arxiv: 2603.25980 · v2 · submitted 2026-03-26 · ⚛️ physics.chem-ph · cs.LG

Recognition: no theorem link

A Priori Sampling of Transition States with Guided Diffusion

Hyukjun Lim , Soojung Yang , Lucas Pin\`ede , Miguel Steiner , Yuanqi Du , Rafael G\'omez-Bombarelli

Authors on Pith no claims yet

Pith reviewed 2026-05-14 23:49 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cs.LG

keywords transition statesdiffusion modelsscore-based modelspotential energy surfacesreaction mechanismsconformational changesgenerative modelssaddle point search

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The pith

A guided diffusion model locates first-order transition states by targeting the isodensity surface between metastable basins without heuristic pathway assumptions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces ASTRA to find transition states on potential energy surfaces by training a score-based diffusion model on metastable state configurations. It then guides the inference process using a composition of conditional scores to reach the surface that separates different metastable basins. A subsequent Score-Aligned Ascent process uses the difference in conditioned scores to approximate a reaction coordinate and combines it with physical forces to converge on saddle points. This method is shown to work across benchmarks including 2D potentials, biomolecular conformational changes, and chemical reactions, often identifying multiple pathways. A sympathetic reader would care because it reduces reliance on good initial guesses that can miss alternative routes in complex systems.

Core claim

ASTRA reframes the transition state search as an inference-time scaling problem for generative models. It 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.

What carries the argument

The composition of conditional scores targeting the isodensity surface between metastable basins, followed by Score-Aligned Ascent that combines score differences with physical forces to locate first-order saddle points.

Load-bearing premise

The assumption that guiding to the isodensity surface and applying score-aligned ascent with physical forces will converge specifically to first-order saddle points rather than minima, higher-order saddles, or other artifacts.

What would settle it

Running the method on a simple 2D potential with a known transition state and observing convergence to a point that is not a first-order saddle, such as a local minimum or a point with zero gradient but positive Hessian eigenvalues.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ASTRA reframes transition-state search as guided diffusion from metastable states plus a score-difference ascent step, which is a clean new angle, but the abstract leaves the precision claims and saddle verification thin.

read the letter

Hi, the main takeaway is that this paper trains a score-based diffusion model only on reactant and product configurations, then guides sampling to the isodensity surface between basins and runs Score-Aligned Ascent (difference of conditioned scores plus physical forces) to locate saddles. That combination avoids the usual initial-guess requirement and can surface multiple pathways, which is the real novelty here compared with nudged-elastic-band or string methods. The approach is straightforward to describe and seems to scale from 2D toy potentials to biomolecular changes and at least one chemical reaction. That generality is worth noting and gives the work a practical edge for systems where good guesses are hard to come by. The soft spot is the validation. The abstract states high precision and successful pathway discovery, yet supplies no error bars, no direct baseline numbers against existing tools, and no mention of Hessian eigenvalue checks to confirm first-order saddles rather than other stationary points on the target surface. The stress-test concern about SAA landing on non-saddle artifacts is therefore still open; if the full manuscript has those diagnostics and failure cases, they need to be front and center. Without them the central claim rests on unshown evidence. This is aimed at computational chemists and biophysicists who routinely hit guess-dependent bottlenecks in reaction or conformational studies. A reader already working with generative models for molecular sampling would pick up the most value. It deserves a serious referee because the framing is new, the equations are standard diffusion plus forces, and the problem it targets is real. I would send it out rather than desk-reject, with the clear expectation that revisions add quantitative benchmarks and explicit saddle verification.

Referee Report

3 major / 2 minor

Summary. The paper introduces ASTRA, which trains a score-based diffusion model on samples from metastable states, composes conditional scores at inference time to target the isodensity surface separating basins, and applies Score-Aligned Ascent (SAA) that uses the difference of conditioned scores as an approximate reaction coordinate combined with physical forces to locate first-order saddle points. It claims this enables a priori discovery of transition states and multiple pathways without heuristic reaction-coordinate assumptions, with validation on 2D potentials, biomolecular conformational changes, and a chemical reaction showing high precision.

Significance. If the SAA procedure is shown to converge reliably to first-order saddles (rather than other stationary points on the isodensity surface), the method would represent a meaningful advance in computational chemistry by providing an unbiased, generative-model-based route to transition-state ensembles and alternative mechanisms. The framing as an inference-time scaling problem for diffusion models is conceptually clean and leverages existing score-based machinery without introducing new fitted parameters beyond guidance weights.

major comments (3)

[Abstract and Section 3] Abstract and Section 3: The central claim that SAA converges to first-order transition states (exactly one negative Hessian eigenvalue along the reaction coordinate) is load-bearing, yet the manuscript supplies no Hessian eigenvalue verification, convergence proof, or explicit failure-mode analysis demonstrating that the score-difference direction plus physical forces avoids local minima or higher-order saddles on the isodensity surface. Without this, the reported precision and multiple-pathway discovery rest on unshown evidence.
[Section 4] Section 4: Validation across scales is asserted to achieve high precision, but the results lack quantitative error bars on saddle-point locations, direct numerical comparisons to established baselines (e.g., NEB or string methods), and details on whether post-hoc filtering of non-saddle points was applied or avoided. This weakens the strength of the empirical support for the method's reliability.
[Section 2.3] Section 2.3: The guidance composition weights are free parameters whose selection is not shown to be independent of the target transition states; the manuscript should demonstrate that their tuning does not implicitly encode pathway information, as this would qualify the 'a priori' and parameter-light character of the approach.

minor comments (2)

[Figure 2] Figure 2 and associated caption: The visualization of SAA trajectories would be clearer with explicit annotation of the isodensity contour and the projected force vectors at each step.
[Section 2] Notation in Section 2: The distinction between the unconditional score and the two conditional scores (one per metastable basin) should be made fully explicit in the equations to avoid ambiguity when composing the guidance term.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments, which highlight important aspects for strengthening the rigor and empirical support of our work. We address each major comment below and indicate the revisions planned for the manuscript.

read point-by-point responses

Referee: [Abstract and Section 3] The central claim that SAA converges to first-order transition states (exactly one negative Hessian eigenvalue along the reaction coordinate) is load-bearing, yet the manuscript supplies no Hessian eigenvalue verification, convergence proof, or explicit failure-mode analysis demonstrating that the score-difference direction plus physical forces avoids local minima or higher-order saddles on the isodensity surface. Without this, the reported precision and multiple-pathway discovery rest on unshown evidence.

Authors: We agree that explicit verification strengthens the central claim. In the revised manuscript we will add Hessian eigenvalue analysis for all located points across the benchmarks to confirm exactly one negative eigenvalue. We will also expand the discussion in Section 3 to explain why the score-difference direction, when combined with physical forces, tends to align with the reaction coordinate on the isodensity surface, and we will include a short analysis of potential failure modes such as convergence to higher-order saddles. A full mathematical convergence proof is beyond the current scope and will be noted as future work; the empirical results on diverse systems nevertheless provide supporting evidence. revision: partial
Referee: [Section 4] Validation across scales is asserted to achieve high precision, but the results lack quantitative error bars on saddle-point locations, direct numerical comparisons to established baselines (e.g., NEB or string methods), and details on whether post-hoc filtering of non-saddle points was applied or avoided. This weakens the strength of the empirical support for the method's reliability.

Authors: We accept that quantitative error bars and baseline comparisons would improve the presentation. The revised Section 4 will report error bars computed from multiple independent runs for saddle-point locations. We will add direct numerical comparisons to NEB and string methods on the 2D potentials and the chemical reaction, using metrics such as RMSD and energy deviation from reference saddles. No post-hoc filtering of non-saddle points was performed; all converged points were retained, and this will be stated explicitly in the methods section. revision: yes
Referee: [Section 2.3] The guidance composition weights are free parameters whose selection is not shown to be independent of the target transition states; the manuscript should demonstrate that their tuning does not implicitly encode pathway information, as this would qualify the 'a priori' and parameter-light character of the approach.

Authors: The weights are chosen according to a general balancing principle between the two conditional scores to reach the isodensity surface and are held fixed across all examples. In the revision we will add an ablation study demonstrating that a range of weight values around the reported settings produces consistent transition-state locations and still recovers multiple pathways. This supports that no pathway-specific information is encoded in the choice of weights. revision: yes

standing simulated objections not resolved

A rigorous mathematical convergence proof for the SAA procedure to first-order saddles on general potential energy surfaces.

Circularity Check

0 steps flagged

Minor self-citation not load-bearing; derivation remains independent

full rationale

The paper proposes ASTRA by training a score-based diffusion model on metastable-state samples, composing conditional scores to target the separating isodensity surface, and applying a new Score-Aligned Ascent (SAA) step that combines score differences with physical forces. No step reduces by construction to a fitted input or self-referential definition; SAA is presented as an algorithmic procedure whose convergence to first-order saddles is an independent claim rather than a tautology. Any citations to prior diffusion literature are standard and non-load-bearing for the central novelty.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard diffusion-model assumptions plus one domain-specific premise about isodensity surfaces; no new entities are postulated and only modest guidance parameters appear to be introduced.

free parameters (1)

guidance composition weights
Parameters that balance conditional scores from each metastable basin; their values are chosen or tuned to reach the separating surface.

axioms (1)

domain assumption The isodensity surface between metastable basins corresponds to the relevant transition-state manifold
Invoked when the guidance step targets that surface as the starting point for SAA.

pith-pipeline@v0.9.0 · 5538 in / 1206 out tokens · 38770 ms · 2026-05-14T23:49:25.671298+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

98 extracted references · 98 canonical work pages · 5 internal anchors

[1]

The Journal of chemical physics3(2), 107–115 (1935)

Eyring, H.: The activated complex in chemical reactions. The Journal of chemical physics3(2), 107–115 (1935)

work page 1935
[2]

Transactions of the Faraday Society34, 29–41 (1938)

Wigner, E.: The transition state method. Transactions of the Faraday Society34, 29–41 (1938)

work page 1938
[3]

Science 334(6055), 517–520 (2011)

Lindorff-Larsen, K., Piana, S., Dror, R.O., Shaw, D.E.: How fast-folding proteins fold. Science 334(6055), 517–520 (2011)

work page 2011
[4]

Multiscale materials modeling for nanomechanics, 195–221 (2016)

Tiwary, P., Walle, A.: A review of enhanced sampling approaches for accelerated molecular dynamics. Multiscale materials modeling for nanomechanics, 195–221 (2016)

work page 2016
[5]

Yang, Y.I., Shao, Q., Zhang, J., Yang, L., Gao, Y.Q.: Enhanced sampling in molecular dynamics. J. Chem. Phys.151(7) (2019)

work page 2019
[6]

arXiv preprint arXiv:2202.04164 (2022)

Hénin, J., Lelièvre, T., Shirts, M.R., Valsson, O., Delemotte, L.: Enhanced sampling methods for molecular dynamics simulations. arXiv preprint arXiv:2202.04164 (2022)

work page arXiv 2022
[7]

Nano Research16(12), 13474–13497 (2023)

Shen, W., Zhou, T., Shi, X.: Enhanced sampling in molecular dynamics simulations and their latest applications – A review. Nano Research16(12), 13474–13497 (2023)

work page 2023
[8]

Dewyer, A.L., Zimmerman, P.M.: Finding Reaction Mechanisms, Intuitive or Otherwise. Org. Biomol. Chem.15(3), 501–504 (2017)

work page 2017
[9]

Simm, G.N., Vaucher, A.C., Reiher, M.: Exploration of Reaction Pathways and Chemical Transformation Networks. J. Phys. Chem. A (2018)

work page 2018
[10]

Unsleber, J.P., Reiher, M.: The Exploration of Chemical Reaction Networks. Annu. Rev. Phys. Chem.71(1), 121–142 (2020)

work page 2020
[11]

Baiardi, A., Grimmel, S.A., Steiner, M., Türtscher, P.L., Unsleber, J.P., Weymuth, T., Reiher, M.: Expansive Quantum Mechanical Exploration of Chemical Reaction Paths. Acc. Chem. Res. 55(1), 35–43 (2022)

work page 2022
[12]

Ismail, I., Majerus, R.C., Habershon, S.: Graph-Driven Reaction Discovery: Progress, Challenges, and Future Opportunities. J. Phys. Chem. A126(40), 7051–7069 (2022)

work page 2022
[13]

Steiner, M., Reiher, M.: Autonomous reaction network exploration in homogeneous and hetero- geneous catalysis. Top. Catal.65(1), 6–39 (2022)

work page 2022
[14]

Steiner, M., Reiher, M.: A human-machine interface for automatic exploration of chemical reaction networks. Nat. Commun.15(1), 3680 (2024)

work page 2024
[15]

Mehdi, S., Smith, Z., Herron, L., Zou, Z., Tiwary, P.: Enhanced sampling with machine learning. Annu. Rev. Phys. Chem.75(2024), 347–370 (2024)

work page 2024
[16]

Mendels, D., Piccini, G., Parrinello, M.: Collective variables from local fluctuations. J. Chem. Phys. Lett.9(11), 2776–2781 (2018)

work page 2018
[17]

Wang, Y., Ribeiro, J.M.L., Tiwary, P.: Past–future information bottleneck for sampling molecular reaction coordinate simultaneously with thermodynamics and kinetics. Nat. Commun.10(1), 3573 (2019)

work page 2019
[18]

arXiv preprint arXiv:2510.18018 (2025)

Kang, P., Zhang, J., Trizio, E., Hou, T., Parrinello, M.: Committors without descriptors. arXiv preprint arXiv:2510.18018 (2025)

work page arXiv 2025
[19]

Trizio, E., Kang, P., Parrinello, M.: Everything everywhere all at once: a probability-based enhanced sampling approach to rare events. Nat. Comput. Sci., 1–10 (2025)

work page 2025
[20]

ACS Catal.15, 9785–9792 (2025)

Das, S., Raucci, U., Trizio, E., Kang, P., Neves, R.P., Ramos, M.J., Parrinello, M.: A machine 43 learning-driven, probability-based approach to enzyme catalysis. ACS Catal.15, 9785–9792 (2025)

work page 2025
[21]

Zhang, J., Bonati, L., Trizio, E., Zhang, O., Kang, Y., Hou, T., Parrinello, M.: Descriptor-free collective variables from geometric graph neural networks. J. Chem. Theory Comput.20(24), 10787–10797 (2024)

work page 2024
[22]

Tan, A.R., Dietschreit, J.C., Gómez-Bombarelli, R.: Enhanced sampling of robust molecular datasets with uncertainty-based collective variables. J. Chem. Phys.162(3) (2025)

work page 2025
[23]

Artificial Intelligence Assists Discovery of Reaction Coordinates and Mechanisms from Molecular Dynamics Simulations

Jung, H., Covino, R., Hummer, G.: Artificial intelligence assists discovery of reaction coordinates and mechanisms from molecular dynamics simulations. arXiv preprint arXiv:1901.04595 (2019)

work page internal anchor Pith review Pith/arXiv arXiv 1901
[24]

Sun, L., Vandermause, J., Batzner, S., Xie, Y., Clark, D., Chen, W., Kozinsky, B.: Multitask machine learning of collective variables for enhanced sampling of rare events. J. Chem. Theory Comput.18(4), 2341–2353 (2022)

work page 2022
[25]

Nature Computational Science3(4), 334–345 (2023)

Jung, H., Covino, R., Arjun, A., Leitold, C., Dellago, C., Bolhuis, P.G., Hummer, G.: Machine-guided path sampling to discover mechanisms of molecular self-organization. Nature Computational Science3(4), 334–345 (2023)

work page 2023
[26]

Research in the Mathematical Sciences6, 1–13 (2019)

Khoo, Y., Lu, J., Ying, L.: Solving for high-dimensional committor functions using artificial neural networks. Research in the Mathematical Sciences6, 1–13 (2019)

work page 2019
[27]

The Journal of Chemical Physics151(5) (2019)

Li, Q., Lin, B., Ren, W.: Computing committor functions for the study of rare events using deep learning. The Journal of Chemical Physics151(5) (2019)

work page 2019
[28]

In: Mathematical and Scientific Machine Learning, pp

Li, H., Khoo, Y., Ren, Y., Ying, L.: A semigroup method for high dimensional committor func- tions based on neural network. In: Mathematical and Scientific Machine Learning, pp. 598–618 (2022). PMLR

work page 2022
[29]

Journal of computational physics488, 112152 (2023)

Strahan, J., Finkel, J., Dinner, A.R., Weare, J.: Predicting rare events using neural networks and short-trajectory data. Journal of computational physics488, 112152 (2023)

work page 2023
[30]

Mitchell,A.R.,Rotskoff,G.M.:Committorguidedestimatesofmoleculartransitionrates.Journal of Chemical Theory and Computation20(21), 9378–9393 (2024)

work page 2024
[31]

Megías, A., Contreras Arredondo, S., Chen, C.G., Tang, C., Roux, B., Chipot, C.: Iterative variational learning of committor-consistent transition pathways using artificial neural networks. Nat. Comput. Sci., 1–11 (2025)

work page 2025
[32]

arXiv preprint arXiv:2507.17700 (2025)

Arredondo, S.C., Tang, C., Talmazan, R.A., Megías, A., Chen, C.G., Chipot, C.: From atoms to dynamics: Learning the committor without collective variables. arXiv preprint arXiv:2507.17700 (2025)

work page arXiv 2025
[33]

Talmazan, R.A., Chipot, C.: From static pathways to dynamic mechanisms: A committor-based data-driven approach to chemical reactions. J. Chem. Inf. Model. (2025)

work page 2025
[34]

Giuseppe Chen, C., Tang, C., Megías, A., Talmazan, R.A., Contreras Arredondo, S., Roux, B., Chipot, C.: Following the committor flow: A data-driven discovery of transition pathways. J. Chem. Theory Comput. (2026)

work page 2026
[35]

In: Mathematical and Scientific Machine Learning, pp

Rotskoff, G.M., Mitchell, A.R., Vanden-Eijnden, E.: Active importance sampling for variational objectives dominated by rare events: Consequences for optimization and generalization. In: Mathematical and Scientific Machine Learning, pp. 757–780 (2022). PMLR

work page 2022
[36]

Kang, P., Trizio, E., Parrinello, M.: Computing the committor with the committor to study the transition state ensemble. Nat. Comput. Sci.4(6), 451–460 (2024)

work page 2024
[37]

Physical Chemistry Chemical Physics22(41), 23618– 23626 (2020)

Pattanaik, L., Ingraham, J.B., Grambow, C.A., Green, W.H.: Generating transition states of 44 isomerization reactions with deep learning. Physical Chemistry Chemical Physics22(41), 23618– 23626 (2020)

work page 2020
[38]

Nature computational science3(12), 1045–1055 (2023)

Duan, C., Du, Y., Jia, H., Kulik, H.J.: Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model. Nature computational science3(12), 1045–1055 (2023)

work page 2023
[39]

Nature Communications15(1), 341 (2024)

Kim, S., Woo, J., Kim, W.Y.: Diffusion-based generative ai for exploring transition states from 2d molecular graphs. Nature Communications15(1), 341 (2024)

work page 2024
[40]

Nature Machine Intelligence7(4), 615–626 (2025)

Duan, C., Liu, G.-H., Du, Y., Chen, T., Zhao, Q., Jia, H., Gomes, C.P., Theodorou, E.A., Kulik, H.J.: Optimal transport for generating transition states in chemical reactions. Nature Machine Intelligence7(4), 615–626 (2025)

work page 2025
[41]

Science389(6761), 9817 (2025)

Lewis, S., Hempel, T., Jiménez-Luna, J., Gastegger, M., Xie, Y., Foong, A.Y.K., Satorras, V.G., Abdin, O., Veeling, B.S., Zaporozhets, I., Chen, Y., Yang, S., Foster, A.E., Schneuing, A., Nigam, J., Barbero, F., Stimper, V., Campbell, A., Yim, J., Lienen, M., Shi, Y., Zheng, S., Schulz, H., Munir, U., Sordillo, R., Tomioka, R., Clementi, C., Noé, F.: Scal...

work page 2025
[42]

Jing, B., Stärk, H., Jaakkola, T., Berger, B.: Generative modeling of molecular dynamics trajectories. Adv. Neural. Inf. Process. Syst.37, 40534–40564 (2024)

work page 2024
[43]

arXiv preprint arXiv:2509.13294 (2025)

Costa, A.d.S., Ponnapati, M., Rubin, D., Smidt, T., Jacobson, J.: Accelerating Protein Molecular Dynamics Simulation with DeepJump. arXiv preprint arXiv:2509.13294 (2025)

work page arXiv 2025
[44]

arXiv preprint arXiv:2503.23794 (2025)

Thiemann, F.L., Reschützegger, T., Esposito, M., Taddese, T., Olarte-Plata, J.D., Martelli, F.: Force-free molecular dynamics through autoregressive equivariant networks. arXiv preprint arXiv:2503.23794 (2025)

work page arXiv 2025
[45]

Nam, J., Steiner, M., Misterka, M., Yang, S., Singhal, A., Gómez-Bombarelli, R.: Transferable learning of reaction pathways from geometric priors. J. Phys. Chem. Lett.16(45), 11690–11699 (2025)

work page 2025
[46]

Journal of Chemical Theory and Computation21(22), 11632–11644 (2025)

Hait, D., Estrada Pabon, J.D., Stohr, M., Martínez, T.J.: Locating ab initio transition states via geodesic construction on machine-learned potential energy surfaces. Journal of Chemical Theory and Computation21(22), 11632–11644 (2025)

work page 2025
[47]

arXiv preprint arXiv:2410.15128 (2024)

Wang, H., Qiu, Y., Wang, Y., Brekelmans, R., Du, Y.: Generalized flow matching for transition dynamics modeling. arXiv preprint arXiv:2410.15128 (2024)

work page arXiv 2024
[48]

arXiv preprint arXiv:2504.18506 (2025)

Raja, S., Šípka, M., Psenka, M., Kreiman, T., Pavelka, M., Krishnapriyan, A.S.: Action- minimization meets generative modeling: Efficient transition path sampling with the onsager- machlup functional. arXiv preprint arXiv:2504.18506 (2025)

work page arXiv 2025
[49]

arXiv preprint arXiv:2507.10530 (2025)

Tuo, P., Chen, J., Li, J.: Flow matching for reaction pathway generation. arXiv preprint arXiv:2507.10530 (2025)

work page arXiv 2025
[50]

Classifier-Free Diffusion Guidance

Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022)

work page internal anchor Pith review Pith/arXiv arXiv 2022
[51]

In: International Conference on Machine Learning, pp

Du, Y., Durkan, C., Strudel, R., Tenenbaum, J.B., Dieleman, S., Fergus, R., Sohl-Dickstein, J., Doucet, A., Grathwohl, W.S.: Reduce, reuse, recycle: Compositional generation with energy- based diffusion models and mcmc. In: International Conference on Machine Learning, pp. 8489– 8510 (2023). PMLR

work page 2023
[52]

In: The Thirteenth International Conference on Learning Representations (2024)

Skreta, M., Atanackovic, L., Bose, J., Tong, A., Neklyudov, K.: The superposition of diffusion models using the itô density estimator. In: The Thirteenth International Conference on Learning Representations (2024)

work page 2024
[53]

In: Forty-second International Conference on Machine Learning (2025)

Skreta, M., Akhound-Sadegh, T., Ohanesian, V., Bondesan, R., Aspuru-Guzik, A., Doucet, A., 45 Brekelmans, R., Tong, A., Neklyudov, K.: Feynman-kac correctors in diffusion: Annealing, guid- ance, and product of experts. In: Forty-second International Conference on Machine Learning (2025)

work page 2025
[54]

arXiv preprint arXiv:2510.11923 (2025)

Nam, J., Máté, B., Toshev, A.P., Kaniselvan, M., Gómez-Bombarelli, R., Chen, R.T., Wood, B., Liu, G.-H., Miller, B.K.: Enhancing diffusion-based sampling with molecular collective variables. arXiv preprint arXiv:2510.11923 (2025)

work page arXiv 2025
[55]

arXiv preprint arXiv:2505.13375 (2025)

Kolloff, C., Höppe, T., Angelis, E., Schreiner, M.J., Bauer, S., Dittadi, A., Olsson, S.: Minimum- excess-work guidance. arXiv preprint arXiv:2505.13375 (2025)

work page arXiv 2025
[56]

Score-Based Generative Modeling through Stochastic Differential Equations

Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 (2020)

work page internal anchor Pith review Pith/arXiv arXiv 2011
[57]

The Journal of chemical physics129(2) (2008)

Del Campo, J.M., Köster, A.M.: A hierarchical transition state search algorithm. The Journal of chemical physics129(2) (2008)

work page 2008
[58]

The Journal of chemical physics120(17), 7877–7886 (2004)

Peters, B., Heyden, A., Bell, A.T., Chakraborty, A.: A growing string method for determining transition states: Comparison to the nudged elastic band and string methods. The Journal of chemical physics120(17), 7877–7886 (2004)

work page 2004
[59]

Journal of chemical theory and computation9(7), 3043–3050 (2013)

Zimmerman, P.: Reliable transition state searches integrated with the growing string method. Journal of chemical theory and computation9(7), 3043–3050 (2013)

work page 2013
[60]

Maiti, S.R., Buttar, D., Duarte, F.: Benchmark of double-ended transition state search methods for metal-catalysed reactions (2025)

work page 2025
[61]

Müller, K., Brown, L.D.: Location of saddle points and minimum energy paths by a constrained simplex optimization procedure. Theor. Chim. Acta53(1), 75–93 (1979)

work page 1979
[62]

The Journal of Physical Chemistry B108(50), 19487–19495 (2004)

Chekmarev, D.S., Ishida, T., Levy, R.M.: Long-time conformational transitions of alanine dipep- tide in aqueous solution: Continuous and discrete-state kinetic models. The Journal of Physical Chemistry B108(50), 19487–19495 (2004)

work page 2004
[63]

Journal of Chemical Theory and Computation19(18), 6151–6159 (2023)

Arts, M., Garcia Satorras, V., Huang, C.-W., Zugner, D., Federici, M., Clementi, C., Noé, F., Pinsler, R., Berg, R.: Two for one: Diffusion models and force fields for coarse-grained molecular dynamics. Journal of Chemical Theory and Computation19(18), 6151–6159 (2023)

work page 2023
[64]

Physical review letters72(23), 3634 (1994)

Molgedey, L., Schuster, H.G.: Separation of a mixture of independent signals using time delayed correlations. Physical review letters72(23), 3634 (1994)

work page 1994
[65]

Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G., Noé, F.: Identification of slow molecular order parameters for markov model construction. J. Chem. Phys.139(1) (2013)

work page 2013
[66]

Reyes, C.A., Karr, A., Ramsperger, C.A., K, A.T.G., Lee, H.J., Picazo, E.: Compartmentalizing donor–acceptor stenhouse adducts for structure–property relationship analysis. J. Am. Chem. Soc.147(1), 10–26 (2024)

work page 2024
[67]

arXiv preprint arXiv:2510.24979 (2025)

Tang, C., Pandey, M.P., Chen, C.G., Megías, A., Dehez, F., Chipot, C.: Breaking the timescale barrier: Generative discovery of conformational free-energy landscapes and transition pathways. arXiv preprint arXiv:2510.24979 (2025)

work page arXiv 2025
[68]

arXiv preprint arXiv:2506.06085 (2025)

Koulischer, F., Handke, F., Deleu, J., Demeester, T., Ambrogioni, L.: Feedback guidance of diffusion models. arXiv preprint arXiv:2506.06085 (2025)

work page arXiv 2025
[69]

Advances in neural information processing systems33, 6840–6851 (2020)

Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems33, 6840–6851 (2020)

work page 2020
[70]

arXiv preprint arXiv:2503.02819 (2025)

Skreta, M., Akhound-Sadegh, T., Ohanesian, V., Bondesan, R., Aspuru-Guzik, A., Doucet, 46 A., Brekelmans, R., Tong, A., Neklyudov, K.: Feynman-kac correctors in diffusion: Annealing, guidance, and product of experts. arXiv preprint arXiv:2503.02819 (2025)

work page arXiv 2025
[71]

arXiv preprint arXiv:2501.06848 (2025)

Singhal, R., Horvitz, Z., Teehan, R., Ren, M., Yu, Z., McKeown, K., Ranganath, R.: A gen- eral framework for inference-time scaling and steering of diffusion models. arXiv preprint arXiv:2501.06848 (2025)

work page arXiv 2025
[72]

In: European Conference on Computer Vision, pp

Liu, N., Li, S., Du, Y., Torralba, A., Tenenbaum, J.B.: Compositional visual generation with composable diffusion models. In: European Conference on Computer Vision, pp. 423–439 (2022). Springer

work page 2022
[73]

Henkelman, G., Jónsson, H.: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys.111(15), 7010–7022 (1999)

work page 1999
[74]

Olsen, R., Kroes, G., Henkelman, G., Arnaldsson, A., Jónsson, H.: Comparison of methods for finding saddle points without knowledge of the final states. J. Chem. Phys.121(20), 9776–9792 (2004)

work page 2004
[75]

The Journal of chemical physics123(22) (2005)

Heyden, A., Bell, A.T., Keil, F.J.: Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method. The Journal of chemical physics123(22) (2005)

work page 2005
[76]

The Journal of chemical physics128(1) (2008)

Kästner, J., Sherwood, P.: Superlinearly converging dimer method for transition state search. The Journal of chemical physics128(1) (2008)

work page 2008
[77]

Journal of Chemical Theory and Computation 6(4), 1136–1144 (2010)

Shang, C., Liu, Z.-P.: Constrained broyden minimization combined with the dimer method for locating transition state of complex reactions. Journal of Chemical Theory and Computation 6(4), 1136–1144 (2010)

work page 2010
[78]

Weymuth, T., Unsleber, J.P., Türtscher, P.L., Steiner, M., Sobez, J.-G., Müller, C.H., Mörchen, M., Klasovita, V., Grimmel, S.A., Eckhoff, M., Csizi, K.-S., Bosia, F., Bensberg, M., Reiher, M.: SCINE– Software for chemical interaction networks. J. Chem. Phys.160(22) (2024)

work page 2024
[79]

Zenodo (2024)

Bensberg, M., Brunken, C., Csizi, K.-S., Grimmel, S.A., Gugler, S., Sobez, J.-G., Steiner, M., Türtscher, P.L., Unsleber, J.P., Vaucher, A., Weymuth, T., Reiher, M.: qcscine/readuct: Release 6.0.0. Zenodo (2024). https://doi.org/10.5281/zenodo.13372944 . https://doi.org/10. 5281/zenodo.13372944

work page doi:10.5281/zenodo.13372944 2024
[80]

Henkelman, G., Uberuaga, B.P., Jónsson, H.: A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys.113(22), 9901–9904 (2000)

work page 2000

Showing first 80 references.