# Understanding and Accelerating Particle-Based Variational Inference

arXiv: https://arxiv.org/abs/1807.01750 · HTML: https://mlsanity.com/paper/1807.01750/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Stein Variational Gradient Descent with Multiple Kernel](https://mlsanity.com/paper/2107.09338/) (2021)
- [Hessian-guided Perturbed Wasserstein Gradient Flows for Escaping Saddle Points](https://mlsanity.com/paper/2509.16974/) (2025)
- [Long-tailed Classification from a Bayesian-decision-theory Perspective](https://mlsanity.com/paper/2303.06075/) (2023)

## Abstract (arXiv)

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.