# Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition

arXiv: https://arxiv.org/abs/2605.25577 · HTML: https://mlsanity.com/paper/2605.25577/

## 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 18 of its 36 references that are in the map.
- First posted on arXiv 25 May 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 18 of 18)

- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Empowering Molecule Discovery for Molecule-Caption Translation with Large Language Models: A ChatGPT Perspective](https://mlsanity.com/paper/2306.06615/) (2023)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [Speak-to-Structure: Evaluating LLMs in Open-domain Natural Language-Driven Molecule Generation](https://mlsanity.com/paper/2412.14642/) (2024)
- [Score-based Generative Diffusion Models for Social Recommendations](https://mlsanity.com/paper/2412.15579/) (2024)
- [MolReFlect: Towards In-Context Fine-grained Alignments between Molecules and Texts](https://mlsanity.com/paper/2411.14721/) (2024)
- [Improving User Controlled Table-To-Text Generation Robustness](https://mlsanity.com/paper/2302.09820/) (2023)
- [GLProtein: Global-and-Local Structure Aware Protein Representation Learning](https://mlsanity.com/paper/2506.06294/) (2025)
- [Graph Defense Diffusion Model](https://mlsanity.com/paper/2501.11568/) (2025)
- [Enhancing Molecular Property Predictions by Learning from Bond Modelling and Interactions](https://mlsanity.com/paper/2603.00568/) (2026)

## Built on by (most cited first, 3 of 3)

- [Unlocking Multimodal Protein Language Models at Inference Time](https://mlsanity.com/paper/2608.25855/) (2026)
- [TreeRef-BFN: Equivariance-Free De Novo Molecule Generation based on 2D Topology and Internal 3D Geometry](https://mlsanity.com/paper/2609.32502/) (2026)
- [Zatom-2: Multitask Pretraining on Atomistic Data for Generative Modeling across Domains](https://mlsanity.com/paper/2610.11454/) (2026)

## Abstract (arXiv)

The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical misalignment between their mathematical formulation and the physical reality of molecules. Existing approaches predominantly treat molecules as unstructured point clouds in Cartesian space, overlooking the intrinsic hierarchical mechanics where bond lengths and bond angles are relatively stiff, whereas torsion angles constitute the dominant flexible degrees of freedom. This lack of manifold awareness forces models to relearn fundamental geometric constraints from scratch, often leading to physically implausible intermediate structures. To address this, we propose GO-Flow that aligns generative modeling with molecular geometry via manifold decomposition. Instead of forcing motion through Euclidean space, GO-Flow decomposes the generation process into three physically motivated subspaces: translation space with linear optimal transport, rotation space with geodesic flows on SO(3), and conformation space with entropic optimal transport. This decomposition injects geometric inductive biases and makes the generative paths better aligned with molecular degrees of freedom. When combined with equivariant neural architectures, it encourages rotation-consistent generation and improves geometric validity. Extensive experiments on GEOM-Drugs and GEOM-QM9 demonstrate that GO-Flow achieves state-of-the-art generation quality. Notably, by learning straighter probability paths on the correct manifolds naturally, our method enables high-fidelity sampling with as few as 50 steps, effectively bridging the gap between structural precision and computational efficiency.