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Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transport

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Diffusion for molecular conformations · 0 citations (OpenAlex)

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Proposes MORPH, a flexible-size 3D geometric-graph generative model that inserts, deletes, substitutes atoms and moves positions via jump-flow matching with unbalanced optimal transport alignment, matching fixed-size SOTA on QM9/GEOM-Drugs while enabling size steering and scaffold decoration.

Problem

Existing 3D molecular diffusion and flow models fix the number of atoms during generation, limiting steerability toward size-linked properties, OOD generation, and use of structural priors such as scaffolds.

Approach

Extends Edit Flows and generator matching to 3D geometric graphs with jump-flow dynamics that allow multiple node insertions and deletions plus atom/bond substitutions and continuous position moves, with training paths defined by an unbalanced optimal transport matching (Hungarian on an augmented cost matrix, Kabsch alignment) between prior and data graphs of different sizes.

Key results

• On QM9, MORPH reaches 99.37% molecule stability and 99.41% validity with 100 NFE, matching SemlaFlow (99.7%, 99.4%) and beating other fixed-size baselines on validity.
• On GEOM-Drugs, MORPH reaches 85.66% molecule stability and 85.16% validity, below SemlaFlow's 97.3% and 93.9% respectively.
• Property-conditioned QM9 models keep relatively high validity when conditioned on up to ~40% more atoms than the training maximum, and the scaffold decoration task reaches 92.54% validity.

Surprising findings

• On GEOM-Drugs, MORPH trails fixed-size SemlaFlow substantially in molecule stability and validity despite strong atom stability.
• Training needs about 2.5x more epochs than SemlaFlow to reach comparable QM9 performance.

Limitations

• Training is more expensive and loss balancing is harder due to jump-process terms; loss weights were untuned.
• Evaluation largely confined to QM9; GEOM-Drugs results are preliminary and weaker than baselines.
• CTMC-based sampling requires many integration steps and cannot easily be reduced to few-step generation.

Experimental setup

Datasets: QM9 GEOM-Drugs

Benchmarks: QM9 GEOM-Drugs PoseBusters

Metrics: atom stability molecule stability validity uniqueness novelty NFE PoseBusters checks MAE of logP MAE of QED validity under size conditioning

Baselines: FlowMol MiDi EQGAT-diff SemlaFlow

Builds on: Edit Flows Conditional Generator Matching SemlaFlow Semla

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