# Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Design

arXiv: https://arxiv.org/abs/2310.05764 · HTML: https://mlsanity.com/paper/2310.05764/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 76 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [PiFold: Toward effective and efficient protein inverse folding](https://mlsanity.com/paper/2209.12643/) (2022)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Graph Denoising Diffusion for Inverse Protein Folding](https://mlsanity.com/paper/2306.16819/) (2023)
- [State-specific protein-ligand complex structure prediction with a multi-scale deep generative model](https://mlsanity.com/paper/2209.15171/) (2022)
- [E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking](https://mlsanity.com/paper/2210.06069/) (2022)
- [Trans-Dimensional Generative Modeling via Jump Diffusion Models](https://mlsanity.com/paper/2305.16261/) (2023)

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

- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [Transferable Boltzmann Generators](https://mlsanity.com/paper/2406.14426/) (2024)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (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)
- [Applications of Modular Co-Design for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2505.18392/) (2025)
- [High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction](https://mlsanity.com/paper/2505.18817/) (2025)
- [dyAb: Flow Matching for Flexible Antibody Design with AlphaFold-driven Pre-binding Antigen](https://mlsanity.com/paper/2503.01910/) (2025)
- [Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension](https://mlsanity.com/paper/2411.18463/) (2024)
- [FlowDock: Geometric Flow Matching for Generative Protein-Ligand Docking and Affinity Prediction](https://mlsanity.com/paper/2412.10966/) (2024)
- [BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation](https://mlsanity.com/paper/2507.00846/) (2025)
- [Compositional Flows for 3D Molecule and Synthesis Pathway Co-design](https://mlsanity.com/paper/2504.08051/) (2025)
- [EnzymeFlow: Generating Reaction-specific Enzyme Catalytic Pockets through Flow Matching and Co-Evolutionary Dynamics](https://mlsanity.com/paper/2410.00327/) (2024)
- [Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials](https://mlsanity.com/paper/2602.22251/) (2026)
- [Energy-Based Flow Matching for Generating 3D Molecular Structure](https://mlsanity.com/paper/2508.18949/) (2025)
- [Flow Autoencoders are Effective Protein Tokenizers](https://mlsanity.com/paper/2510.00351/) (2025)
- [SigmaDock: Untwisting Molecular Docking With Fragment-Based SE(3) Diffusion](https://mlsanity.com/paper/2511.04854/) (2025)
- [Path Gradients after Flow Matching](https://mlsanity.com/paper/2505.10139/) (2025)
- [3D Molecule Generation from Rigid Motifs via SE(3) Flows](https://mlsanity.com/paper/2601.16955/) (2026)
- [Fast Organic Crystal Structure Prediction with Unit Cell Flow Matching](https://mlsanity.com/paper/2606.03199/) (2026)
- [Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2506.06305/) (2025)
- [Efficient Antibody Structure Refinement Using Energy-Guided SE(3) Flow Matching](https://mlsanity.com/paper/2410.16673/) (2024)
- [PROflow: An iterative refinement model for PROTAC-induced structure prediction](https://mlsanity.com/paper/2405.06654/) (2024)
- [Efficient Generation of Molecular Clusters with Dual-Scale Equivariant Flow Matching](https://mlsanity.com/paper/2410.07539/) (2024)
- [polyGen: A Learning Framework for Atomic-level Polymer Structure Generation](https://mlsanity.com/paper/2504.17656/) (2025)
- [Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery](https://mlsanity.com/paper/2512.22597/) (2025)
- [Contrastive-Augmented Flow Matching for Style-Content Disentanglement](https://mlsanity.com/paper/2607.12404/) (2026)
- [Equivariant Flow Matching for Electron Density Prediction](https://mlsanity.com/paper/2610.02651/) (2026)

## Abstract (arXiv)

A significant amount of protein function requires binding small molecules, including enzymatic catalysis. As such, designing binding pockets for small molecules has several impactful applications ranging from drug synthesis to energy storage. Towards this goal, we first develop HarmonicFlow, an improved generative process over 3D protein-ligand binding structures based on our self-conditioned flow matching objective. FlowSite extends this flow model to jointly generate a protein pocket's discrete residue types and the molecule's binding 3D structure. We show that HarmonicFlow improves upon state-of-the-art generative processes for docking in simplicity, generality, and average sample quality in pocket-level docking. Enabled by this structure modeling, FlowSite designs binding sites substantially better than baseline approaches.