# Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences

arXiv: https://arxiv.org/abs/2505.22008 · HTML: https://mlsanity.com/paper/2505.22008/

## Key facts

- Cited by 5 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 44 of its 73 references that are in the map.
- First posted on arXiv 28 May 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)
- LLM alignment / RLHF / preference optimisation / [Diffusion and multimodal model alignment](https://mlsanity.com/alignment/diffusion-and-multimodal-model-alignment/)

## Builds on (most cited first, 30 of 44)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Aligning Text-to-Image Models using Human Feedback](https://mlsanity.com/paper/2302.12192/) (2023)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Human Preference Score: Better Aligning Text-to-Image Models with Human Preference](https://mlsanity.com/paper/2303.14420/) (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)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Aesthetic Post-Training Diffusion Models from Generic Preferences with Step-by-step Preference Optimization](https://mlsanity.com/paper/2406.04314/) (2024)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [PRDP: Proximal Reward Difference Prediction for Large-Scale Reward Finetuning of Diffusion Models](https://mlsanity.com/paper/2402.08714/) (2024)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)

## Built on by (most cited first, 5 of 5)

- [Training-Free Data Assimilation with GenCast](https://mlsanity.com/paper/2509.18811/) (2025)
- [DAWP: A framework for global observation forecasting via Data Assimilation and Weather Prediction in satellite observation space](https://mlsanity.com/paper/2510.15978/) (2025)
- [Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification](https://mlsanity.com/paper/2603.04395/) (2026)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [SynWeather: Weather Observation Data Synthesis across Multiple Regions and Variables via a General Diffusion Transformer](https://mlsanity.com/paper/2511.08291/) (2025)

## Abstract (arXiv)

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is fundamentally ill-posed due to the sparsity of observations relative to the high-dimensional state space. Traditional methods address this challenge by simplifying background priors to regularize the solution, which are empirical and require continual tuning for application. Inspired by alignment techniques in text-to-image diffusion models, we propose Align-DA, which formulates DA as a generative process and uses reward signals to guide background priors, replacing manual tuning with data-driven alignment. Specifically, we train a score-based model in the latent space to approximate the background-conditioned prior, and align it using three complementary reward signals for DA: (1) assimilation accuracy, (2) forecast skill initialized from the assimilated state, and (3) physical adherence of the analysis fields. Experiments with multiple reward signals demonstrate consistent improvements in analysis quality across different evaluation metrics and observation-guidance strategies. These results show that preference alignment, implemented as a soft constraint, can automatically adapt complex background priors tailored to DA, offering a promising new direction for advancing the field.