# Transferable Boltzmann Generators

arXiv: https://arxiv.org/abs/2406.14426 · HTML: https://mlsanity.com/paper/2406.14426/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 72 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 30 of 41)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [Smooth Normalizing Flows](https://mlsanity.com/paper/2110.00351/) (2021)
- [A new perspective on building efficient and expressive 3D equivariant graph neural networks](https://mlsanity.com/paper/2304.04757/) (2023)
- [Protein Conformation Generation via Force-Guided SE(3) Diffusion Models](https://mlsanity.com/paper/2403.14088/) (2024)

## Built on by (most cited first, 30 of 46)

- [Scalable Equilibrium Sampling with Sequential Boltzmann Generators](https://mlsanity.com/paper/2502.18462/) (2025)
- [Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2506.16471/) (2025)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional](https://mlsanity.com/paper/2504.18506/) (2025)
- [FEAT: Free energy Estimators with Adaptive Transport](https://mlsanity.com/paper/2504.11516/) (2025)
- [Temperature-Annealed Boltzmann Generators](https://mlsanity.com/paper/2501.19077/) (2025)
- [FALCON: Few-step Accurate Likelihoods for Continuous Flows](https://mlsanity.com/paper/2512.09914/) (2025)
- [FlashMD: long-stride, universal prediction of molecular dynamics](https://mlsanity.com/paper/2505.19350/) (2025)
- [Amortized Sampling with Transferable Normalizing Flows](https://mlsanity.com/paper/2508.18175/) (2025)
- [Harmonic Path Integral Diffusion](https://mlsanity.com/paper/2409.15166/) (2024)
- [Scalable Boltzmann Generators for equilibrium sampling of large-scale materials](https://mlsanity.com/paper/2509.25486/) (2025)
- [Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics](https://mlsanity.com/paper/2510.07589/) (2025)
- [On scalable and efficient training of diffusion samplers](https://mlsanity.com/paper/2505.19552/) (2025)
- [Learning Boltzmann Generators via Constrained Mass Transport](https://mlsanity.com/paper/2510.18460/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules](https://mlsanity.com/paper/2506.03157/) (2025)
- [BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation](https://mlsanity.com/paper/2507.00846/) (2025)
- [Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling](https://mlsanity.com/paper/2509.03726/) (2025)
- [Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics](https://mlsanity.com/paper/2601.22123/) (2026)
- [Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides](https://mlsanity.com/paper/2408.15126/) (2024)
- [MarS-FM: Generative Modeling of Molecular Dynamics via Markov State Models](https://mlsanity.com/paper/2509.24779/) (2025)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [JAMUN: Bridging Smoothed Molecular Dynamics and Score-Based Learning for Conformational Ensembles](https://mlsanity.com/paper/2410.14621/) (2024)
- [Protein Language Model Embeddings Improve Generalization of Implicit Transfer Operators](https://mlsanity.com/paper/2602.11216/) (2026)
- [Path Gradients after Flow Matching](https://mlsanity.com/paper/2505.10139/) (2025)
- [Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space](https://mlsanity.com/paper/2509.02196/) (2025)
- [Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials](https://mlsanity.com/paper/2510.11148/) (2025)
- [Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularization](https://mlsanity.com/paper/2602.03729/) (2026)
- [Unified Biomolecular Trajectory Generation via Pretrained Variational Bridge](https://mlsanity.com/paper/2602.07588/) (2026)
- [Boltzmann-Expected Molecular Design with Decoupled Annealing Flows](https://mlsanity.com/paper/2607.19519/) (2026)

## Abstract (arXiv)

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a normalizing flow from a simple prior distribution to the target Boltzmann distribution of interest. Recently, flow matching has been employed to train Boltzmann Generators for small molecular systems in Cartesian coordinates. We extend this work and propose a first framework for Boltzmann Generators that are transferable across chemical space, such that they predict zero-shot Boltzmann distributions for test molecules without being retrained for these systems. These transferable Boltzmann Generators allow approximate sampling from the target distribution of unseen systems, as well as efficient reweighting to the target Boltzmann distribution. The transferability of the proposed framework is evaluated on dipeptides, where we show that it generalizes efficiently to unseen systems. Furthermore, we demonstrate that our proposed architecture enhances the efficiency of Boltzmann Generators trained on single molecular systems.