# Training-Free Bayesian Filtering with Generative Emulators

arXiv: https://arxiv.org/abs/2605.20028 · HTML: https://mlsanity.com/paper/2605.20028/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (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)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [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)
- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusion](https://mlsanity.com/paper/2502.07532/) (2025)
- [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)

## Built on by (most cited first, 4 of 4)

- [Generative Model Proposal based Particle Filtering for Data Assimilation](https://mlsanity.com/paper/2607.01012/) (2026)
- [EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation](https://mlsanity.com/paper/2609.35944/) (2026)
- [DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants](https://mlsanity.com/paper/2610.03314/) (2026)
- [Accounting for model error in ensemble variational data assimilation through learned generative dynamics](https://mlsanity.com/paper/2610.17333/) (2026)

## Abstract (arXiv)

Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and observations, but suffer from poor scalability in high dimensions. In this work, we show that diffusion-based emulators of dynamical systems can be used to implement, without additional training, an optimal variant of particle filters that has remained largely unexplored due to implementation challenges with classical numerical solvers. Experiments on nonlinear chaotic systems, including atmospheric dynamics, demonstrate that the proposed approach successfully scales particle filtering to high-dimensional settings.