Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery

Molecular energy landscape exploration has evolved from classical quantum chemistry methods like DFT and ab initio calculations to machine learning-driven approaches. Early methods provided high accuracy but suffered from high computational costs, limiting large-scale applications. Recent developments include generative models such as GeoDiff, Torsional Diffusion, and flow-based models like GeoMol and AvgFlow, which improve sampling efficiency and geometric consistency. Despite these advances, accurately modeling the entire energy landscape and reliably identifying the ground state remain unresolved challenges. Existing models often focus on either diversity sampling or single-structure prediction, lacking a unified framework that combines both. The need for efficient, physically meaningful conformer generation and ranking continues to drive research, especially for drug discovery and materials design where rapid screening of low-energy structures is critical.

The core issue is how to efficiently generate diverse low-energy conformations and accurately identify the true ground state within a minimal number of sampling steps. Traditional physics-based methods are computationally intensive, unsuitable for large datasets. Generative models can produce diverse conformers but lack reliable energy calibration, making it difficult to select the most stable structures. Deterministic predictors focus on a single conformation, missing the broader ensemble variability. This fragmentation hampers high-throughput applications. The challenge is to develop a unified, scalable framework that can generate, evaluate, and rank conformations efficiently, ensuring physical relevance and computational feasibility.

The key innovations include: 1) a flow matching framework that learns a reversible transformation from a prior distribution to molecular conformations, ensuring geometric consistency; 2) an explicit neural energy model trained via energy matching and supervised fine-tuning, capturing the energy landscape across diverse molecules; 3) an energy-guided ODE sampling strategy that directs trajectories toward low-energy regions with only 1-2 steps, vastly improving efficiency; 4) a unified approach that supports both conformer diversity and energy-based ranking, enabling ground-state identification without separate models. These innovations address the limitations of existing methods by combining efficiency, physical interpretability, and accuracy in a single framework.

• �� Define a prior distribution (e.g., Gaussian) for initial conformer sampling.
• �� Use flow matching to learn a reversible transformation from the prior to the conformational distribution, ensuring geometric consistency.
• �� Train a neural energy model (e.g., GINE) with energy matching loss to predict molecular energies accurately.
• �� Fine-tune the energy model supervisedly on molecule-specific data for better energetic accuracy.
• �� During sampling, solve an energy-guided ODE that incorporates the learned energy gradient, steering conformations toward low-energy regions in 1-2 steps.
• �� Use the learned energy scores to rank generated conformers, selecting the lowest-energy candidates.
• �� For ground-state prediction, generate multiple conformers and select the one with the lowest energy score.
• �� Train the entire framework jointly, balancing conformational diversity and energy calibration objectives.

Experiments utilize GEOM-QM9 and GEOM-Drugs datasets, evaluating conformer generation quality via RMSD-based coverage and minimum RMSD metrics, and energy ranking via correlation with GFn2-xTB energies. Baselines include GeoDiff, Torsional Diffusion, and AvgFlow. Metrics assess the effectiveness of few-step sampling (1-2 steps), with hyperparameters tuned for guidance strength and ensemble size. Ablation studies analyze the impact of energy guidance and model components. The experiments demonstrate that EnFlow achieves state-of-the-art performance in conformer coverage (>95%) with minimal steps, and the energy scores align strongly with quantum-chemical energies, validating the physical relevance of the learned energy model.

EnFlow surpasses baselines in conformer coverage and structural accuracy at 1-2 steps, with coverage >95% and RMSD <0.03 Å. Energy scores correlate with GFn2-xTB energies (median Spearman 0.82), enabling reliable ranking. The model effectively identifies ground states, with median rank correlation improving by 17% over baselines. Energy-based selection further refines conformer quality, demonstrating the dual role of the energy model in generation and ranking. These results confirm that explicit energy landscape modeling enhances sampling efficiency and structural fidelity, especially under limited sampling budgets.

This framework is directly applicable to drug discovery, enabling rapid screening of low-energy conformations for candidate molecules. It can accelerate materials design by efficiently exploring conformational space and identifying stable structures. The approach also benefits large-scale virtual screening pipelines, reducing computational costs while maintaining accuracy. Future integration with experimental data and extension to larger biomolecules could further expand its industrial impact, enabling more reliable and scalable molecular modeling workflows.

The accuracy of energy-based ranking depends on the trained energy model, which may not generalize well to unseen or complex molecules. The current approach is primarily validated on small molecules; scaling to larger biomolecules or proteins poses challenges due to increased conformational complexity and computational demands. The training process involves multiple loss components and hyperparameters, increasing complexity. Further, the model's performance in dynamic or reaction pathways remains unexplored, requiring future research to address these limitations.