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REVIEW 3 major objections 5 minor 36 references

P2DFlow: A Protein Ensemble Generative Model with SE(3) Flow Matching

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read P2DFlow claims that SE(3) flow matching with an 'approximate energy' condition generates protein ensembles that resemble MD ground truth more closely than two baselines.

desk verdict The approximate-energy conditioner is a genuine new idea and clearly helps in the ablation, but the inference-time sampling procedure for it is underspecified, which leaves the headline comparison against zero-shot baselines open to an information-leakage critique. read the letter →

arxiv 2411.17196 v2 pith:SKWMJX43 submitted 2024-11-26 physics.bio-ph cs.LG

Yaowei Jin , Qi Huang , Ziyang Song , Mingyue Zheng , Dan Teng , Qian Shi This is my paper · ORCID
classification physics.bio-phcs.LG
keywords proteinensemblesflowmatchingSE(3)equivarianceconformationaldynamicsmolecularsurrogateESMFoldpriorapproximateenergyequivariantgraphneuralnetwork
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

This paper claims that protein conformational ensembles can be generated by a flow-matching model that starts from perturbed ESMFold predictions and is conditioned on a scalar 'approximate energy' derived from the ensemble's density in the radius-of-gyration/RMSD plane. On roughly a hundred test proteins from the ATLAS MD dataset, the generated ensembles are closer to the ground-truth MD distributions than two current generative baselines across validity, fidelity, and contact-dynamics metrics. The method also samples both open and closed states of two well-studied multi-state proteins and reproduces residue flexibility profiles. If the result holds, P2DFlow is a fast proxy for molecular dynamics simulations of backbone ensembles.

What carries the argument

The machinery is SE(3) flow matching on rigid frames: the backbone of each residue is represented as a frame (rotation plus translation) in SE(3), interpolated along optimal-transport straight paths on rotations (geodesics) and translations, with the vector field learned by an equivariant network built from Invariant Point Attention and E(n)-equivariant graph neural network layers. The 'approximate energy' is a scalar condition computed from a 2D Gaussian kernel density over radius-of-gyration and RMSD, converted to an energy through the Boltzmann equation; this scalar is fed to the network to distinguish intermediate states. A strong prior, ESMFold predictions with Gaussian coordinate perturbation, provides the flow with a physically reasonable starting geometry, and a Kabsch pre-alignment plus a center-of-mass subtraction enforce equivariance. An auxiliary loss on reconstructed atom coordinates and distance matrices helps the model recover all-atom geometry.

What would settle it

An ablation that replaces the Boltzmann-sampled 'approximate energy' with a fixed median value, evaluated on the same ATLAS test set: if the fidelity metrics (PWD/RG Jensen-Shannon divergences, weak/transient contact Jaccard similarities) do not degrade, the conditioning dimension is not carrying the claimed work.

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Extended reading notes

Core claim

The central claim is that the distribution of protein backbone conformations from MD can be learned as a flow from a strong structural prior, ESMFold predictions with coordinate noise, to the ensemble distribution, provided the target state is labeled by an 'approximate energy'. The 'approximate energy' is obtained by projecting an MD ensemble onto a 2D plane spanned by radius of gyration and RMSD to the crystal structure, estimating the Gaussian kernel density, and converting it via the Boltzmann relation. At inference the model draws this scalar from a Boltzmann distribution and keeps it fixed as a condition while integrating the SE(3) flow. The discovery, as the authors state it, is that this extra dimension prevents the model from generating non-existent intermediate states and lets a single model reproduce observable dynamics such as weak and transient contacts, open/closed transitions, and per-residue fluctuations more accurately than the baselines.

Load-bearing premise

The load-bearing premise is that the sampler's 'approximate energy' distribution, drawn from a Boltzmann distribution at inference, is the right conditioning for a new protein; since that energy is derived from an MD ensemble's geometry-density map, a protein without MD data has no defined way to set it.

Editorial extensions

If this is right

  • On the ATLAS test set, P2DFlow's sampled structures pass steric, bond, and Ramachandran sanity checks more often than the baselines, with steric validity at 94.1% versus 72.5% and 66.7%.
  • The generated ensembles have lower Jensen-Shannon divergence to MD for pairwise distances and radius of gyration, and a much lower 2-Wasserstein distance (15.2 versus 33.6 and 78.2), meaning the whole distribution, not just the average, is closer to MD.
  • Weak and transient contact Jaccard similarities are higher (0.710 and 0.422), indicating that the model recovers residue pairs that dissociate or associate under thermal fluctuation.
  • P2DFlow can populate both open and closed states of D-ribose binding protein and adenylate kinase, and an autoregressive resampling scheme with the farthest sample as a new prior expands conformational coverage.
  • Used as a proxy for MD, the model generates backbone ensembles in a fraction of the cost, potentially enabling ensemble-based analysis of protein function at scale.

Reading between the lines

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

  • The 'approximate energy' is defined per MD ensemble, so applying P2DFlow to a protein without MD data would require estimating the Boltzmann distribution over RG/RMSD from sequence or a single structure; the paper gives no such calibration, which limits zero-shot use.
  • The conditioning mechanism is testable: one could sample energies at the extremes of the training distribution and check whether the generated structures occupy the corresponding RG/RMSD regions, and whether the marginal density matches the kernel density used to define the energies.
  • Because the prior comes from ESMFold, the model inherits ESMFold's bias toward the predicted static structure, which is visible in the bias toward one state; this suggests ensemble coverage could be improved at the prior level, not only by autoregressive resampling.
  • The backbone-only design leaves side-chain conformations out; adding torsion prediction or explicit side-chain frames would be a natural extension, but the paper does not address it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes P2DFlow, a generative model based on SE(3) flow matching that aims to predict protein conformational ensembles from sequence. The method uses an ESMFold prediction with added Gaussian noise as a prior, and introduces an 'approximate energy' conditioning variable obtained by projecting MD ensembles onto the radius-of-gyration (RG)/RMSD plane, computing a Gaussian kernel density, and converting density to energy via the Boltzmann equation. The model is trained on the ATLAS MD dataset and evaluated on roughly 100 held-out ATLAS ensembles. The authors compare against AlphaFlow and STR2STR using validity, fidelity, and dynamics metrics, and report that P2DFlow outperforms both baselines on all metrics. They also present case studies on domain motions, PCA projections, weak and transient contacts, and RMSF profiles.

Significance. If the claims are substantiated, P2DFlow would be a valuable contribution: a fast, sequence-conditional generative model for protein ensembles could serve as a proxy for expensive MD simulations and would be broadly useful in structural biology and drug discovery. The paper introduces an interesting conditioning mechanism and the authors have released code. However, the current evidence is undermined by two load-bearing issues: the test-time sampling procedure for 'approximate energy' is not specified and may leak ground-truth MD information, and the baseline comparison is not controlled because AlphaFlow and STR2STR are used zero-shot rather than trained on the ATLAS training split. The absence of uncertainty quantification in the headline results further weakens the comparison. The core idea is defensible, but the manuscript needs additional experiments and analysis before the central claim can be accepted.

major comments (3)
  1. [Section 2.2] The 'approximate energy' conditioner is defined per MD ensemble as a function of the Gaussian KDE in the RG/RMSD plane, with density converted to energy via the Boltzmann equation. At inference, the text says only 'We then sample the approximate energy from Boltzmann Distribution' without specifying what distribution is used for a test protein. If the sampled energies are drawn from the target test protein's MD-derived distribution, then the model is conditioned with information about the ground-truth ensemble that AlphaFlow and STR2STR do not receive; this would make the Table 1 comparison unfair and directly contradict the claim that P2DFlow predicts ensembles 'without the need for expensive MD simulations.' If, instead, a training-set or global Boltzmann distribution is used, there is no argument that those energies correspond to an unseen protein's conformational distribution, and a mismatch could systematically misdirect generation. The manuscript provides no calibration procedure, no ablation of the sampling distribution, and no discussion of the train/inference discrepancy. This is the load-bearing premise of the central claim and it is unsecured.
  2. [Section 3.1 (Baseline)] The baseline comparison is not controlled: P2DFlow is trained on ATLAS training ensembles, while AlphaFlow and STR2STR are evaluated using pretrained weights in a zero-shot manner. The paper states 'We use their pretrained weights offered at GitHub to sample ensembles on the test set' but does not fine-tune or train those baselines on the same ATLAS training split. Consequently, the reported improvements in Table 1 may reflect a training-domain advantage rather than an architectural or methodological advantage of P2DFlow. To support the claim that P2DFlow 'outperforms' these baselines, the authors should either train the baselines on the same ATLAS split with comparable compute, or clearly restrict the claim to the zero-shot setting and discuss the implications.
  3. [Table 1 and Figure 3] The central evaluation table reports only single point estimates for each metric, with no error bars, standard deviations, or significance tests across the approximately 100 test ensembles. Given the large variability expected across proteins, the claim that P2DFlow outperforms AlphaFlow and STR2STR on every metric is not statistically supported. Figure 3 provides histograms and fitted Gaussian curves, but these are also qualitative and lack per-protein paired comparisons. The authors should report per-protein distributions, confidence intervals, and paired significance tests (e.g., Wilcoxon signed-rank) for the main metrics.
minor comments (5)
  1. [Section 2.1, Eq. (6)] The loss in Eq. (6) is written with a 1/(1-t)^2 factor, but the text immediately after says this factor is replaced by 1/(1-min{t,0.9})^2 to prevent loss explosion. Please align the equation with the actual implementation.
  2. [Section 2.2] The phrase 'sample the approximate energy from Boltzmann Distribution' requires a temperature parameter and a specification of the energy function's normalization. The current description is not sufficient to reproduce the sampling procedure.
  3. [Section 2.1] The generation process is described as 'autoregressive sampling,' but the method solves an ODE via Euler integration and does not appear to be autoregressive in the usual sense. Please clarify or reword.
  4. [Section 3.2.1] The text mentions a 'box plot distribution' that 'further corroborates this observation,' but Figure 3 only shows histograms. Please either add the box plot or remove the reference.
  5. [Section 3.1] The paper states that ~100 ensembles were randomly chosen from ATLAS excluding the training set, but it does not specify how many distinct proteins this corresponds to or how the training/test split was defined. Please report the exact split and ensure there is no sequence-level leakage.

Circularity Check

1 steps flagged · score 6.0 of 10

The approximate-energy conditioner is defined from the ground-truth MD ensemble, and at inference the only specified way to sample it is from that same ensemble, injecting the target's RG/RMSD density into generation and partially forcing the fidelity metrics.

  1. self definitional [Section 2.2 (definition of 'approximate energy' and sampling process; Figure 2); Section 3.1 (ATLAS training/evaluation)]
    "We project the molecular dynamics (MD) simulation ensembles onto a two-dimensional plane defined by the radius of gyration (RG) and the root-mean-square deviation (RMSD) relative to the crystal structure. We then compute the Gaussian kernel density of this 2D map and apply the Boltzmann Equation to convert the density values into ‘approximate energy’ values after normalization. ... We then sample the 'approximate energy' from Boltzmann Distribution, and keep it unchanged throughout the entire autoregressive sampling process to guide the generation."

    The conditioning variable is not an independent physical quantity: it is computed from the very MD ensemble the model is supposed to predict. At inference the only defined Boltzmann distribution for 'approximate energy' is the one derived from a target MD ensemble, since the text gives no sequence-based estimator, calibration, or learned prior for it. For ATLAS test proteins, the target MD ensembles are available, so this procedure would inject the ground-truth RG/RMSD density into generation.

full rationale

The flow-matching core (SE(3) OT interpolation, IPA/EGNN backbone, auxiliary structure loss, ESMFold-plus-noise prior) is standard and internally consistent, and the comparisons to AlphaFlow and STR2STR use external pretrained models, so there is no self-citation circularity. The single load-bearing circular step is the 'approximate energy' conditioner. That input is defined by kernel-density estimation over the RG/RMSD projection of an MD ensemble, and at inference the paper says only that the value is sampled from a Boltzmann distribution and held fixed; no procedure is given to obtain that distribution for a new protein without MD data. Because the evaluation set is drawn from ATLAS, whose MD ensembles define each test protein's approximate energy, the model can be—and, as written, the only fully specified way to condition it is to be—supplied with a summary of the ground truth it is then scored against. This does not make the whole derivation equivalent to its input: the model still generates all-atom coordinates and must pass validity checks. But it partially forces the very distributional metrics used to claim superiority. Score 6 reflects a central prediction that is partly reducible to the target-derived conditioner, while acknowledging the remaining learned structure generation is not circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central claim depends on several unreported hyperparameters and on the assumption that the MD-derived 'approximate energy' can be transferred to new proteins at inference. The most important ad hoc element is the 'approximate energy' itself.

free parameters (4)
  • prior noise variance
    Gaussian noise added to ESMFold coordinates to form the prior distribution; variance is not reported.
  • approximate energy KDE bandwidth
    Bandwidth for Gaussian kernel density estimation over the RG/RMSD plane; not reported.
  • Boltzmann sampling temperature
    Temperature used to sample 'approximate energy' from the Boltzmann distribution; not reported.
  • auxiliary loss weight alpha
    Weight of the auxiliary atom-coordinate and distance-matrix losses in Eq. (6); not reported.
assumptions (5)
  • standard math Flow matching with optimal transport paths can learn the target distribution.
    Used in Section 2.1; standard generative modeling theory.
  • domain assumption ESMFold and ESM-2 provide accurate sequence representations and starting structures.
    Relies on ESMFold prediction as prior and ESM-2 embeddings; assumes these are reliable for arbitrary sequences.
  • domain assumption ATLAS MD simulations represent the true equilibrium ensemble of each protein.
    Training and evaluation assume MD data are ground truth; if MD is biased or short, learned ensembles inherit that bias.
  • ad hoc to paper The 'approximate energy' computed from the MD ensemble is a sufficient conditioning signal.
    A 2D density over RG and RMSD is used to represent ensemble state; no proof is given that this low-dimensional summary captures the diversity relevant for structure generation.
  • ad hoc to paper The Boltzmann relation between density and approximate energy is valid.
    Density is converted to energy through the Boltzmann equation, but the paper does not state the exact relation or constants.
invented entities (1)
  • approximate energy
    purpose: Conditioning variable that encodes the position of a conformer in the RG/RMSD density map of the MD ensemble, used to guide flow generation.
    It is defined operationally from the MD ensemble itself and is not independently measurable; no falsifiable prediction outside the training data.

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Cite this review

Pith. "Pith review of P2DFlow: A Protein Ensemble Generative Model with SE(3) Flow Matching." pith.science (2026). https://pith.science/paper/SKWMJX43

@misc{pith2026241117196,
  author       = {Pith},
  title        = {Pith review of: P2DFlow: A Protein Ensemble Generative Model with SE(3) Flow Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SKWMJX43}},
  note         = {Machine review of arXiv:2411.17196}
}
read the original abstract

Biological processes, functions, and properties are intricately linked to the ensemble of protein conformations, rather than being solely determined by a single stable conformation. In this study, we have developed P2DFlow, a generative model based on SE(3) flow matching, to predict the structural ensembles of proteins. We specifically designed a valuable prior for the flow process and enhanced the model's ability to distinguish each intermediate state by incorporating an additional dimension to describe the ensemble data, which can reflect the physical laws governing the distribution of ensembles, so that the prior knowledge can effectively guide the generation process. When trained and evaluated on the MD datasets of ATLAS, P2DFlow outperforms other baseline models on extensive experiments, successfully capturing the observable dynamic fluctuations as evidenced in crystal structure and MD simulations. As a potential proxy agent for protein molecular simulation, the high-quality ensembles generated by P2DFlow could significantly aid in understanding protein functions across various scenarios. Code is available at https://github.com/BLEACH366/P2DFlow

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Reference graph

Works this paper leans on

36 extracted references · 28 canonical work pages

  1. [1]

    Vögele, M., Zhang, B. W., Kaindl, J.; Wang, L., Is the functional response of a receptor determined by the thermodynamics of ligand binding? Journal of Chemical Theory and Computation 2023, 19 (22), 8414-8422

    work page 2023

  2. [2]

    D., Borowsky, J

    Meller, A., Ward, M. D., Borowsky, J. H., et al., Predicting the locations of cryptic pockets from single protein structures using the PocketMiner graph neural network. Biophysical journal 2023, 122 (3), 445a

    work page 2023

  3. [3]

    BioRxiv 2022, 2022.07

    Wu, R., Ding, F., Wang, R., et al., High -resolution de novo structure prediction from primary sequence. BioRxiv 2022, 2022.07. 21.500999

    work page 2022

  4. [4]

    The Twelfth International Conference on Learning Representations 2024

    Lu, J., Zhong, B., Zhang, Z.; Tang, J., Str2str: A score -based framework for zero- shot protein conformation sampling. The Twelfth International Conference on Learning Representations 2024

    work page 2024

  5. [5]

    Nature 2021, 596 (7873), 583-589

    Jumper, J., Evans, R., Pritzel, A., et al., Highly accurate protein structure prediction with AlphaFold. Nature 2021, 596 (7873), 583-589

    work page 2021

  6. [6]

    Science 2023, 379 (6637), 1123-1130

    Lin, Z., Akin, H., Rao, R., et al., Evolutionary -scale prediction of atomic -level protein structure with a language model. Science 2023, 379 (6637), 1123-1130

    work page 2023

  7. [7]

    J., Protein structure prediction has reached the single -structure frontier

    Lane, T. J., Protein structure prediction has reached the single -structure frontier. Nature Methods 2023, 20 (2), 170-173

    work page 2023

  8. [8]

    E., Structural biology is solved—now what? Nature methods 2022, 19 (1), 24-26

    Ourmazd, A., Moffat, K.; Lattman, E. E., Structural biology is solved—now what? Nature methods 2022, 19 (1), 24-26

    work page 2022

Show all 36 references
  1. [9]

    Bioinformatics 2022, 38 (10), 2742-2748

    Saldañ o, T., Escobedo, N., Marchetti, J., et al., Impact of protein conformational diversity on AlphaFold predictions. Bioinformatics 2022, 38 (10), 2742-2748

    2022

  2. [10]

    L., AlphaFold2 fails to predict protein fold switching

    Chakravarty, D.; Porter, L. L., AlphaFold2 fails to predict protein fold switching. Protein Science 2022, 31 (6), e4353

    2022

  3. [11]

    E., Maragakis, P., Lindorff -Larsen, K., et al., Atomic -level characterization of the structural dynamics of proteins

    Shaw, D. E., Maragakis, P., Lindorff -Larsen, K., et al., Atomic -level characterization of the structural dynamics of proteins. Science 2010, 330 (6002), 341- 346

    2010

  4. [12]

    M.; Valleau, J

    Torrie, G. M.; Valleau, J. P., Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. Journal of Computational Physics 1977, 23 (2), 187-199

    1977

  5. [13]

    Proceedings of the national academy of sciences 2002, 99 (20), 12562-12566

    Laio, A.; Parrinello, M., Escaping free -energy minima. Proceedings of the national academy of sciences 2002, 99 (20), 12562-12566

    2002

  6. [14]

    Science 2019, 365 (6457), eaaw1147

    Noé , F., Olsson, S., Kö hler, J.; Wu, H., Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning. Science 2019, 365 (6457), eaaw1147

    2019

  7. [15]

    K., Ojoawo, A., Otten, R., et al., Predicting multiple conformations via sequence clustering and AlphaFold2

    Wayment-Steele, H. K., Ojoawo, A., Otten, R., et al., Predicting multiple conformations via sequence clustering and AlphaFold2. Nature 2024, 625 (7996), 832- 839

    2024

  8. [16]

    A.; Mchaourab, H

    Stein, R. A.; Mchaourab, H. S., SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2. PLOS Computational Biology 2022, 18 (8), e1010483

    2022

  9. [17]

    S.; Meiler, J., Sampling alternative conformational states of transporters and receptors with AlphaFold2

    Del Alamo, D., Sala, D., Mchaourab, H. S.; Meiler, J., Sampling alternative conformational states of transporters and receptors with AlphaFold2. Elife 2022, 11, e75751

    2022

  10. [18]

    arXiv preprint arXiv:2306.05445 2023

    Zheng, S., He, J., Liu, C., et al., Towards predicting equilibrium distributions for molecular systems with deep learning. arXiv preprint arXiv:2306.05445 2023

    2023 arXiv

  11. [19]

    bioRxiv 2024, 2024.12

    Lewis, S., Hempel, T., Jimé nez Luna, J., et al., Scalable emulation of protein equilibrium ensembles with generative deep learning. bioRxiv 2024, 2024.12. 05.626885

    2024

  12. [20]

    bioRxiv 2024, 2024.06

    Tang, Y., Yu, M., Bai, G., et al., Deep learning of protein energy landscape and conformational dynamics from experimental structures in PDB. bioRxiv 2024, 2024.06. 27.600251

    2024

  13. [21]

    arXiv preprint arXiv:2402.04845 2024

    Jing, B., Berger, B.; Jaakkola, T., AlphaFold Meets Flow Matching for Generating Protein Ensembles. arXiv preprint arXiv:2402.04845 2024

    2024 arXiv

  14. [22]

    -C.; Galochkina, T., ATLAS: protein flexibility description from atomistic molecular dynamics simulations

    Vander Meersche, Y., Cretin, G., Gheeraert, A., Gelly, J. -C.; Galochkina, T., ATLAS: protein flexibility description from atomistic molecular dynamics simulations. Nucleic Acids Research 2024, 52 (D1), D384-D392

    2024

  15. [23]

    T., Ben -Hamu, H., Nickel, M.; Le, M., Flow matching for generative modeling

    Lipman, Y., Chen, R. T., Ben -Hamu, H., Nickel, M.; Le, M., Flow matching for generative modeling. International Conference on Learning Representations 2023

    2023

  16. [24]

    T., Rubanova, Y., Bettencourt, J.; Duvenaud, D

    Chen, R. T., Rubanova, Y., Bettencourt, J.; Duvenaud, D. K., Neural ordinary differential equations. Advances in neural information processing systems 2018, 31

    2018

  17. [25]

    arXiv preprint arXiv:2209.14734 2022

    Vignac, C., Krawczuk, I., Siraudin, A., et al., Digress: Discrete denoising diffusion for graph generation. arXiv preprint arXiv:2209.14734 2022

    2022 arXiv

  18. [26]

    arXiv preprint arXiv:2304.02198 2023

    Jing, B., Erives, E., Pao -Huang, P., et al., Eigenfold: Generative protein structure prediction with diffusion models. arXiv preprint arXiv:2304.02198 2023

    2023 arXiv

  19. [27]

    Harmonic prior self-conditioned flow matching for multi -ligand docking and binding site design

    Stark, H., Jing, B., Barzilay, R.; Jaakkola, T. Harmonic prior self-conditioned flow matching for multi -ligand docking and binding site design. In NeurIPS 2023 AI for Science Workshop, 2023

    2023

  20. [28]

    S.; Vanden-Eijnden, E

    Albergo, M. S.; Vanden-Eijnden, E. J. a. p. a., Building normalizing flows with stochastic interpolants. In The Eleventh International Conference on Learning Representations 2022

    2022

  21. [29]

    T.; Lipman, Y., Riemannian flow matching on general geometries

    Chen, R. T.; Lipman, Y., Riemannian flow matching on general geometries. arXiv preprint arXiv:2302.03660 2023

    2023 arXiv

  22. [30]

    Y., et al., Fast protein backbone generation with SE (3) flow matching

    Yim, J., Campbell, A., Foong, A. Y., et al., Fast protein backbone generation with SE (3) flow matching. arXiv preprint arXiv:2310.05297 2023

    2023 arXiv

  23. [31]

    -A., Ben -Hamu, H., Domingo -Enrich, C., et al., Multisample flow matching: Straightening flows with minibatch couplings

    Pooladian, A. -A., Ben -Hamu, H., Domingo -Enrich, C., et al., Multisample flow matching: Straightening flows with minibatch couplings. arXiv preprint arXiv:2304.14772 2023

    2023 arXiv

  24. [32]

    L., De Bortoli, V., et al., Se (3) diffusion model with application to protein backbone generation

    Yim, J., Trippe, B. L., De Bortoli, V., et al., Se (3) diffusion model with application to protein backbone generation. arXiv preprint arXiv:2302.02277 2023

    2023 arXiv

  25. [33]

    J., Akhound -Sadegh, T., Huguet, G., et al., Se (3) -stochastic flow matching for protein backbone generation

    Bose, A. J., Akhound -Sadegh, T., Huguet, G., et al., Se (3) -stochastic flow matching for protein backbone generation. arXiv preprint arXiv:2310.02391 2023

    2023 arXiv

  26. [34]

    G., Hoogeboom, E.; Welling, M

    Satorras, V. G., Hoogeboom, E.; Welling, M. E (n) equivariant graph neural networks. In International conference on machine learning , PMLR: 2021; pp 9323 - 9332

    2021

  27. [35]

    Advances in Neural Information Processing Systems 2024, 36

    Klein, L., Krä mer, A.; Noé , F., Equivariant flow matching. Advances in Neural Information Processing Systems 2024, 36

    2024

  28. [36]

    T., Nickel, M., Le, M.; Lipman, Y

    Shaul, N., Chen, R. T., Nickel, M., Le, M.; Lipman, Y. On kinetic optimal probability paths for generative models. In International Conference on Machine Learning, PMLR: 2023; pp 30883-30907. Table of Contents

    2023

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Reviewed August 12, 2026 · model on record in the stance chip above.