# Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Space

arXiv: https://arxiv.org/abs/2506.00771 · HTML: https://mlsanity.com/paper/2506.00771/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [In-context Autoencoder for Context Compression in a Large Language Model](https://mlsanity.com/paper/2307.06945/) (2023)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [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)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Uncovering the Disentanglement Capability in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2212.08698/) (2022)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [Enjoy Your Editing: Controllable GANs for Image Editing via Latent Space Navigation](https://mlsanity.com/paper/2102.01187/) (2021)
- [MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space](https://mlsanity.com/paper/2404.12141/) (2024)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Generating 3D Molecular Structures Conditional on a Receptor Binding Site with Deep Generative Models](https://mlsanity.com/paper/2010.14442/) (2020)
- [Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations](https://mlsanity.com/paper/2404.15766/) (2024)
- [DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization](https://mlsanity.com/paper/2403.13829/) (2024)
- [UniGEM: A Unified Approach to Generation and Property Prediction for Molecules](https://mlsanity.com/paper/2410.10516/) (2024)
- [ShEPhERD: Diffusing shape, electrostatics, and pharmacophores for bioisosteric drug design](https://mlsanity.com/paper/2411.04130/) (2024)
- [UniMoMo: Unified Generative Modeling of 3D Molecules for De Novo Binder Design](https://mlsanity.com/paper/2503.19300/) (2025)
- [Auto-Encoding Molecular Conformations](https://mlsanity.com/paper/2101.01618/) (2021)

## Built on by (most cited first, 3 of 3)

- [MolPIF: A Parameter Interpolation Flow Model for Molecule Generation](https://mlsanity.com/paper/2507.13762/) (2025)
- [LEGO-MOF: Equivariant Latent Manipulation for Editable, Generative, and Optimizable MOF Design](https://mlsanity.com/paper/2604.13520/) (2026)
- [Smoothing Dark Areas in Molecular Latent Diffusion](https://mlsanity.com/paper/2606.13955/) (2026)

## Abstract (arXiv)

Medicinal chemists often optimize drugs considering their 3D structures and designing structurally distinct molecules that retain key features, such as shapes, pharmacophores, or chemical properties. Previous deep learning approaches address this through supervised tasks like molecule inpainting or property-guided optimization. In this work, we propose a flexible zero-shot molecule manipulation method by navigating in a shared latent space of 3D molecules. We introduce a Variational AutoEncoder (VAE) for 3D molecules, named MolFLAE, which learns a fixed-dimensional, E(3)-equivariant latent space independent of atom counts. MolFLAE encodes 3D molecules using an E(3)-equivariant neural network into fixed number of latent nodes, distinguished by learned embeddings. The latent space is regularized, and molecular structures are reconstructed via a Bayesian Flow Network (BFN) conditioned on the encoder's latent output. MolFLAE achieves competitive performance on standard unconditional 3D molecule generation benchmarks. Moreover, the latent space of MolFLAE enables zero-shot molecule manipulation, including atom number editing, structure reconstruction, and coordinated latent interpolation for both structure and properties. We further demonstrate our approach on a drug optimization task for the human glucocorticoid receptor, generating molecules with improved hydrophilicity while preserving key interactions, under computational evaluations. These results highlight the flexibility, robustness, and real-world utility of our method, opening new avenues for molecule editing and optimization.