# Annealed Stein Variational Gradient Descent

arXiv: https://arxiv.org/abs/2101.09815 · HTML: https://mlsanity.com/paper/2101.09815/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 24 Jan 2021.

## Builds on (most cited first, 12 of 12)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [Variational Tempering](https://mlsanity.com/paper/1411.1810/) (2014)
- [Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory](https://mlsanity.com/paper/1809.01293/) (2018)
- [Stein Variational Gradient Descent Without Gradient](https://mlsanity.com/paper/1806.02775/) (2018)
- [Kernel Stein Generative Modeling](https://mlsanity.com/paper/2007.03074/) (2020)

## Built on by (most cited first, 26 of 26)

- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [On Stein Variational Neural Network Ensembles](https://mlsanity.com/paper/2106.10760/) (2021)
- [Neural Variational Gradient Descent](https://mlsanity.com/paper/2107.10731/) (2021)
- [Repulsive Latent Score Distillation for Solving Inverse Problems](https://mlsanity.com/paper/2406.16683/) (2024)
- [Towards Healing the Blindness of Score Matching](https://mlsanity.com/paper/2209.07396/) (2022)
- [Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent](https://mlsanity.com/paper/2106.07832/) (2021)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [Adaptive Annealed Importance Sampling with Constant Rate Progress](https://mlsanity.com/paper/2306.15283/) (2023)
- [Stein Variational Goal Generation for adaptive Exploration in Multi-Goal Reinforcement Learning](https://mlsanity.com/paper/2206.06719/) (2022)
- [Annealed Stein Variational Gradient Descent for Improved Uncertainty Estimation in Full-Waveform Inversion](https://mlsanity.com/paper/2410.13249/) (2024)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)
- [Long-time asymptotics of noisy SVGD outside the population limit](https://mlsanity.com/paper/2406.11929/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Long-tailed Classification from a Bayesian-decision-theory Perspective](https://mlsanity.com/paper/2303.06075/) (2023)
- [ELBOing Stein: Variational Bayes with Stein Mixture Inference](https://mlsanity.com/paper/2410.22948/) (2024)
- [Making Reliable and Flexible Decisions in Long-tailed Classification](https://mlsanity.com/paper/2501.14090/) (2025)
- [A Framework for Controllable Multi-objective Learning with Annealed Stein Variational Hypernetworks](https://mlsanity.com/paper/2506.06715/) (2025)
- [Accelerating Convergence of Stein Variational Gradient Descent via Deep Unfolding](https://mlsanity.com/paper/2402.15125/) (2024)
- [Stein Variational Newton Neural Network Ensembles](https://mlsanity.com/paper/2411.01887/) (2024)
- [Entropy-regularized Gradient Estimators for Approximate Bayesian Inference](https://mlsanity.com/paper/2503.11964/) (2025)
- [Towards Intrinsically Calibrated Uncertainty Quantification in Industrial Data-Driven Models via Diffusion Sampler](https://mlsanity.com/paper/2604.01870/) (2026)
- [Variational Inference via Entropic Transport Descent](https://mlsanity.com/paper/2606.25265/) (2026)
- [Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD](https://mlsanity.com/paper/2608.28827/) (2026)
- [Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling](https://mlsanity.com/paper/2610.02081/) (2026)
- [Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent](https://mlsanity.com/paper/2610.19187/) (2026)

## Abstract (arXiv)

Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention in the approximate inference literature for its flexibility and accuracy. We empirically explore the ability of this method to sample from multi-modal distributions and focus on two important issues: (i) the inability of the particles to escape from local modes and (ii) the inefficacy in reproducing the density of the different regions. We propose an annealing schedule to solve these issues and show, through various experiments, how this simple solution leads to significant improvements in mode coverage, without invalidating any theoretical properties of the original algorithm.