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.
View on arXiv@article{shen2025_2504.08051,
title={ Compositional Flows for 3D Molecule and Synthesis Pathway Co-design },
author={ Tony Shen and Seonghwan Seo and Ross Irwin and Kieran Didi and Simon Olsson and Woo Youn Kim and Martin Ester },
journal={arXiv preprint arXiv:2504.08051},
year={ 2025 }
}