  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 \citep{shi2021understanding}. 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 $W_2$ 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.
