# Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems

arXiv: https://arxiv.org/abs/2309.11490 · HTML: https://mlsanity.com/paper/2309.11490/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [Sliced Iterative Normalizing Flows](https://mlsanity.com/paper/2007.00674/) (2020)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Pathfinder: Parallel quasi-Newton variational inference](https://mlsanity.com/paper/2108.03782/) (2021)
- [Automatic structured variational inference](https://mlsanity.com/paper/2002.00643/) (2020)
- [A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems](https://mlsanity.com/paper/1505.03876/) (2015)
- [Adaptive regularisation for ensemble Kalman inversion](https://mlsanity.com/paper/2006.14980/) (2020)
- [Parameterizations for Ensemble Kalman Inversion](https://mlsanity.com/paper/1709.01781/) (2017)

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

- [Empirical evaluation of normalizing flows in Markov Chain Monte Carlo](https://mlsanity.com/paper/2412.17136/) (2024)
- [Reducing normalizing flow complexity for MCMC preconditioning](https://mlsanity.com/paper/2511.02345/) (2025)

## Abstract (arXiv)

For many scientific inverse problems we are required to evaluate an expensive forward model. Moreover, the model is often given in such a form that it is unrealistic to access its gradients. In such a scenario, standard Markov Chain Monte Carlo algorithms quickly become impractical, requiring a large number of serial model evaluations to converge on the target distribution. In this paper we introduce Flow Annealed Kalman Inversion (FAKI). This is a generalization of Ensemble Kalman Inversion (EKI), where we embed the Kalman filter updates in a temperature annealing scheme, and use normalizing flows (NF) to map the intermediate measures corresponding to each temperature level to the standard Gaussian. In doing so, we relax the Gaussian ansatz for the intermediate measures used in standard EKI, allowing us to achieve higher fidelity approximations to non-Gaussian targets. We demonstrate the performance of FAKI on two numerical benchmarks, showing dramatic improvements over standard EKI in terms of accuracy whilst accelerating its already rapid convergence properties (typically in O(10) steps).