Pith. sign in

REVIEW 3 major objections 5 minor 61 references

Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The paper proposes SO(3)-Averaged Flow, a flow-matching training objective that integrates over molecular rotations in closed form, and shows it converges faster and enables one-step conformer generation.

desk verdict Genuine new objective with clean math and strong reflow/distillation results, but the DiT efficiency claim is confounded by an unsupported switch to an ODE-simulated interpolant. read the letter →

arxiv 2507.09785 v1 pith:X43WL3DM submitted 2025-07-13 cs.LG physics.chem-ph

Zhonglin Cao , Mario Geiger , Allan dos Santos Costa , Danny Reidenbach , Karsten Kreis , Tomas Geffner , Franco Pellegrini , Guoqing Zhou
show 1 more author
Emine Kucukbenli
This is my paper · ORCID
classification cs.LGphysics.chem-ph
keywords molecularconformergenerationflowmatchingSO(3)-averagedreflowdistillationone-stepequivariantgraphneuralnetworksdiffusiontransformer
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 introduces SO(3)-Averaged Flow, a flow-matching objective for molecular conformer generation that computes the expected flow over all rotations of each target conformer analytically, removing the need to rotationally align noise and data before training. The authors argue that this objective converges in far fewer training epochs to better coverage and RMSD than conditional optimal transport or Kabsch-aligned flow, and that combining it with reflow and distillation yields high-quality conformers in two or even one ODE step. On GEOM-QM9 the resulting DiT model outperforms all baselines on every reported metric, and on GEOM-Drugs the one-step distilled model beats all compared one-step and two-step baselines. If these results hold, fast and accurate conformer generation becomes practical for large-scale virtual screening, where per-sample sampling cost has been the bottleneck.

What carries the argument

The SO(3)-Averaged Flow objective: the conditional vector field $$u_t(x) = \frac{[\partial_\$\alpha$ \log Z_t(x,\$\alpha$)]_{\$\alpha$=0} - x}{1-t},$$ where $Z_t$ is a sum over conformers of closed-form integrals $$\int_{SO(3)} \exp(\mathrm{tr}(F R^T))\, dR$$ evaluated with the matrix-Fisher formula. This object carries the argument because it makes rotation invariance a property of the training target rather than of a chosen alignment, and it is what allows Averaged Flow to converge faster while remaining architecture-agnostic.

What would settle it

Train the non-equivariant DiT on GEOM-Drugs with the Averaged Flow objective using the linear interpolant and the same epoch budget; if its final coverage and RMSD match AvgFlowDiT, then the integration interpolant is not load-bearing and the main reason for the added training complexity collapses.

Watch

Extended reading notes

Core claim

The central claim is that rotation symmetry in the conformer distribution can be integrated out of the flow-matching objective instead of being handled by data alignment. Rather than randomly assigning a rotation to each target conformer or aligning the noise to the target with Kabsch, the paper trains the velocity field against the exact conditional flow averaged over the Haar measure of SO(3), using a closed-form matrix-Fisher integral. In the paper's own terms, this objective converges faster to better generation quality for both equivariant and non-equivariant architectures, and reflow plus distillation then straightens the trajectories enough that one-step generation surpasses all compared baselines on GEOM-Drugs and reaches state-of-the-art on GEOM-QM9.

Load-bearing premise

All DiT results rest on the unstated assumption that a non-equivariant network needs the 20-step ODE-integrated interpolant for Averaged Flow training rather than the simple linear interpolant; if the linear interpolant worked equally well, the reported training-efficiency advantage would shrink and the DiT experiments would need to be regenerated.

Editorial extensions

If this is right

  • On GEOM-QM9, AvgFlowDiT outperforms all baselines on all four metrics, including COV-R of 96.0%, AMR-R of 0.082 Å, COV-P of 95.0%, and AMR-P of 0.088 Å.
  • Reflow and distillation reduce sampling to two or one ODE steps; the one-step AvgFlowDiT-D on GEOM-Drugs reaches COV-R 76.8% and COV-P 61.0%, beating all one-step and two-step baselines by a wide margin.
  • The Averaged Flow objective is architecture-agnostic: it improves both a small equivariant NequIP model and a 52M-parameter non-equivariant DiT model compared with conditional OT and Kabsch-aligned training.
  • Few-step sampling becomes extremely cheap: the two-step NequIP model generates a conformer in 2.68 ms, reported as 21 to 50 times faster than MCF variants sampled with three DDIM steps.
  • The paper shows reflow is necessary when fewer than about five ODE steps are used; without reflow, NequIP coverage collapses to zero at one step, while reflow and distillation preserve quality down to one step.

Reading between the lines

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

  • Editorial extension: the same averaging idea should transfer to any generation task whose target distribution is invariant under a compact group with a tractable Haar integral, such as protein backbone generation or point-cloud modeling; the paper claims this generality but does not test it.
  • Editorial extension: the paper never ablates the linear interpolant for non-equivariant networks; if the linear interpolant worked as well as the 20-step ODE integration, the DiT pipeline would be simpler and cheaper than reported.
  • Editorial extension: at one-step generation quality, the practical bottleneck for virtual screening likely shifts from sampling cost to dataset construction, property prediction, and the choice of coverage thresholds such as δ = 0.5 Å or 0.75 Å, which the paper does not examine.
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

3 major / 5 minor

Summary. The paper proposes SO(3)-Averaged Flow Matching, a training objective that analytically marginalizes the conditional flow target over the rotation group, removing the need for explicit rotational alignment between noise and conformer data. The objective is tested with two architectures: an equivariant NequIP model and a non-equivariant DiT model, on GEOM-QM9 and GEOM-Drugs. The paper also applies reflow and distillation to straighten flow trajectories, enabling two-step and one-step conformer generation. The authors report faster convergence for the averaged objective compared with conditional OT and Kabsch-aligned flow, state-of-the-art results on GEOM-QM9 for AvgFlowDiT, competitive results on GEOM-Drugs, and strong one-step generation quality after distillation.

Significance. If the empirical claims hold, this is a significant contribution: the closed-form averaged target avoids rotational alignment and is architecture-agnostic in principle; reflow/distillation delivers one-step conformer generation at reported speeds of 2.68 microseconds per conformer for NequIP and 14.6 ms for DiT. The mathematical derivation in Eqs. (1)-(8) is clean and internally consistent, and the paper ships a Python implementation of the averaged target in Appendix C.1. The central empirical claims, however, currently rest on single training runs, a 300-molecule subset without variance, and a DiT comparison whose training interpolant differs between the averaged objective and the baselines.

major comments (3)
  1. [Sec. 2.2, Sec. 3.1, Eq. (9), Algorithm 1] There is a time-index inconsistency in the linear interpolant. The paper defines t=0 as noise and t=1 as data, and the conditional path in Eq. (3) has mean t*x1 at time t. As written, Eq. (9) gives xt = t*x0 + (1-t)*x1, so t=0 yields the data point x1 and t=1 yields the noise x0, i.e., the time-reversed interpolation. Algorithm 1 repeats this reversed form. If this is not a typographical error, the training objective for the equivariant model does not correspond to the averaged flow defined by Eqs. (3)-(5); if it is a typo, all occurrences of Eq. (9) (including the reflow objective Eq. (11) where x'_t is used) must be corrected. Either way, the current text is not reproducible and the equivariant results in Fig. 2a and Tables 1-2 are affected.
  2. [Sec. 3.1, Eq. (10), Fig. 2b, Tables 1-2] For non-equivariant networks, the paper states without supporting ablation that Averaged Flow training 'requires' the integration interpolant xt = x0 + int_0^t u_tau dtau, approximated with 20 fixed Euler steps, while the comparison objectives (conditional OT and Kabsch alignment) use the linear interpolant for the DiT baselines. This confounds the claimed convergence advantage in Fig. 2b and the DiT rows of Tables 1-2 with a change in training distribution: AvgFlowDiT is trained on ODE-trajectory samples, whereas Cond.OTDiT and KabschDiT are trained on linear interpolants. Moreover, the 20-step ODE simulation is not included in the overhead benchmark reported in Table C.2 (Appendix Table 7). Since sampling xt by a linear interpolant and regressing on the marginal target ut(xt) of Eq. (5) is a valid flow-matching objective, the authors should provide an ablation of AvgFlowDiT with the linear interpolant and report the actual per-step training cost including the interpolant; otherwise the architecture-agnostic faster-training claim for DiT is not established.
  3. [Fig. 2, Tables 1-2] No error bars, number of seeds, or confidence intervals are reported. Fig. 2 reports convergence curves on a 300-molecule subset from single runs, and the state-of-the-art claims in Tables 1-2 are point estimates without uncertainty. Some reported differences are small (e.g., Fig. 2a AMR-P of 0.814 vs 0.815 at different epochs), so it is not possible for the reader to judge whether the observed improvements are significant. The authors should provide at least a small number of seeds or confidence intervals for the main convergence and SOTA comparisons, or explicitly state and justify single-run reporting.
minor comments (5)
  1. [Sec. 3.1, Table C.2] The text references 'Table C.2' for the computation time benchmark, but the appendix table is numbered Table 7. Please make the cross-reference consistent.
  2. [Sec. 3.2, Eq. (11)] The reflow loss uses x'_t without defining it. Please state explicitly, e.g., x'_t = (1-t)x'_0 + t x'_1, in a way that is consistent with the corrected interpolant convention.
  3. [Sec. 3.1, Appendix B.3.1] Sec. 3.1 says the conformer ensemble expectation is approximated by sampling one conformer uniformly per training epoch, following previous works with uniform qhat. Appendix B.3.1 says 'We selected the top-30 conformers for model training.' These statements are inconsistent; please clarify whether qhat is uniform over all conformers or over a top-30 subset, and specify when the subset is used.
  4. [Appendix B.3.1] There is a typo: 'to maixmize the utilization' should be 'to maximize the utilization.'
  5. [Fig. 2 caption] The caption says the trained models 'consistently converge to better performance,' but no error bars or repeated runs are shown; please align the caption wording with the actual experimental evidence.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the SO(3)-averaged target is analytic and externally benchmarked; only a minor non-load-bearing self-citation and an unsupported interpolant-switch claim appear.

full rationale

The paper's central training objective (Eq. 8) regresses a network onto u_t(x_t), which is computed analytically from Eqs. 3-7 using the closed-form SO(3) integral of Mohlin et al.; no parameter is fitted to the benchmark quantities (COV/AMR), and the GEOM-QM9/GEOM-Drugs evaluations are external. Reflow (Eq. 11) and distillation (Eq. 12) follow the standard rectified-flow procedure, where the coupling is produced by the model itself; this is the method, not a circular derivation. The only manuscript passage that could be mistaken for circularity is Section 3.1's claim that non-equivariant networks 'require' the integration interpolant (Eq. 10) approximated with 20 Euler steps. This is an empirical assertion with no supporting ablation, and Fig. 2b thereby compares AvgFlowDiT under Eq. 10 against baselines under the linear interpolant; that is a potential confound of the comparison and a support gap, but it is not a reduction of the central claim to its own inputs by construction. There is one minor self-citation: the DiT pairwise-bias design is credited as 'proven highly effective' in ProteinA (Geffner et al., 2025), a paper with overlapping authors, but this citation is not load-bearing for the Averaged Flow derivation or the benchmark claims. Overall circularity score 1.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central derivation rests on standard flow matching and matrix Fisher analysis; the main paper-specific choices are the integration interpolant and the reflow time-sampling exponent. No new physical entities are introduced.

free parameters (6)
  • lambda (reflow time-sampling exponent) = -1.2
    Chosen by hand to focus reflow training on t<0.5 (Section 3.2, Fig. 7). Affects reflow quality but is not fit to data.
  • integration interpolant Euler steps = 20
    Fixed number of Euler steps to solve Eq. 10 for non-equivariant architectures (Section 3.1). Larger steps improve accuracy at higher training cost; the value is chosen by hand.
  • conditional path metric Sigma = unspecified; code offers identity and graph Laplacian
    The derivation allows a general N x N covariance; the appendix code provides avg_flow (identity) and avg_harmonic_flow (graph Laplacian). The paper does not state which was used in the reported experiments. The choice changes the flow path and therefore the target vector field.
  • number of training conformers per molecule = top-30
    In B.3.1 the NequIP model is trained on the top-30 CREST conformers per molecule. This is a data-selection choice that affects the learned ensemble.
  • conformer weighting qhat = uniform
    Section 3.1: 'Following previous works (Jing et al., 2022), qhat(ˆx) is taken as a uniform distribution over all conformers.' This is an assumption about the target ensemble, not a fitted number, but it is a modeling choice.
  • conformer ensemble sampling per training step = 1
    Section 3.1: 'in practice, we approximate the expectation of the conformer ensemble by sampling one conformer in each training epoch.' This replaces the sum over conformers in Eq. 7 with a single sample.
assumptions (5)
  • domain assumption The conformer distribution q(x) is invariant under SO(3) and can be decomposed as orbits with Haar-measure integral (Eq. 1).
    Section 3.1, used to justify averaging over rotations. Holds for conformer ensembles but not for chiral-specific orientation-sensitive tasks.
  • standard math The conditional probability path is Gaussian with linear mean (Eq. FM10/FM11); the vector field ut(x|x1) = (x1 - x)/(1-t).
    Section 2.2, from Lipman et al. 2023. Standard flow matching construction.
  • standard math The closed-form integral over SO(3) of exp(tr(F R^T)) from Mohlin et al. (2020) is valid and numerically reliable for the F matrices encountered.
    Section 3.1, Eq. 6. Used to evaluate log Z_t; the appendix implementation includes numerical quadrature and derivatives.
  • standard math Reflow reduces transport cost and straightens trajectories (Liu et al. 2022), and the distilled one-step model (Eq. 12) preserves marginal quality.
    Section 3.2, cited from rectified flow literature; the empirical validity for molecular conformers is tested in Section 4.
  • ad hoc to paper For non-equivariant networks, the integration interpolant (Eq. 10) is required for Averaged Flow training.
    Section 3.1, stated as an empirical finding with no ablation. All DiT results depend on this choice.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow." pith.science (2026). https://pith.science/paper/X43WL3DM

@misc{pith2026250709785,
  author       = {Pith},
  title        = {Pith review of: Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X43WL3DM}},
  note         = {Machine review of arXiv:2507.09785}
}
read the original abstract

Fast and accurate generation of molecular conformers is desired for downstream computational chemistry and drug discovery tasks. Currently, training and sampling state-of-the-art diffusion or flow-based models for conformer generation require significant computational resources. In this work, we build upon flow-matching and propose two mechanisms for accelerating training and inference of generative models for 3D molecular conformer generation. For fast training, we introduce the SO(3)-Averaged Flow training objective, which leads to faster convergence to better generation quality compared to conditional optimal transport flow or Kabsch-aligned flow. We demonstrate that models trained using SO(3)-Averaged Flow can reach state-of-the-art conformer generation quality. For fast inference, we show that the reflow and distillation methods of flow-based models enable few-steps or even one-step molecular conformer generation with high quality. The training techniques proposed in this work show a path towards highly efficient molecular conformer generation with flow-based models.

Figures

Figures reproduced from arXiv: 2507.09785 by the authors.

Figure 1
Figure 1. SO(3)-Averaged Flow and Reflow (a) We illustrate a comparison between our approach Averaged Flow, conditional OT and Kabsch + Flow. While conditional OT randomly assigns any rotation of the data, Kabsch + Flow assigns the rotation of largest overlap. Our method instead computes the expected flow across all rotations. (b) Flow trajectory visualization before and after the reflow with 100 Euler steps. The flow traject… view at source ↗
Figure 2
Figure 2. Comparison between training objectives. Both (a) NequIP and (b) DiT model trained with Averaged Flow consistently converge to better performance on a 300-molecule GEOM-Drugs test subset. The other two objectives we compared Averaged Flow to are: (i) Conditional OT and (ii) Kabsch alignment of noise x0 with conformer x1 before conditional OT (Hassan et al., 2024). 4. Experiments Following previous works, we train and… view at source ↗
Figure 3
Figure 3. shows the the performance of our NequIP model using Euler solver with number of steps Nstep ∈ {1, 2, 3, 5, 10, 20, 50, 100}. The performance of the mod￾els is evaluated with the same four metrics on a subset of the GEOM-Drugs test set containing 300 molecules. Over￾all, AvgFlowNequIP performs better when Nstep ≥ 10 than AvgFlowNequIP-R. When Nstep < 10, the performance of AvgFlowNequIP starts to collapse and eventua… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Single function call wall-clock time comparison. 5. Conclusion We have presented SO(3)-Averaged Flow as a new objective to accelerate the training of flow-matching models for molec￾ular conformer generation. Averaged Flow leads to faster convergence and better performa…
Figure 5
Figure 5. Figure 5: Modified NequIP model architecture (a) Overview of the modified NequIP architecture for the flow vector field prediction. (b) Details of the interaction block, where atomic features are mixed and refined with relative distance vectors ⃗r and edge features E. (c) In the…
Figure 6
Figure 6. Figure 6: DiT model architecture. (a) The overview of DiT. (b) The details of the adaptive multi-head attention with pairwise bias and adaptive transition block [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: The distribution of t during reflow The distribution of t during reflow is sampled from p(t) ∝ Exp(λt), where λ = −1.2. The distribution is visualized in [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Comparison between ODE trajectories. Visualization of selected generated conformers (SMILES attached) and the ODE trajectories. Orange trajectories are from AvgFlowDiT before reflow, and green trajectories are from AvgFlowDiT-D after reflow+distillation. Carbon atoms a…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 33 canonical work pages

  1. [1]

    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 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    J., Bambrick, J., et al

    Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ronneberger, O., Willmore, L., Ballard, A. J., Bambrick, J., et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, 630 0 (8016): 0 493--500, 2024

    work page 2024

  3. [3]

    Albergo, M. S. and Vanden-Eijnden, E. Building normalizing flows with stochastic interpolants. In The Eleventh International Conference on Learning Representations (ICLR), 2023

    work page 2023

  4. [4]

    and Gomez-Bombarelli, R

    Axelrod, S. and Gomez-Bombarelli, R. Geom, energy-annotated molecular conformations for property prediction and molecular generation. Scientific Data, 9 0 (1): 0 185, 2022

    2022

  5. [5]

    Gfn2-xtb—an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions

    Bannwarth, C., Ehlert, S., and Grimme, S. Gfn2-xtb—an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. Journal of chemical theory and computation, 15 0 (3): 0 1652--1671, 2019

    work page 2019

  6. [6]

    P., Kornbluth, M., Molinari, N., Smidt, T

    Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications, 13 0 (1): 0 2453, 2022

    work page 2022

  7. [7]

    Comparison of combinatorial fragment spaces and its application to ultralarge make-on-demand compound catalogs

    Bellmann, L., Penner, P., Gastreich, M., and Rarey, M. Comparison of combinatorial fragment spaces and its application to ultralarge make-on-demand compound catalogs. Journal of Chemical Information and Modeling, 62 0 (3): 0 553--566, 2022

    work page 2022

  8. [8]

    Chirikjian, G. S. and Kyatkin, A. B. Engineering applications of noncommutative harmonic analysis: with emphasis on rotation and motion groups. CRC press, 2000

    work page 2000

Show all 61 references
  1. [9]

    Vision transformers need registers

    Darcet, T., Oquab, M., Mairal, J., and Bojanowski, P. Vision transformers need registers. arXiv preprint arXiv:2309.16588, 2023

    2023 arXiv

  2. [10]

    P., Caron, M., Geirhos, R., Alabdulmohsin, I., et al

    Dehghani, M., Djolonga, J., Mustafa, B., Padlewski, P., Heek, J., Gilmer, J., Steiner, A. P., Caron, M., Geirhos, R., Alabdulmohsin, I., et al. Scaling vision transformers to 22 billion parameters. In International Conference on Machine Learning, pp.\ 7480--7512. PMLR, 2023

    2023

  3. [11]

    P., Joshi, C

    Dwivedi, V. P., Joshi, C. K., Luu, A. T., Laurent, T., Bengio, Y., and Bresson, X. Benchmarking graph neural networks. Journal of Machine Learning Research, 24 0 (43): 0 1--48, 2023

    2023

  4. [12]

    Scaling rectified flow transformers for high-resolution image synthesis

    Esser, P., Kulal, S., Blattmann, A., Entezari, R., M \"u ller, J., Saini, H., Levi, Y., Lorenz, D., Sauer, A., Boesel, F., et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first International Conference on Machine Learning, 2024

    2024

  5. [13]

    Geomol: Torsional geometric generation of molecular 3d conformer ensembles

    Ganea, O., Pattanaik, L., Coley, C., Barzilay, R., Jensen, K., Green, W., and Jaakkola, T. Geomol: Torsional geometric generation of molecular 3d conformer ensembles. Advances in Neural Information Processing Systems, 34: 0 13757--13769, 2021

    2021

  6. [14]

    Proteina: Scaling flow-based protein structure generative models

    Geffner, T., Didi, K., Zhang, Z., Reidenbach, D., Cao, Z., Yim, J., Geiger, M., Dallago, C., Kucukbenli, E., Vahdat, A., et al. Proteina: Scaling flow-based protein structure generative models. arXiv preprint arXiv:2503.00710, 2025

    2025 arXiv

  7. [15]

    and Smidt, T

    Geiger, M. and Smidt, T. e3nn: Euclidean neural networks, 2022. URL https://arxiv.org/abs/2207.09453

    2022 arXiv

  8. [16]

    Geiger, M., Smidt, T., M., A., Miller, B. K., Boomsma, W., Dice, B., Lapchevskyi, K., Weiler, M., Tyszkiewicz, M., Batzner, S., Madisetti, D., Uhrin, M., Frellsen, J., Jung, N., Sanborn, S., Wen, M., Rackers, J., Rød, M., and Bailey, M. Euclidean neural networks: e3nn, April 2...

    2022 doi

  9. [17]

    Exploration of chemical compound, conformer, and reaction space with meta-dynamics simulations based on tight-binding quantum chemical calculations

    Grimme, S. Exploration of chemical compound, conformer, and reaction space with meta-dynamics simulations based on tight-binding quantum chemical calculations. Journal of chemical theory and computation, 15 0 (5): 0 2847--2862, 2019

    2019

  10. [18]

    W., Ma, W.-Y., Ma, J., and Peng, J

    Guan, J., Qian, W. W., Ma, W.-Y., Ma, J., and Peng, J. Energy-inspired molecular conformation optimization. In international conference on learning representations, 2021

    2021

  11. [19]

    R., Mathiowetz, A

    Guimar\ a es, C. R., Mathiowetz, A. M., Shalaeva, M., Goetz, G., and Liras, S. Use of 3d properties to characterize beyond rule-of-5 property space for passive permeation. Journal of chemical information and modeling, 52 0 (4): 0 882--890, 2012

    2012

  12. [20]

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

    Hassan, M., Shenoy, N., Lee, J., St \"a rk, H., Thaler, S., and Beaini, D. Et-flow: Equivariant flow-matching for molecular conformer generation. Advances in Neural Information Processing Systems, 37: 0 128798--128824, 2024

    2024

  13. [21]

    Hawkins, P. C. Conformation generation: the state of the art. Journal of chemical information and modeling, 57 0 (8): 0 1747--1756, 2017

    2017

  14. [22]

    C., Skillman, A

    Hawkins, P. C., Skillman, A. G., Warren, G. L., Ellingson, B. A., and Stahl, M. T. Conformer generation with omega: algorithm and validation using high quality structures from the protein databank and cambridge structural database. Journal of chemical information and modeling,...

    2010

  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]

    Perceiver io: A general architecture for structured inputs & outputs

    Jaegle, A., Borgeaud, S., Alayrac, J.-B., Doersch, C., Ionescu, C., Ding, D., Koppula, S., Zoran, D., Brock, A., Shelhamer, E., et al. Perceiver io: A general architecture for structured inputs & outputs. arXiv preprint arXiv:2107.14795, 2021

    2021 arXiv

  17. [25]

    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

  18. [26]

    Eigenfold: Generative protein structure prediction with diffusion models

    Jing, B., Erives, E., Pao-Huang, P., Corso, G., Berger, B., and Jaakkola, T. Eigenfold: Generative protein structure prediction with diffusion models. arXiv preprint arXiv:2304.02198, 2023

    2023 arXiv

  19. [27]

    Rdkit: open-source cheminformatics http://www

    Landrum, G. Rdkit: open-source cheminformatics http://www. rdkit. org. Google Scholar There is no corresponding record for this reference, 3 0 (8), 2016

    2016

  20. [28]

    Disco: Diffusion schr \"o dinger bridge for molecular conformer optimization

    Lee, D., Lee, D., Bang, D., and Kim, S. Disco: Diffusion schr \"o dinger bridge for molecular conformer optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp.\ 13365--13373, 2024 a

    2024

  21. [29]

    Improving the training of rectified flows

    Lee, S., Lin, Z., and Fanti, G. Improving the training of rectified flows. Advances in neural information processing systems, 37: 0 63082--63109, 2024 b

    2024

  22. [30]

    Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations

    Liao, Y.-L., Wood, B., Das, A., and Smidt, T. Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations. arXiv preprint arXiv:2306.12059, 2023

    2023 arXiv

  23. [31]

    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

  24. [32]

    Rectified flow: A marginal preserving approach to optimal transport

    Liu, Q. Rectified flow: A marginal preserving approach to optimal transport. arXiv preprint arXiv:2209.14577, 2022

    2022 arXiv

  25. [33]

    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

  26. [34]

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

    Liu, X., Gong, C., and qiang liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. In The Eleventh International Conference on Learning Representations (ICLR), 2023 a

    2023

  27. [35]

    Instaflow: One step is enough for high-quality diffusion-based text-to-image generation

    Liu, X., Zhang, X., Ma, J., Peng, J., et al. Instaflow: One step is enough for high-quality diffusion-based text-to-image generation. In The Twelfth International Conference on Learning Representations, 2023 b

    2023

  28. [36]

    and Hutter, F

    Loshchilov, I. and Hutter, F. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017

    2017 arXiv

  29. [37]

    Predicting molecular conformation via dynamic graph score matching

    Luo, S., Shi, C., Xu, M., and Tang, J. Predicting molecular conformation via dynamic graph score matching. Advances in Neural Information Processing Systems, 34: 0 19784--19795, 2021

    2021

  30. [38]

    On distillation of guided diffusion models

    Meng, C., Rombach, R., Gao, R., Kingma, D., Ermon, S., Ho, J., and Salimans, T. On distillation of guided diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.\ 14297--14306, 2023

    2023

  31. [39]

    Probabilistic orientation estimation with matrix fisher distributions

    Mohlin, D., Sullivan, J., and Bianchi, G. Probabilistic orientation estimation with matrix fisher distributions. In Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., and Lin, H. (eds.), Advances in Neural Information Processing Systems, volume 33, pp.\ 4884--4893. Curran A...

    2020

  32. [40]

    and Bechtolsheim, L

    Nachbin, L. and Bechtolsheim, L. The haar integral. (No Title), 1965

    1965

  33. [41]

    and Xie, S

    Peebles, W. and Xie, S. Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pp.\ 4195--4205, 2023

    2023

  34. [42]

    Automated exploration of the low-energy chemical space with fast quantum chemical methods

    Pracht, P., Bohle, F., and Grimme, S. Automated exploration of the low-energy chemical space with fast quantum chemical methods. Physical Chemistry Chemical Physics, 22 0 (14): 0 7169--7192, 2020

    2020

  35. [43]

    S., Grant, J

    Rush, T. S., Grant, J. A., Mosyak, L., and Nicholls, A. A shape-based 3-d scaffold hopping method and its application to a bacterial protein- protein interaction. Journal of medicinal chemistry, 48 0 (5): 0 1489--1495, 2005

    2005

  36. [44]

    and Ho, J

    Salimans, T. and Ho, J. Progressive distillation for fast sampling of diffusion models. arXiv preprint arXiv:2202.00512, 2022

    2022 arXiv

  37. [45]

    Schwab, C. H. Conformations and 3d pharmacophore searching. Drug Discovery Today: Technologies, 7 0 (4): 0 e245--e253, 2010

    2010

  38. [46]

    Learning gradient fields for molecular conformation generation

    Shi, C., Luo, S., Xu, M., and Tang, J. Learning gradient fields for molecular conformation generation. In International conference on machine learning, pp.\ 9558--9568. PMLR, 2021

    2021

  39. [47]

    and MacKerell Jr, A

    Shim, J. and MacKerell Jr, A. D. Computational ligand-based rational design: role of conformational sampling and force fields in model development. MedChemComm, 2 0 (5): 0 356--370, 2011

    2011

  40. [48]

    Simm, G. N. and Hern \'a ndez-Lobato, J. M. A generative model for molecular distance geometry. arXiv preprint arXiv:1909.11459, 2019

    1909 arXiv

  41. [49]

    Denoising diffusion implicit models

    Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502, 2020

    2010 arXiv

  42. [50]

    and Dhariwal, P

    Song, Y. and Dhariwal, P. Improved techniques for training consistency models. arXiv preprint arXiv:2310.14189, 2023

    2023 arXiv

  43. [51]

    Consistency models

    Song, Y., Dhariwal, P., Chen, M., and Sutskever, I. Consistency models. arXiv preprint arXiv:2303.01469, 2023

    2023 arXiv

  44. [52]

    and Olson, A

    Trott, O. and Olson, A. J. Autodock vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. Journal of computational chemistry, 31 0 (2): 0 455--461, 2010

    2010

  45. [53]

    Runge--kutta pairs of order 5 (4) satisfying only the first column simplifying assumption

    Tsitouras, C. Runge--kutta pairs of order 5 (4) satisfying only the first column simplifying assumption. Computers & Mathematics with Applications, 62 0 (2): 0 770--775, 2011

    2011

  46. [54]

    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

  47. [55]

    Smiles, a chemical language and information system

    Weininger, D. Smiles, a chemical language and information system. 1. introduction to methodology and encoding rules. Journal of chemical information and computer sciences, 28 0 (1): 0 31--36, 1988

    1988

  48. [56]

    Fast point cloud generation with straight flows

    Wu, L., Wang, D., Gong, C., Liu, X., Xiong, Y., Ranjan, R., Krishnamoorthi, R., Chandra, V., and Liu, Q. Fast point cloud generation with straight flows. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.\ 9445--9454, 2023

    2023

  49. [57]

    Efficient streaming language models with attention sinks

    Xiao, G., Tian, Y., Chen, B., Han, S., and Lewis, M. Efficient streaming language models with attention sinks. arXiv preprint arXiv:2309.17453, 2023

    2023 arXiv

  50. [58]

    An end-to-end framework for molecular conformation generation via bilevel programming

    Xu, M., Wang, W., Luo, S., Shi, C., Bengio, Y., Gomez-Bombarelli, R., and Tang, J. An end-to-end framework for molecular conformation generation via bilevel programming. In International conference on machine learning, pp.\ 11537--11547. PMLR, 2021

    2021

  51. [59]

    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. arXiv preprint arXiv:2203.02923, 2022

    2022 arXiv

  52. [60]

    Group theory in a nutshell for physicists, volume 17

    Zee, A. Group theory in a nutshell for physicists, volume 17. Princeton University Press, 2016

    2016

  53. [61]

    Direct molecular conformation generation

    Zhu, J., Xia, Y., Liu, C., Wu, L., Xie, S., Wang, Y., Wang, T., Qin, T., Zhou, W., Li, H., et al. Direct molecular conformation generation. arXiv preprint arXiv:2202.01356, 2022

    2022 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.