Path Gradients after Flow Matching
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize the length of the flow integration trajectories. We investigate the benefits of using path gradients to fine-tune CNFs initially trained by Flow Matching, in the setting where a target energy is known. Our experiments show that this hybrid approach yields up to a threefold increase in sampling efficiency for molecular systems, all while using the same model, a similar computational budget and without the need for additional sampling. Furthermore, by measuring the length of the flow trajectories during fine-tuning, we show that path gradients largely preserve the learned structure of the flow.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 41 of its 72 references that are in the map. First posted on arXiv 15 May 2025.
Builds on
41 of 72 references.
Closest ancestors · 5
Same direction, newest first
- 2024AlphaFold Meets Flow Matching for Generating Protein Ensembles7 Feb
- 2023Equivariant flow matching26 Jun
- 2022Flow Matching for Generative Modeling6 Oct
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
- 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
Other references · 36
- 2020Denoising Diffusion Probabilistic Modelscited by 21,076
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
- 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2015Variational Inference with Normalizing Flowscited by 2,170
- 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
- 2021E(n) Equivariant Graph Neural Networkscited by 965
- 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
- 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
- 2024Pyramidal Flow Matching for Efficient Video Generative Modelingcited by 366
- 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
- 2022Torsional Diffusion for Molecular Conformer Generationcited by 263
24 more
- 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
- 2021E(n) Equivariant Normalizing Flowscited by 165
- 2022Flow Annealed Importance Sampling Bootstrapcited by 127
- 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 98
- 2020Sampling using SU(N) gauge equivariant flowscited by 84
- 2020Targeted free energy estimation via learned mappingscited by 67
- 2023Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamicscited by 66
- 2021Smooth Normalizing Flowscited by 53
- 2024Transferable Boltzmann Generatorscited by 46
- 2018Doubly Reparameterized Gradient Estimators for Monte Carlo Objectivescited by 41
- 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 38
- 2020Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimizationcited by 37
- 2023Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Designcited by 30
- 2023Free-form Flows: Make Any Architecture a Normalizing Flowcited by 26
- 2023Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theoriescited by 25
- 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 23
- 2023Normalizing flows for lattice gauge theory in arbitrary space-time dimensioncited by 23
- 2024Efficient mapping of phase diagrams with conditional Boltzmann Generatorscited by 18
- 2021Generalized Doubly Reparameterized Gradient Estimatorscited by 14
- 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 11
- 2024Scalable Normalizing Flows Enable Boltzmann Generators for Macromoleculescited by 10
- 2020Computing Absolute Free Energy with Deep Generative Modelscited by 7
- 2024Fast and Unified Path Gradient Estimators for Normalizing Flowscited by 5
- 2024Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VIcited by 5
Built on by
Citing papers per year: 2025: 1; 2026: 2.
3 papers.
- 2025Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Samplingcited by 7
- 2026Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularizationcited by 3
- 2026Scaling Online Optimal Transport Minibatches for Flow Matchingcited by 0
- 2026Scaling Online Optimal Transport Minibatches for Flow Matching13 Oct 2026
- 2026Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularization3 Feb 2026
- 2025Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling3 Sep 2025
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