Pith. sign in

REVIEW 5 major objections 5 minor 71 references

Energy-Based Flow Matching for Generating 3D Molecular Structure

T0 review · 5 major / 5 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 Training a flow map to refine its own predicted structure — the paper's 'idempotent flow map' — improves 3D molecular generation for docking and protein design at equal compute.

desk verdict A cheap, plausible booster for molecular flow matching, but the headline protein gains are likely inflated by checkpoint selection on the test metric, and the convergence proof is circular. read the letter →

arxiv 2508.18949 v1 pith:XAXW34I3 submitted 2025-08-26 cs.LG

Wenyin Zhou , Christopher Iliffe Sprague , Vsevolod Viliuga , Matteo Tadiello , Arne Elofsson , Hossein Azizpour This is my paper
classification cs.LG
keywords idempotentflowmapenergy-basedmatchingmoleculardockingproteinbackbonegenerationconditionalstructurerefinementgenerativemodeling3D
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 proposes IDFlow, a training-and-inference modification to flow matching for 3D molecular structure generation, and claims it improves both protein-ligand docking and protein backbone design. The mechanism is to add one objective to the standard conditional flow matching loss: the network must map its own predicted structure back to the true structure, with gradients detached, making the flow map approximately idempotent. Viewed through an energy-based lens, where the reconstruction error acts as an energy function, this shapes the loss landscape with the model's own contrastive samples and doubles as a predictor-refiner sampler at inference. The reported gains come at matched sampling budget: on PDBBind docking, RMSD<2 success rises from 30.1% to 35.6% (and 28.3% to 34.7% on the time-split radius pocket), and protein backbone designability rises from 0.824 to 0.927 over FrameFlow at 200 function evaluations. If the claims hold, the practical significance is a cheap, geometry-agnostic upgrade applicable to existing x1-parameterized flow matching models.

What carries the argument

The idempotent refinement objective L_R (Eq. 21) is the load-bearing mechanism: a detached-gradient loss that trains the flow map to map its own prediction ˆx1 onto the true structure x1. It is built on the reconstruction-error energy E(ˆx1) = ||f_θ(ˆx1) − ˆx1||², an energy architecture borrowed from energy-based learning, so that contrastive samples generated by the model itself — not only the interpolated trajectory points — shape the loss landscape. Because the same network serves as sampler and refiner, inference becomes a predictor-refiner sampler: each ODE step makes a prediction and refines it once, and the single extra hyperparameter K_max controls how many refinement iterations are

What would settle it

Take a trained IDFlow model and a CFM-only control on the same docking split; iterate each model on its own outputs and audit the fixed points — do outputs stabilize, and are the stable outputs valid structures (low RMSD to training data, or passing designability)? If many fixed points are junk geometries, or if the CFM-only model is already idempotent, the mechanism the paper attributes to the new loss is called into question even if the headline gaps (35.6 vs 30.1, 34.7 vs 28.3 at RMSD<2) reproduce.

Watch

Extended reading notes

Core claim

The central claim is that an x1-parameterized flow map can be made approximately idempotent — f_θ(f_θ(x)) ≈ f_θ(x) — by adding the detached-gradient refinement loss L_R = E||f_θ(ˆx1.detach()) − x1||², where ˆx1 is the network's own prediction. With the reconstruction error read as an energy function, E(ˆx1) = ||f_θ(ˆx1) − ˆx1||², this shapes the loss landscape with the model's own contrastive samples: off-manifold predictions are pushed toward the data while the standard conditional flow matching loss anchors the trajectory. Training alternates between the CFM and refinement objectives (up to K_max iterations); inference runs one prediction plus one refinement per Euler step. The empirical c

Load-bearing premise

The theoretical guarantee that iterating the refiner lands on true structures assumes the network's fixed points coincide exactly with the data manifold — that every structure the refiner leaves unchanged is a genuine molecular structure, which no training step explicitly enforces.

Editorial extensions

If this is right

  • On single-ligand docking, IDFlow beats HarmonicFlow and product-space diffusion at matched inference budget, with RMSD<2 gains of 5.5 and 6.4 percentage points on the hardest PDBBind splits; on multi-ligand docking (Binding MOAD) it raises RMSD<5 success from 75.0% to 83.1%.
  • On protein backbone generation, IDFlow lifts designability from 0.824 (FrameFlow) to 0.927 at 200 function evaluations, approaching FoldFlow2 (0.94) while retaining mixed alpha-helix and beta-strand content rather than collapsing to all-helix structures.
  • The framework works in both Euclidean coordinate space (docking) and Riemannian SE(3) frame space (backbones), indicating that idempotent self-refinement is a geometry-agnostic component of x1-parameterized flow matching.
  • IDFlow degrades less than FrameFlow when the sampling budget shrinks (SCOPe experiments at 30 NFEs), so the objective also stabilizes short sampling trajectories, not only long ones.
  • The predictor-refiner loop draws a direct line from generative flow matching to iterative structure refinement as used in AlphaFold, casting refinement as an in-model ingredient rather than a post-hoc relaxation step.

Reading between the lines

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

  • The residual ||f_θ(x) − x|| of the trained map is a built-in confidence score: the generator could rank its own samples at inference, replacing the separately trained confidence models that docking pipelines currently use. The paper draws the analogy to confidence models but never turns it into an operating procedure.
  • Because the objective assumes only an x1-parameterization and a differentiable refiner, it should transfer as a drop-in booster to other generative tasks built on the same parameterization — small-molecule conformer generation, point clouds, or any learned denoiser — not just molecular geometry.
  • A missing control: whether a CFM-only model is already approximately idempotent. If it is, the reported gains would come from the detached-gradient anchoring to the true x1 rather than from idempotency itself, and future work should target the anchoring mechanism instead.
  • The fixed points of the trained network are never audited. If a meaningful fraction of stable outputs are junk geometries, the convergence-to-manifold interpretation (Eq. 17) fails while the benchmarks still improve; auditing fixed-point validity would separate mechanism from metric.
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

5 major / 5 minor

Summary. The paper proposes IDFlow, an energy-based refinement technique for x1-parameterized flow matching on 3D molecular structure generation. The reconstruction error E(x)=||f_theta(x)-x||^2 is used as an energy function, and training alternates the standard conditional flow matching loss with a detached-gradient idempotent loss L_R (Eq. 21) that iteratively refines the model's own predictions. At inference, one refinement is inserted per Euler step (Algorithm 2). Experiments cover single- and multi-ligand docking on PDBBind and BindingMOAD, and protein backbone generation on SCOPe and PDB, with matched NFE budgets against HarmonicFlow, FrameFlow, and diffusion baselines. The paper reports consistent improvements, most notably designability 0.927 vs. 0.824 for PDB backbones at 200 NFEs, and claims a convergence guarantee for the iterated flow map (Eq. 17).

Significance. If the empirical claim holds, IDFlow is a simple, largely orthogonal booster for x1-parameterized flow matching on molecular geometry, applicable to both Euclidean and Riemannian settings, and the public code release is a practical strength. The designability gains on protein backbones and the docking gains at matched NFE are potentially useful for practitioners. However, the theoretical framing is substantially overstated: the convergence guarantee in Sec. 3.2 is not derived, and the Appendix derivation is circular. More importantly, the checkpoint-selection protocol for the protein backbone experiments may inflate the headline designability number. The empirical contribution is plausible but currently not rigorously established for the strongest claims.

major comments (5)
  1. [Sec. 3.2, Eq. (17)] The convergence claim f_infinity(x) in {x : grad E(x)=0} = M does not follow from the nonnegativity of E. Iterating the learned network f_theta is not the same as following the gradient flow of E, and the critical points of E need not coincide with the data manifold. Moreover, spurious fixed points of f are not data points. The statement that 'the convergence of the flow map is further guaranteed' is unsupported. Please either provide a rigorous argument (including conditions on f_theta, e.g., contractivity or an explicit gradient-flow construction) or explicitly reframe Eq. (17) as a motivation/heuristic rather than a guarantee.
  2. [App. B.4, Eq. (29)] This derivation is circular. The equation sets G(hat_x1) = x' and then evaluates grad E at x' with G(hat_x1)=x1; substituting G(hat_x1)=x1 into the final expression makes it vanish by assumption, not by optimization. This does not show that the refinement loss L_R is the gradient of the negative log-likelihood energy. Please rewrite this passage so that the relationship between Eq. (28), Eq. (29), and the proposed L_R (Eq. 21) is stated as an analogy or design choice, not a proof.
  3. [App. E.2.2, Table 3] The checkpoint-selection protocol selects the checkpoint with the highest designability on the model's own generated samples, with no held-out validation split. The reported IDFlow designability (0.927 +/- 0.020) is therefore a maximum over checkpoints, while the FrameFlow baseline (0.824) is taken from Wagner et al. (2024) and was likely not selected by the same sweeping protocol. This makes the 10.3-point gap potentially inflated. Please report the epoch at which the selected checkpoint was obtained, provide the mean/standard error obtained by fixing the checkpoint by a validation criterion (e.g., a separate validation set or a fixed training epoch), and, if feasible, apply the same checkpoint sweep to the baseline.
  4. [Table 1] The docking results are stated to be averaged over three runs, but no standard deviations or confidence intervals are reported. The headline improvements (%<2 of 5.5 and 6.4 percentage points) are within a range where run-to-run variance could be material. Please add per-cell standard deviations (or confidence intervals) for Tables 1, 2, and 6, and state whether the three runs differ only in seed or in data subsampling. Without this, the statistical significance of the reported docking gains cannot be assessed.
  5. [App. B.3, Eq. (25)] The idempotency claim f(f(x)) = E[E[x1 | x_t=x]] = E[x1 | x_t=x] is not justified. Iterating the function corresponds to conditioning on a new, different random variable; the equality would require a nested sigma-field or a self-consistency condition that is not established. This is another instance where idempotency is asserted rather than derived. Please remove or replace with a clearly stated heuristic or a proof under explicit assumptions.
minor comments (5)
  1. [Sec. 2.2, Eq. (10)] Typo: 'Euclidian' should be 'Euclidean'.
  2. [Table 2] The baseline name is rendered as 'EIGEN FOLD DIFFUSION'; the intended model appears to be EigenFold (Jing et al., 2024). Please correct the naming for consistency with the references.
  3. [Sec. 3.4] The description of the training-time refinement loop says 'only K-1 outputs need to be stored' but Algorithm 1 appends all k+1 predictions to x1_list. Please clarify the memory claim and align the pseudocode with the text.
  4. [App. F, Fig. 5] The caption states IDFlow uses 10 steps while HarmonicFlow uses 20 steps. If the comparison is intended to be at matched NFE, please state explicitly that the energy is computed after refinement in both cases, and clarify why a different number of ODE steps is used.
  5. [Sec. 4.2] The novelty metric is reported as '0.72 +/- 0.01' for IDFlow(200) but the definition in App. E.2.1 states that novelty is the TM score to the closest natural protein, with lower being better (consistent with Table 3's arrow). The text says 'competitive at diversity and novelty'; please make the direction of all metrics explicit in the table caption.

Circularity Check

2 steps flagged · score 6.0 of 10

The empirical IDFlow gains are independent, but the paper's theoretical convergence/idempotency derivation is circular: the energy is defined through the very network being trained, and the gradient-zero condition is obtained by assuming the refiner already outputs the target data.

  1. self definitional [Section 3.2, Eq. 13 and Eq. 17]
    "Assuming G is a function that perfectly maps any ˆx1 to x1 on the data manifold, Eq. 13 will assign high energy (larger reconstruction error) to ‘bad’ ˆx1 and low energy (smaller reconstruction error) to ‘good’ ˆx1. ... Interestingly, as the energy in Eq. 13 is lower bounded by 0, the convergence of the flow map is further guaranteed as: f∞(x) ∈ {x ∈ Rn | ∇xE(x) = 0} = M, (17)"

    The energy is E(ˆx1) = ||G(ˆx1) − ˆx1||^2, and later G is identified with the trained flow map fθ (Eqs. 18, 21). Thus the set {x : ∇xE(x) = 0} is, by construction, the fixed-point set of the network being trained, not an independently characterized data manifold M. The conclusion f∞(x) ∈ M assumes G already maps arbitrary points onto the data manifold—the exact property the idempotent training objective is supposed to create. Lower boundedness of E does not imply convergence to a zero-gradient point, and even if it did, such points need not be data.

  2. self definitional [Appendix B.4, Eq. 29]
    "G(ˆx1) = x′ ∇E(ˆx1) = ∇( 1 2σ2 1 (x′ − x1)⊤(x′ − x1)) = −∇log p(ˆx1|x1) = 1 σ2 1 (∇G(ˆx1))(G(ˆx1) − x1) = 0 (29). Observing Eq. 29, the term could be optimized if the neural refiner G approximates the x1, which aligns with the proposed idempotent objective 21."

    The equality to zero in Eq. 29 holds only if G(ˆx1) = x1, i.e. if the neural refiner already outputs the ground-truth target. That is precisely the property the idempotent objective LR = ||G(ˆx1) − x1||^2 is meant to learn. The derivation therefore assumes its conclusion; it provides no independent argument that a trained G reaches the data manifold. The paper even states the term could be optimized if G approximates x1, which is the training target, not a consequence.

full rationale

The headline empirical claim—adding the detached-gradient refinement loss L_R (Eq. 21) improves docking and protein-backbone generation over HarmonicFlow, FrameFlow, and product-space diffusion—is a genuine experiment: the reported gains in Tables 1–3 are not entailed by the loss definition, and the comparisons are made against external baselines at matched NFE budgets. That part is self-contained and not circular. However, the paper's theoretical framing is circular in two explicit places. The energy E in Eq. 13 is defined through the network being trained (G = fθ), so the claimed convergence guarantee f∞(x) ∈ {x : ∇E = 0} = M (Eq. 17) merely restates the training objective's fixed-point condition, not an independent property of the data manifold. Appendix B.4's Eq. 29 is even more directly circular: it substitutes G(ˆx1) = x1 to obtain ∇E = 0, which is the very property to be established. Thus the 'theoretically justified' convergence/idempotency result reduces by construction to the loss being optimized. I also note App. E.2.2's checkpoint selection on the designability metric and the lack of error bars in Table 1; these are evaluation-bias concerns, not circularity, but they should be weighed when interpreting the numerical headline. The self-citations (Sprague et al. 2024; Wagner et al. 2024 with overlapping authors) are used only as related-work or baseline context, not to justify the circular steps. Overall, the central empirical result remains independent, but the paper's own derivation chain contains a partial circularity in its theoretical claims, giving a score of 6.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim rests on hyperparameters chosen by hand (refinement iteration count, 50/50 alternation, inference refinement count, path noise scale), on the standard flow matching conditional-expectation interpretation, and on two ad hoc theoretical premises: critical points of the reconstruction energy equal the data manifold, and iterating the trained network equals gradient flow of that energy. Neither premise is proven, and App. B.4's derivation of the energy gradient assumes the conclusion. No new physical or model entities are introduced; idempotency is a trained property, not a new object. The empirical claim is grounded in public benchmarks, so the ledger concerns the theoretical framing more than the experiments.

free parameters (4)
  • Kmax (max refinement iterations during training) = 2 (docking), 1 (backbone)
    Tuned by hand: increasing Kmax beyond 2 gives diminishing returns (Sec. 3.4); backbone experiments are memory-limited to Kmax = 1 (App. E.2.2).
  • Inference refinement count k per step = 1
    Ablated in Fig. 3; performance peaks at one refinement and degrades beyond, attributed to ODE discretization error.
  • Training alternation probability m = 0.5
    Chosen, not ablated: 50% of training uses CFM and 50% uses the idempotent objective (Alg. 1, Sec. 3.4).
  • Conditional path noise scale sigma_t = 0.5 (constant, docking)
    Inherited from the HarmonicFlow setup (App. E.1.3); a path design choice not independently justified here.
assumptions (7)
  • domain assumption The learned flow map approximates the conditional expectation E[X1|Xt=x] (Eq. 9).
    Standard denoiser interpretation in diffusion/flow matching; used to argue idempotency of the map via Eq. 25.
  • ad hoc to paper Critical points of the reconstruction energy E(x) = ||f(x) - x||^2 coincide with the data manifold M (Eq. 17).
    Asserted without proof; spurious fixed points of f are generally not data points. This premise is central to the claimed convergence guarantee.
  • ad hoc to paper Iterating the trained network equals gradient flow of E, so f_infinity lands on the data manifold (Eqs. 16-17).
    The trained f is not constructed as a gradient step on E, so its infinite iteration is not the gradient flow of E.
  • domain assumption Training on the model's own detached predictions is distributionally matched to inference, so one refinement per Euler step improves the trajectory.
    Borrowed from self-conditioning (Chen et al. 2023); the paper alternates CFM and refinement losses rather than conditioning the CFM loss, so the match is only partial.
  • standard math Boltzmann conversion p(x) = exp(-E(x))/Z (Eq. 14) and score = -grad E (Eq. 15).
    Standard EBM background; motivates the energy view but is not used to derive the objective.
  • standard math Riemannian exponential/log maps on SO(3) via Rodrigues formula (Eqs. 32-33) and SE(3) geodesic as the product of SO(3) and R3.
    Standard geometry background from the SE(3) flow matching literature (FrameFlow, FoldFlow).
  • ad hoc to paper App. B.4 derives the refinement gradient by assuming G(hat_x1) = x1 (Eq. 29).
    The property to be proven is assumed inside the derivation; the same slip supports Eq. 17 in the main text.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Energy-Based Flow Matching for Generating 3D Molecular Structure." pith.science (2026). https://pith.science/paper/XAXW34I3

@misc{pith2026250818949,
  author       = {Pith},
  title        = {Pith review of: Energy-Based Flow Matching for Generating 3D Molecular Structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XAXW34I3}},
  note         = {Machine review of arXiv:2508.18949}
}
read the original abstract

Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules' constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent advances in generative modeling, such as diffusion models and flow matching, have made great progress on these tasks by modeling molecular conformations as a distribution. In this work, we focus on flow matching and adopt an energy-based perspective to improve training and inference of structure generation models. Our view results in a mapping function, represented by a deep network, that is directly learned to \textit{iteratively} map random configurations, i.e. samples from the source distribution, to target structures, i.e. points in the data manifold. This yields a conceptually simple and empirically effective flow matching setup that is theoretically justified and has interesting connections to fundamental properties such as idempotency and stability, as well as the empirically useful techniques such as structure refinement in AlphaFold. Experiments on protein docking as well as protein backbone generation consistently demonstrate the method's effectiveness, where it outperforms recent baselines of task-associated flow matching and diffusion models, using a similar computational budget.

Figures

Figures reproduced from arXiv: 2508.18949 by the authors.

Figure 1
Figure 1. Training paradigm of standard flow matching and IDFlow. x0 and x1 are samples from the source and target distribution p0(x) and p1(x), xt is the linear interpolant between the source and target sample, xˆ1 is the prediction of the network, fθ(ˆx1) is the refined prediction, LCFM is the conditional flow matching loss and LR is the refinement loss. (a) Flow matching: directly predict the data xˆ1 given the interpolant… view at source ↗
Figure 2
Figure 2. Designable protein backbones generated by IDFlow at various length N = {100, 150, 200, 250, 300} [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Ablation on the number of refinements k at test time inference. 6. Conclusion We present an energy-based formulation for flow matching, an enhanced training framework for flow matching com￾bined with the EBMs for 3D molecular structure generation. We provide a specific instance of the proposed framework, IDFlow, which considers the reconstruction error as the en￾ergy function, shaping the loss landscape with contras… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The validation metric curve of docking on PDBBind of radius pocket time split. The fraction of validation RMSD < 2A vs. ˚ epoch time for IDFlow and HarmonicFlow. Top-k accuracy on docking. The top-k accuracy assumes the known ground truth and picks up the sample with t…
Figure 5
Figure 5. Figure 5: L2 error at each step during sampling averaging over the test set for HarmonicFlow and IDFlow. The energy of IDFlow is calculated by L2 error after refinement at each step, with total of 10 steps. For HarmonicFlow, we sample 20 steps with refinement for computing the L…
Figure 6
Figure 6. Figure 6: Designability and diversity comparison vs. NFEs on SCOPe dataset. G. Visualization [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]
Figure 7
Figure 7. Figure 7: Six randomly selected generated complexes on the radius pocket docking on 30% sequence similarity split. The one in blue is the ground truth, and the one in green is generated from IDFlow. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]
Figure 8
Figure 8. Figure 8: Designable Backbones at length [100, 150, 200, 250, 300] trained on PDB. Protein length from top to bottom [300, 250, 200, 150, 100]. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

71 extracted references · 47 canonical work pages

  1. [1]

    Albergo, M. S. and Vanden-Eijnden, E. Building normalizing flows with stochastic interpolants. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=li7qeBbCR1t

    work page 2023

  2. [2]

    R., Wang, J., Cong, Q., Kinch, L

    Baek, M., DiMaio, F., Anishchenko, I., Dauparas, J., Ovchinnikov, S., Lee, G. R., Wang, J., Cong, Q., Kinch, L. N., Schaeffer, R. D., et al. Accurate prediction of protein structures and interactions using a three-track neural network. Science, 373 0 (6557): 0 871--876, 2021

    work page 2021

  3. [3]

    D-flow: Differentiating through flows for controlled generation

    Ben-Hamu, H., Puny, O., Gat, I., Karrer, B., Singer, U., and Lipman, Y. D-flow: Differentiating through flows for controlled generation. arXiv preprint arXiv:2402.14017, 2024

    arXiv 2024

  4. [4]

    C., Korablyov, M., Bronstein, M

    Bose, J., Akhound-Sadegh, T., Huguet, G., FATRAS, K., Rector-Brooks, J., Liu, C.-H., Nica, A. C., Korablyov, M., Bronstein, M. M., and Tong, A. SE (3)-stochastic flow matching for protein backbone generation. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=kJFIH23hXb

    work page 2024

  5. [5]

    Riemannian flow matching policy for robot motion learning

    Braun, M., Jaquier, N., Rozo, L., and Asfour, T. Riemannian flow matching policy for robot motion learning. arXiv preprint arXiv:2403.10672, 2024

    arXiv 2024

  6. [6]

    M., and Deane, C

    Buttenschoen, M., Morris, G. M., and Deane, C. M. Posebusters: Ai-based docking methods fail to generate physically valid poses or generalise to novel sequences. Chemical Science, 15 0 (9): 0 3130--3139, 2024

    work page 2024

  7. [7]

    Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design

    Campbell, A., Yim, J., Barzilay, R., Rainforth, T., and Jaakkola, T. Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design. arXiv preprint arXiv:2402.04997, 2024

    arXiv 2024

  8. [8]

    K., and Brenner, S

    Chandonia, J.-M., Guan, L., Lin, S., Yu, C., Fox, N. K., and Brenner, S. E. Scope: improvements to the structural classification of proteins--extended database to facilitate variant interpretation and machine learning. Nucleic acids research, 50 0 (D1): 0 D553--D559, 2022

    work page 2022

Show all 71 references
  1. [9]

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

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

    2018

  2. [10]

    Chen, R. T. Q. and Lipman, Y. Flow matching on general geometries. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=g7ohDlTITL

    2024

  3. [11]

    Analog bits: Generating discrete data using diffusion models with self-conditioning

    Chen, T., ZHANG, R., and Hinton, G. Analog bits: Generating discrete data using diffusion models with self-conditioning. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=3itjR9QxFw

    2023

  4. [12]

    Cheng, A., Lo, A., Lee, K. L. K., Miret, S., and Aspuru-Guzik, A. Stiefel flow matching for moment-constrained structure elucidation. arXiv preprint arXiv:2412.12540, 2024

    2024 arXiv

  5. [13]

    Corso, G., St \"a rk, H., Jing, B., Barzilay, R., and Jaakkola, T. S. Diffdock: Diffusion steps, twists, and turns for molecular docking. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=kKF8_K-mBbS

    2023

  6. [14]

    Corso, G., Deng, A., Polizzi, N., Barzilay, R., and Jaakkola, T. S. Deep confident steps to new pockets: Strategies for docking generalization. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=UfBIxpTK10

    2024

  7. [15]

    R., Getz, N., Barzilay, R., Jaakkola, T., and Krause, A

    Corso, G., Somnath, V. R., Getz, N., Barzilay, R., Jaakkola, T., and Krause, A. Composing unbalanced flows for flexible docking and relaxation. In The Thirteenth International Conference on Learning Representations, 2025. URL https://openreview.net/forum?id=gHLWTzKiZV

    2025

  8. [16]

    J., Milles, L

    Dauparas, J., Anishchenko, I., Bennett, N., Bai, H., Ragotte, R. J., Milles, L. F., Wicky, B. I. M., Courbet, A., de Haas, R. J., Bethel, N., Leung, P. J. Y., Huddy, T. F., Pellock, S., Tischer, D., Chan, F., Koepnick, B., Nguyen, H., Kang, A., Sankaran, B., Bera, A. K., King,...

    2022

  9. [17]

    C., Xiong, G., Zhang, W., Yang, R., Cieplak, P., Luo, R., Lee, T., et al

    Duan, Y., Wu, C., Chowdhury, S., Lee, M. C., Xiong, G., Zhang, W., Yang, R., Cieplak, P., Luo, R., Lee, T., et al. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. Journal of computational chem...

    1999

  10. [18]

    and Huber, R

    Engh, R. and Huber, R. Structure quality and target parameters. 2012

    2012

  11. [19]

    K., Brenner, S

    Fox, N. K., Brenner, S. E., and Chandonia, J.-M. Scope: Structural classification of proteins—extended, integrating scop and astral data and classification of new structures. Nucleic acids research, 42 0 (D1): 0 D304--D309, 2014

    2014

  12. [20]

    and Smidt, T

    Geiger, M. and Smidt, T. e3nn: Euclidean neural networks. arXiv preprint arXiv:2207.09453, 2022

    2022 arXiv

  13. [21]

    J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y

    Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. Generative adversarial networks, 2014. URL https://arxiv.org/abs/1406.2661

    2014 arXiv

  14. [22]

    Et-flow: Equivariant flow-matching for molecular conformer generation

    Hassan, M., Shenoy, N., Lee, J., Stark, H., Thaler, S., and Beaini, D. Et-flow: Equivariant flow-matching for molecular conformer generation. arXiv preprint arXiv:2410.22388, 2024

    2024 arXiv

  15. [23]

    Denoising diffusion probabilistic models

    Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020

    2020

  16. [24]

    G., Vignac, C., and Welling, M

    Hoogeboom, E., Satorras, V. G., Vignac, C., and Welling, M. Equivariant diffusion for molecule generation in 3d. In International conference on machine learning, pp.\ 8867--8887. PMLR, 2022

    2022

  17. [25]

    L., Smith, R

    Hu, L., Benson, M. L., Smith, R. D., Lerner, M. G., and Carlson, H. A. Binding moad (mother of all databases). Proteins: Structure, Function, and Bioinformatics, 60 0 (3): 0 333--340, 2005

    2005

  18. [26]

    Re-dock: Towards flexible and realistic molecular docking with diffusion bridge

    Huang, Y., Zhang, O., Wu, L., Tan, C., Lin, H., Gao, Z., Li, S., Li, S., et al. Re-dock: Towards flexible and realistic molecular docking with diffusion bridge. arXiv preprint arXiv:2402.11459, 2024

    2024 arXiv

  19. [27]

    Sequence-augmented se (3)-flow matching for conditional protein backbone generation

    Huguet, G., Vuckovic, J., Fatras, K., Thibodeau-Laufer, E., Lemos, P., Islam, R., Liu, C.-H., Rector-Brooks, J., Akhound-Sadegh, T., Bronstein, M., et al. Sequence-augmented se (3)-flow matching for conditional protein backbone generation. Advances in neural information proces...

    2024

  20. [28]

    Torsional diffusion for molecular conformer generation

    Jing, B., Corso, G., Chang, J., Barzilay, R., and Jaakkola, T. Torsional diffusion for molecular conformer generation. Advances in Neural Information Processing Systems, 35: 0 24240--24253, 2022

    2022

  21. [29]

    Alphafold meets flow matching for generating protein ensembles

    Jing, B., Berger, B., and Jaakkola, T. Alphafold meets flow matching for generating protein ensembles. arXiv preprint arXiv:2402.04845, 2024

    2024 arXiv

  22. [30]

    Highly accurate protein structure prediction with alphafold

    Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Z \' dek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. nature, 596 0 (7873): 0 583--589, 2021

    2021

  23. [31]

    and Ben-Tal, N

    Kessel, A. and Ben-Tal, N. Introduction to proteins: structure, function, and motion. Chapman and Hall/CRC, 2018

    2018

  24. [32]

    Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014

    2014 arXiv

  25. [33]

    Kingma, D. P. and Welling, M. Auto-encoding variational bayes, 2013

    2013

  26. [34]

    From machine learning to autonomous intelligence: Lecture 2, 2022

    LeCun, Y. From machine learning to autonomous intelligence: Lecture 2, 2022. URL https://leshouches2022.github.io/SLIDES/lecun-20220720-leshouches-02.pdf. Accessed: 2024-10-02

    2022

  27. [35]

    A tutorial on energy-based learning

    LeCun, Y., Chopra, S., Hadsell, R., Ranzato, M., Huang, F., et al. A tutorial on energy-based learning. Predicting structured data, 1 0 (0), 2006

    2006

  28. [36]

    Evolutionary-scale prediction of atomic-level protein structure with a language model

    Lin, Z., Akin, H., Rao, R., Hie, B., Zhu, Z., Lu, W., Smetanin, N., Verkuil, R., Kabeli, O., Shmueli, Y., et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science, 379 0 (6637): 0 1123--1130, 2023

    2023

  29. [37]

    Lipman, Y., Chen, R. T. Q., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=PqvMRDCJT9t

    2023

  30. [38]

    T., Lopez-Paz, D., Ben-Hamu, H., and Gat, I

    Lipman, Y., Havasi, M., Holderrieth, P., Shaul, N., Le, M., Karrer, B., Chen, R. T., Lopez-Paz, D., Ben-Hamu, H., and Gat, I. Flow matching guide and code. arXiv preprint arXiv:2412.06264, 2024

    2024 arXiv

  31. [39]

    Flow straight and fast: Learning to generate and transfer data with rectified flow

    Liu, X., Gong, C., and Liu, Q. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003, 2022

    2022 arXiv

  32. [40]

    Forging the basis for developing protein--ligand interaction scoring functions

    Liu, Z., Su, M., Han, L., Liu, J., Yang, Q., Li, Y., and Wang, R. Forging the basis for developing protein--ligand interaction scoring functions. Accounts of chemical research, 50 0 (2): 0 302--309, 2017

    2017

  33. [41]

    TANKB ind: Trigonometry-aware neural networks for drug-protein binding structure prediction

    Lu, W., Wu, Q., Zhang, J., Rao, J., Li, C., and Zheng, S. TANKB ind: Trigonometry-aware neural networks for drug-protein binding structure prediction. In Oh, A. H., Agarwal, A., Belgrave, D., and Cho, K. (eds.), Advances in Neural Information Processing Systems, 2022. URL http...

    2022

  34. [42]

    G., and Zheng, S

    Lu, W., Zhang, J., Huang, W., Zhang, Z., Jia, X., Wang, Z., Shi, L., Li, C., Wolynes, P. G., and Zheng, S. Dynamicbind: predicting ligand-specific protein-ligand complex structure with a deep equivariant generative model. Nature Communications, 15 0 (1): 0 1071, 2024

    2024

  35. [43]

    A., and Wegner, J

    M \'e ndez-Lucio, O., Ahmad, M., del Rio-Chanona, E. A., and Wegner, J. K. A geometric deep learning approach to predict binding conformations of bioactive molecules. Nature Machine Intelligence, 3 0 (12): 0 1033--1039, 2021

    2021

  36. [44]

    Fabind: Fast and accurate protein-ligand binding

    Pei, Q., Gao, K., Wu, L., Zhu, J., Xia, Y., Xie, S., Qin, T., He, K., Liu, T.-Y., and Yan, R. Fabind: Fast and accurate protein-ligand binding. Advances in Neural Information Processing Systems, 36, 2024

    2024

  37. [45]

    DiffDock-Pocket : Diffusion for pocket-level docking with sidechain flexibility

    Plainer, M., Toth, M., Dobers, S., St \"a rk, H., Corso, G., Marquet, C., and Barzilay, R. DiffDock-Pocket : Diffusion for pocket-level docking with sidechain flexibility. 2023

    2023

  38. [46]

    Pooladian, A.-A., Ben-Hamu, H., Domingo-Enrich, C., Amos, B., Lipman, Y., and Chen, R. T. Multisample flow matching: Straightening flows with minibatch couplings. arXiv preprint arXiv:2304.14772, 2023

    2023 arXiv

  39. [47]

    F., and Anandkumar, A

    Qiao, Z., Nie, W., Vahdat, A., Miller III, T. F., and Anandkumar, A. State-specific protein--ligand complex structure prediction with a multiscale deep generative model. Nature Machine Intelligence, 6 0 (2): 0 195--208, 2024

    2024

  40. [48]

    W., Evans, R., Jumper, J., Kirkpatrick, J., Sifre, L., Green, T., Qin, C., Z \' dek, A., Nelson, A

    Senior, A. W., Evans, R., Jumper, J., Kirkpatrick, J., Sifre, L., Green, T., Qin, C., Z \' dek, A., Nelson, A. W., Bridgland, A., et al. Improved protein structure prediction using potentials from deep learning. Nature, 577 0 (7792): 0 706--710, 2020

    2020

  41. [49]

    V., Gandelsman, Y., Mosseri, I., Rubinstein, M., and Efros, A

    Shocher, A., Dravid, A. V., Gandelsman, Y., Mosseri, I., Rubinstein, M., and Efros, A. A. Idempotent generative network. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=XIaS66XkNA

    2024

  42. [50]

    and Ermon, S

    Song, Y. and Ermon, S. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019

    2019

  43. [51]

    P., Kumar, A., Ermon, S., and Poole, B

    Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=PxTIG12RRHS

    2021

  44. [52]

    Consistency models

    Song, Y., Dhariwal, P., Chen, M., and Sutskever, I. Consistency models. In International Conference on Machine Learning, pp.\ 32211--32252. PMLR, 2023

    2023

  45. [53]

    I., Elofsson, A., and Azizpour, H

    Sprague, C. I., Elofsson, A., and Azizpour, H. Incorporating stability into flow matching. In ICML 2024 Workshop on Structured Probabilistic Inference & Generative Modeling , 2024. URL https://openreview.net/forum?id=FLRlzO5jcv

    2024

  46. [54]

    Equibind: Geometric deep learning for drug binding structure prediction

    St \"a rk, H., Ganea, O., Pattanaik, L., Barzilay, R., and Jaakkola, T. Equibind: Geometric deep learning for drug binding structure prediction. In International conference on machine learning, pp.\ 20503--20521. PMLR, 2022

    2022

  47. [55]

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

    St \"a rk, H., Jing, B., Barzilay, R., and Jaakkola, T. Harmonic self-conditioned flow matching for multi-ligand docking and binding site design. arXiv preprint arXiv:2310.05764, 2023

    2023 arXiv

  48. [56]

    Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds

    Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., and Riley, P. Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds. arXiv preprint arXiv:1802.08219, 2018

    2018 arXiv

  49. [57]

    Improving and generalizing flow-based generative models with minibatch optimal transport

    Tong, A., FATRAS, K., Malkin, N., Huguet, G., Zhang, Y., Rector-Brooks, J., Wolf, G., and Bengio, Y. Improving and generalizing flow-based generative models with minibatch optimal transport. Transactions on Machine Learning Research, 2024. ISSN 2835-8856. URL https://openrevie...

    2024

  50. [58]

    L., Yim, J., Tischer, D., Baker, D., Broderick, T., Barzilay, R., and Jaakkola, T

    Trippe, B. L., Yim, J., Tischer, D., Baker, D., Broderick, T., Barzilay, R., and Jaakkola, T. Diffusion probabilistic modeling of protein backbones in 3d for the motif-scaffolding problem. arXiv preprint arXiv:2206.04119, 2022

    2022 arXiv

  51. [59]

    S., Tumescheit, C., Mirdita, M., Lee, J., Gilchrist, C

    Van Kempen, M., Kim, S. S., Tumescheit, C., Mirdita, M., Lee, J., Gilchrist, C. L., S \"o ding, J., and Steinegger, M. Fast and accurate protein structure search with foldseek. Nature biotechnology, 42 0 (2): 0 243--246, 2024

    2024

  52. [60]

    Generating highly designable proteins with geometric algebra flow matching

    Wagner, S., Seute, L., Viliuga, V., Wolf, N., Gr \"a ter, F., and Stuehmer, J. Generating highly designable proteins with geometric algebra flow matching. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id...

    2024

  53. [61]

    A., Jaitly, N., Susskind, J

    Wang, Y., Elhag, A. A., Jaitly, N., Susskind, J. M., and Bautista, M. \'A . Swallowing the bitter pill: Simplified scalable conformer generation. In Forty-first International Conference on Machine Learning, 2024

    2024

  54. [62]

    L., Juergens, D., Bennett, N

    Watson, J. L., Juergens, D., Bennett, N. R., Trippe, B. L., Yim, J., Eisenach, H. E., Ahern, W., Borst, A. J., Ragotte, R. J., Milles, L. F., et al. De novo design of protein structure and function with rfdiffusion. Nature, 620 0 (7976): 0 1089--1100, 2023

    2023

  55. [63]

    E., Yang, K

    Wu, K. E., Yang, K. K., van den Berg, R., Alamdari, S., Zou, J. Y., Lu, A. X., and Amini, A. P. Protein structure generation via folding diffusion. Nature communications, 15 0 (1): 0 1059, 2024

    2024

  56. [64]

    Geodiff: A geometric diffusion model for molecular conformation generation

    Xu, M., Yu, L., Song, Y., Shi, C., Ermon, S., and Tang, J. Geodiff: A geometric diffusion model for molecular conformation generation. In International Conference on Learning Representations, 2022 a . URL https://openreview.net/forum?id=PzcvxEMzvQC

    2022

  57. [65]

    Poisson flow generative models

    Xu, Y., Liu, Z., Tegmark, M., and Jaakkola, T. Poisson flow generative models. Advances in Neural Information Processing Systems, 35: 0 16782--16795, 2022 b

    2022

  58. [66]

    Pfgm++: Unlocking the potential of physics-inspired generative models

    Xu, Y., Liu, Z., Tian, Y., Tong, S., Tegmark, M., and Jaakkola, T. Pfgm++: Unlocking the potential of physics-inspired generative models. In International Conference on Machine Learning, pp.\ 38566--38591. PMLR, 2023

    2023

  59. [67]

    Y., Gastegger, M., Jim \'e nez-Luna, J., Lewis, S., Satorras, V

    Yim, J., Campbell, A., Foong, A. Y., Gastegger, M., Jim \'e nez-Luna, J., Lewis, S., Satorras, V. G., Veeling, B. S., Barzilay, R., Jaakkola, T., et al. Fast protein backbone generation with se (3) flow matching. arXiv preprint arXiv:2310.05297, 2023 a

    2023 arXiv

  60. [68]

    L., De Bortoli, V., Mathieu, E., Doucet, A., Barzilay, R., and Jaakkola, T

    Yim, J., Trippe, B. L., De Bortoli, V., Mathieu, E., Doucet, A., Barzilay, R., and Jaakkola, T. Se (3) diffusion model with application to protein backbone generation. arXiv preprint arXiv:2302.02277, 2023 b

    2023 arXiv

  61. [69]

    E3bind: An end-to-end equivariant network for protein-ligand docking

    Zhang, Y., Cai, H., Shi, C., and Tang, J. E3bind: An end-to-end equivariant network for protein-ligand docking. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=sO1QiAftQFv

    2023

  62. [70]

    Energy-based generative adversarial networks

    Zhao, J., Mathieu, M., and LeCun, Y. Energy-based generative adversarial networks. In International Conference on Learning Representations, 2017. URL https://openreview.net/forum?id=ryh9pmcee

    2017

  63. [71]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

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