# Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler

arXiv: https://arxiv.org/abs/2609.06905 · HTML: https://mlsanity.com/paper/2609.06905/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm](https://mlsanity.com/paper/2012.12810/) (2020)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling](https://mlsanity.com/paper/2109.13055/) (2021)
- [Improved dimension dependence of a proximal algorithm for sampling](https://mlsanity.com/paper/2302.10081/) (2023)
- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [The Boomerang Sampler](https://mlsanity.com/paper/2006.13777/) (2020)
- [Exact simulation of diffusions and improved algorithms for log-concave sampling](https://mlsanity.com/paper/2608.05022/) (2026)
- [Windowed thinning and query complexity for the bouncy particle and Zigzag samplers](https://mlsanity.com/paper/2607.28413/) (2026)

## Built on by (most cited first, 2 of 2)

- [Efficient Mass Matrix Estimation with Gaussian Cooling](https://mlsanity.com/paper/2610.04806/) (2026)
- [Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling](https://mlsanity.com/paper/2610.16248/) (2026)

## Abstract (arXiv)

We study the problem of sampling from μ(dx)propto e-V(x),dx on ℝd, where V is α-strongly convex and β-smooth, and write kappa:=β/α. We design and analyze the Proximal Bouncy Particle Sampler (Proximal BPS), a new sampler that combines ideas from the proximal sampler and the bouncy particle sampler. From a warm start initialization with  O(1)  R'enyi divergence w.r.t. μ, Proximal BPS returns a sample whose law is varepsilon-close to μ in total variation distance using widetilde O(√kappa,d1/4 ,polylog(1/varepsilon)) gradient queries in expectation.