# Compositional Flows for 3D Molecule and Synthesis Pathway Co-design

arXiv: https://arxiv.org/abs/2504.08051 · HTML: https://mlsanity.com/paper/2504.08051/

## Key facts

- Cited by 6 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 42 of its 76 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## 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 42)

- [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)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [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)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Generating 3D Molecules Conditional on Receptor Binding Sites with Deep Generative Models](https://mlsanity.com/paper/2110.15200/) (2021)
- [The Synthesizability of Molecules Proposed by Generative Models](https://mlsanity.com/paper/2002.07007/) (2020)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2309.17296/) (2023)
- [TEDi: Temporally-Entangled Diffusion for Long-Term Motion Synthesis](https://mlsanity.com/paper/2307.15042/) (2023)
- [MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space](https://mlsanity.com/paper/2404.12141/) (2024)

## Built on by (most cited first, 6 of 6)

- [SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modeling](https://mlsanity.com/paper/2507.11818/) (2025)
- [A Genetic Algorithm for Navigating Synthesizable Molecular Spaces](https://mlsanity.com/paper/2509.20719/) (2025)
- [Synthesizable Molecular Generation via Soft-constrained GFlowNets with Rich Chemical Priors](https://mlsanity.com/paper/2602.04119/) (2026)
- [Generating Developable 3D Molecules via Pocket-Conditioned Diffusion and Property-Aware Optimization](https://mlsanity.com/paper/2607.12349/) (2026)
- [SynLaD: Latent Diffusion for Generating Synthesizable Molecules Conditioned on 3D Pharmacophore Profiles](https://mlsanity.com/paper/2607.01105/) (2026)
- [DBMol: Design of High-Affinity, Target-Specific Small Molecules through Structure Prediction Models](https://mlsanity.com/paper/2607.19237/) (2026)

## Abstract (arXiv)

Many generative applications, such as synthesis-based 3D molecular design, involve constructing compositional objects with continuous features. Here, we introduce Compositional Generative Flows (CGFlow), a novel framework that extends flow matching to generate objects in compositional steps while modeling continuous states. Our key insight is that modeling compositional state transitions can be formulated as a straightforward extension of the flow matching interpolation process. We further build upon the theoretical foundations of generative flow networks (GFlowNets), enabling reward-guided sampling of compositional structures. We apply CGFlow to synthesizable drug design by jointly designing the molecule's synthetic pathway with its 3D binding pose. Our approach achieves state-of-the-art binding affinity on all 15 targets from the LIT-PCBA benchmark, and 5.8× improvement in sampling efficiency compared to 2D synthesis-based baseline. To our best knowledge, our method is also the first to achieve state of-art-performance in both Vina Dock (-9.38) and AiZynth success rate (62.2%) on the CrossDocked benchmark.