# Exact simulation of diffusions and improved algorithms for log-concave sampling

arXiv: https://arxiv.org/abs/2608.05022 · HTML: https://mlsanity.com/paper/2608.05022/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2026.

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

- [Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler](https://mlsanity.com/paper/2609.06905/) (2026)
- [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 exact simulation of diffusions via rejection sampling on path space using unbiased estimators of the density ratio obtained from Girsanov's theorem. When applied to the underdamped Langevin diffusion, it yields an algorithm for sampling from a strongly log-concave and log-smooth distribution with condition number kappa, in dimension d, to accuracy varepsilon in R'enyi divergence, in widetilde O(kappa2/3 d1/3,polylog(1/varepsilon)) queries. Under a third derivative bound, the dimension dependence improves to d1/5. This improves substantially over the prior state-of-the-art complexity of widetilde O(kappa d1/2,polylog(1/varepsilon)) for the Metropolis-adjusted Langevin algorithm, and over the d1/4 dimension dependence of Metropolized Hamiltonian Monte Carlo under the same third derivative bound. We also present applications to the mirror Langevin diffusion, and for obtaining Fisher information bounds in the non-log-concave case.