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Straight-Line Diffusion Model for Efficient 3D Molecular Generation
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Proposes the Straight-Line Diffusion Model (SLDM), a diffusion process with schedule x_t=(1-t)x_0+σε whose ODE trajectory is near-linear, enabling accurate sampling with very few steps for 3D molecule generation.
Problem
Diffusion-based 3D molecular generation needs many sampling steps (e.g., ~1000) to reach high molecular stability, because first-order ODE sampling truncation error is large when trajectories are curved.
Approach
Reformulate the diffusion schedule (mu(t)=1-t/T, small constant sigma) so the ODE trajectory is near-linear (second derivative ~0), letting plain Euler steps tolerate large step sizes; add a Langevin-corrected sampler with time-annealed temperature.
Key results
- On QM9 unconditional generation, SLDM (T=1000) reaches 95.42% molecule stability versus 90.87% for GeoBFN (T=1000).
- SLDM with T=50 reaches 93.37% molecule stability on QM9, and the paper reports about 100x faster sampling than EDM and roughly 70x over GeoBFN and EquiFM.
- On GEOM-Drugs, SLDM (T=50) achieves 89.03% atom stability versus 85.60% for GeoBFN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the SLDM straight-line diffusion schedule instead of GeoBFN | Unconditional QM9 molecule generation · QM9 | molecule stability (%): 90.87 -> 93.37 | Helped |
| Use the SLDM straight-line diffusion schedule instead of GeoBFN | Unconditional QM9 molecule generation · QM9 | validity (%): 95.31 -> 96.24 | Helped |
| Use the SLDM straight-line diffusion schedule instead of GeoBFN | Unconditional QM9 molecule generation · QM9 | V*U (%): 92.96 -> 93.63 | Helped |
| Use SLDM with 50 sampling steps instead of GeoBFN with 1000 steps | Unconditional QM9 molecule generation · QM9 | molecule stability (%): 90.87 -> 93.37 | Helped |
| Use the SLDM schedule instead of the best baseline | Unconditional GEOM-Drugs molecule generation · GEOM-Drugs | atom stability (%): 87.0 -> 89.03 | Helped |
| Use the SLDM schedule instead of the best baseline | Unconditional GEOM-Drugs molecule generation · GEOM-Drugs | validity (%): 99.3 -> 99.57 | Helped |
| Use SLDM sampling instead of EDM sampling | Unconditional molecular generation · QM9 | sampling efficiency: 100-fold | Helped |
| Use SLDM sampling instead of GeoBFN or EquiFM sampling | Unconditional molecular generation · QM9 | sampling efficiency: around 70× | Helped |
| Use SLDM for conditional generation instead of previous state-of-the-art methods | Conditional QM9 molecule generation · QM9 | sampling efficiency: 20-fold | Helped |
Surprising findings
- Skipping the t=1 sampling step had no noticeable harm, which the authors attribute to Langevin dynamics providing error correction and results being robust to prior variance.
Limitations
- Initial sampling steps deviate from a straight line, introducing sampling error that is mitigated only by Langevin correction.
- Choice of sigma and temperature schedule are empirical; the theory only guarantees near-linearity as sigma goes to zero and sigma(0) is not exactly zero.
- Atom types are predicted from generated coordinates via UniGEM rather than generated jointly.
Experimental setup
Datasets: QM9 GEOM-Drugs
Benchmarks: QM9 GEOM-Drugs
Metrics: atom stability molecule stability validity V*U MAE
Baselines: E-NF G-Schnet EDM GDM EDM-Bridge GeoLDM EquiFM GeoBFN END
Builds on: EDM flow matching Bayesian flow networks EquiFM GeoBFN
Closest papers by meaning
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.89)
- NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation (ICLR 2025 · similarity 0.88)
- Equivariant Neural Diffusion for Molecule Generation (NeurIPS 2024 · similarity 0.87)
- Sampling 3D Molecular Conformers with Diffusion Transformers (NeurIPS 2025 · similarity 0.87)
- Conditional Synthesis of 3D Molecules with Time Correction Sampler (NeurIPS 2024 · similarity 0.87)
- Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.86)
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