# Accelerating Langevin Sampling with Birth-death

arXiv: https://arxiv.org/abs/1905.09863 · HTML: https://mlsanity.com/paper/1905.09863/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 30 of 46)

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- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flow](https://mlsanity.com/paper/2302.12229/) (2023)
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- [Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspective](https://mlsanity.com/paper/2212.08791/) (2022)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
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- [Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows](https://mlsanity.com/paper/2406.17263/) (2024)
- [DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2112.00945/) (2021)
- [Importance Corrected Neural JKO Sampling](https://mlsanity.com/paper/2407.20444/) (2024)
- [Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows](https://mlsanity.com/paper/2506.05905/) (2025)
- [Accelerate Langevin Sampling with Birth-Death Process and Exploration Component](https://mlsanity.com/paper/2305.05529/) (2023)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics](https://mlsanity.com/paper/2411.00214/) (2024)
- [Connections between sequential Bayesian inference and evolutionary dynamics](https://mlsanity.com/paper/2411.16366/) (2024)
- [New affine invariant ensemble samplers and their dimensional scaling](https://mlsanity.com/paper/2505.02987/) (2025)
- [A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows](https://mlsanity.com/paper/2507.04330/) (2025)
- [Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow](https://mlsanity.com/paper/2311.13159/) (2023)

## Abstract (arXiv)

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanism to accelerate the mixing of Langevin diffusion. Our algorithm is motivated by its mean field partial differential equation (PDE), which is a Fokker-Planck equation supplemented by a nonlocal birth-death term. This PDE can be viewed as a gradient flow of the Kullback-Leibler divergence with respect to the Wasserstein-Fisher-Rao metric. We prove that under some assumptions the asymptotic convergence rate of the nonlocal PDE is independent of the potential barrier, in contrast to the exponential dependence in the case of the Langevin diffusion. We illustrate the efficiency of the birth-death accelerated Langevin method through several analytical examples and numerical experiments.