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Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials

arXiv 2512.22153 ↗First posted 15 Dec 2025stat.CO cs.LG stat.MLcited by 0

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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.

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.

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References · 18

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,061
  4. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 217
  5. 2023Denoising Diffusion Samplerscited by 149
  6. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  7. 2019Safe Policies for Reinforcement Learning via Primal-Dual Methodscited by 79
  8. 2018Mirrored Langevin Dynamicscited by 61
  9. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  10. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  11. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
  12. 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
6 more
  1. 2025Training-Free Safe Denoisers for Safe Use of Diffusion Modelscited by 21
  2. 2022Annealed Langevin Dynamics for Massive MIMO Detectioncited by 16
  3. 2022Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingcited by 13
  4. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  5. 2022Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlocited by 6
  6. 2022Accelerated massive MIMO detector based on annealed underdamped Langevin dynamicscited by 2

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