# Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation

arXiv: https://arxiv.org/abs/2404.19739 · HTML: https://mlsanity.com/paper/2404.19739/

## Key facts

- Cited by 54 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 46 of its 58 references that are in the map.
- First posted on arXiv 30 Apr 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, 30 of 46)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [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)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (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)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)

## Built on by (most cited first, 30 of 54)

- [Fisher Flow Matching for Generative Modeling over Discrete Data](https://mlsanity.com/paper/2405.14664/) (2024)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [Flow matching achieves almost minimax optimal convergence](https://mlsanity.com/paper/2405.20879/) (2024)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models](https://mlsanity.com/paper/2504.10283/) (2025)
- [Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning](https://mlsanity.com/paper/2511.22640/) (2025)
- [Multi-domain Distribution Learning for De Novo Drug Design](https://mlsanity.com/paper/2508.17815/) (2025)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [TABASCO: A Fast, Simplified Model for Molecular Generation with Improved Physical Quality](https://mlsanity.com/paper/2507.00899/) (2025)
- [Exploring Discrete Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2411.16644/) (2024)
- [On the minimax optimality of Flow Matching through the connection to kernel density estimation](https://mlsanity.com/paper/2504.13336/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Controlled Generation with Equivariant Variational Flow Matching](https://mlsanity.com/paper/2506.18340/) (2025)
- [GEOM-Drugs Revisited: Toward More Chemically Accurate Benchmarks for 3D Molecule Generation](https://mlsanity.com/paper/2505.00169/) (2025)
- [Efficient Tail-Aware Generative Optimization via Flow Model Fine-Tuning](https://mlsanity.com/paper/2602.16796/) (2026)
- [BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation](https://mlsanity.com/paper/2507.00846/) (2025)
- [Verifier-Constrained Flow Expansion for Discovery Beyond the Data](https://mlsanity.com/paper/2602.15984/) (2026)
- [Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpening](https://mlsanity.com/paper/2503.14975/) (2025)
- [RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesis](https://mlsanity.com/paper/2506.04439/) (2025)
- [Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching](https://mlsanity.com/paper/2506.07199/) (2025)
- [Distribution estimation via Flow Matching with Lipschitz guarantees](https://mlsanity.com/paper/2509.02337/) (2025)
- [Scalable and Cost-Efficient de Novo Template-Based Molecular Generation](https://mlsanity.com/paper/2506.19865/) (2025)
- [SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modeling](https://mlsanity.com/paper/2507.11818/) (2025)
- [Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matching](https://mlsanity.com/paper/2512.18184/) (2025)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching](https://mlsanity.com/paper/2512.12198/) (2025)
- [Clifford Group Equivariant Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2504.15773/) (2025)
- [Simplex-to-Euclidean Bijections for Categorical Flow Matching](https://mlsanity.com/paper/2510.27480/) (2025)
- [3D Molecule Generation from Rigid Motifs via SE(3) Flows](https://mlsanity.com/paper/2601.16955/) (2026)

## Abstract (arXiv)

Deep generative models that produce novel molecular structures have the potential to facilitate chemical discovery. Diffusion models currently achieve state of the art performance for 3D molecule generation. In this work, we explore the use of flow matching, a recently proposed generative modeling framework that generalizes diffusion models, for the task of de novo molecule generation. Flow matching provides flexibility in model design; however, the framework is predicated on the assumption of continuously-valued data. 3D de novo molecule generation requires jointly sampling continuous and categorical variables such as atom position and atom type. We extend the flow matching framework to categorical data by constructing flows that are constrained to exist on a continuous representation of categorical data known as the probability simplex. We call this extension SimplexFlow. We explore the use of SimplexFlow for de novo molecule generation. However, we find that, in practice, a simpler approach that makes no accommodations for the categorical nature of the data yields equivalent or superior performance. As a result of these experiments, we present FlowMol, a flow matching model for 3D de novo generative model that achieves improved performance over prior flow matching methods, and we raise important questions about the design of prior distributions for achieving strong performance in flow matching models. Code and trained models for reproducing this work are available at https://github.com/dunni3/FlowMol