Organizations: School of Computer Science & School of Artificial Intelligence, Shanghai Jiao Tong University, Shanghai, 200240, Shanghai, China. · Shanghai Innovation Institute, Shanghai, 200231, Shanghai, China. · School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei, 230026, Anhui, China. · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou, 215123, Jiangsu, China. · School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200262, Shanghai, China. · School of Mathematical Sciences, Key Laboratory of MEA, and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, Shanghai, China.
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.
Figures & tables
Figure 1: Overview of TransTS for reaction-transformation-aware transition-state generation and validation. The framework integrates reaction-transformation-aware representation learning, conditional transition-state generation and quantum-chemical validation. a , Training and generalization setting. TransTS is trained under IID settings using Transition1x or the enlarged Transition1x+RGD1 dataset, and evaluated on the corresponding Transition1x test set as well as zero-shot OOD reaction datasets, including GDB-10-rxn and GDB-17-rxn. b , TransTS framework. Atom-mapped reactant and product structures are first encoded into reaction-transformation-aware representations to capture atom-wise structural changes between reaction endpoints. The extracted reaction context is subsequently injected into an anchor-aligned conditional flow matching framework, which evolves noisy initial states into transition-state geometries. c , Transition-state validation. Generated structures are first evaluated by pre-optimization geometric accuracy using RMSD against reference transition states. Quantum-chemical refinement is then performed through saddle-point optimization and intrinsic reaction coordinate analysis, where optimization-success and reaction-correctness rates quantify first-order saddle-point identification and recovery of the intended elementary reaction, respectively.
Figure 2: Model architecture for reaction-transformation-aware TS generation. The architecture is organized into a reaction-transformation-aware dual encoder, a time-conditioned equivariant TS generator, and two expanded interaction modules. In the upper-left block, atom-mapped reactant and product conformations are encoded by shared-parameter branches, with Cross-State Fusion exchanging information between corresponding atoms to make endpoint-dependent structural changes explicit. In the lower-left block, the generator evolves the noisy TS representation as a generation state and conditions it on the encoded reactant and product contexts through symmetric Reaction-Context Injection. The right-side blocks expand the two key interactions: Cross-State Fusion updates endpoint state representations using counterpart context representations, whereas Reaction-Context Injection integrates reactant and product contexts into the TS generation state through scalar FiLM modulation and equivariant vector fusion.
Figure 3: Cross-model IID Transition1x performance with and without RGD1 augmentation. Panels compare TransTS with baseline TS-generation models; T1x denotes the Transition1x dataset. a , Pre-optimization RMSD distributions for models trained on T1x. RMSD is reported against the original Transition1x labels and the post-checked Transition1x subset. Violin plots show per-reaction RMSD distributions; the embedded box spans Q1–Q3, where Q1 and Q3 denote the 25th and 75th percentiles, and the circle marks the median. b , Post-optimization outcome rates for the same T1x-trained models, including invalid, optimization-success, and reaction-correctness rates. c , RMSD distributions after training on T1x+RGD1, shown with the same violin, interquartile-range, and median markers as in a . d , Post-optimization outcome rates after T1x+RGD1 training, using the same outcome definitions as in b .
Figure 4: Zero-shot OOD performance on GDB-10-rxn and GDB-17-rxn. Panels compare TransTS with baseline TS-generation models under the indicated OOD test dataset and training set; T1x denotes the Transition1x dataset. OA-ReactDiff is not shown for GDB-10-rxn after T1x+RGD1 training or for either GDB-17-rxn training setting because it produced no valid structures in these settings. a , Pre-optimization RMSD distributions on GDB-10-rxn and GDB-17-rxn for models trained on T1x or T1x+RGD1. Violin plots show per-reaction RMSD distributions; the embedded box spans Q1–Q3, where Q1 and Q3 denote the 25th and 75th percentiles, and the circle marks the median. b , Post-optimization outcome rates for the same OOD settings, including invalid, optimization-success, and reaction-correctness rates. c , Reaction-correctness counts for TransTS and React-OT stratified by graph-defined B n F m bond-rearrangement class, where n and m denote the numbers of broken and formed bonds, respectively. B0F0 denotes cases without graph-level bond breakage, formation, or bond-order change, but can still include conformational or stereochemical endpoint rearrangements; NO_SMILES and Other follow the stratification protocol in Supplementary Sec. 3.2 .
Figure 5: Scaling behavior from Transition1x to Transition1x+RGD1 training. Panels summarize the change from Transition1x-only training to Transition1x+RGD1 training. a , Scaling behavior on Transition1x, including median RMSD against both the original labels and the post-checked subset, together with post-optimization outcome rates. b , Scaling behavior on the OOD benchmarks, with rows denoting GDB-10-rxn and GDB-17-rxn and columns denoting median RMSD, optimization success and reaction correctness. Paired markers connect each model across the two training regimes, showing both the scaled performance and the corresponding change from the Transition1x-only setting.
Figure 6: Reaction-center structural evolution in zero-shot OOD transition-state generation. a , Structural comparison for two GDB-10-rxn cases. Columns compare the reference transition state, React-OT, MolGEN and TransTS from left to right. Reaction-center atoms and selected interatomic distances are annotated in each structure. Red edges indicate bond cleavage or a bond-order decrease along the reaction coordinate, whereas green edges indicate bond formation or a bond-order increase. b,c , Summaries of selected reaction-core interatomic distances for Sample 1 and Sample 2, respectively. Distances are reported in Å for atom pairs involved in the reaction-core transformation.
Hyperparameter
T1x
T1x+RGD1
Embedding dimension
384
512
Invariant layers
2
3
SE(3) layers
5
6
Attention heads
6
8
Decay factor γ
0.999
0.9993
Warm-up (epochs)
10
20
Supplementary Table 1: Model-specific training settings for the two reported variants. Shared settings are given in the text.
Training set
Model
T1x-original
T1x-clean
GDB-10-rxn
GDB-17-rxn
T1x
OA-ReactDiff Duan et al. (2023)
0.162 [0.061, 0.572]
0.146 [0.061, 0.561]
1.095 [0.922, 1.300]
–
React-OT Duan et al. (2025)
0.100 [0.056, 0.212]
0.098 [0.054, 0.207]
0.401 [0.272, 0.559]
0.485 [0.362, 0.560]
MolGEN Tuo et al. (2026)
0.137 [0.069, 0.251]
0.138 [0.067, 0.254]
0.445 [0.286, 0.673]
1.691 [0.725, 1.974]
TransTS
0.171 [0.097, 0.290]
0.168 [0.091, 0.291]
0.379 [0.270, 0.489]
0.429 [0.336, 0.553]
T1x + RGD1
OA-ReactDiff Duan et al. (2023)
0.092 [0.043, 0.441]
0.084 [0.043, 0.423]
–
–
React-OT Duan et al. (2025)
0.083 [0.047, 0.188]
0.083 [0.046, 0.180]
0.410 [0.245, 0.627]
0.582 [0.418, 0.727]
Supplementary Table 2: Pre-optimization RMSD statistics. Values are median [Q1, Q3] in Å, where Q1 and Q3 denote the 25th and 75th percentiles. T1x-original uses the original Transition1x labels, whereas T1x-clean uses the post-checked clean subset. Lower median RMSD is better. Bold and underlined entries denote the best and second-best results, respectively, within each training setting and metric column.
Training set
Model
T1x
GDB-10-rxn
GDB-17-rxn
Invalid
Success
Correct.
Invalid
Success
Correct.
Invalid
Success
Correct.
T1x
OA-ReactDiff Duan et al. (2023)
0.0
93.7
30.3
64.1
27.5
0.8
–
–
–
React-OT Duan et al. (2025)
0.0
96.5
73.2
0.3
82.9
41.8
6.3
59.2
24.7
MolGEN Tuo et al. (2026)
0.7
92.3
39.4
0.1
72.9
21.4
1.1
20.1
3.4
TransTS
0.0
94.1
71.8
0.1
80.6
55.1
0.6
63.2
37.9
T1x + RGD1
OA-ReactDiff Duan et al. (2023)
0.0
97.2
34.8
100.0
0.0
0.0
–
–
–
Supplementary Table 3: Post-optimization outcome rates (%). Invalid, success and correctness rates are computed over all reactions in each evaluated set. Lower invalid rate is better; higher success and correctness rates are better. Bold and underlined entries denote the best and second-best results, respectively, within each training setting and metric column.
Supplementary Fig. 1: OOD bond-rearrangement class distributions. Reaction counts are shown for the retained graph-defined B n F m classes in GDB-10-rxn and GDB-17-rxn. Percentages use the full dataset sizes as denominators: 779 reactions for GDB-10-rxn and 174 reactions for GDB-17-rxn. The NO_SMILES class is retained as a standalone class, whereas Other contains the compressed long-tail chemical B n F m classes.
Supplementary Fig. 2: Optimization-success counts stratified by OOD bond-rearrangement class. Absolute success counts are shown after saddle-point optimization. Each row corresponds to one OOD dataset and training-set combination, and bars compare TransTS with baseline TS-generation models within each retained B n F m class. OA-ReactDiff is not shown for GDB-10-rxn after T1x+RGD1 training or for either GDB-17-rxn training setting because it produced no valid structures in these settings.
Supplementary Fig. 3: Reaction-correctness counts stratified by OOD bond-rearrangement class. Absolute correctness counts are shown after saddle-point optimization. Each row corresponds to one OOD dataset and training-set combination, and bars compare TransTS with baseline TS-generation models within each retained B n F m class. OA-ReactDiff is not shown for GDB-10-rxn after T1x+RGD1 training or for either GDB-17-rxn training setting because it produced no valid structures in these settings.
Supplementary Fig. 4: Median pre-optimization RMSD stratified by OOD bond-rearrangement class. Heatmaps report the median pre-optimization RMSD for each model and retained B n F m class. Rows of panels correspond to GDB-10-rxn and GDB-17-rxn, and columns correspond to T1x and T1x+RGD1 training. Lower RMSD values indicate closer coordinate-level agreement with the reference TS before saddle-point optimization. Blank entries indicate settings with no valid RMSD values after filtering or settings in which the model produced no valid structures.
Transition states, the first-order saddle points on the potential energy surfaces, govern the kinetics and mechanisms of chemical reactions and conformational changes. Locating them is challenging because transition pathways are topologically complex and can proceed via an ensemble of diverse routes. Existing methods address these challenges by introducing heuristic assumptions about the pathway or reaction coordinates, which limits their applicability when a good initial guess is unavailable or when the guess precludes alternative, potentially relevant pathways. We propose to bypass such heuristic limitations by introducing ASTRA, A Priori Sampling of TRAnsition States with Guided Diffusion, which reframes the transition state search as an inference-time scaling problem for generative models. ASTRA trains a score-based diffusion model on configurations from known metastable states. Then, ASTRA guides inference toward the isodensity surface separating the basins of metastable states via a principled composition of conditional scores. A Score-Aligned Ascent (SAA) process then approximates a reaction coordinate from the difference between conditioned scores and combines it with physical forces to drive convergence onto first-order transition states. Validated on benchmarks ranging from 2D potentials to biomolecular conformational changes and a chemical reaction, ASTRA locates transition states with high precision and discovers multiple reaction pathways, enabling mechanistic studies of complex molecular systems.
Hyukjun Lim, Soojung Yang, Lucas Pinède +3
Department of Materials Science and Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea. · Computational and Systems Biology, MIT, 77 Massachusetts Avenue, Cambridge, 02139, Massachusetts, USA. · Chimie ParisTech, PSL University, 11 rue Pierre et Marie Curie, Paris, 75005, France. +2
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.
Seungheun Baek, Mogan Gim, Jaewoo Kang
Department of Computer Science Korea University Seoul, South Korea · Department of Biomedical Engineering Hankuk University of Foreign Studies Yongin, South Korea
Mapping a chemical reaction network, the graph of minima and transition states (TS) and the elementary reactions connecting them, is the natural language of chemistry, from catalysis to combustion to the origin of life. Constructing such a reaction network for a given chemistry has been impractical: it requires finding and characterizing tens of thousands of TS, a task for which traditional methods such as density functional theory (DFT) are typically prohibitively slow and require reactant and product as input. We introduce ReactionAtlas, which builds a reaction network ab origine from a handful of seed molecules and without hand-crafted rules. Specifically, our machine-learned generative model proposes reactions from kinetically sampled candidate compounds and a DFT-trained machine learned force field (MLFF) filters them to valid TS, the resulting products of which enter the search as new seeds. Starting from eight pre-biotic seeds (CH2O, H2O, OH−, H3O+, CO2, H2CO3, HCO3−, H), ReactionAtlas discovers ∼47,000 reactions among ∼12,000 compounds. The MLFF TSs match the PBE0 references within 0.5 Å RMSD in 85% of the cases and can be easily brought to the PBE0 level. Thus, ReactionAtlas maps small carbohydrate chemistry up to C4H8O4 at unprecedented scale and accuracy, including charge and stereo information. It enables novel insights into many well-studied reaction paths, including the formose cycle, which we highlight for its centrality to the chemical origins of life. Notably, our framework also allows establishing alternative reaction pathways for formose chemistry.
Stefan Gugler, Max Eissler, Khaled Kahouli +1
BIFOLD – Berlin Institute for the Foundations of Learning and Data, Berlin, Germany. · Machine Learning Group, TU Berlin, Berlin, Germany. · Department of Artificial Intelligence, Korea University, Seoul, South Korea. +1