# Improving Molecular Graph Generation with Flow Matching and Optimal Transport

arXiv: https://arxiv.org/abs/2411.05676 · HTML: https://mlsanity.com/paper/2411.05676/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 16 of its 70 references that are in the map.
- First posted on arXiv 8 Nov 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 16 of 16)

- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [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)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation](https://mlsanity.com/paper/2307.01646/) (2023)
- [Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation](https://mlsanity.com/paper/2402.03687/) (2024)
- [Generative Modelling of Structurally Constrained Graphs](https://mlsanity.com/paper/2406.17341/) (2024)
- [Graph Diffusion Policy Optimization](https://mlsanity.com/paper/2402.16302/) (2024)
- [Generating Graphs via Spectral Diffusion](https://mlsanity.com/paper/2402.18974/) (2024)

## Built on by (most cited first, 10 of 10)

- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matching](https://mlsanity.com/paper/2502.15805/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening](https://mlsanity.com/paper/2512.01190/) (2025)
- [Unveiling and Steering Connectome Organization with Interpretable Latent Variables](https://mlsanity.com/paper/2505.13011/) (2025)
- [Reward Transport: Property Control in Flow Matching via Noise-Space Alignment](https://mlsanity.com/paper/2607.08781/) (2026)
- [Embedded Graph Flows for Categorical Graph Generation](https://mlsanity.com/paper/2609.05328/) (2026)
- [A Systematic Evaluation of Molecule Generation Models for De Novo Drug Design: From Benchmarks to Practical Insights](https://mlsanity.com/paper/2609.10099/) (2026)
- [Stable Transformers for Graph Generation](https://mlsanity.com/paper/2609.39739/) (2026)

## Abstract (arXiv)

Generating molecular graphs is crucial in drug design and discovery but remains challenging due to the complex interdependencies between nodes and edges. While diffusion models have demonstrated their potentiality in molecular graph design, they often suffer from unstable training and inefficient sampling. To enhance generation performance and training stability, we propose GGFlow, a discrete flow matching generative model incorporating optimal transport for molecular graphs and it incorporates an edge-augmented graph transformer to enable the direct communications among chemical bounds. Additionally, GGFlow introduces a novel goal-guided generation framework to control the generative trajectory of our model, aiming to design novel molecular structures with the desired properties. GGFlow demonstrates superior performance on both unconditional and conditional molecule generation tasks, outperforming existing baselines and underscoring its effectiveness and potential for wider application.