# Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm

arXiv: https://arxiv.org/abs/1608.04471 · HTML: https://mlsanity.com/paper/1608.04471/

## Key facts

- Cited by 507 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2016.

## Built on by (most cited first, 30 of 507)

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- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
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- [Safe Imitation Learning via Fast Bayesian Reward Inference from Preferences](https://mlsanity.com/paper/2002.09089/) (2020)
- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Diversify and Disambiguate: Learning From Underspecified Data](https://mlsanity.com/paper/2202.03418/) (2022)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
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- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
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- [Probability flow solution of the Fokker-Planck equation](https://mlsanity.com/paper/2206.04642/) (2022)
- [Diminishing Uncertainty within the Training Pool: Active Learning for Medical Image Segmentation](https://mlsanity.com/paper/2101.02323/) (2021)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [LiBRe: A Practical Bayesian Approach to Adversarial Detection](https://mlsanity.com/paper/2103.14835/) (2021)
- [Normalizing flow neural networks by JKO scheme](https://mlsanity.com/paper/2212.14424/) (2022)
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## Abstract (arXiv)

We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of functional gradient descent that minimizes the KL divergence. Empirical studies are performed on various real world models and datasets, on which our method is competitive with existing state-of-the-art methods. The derivation of our method is based on a new theoretical result that connects the derivative of KL divergence under smooth transforms with Stein's identity and a recently proposed kernelized Stein discrepancy, which is of independent interest.