# Generating Physically Consistent Molecules with Energy-Based Models

arXiv: https://arxiv.org/abs/2605.18381 · HTML: https://mlsanity.com/paper/2605.18381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 61 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generation](https://mlsanity.com/paper/2305.07508/) (2023)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [PyG 2.0: Scalable Learning on Real World Graphs](https://mlsanity.com/paper/2507.16991/) (2025)
- [Mirror Diffusion Models for Constrained and Watermarked Generation](https://mlsanity.com/paper/2310.01236/) (2023)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [The Mirror Langevin Algorithm Converges with Vanishing Bias](https://mlsanity.com/paper/2109.12077/) (2021)
- [Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generation](https://mlsanity.com/paper/2305.12347/) (2023)
- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [UniGEM: A Unified Approach to Generation and Property Prediction for Molecules](https://mlsanity.com/paper/2410.10516/) (2024)

## Abstract (arXiv)

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.