Generating Physically Consistent Molecules with Energy-Based Models

2026-05-18

AI Summary

This work addresses the challenges of enforcing physical consistency and modeling Boltzmann energy landscapes in 3D molecular generation by introducing EBMol, the first energy-based model for this task that incorporates an energy-inductive bias. EBMol models molecular energy via an atom-wise additive scalar potential and is trained using a flow-inspired rectified field matching objective. Efficient sampling is achieved through Mirror-Langevin dynamics combined with parallel tempering. The method guarantees physical consistency without explicit simulation and enables zero-shot linker design and shape-guided controllable generation. Evaluated on QM9 and GEOM-Drugs, EBMol achieves state-of-the-art performance, and its learned energy function serves as a reliable scoring metric for conformational quality.

Abstract

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from. Diffusion and flow-matching models sidestep these difficulties by learning a time-conditional score or transport field between noise and data, losing the energy inductive bias in exchange for a more tractable training objective. We introduce EBMol, an energy-based model (EBM) that restores this inductive bias by learning an atom-additive scalar potential without explicit simulation during training. Our method employs a flow-inspired Restoring Field Matching objective to approximate the energy landscape. We adopt the Mirror-Langevin algorithm for sampling, enabling unified updates of atomic positions and types, and incorporate parallel tempering for inference-time compute scaling. EBMol is the first EBM for 3D molecular generation to achieve state-of-the-art performance on QM9 and GEOM-Drugs. Moreover, we show that the learned energy landscape serves as a principled quality metric for ranking and filtering configurations, and demonstrate controllable generation without retraining through shape-steered sampling via potential composition and zero-shot linker design.

Problem

• energy-based model
• molecular generation
• Boltzmann distribution
• 3D molecular structure
• physically consistent modeling

Innovation

• Energy-Based Model
• Restoring Field Matching
• Mirror-Langevin Sampling
• Atom-Additive Potential
• Controllable Molecular Generation