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3D Molecule Generation from Rigid Motifs via SE(3) Flows

Roman Poletukhin, Marcel Kollovieh, Eike Eberhard, Stephan Günnemann

TL;DR

This work tackles 3D molecule generation by shifting from atom-centric representations to modular rigid motifs modeled on the SE($3$) manifold. It introduces MotiFlow, a multimodal flow framework that jointly learns discrete motif identities via a CTMC-style discrete flow and continuous motif configurations via SE($3$) flow matching, with canonicalisation and symmetry handling to enable robust generation. Empirically, MotiFlow achieves comparable or superior results to atom-based baselines on QM9 and GEOM-Drugs, while requiring 2–10x fewer generation steps and achieving 3.5x compression in representation; it also demonstrates strong conditional generation capabilities. This approach promises scalable, high-quality 3D molecule generation with practical benefits for drug discovery and materials design, while highlighting future directions in vocabulary design and joint 2D-3D modelling.

Abstract

Three-dimensional molecular structure generation is typically performed at the level of individual atoms, yet molecular graph generation techniques often consider fragments as their structural units. Building on the advances in frame-based protein structure generation, we extend these fragmentation ideas to 3D, treating general molecules as sets of rigid-body motifs. Utilising this representation, we employ SE(3)-equivariant generative modelling for de novo 3D molecule generation from rigid motifs. In our evaluations, we observe comparable or superior results to state-of-the-art across benchmarks, surpassing it in atom stability on GEOM-Drugs, while yielding a 2x to 10x reduction in generation steps and offering 3.5x compression in molecular representations compared to the standard atom-based methods.

3D Molecule Generation from Rigid Motifs via SE(3) Flows

TL;DR

This work tackles 3D molecule generation by shifting from atom-centric representations to modular rigid motifs modeled on the SE() manifold. It introduces MotiFlow, a multimodal flow framework that jointly learns discrete motif identities via a CTMC-style discrete flow and continuous motif configurations via SE() flow matching, with canonicalisation and symmetry handling to enable robust generation. Empirically, MotiFlow achieves comparable or superior results to atom-based baselines on QM9 and GEOM-Drugs, while requiring 2–10x fewer generation steps and achieving 3.5x compression in representation; it also demonstrates strong conditional generation capabilities. This approach promises scalable, high-quality 3D molecule generation with practical benefits for drug discovery and materials design, while highlighting future directions in vocabulary design and joint 2D-3D modelling.

Abstract

Three-dimensional molecular structure generation is typically performed at the level of individual atoms, yet molecular graph generation techniques often consider fragments as their structural units. Building on the advances in frame-based protein structure generation, we extend these fragmentation ideas to 3D, treating general molecules as sets of rigid-body motifs. Utilising this representation, we employ SE(3)-equivariant generative modelling for de novo 3D molecule generation from rigid motifs. In our evaluations, we observe comparable or superior results to state-of-the-art across benchmarks, surpassing it in atom stability on GEOM-Drugs, while yielding a 2x to 10x reduction in generation steps and offering 3.5x compression in molecular representations compared to the standard atom-based methods.
Paper Structure (51 sections, 15 equations, 7 figures, 11 tables)

This paper contains 51 sections, 15 equations, 7 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Background
  4. Flow Matching on $\mathrm{SE}(3)$ Manifold
  5. Geometric Preliminaries
  6. $\mathrm{SE}(3)$ Flow Matching
  7. Discrete Flows
  8. CTMC Dynamics
  9. Discrete Flow Matching
  10. Method
  11. Rigid-Motif Decomposition
  12. Canonicalisation and Vocabulary
  13. Multimodal Flow on $\mathrm{SE}(3)^K \times \mathcal{V}_m^K$
  14. Continuous Dynamics
  15. Discrete Dynamics
  16. ...and 36 more sections

Figures (7)

  • Figure 1: Molecule $\bm{\mathcal{M}}$ is generated from motifs $\mathcal{M}$ in a joint flow on the product space of rigid frames $\mathbf{T}$ and motif classes $m$.
  • Figure 2: Comparison of molecular representations on QMugs dataset qmugs. Fragmentation is reported for $\alpha = 0.1$.
  • Figure 3: Examples of results for the conditional tasks on QM9: atom composition (left) and fingerprint substructure (right).
  • Figure 4: Resulting sets of rigid motifs for a GEOM-Drugs molecule $\text{C}_{17}\text{H}_{15}\text{N}_{3}\text{O}_{4}\text{S}$ under different fragmentation strategies.
  • Figure 5: Comparison of sampled motif types to their frequencies in the training distribution of QMugs. A ratio of 1 is optimal.
  • ...and 2 more figures