# EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation

arXiv: https://arxiv.org/abs/2609.35944 · HTML: https://mlsanity.com/paper/2609.35944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## 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, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [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)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior](https://mlsanity.com/paper/2501.18913/) (2025)
- [Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation](https://mlsanity.com/paper/2507.02608/) (2025)
- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [A Score-based Nonlinear Filter for Data Assimilation](https://mlsanity.com/paper/2306.09282/) (2023)
- [Training-Free Data Assimilation with GenCast](https://mlsanity.com/paper/2509.18811/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [Training-Free Bayesian Filtering with Generative Emulators](https://mlsanity.com/paper/2605.20028/) (2026)
- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)

## Abstract (arXiv)

Data Assimilation (DA) aims to recover the full state of a dynamical system that is only partially observed. A solution is to use Score-based models to generate physically consistent trajectories that agree with the observations. These Autoregressive Diffusion models are trained by conditioning on the previous state; however, they do not take into account the uncertainty of their past predictions. We propose a new diffusion-based assimilation algorithm that dynamically balances the confidence in the current state and the new observations. Crucially, we choose to learn the distribution of the joint state containing both the past and future. This allows us to use a modified version of En4DVar, a classical DA algorithm that relies on the covariance of an ensemble of particles. Experiments on fluid and traffic flow simulations show improved reconstruction performance, especially in situations where observations are sparse and non-homogeneous.