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3D Molecule Generation from Rigid Motifs via $\mathrm{SE}(3)$ Flows

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Diffusion for molecular conformations

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Proposes MotiFlow, which generates 3D molecules as sets of SE(3) rigid motifs with multimodal flow matching (SE(3) flow for frames, discrete masking flow for motif types), reaching state-of-the-art atom stability on GEOM-Drugs with 100 steps.

Problem

Existing 3D molecule generators operate on individual atoms with many sampling steps and discard chemical modularity; fragment-based approaches are well established for 2D graphs but underexplored in 3D.

Approach

Represent molecules as sets of rigid-body motifs (frames in SE(3) plus a discrete motif type from a data-driven vocabulary with symmetry groups), and jointly generate them with an SE(3) flow for poses and a discrete masking flow for motif identities, using a FoldFlow-based IPA backbone.

Key results

• On GEOM-Drugs with 100 steps, MotiFlow reaches 95.0% atom stability versus 87.2% for END (best baseline), with V x C 81.2%.
• On QM9 unconditional generation with 100 steps, MotiFlow achieves 92.6% molecular stability versus 90.9% for GeoBFN at 1000 steps.
• On QM9 composition-conditioned generation, cMotiFlow reaches 95.4% matching versus 91.5% for cEND at 500 steps.

Surprising findings

• Coarser planar-ring fragmentation gives higher atom stability, but uncommon motifs are undersampled as the vocabulary threshold decreases.
• On QM9, MotiFlow has lower uniqueness (V x U 86.3%) than the best atom-based baseline EquiFM (93.5%).

Limitations

• Predefined motif vocabulary trades off vocabulary size against coverage of rare substructures.
• Does not model the 2D bond graph beyond intra-motif connectivity, so it is not compared to joint 2D/3D methods.
• Reliance on bond inference from interatomic distances for evaluation; molecular stability not reported on GEOM-Drugs.

Experimental setup

Datasets: QM9 GEOM-Drugs QMugs

Benchmarks: QM9 GEOM-Drugs QMugs

Metrics: atom stability molecular stability validity validity x uniqueness validity x connectivity total variation strain energy SA QED composition matching

Baselines: EDM EDM-Bridge GeoLDM EquiFM END EDM* GeoBFN cEDM EEGSDE cEND

Builds on: FoldFlow Riemannian flow matching multimodal flow discrete flow matching GeoDiff EDM

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