Sampling Boltzmann distributions via normalizing flow approximation of transport maps

• URL: http://arxiv.org/abs/2603.14258v1
• Date: Sun, 15 Mar 2026 07:28:10 GMT
• Title: Sampling Boltzmann distributions via normalizing flow approximation of transport maps
• Abstract summary: We prove the existence of a normalizing flow between the reference measure and the true Boltzmann distribution up to an arbitrarily small error in the Wasserstein distance.<n>We observe that the RealNVP architecture does not just successfully capture the equilibrium Boltzmann distribution but also the metastable dynamics.
• Score: 0.14323566945483493
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In a celebrated paper \cite{noe2019boltzmann}, Noé, Olsson, Köhler and Wu introduced an efficient method for sampling high-dimensional Boltzmann distributions arising in molecular dynamics via normalizing flow approximation of transport maps. Here, we place this approach on a firm mathematical foundation. We prove the existence of a normalizing flow between the reference measure and the true Boltzmann distribution up to an arbitrarily small error in the Wasserstein distance. This result covers general Boltzmann distributions from molecular dynamics, which have low regularity due to the presence of interatomic Coulomb and Lennard-Jones interactions. The proof is based on a rigorous construction of the Moser transport map for low-regularity endpoint densities and approximation theorems for neural networks in Sobolev spaces. Numerical simulations for a simple model system and for the alanine dipeptide molecule confirm that the true and generated distributions are close in the Wasserstein distance. Moreover we observe that the RealNVP architecture does not just successfully capture the equilibrium Boltzmann distribution but also the metastable dynamics.

Related papers

• Weighted Stochastic Differential Equation to Implement Wasserstein-Fisher-Rao Gradient Flow [0.0]
  A promising line of work leverages tools from information geometry to augment diffusion-based samplers with mass reweighting mechanisms.<n>Our work provides a preliminary but rigorous investigation of WFR-based sampling dynamics, and aims to clarify their theoretical structure as a foundation for future developments.
  arXiv  Detail & Related papers  (2025-12-19T18:31:27Z)
• Torsional-GFN: a conditional conformation generator for small molecules [75.91029322687771]
  We introduce a conditional GFlowNet specifically designed to sample conformations of molecules proportionally to their Boltzmann distribution.<n>Our work presents a promising avenue for scaling the proposed approach to larger molecular systems.
  arXiv  Detail & Related papers  (2025-07-15T21:53:25Z)
• BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation [1.2874523233023452]
  Efficient sampling from the Boltzmann distribution is a key challenge for modeling complex physical systems such as molecules.<n>We train an energy-based model (EBM) to approximate likelihoods using both noise contrastive estimation (NCE) and score matching.<n>Our approach also exhibits effective transfer learning, generalizing to new systems at inference time and achieving at least a $6times$ speedup over standard MD.
  arXiv  Detail & Related papers  (2025-07-01T15:18:28Z)
• Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models [50.77646970127369]
  We propose an energy-based diffusion model with a Fokker--Planck-derived regularization term to enforce consistency.<n>We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins.
  arXiv  Detail & Related papers  (2025-06-20T16:38:29Z)
• Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities [93.13866975467549]
  We propose Progressive Inference-Time Annealing (PITA) to learn diffusion-based samplers.<n>PITA combines two complementary techniques: Annealing of the Boltzmann distribution and Diffusion smoothing.<n>It enables equilibrium sampling of N-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates.
  arXiv  Detail & Related papers  (2025-06-19T17:14:22Z)
• On the Contractivity of Stochastic Interpolation Flow [0.0]
  We investigate, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling.<n>We show that for a base distribution and a strongly log-concave target distribution, the flow map is Lipschitz with a sharp constant which matches that of Caffarelli's theorem for optimal transport maps.<n>We are further able to construct Lipschitz transport maps between non-Gaussian distributions, generalizing some recent constructions in the literature on transport methods for establishing functional inequalities.
  arXiv  Detail & Related papers  (2025-04-14T19:10:22Z)
• Scalable Equilibrium Sampling with Sequential Boltzmann Generators [60.00515282300297]
  We extend the Boltzmann generator framework with two key contributions.<n>The first is a highly efficient Transformer-based normalizing flow operating directly on all-atom Cartesian coordinates.<n>In particular, we perform inference-time scaling of flow samples using a continuous-time variant of sequential Monte Carlo.
  arXiv  Detail & Related papers  (2025-02-25T18:59:13Z)
• Simulating the Hubbard Model with Equivariant Normalizing Flows [0.0]
  normalizing flows have been successfully applied to accurately learn the Boltzmann distribution.<n>We present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model.
  arXiv  Detail & Related papers  (2025-01-13T14:40:42Z)
• Flow Perturbation to Accelerate Unbiased Sampling of Boltzmann distribution [2.103187931015573]
  Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application is hindered by the computational cost of obtaining the Jacobian of the flow. We introduce the flow perturbation method, which incorporates optimized perturbations into the flow. By reweighting trajectories generated by the perturbed flow, our method achieves unbiased sampling of the Boltzmann distribution with orders of magnitude speedup.
  arXiv  Detail & Related papers  (2024-07-15T12:29:17Z)
• Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems [78.96969465641024]
  We extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We also study time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result.
  arXiv  Detail & Related papers  (2023-12-02T13:01:29Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.