/) (2026) ## Abstract (arXiv) Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models have shown great potential for DA tasks, most existing approaches remain purely data-driven and often overlook the physical laws that govern complex atmospheric dynamics. As a result, they may yield physically inconsistent reconstructions that impair downstream applications. To overcome this limitation, we propose PhyDA, a physics-guided diffusion framework designed to ensure physical coherence in atmospheric data assimilation. PhyDA introduces two key components: (1) a Physically Regularized Diffusion Objective that integrates physical constraints into the training process by penalizing deviations from known physical laws expressed as partial differential equations, and (2) a Virtual Reconstruction Encoder that bridges observational sparsity for structured latent representations, further enhancing the model's ability to infer complete and physically coherent states. Experiments on the ERA5 reanalysis dataset demonstrate that PhyDA achieves superior accuracy and better physical plausibility compared to state-of-the-art baselines. Our results emphasize the importance of combining generative modeling with domain-specific physical knowledge and show that PhyDA offers a promising direction for improving real-world data assimilation systems.