Pith. sign in

REVIEW 2 major objections 3 minor 2 cited by

Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior

T0 review · 2 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A new inference-time steering method, FK-CFM, applies Feynman-Kac resampling to conditional flow matching, letting users tilt a trained model's output toward any energy potential without retraining.

desk verdict FK steering for flow matching is genuinely new and the chirality application is strong; the real soft spot is the gap between the telescoping-potential theorem and the one-shot reward actually implemented. read the letter →

arxiv 2509.01543 v1 pith:CVHPEDH7 submitted 2025-09-01 cs.LG

Konstantin Mark , Leonard Galustian , Maximilian P.-P. Kovar , Esther Heid This is my paper
classification cs.LG
keywords conditionalflowmatchingFeynman-Kacsteeringinference-timeenergy-tiltedposteriorparticlefilteringchiralitytransitionstatepredictiongenerativemodels
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that Feynman-Kac steering, a particle-resampling technique previously used for diffusion models, can be transferred to conditional flow matching. It proves that adding a diffusion term and a score correction to a flow's ODE preserves the marginals while enabling resampling without particle collapse, and that if path potentials telescope to exp(-lambda U(x1)), the particle cloud converges to the tilted distribution. The one-shot Euler endpoint reward makes steering cheap because it reuses the velocity already computed for the next integration step. On synthetic benchmarks, FK-CFM isolates modes in high dimensions where importance sampling fails, and in the applied setting it steers GoFlow to generate transition states with correct chirality from 2D graphs alone, cutting persistent chirality errors from 9.0% to 0.7%. If correct, this is the first extension of Feynman-Kac steering to flow matching and the first generative model producing stereochemically correct transition states from graph input.

What carries the argument

The central object is the stochastic representation of a CFM path: given a flow field v_t generating path p_t with a Gaussian prior, the SDE dY_t = (v_t + (sigma^2/2) grad log p_t) dt + sigma(t) I dB_t has the same marginals (Theorem 1 / Corollary 3). This lets the FK particle filter resample without collapsing all trajectories to a single point. The second load-bearing identity is the product condition (Eq. 13): the intermediate potentials G_i must multiply along the path to exp(-lambda U(x1)); Algorithm 1 approximates this with a one-shot Euler reward and a difference schedule, using the velocity already computed for the next step so steering adds no extra forward passes.

What would settle it

Construct a CFM model with a deliberately curved path (e.g., a large-angle circular interpolation or a highly nonlinear schedule), run FK-CFM with a known potential U, and compare the empirical endpoint distribution against the true tilted distribution p1 exp(-lambda U)/Z over many seeds; a systematic deviation growing with curvature and lambda would confirm the one-shot bias. Alternatively, measure the gap between the true final reward U(x1) and the one-shot estimate U(x + (1-t)v(x,t)) along steered trajectories—a large gap indicates the steering target is misspecified.

Watch

Extended reading notes

Core claim

FK-CFM is an inference-time steering method that tilts a conditional flow matching model's output distribution toward low values of a user-specified potential U(x). The method simulates a cloud of particles, computes at each integration step a one-shot estimate of the final reward—y = x + (1-t)v(x,t)—resamples particles according to a difference schedule of these rewards, and injects Gaussian noise with a score correction so the marginals are preserved. The paper proves convergence: when the product of intermediate potentials equals exp(-lambda U(x1)), the resampled cloud converges to p1(x) exp(-lambda U(x)) as the particle count goes to infinity. The authors demonstrate this on synthetic ti

Load-bearing premise

The steering guarantee holds only if the path potentials telescope exactly to exp(-lambda U(finalsample)); the implementation instead evaluates the potential U at a one-shot Euler endpoint y = x + (1-t)v(x,t), so for flows with strong curvature the resampled cloud converges to the distribution tilted by U(one-shot estimate), not by U, and no bound on that bias is provided.

Editorial extensions

If this is right

  • FK-CFM steers any CFM model at inference time, without retraining or backpropagation, needing only velocity evaluations and optionally a score model.
  • The one-shot reward reuses the next step's velocity, making steering computationally nearly free per step; higher-order and multi-step reward estimates trade extra evaluations for accuracy on curved flows.
  • With continuous potentials, FK-CFM isolates rare modes in high dimensions with small particle counts, where importance sampling degenerates.
  • Steering GoFlow with the chiral-volume potential removes the wrong-chirality failure mode in transition-state prediction, producing correct stereochemistry from 2D graphs—a task the authors say no prior generative model solved.
  • The framework extends to non-Gaussian priors by training a score model concurrently (e.g., via SF²M), enabling stochastic steering beyond the Gaussian assumption.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The one-shot endpoint bias suggests a direct test: on a deliberately curved CFM path (e.g., a nonlinear interpolation schedule), FK-CFM's effective target should drift away from U(x1) toward U(x + (1-t)v) as curvature grows; measuring this drift would quantify the bias.
  • The chiral-volume potential is additive, so the same resampling machinery could combine it with other geometric rewards (steric clash, bond-length constraints) to enforce multiple physical constraints at once.
  • The high-dimensional mode-isolation result hints that FK-CFM could serve as a general constrained-sampling tool for scientific generative models such as protein conformers or materials, where retraining is expensive and constraints are often non-differentiable—though the paper does not test this.
  • A systematic study of particle counts, resampling schedules, and potential tempering would be needed to turn FK-CFM from a demonstration into a predictive engineering tool; the paper leaves the variance behavior of the estimator unanalyzed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper introduces Feynman-Kac (FK) steering for conditional flow matching (CFM), extending a framework previously developed for diffusion models. The authors prove that a CFM velocity field can be augmented with an isotropic diffusion term and an analytic score correction so that the resulting SDE preserves the flow-matching marginals (Theorem 1, Proposition 2, Corollary 3). They then define a sequential Monte Carlo resampling scheme with energy-based potentials, targeting the tilted distribution p1(x) exp(-λU(x)). The method is evaluated on synthetic tasks, including high-dimensional mode isolation and comparisons with guidance flow matching, and on a chemistry application: steering GoFlow transition-state predictions with a chiral-volume potential. The reported chirality results are strong: persistent chirality error drops from 9.0% to 0.7% and RMSE from 0.527 to 0.369 Å. The authors claim this is the first generative model producing stereochemically correct transition states from 2D graph information alone.

Significance. If the result holds, FK-CFM is a useful inference-time steering method that fills a real gap in the flow-matching literature. The central derivation is clean and standard, and several strengths deserve explicit credit: the code is open-source, the synthetic benchmarks use externally defined tilted targets, and the chirality metrics are external to the steering potential. The high-dimensional mode-isolation experiment directly addresses a known weakness of importance sampling and of some guidance methods. The paper is honest about limitations, including the reliance on a score model for stochastic injection and the heuristic nature of intermediate reward estimation. The main caveat is that the formal convergence statement is not fully connected to the exact implementation described in the text, which is fixable but needs attention.

major comments (2)
  1. [Section II C, Algorithm 1, lines 3-10] As printed, the pseudocode computes vs = vθ(xs,t) once before the loop and never recomputes it after propagation or resampling. This means both the SDE propagation and the one-shot endpoint ys use the velocity at t=0 for all later steps. This does not implement the method described in the text, which states that vθ_ti(x_i) is evaluated at the current state and reused for the next ODE/SDE step. The algorithm must recompute vs at the current state/time at each iteration, and the text should state whether the one-shot endpoint uses the pre- or post-propagation velocity. Without this correction, the pseudocode is not a valid CFM steering rule except for exactly straight or constant-velocity flows.
  2. [Section II C, Eq. (13) and harmonic-sum schedule] The paper says the harmonic-sum schedule was used throughout the experiments, but Algorithm 1 implements a difference schedule without a final G_n term. The convergence condition in Eq. (13) is for potentials whose product telescopes to exp(-λU(x1)). For the harmonic-sum schedule, the final correction G_n = exp(-λU(x1)) / (∏G_i) (or an equivalent statement) must be given explicitly, together with precise definitions of L, ℓ, and H_L. I do not regard the one-shot endpoint as causing asymptotic bias: in the difference schedule the reward differences telescope to U(x1), and the final step evaluates the actual terminal point, so the one-shot approximation affects resampling efficiency rather than the limiting target. The missing piece is a formal specification of the potentials actually used in each experiment and a verification that Eq. (13) holds for that schedule. This is needed to connec
minor comments (3)
  1. [Eq. (13)] The right-hand side of Eq. (13) appears to use x_i, but it should be the terminal variable, e.g. exp(-λU(x_n)) or exp(-λU(x1)). Please correct this to avoid ambiguity.
  2. [Section III B and Table I] The text says 'we evaluated FKS' but the method is called FK elsewhere. Also, the caption 'G CFM' is unclear; it should be 'GFM' or 'MC-CFM' to match the notation in Section III B.
  3. [Appendix A.3] For the TS-generation experiment, λ and the diffusion variance schedule are given, but the number of FK particles and the resampling cadence are not stated in the appendix. Please include these reproducibility details.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-referential validation in the chirality application; no load-bearing circularity in the FK-CFM derivation.

  1. self definitional [Section III C, Eq. (14), and Table II]
    "The final potential for any geometry is the sum over all chiral centres of both reactant and product of this directed tetrahedral volume. ... We define a thresholded chirality error at reactions for which there is a (not necessarily reaction consistent) chiral centre where the sign of V~ is inconsistent with the chirality dictated by the 2D-graph and the absolute value of V~ exceeds a threshold θ."

    The steering potential U is built from the signed chiral volume (Eq. 14) with the sign fixed by reactant/product chirality; the PCE and TCE metrics are defined by the same signed chiral volume (or its normalized version) being inconsistent with that chirality. Hence a drop in PCE/TCE after steering is, to first order, a restatement that the algorithm decreased its own objective. This is not fully circular because the paper also reports RMSE against external QM ground-truth TS geometries, which improves independently (0.527 to 0.369 Å), but the headline chirality-error numbers are partly self-referential.

full rationale

The core derivation is not circular: FK steering for CFM is constructed by combining the external Feynman-Kac framework [16] with the standard SDE representation (Theorem 1 and Corollary 3), and the synthetic benchmarks use externally specified tilted targets and measure Wasserstein distance, so success is not encoded in the inputs. The chirality application does contain a partial self-referential loop in evaluation: the steering potential and the PCE/TCE metrics are both defined by the same signed tetrahedral chiral volume, so the reported error reduction partly reflects optimization of the metric itself. This is mitigated by the independent RMSE-to-ground-truth improvement and by the acknowledgments in Section IV about score reliance and out-of-distribution steering. One additional correctness risk, noted in Section II C and Algorithm 1, is that the one-shot endpoint reward makes the implemented target approximately p1 exp(-lambda U(one-shot)), not p1 exp(-lambda U(x1)), unless paths are straight; this is an approximation gap rather than a circular derivation. Self-citation of GoFlow [22] is as a base model and does not carry the proof burden. Overall score 2 reflects one minor self-referential metric, not a structurally circular derivation.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The method leans on cited SDE and FK theory (Theorem 1 from [35], Proposition 2 from [11]/[36], convergence from [16]) plus six hand-chosen parameters (lambda, sigma, w, resampling cadence, harmonic weighting, metric threshold theta). The dominant load-bearing assumption beyond the quoted theorems is that one-shot Euler endpoints predict terminal rewards well enough for resampling (axiom 6). The GoFlow application additionally assumes a Gaussian score despite non-Gaussian training data (axiom 3, empirical patch). No invented entities; the chiral volume is a geometric functional of existing atom positions and CIP-priority orderings (Eq. 14).

free parameters (6)
  • Steering temperature lambda = 0.4 (TS experiment); unstated for synthetic benchmarks
    Controls the tilt strength exp(-lambda U); hand-chosen per experiment, no sensitivity analysis reported (Section III C, Appendix A.3).
  • Diffusion variance schedule sigma(t) = 0.3 to 0 linear in TS; 2.0 constant in high-dim
    Injected noise plus score correction; chosen by hand; the paper notes unsteered SDE inference matches deterministic inference but does not tune sigma for steering (Section II B, Appendix A).
  • Harmonic-sum time weighting 1/((L+1-l) H_L) = used in all experiments
    Ad hoc time-dependent factor multiplying the one-shot reward to emphasize later resampling steps; the paper says it 'often ended up' using this (Section II C).
  • Potential strength w in high-dim mode isolation = unspecified ('large values of w')
    Tilt magnitude for the indicator and distance potentials in Section III A; the value is not reported, which affects exact reproduction of Figures 3 and 4.
  • Resampling cadence = every 3 steps (high-dim), every 5 or 10 steps (2D comparison)
    Number of integration steps between resampling events; hand-chosen, and the paper is internally inconsistent (Appendix A2 says every 10, Fig. 9 caption says every 5).
  • Chirality-error threshold theta = 0.25
    Threshold on the normalized chiral volume for the TCE metric; an evaluation-side free choice that directly affects the Table II percentages.
assumptions (7)
  • standard math Continuity equation / mass conservation: dt p_t = -div(v_t p_t) characterizes flows that generate p_t (Eq. 1)
    Invoked in Section II A to define generated paths and in the proof of Theorem 1 (Section II B).
  • standard math Fokker-Planck correspondence: a drift-diffusion SDE with drift w and diffusion sigma has marginals solving dt p = -div(wp) + (sigma^2/2) Laplace(p) (Eq. 10)
    The core of Theorem 1's proof; standard Ito calculus, accepted without independent check in the paper.
  • standard math Gaussian-prior score identity: grad log p_t(x) = (1/beta_t)(alpha_dot_t/alpha_t * beta_t - beta_dot_t)(v_t(x) - (alpha_dot_t/alpha_t) x) (Eq. 11)
    Quoted as Proposition 2 from [11, B.4] and [36, Prop. 1]; it turns the marginal-preserving SDE into a practical rule. It holds only for p0 Gaussian, which the TS application violates via Kabsch alignments and patches empirically (Appendix A.3).
  • domain assumption Feynman-Kac particle-system convergence: as k goes to infinity the resampled particle cloud targets p1 exp(-lambda U) when the product of potentials equals exp(-lambda U) (Eq. 13)
    Imported from [16] for diffusion; the paper does not reprove it for the CFM setting, and the implementation relaxes the exact-telescoping hypothesis to one-shot endpoint estimates.
  • standard math Locally Lipschitz velocity field for well-posed ODE/SDE integration
    Regularity condition stated as a hypothesis in Theorem 1 and Proposition 2; standard and unproblematic.
  • ad hoc to paper Flow-path straightness sufficient for the one-shot Euler endpoint x + (1-t) v_theta(x,t) to approximate the terminal sample well enough for reward-based resampling
    The paper's own caveat: 'depending on the straightness of the paths generated by the flow matching model, this method can lead to a cheap but effective estimation of the final reward' (Section II C). Load-bearing and never quantified.
  • domain assumption Score model availability (or Gaussian formula) for the injected diffusion, needed to keep SDE marginals equal to p_t
    Explicitly named in Section IV as 'the main limitation of FK as presented here is the reliance on a tractable score for the injection of stochasticity during inference'.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior." pith.science (2026). https://pith.science/paper/CVHPEDH7

@misc{pith2026250901543,
  author       = {Pith},
  title        = {Pith review of: Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CVHPEDH7}},
  note         = {Machine review of arXiv:2509.01543}
}
read the original abstract

Conditional Flow Matching(CFM) represents a fast and high-quality approach to generative modelling, but in many applications it is of interest to steer the generated samples towards precise requirements. While steering approaches like gradient-based guidance, sequential Monte Carlo steering or Feynman-Kac steering are well established for diffusion models, they have not been extended to flow matching approaches yet. In this work, we formulate this requirement as tilting the output with an energy potential. We derive, for the first time, Feynman-Kac steering for CFM. We evaluate our approach on a set of synthetic tasks, including the generation of tilted distributions in a high-dimensional space, which is a particularly challenging case for steering approaches. We then demonstrate the impact of Feynman-Kac steered CFM on the previously unsolved challenge of generated transition states of chemical reactions with the correct chirality, where the reactants or products can have a different handedness, leading to geometric constraints of the viable reaction pathways connecting reactants and products. Code to reproduce this study is avaiable open-source at https://github.com/heid-lab/fkflow.

Figures

Figures reproduced from arXiv: 2509.01543 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of FK on a toy flow matching model from a Gaussian distribution (bottom) towards a mixture of two [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Illustration of the main steps in an iteration of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Success rate (top) and sliced Wasserstein-2 approxi [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Success rate for FK with the indicator potential for [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Distributions generate by Monte Carlo Guidance [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Exemplary ground-truth reaction, and the TS struc [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. RMSE to the ground truth for both the base model (left) and a FK model with a chiral potential (right). The [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Evaluation of Guidance Flow Matching with Monte Carlo Guidance (MC) and deterministic Feynman-Kac steering [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Exemplary ground-truth reaction with a wrong TS. [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Learning to Assist: Collaborative VLAs for Implicit Human-Robot Collaboration

    cs.RO 2026-06 conditional novelty 6.0 of 10

    VLA models with inference-time steering mitigate action leakage in implicit human-robot collaboration, supporting longer horizons and yielding faster, more reliable assembly than shorter-horizon baselines in a 16-pers...

  2. A Theory on Flow Matching with Neural Networks

    cs.LG 2026-06 unverdicted novelty 6.0 of 10

    Establishes convergence guarantees for overparameterized 2-layer ReLU networks in flow matching, generalization bounds for the velocity-field objective, and Wasserstein guarantees for generated samples, using multi-ta...

Reference graph

Works this paper leans on

49 extracted references · 32 canonical work pages · cited by 2 Pith papers

  1. [1]

    Flow Matching for Generative Modeling,

    Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow Matching for Generative Modeling,” (2023), arXiv:2210.02747 [cs]

    arXiv 2023

  2. [2]

    Calculate potential of one-shot

    work page

  3. [3]

    Resample based on potential

    work page

  4. [4]

    SDE step FIG. 2. Illustration of the main steps in an iteration of Feynman-Kac flow matching inference. Based on the velocity vectors from a flow matching model (1.) an energy potential is evaluated at the one-shot approximation for t = 1 (2.). The particles are then resampled (3.) before the SDE integration step (4.) which reuses the previously calculate...

    work page 2024

  5. [5]

    Tamir, N

    E. Tamir, N. Laabid, M. Heinonen, V. Garg, and A. Solin, in ICML 2024 Workshop on Structured Proba- bilistic Inference{\&} Generative Modeling (2024)

    work page 2024

  6. [6]

    St¨ ark, B

    H. St¨ ark, B. Jing, R. Barzilay, and T. Jaakkola, arXiv preprint arXiv:2310.05764 (2023)

    arXiv 2023

  7. [7]

    Y. Guo, C. Du, Z. Ma, X. Chen, and K. Yu, in ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)(IEEE, 2024) pp. 11121–11125

    work page 2024

  8. [8]

    Davtyan, S

    A. Davtyan, S. Sameni, and P. Favaro, in Proceedings of the IEEE/CVF International Conference on Computer Vision (2023) pp. 23263–23274

    work page 2023

Show all 49 references
  1. [9]

    Zheng, M

    Q. Zheng, M. Le, N. Shaul, Y. Lipman, A. Grover, and R. T. Chen, arXiv preprint arXiv:2311.13443 (2023)

    2023 arXiv

  2. [10]

    Path Integral Sampler: a stochastic control approach for sampling,

    Q. Zhang and Y. Chen, “Path Integral Sampler: a stochastic control approach for sampling,” (2022), arXiv:2111.15141 [cs]

    2022 arXiv

  3. [11]

    Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control,

    C. Domingo-Enrich, M. Drozdzal, B. Karrer, and R. T. Q. Chen, “Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control,” (2025), arXiv:2409.08861 [cs]

    2025 arXiv

  4. [12]

    B. Jing, B. Berger, and T. Jaakkola, arXiv preprint arXiv:2402.04845 (2024)

    2024 arXiv

  5. [13]

    Q. Tian, Y. Xu, Y. Yang, Z. Wang, Z. Liu, P. Yan, and X. Li, arXiv preprint arXiv:2412.11082 (2024)

    2024 arXiv

  6. [14]

    Clark, P

    K. Clark, P. Vicol, K. Swersky, and D. J. Fleet, (2024)

    2024

  7. [15]

    Derivative-Free Guidance in Continuous and Dis- crete Diffusion Models with Soft Value-Based Decoding,

    X. Li, Y. Zhao, C. Wang, G. Scalia, G. Eraslan, S. Nair, T. Biancalani, S. Ji, A. Regev, S. Levine, and M. Ue- hara, “Derivative-Free Guidance in Continuous and Dis- crete Diffusion Models with Soft Value-Based Decoding,” (2024), arXiv:2408.08252 [cs]

    2024 arXiv

  8. [16]

    A General Frame- work for Inference-time Scaling and Steering of Diffusion Models,

    R. Singhal, Z. Horvitz, R. Teehan, M. Ren, Z. Yu, K. McKeown, and R. Ranganath, “A General Frame- work for Inference-time Scaling and Steering of Diffusion Models,” (2025), arXiv:2501.06848 [cs]

    2025 arXiv

  9. [17]

    Branched Schr\

    S. Tang, Y. Zhang, A. Tong, and P. Chatterjee, “Branched Schr\”odinger Bridge Matching,” (2025)

    2025

  10. [18]

    Universal Guidance for Diffusion Models,

    A. Bansal, H.-M. Chu, A. Schwarzschild, S. Sen- gupta, M. Goldblum, J. Geiping, and T. Goldstein, “Universal Guidance for Diffusion Models,” (2023), arXiv:2302.07121 [cs]

    2023 arXiv

  11. [19]

    L. Wu, B. L. Trippe, C. A. Naesseth, D. Blei, and J. P. Cunningham (2023)

    2023

  12. [20]

    S. Kim, J. Woo, and W. Y. Kim, Nature Communi- cations 15, 341 (2024), publisher: Nature Publishing Group

    2024

  13. [21]

    Duan, G.-H

    C. Duan, G.-H. Liu, Y. Du, T. Chen, Q. Zhao, H. Jia, C. P. Gomes, E. A. Theodorou, and H. J. Kulik, Nature Machine Intelligence 7, 615 (2025), publisher: Nature Publishing Group

    2025

  14. [22]

    GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation,

    M. Xu, L. Yu, Y. Song, C. Shi, S. Ermon, and J. Tang, “GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation,” (2022), arXiv:2203.02923 [cs]

    2022 arXiv

  15. [23]

    ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation,

    M. Hassan, N. Shenoy, J. Lee, H. Stark, S. Thaler, and D. Beaini, “ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation,” (2024), arXiv:2410.22388 [q-bio]

    2024 arXiv

  16. [24]

    Torsional Diffusion for Molecular Con- former Generation,

    B. Jing, G. Corso, J. Chang, R. Barzilay, and T. Jaakkola, “Torsional Diffusion for Molecular Con- former Generation,” (2023), arXiv:2206.01729 [physics]

    2023 arXiv

  17. [25]

    mentions inadequacy of many of the datasets includ- ing QM9 [27] for judging performance of models on com- plex chiral tasks. Datasets like GEOM [28] based on QM9 that are extensively used for benchmarking con- former generation tasks could, by extension, be a reason for a lac...

  18. [26]

    Chi- ENN: Embracing Molecular Chirality with Graph Neural Networks,

    P. Gai´ nski, M. Koziarski, J. Tabor, and M.´Smieja, “Chi- ENN: Embracing Molecular Chirality with Graph Neural Networks,” (2023), arXiv:2307.02198 [cs]

    2023 arXiv

  19. [27]

    GoFlow: Efficient Transition State Geometry Prediction with Flow Matching and E(3)- Equivariant Neural Networks,

    L. Galustian, K. Mark, J. Karwounopoulos, M. P.-P. Ko- var, and E. Heid, “GoFlow: Efficient Transition State Geometry Prediction with Flow Matching and E(3)- Equivariant Neural Networks,” (2025)

    2025

  20. [28]

    Adaptive Transition State Refinement with Learned Equilibrium Flows,

    S. Darouich, V. Tong, T. Bien, J. K¨ astner, and M. Niepert, “Adaptive Transition State Refinement with Learned Equilibrium Flows,” (2025), arXiv:2507.16521 10 [physics]

    2025 arXiv

  21. [29]

    GeoMol: Torsional Geometric Generation of Molecu- lar 3D Conformer Ensembles,

    O.-E. Ganea, L. Pattanaik, C. W. Coley, R. Barzi- lay, K. F. Jensen, W. H. Green, and T. S. Jaakkola, “GeoMol: Torsional Geometric Generation of Molecu- lar 3D Conformer Ensembles,” (2021), arXiv:2106.07802 [physics]

    2021 arXiv

  22. [30]

    Message Passing Net- works for Molecules with Tetrahedral Chirality,

    L. Pattanaik, O.-E. Ganea, I. Coley, K. F. Jensen, W. H. Green, and C. W. Coley, “Message Passing Net- works for Molecules with Tetrahedral Chirality,” (2020), arXiv:2012.00094 [q-bio]

    2020 arXiv

  23. [31]

    Boltz-1: Democratizing Biomolecular Interaction Mod- eling,

    J. Wohlwend, G. Corso, S. Passaro, N. Getz, M. Reveiz, K. Leidal, W. Swiderski, L. Atkinson, T. Portnoi, I. Chinn, J. Silterra, T. Jaakkola, and R. Barzilay, “Boltz-1: Democratizing Biomolecular Interaction Mod- eling,” (2025), pages: 2024.11.19.624167 Section: New Results

    2025

  24. [32]

    The difficulty of generating chirality-aware geometries is exacerbated in the setting of TS generation

    improve accuracy in chiral centres by adding chirality based angle gradients as features. The difficulty of generating chirality-aware geometries is exacerbated in the setting of TS generation. Primarily, chirality is not well-defined for TS, but rather comes to- gether as a s...

  25. [33]

    Ramakrishnan, P

    R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. von Lilienfeld, Scientific Data 1, 140022 (2014), publisher: Nature Publishing Group

    2014

  26. [34]

    Axelrod and R

    S. Axelrod and R. G´ omez-Bombarelli, Scientific Data 9, 185 (2022), publisher: Nature Publishing Group

    2022

  27. [35]

    Swallowing the Bitter Pill: Simplified Scalable Conformer Generation,

    Y. Wang, A. A. Elhag, N. Jaitly, J. M. Susskind, and M. A. Bautista, “Swallowing the Bitter Pill: Simplified Scalable Conformer Generation,” (2024), arXiv:2311.17932 [physics]

    2024 arXiv

  28. [36]

    Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transport,

    H. Hong, W. Lin, and K. C. Tan, “Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transport,” (2025), arXiv:2405.15252 [cs]

    2025 arXiv

  29. [37]

    Accelerat- ing Biomolecular Modeling with AtomWorks and RF3,

    N. Corley, S. Mathis, R. Krishna, M. S. Bauer, T. R. Thompson, W. Ahern, M. W. Kazman, R. I. Brent, K. Didi, A. Kubaney, L. McHugh, A. Nagle, A. Fa- vor, M. Kshirsagar, P. Sturmfels, Y. Li, J. Butcher, B. Qiang, L. L. Schaaf, R. Mitra, K. Campbell, O. Zhang, R. Weissman, I. R....

    2025

  30. [38]

    R. Feng, C. Yu, W. Deng, P. Hu, and T. Wu (2025)

    2025

  31. [39]

    Villani et al., Optimal transport: old and new, Vol

    C. Villani et al., Optimal transport: old and new, Vol. 338 (Springer, 2008)

    2008

  32. [40]

    Maoutsa, S

    D. Maoutsa, S. Reich, and M. Opper, Entropy 22, 802 (2020), arXiv:2006.00702 [cond-mat]

    2020 arXiv

  33. [41]

    Holderrieth and E

    P. Holderrieth and E. Erives, (2025)

    2025

  34. [42]

    Simulation- free Schr¨ odinger bridges via score and flow matching,

    A. Tong, N. Malkin, K. Fatras, L. Atanackovic, Y. Zhang, G. Huguet, G. Wolf, and Y. Bengio, “Simulation- free Schr¨ odinger bridges via score and flow matching,” (2024), arXiv:2307.03672 [cs]

    2024 arXiv

  35. [43]

    Improving and generalizing flow-based generative models with mini- batch optimal transport,

    A. Tong, K. Fatras, N. Malkin, G. Huguet, Y. Zhang, J. Rector-Brooks, G. Wolf, and Y. Bengio, “Improving and generalizing flow-based generative models with mini- batch optimal transport,” (2024), arXiv:2302.00482 [cs]

    2024 arXiv

  36. [44]

    Spiekermann, L

    K. Spiekermann, L. Pattanaik, and W. H. Green, Sci- entific Data 9, 417 (2022), publisher: Nature Publishing Group. APPENDIX A. Experiment details

    2022

  37. [45]

    The model architecture is a four layer MLP with a width of 128

    High-dimensional mode isolation For each dimension d we train a ([SF] ²M) model on the prior and target distributions described in the text. The model architecture is a four layer MLP with a width of 128. The batch size is held constant at 512 but we increase the number of tra...

  38. [46]

    For GFM inference we directly took the hyperparameters as given where possible

    Comparison with Guidance We performed the comparison directly using training scripts as given in [33], wrapping them for FK inference. For GFM inference we directly took the hyperparameters as given where possible. For OT CFM, only the hyperpa- rameters for the pair Uniform to...

  39. [47]

    TS generation We trained GoFlow with the same parameters as in

  40. [48]

    (5.2M parameter model). For the transformation into an SDE we assumed a Gaussian prior despite the Kabsch rotations that technically happen during training - experimentally no difference in performance occurred between the deterministic inference and SDE inference with no stee...

  41. [49]

    Inconsistent ground truth data For some reactions in RDB7, we find that the TS chi- rality is inconsistent with the reactant and product chi- rality, as shown for an example reaction in Fig. 10. The generated TS with FK, in contrast, depicts the correct chirality and, importan...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.