# Fast and Efficient Parallel Sampling Using Higher Order Langevin Dynamics

arXiv: https://arxiv.org/abs/2510.18242 · HTML: https://mlsanity.com/paper/2510.18242/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2025.

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

- [Picard Proximal Monte Carlo for Parallel Bayesian Imaging with Score-Based Generative Priors](https://mlsanity.com/paper/2608.17666/) (2026)
- [Global Convergence of Third-Order Langevin Dynamics for Non-Convex Optimization via Simulated Annealing](https://mlsanity.com/paper/2609.28611/) (2026)

## Abstract (arXiv)

We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps in the dimension d, the target accuracy varepsilon-1, or both. Picard-based parallel sampling methods reduce this sequential depth to polylogarithmic scale by solving for many time-discretization points in parallel; however, existing guarantees often require a polynomial number of processors, leading to substantial memory and gradient-evaluation costs in high dimensions. We show that higher-order Langevin structure can reduce this parallel resource burden while preserving polylogarithmic sequential depth. Our method combines arbitrary-order Langevin dynamics with blockwise Lagrange polynomial interpolation. This sharper discretization reduces the number of parallel points required to achieve a target accuracy. Our results cover both higher-order smooth potentials and ridge-separable potentials, including models such as Bayesian logistic regression and two-layer neural networks, and improve upon the space complexity of the current literature on parallel log-concave sampling.