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Learning 3D Anisotropic Noise Distributions Improves Molecular Force Fields
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Proposes AniDS, a coordinate-denoising framework that generates atom-specific full covariance (anisotropic, heteroscedastic) Gaussian noise via a structure-aware VAE-style noise generator, improving molecular force field prediction on MD17 and OC22.
Problem
Existing coordinate denoising for 3D molecular pretraining assumes isotropic and homoscedastic atomic motions, which oversimplifies molecular dynamics and limits force field learning.
Approach
Generate per-atom full covariance matrices as an isotropic base minus pairwise anisotropic corrections (built from learned pairwise weights and bond directions), guaranteeing symmetry, positive semi-definiteness, and SO(3)-equivariance, and train a denoising autoencoder with a score-matching-style loss linked to force fields.
Key results
- On MD17 force prediction, AniDS (Lmax=2) achieves average MAE 0.072 kcal/mol, an 8.9% relative improvement over DeNS (Lmax=3).
- On OC22 S2EF-Total validation, EquiformerV2 + AniDS reaches force F-MAE 22.4 meV/Å avg (+6.2% over DeNS) and energy E-MAE 447.7 meV (+3.2%).
- Ablation on aspirin (pretrain+finetune) shows force MAE 0.1118 for AniDS vs 0.1178 for DeNS and 0.1143 for DenoiseVAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use structure-aware anisotropic noise instead of DeNS isotropic noise | EquiformerV2 · MD17 test (Avg) | force MAE: 0.079 -> 0.072 | Helped |
| Add AniDS auxiliary denoising instead of DeNS | EquiformerV2 · OC22 S2EF-Total validation (Force Avg) | force F-MAE: 23.89 -> 22.4 | Helped |
| Add AniDS auxiliary denoising instead of DeNS | EquiformerV2 · OC22 S2EF-Total validation (Energy Avg) | energy E-MAE: 462.3 -> 447.7 | Helped |
| Add AniDS auxiliary denoising instead of DeNS | EquiformerV2 · rMD17 Benzene | force MAE: 2.28 -> 2.31 | Hurt |
| Add AniDS auxiliary denoising instead of DeNS | EquiformerV2 · rMD17 Toluene | force MAE: 11.37 -> 10.7 | Helped |
| Add AniDS auxiliary denoising instead of DeNS | EquiformerV2 · rMD17 Uracil | force MAE: 34.46 -> 28.8 | Helped |
| Add AniDS auxiliary training instead of DeNS | EquiformerV2 · ALEXANDRIA test (MPtrj-trained) | force MAE: 0.0134 -> 0.0124 | Helped |
| Use subtractive rather than additive anisotropic correction (ablation) | EqV2-AniDS · MD17 Aspirin | force MAE: 0.1128 -> 0.1118 | Helped |
| Add anisotropic noise rather than isotropic DeNS noise (ablation) | EquiformerV2 pretraining · MD17 Aspirin | force MAE: 0.1178 -> 0.1118 | Helped |
| Add atom-adaptive isotropic noise instead of fixed-scale isotropic noise (ablation) | EquiformerV2 pretraining · MD17 Aspirin | force MAE: 0.1178 -> 0.1143 | Helped |
| Add denoising auxiliary loss during fine-tuning (ablation) | EqV2-AniDS · MD17 Aspirin | force MAE: 0.1369 -> 0.1118 | Helped |
| Set σp=0.1 rather than σp=0.5 (ablation) | AniDS · MD17 Aspirin | force MAE: 0.13018 -> 0.11180 | Helped |
Limitations
- Models only pairwise atomic correlations and does not capture higher-order (three-body or more) coupled motions.
- Approximates force field learning via noise distribution modeling; requires supervised force learning for high accuracy.
- Needs KL-based pre-training of the noise generator for stability in some settings.
Experimental setup
Datasets: PCQM4Mv2 MD17 rMD17 MD22 OC22 MPtrj ALEXANDRIA
Benchmarks: MD17 OC22 S2EF-Total rMD17 MPtrj (tested on ALEXANDRIA subset)
Metrics: force MAE energy MAE stress MAE
Baselines: SchNet DimeNet PaiNN TorchMD-NET NequIP SE(3)-DDM Frad Slide DeNS DenoiseVAE GemNet-OC E2former
Builds on: DenoiseVAE DeNS EquiformerV2 GeoMFormer Coordinate denoising
Closest papers by meaning
- Sliced Denoising: A Physics-Informed Molecular Pre-Training Method (ICLR 2024 · similarity 0.90)
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.87)
- 3D Denoisers Are Good 2D Teachers: Molecular Pretraining via Denoising and Cross-Modal Distillation (AAAI 2025 · similarity 0.86)
- Structure-based drug design by denoising voxel grids (ICML 2024 · similarity 0.86)
- SubgDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learning (NeurIPS 2024 · similarity 0.85)
- Few-Step Cofolding with All-Atom Flow Maps (NeurIPS 2026 · similarity 0.84)
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