# Stein transport for Bayesian inference arXiv: https://arxiv.org/abs/2409.01464 ยท HTML: https://mlsanity.com/paper/2409.01464/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Builds on 54 of its 112 references that are in the map. - First posted on arXiv 2 Sep 2024. ## Builds on (most cited first, 30 of 54) - [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) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016) - [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022) - [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016) - [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016) - [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016) - [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018) - [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017) - [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016) - [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015) - [Solving and Learning Nonlinear PDEs with Gaussian Processes](https://mlsanity.com/paper/2103.12959/) (2021) - [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019) - [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017) - [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020) - [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017) - [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019) - [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016) - [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020) - [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020) - [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014) - [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021) - [The Information Geometry of Mirror Descent](https://mlsanity.com/paper/1310.7780/) (2013) - [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018) - [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017) - [Statistical optimal transport](https://mlsanity.com/paper/2407.18163/) (2024) - [Accelerating Langevin Sampling with Birth-death](https://mlsanity.com/paper/1905.09863/) (2019) - [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024) - [Scaling limit of the Stein variational gradient descent: the mean field regime](https://mlsanity.com/paper/1805.04035/) (2018) ## Built on by (most cited first, 11 of 11) - [Telegrapher's Generative Model via Kac Flows](https://mlsanity.com/paper/2506.20641/) (2025) - [Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows](https://mlsanity.com/paper/2506.05905/) (2025) - [Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics](https://mlsanity.com/paper/2411.00214/) (2024) - [A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows](https://mlsanity.com/paper/2507.04330/) (2025) - [Towards understanding Accelerated Stein Variational Gradient Flow -- Analysis of Generalized Bilinear Kernels for Gaussian target distributions](https://mlsanity.com/paper/2509.04008/) (2025) - [An operator splitting analysis of Wasserstein--Fisher--Rao gradient flows](https://mlsanity.com/paper/2511.18060/) (2025) - [Machine-Learned Sampling of Conditioned Path Measures](https://mlsanity.com/paper/2506.01904/) (2025) - [Adaptive Kernel Selection for Stein Variational Gradient Descent](https://mlsanity.com/paper/2510.02067/) (2025) - [Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows](https://mlsanity.com/paper/2609.18118/) (2026) - [Interacting particle guidance for sampling reward-tilted generative priors](https://mlsanity.com/paper/2609.37227/) (2026) - [Density Ratio Estimation with Stein Displacement Fields](https://mlsanity.com/paper/2610.12437/) (2026) ## Abstract (arXiv) We introduce textitStein transport, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen from a reproducing kernel Hilbert space and can be derived either through a suitable kernel ridge regression formulation or as an infinitesimal optimal transport map in the Stein geometry. The update equations of Stein transport resemble those of Stein variational gradient descent (SVGD), but introduce a time-varying score function as well as specific weights attached to the particles. While SVGD relies on convergence in the long-time limit, Stein transport reaches its posterior approximation at finite time t=1. Studying the mean-field limit, we discuss the errors incurred by regularisation and finite-particle effects, and we connect Stein transport to birth-death dynamics and Fisher-Rao gradient flows. In a series of experiments, we show that in comparison to SVGD, Stein transport not only often reaches more accurate posterior approximations with a significantly reduced computational budget, but that it also effectively mitigates the variance collapse phenomenon commonly observed in SVGD.