ReCurveflow: A Flow Matching Framework that Learns Curved Reaction Trajectories to Predict Transition State Geometries

Seungheun Baek; Mogan Gim; Jaewoo Kang

cs.AIAug 21, 2026

ReCurveflow: A Flow Matching Framework that Learns Curved Reaction Trajectories to Predict Transition State Geometries

Authors: Seungheun Baek, Mogan Gim, Jaewoo Kang

Organizations: Department of Computer Science Korea University Seoul, South Korea · Department of Biomedical Engineering Hankuk University of Foreign Studies Yongin, South Korea

Abstract

Predicting transition states (TS) in chemical reactions is crucial, as they provide insights into reaction mechanisms. Recent work on TS prediction have focused on flow matching supervised on straight linear paths that do not align with actual reaction trajectories. We propose a novel flow matching-based framework ReCurveflow that learns to predict TS geometries supervised on continuously curved reference paths interpolated from a full NEB-derived band of molecular geometries. We also introduce off-path correction, which grants ReCurveflow with the ability to produce corrective velocity fields when engaged off-path geometry states during inference rollout, leading to better resistance against exposure bias and accuracy in TS prediction. Across three data splits and six evaluation metrics, ReCurveflow achieves the best result on the majority of split-metric combinations against seven baselines. Qualitative analyses further show that ReCurveflow generates reaction trajectories with energy profiles that closely track the reference NEB path, provides initializations that ease the NEB optimization bottleneck, and exhibits the intended corrective behavior in its learned velocity fields. The ReCurveflow codebase is publicly available at https://github.com/dmis-lab/ReCurveflow.

Figures & tables

Split	Model	RMSD $\downarrow$ (Å)	RMSD $\circ$ $\downarrow$ (Å)	D-MAE $\downarrow$ (Å)	Angle MAE $\downarrow$ ( ∘ )	Dihedral MAE $\downarrow$ ( ∘ )	Steric Clashes $\downarrow$
Native	ReCurveflow ( ours )	0.1423 $\pm$ 0.0029	0.1430 $\pm$ 0.0025	0.0953 $\pm$ 0.0023	3.6726 $\pm$ 0.1665	16.3456 $\pm$ 0.3813	0.0515 $\pm$ 0.0218
	FragmentFlow	0.2947 $\pm$ 0.0039	0.2952 $\pm$ 0.0037	0.1250 $\pm$ 0.0014	5.6060 $\pm$ 0.0817	19.1161 $\pm$ 0.4772	0.1052 $\pm$ 0.0029
	React-OT	0.3181 $\pm$ 0.0208	0.3195 $\pm$ 0.0197	0.1347 $\pm$ 0.0090	6.0807 $\pm$ 0.3202	20.6216 $\pm$ 1.4188	0.1261 $\pm$ 0.0114
	GoFlow	0.3320 $\pm$ 0.0175	0.6111 $\pm$ 0.0138	0.1108 $\pm$ 0.0072	3.7314 $\pm$ 0.3844	48.2212 $\pm$ 1.4943	0.0892 $\pm$ 0.0031
	MolGen	0.2748 $\pm$ 0.0298	0.6240 $\pm$ 0.0746	0.0975 $\pm$ 0.0113	3.4853 $\pm$ 0.4585	47.4763 $\pm$ 2.0883	0.0920 $\pm$ 0.0161
	MEPIN	0.3788 $\pm$ 0.0032	0.3944 $\pm$ 0.0215	0.1591 $\pm$ 0.0024	6.4861 $\pm$ 0.1579	23.6957 $\pm$ 0.1985	0.0439 $\pm$ 0.0115

Table 1: Transition state prediction results on different data splits. Lower is better for all metrics. The best and second-best results are highlighted in bold and underlined, respectively.

Model	RMSD	D-MAE	Angle MAE	Dihedral MAE	Steric
ReCurveflow	0.1423 (0.0029)	0.0953 (0.0023)	3.6726 (0.1665)	16.3456 (0.3813)	0.0515 (0.0218)
w/o POPC	0.1510 (0.0051)	0.0999 (0.0047)	3.8442 (0.1939)	17.2167 (0.7750)	0.0861 (0.0075)
w/o ROPC	0.1538 (0.0023)	0.1071 (0.0021)	4.3021 (0.0955)	17.6225 (0.2269)	0.0924 (0.0117)
w/o both	0.1680 (0.0030)	0.1261 (0.0035)	5.4284 (0.1811)	19.1725 (0.5580)	0.1042 (0.0168)

Table 2: Ablation study on Off-Path Self-Correction.

Figure 2: Comparison between ReCurveflow and ReCurveflow w/o OS based on energy profiles.

Figure 3: Comparison of NEB optimization from different initializations.

Figure 4: Analysis on Off-Path Correction Dynamics

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Group	Hyperparameter	Value
Architecture	layers / hidden dim / cutoff	6 / 512 / 6 Å
	max neighbors	32
Gaussian tube	$\sigma$ / $\sigma_{\mathrm{fl}}$	0.05 / 0.05
Off-Path Correction	$k$ / $\lambda$	10 / 0.5
Rollout	$K$ / $\beta$ / $\sigma_{\mathrm{a}}$	25 / 0.5 / 0.1
Bidirectional ensemble	$p_{\mathrm{swap}}$	0.5

Appendix

Table 3: Hyperparameters used for training ReCurveflow.

Metric	Ours	w/o OS
Path RMSD ( $\downarrow$ )	0.101	0.129
R/P RMSD ( $\downarrow$ )	0.013	0.058
Barrier Overshoot ( $\downarrow$ )	2.38	9.26
R/P Energy Error ( $\downarrow$ )	0.055	1.90

Appendix

Table 4: Effect of On-Trajectory State (OS) images on generated reaction paths. Lower is better for all metrics.

Figure 5: Case study on reaction rxn0347.

Figure 6: Case study on reaction rxn2550.

Figure 7: Case study on reaction rxn4520.

Figure 8: Case study on reaction rxn5687.

Panel of Figure 9 — Figure 9: Kinetics-guided reaction design. (a) Activation-barrier ranking is feasible only when valid transition-state geometries are obtained for both candidate reactions. ReCurveflow generates valid transition states substantially more often than previous methods, enabling reliable pathway ranking. (b) Representative reaction group producing the same product. ReCurveflow accurately predicts both transition-state geometries and correctly identifies the lower-barrier pathway, whereas the baselines fail to obtain a valid transition state for at least one reaction.

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Kaipeng Zeng, Wenxi Zhai, Shengrui Xu, Jie Zhao+4

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Quantum Chemistry Molecular Generation Flow Matching

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Transition-state (TS) structures define the energetic barriers and mechanistic pathways of elementary chemical reactions, yet their identification remains computationally demanding because conventional saddle-point searches require expensive quantum-mechanical calculations. Recent machine-learning approaches have accelerated TS generation by predicting structures from reaction endpoint information, but they primarily learn geometric correspondence between endpoints and TSs, leaving the structural transformations underlying elementary reactions implicitly represented. To address this limitation, we introduce TransTS, a reaction-transformation-aware framework for generalizable TS generation from atom-mapped reactant-product pairs. TransTS explicitly learns atom-level structural transformations between reaction endpoints and integrates them with a unified atom-aligned geometric representation of reactants, TSs and products, enabling reaction-aware equivariant generation of TS geometries. TransTS is designed to provide reliable TS initial guesses for subsequent quantum-chemical refinement, where generated structures are evaluated not only by geometric similarity but also by their ability to converge to validated saddle points and recover the intended reaction pathways. Across IID and zero-shot OOD benchmarks, TransTS demonstrates improved TS initialization quality, with particularly strong generalization to unseen reaction distributions. On the challenging GDB-10-rxn and GDB-17-rxn OOD benchmarks, TransTS generates TS candidates that more frequently converge to validated saddle points and recover the intended elementary reactions after refinement than existing approaches under the same training regime. Scaling reaction coverage and model capacity further improves both geometric fidelity and refinement outcomes.

Abstract

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