# Geometric Representation Condition Improves Equivariant Molecule Generation

arXiv: https://arxiv.org/abs/2410.03655 · HTML: https://mlsanity.com/paper/2410.03655/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 72 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)

## Built on by (most cited first, 13 of 13)

- [Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner](https://mlsanity.com/paper/2510.03206/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Learning Diffusion Models with Flexible Representation Guidance](https://mlsanity.com/paper/2507.08980/) (2025)
- [Straight-Line Diffusion Model for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2503.02918/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [Self-Conditioned Denoising for Atomistic Representation Learning](https://mlsanity.com/paper/2603.17196/) (2026)
- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [Geometric Mixture Models for Electrolyte Conductivity Prediction](https://mlsanity.com/paper/2510.15403/) (2025)
- [FlashMol: High-Quality Molecule Generation in as Few as Four Steps](https://mlsanity.com/paper/2605.07020/) (2026)
- [Toward Better Geometric Representations for Molecule Generative Models](https://mlsanity.com/paper/2605.07693/) (2026)
- [Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluation](https://mlsanity.com/paper/2607.28776/) (2026)
- [SurfSpec: Enhancing Off-Target-Agnostic Specificity by Bounding Pocket-Ligand Geometric Mismatch](https://mlsanity.com/paper/2609.02963/) (2026)

## Abstract (arXiv)

Recent advances in molecular generative models have demonstrated great promise for accelerating scientific discovery, particularly in drug design. However, these models often struggle to generate high-quality molecules, especially in conditional scenarios where specific molecular properties must be satisfied. In this work, we introduce GeoRCG, a general framework to improve molecular generative models by integrating geometric representation conditions with provable theoretical guarantees. We decompose the generation process into two stages: first, generating an informative geometric representation; second, generating a molecule conditioned on the representation. Compared with single-stage generation, the easy-to-generate representation in the first stage guides the second stage generation toward a high-quality molecule in a goal-oriented way. Leveraging EDM and SemlaFlow as base generators, we observe significant quality improvements in unconditional molecule generation on the widely used QM9 and GEOM-DRUG datasets. More notably, in the challenging conditional molecular generation task, our framework achieves an average 50% performance improvement over state-of-the-art approaches, highlighting the superiority of conditioning on semantically rich geometric representations. Furthermore, with such representation guidance, the number of diffusion steps can be reduced to as small as 100 while largely preserving the generation quality achieved with 1,000 steps, thereby significantly reducing the generation iterations needed. Code is available at https://github.com/GraphPKU/GeoRCG.