Energy-Based Flow Matching for Generating 3D Molecular Structure

Wenyin Zhou, Christopher Iliffe Sprague, Vsevolod Viliuga, Matteo Tadiello, Arne Elofsson, Hossein Azizpour
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:79168-79191, 2025.

Abstract

Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules’ constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution. In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to iteratively map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method’s effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhou25w, title = {Energy-Based Flow Matching for Generating 3{D} Molecular Structure}, author = {Zhou, Wenyin and Sprague, Christopher Iliffe and Viliuga, Vsevolod and Tadiello, Matteo and Elofsson, Arne and Azizpour, Hossein}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {79168--79191}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhou25w/zhou25w.pdf}, url = {https://proceedings.mlr.press/v267/zhou25w.html}, abstract = {Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules’ constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution. In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to iteratively map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method’s effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.} }
Endnote
%0 Conference Paper %T Energy-Based Flow Matching for Generating 3D Molecular Structure %A Wenyin Zhou %A Christopher Iliffe Sprague %A Vsevolod Viliuga %A Matteo Tadiello %A Arne Elofsson %A Hossein Azizpour %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhou25w %I PMLR %P 79168--79191 %U https://proceedings.mlr.press/v267/zhou25w.html %V 267 %X Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules’ constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution. In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to iteratively map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method’s effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.
APA
Zhou, W., Sprague, C.I., Viliuga, V., Tadiello, M., Elofsson, A. & Azizpour, H.. (2025). Energy-Based Flow Matching for Generating 3D Molecular Structure. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:79168-79191 Available from https://proceedings.mlr.press/v267/zhou25w.html.

Related Material