# Hessian-Free High-Resolution Nesterov Acceleration for Sampling

arXiv: https://arxiv.org/abs/2006.09230 · HTML: https://mlsanity.com/paper/2006.09230/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling](https://mlsanity.com/paper/2109.13055/) (2021)
- [Sqrt(d) Dimension Dependence of Langevin Monte Carlo](https://mlsanity.com/paper/2109.03839/) (2021)
- [LanPaint: Training-Free Diffusion Inpainting with Asymptotically Exact and Fast Conditional Sampling](https://mlsanity.com/paper/2502.03491/) (2025)
- [Accelerated Markov Chain Monte Carlo Algorithms on Discrete States](https://mlsanity.com/paper/2505.12599/) (2025)
- [Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2606.28808/) (2026)
- [Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling](https://mlsanity.com/paper/2608.25052/) (2026)
- [Accelerated Regularized Wasserstein Proximal Sampling Algorithms](https://mlsanity.com/paper/2601.09848/) (2026)

## Abstract (arXiv)

Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed citepshi2021understanding. This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods. More precisely, we reformulate the optimizer of NAG for strongly convex functions (NAG-SC) as a Hessian-Free High-Resolution ODE, change its high-resolution coefficient to a hyperparameter, inject appropriate noise, and discretize the resulting diffusion process. The acceleration effect of the new hyperparameter is quantified and it is not an artificial one created by time-rescaling. Instead, acceleration beyond underdamped Langevin in W2 distance is quantitatively established for log-strongly-concave-and-smooth targets, at both the continuous dynamics level and the discrete algorithm level. Empirical experiments in both log-strongly-concave and multi-modal cases also numerically demonstrate this acceleration.