# Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials

arXiv: https://arxiv.org/abs/2512.22153 · HTML: https://mlsanity.com/paper/2512.22153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Safe Policies for Reinforcement Learning via Primal-Dual Methods](https://mlsanity.com/paper/1911.09101/) (2019)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space](https://mlsanity.com/paper/2202.01908/) (2022)
- [Training-Free Safe Denoisers for Safe Use of Diffusion Models](https://mlsanity.com/paper/2502.08011/) (2025)
- [Annealed Langevin Dynamics for Massive MIMO Detection](https://mlsanity.com/paper/2205.05776/) (2022)
- [Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Sampling](https://mlsanity.com/paper/2212.00570/) (2022)
- [Constrained Sampling with Primal-Dual Langevin Monte Carlo](https://mlsanity.com/paper/2411.00568/) (2024)
- [Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlo](https://mlsanity.com/paper/2210.11925/) (2022)
- [Accelerated massive MIMO detector based on annealed underdamped Langevin dynamics](https://mlsanity.com/paper/2210.15071/) (2022)

## Abstract (arXiv)

We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.