# VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation

arXiv: https://arxiv.org/abs/2405.13711 · HTML: https://mlsanity.com/paper/2405.13711/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilation](https://mlsanity.com/paper/2312.12455/) (2023)
- [Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation](https://mlsanity.com/paper/2101.02121/) (2021)
- [Score-based Data Assimilation for a Two-Layer Quasi-Geostrophic Model](https://mlsanity.com/paper/2310.01853/) (2023)
- [Data Assimilation in the Latent Space of a Neural Network](https://mlsanity.com/paper/2012.12056/) (2020)

## Built on by (most cited first, 2 of 2)

- [PnP-DA: Towards Principled Plug-and-Play Integration of Variational Data Assimilation and Generative Models](https://mlsanity.com/paper/2508.00325/) (2025)
- [FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matching](https://mlsanity.com/paper/2602.06800/) (2026)

## Abstract (arXiv)

Data assimilation refers to a set of algorithms designed to compute the optimal estimate of a system's state by refining the prior prediction (known as background states) using observed data. Variational assimilation methods rely on the maximum likelihood approach to formulate a variational cost, with the optimal state estimate derived by minimizing this cost. Although traditional variational methods have achieved great success and have been widely used in many numerical weather prediction centers, they generally assume Gaussian errors in the background states, which limits the accuracy of these algorithms due to the inherent inaccuracies of this assumption. In this paper, we introduce VAE-Var, a novel variational algorithm that leverages a variational autoencoder (VAE) to model a non-Gaussian estimate of the background error distribution. We theoretically derive the variational cost under the VAE estimation and present the general formulation of VAE-Var; we implement VAE-Var on low-dimensional chaotic systems and demonstrate through experimental results that VAE-Var consistently outperforms traditional variational assimilation methods in terms of accuracy across various observational settings.