# The equivalence between Stein variational gradient descent and black-box variational inference

arXiv: https://arxiv.org/abs/2004.01822 · HTML: https://mlsanity.com/paper/2004.01822/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2020.

## Built on by (most cited first, 3 of 3)

- [A Neural Tangent Kernel Perspective of GANs](https://mlsanity.com/paper/2106.05566/) (2021)
- [Unifying GANs and Score-Based Diffusion as Generative Particle Models](https://mlsanity.com/paper/2305.16150/) (2023)
- [Analysis of Kernel Mirror Prox for Measure Optimization](https://mlsanity.com/paper/2403.00147/) (2024)

## Abstract (arXiv)

We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.