# LEGO-MOF: Equivariant Latent Manipulation for Editable, Generative, and Optimizable MOF Design

arXiv: https://arxiv.org/abs/2604.13520 · HTML: https://mlsanity.com/paper/2604.13520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 18 of 18)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Design](https://mlsanity.com/paper/2310.10732/) (2023)
- [MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks](https://mlsanity.com/paper/2410.17270/) (2024)
- [System of Agentic AI for the Discovery of Metal-Organic Frameworks](https://mlsanity.com/paper/2504.14110/) (2025)
- [Rapid Design of Top-Performing Metal-Organic Frameworks with Qualitative Representations of Building Blocks](https://mlsanity.com/paper/2302.09184/) (2023)
- [Prediction of the electron density of states for crystalline compounds with Atomistic Line Graph Neural Networks (ALIGNN)](https://mlsanity.com/paper/2201.08348/) (2022)
- [Mofasa: A Step Change in Metal-Organic Framework Generation](https://mlsanity.com/paper/2512.01756/) (2025)
- [Building-Block Aware Generative Modeling for 3D Crystals of Metal Organic Frameworks](https://mlsanity.com/paper/2505.08531/) (2025)
- [Efficient Computation of Multiple Density-Based Clustering Hierarchies](https://mlsanity.com/paper/1709.04545/) (2017)
- [Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Space](https://mlsanity.com/paper/2506.00771/) (2025)
- [EGMOF: Efficient Generation of Metal-Organic Frameworks Using a Hybrid Diffusion-Transformer Architecture](https://mlsanity.com/paper/2511.03122/) (2025)

## Abstract (arXiv)

Metal-organic frameworks (MOFs) are highly promising for carbon capture, yet navigating their vast design space remains challenging. Recent deep generative models enable de novo MOF design but primarily act as feed-forward structure generators. By heavily relying on predefined building block libraries and non-differentiable post-optimization, they fundamentally sever the information flow required for continuous structural editing. Here, we propose a target-driven generative framework focused on continuous structural manipulation. At its core is LinkerVAE, which maps discrete 3D chemical graphs into a continuous, SE(3)-equivariant latent space. This smooth manifold unlocks geometry-aware manipulations, including implicit chemical style transfer and zero-shot isoreticular expansion. Building upon this, we introduce a test-time optimization (TTO) strategy, utilizing an accurate surrogate model to continuously optimize the latent graphs of existing MOFs toward desired properties. This approach systematically enhances carbon capture performance, achieving a striking average relative boost of 147.5% in pure CO2 uptake while strictly preserving structural validity. Integrated with a latent diffusion model and rigid-body assembly for full MOF construction, our framework establishes a scalable, fully differentiable pathway for both the automated discovery, targeted optimization and editing of functional materials.