# Counterdiabatic Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2602.21272 · HTML: https://mlsanity.com/paper/2602.21272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 24 Feb 2026.

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

- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [An invitation to sequential Monte Carlo samplers](https://mlsanity.com/paper/2007.11936/) (2020)
- [Liouville Flow Importance Sampler](https://mlsanity.com/paper/2405.06672/) (2024)
- [Transport meets Variational Inference: Controlled Monte Carlo Diffusions](https://mlsanity.com/paper/2307.01050/) (2023)
- [The Geometric Foundations of Hamiltonian Monte Carlo](https://mlsanity.com/paper/1410.5110/) (2014)
- [Path-Guided Particle-based Sampling](https://mlsanity.com/paper/2412.03312/) (2024)

## Built on by (most cited first, 1 of 1)

- [Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling](https://mlsanity.com/paper/2607.15682/) (2026)

## Abstract (arXiv)

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling citedoucet2001introduction. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by citesels2017minimizing, where a learned counterdiabatic term added to the Hamiltonian allows for efficient quantum state preparation, we propose Counterdiabatic Hamiltonian Monte Carlo (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.