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Energy-Guided Flow Matching Enables Few-Step Conformer Generation and Ground-State Identification

Guikun Xu, Xiaohan Yi, Peilin Zhao, Yatao Bian

TL;DR

EnFlow presents a unified framework that simultaneously generates low-energy conformer ensembles and identifies ground-state conformations by coupling energy-guided flow matching with an explicit energy model. It extends flow matching to non-Gaussian priors via Harmonic Priors and trains an energy-based model using Energy Matching, enabling guided sampling toward lower-energy regions. The learned energy landscape also serves as a fast surrogate for ground-state screening, delivering state-of-the-art performance on GEOM-QM9 and GEOM-Drugs with few ODE steps and robust ground-state certification. This approach offers a thermodynamically consistent, efficient pathway for conformer generation and ground-state identification with potential impact on drug design and materials science.

Abstract

Generating low-energy conformer ensembles and identifying ground-state conformations from molecular graphs remain computationally demanding with physics-based pipelines. Current learning-based approaches often suffer from a fragmented paradigm: generative models capture diversity but lack reliable energy calibration, whereas deterministic predictors target a single structure and fail to represent ensemble variability. Here we present EnFlow, a unified framework that couples flow matching (FM) with an explicitly learned energy model through an energy-guided sampling scheme defined along a non-Gaussian FM path. By incorporating energy-gradient guidance during sampling, our method steers trajectories toward lower-energy regions, substantially improving conformational fidelity, particularly in the few-step regime. The learned energy function further enables efficient energy-based ranking of generated ensembles for accurate ground-state identification. Extensive experiments on GEOM-QM9 and GEOM-Drugs demonstrate that EnFlow simultaneously improves generation metrics with 1--2 ODE-steps and reduces ground-state prediction errors compared with state-of-the-art methods.

Energy-Guided Flow Matching Enables Few-Step Conformer Generation and Ground-State Identification

TL;DR

EnFlow presents a unified framework that simultaneously generates low-energy conformer ensembles and identifies ground-state conformations by coupling energy-guided flow matching with an explicit energy model. It extends flow matching to non-Gaussian priors via Harmonic Priors and trains an energy-based model using Energy Matching, enabling guided sampling toward lower-energy regions. The learned energy landscape also serves as a fast surrogate for ground-state screening, delivering state-of-the-art performance on GEOM-QM9 and GEOM-Drugs with few ODE steps and robust ground-state certification. This approach offers a thermodynamically consistent, efficient pathway for conformer generation and ground-state identification with potential impact on drug design and materials science.

Abstract

Generating low-energy conformer ensembles and identifying ground-state conformations from molecular graphs remain computationally demanding with physics-based pipelines. Current learning-based approaches often suffer from a fragmented paradigm: generative models capture diversity but lack reliable energy calibration, whereas deterministic predictors target a single structure and fail to represent ensemble variability. Here we present EnFlow, a unified framework that couples flow matching (FM) with an explicitly learned energy model through an energy-guided sampling scheme defined along a non-Gaussian FM path. By incorporating energy-gradient guidance during sampling, our method steers trajectories toward lower-energy regions, substantially improving conformational fidelity, particularly in the few-step regime. The learned energy function further enables efficient energy-based ranking of generated ensembles for accurate ground-state identification. Extensive experiments on GEOM-QM9 and GEOM-Drugs demonstrate that EnFlow simultaneously improves generation metrics with 1--2 ODE-steps and reduces ground-state prediction errors compared with state-of-the-art methods.
Paper Structure (69 sections, 1 theorem, 48 equations, 12 figures, 5 tables, 3 algorithms)

This paper contains 69 sections, 1 theorem, 48 equations, 12 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Results
  3. Notations and Problem Definition
  4. Main Notations:
  5. Problem Definition:
  6. Datasets, Metrics, and Baselines
  7. Datasets:
  8. Metrics for Conformer Ensemble Generation:
  9. Metrics for Ground-State Conformation Prediction:
  10. Baselines:
  11. EnFlow Enhances Fidelity in Conformer Generation with Few ODE Steps
  12. Results on GEOM-QM9:
  13. Results on GEOM-Drugs:
  14. EnFlow Delivers Robust Ground-state Conformation Selection
  15. Ground-State Conformation Prediction on GEOM-Drugs:
  16. ...and 54 more sections

Key Result

Theorem 3.1

Adding the guidance VF $g_{t}(x_{t})$ to the original VF $v_{t}(x_{t})$ will form VF $v'_{t}(x_{t})$ that generates $p_{t} '(x_{t}) = \int p_{t}(x_{t}|z)p'(z)dz$, as long as $g_{t}(x_{t})$ follows: $Z = \int e^{-J(x)}p(x) dx$ is the normalization constant. $\mathcal{P}= \frac{\pi'(x_{0}|x_{1})}{\pi(

Figures (12)

  • Figure 1: (a) Potential energy landscape of molecular conformations: low-energy conformers populate local minima, and the ground-state conformation corresponds to the global minimum. (b) Existing generative methods can sample diverse low-energy conformers but struggle to reliably identify the ground state, whereas deterministic methods predict a single structure near the ground state and fail to capture the ensemble variability. (c) Our EnFlow framework unifies both capabilities: it efficiently generates low-energy conformational ensembles and accurately identifies the ground-state conformation by leveraging a learned, explicit energy function that simultaneously guides the generative process.
  • Figure 2: EnFlow illustrations. (a) The energy-guided flow matching framework, in which an EBM trained via the Energy Matching technique provides guidance during the flow matching process. (b) Architectural overview of the vector field and the energy model. For comparision fairness, we used the same backbone architecture as that of ET-Flow hassan2024flow (c) Illustration of improved one-step ODE sampling achieved through energy-guided sampling. (d) Using the well-trained energy function to certify the ground-state conformation.
  • Figure 3: Joint performance on GEOM-Drugs across molecular conformation generation and ground-state conformation prediction tasks.
  • Figure 4: Model architectures in this work. (a) Following ET-Flow fan2024ec, the main learnable neural network is $\mathtt{TorchMD}\text{-}\mathtt{NET}$tholke2022torchmd, modified to incorporate time as an additional input feature, as illustrated in the left panel. The right panel shows how $\mathtt{TorchMD}\text{-}\mathtt{NET}$ is used as both a vector field model and an energy model. (b) Details of the Equivariant Attention Layer and Multi-Head Attention components in $\mathtt{TorchMD}\text{-}\mathtt{NET}$, with the illustration adapted from the ET-Flow fan2024ec resources.
  • Figure 5: Ablation study of guidance strengths $\lambda_{t}$ for 5-step (a) and 50-step (b) ODE sampling on GEOM-QM9, and for 5-step (c) ODE sampling on GEOM-Drugs. The table reports Recall and Precision metrics at a fixed RMSD threshold of $\delta = 0.5$ Å for GEOM-QM9 and $\delta = 0.75$ Å for GEOM-Drugs, together with the mean predicted energy $J_{\phi}$. The plots depict how these metrics vary as a function of the RMSD threshold $\delta$.
  • ...and 7 more figures

Theorems & Definitions (1)

  • Theorem 3.1: Theorem 3.1 of Ref. feng2025guidance