Research map / Probabilistic and scientific modeling / Variational and generative sampling
Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model
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Proposes A2A-FM, a flow-matching condition transfer model that learns all-to-all pairwise optimal transports from general (including non-grouped, continuous-condition) data via a joint OT coupling with a condition-distance penalty.
Problem
Learning all-to-all condition transfer maps between conditional distributions when conditions are continuous and each condition has few samples (non-grouped data), where existing all-to-all methods require grouped data.
Approach
A minibatch OT coupling with a cost that adds beta-weighted squared distances between both source and target conditions, so that as beta and N grow the coupling converges to pairwise OT for almost every condition pair; the coupled pairs train a (c1,c2)-conditioned flow matching vector field.
Key results
- On QED nearby sampling, A2A-FM reaches 97.5% success versus 95.6% for COATI-LDM (the best baseline listed).
- On LogP-TPSA, A2A-FM achieves AUC 0.990 versus 0.819 for OT-CFM and 0.583 for SI (K=10).
- On synthetic non-grouped data, A2A-FM's MSE from pairwise OT is 1.51e-2 versus 4.90e-2 for Multimarginal SI and 6.77e-2 for partial diffusion.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use A2A-FM coupling instead of generalized geodesic coupling | Synthetic grouped data · Synthetic grouped data | MSE from pairwise OT: (1.03±0.04)× 10⁰ -> (5.81± 2.22)×10⁻² | Helped |
| Use A2A-FM instead of partial diffusion | Synthetic non-grouped data · Synthetic non-grouped data | MSE from pairwise OT: (6.77± 0.14)× 10⁻² -> (1.51± 0.17)×10⁻² | Helped |
| Use A2A-FM instead of Multimarginal SI | Synthetic non-grouped data · Synthetic non-grouped data | MSE from pairwise OT: (4.90± 0.28)× 10⁻² -> (1.51± 0.17)×10⁻² | Helped |
| Use A2A-FM for nearby sampling instead of MolMIM | Nearby sampling · Nearby sampling | Success (%): 94.6 -> 97.5 | Helped |
| Use A2A-FM for nearby sampling instead of COATI-LDM | Nearby sampling · Nearby sampling | Success (%): 95.6 -> 97.5 | Helped |
| Use A2A-FM instead of OT-CFM | LogP-TPSA · LogP-TPSA | AUC: 0.819 -> 0.990 | Helped |
| Enforce antisymmetry in the vector field (ablation) | A2A-FM · QED optimization | Success rate: 94.6% -> 97.5% | Helped |
Surprising findings
- Adding an antisymmetry constraint on the vector field raised QED success from 94.6% to 97.5%.
- Directly replacing a single condition with (c1,c2) in conditional OT fails to learn maps between distinct conditions.
Limitations
- Trade-off in beta: large beta approximates pairwise OT poorly, small beta reduces terminal precision; beta chosen heuristically as N^(1/(2d_c))
- Theoretical convergence holds only in the infinite-sample, large-beta limit; cyclic consistency not enforced
Experimental setup
Datasets: ZINC22 (500K subset) synthetic Gaussian mixtures synthetic 2D polar quadrant data LogP-TPSA benchmark initial molecules (1,024 from ZINC22)
Benchmarks: QED optimization (nearby sampling) LogP-TPSA sampling efficiency synthetic pairwise OT MSE
Metrics: success rate (%) AUC of Pr(c_err) vs Pr(Tanimoto) MSE from pairwise OT
Baselines: Partial diffusion with classifier-free guidance Multimarginal SI OT-CFM DESMILES QMO MolMIM COATI-LDM
Builds on: OT-CFM conditional optimal transport Multimarginal stochastic interpolants partial diffusion flow matching
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