Pith. sign in

REVIEW 2 major objections 5 minor 64 references

Structure pretraining plus a temporal interpolator turns scarce MD data into chemically realistic trajectories.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-13 12:04 UTC

load-bearing objection Solid, well-ablated recipe that turns conformer pretraining into better all-atom MD trajectories; the cross-Hamiltonian prior gap is real but does not sink the empirical claim. the 2 major comments →

arxiv 2604.03911 v1 submitted 2026-04-05 cs.LG q-bio.QM

Align Your Structures: Generating Trajectories with Structure Pretraining for Molecular Dynamics

Aniketh Iyengar , Jiaqi Han , Pengwei Sun , Mingjian Jiang , Jianwen Xie , Stefano Ermon This is my paper
classification cs.LG q-bio.QM
keywords molecular dynamicsstructure pretrainingdiffusion modelstemporal interpolatorconformer generationequivariant networkstrajectory generation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Molecular dynamics trajectories are hard to generate with deep models because long, realistic simulations are expensive and the joint space of many atomic frames is huge. This paper claims that the problem can be split cleanly: first learn how molecules sit in space from abundant static conformer data, then learn only how those frames should line up in time from the scarce MD data. A diffusion model is pretrained on large conformer sets; an equivariant temporal interpolator is then trained on top of it so that the final sampler mixes the frozen structure predictions with a learned temporal correction. The authors show that this two-stage route produces trajectories whose bond lengths, angles, torsions, slow modes, and energies match reference MD far more closely than models trained only on trajectories, across small molecules, tetrapeptides, and a protein monomer, and for unconditional generation, forward simulation, and interpolation.

Core claim

A conformer diffusion model pretrained on large static structure data, combined with an equivariant temporal interpolator that linearly mixes its outputs with a temporal network, yields MD trajectories whose geometric, dynamical, and energetic statistics are substantially closer to reference simulations than trajectory-only baselines, because the interpolator only has to learn residual temporal correlations from limited MD data.

What carries the argument

The equivariant temporal interpolator (Eq. 3 and its cascaded block form): a learnable mixing coefficient blends the frozen structure denoiser with a temporal attention network, inducing an intermediate distribution that interpolates between the product of independent frames and the true MD joint.

Load-bearing premise

The frozen conformer model already produces frames close enough to real MD marginals that the temporal module only needs residual corrections; if the prior is far off, limited MD data cannot recover realistic dynamics.

What would settle it

Train the same architecture without structure pretraining (or freeze a deliberately poor conformer model) on the same MD splits and check whether bond-length, torsion, TICA, and energy Wasserstein distances remain as low as the reported pretrained numbers; a large collapse would refute the claim that the product distribution is a useful anchor.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • MD generative models can be trained for many more molecules by recycling large public conformer libraries instead of running new long simulations for every system.
  • Unconditional, forward, and interpolation sampling become different modes of the same pretrained architecture simply by changing the conditioning mask and the mixing coefficient.
  • Energy and slow-mode fidelity improve enough that short generative roll-outs can substitute for some intermediate-length classical MD runs in screening pipelines.
  • The same pretrain-then-align pattern extends at least to tetrapeptides and protein monomers, suggesting a path toward larger biomolecular systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the interpolator truly only learns residual dynamics, the same frozen structure backbone could be reused across force fields or temperatures by swapping only the temporal module.
  • The learned mixing coefficients encode a soft hierarchy (early layers keep structure, later layers push dynamics), which could be inspected as a diagnostic of how far a given MD dataset sits from its conformer prior.
  • Long-horizon error still accumulates; adding force- or energy-guided sampling at inference may be a direct next experiment that does not require new architecture.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper proposes EGINTERPOLATOR, a two-stage diffusion framework for MD trajectory generation: a geometric diffusion model is first pretrained on large-scale conformer ensembles (GEOM-QM9/Drugs), after which an equivariant temporal interpolator (Eq. 3, with simple and cascaded variants) is trained on scarce MD trajectories to enforce temporal consistency. The interpolator mixes frozen structure-model scores with a learnable temporal network via a coefficient α (or per-block α^(l)), theoretically inducing an intermediate target distribution (Theorem 4.1). The method is evaluated on unconditional generation, forward simulation (with block roll-outs), and interpolation/transition-path sampling for small molecules, then extended to tetrapeptides (Timewarp) and a protein-monomer setting (ATLAS/Boltz-1 backbone). Reported gains are large reductions in JSD on bond/angle/torsion/TICA distributions, improved MSM path probabilities, and substantially lower Wasserstein-1 energy distances versus GeoTDM and autoregressive baselines, plus ablations removing pretraining or the cascade.

Significance. If the central claim holds, the work offers a practical and conceptually clean remedy for the twin bottlenecks of MD data scarcity and high-dimensional trajectory modeling by decomposing the problem into structure generation plus residual temporal alignment. The design is supported by a clean score-matching argument (Theorem 4.1), SE(3)-equivariance proofs, extensive multi-task experiments (including energy profiles and MSM path statistics), ablations, and public code. These elements make the contribution more than incremental relative to prior molecule-specific or torsion-only MD generators; successful generalization across chemical space would be valuable for ML-accelerated sampling in chemistry and drug discovery.

major comments (2)
  1. The load-bearing claim that the frozen conformer product ˆpmd = ∏ pcf(x^(t)) supplies a useful anchor for residual temporal learning (Theorem 4.1, §4.1–4.2) is not adequately stress-tested against distribution shift. GEOM conformers are produced by CREST/GFN2-xTB metadynamics, while the MD trajectories use classical OpenFF force fields + explicit solvent at 300 K (§5.1–5.2, B.2). These ensembles differ in both Hamiltonian and sampling protocol. Table 2 only removes pretraining entirely (EGINTERPOLATOR-N); the peptide experiments construct the conformer set from the same MD frames (B.1.1), so they do not probe cross-distribution transfer. Without a matched-prior control, energy/JSD comparisons of the two ensembles, or an ablation that freezes a deliberately mismatched structure model, it remains unclear how much of the reported gains (Tables 1, 7–8, Figs. 4–6) are attributable to a faithf
  2. Long-horizon fidelity is central to the claim of “chemically realistic MD trajectories,” yet block-diffusion roll-outs exhibit progressive energy deterioration (A.7.2, Tables 7–9). While the authors note mild early-block degradation and later compounding, the main tables report only short (4-block) or parallelized evaluations; the 16-block Drugs experiment (A.5) still shows elevated JSD relative to short roll-outs. A quantitative bound or mitigation strategy (e.g., energy/force guidance, re-anchoring) is needed before the dynamical and energetic superiority claims can be considered fully established for simulation-length trajectories.
minor comments (5)
  1. Typos and wording: “thr training flexibility” (§4.2), “thr” elsewhere; “physio-realistic” appears repeatedly and should be standardized to “physically realistic.”
  2. Figure 3 caption and panel labels mix BASICES results with the later EGINTERPOLATOR narrative; clarify that panel A is purely the pretrained structure model.
  3. Notation for the interpolation coefficient is overloaded (scalar α, per-layer α^(l), logits k, inference-time λ). A short glossary or consistent superscript would help.
  4. Protein results (§5.8, Fig. 6D) are described as “preliminary” and shown for a single example; either expand the quantitative panel or move the claim to future work.
  5. Appendix A.1 comparison with MDGen is useful but the N/A entries for bond metrics should be explained (MDGen is torsion-parameterized).

Circularity Check

1 steps flagged

No load-bearing circularity: Theorem 4.1 is a standard score-identity derivation of an intermediate target, empirical gains rest on external MD oracles/baselines, and GeoTDM self-citation supplies only an architectural component.

specific steps
  1. self citation load bearing [§4.3 / §2 (instantiation of temporal network)]
    "For the temporal network, we utilize the Equivariant Temporal Attention Layer introduced in Han et al. (2024) to capture the temporal dependency with attention"

    The ETLayer is taken from prior work by overlapping authors (GeoTDM). This is ordinary architectural reuse, not a uniqueness claim or a premise that forces the paper's main result; the interpolator design, the pretraining decomposition, and all quantitative claims remain independent of that citation.

full rationale

The paper's central derivation (structure pretraining + temporal interpolator) does not reduce by construction to its inputs. Theorem 4.1 starts from the usual diffusion score-matching identity (ϵ = −√(1−ᾱ) ∇ log p) under the perfect-modeling assumption and algebraically shows that the linear mix of Eq. 3 induces the intermediate ˜pmd ∝ pmd^β ˆpmd^{1−β}; the target MD distribution is never defined in terms of a fitted quantity, nor is any reported metric forced by the fit of α. α is a learned scalar (or per-block) coefficient whose values are reported post-hoc for interpretability; they are not free knobs used to manufacture the JSD/W1 numbers. Conformer pretraining uses the external GEOM ensembles; MD fine-tuning and all evaluation use independently simulated OpenMM trajectories (or Timewarp/ATLAS) with held-out molecules and an MD-ORACLE baseline. The only self-citation of note is the reuse of the Equivariant Temporal Attention Layer from GeoTDM (Han et al. 2024, overlapping senior author); that citation supplies a building block, not a uniqueness theorem or a load-bearing premise that forbids alternatives. Ablations (EGINTERPOLATOR-N, STACK, α=1) further isolate the contribution of pretraining and the interpolator against the same external metrics. Consequently the derivation chain is self-contained against external benchmarks; the score is raised only trivially for the non-load-bearing architectural self-citation.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 1 invented entities

The central claim rests on standard diffusion and equivariance machinery plus the modeling choice that a frozen conformer prior plus a linear (or cascaded) mix of scores is sufficient to recover MD dynamics from limited trajectory data. Free parameters are ordinary ML hyper-parameters and the learned α; no new physical constants are fitted. The only invented entity is the interpolator module itself.

free parameters (4)
  • interpolation coefficient α (or per-layer α^(l)) = learned, typically logits in [-0.25,0.25]
    Learnable sigmoid-parameterized scalar(s) that control the mix between structure and temporal scores; optimized on MD data and later ablated.
  • diffusion noise schedule β_τ / ᾱ_τ and number of steps (1000) = linear schedule, T=1000
    Standard DDPM schedule chosen by hand; affects both pretraining and fine-tuning.
  • trajectory length / Δt and block size for roll-outs = Δt=5.2 ps (small mol), 10 ps (tetrapeptide), 100 ps (protein)
    Chosen to match available MD frame rates (5.2 ps, 10 ps, 100 ps) and memory limits; not derived.
  • architecture widths (hidden dim 128, 6 layers, etc.) = 128-dim, ~3.3 M params total
    Hyper-parameters of EGCL + ETLayer stacks; selected for capacity vs. compute.
axioms (4)
  • domain assumption SE(3)-equivariant score networks induce SE(3)-invariant marginals for both structure and trajectory models.
    Standard in geometric diffusion (GeoDiff, EDM, EGNN); used throughout §3–4 and proved for the interpolator in App. D.2.
  • standard math The denoiser of a well-trained diffusion model approximates the score of the data distribution (Song & Ermon identity).
    Invoked to prove Theorem 4.1 that the interpolator targets a geometric-mean intermediate distribution.
  • domain assumption Large-scale conformer ensembles (GEOM, CREST/xTB) share enough support with physio-realistic MD marginals that a frozen structure model is a useful prior.
    Core premise of the two-stage pipeline; if false, pretraining transfers little useful information.
  • domain assumption MD trajectories can be treated as fixed-length sequences of geometric graphs and generated holistically by a single diffusion process rather than only by Markovian next-step models.
    Shared with GeoTDM and MDGen; enables the unconditional and interpolation settings.
invented entities (1)
  • EGINTERPOLATOR (simple and cascaded temporal interpolator blocks) no independent evidence
    purpose: Linearly (or block-wise) mixes frozen structure scores with a trainable equivariant temporal network so that the temporal module only learns residual correlations.
    The module and its α-parameterization are introduced in §4.2; no independent physical existence outside the architecture.

pith-pipeline@v1.1.0-grok45 · 37496 in / 3026 out tokens · 32788 ms · 2026-07-13T12:04:18.221215+00:00 · methodology

0 comments
read the original abstract

Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

64 extracted references · 4 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]

    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command n...

  3. [3]

    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@first@sw \@firstoftwo \@ifundefined NAT@b*@#2 \@firstoftwo @num @NAT@ctr \@secondoft...

  4. [4]

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibsetup #1 @NAT@ctr @ @openbib .11em \@plus.33em \@minus.07em 4000 4000 `\.\@m @bibit...

    2026

  5. [5]

    B. J. Alder and T. E. Wainwright. Studies in molecular dynamics. i. general method. The Journal of Chemical Physics, 31 0 (2): 0 459--466, August 1959. doi:10.1063/1.1730376. URL https://doi.org/10.1063/1.1730376

    doi:10.1063/1.1730376 1959

  6. [6]

    Andrej Antalík, Andrea Levy, Sonata Kvedaravičiūtė, Sophia K. Johnson, David Carrasco-Busturia, Bharath Raghavan, François Mouvet, Angela Acocella, Sambit Das, Vikram Gavini, Davide Mandelli, Emiliano Ippoliti, Simone Meloni, Paolo Carloni, Ursula Rothlisberger, and Jógvan Magnus Haugaard Olsen. Mimic: A high-performance framework for multiscale molecular...

    work page doi:10.1063/5.0211053 2024

  7. [7]

    Geom: Energy-annotated molecular conformations for property prediction and molecular generation, 2022

    Simon Axelrod and Rafael Gomez-Bombarelli. Geom: Energy-annotated molecular conformations for property prediction and molecular generation, 2022. URL https://arxiv.org/abs/2006.05531

    Pith/arXiv arXiv 2022

  8. [8]

    Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization, 2016. URL https://arxiv.org/abs/1607.06450

    Pith/arXiv arXiv 2016

  9. [9]

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

    Christoph Bannwarth, Sebastian Ehlert, and Stefan Grimme. 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. doi:10.1021/acs.jctc.8b01176. URL https://doi.o...

    doi:10.1021/acs.jctc.8b01176 2019

  10. [10]

    Berman, John Westbrook, Zukang Feng, Gary Gilliland, T

    Helen M. Berman, John Westbrook, Zukang Feng, Gary Gilliland, T. N. Bhat, Helge Weissig, Ilya N. Shindyalov, and Philip E. Bourne. The protein data bank. Nucleic Acids Research, 28 0 (1): 0 235--242, 01 2000. ISSN 0305-1048. doi:10.1093/nar/28.1.235. URL https://doi.org/10.1093/nar/28.1.235

    doi:10.1093/nar/28.1.235 2000

  11. [11]

    Align your latents: High-resolution video synthesis with latent diffusion models, 2023

    Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models, 2023. URL https://arxiv.org/abs/2304.08818

    Pith/arXiv arXiv 2023

  12. [12]

    Madin, David F

    Simon Boothroyd, Pavan Kumar Behara, Owen C. Madin, David F. Hahn, Hyesu Jang, Vytautas Gapsys, Jeffrey R. Wagner, Joshua T. Horton, David L. Dotson, Matthew W. Thompson, Jessica Maat, Trevor Gokey, Lee-Ping Wang, Daniel J. Cole, Michael K. Gilson, John D. Chodera, Christopher I. Bayly, Michael R. Shirts, and David L. Mobley. Development and benchmarking ...

    doi:10.1021/acs.jctc.3c00039 2023

  13. [13]

    Geometric and physical quantities improve e(3) equivariant message passing, 2022

    Johannes Brandstetter, Rob Hesselink, Elise van der Pol, Erik J Bekkers, and Max Welling. Geometric and physical quantities improve e(3) equivariant message passing, 2022. URL https://arxiv.org/abs/2110.02905

    Pith/arXiv arXiv 2022

  14. [14]

    Video generation models as world simulators

    Tim Brooks, Bill Peebles, Connor Holmes, Will DePue, Yufei Guo, Li Jing, David Schnurr, Joe Taylor, Troy Luhman, Eric Luhman, Clarence Ng, Ricky Wang, and Aditya Ramesh. Video generation models as world simulators. 2024. URL https://openai.com/research/video-generation-models-as-world-simulators

    2024

  15. [15]

    u tt, and Klaus-Robert M \

    Stefan Chmiela, Alexandre Tkatchenko, Huziel E Sauceda, Igor Poltavsky, Kristof T Sch \"u tt, and Klaus-Robert M \"u ller. Machine learning of accurate energy-conserving molecular force fields. Science advances, 3 0 (5): 0 e1603015, 2017

    2017

  16. [16]

    Particle mesh ewald: An n·log(n) method for ewald sums in large systems

    Tom Darden, Darrin York, and Lee Pedersen. Particle mesh ewald: An n·log(n) method for ewald sums in large systems. The Journal of Chemical Physics, 98 0 (12): 0 10089--10092, 1993. ISSN 0021-9606. doi:10.1063/1.464397

    doi:10.1063/1.464397 1993

  17. [17]

    Equijump: Protein dynamics simulation via so(3)-equivariant stochastic interpolants, 2024

    Allan dos Santos Costa, Ilan Mitnikov, Franco Pellegrini, Ameya Daigavane, Mario Geiger, Zhonglin Cao, Karsten Kreis, Tess Smidt, Emine Kucukbenli, and Joseph Jacobson. Equijump: Protein dynamics simulation via so(3)-equivariant stochastic interpolants, 2024. URL https://arxiv.org/abs/2410.09667

    Pith/arXiv arXiv 2024

  18. [18]

    Chodera, Robert T

    Peter Eastman, Jason Swails, John D. Chodera, Robert T. McGibbon, Yutong Zhao, Kyle A. Beauchamp, Lee-Ping Wang, Andrew C. Simmonett, Matthew P. Harrigan, Chaya D. Stern, Rafal P. Wiewiora, Bernard R. Brooks, and Vijay S. Pande. Openmm 7: Rapid development of high performance algorithms for molecular dynamics. PLOS Computational Biology, 13 0 (7): 0 1--17...

    doi:10.1371/journal.pcbi.1005659 2017

  19. [19]

    Fuchs, Daniel E

    Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, and Max Welling. Se(3)-transformers: 3d roto-translation equivariant attention networks, 2020. URL https://arxiv.org/abs/2006.10503

    Pith/arXiv arXiv 2020

  20. [20]

    Coley, Regina Barzilay, Klavs F

    Octavian-Eugen Ganea, Lagnajit Pattanaik, Connor W. Coley, Regina Barzilay, Klavs F. Jensen, William H. Green, and Tommi S. Jaakkola. Geomol: Torsional geometric generation of molecular 3d conformer ensembles, 2021. URL https://arxiv.org/abs/2106.07802

    Pith/arXiv arXiv 2021

  21. [21]

    Smith, and Adrian E

    Xiang Gao, Farhad Ramezanghorbani, Olexandr Isayev, Justin S. Smith, and Adrian E. Roitberg. Torchani: A free and open source pytorch-based deep learning implementation of the ani neural network potentials. Journal of Chemical Information and Modeling, 60 0 (7): 0 3408--3415, 2020. doi:10.1021/acs.jcim.0c00451. URL https://doi.org/10.1021/acs.jcim.0c00451...

    doi:10.1021/acs.jcim.0c00451 2020

  22. [22]

    Geometric trajectory diffusion models

    Jiaqi Han, Minkai Xu, Aaron Lou, Haotian Ye, and Stefano Ermon. Geometric trajectory diffusion models. arXiv preprint arXiv:2410.13027, 2024

    Pith/arXiv arXiv 2024

  23. [23]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020 a

    2020

  24. [24]

    Denoising diffusion probabilistic models, 2020 b

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models, 2020 b . URL https://arxiv.org/abs/2006.11239

    Pith/arXiv arXiv 2020

  25. [25]

    Equivariant diffusion for molecule generation in 3d

    Emiel Hoogeboom, V ctor Garcia Satorras, Cl \'e ment Vignac, and Max Welling. Equivariant diffusion for molecule generation in 3d. In International conference on machine learning, pp.\ 8867--8887. PMLR, 2022 a

    2022

  26. [26]

    Equivariant diffusion for molecule generation in 3d, 2022 b

    Emiel Hoogeboom, Victor Garcia Satorras, Clément Vignac, and Max Welling. Equivariant diffusion for molecule generation in 3d, 2022 b . URL https://arxiv.org/abs/2203.17003

    Pith/arXiv arXiv 2022

  27. [27]

    Estimation of non-normalized statistical models by score matching

    Aapo Hyv \"a rinen and Peter Dayan. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research, 6 0 (4), 2005

    2005

  28. [28]

    Bowen Jing, Stephan Eismann, Patricia Suriana, Raphael J. L. Townshend, and Ron Dror. Learning from protein structure with geometric vector perceptrons, 2021. URL https://arxiv.org/abs/2009.01411

    Pith/arXiv arXiv 2021

  29. [29]

    Alphafold meets flow matching for generating protein ensembles, 2024 a

    Bowen Jing, Bonnie Berger, and Tommi Jaakkola. Alphafold meets flow matching for generating protein ensembles, 2024 a . URL https://arxiv.org/abs/2402.04845

    Pith/arXiv arXiv 2024

  30. [31]

    Generative modeling of molecular dynamics trajectories, 2024 c

    Bowen Jing, Hannes Stärk, Tommi Jaakkola, and Bonnie Berger. Generative modeling of molecular dynamics trajectories, 2024 c . URL https://arxiv.org/abs/2409.17808

    Pith/arXiv arXiv 2024

  31. [32]

    Highly accurate protein structure prediction with AlphaFold

    John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Z \' dek, Anna Potapenko, Alex Bridgland, Clemens Meyer, Simon A A Kohl, Andrew J Ballard, Andrew Cowie, Bernardino Romera-Paredes, Stanislav Nikolov, Rishub Jain, Jonas Adler, Trevor Back, Stig Petersen, David Reiman...

    doi:10.1038/s41586-021-03819-2 2021

  32. [33]

    A solution for the best rotation to relate two sets of vectors

    Wolfgang Kabsch. A solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, 32 0 (5): 0 922--923, 1976

    1976

  33. [34]

    Leon Klein, Andrew Y. K. Foong, Tor Erlend Fjelde, Bruno Mlodozeniec, Marc Brockschmidt, Sebastian Nowozin, Frank Noé, and Ryota Tomioka. Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics, 2023. URL https://arxiv.org/abs/2302.01170

    Pith/arXiv arXiv 2023

  34. [35]

    Escaping free-energy minima

    Alessandro Laio and Michele Parrinello. Escaping free-energy minima. Proceedings of the National Academy of Sciences, 99 0 (20): 0 12562--12566, 2002. doi:10.1073/pnas.202427399. URL https://www.pnas.org/doi/abs/10.1073/pnas.202427399

    doi:10.1073/pnas.202427399 2002

  35. [36]

    Levine, Muhammed Shuaibi, Evan Walter Clark Spotte-Smith, Michael G

    Daniel S. Levine, Muhammed Shuaibi, Evan Walter Clark Spotte-Smith, Michael G. Taylor, Muhammad R. Hasyim, Kyle Michel, Ilyes Batatia, Gábor Csányi, Misko Dzamba, Peter Eastman, Nathan C. Frey, Xiang Fu, Vahe Gharakhanyan, Aditi S. Krishnapriyan, Joshua A. Rackers, Sanjeev Raja, Ammar Rizvi, Andrew S. Rosen, Zachary Ulissi, Santiago Vargas, C. Lawrence Zi...

    arXiv 2025

  36. [37]

    Andrew McCammon, Bruce R

    J. Andrew McCammon, Bruce R. Gelin, and Martin Karplus. Dynamics of folded proteins. Nature, 267 0 (5612): 0 585--590, 1977. doi:10.1038/267585a0

    work page doi:10.1038/267585a0 1977

  37. [38]

    openforcefield/openff-forcefields, January 2024

    Alexandra McIsaac, Pavan Kumar Behara, Trevor Gokey, Chapin Cavender, Joshua Horton, Lily Wang, Hyesu Jang, Jeffrey Wagner, Daniel Cole, Christopher Bayly, and David Mobley. openforcefield/openff-forcefields, January 2024. URL https://doi.org/10.5281/zenodo.10553473

    work page doi:10.5281/zenodo.10553473 2024

  38. [39]

    Atlas: protein flexibility description from atomistic molecular dynamics simulations

    Yann Vander Meersche, Gabriel Cretin, Aria Gheeraert, Jean-Christophe Gelly, and Tatiana Galochkina. Atlas: protein flexibility description from atomistic molecular dynamics simulations. Nucleic Acids Research, 52 0 (D1): 0 D384--D392, 2024. doi:10.1093/nar/gkad1084

    doi:10.1093/nar/gkad1084 2024

  39. [40]

    Geometry-complete diffusion for 3d molecule generation and optimization, 2024

    Alex Morehead and Jianlin Cheng. Geometry-complete diffusion for 3d molecule generation and optimization, 2024. URL https://arxiv.org/abs/2302.04313

    Pith/arXiv arXiv 2024

  40. [41]

    Boltzmann generators -- sampling equilibrium states of many-body systems with deep learning, 2019

    Frank Noé, Simon Olsson, Jonas Köhler, and Hao Wu. Boltzmann generators -- sampling equilibrium states of many-body systems with deep learning, 2019. URL https://arxiv.org/abs/1812.01729

    Pith/arXiv arXiv 2019

  41. [42]

    Equivariant blurring diffusion for hierarchical molecular conformer generation, 2024

    Jiwoong Park and Yang Shen. Equivariant blurring diffusion for hierarchical molecular conformer generation, 2024. URL https://arxiv.org/abs/2410.20255

    Pith/arXiv arXiv 2024

  42. [43]

    Boltz-2: Towards accurate and efficient binding affinity prediction

    Saro Passaro, Gabriele Corso, Jeremy Wohlwend, Mateo Reveiz, Stephan Thaler, Vignesh Ram Somnath, Noah Getz, Tally Portnoi, Julien Roy, Hannes Stark, David Kwabi-Addo, Dominique Beaini, Tommi Jaakkola, and Regina Barzilay. Boltz-2: Towards accurate and efficient binding affinity prediction. bioRxiv, 2025. doi:10.1101/2025.06.14.659707. URL https://www.bio...

    doi:10.1101/2025.06.14.659707 2025

  43. [44]

    Powers, Tianyu Lu, Rohan V

    Alexander S. Powers, Tianyu Lu, Rohan V. Koodli, Minkai Xu, Siyi Gu, Masha Karelina, and Ron O. Dror. Medsage: Bridging generative ai and medicinal chemistry for structure-based design of small molecule drugs. bioRxiv, 2025. doi:10.1101/2025.05.10.653107. URL https://www.biorxiv.org/content/early/2025/05/15/2025.05.10.653107

    work page doi:10.1101/2025.05.10.653107 2025

  44. [45]

    A. Rahman. Correlations in the motion of atoms in liquid argon. Phys. Rev., 136: 0 A405--A411, Oct 1964. doi:10.1103/PhysRev.136.A405. URL https://link.aps.org/doi/10.1103/PhysRev.136.A405

    doi:10.1103/physrev.136.a405 1964

  45. [46]

    Quantum chemistry structures and properties of 134 kilo molecules

    Raghunathan Ramakrishnan, Pavlo O Dral, Matthias Rupp, and O Anatole von Lilienfeld. Quantum chemistry structures and properties of 134 kilo molecules. Scientific Data, 1, 2014

    2014

  46. [47]

    High-resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bj \"o rn Ommer. High-resolution image synthesis with latent diffusion models. 2022 ieee. In CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.\ 10674--10685, 2021

    2022

  47. [48]

    E(n) equivariant normalizing flows

    Victor Garcia Satorras, Emiel Hoogeboom, Fabian Bernd Fuchs, Ingmar Posner, and Max Welling. E(n) equivariant normalizing flows. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, 2021 a . URL https://openreview.net/forum?id=N5hQI_RowVA

    2021

  48. [49]

    E(n) equivariant graph neural networks

    Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E(n) equivariant graph neural networks. arXiv preprint arXiv:2102.09844, 2021 b

    Pith/arXiv arXiv 2021

  49. [50]

    Scherer, Benjamin Trendelkamp-Schroer, Fabian Paul, Guillermo P \'e rez-Hernández, Moritz Hoffmann, Nuria Plattner, Christoph Wehmeyer, Jan-Hendrik Prinz, and Frank No \'e

    Martin K. Scherer, Benjamin Trendelkamp-Schroer, Fabian Paul, Guillermo P \'e rez-Hernández, Moritz Hoffmann, Nuria Plattner, Christoph Wehmeyer, Jan-Hendrik Prinz, and Frank No \'e . Pyemma 2: A software package for estimation, validation, and analysis of markov models. Journal of Chemical Theory and Computation, 11 0 (11): 0 5525--5542, 2015. doi:10.102...

    doi:10.1021/acs.jctc.5b00743 2015

  50. [51]

    Shaw, Ron O

    David E. Shaw, Ron O. Dror, John K. Salmon, J. P. Grossman, Kenneth M. Mackenzie, Joseph A. Bank, Cliff Young, Martin M. Deneroff, Brannon Batson, Kevin J. Bowers, Edmond Chow, Michael P. Eastwood, Douglas J. Ierardi, John L. Klepeis, Jeffrey S. Kuskin, Richard H. Larson, Kresten Lindorff-Larsen, Paul Maragakis, Mark A. Moraes, Stefano Piana, Yibing Shan,...

    doi:10.1145/1654059.1654126 2009

  51. [52]

    Learning gradient fields for molecular conformation generation

    Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular conformation generation. In International conference on machine learning, pp.\ 9558--9568. PMLR, 2021 a

    2021

  52. [53]

    Learning gradient fields for molecular conformation generation, 2021 b

    Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular conformation generation, 2021 b . URL https://arxiv.org/abs/2105.03902

    Pith/arXiv arXiv 2021

  53. [54]

    Deep unsupervised learning using nonequilibrium thermodynamics

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning, pp.\ 2256--2265. PMLR, 2015

    2015

  54. [55]

    Generative modeling by estimating gradients of the data distribution

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

    2019

  55. [56]

    Score-based generative modeling through stochastic differential equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=PxTIG12RRHS

    2021

  56. [57]

    Roformer: Enhanced transformer with rotary position embedding, 2023

    Jianlin Su, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu. Roformer: Enhanced transformer with rotary position embedding, 2023. URL https://arxiv.org/abs/2104.09864

    Pith/arXiv arXiv 2023

  57. [58]

    Torchmd-net: Equivariant transformers for neural network based molecular potentials, 2022

    Philipp Thölke and Gianni De Fabritiis. Torchmd-net: Equivariant transformers for neural network based molecular potentials, 2022. URL https://arxiv.org/abs/2202.02541

    Pith/arXiv arXiv 2022

  58. [59]

    experiments

    Loup Verlet. Computer "experiments" on classical fluids. i. thermodynamical properties of lennard-jones molecules. Phys. Rev., 159: 0 98--103, Jul 1967. doi:10.1103/PhysRev.159.98. URL https://link.aps.org/doi/10.1103/PhysRev.159.98

    doi:10.1103/physrev.159.98 1967

  59. [60]

    Boltz-1: Democratizing biomolecular interaction modeling

    Jeremy Wohlwend, Gabriele Corso, Saro Passaro, Mateo Reveiz, Ken Leidal, Wojtek Swiderski, Tally Portnoi, Itamar Chinn, Jacob Silterra, Tommi Jaakkola, and Regina Barzilay. Boltz-1: Democratizing biomolecular interaction modeling. bioRxiv, 2024. doi:10.1101/2024.11.19.624167. URL https://www.biorxiv.org/content/early/2024/11/20/2024.11.19.624167. Preprint

    doi:10.1101/2024.11.19.624167 2024

  60. [61]

    Geometric-facilitated denoising diffusion model for 3d molecule generation

    Can Xu, Haosen Wang, Weigang Wang, Pengfei Zheng, and Hongyang Chen. Geometric-facilitated denoising diffusion model for 3d molecule generation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp.\ 338--346, 2024 a

    2024

  61. [62]

    Geodiff: A geometric diffusion model for molecular conformation generation

    Minkai Xu, Lantao Yu, Yang Song, Chence Shi, Stefano Ermon, and Jian Tang. Geodiff: A geometric diffusion model for molecular conformation generation. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=PzcvxEMzvQC

    2022

  62. [63]

    Geometric latent diffusion models for 3d molecule generation

    Minkai Xu, Alexander Powers, Ron Dror, Stefano Ermon, and Jure Leskovec. Geometric latent diffusion models for 3d molecule generation. In International Conference on Machine Learning. PMLR, 2023

    2023

  63. [64]

    Equivariant graph neural operator for modeling 3d dynamics

    Minkai Xu, Jiaqi Han, Aaron Lou, Jean Kossaifi, Arvind Ramanathan, Kamyar Azizzadenesheli, Jure Leskovec, Stefano Ermon, and Anima Anandkumar. Equivariant graph neural operator for modeling 3d dynamics. In Forty-first International Conference on Machine Learning, 2024 b . URL https://openreview.net/forum?id=dccRCYmL5x

    2024

  64. [65]

    Tuckerman, and Jian Liu

    Zhijun Zhang, Xinzijian Liu, Kangyu Yan, Mark E. Tuckerman, and Jian Liu. Unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics. The Journal of Physical Chemistry A, 123 0 (28): 0 6056--6079, 2019. doi:10.1021/acs.jpca.9b02771. URL https://doi.org/10.1021/acs.jpca.9b02771. PMID: 31117592

    doi:10.1021/acs.jpca.9b02771 2019