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SymDrift: One-Shot Generative Modeling under Symmetries

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

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Proposes SymDrift, a symmetry-aware drifting model for one-shot generation of symmetric molecular distributions (conformers, transition states), using either Kabsch-based alignment of drift pairs or a G-invariant type-resolved distance embedding.

Problem

Drifting models assume a well-defined target distribution, but for G-invariant physical systems trained on non-invariant empirical data, equivariant generators do not reproduce the drift of the symmetrized target, and enforcing symmetry naively is costly.

Approach

Make the drifting field itself symmetry-aware: (i) align each generated/target pair via optimal rotation (Kabsch) and permutation before computing the kernel drift, and (ii) compute the drift in a G-invariant embedding of sorted type-resolved pairwise distances, avoiding explicit group averaging.

Key results

• On GEOM-QM9 (delta 0.5 Å), SymDrift with DiTMC+airPE (B) achieves the best AMR-P mean 0.124 Å and coverage-P 93.7% among one-step methods, at 1.4 ms inference.
• On GEOM-DRUGS, SymDrift (DiTMC+airPE L) reaches the best one-step precision metrics (coverage-P 63.2%, AMR-P 0.676 Å) with 0.7 ms inference.
• On RDB7 transition states, SymDrift with GoFlow (L) architecture achieves RMSD mean 0.328 Å in 1.3 ms, matching the 25-step GoFlow baseline (0.328 Å) and far outperforming one-step TSGen (0.782 Å).

Surprising findings

• Applying the base coordinate drift to an equivariant architecture causes complete training collapse, giving 0% coverage at 0.5 Å.
• Theorem shows that the drift from an equivariant generator on the unsymmetrized empirical distribution generally differs from the drift of the symmetrized target.

Limitations

• Training is slower because of hierarchical class sampling and pairwise alignment or embedding overhead.
• The sorted type-resolved distance embedding is invariant but not injective; it can alias distinct conformers (11.3% of QM9 molecules with type-based orbits).
• Recall metrics on GEOM-Drugs lag multi-step baselines such as MCF and ET-Flow.

Experimental setup

Datasets: GEOM-QM9 GEOM-Drugs RDB7

Benchmarks: GEOM-QM9 GEOM-Drugs RDB7

Metrics: Coverage (recall/precision) AMR (recall/precision) RMSD DMAE inference time

Baselines: GeoDiff MCF ET-Flow OrbDiff DiTMC GeoMol AvgFlow EnFlow TsDiff GoFlow TSGen

Builds on: drifting models ET-Flow DiTMC GoFlow Kabsch algorithm

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