# Riemannian Stein Variational Gradient Descent for Bayesian Inference

arXiv: https://arxiv.org/abs/1711.11216 · HTML: https://mlsanity.com/paper/1711.11216/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 24 of 24)

- [Sampling with Mirrored Stein Operators](https://mlsanity.com/paper/2106.12506/) (2021)
- [Sampling with Mollified Interaction Energy Descent](https://mlsanity.com/paper/2210.13400/) (2022)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent](https://mlsanity.com/paper/2305.14076/) (2023)
- [Grassmann Stein Variational Gradient Descent](https://mlsanity.com/paper/2202.03297/) (2022)
- [Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning](https://mlsanity.com/paper/2106.00252/) (2021)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2112.00945/) (2021)
- [Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents](https://mlsanity.com/paper/2203.10592/) (2022)
- [Analytical Survey of Learning with Low-Resource Data: From Analysis to Investigation](https://mlsanity.com/paper/2510.08962/) (2025)
- [A Unifying and Canonical Description of Measure-Preserving Diffusions](https://mlsanity.com/paper/2105.02845/) (2021)
- [Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference](https://mlsanity.com/paper/2105.05489/) (2021)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)
- [De-randomizing MCMC dynamics with the diffusion Stein operator](https://mlsanity.com/paper/2110.03768/) (2021)
- [A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel](https://mlsanity.com/paper/2111.10722/) (2021)
- [Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA](https://mlsanity.com/paper/2411.00259/) (2024)
- [A Survey of Learning on Small Data: Generalization, Optimization, and Challenge](https://mlsanity.com/paper/2207.14443/) (2022)
- [ELBOing Stein: Variational Bayes with Stein Mixture Inference](https://mlsanity.com/paper/2410.22948/) (2024)
- [Keep your distance: learning dispersed embeddings on mathbbSm](https://mlsanity.com/paper/2502.08231/) (2025)
- [Functional Gradient Flows for Constrained Sampling](https://mlsanity.com/paper/2410.23170/) (2024)
- [Stein Variational Newton Neural Network Ensembles](https://mlsanity.com/paper/2411.01887/) (2024)
- [Accelerating Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2504.03158/) (2025)
- [Geometry-Aware Bayesian Parameter-Efficient Fine-Tuning on the Stiefel Manifold via Stein Variational Gradient Descent](https://mlsanity.com/paper/2609.08354/) (2026)

## Abstract (arXiv)

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.