# Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transport

arXiv: https://arxiv.org/abs/2606.07239 · HTML: https://mlsanity.com/paper/2606.07239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 30 of 40)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Levenshtein Transformer](https://mlsanity.com/paper/1905.11006/) (2019)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2309.17296/) (2023)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Trans-Dimensional Generative Modeling via Jump Diffusion Models](https://mlsanity.com/paper/2305.16261/) (2023)
- [Beyond In-Place Corruption: Insertion and Deletion In Denoising Probabilistic Models](https://mlsanity.com/paper/2107.07675/) (2021)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)
- [Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generation](https://mlsanity.com/paper/2311.16199/) (2023)
- [OneFlow: Concurrent Mixed-Modal and Interleaved Generation with Edit Flows](https://mlsanity.com/paper/2510.03506/) (2025)
- [Applications of Modular Co-Design for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2505.18392/) (2025)
- [TABASCO: A Fast, Simplified Model for Molecular Generation with Improved Physical Quality](https://mlsanity.com/paper/2507.00899/) (2025)

## Built on by (most cited first, 2 of 2)

- [Ensemble-Conditioned Molecular Design](https://mlsanity.com/paper/2609.15077/) (2026)
- [Grand Canonical Generators](https://mlsanity.com/paper/2610.00683/) (2026)

## Abstract (arXiv)

The success of generative molecular design hinges on a model's steerability toward high-reward samples. Because many molecular properties are intrinsically linked to molecular size, accurately capturing the joint distribution of properties and the number of atoms is essential. However, current diffusion and flow-based models fix the number of atoms, which ultimately limits their ability to navigate this complex relationship. To address this, we introduce Morph, a flexible-size generative model for conditional and unconditional 3D molecular design based on geometric graphs. By dynamically adapting size, Morph can seamlessly integrate existing structural priors, like scaffolds, and significantly enhances property steering. We show that Morph matches current fixed-size state-of-the-art models while offering the benefit of unparalleled sampling flexibility. We demonstrate out-of-distribution generation in regimes where previous models fail, paving the way for enhanced generative modeling for molecular design.