Pith. sign in

REVIEW 2 major objections 5 minor 2 cited by

Stiefel Flow Matching for Moment-Constrained Structure Elucidation

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Moment-constrained molecular point clouds form a submanifold of the Stiefel manifold St(n,4), and flow matching on that manifold yields 3D structures that satisfy the moments exactly and outperform Euclidean diffusion.

desk verdict Genuinely new geometry for exact moment constraints with a credible QM9 win; the GEOM claim overstates because only one side is filtered, but the paper deserves a serious referee. read the letter →

arxiv 2412.12540 v2 pith:EXKHAOPV submitted 2024-12-17 cs.LG physics.chem-ph

Austin Cheng , Alston Lo , Kin Long Kelvin Lee , Santiago Miret , Alán Aspuru-Guzik This is my paper · ORCID
classification cs.LGphysics.chem-ph
keywords StiefelmanifoldflowmatchingmolecularstructureelucidationmomentsofinertiarotationalspectroscopyequivariantoptimaltransportRiemanniangenerativemodel
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 addresses molecular structure elucidation: given only a molecular formula and three moments of inertia, predict the full 3D structure of the molecule. The authors show that the set of point clouds with exactly those moments is a submanifold of the Stiefel manifold St(n,4), so a generative model can be confined to structures that satisfy the moments by construction. They introduce Stiefel Flow Matching, a Riemannian flow matching method on this manifold, with an equivariant optimal transport coupling that shortens learned paths. On QM9 and GEOM, the method achieves higher success rates at strict RMSD thresholds while using fewer function evaluations than Euclidean diffusion models. It matters because rotational spectroscopy measures moments to high precision, and exact constraints turn that precision into a hard geometric constraint rather than a soft penalty.

What carries the argument

The load-bearing object is the map $U_{i,:} = (\sqrt{m_i/P_X}\,x_i,\; \sqrt{m_i/P_Y}\,y_i,\; \sqrt{m_i/P_Z}\,z_i,\; \sqrt{m_i/M})$, whose columns are orthonormal exactly when the center-of-mass and principal-axis constraints hold. The feasible space $\mathcal{M} = \{U \in \mathrm{St}(n,4) : U_{:,4} = \hat{m}\}$ is totally geodesic, so shortest paths between moment-satisfying structures stay in $\mathcal{M}$ and the Stiefel exponential and logarithm can be computed in St(n,3) after discarding the fixed column. Riemannian flow matching trains a reflection- and permutation-equivariant network to regress geodesic velocities, and an approximate optimal transport coupling over reflections and atom permutations shortens the learned paths.

What would settle it

Take any molecule with $P_X>P_Y>P_Z>0$, build $U$ from Equation (4), and check $U^\top U = I$; if any moment-satisfying point cloud yields a non-orthonormal $U$, the central embedding claim fails. For the empirical superiority claim, an independent evaluation on the same QM9/GEOM splits with an equally sized Euclidean diffusion model and identical compute that reports a higher success rate at 0.25 Å RMSD than Stiefel FM would refute it.

Watch

Extended reading notes

Core claim

The central discovery is that moment-constrained molecular structures are not merely approximately orthogonal: after mass-scaling coordinates and appending the unit mass vector, any point cloud with the prescribed moments of inertia becomes an orthonormal n×4 matrix, i.e. a point of St(n,4), and the feasible set is the totally geodesic submanifold whose last column is fixed. Consequently, flows and geodesics can be computed entirely on the Stiefel manifold, and every generated sample obeys the moments exactly. The paper further shows that permutation and reflection equivariance can be encoded in the network and that approximate equivariant optimal transport over reflections and atom permutations produces shorter, simpler generation trajectories. Empirically, on QM9 and GEOM, Stiefel Flow Matching has zero moment error, higher or comparable success rates under 0.25 Å and 0.10 Å RMSD thresholds, and lower sampling cost than Euclidean diffusion baselines, with the GEOM comparison favoring Stiefel FM after validity filtering.

Load-bearing premise

The construction requires the molecule to be a nonplanar asymmetric rotor with three strictly distinct positive moments of inertia; planar, linear, and exactly symmetric molecules break the mapping (division by zero or non-unique principal axes), so the empirical claims do not extend to them.

Editorial extensions

If this is right

  • Every generated sample has exactly the target moments, eliminating moment-violation error by construction rather than by soft penalty or projection.
  • Stiefel Flow Matching reaches higher success rates at 0.25 Å and 0.10 Å RMSD thresholds than Euclidean diffusion models on QM9, and higher success than any baseline on GEOM once samples are filtered for validity.
  • Sampling requires 200 function evaluations instead of 1000, so generation is roughly five times cheaper while remaining competitive or better in accuracy.
  • Equivariant optimal transport reduces average generation curve length, from 1.696 to 1.547 on QM9 and from 1.421 to 1.344 on GEOM, meaning simpler and shorter learned flows.
  • Projecting Euclidean diffusion outputs onto the moment-satisfying manifold does not improve success, because projection leaves correct structures unchanged while only distorting incorrect ones.

Reading between the lines

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

  • Inference: The same Stiefel embedding could likely be adapted to planar and linear molecules by dropping to St(n,3) or St(n,2) constructions, extending exact moment constraints to molecules the current paper excludes.
  • Inference: In a real structure elucidation campaign, where thousands of samples are affordable, exact moment constraints could be combined with quantum-chemistry stability filtering to produce a practical candidate-generation workflow, as the paper's combined success rates hint.
  • Inference: The construction is not specific to chemistry; any generative task with orthogonality constraints, such as molecular orbitals or orthogonal neural network weights, could use the same Stiefel flow matching recipe.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper introduces Stiefel Flow Matching, a Riemannian flow-matching model that generates 3D molecular structures from a molecular formula and exact moments of inertia. The authors prove that the set of n-atom point clouds with fixed planar moments, zero center of mass, and principal-axis orientation is embedded as a totally geodesic submanifold of St(n,4) equivalent to St(n-1,3), so that geodesics and logarithms can be computed by reducing to St(n,3). The construction guarantees exact moment satisfaction by design. The method adds reflection/permutation equivariance and an approximate equivariant optimal transport coupling. On QM9, Stiefel FM reports higher success rates at lower NFE than Euclidean diffusion baselines. On GEOM, higher success rates are reported only after generating 30 samples and filtering to up to 10 valid samples, a protocol not applied to the diffusion baselines.

Significance. The mathematical construction is elegant, self-contained, and likely reusable beyond this application; the proofs in Appendix B are clear, and the released code is a reproducibility asset. The QM9 result (15.17% vs 13.65% for KREED-XL, roughly 3.5 standard errors) credibly supports the central claim for that dataset. However, the GEOM comparison that supports the abstract's 'even on high-dimensional manifolds' claim is confounded by a filtering protocol applied only to the proposed method. If the authors add a matched-protocol baseline or scale back the claim, the paper would be a solid contribution to generative modeling on constrained manifolds.

major comments (2)
  1. [Section 4, Table 2] The GEOM success-rate comparison is confounded. Stiefel FM(-OT) (filter) rows score up to K=10 valid structures selected from 30 raw samples, whereas KREED-XL is scored on K=10 raw samples, of which only 30.71% are valid on average (about 3.07 per molecule). Because the success metric is the minimum RMSD over the scored samples, the reported advantage (3.94% vs 3.54% for Stiefel FM-OT (filter) vs KREED-XL) may simply reflect the larger effective number of scored samples rather than a genuine superiority of the manifold model. The paper's stated rationale, 'generate a similar number of valid structures for each model,' is not implemented for the baseline. Please apply the same 30-sample generate-and-filter-to-10-valid protocol to KREED-XL (and KREED), and also report per-sample success rates, or restrict the abstract's GEOM claim.
  2. [Abstract and Conclusion] The abstract and conclusion state that Stiefel Flow Matching achieves higher success rates 'even on high-dimensional manifolds corresponding to large molecules in the GEOM dataset.' This claim is currently unsupported because the only GEOM configuration with a statistically notable advantage (Stiefel FM-OT (filter), 3.94% vs 3.54%) uses an asymmetric evaluation protocol. If the matched-protocol experiment in the preceding comment shows no advantage, the abstract and conclusion should be revised to restrict the success-rate claim to QM9 or to report the GEOM result as comparable under matched evaluation.
minor comments (5)
  1. [Appendix A.2] The limitation that the method cannot handle exactly planar or linear molecules is stated only in the appendix; consider adding a sentence to the abstract or contributions so that the scope of the empirical claims is clear.
  2. [Table 2 caption] The caption says 'When adjusted to generate the same number of valid molecules,' but the adjustment is applied only to the Stiefel FM rows; please specify the exact protocol (30 raw samples, retain up to 10 valid) and state that it is not applied to the baseline rows.
  3. [Appendix E] The text says the 1-iteration approximate distance 'empirically validate[s] that the 1-iteration approximate distance used in Algorithm 4 is an upper bound on the true distance,' but no upper-bound test is shown; the reported Spearman correlation only validates ordering. Either demonstrate the upper-bound property or rephrase to avoid claiming it.
  4. [Section 4, NFE definition] The NFE column is used to compare computational cost, but the units are ambiguous: in Table 2 the filter rows show 600 NFE for 30 samples, which suggests NFE is per molecule (one network call per timestep on a batch), while Table 1's '20% of computation' comparison uses 200 vs 1000. Please define NFE explicitly in the text.
  5. [Table 2, filter rows] For the filter rows, report the average number of valid samples actually retained per molecule after filtering; this number is needed to interpret the success-rate comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Stiefel embedding is derived from the moment constraints, and the headline success metrics are external RMSD benchmarks; the GEOM filtering issue is a fairness concern, not a circularity.

full rationale

Walking the claimed derivation chain, I find no step that reduces to its own inputs. Equation (4) constructs U from X and the paper verifies orthonormality directly against Equation (2); Equation (5) then defines M as the set of moment-satisfying point clouds, and Appendix B.7 proves the total-geodesy and St(n-1,3) equivalence rather than importing them. The flow-matching loss (Equation 8) and sampling (Algorithm 3) are standard Riemannian flow matching applied to this derived manifold. The zero moment "Error" in Tables 1 and 2 is a by-construction property of sampling on M, not a fitted quantity and not used as evidence of learning; it is a design guarantee. Success rates use RMSD to held-out QM9 and GEOM ground-truth structures, which is an external benchmark. The GEOM validity-filtered comparison in Table 2 is a possible evaluation fairness issue, because Stiefel FM-OT (filter) scores up to 10 valid samples while KREED-XL effectively scores about 3 valid samples, but this is not circularity: no parameter is fitted to the benchmark and no output equals an input by construction. Self-citations to Cheng et al. supply data splits, the RMSD routine, and the KREED baselines; these are conventions or comparators, not load-bearing premises. Appendix A.2 explicitly narrows scope to nonplanar asymmetric rotors, which is a limitation but not a circularity. Appendix E's wording that the one-iteration approximate distance is an upper bound is under-supported by the reported Spearman correlations, but that is an evidence-quality issue rather than an input-output equivalence. Overall, no circular step was found.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central derivation relies on standard Stiefel manifold geometry from the cited literature, plus the domain assumption that experimental moments correspond to equilibrium rigid-rotor structures. No free parameters are fitted to make the geometry work; the model's neural network weights are learned from data in the standard way. The main domain restriction is the asymmetric-rotor assumption P_X > P_Y > P_Z > 0, which excludes planar, linear, and symmetric-top molecules.

free parameters (2)
  • Logarithm iteration cap = 20
    Algorithm 2 caps the inner loop at 20 iterations; Appendix E shows 2-4% of cases do not converge, adding small error to geodesic computations during training.
  • OT search budget (R, L) = unspecified
    Algorithm 4's greedy random search uses unspecified restarts R and local search budget L; these affect the quality of the optimal transport coupling and therefore Stiefel FM-OT performance.
assumptions (3)
  • standard math Exponential and logarithmic maps on St(n,p) under the canonical metric can be computed as in Edelman et al. (1998) and Zimmermann and Hüper (2022).
    The flow matching training and sampling rely on these maps; the paper cites and reproduces the algorithms.
  • domain assumption A molecule is modeled as a rigid point cloud at its equilibrium geometry, and the experimental moments correspond (after rovibrational correction) to the planar dyadic eigenvalues.
    The entire construction equates moments of inertia with the principal-axis planar dyadic. Zero-point vibrational averaging introduces about 1% differences, acknowledged in Appendix A.4.
  • domain assumption The molecule is a nonplanar asymmetric rotor with P_X > P_Y > P_Z > 0.
    Required for the U construction, Equation (4), to be finite and for principal axes to be unique; stated in Appendix A.2 and enforced by dataset filtering.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stiefel Flow Matching for Moment-Constrained Structure Elucidation." pith.science (2026). https://pith.science/paper/EXKHAOPV

@misc{pith2026241212540,
  author       = {Pith},
  title        = {Pith review of: Stiefel Flow Matching for Moment-Constrained Structure Elucidation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXKHAOPV}},
  note         = {Machine review of arXiv:2412.12540}
}
abstract

Molecular structure elucidation is a fundamental step in understanding chemical phenomena, with applications in identifying molecules in natural products, lab syntheses, forensic samples, and the interstellar medium. We consider the task of predicting a molecule's all-atom 3D structure given only its molecular formula and moments of inertia, motivated by the ability of rotational spectroscopy to measure these moments. While existing generative models can conditionally sample 3D structures with approximately correct moments, this soft conditioning fails to leverage the many digits of precision afforded by experimental rotational spectroscopy. To address this, we first show that the space of $n$-atom point clouds with a fixed set of moments of inertia is embedded in the Stiefel manifold $\mathrm{St}(n, 4)$. We then propose Stiefel Flow Matching as a generative model for elucidating 3D structure under exact moment constraints. Additionally, we learn simpler and shorter flows by finding approximate solutions for equivariant optimal transport on the Stiefel manifold. Empirically, enforcing exact moment constraints allows Stiefel Flow Matching to achieve higher success rates and faster sampling than Euclidean diffusion models, even on high-dimensional manifolds corresponding to large molecules in the GEOM dataset.

Figures

Figures reproduced from arXiv: 2412.12540 by the authors.

Figure 1
Figure 1. Stiefel Flow Matching learns to elucidate 3D molecular structure from moments and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Histograms of minimum RMSD for predicted QM9 examples show two distinct clusters for [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. (Left) Learned sampling trajectories for Stiefel FM and Stiefel FM-OT on QM9. Each column begins generation from the same noise. (Right) Histogram of curve lengths of all QM9 sampling trajectories for Stiefel FM and Stiefel FM-OT. Permutation and reflection alignment lead to simpler and shorter paths. Evaluating RMSD is nontrivial because the generated and ground truth structure must first be aligned under same-atom… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Histograms of minimum RMSD for predicted GEOM examples. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Selected QM9 examples. Best viewed zoomed in. Examples are sorted by RMSD to ground [PITH_FULL_IMAGE:figures/full_fig_p028_5.png]
Figure 6
Figure 6. Figure 6: Selected GEOM examples. Best viewed zoomed in. Examples are sorted by RMSD to [PITH_FULL_IMAGE:figures/full_fig_p028_6.png]
Figure 7
Figure 7. Figure 7: Normalized histogram of curve lengths of success and failure examples of Stiefel FM on the [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: Equivariant optimal transport shortens generation trajectories for GEOM. However, gener [PITH_FULL_IMAGE:figures/full_fig_p029_8.png]
Figure 9
Figure 9. Figure 9: Equivariant optimal transport aligns noise samples [PITH_FULL_IMAGE:figures/full_fig_p030_9.png]
Figure 10
Figure 10. Figure 10: Histograms of the number of inner iterations of the Stiefel logarithm required to converge [PITH_FULL_IMAGE:figures/full_fig_p031_10.png]
Figure 11
Figure 11. Figure 11: Parity plots comparing the 1-iteration approximate Stiefel distance to the true Stiefel [PITH_FULL_IMAGE:figures/full_fig_p031_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. InertialAR: Autoregressive 3D Molecule Generation with Inertial Frames

    cs.LG 2025-10 conditional novelty 6.0 of 10

    An autoregressive transformer with inertial-frame tokenization and geometric rotary positional encoding reports state-of-the-art validity and stability on QM9, GEOM-Drugs, and B3LYP, plus strong functional-group-condi...

  2. Energy-Based Flow Matching for Generating 3D Molecular Structure

    cs.LG 2025-08 conditional novelty 5.0 of 10

    IDFlow trains a flow matching network to refine its own predicted 3D molecular structure, improving docking and protein backbone generation over HarmonicFlow and FrameFlow baselines.

Reference graph

Works this paper leans on

118 extracted references · 46 canonical work pages · cited by 2 Pith papers

  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]

    Fast and accurate optimization on the orthogonal manifold without retraction

    Pierre Ablin and Gabriel Peyr \'e . Fast and accurate optimization on the orthogonal manifold without retraction. In International Conference on Artificial Intelligence and Statistics, pp.\ 5636--5657. PMLR, 2022

    2022

  3. [3]

    Accurate structure prediction of biomolecular interactions with alphafold 3

    Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew J Ballard, Joshua Bambrick, et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, pp.\ 1--3, 2024

    2024

  4. [4]

    Optimization algorithms on matrix manifolds

    P-A Absil, Robert Mahony, and Rodolphe Sepulchre. Optimization algorithms on matrix manifolds. Princeton University Press, 2008

    2008

  5. [5]

    An optimisation on the grassmannian with applications to quantum chemistry

    Yuri Alexandre Aoto and M \'a rcio Fabiano da Silva. An optimisation on the grassmannian with applications to quantum chemistry. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 8 0 (1), 2021

    2021

  6. [6]

    GEOM , energy-annotated molecular conformations for property prediction and molecular generation

    Simon Axelrod and Rafael Gomez-Bombarelli. GEOM , energy-annotated molecular conformations for property prediction and molecular generation. Scientific Data, 9 0 (1): 0 1--14, 2022

    2022

  7. [7]

    Stationary kernels and gaussian processes on lie groups and their homogeneous spaces i: the compact case

    Iskander Azangulov, Andrei Smolensky, Alexander Terenin, and Viacheslav Borovitskiy. Stationary kernels and gaussian processes on lie groups and their homogeneous spaces i: the compact case. arXiv preprint arXiv:2208.14960, 2022

    arXiv 2022

  8. [8]

    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

    2019

Show all 118 references
  1. [9]

    A grassmann manifold handbook: Basic geometry and computational aspects

    Thomas Bendokat, Ralf Zimmermann, and P-A Absil. A grassmann manifold handbook: Basic geometry and computational aspects. Advances in Computational Mathematics, 50 0 (1): 0 1--51, 2024

    2024

  2. [10]

    Bronstein, and Alexander Tong

    Joey Bose, Tara Akhound-Sadegh, Guillaume Huguet, Kilian FATRAS, Jarrid Rector-Brooks, Cheng-Hao Liu, Andrei Cristian Nica, Maksym Korablyov, Michael M. Bronstein, and Alexander Tong. SE (3)-stochastic flow matching for protein backbone generation. In The Twelfth International...

    2024

  3. [11]

    The rotational spectrum of epifluorohydrin measured by chirped-pulse fourier transform microwave spectroscopy

    Gordon G Brown, Brian C Dian, Kevin O Douglass, Scott M Geyer, and Brooks H Pate. The rotational spectrum of epifluorohydrin measured by chirped-pulse fourier transform microwave spectroscopy. Journal of Molecular Spectroscopy, 238 0 (2): 0 200--212, 2006

    2006

  4. [12]

    A broadband fourier transform microwave spectrometer based on chirped pulse excitation

    Gordon G Brown, Brian C Dian, Kevin O Douglass, Scott M Geyer, Steven T Shipman, and Brooks H Pate. A broadband fourier transform microwave spectrometer based on chirped pulse excitation. Review of Scientific Instruments, 79 0 (5), 2008

    2008

  5. [13]

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

    Andrew Campbell, Jason Yim, Regina Barzilay, Tom Rainforth, and Tommi Jaakkola. Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design. arXiv preprint arXiv:2402.04997, 2024

    2024 arXiv

  6. [14]

    Statistics on the stiefel manifold: theory and applications

    Rudrasis Chakraborty and Baba C Vemuri. Statistics on the stiefel manifold: theory and applications. 2019

    2019

  7. [15]

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

    2024

  8. [16]

    Decentralized riemannian gradient descent on the stiefel manifold

    Shixiang Chen, Alfredo Garcia, Mingyi Hong, and Shahin Shahrampour. Decentralized riemannian gradient descent on the stiefel manifold. In International Conference on Machine Learning, pp.\ 1594--1605. PMLR, 2021

    2021

  9. [17]

    Determining 3d structure from molecular formula and isotopologue rotational spectra in natural abundance with reflection-equivariant diffusion

    Austin H Cheng, Alston Lo, Santiago Miret, Brooks H Pate, and Al \'a n Aspuru-Guzik. Determining 3d structure from molecular formula and isotopologue rotational spectra in natural abundance with reflection-equivariant diffusion. The Journal of Chemical Physics, 160 0 (12), 2024

    2024

  10. [18]

    Distributions of orientations on stiefel manifolds

    Yasuko Chikuse. Distributions of orientations on stiefel manifolds. Journal of multivariate analysis, 33 0 (2): 0 247--264, 1990

    1990

  11. [19]

    Concentrated matrix langevin distributions

    Yasuko Chikuse. Concentrated matrix langevin distributions. Journal of Multivariate Analysis, 85 0 (2): 0 375--394, 2003

    2003

  12. [20]

    Diffusion posterior sampling for general noisy inverse problems

    Hyungjin Chung, Jeongsol Kim, Michael Thompson Mccann, Marc Louis Klasky, and Jong Chul Ye. Diffusion posterior sampling for general noisy inverse problems. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=OnD9zGAGT0k

    2023

  13. [21]

    Diffdock: Diffusion steps, twists, and turns for molecular docking

    Gabriele Corso, Hannes St \"a rk, Bowen Jing, Regina Barzilay, and Tommi Jaakkola. Diffdock: Diffusion steps, twists, and turns for molecular docking. arXiv preprint arXiv:2210.01776, 2022

    2022 arXiv

  14. [22]

    Jaakkola

    Gabriele Corso, Yilun Xu, Valentin De Bortoli, Regina Barzilay, and Tommi S. Jaakkola. Particle guidance: non-i.i.d. diverse sampling with diffusion models. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=KqbCvIFBY7

    2024

  15. [23]

    Riemannian score-based generative modelling

    Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, and Arnaud Doucet. Riemannian score-based generative modelling. Advances in Neural Information Processing Systems, 35: 0 2406--2422, 2022

    2022

  16. [24]

    Demaison, James E

    J. Demaison, James E. Boggs, and Attila G. Cs \'a sz \'a r (eds.). Equilibrium Molecular Structures: From Spectroscopy to Quantum Chemistry. CRC Press, Boca Raton, 2011. ISBN 978-1-4398-1132-0

    2011

  17. [25]

    Diffusion models beat GAN s on image synthesis

    Prafulla Dhariwal and Alexander Quinn Nichol. Diffusion models beat GAN s on image synthesis. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, 2021

    2021

  18. [26]

    Continuous diffusion for categorical data

    Sander Dieleman, Laurent Sartran, Arman Roshannai, Nikolay Savinov, Yaroslav Ganin, Pierre H Richemond, Arnaud Doucet, Robin Strudel, Chris Dyer, Conor Durkan, et al. Continuous diffusion for categorical data. arXiv preprint arXiv:2211.15089, 2022

    2022 arXiv

  19. [27]

    Domingos, Crist \'o bal P \'e rez, Mark D

    S \'e rgio R. Domingos, Crist \'o bal P \'e rez, Mark D. Marshall, Helen O. Leung, and Melanie Schnell. Assessing the performance of rotational spectroscopy in chiral analysis. Chemical Science, 11 0 (40): 0 10863--10870, October 2020. ISSN 2041-6539. doi:10.1039/D0SC03752D

    2020 doi

  20. [28]

    Reduce, reuse, recycle: Compositional generation with energy-based diffusion models and mcmc

    Yilun Du, Conor Durkan, Robin Strudel, Joshua B Tenenbaum, Sander Dieleman, Rob Fergus, Jascha Sohl-Dickstein, Arnaud Doucet, and Will Sussman Grathwohl. Reduce, reuse, recycle: Compositional generation with energy-based diffusion models and mcmc. In International conference o...

  21. [29]

    Faenet: Frame averaging equivariant gnn for materials modeling

    Alexandre Agm Duval, Victor Schmidt, Alex Hern \'a ndez-Garc \'i a, Santiago Miret, Fragkiskos D Malliaros, Yoshua Bengio, and David Rolnick. Faenet: Frame averaging equivariant gnn for materials modeling. In International Conference on Machine Learning, pp.\ 9013--9033. PMLR, 2023

    2023

  22. [30]

    The geometry of algorithms with orthogonality constraints

    Alan Edelman, Tom \'a s A Arias, and Steven T Smith. The geometry of algorithms with orthogonality constraints. SIAM journal on Matrix Analysis and Applications, 20 0 (2): 0 303--353, 1998

    1998

  23. [31]

    Scaling rectified flow transformers for high-resolution image synthesis

    Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas M \"u ller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. arXiv preprint arXiv:2403.03206, 2024

    2024 arXiv

  24. [32]

    PyTorch Lightning , March 2019

    William Falcon and The PyTorch Lightning team . PyTorch Lightning , March 2019. URL https://github.com/Lightning-AI/lightning

    2019

  25. [33]

    Fast Graph Representation Learning with PyTorch Geometric , May 2019 a

    Matthias Fey and Jan Eric Lenssen. Fast Graph Representation Learning with PyTorch Geometric , May 2019 a . URL https://github.com/pyg-team/pytorch_geometric

    2019

  26. [34]

    Fast graph representation learning with pytorch geometric

    Matthias Fey and Jan Eric Lenssen. Fast graph representation learning with pytorch geometric. arXiv preprint arXiv:1903.02428, 2019 b

    1903 arXiv

  27. [35]

    Optimization flows landing on the stiefel manifold

    Bin Gao, Simon Vary, Pierre Ablin, and P-A Absil. Optimization flows landing on the stiefel manifold. IFAC-PapersOnLine, 55 0 (30): 0 25--30, 2022

    2022

  28. [36]

    Discrete flow matching

    Itai Gat, Tal Remez, Neta Shaul, Felix Kreuk, Ricky TQ Chen, Gabriel Synnaeve, Yossi Adi, and Yaron Lipman. Discrete flow matching. arXiv preprint arXiv:2407.15595, 2024

    2024 arXiv

  29. [37]

    Microwave molecular spectra, volume 18

    Walter Gordy, Robert L Cook, and Arnold Weissberger. Microwave molecular spectra, volume 18. Wiley New York, 1984. URL https://app.knovel.com/kn/resources/kpMMSE0001/toc

    1984

  30. [38]

    Eigen v3

    Ga\" e l Guennebaud, Beno\^ i t Jacob, et al. Eigen v3. http://eigen.tuxfamily.org, 2010

    2010

  31. [39]

    Harris, K

    Charles R. Harris, K. Jarrod Millman, Stéfan J van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fer...

    2020

  32. [40]

    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

    2020

  33. [41]

    Generator matching: Generative modeling with arbitrary markov processes

    Peter Holderrieth, Marton Havasi, Jason Yim, Neta Shaul, Itai Gat, Tommi Jaakkola, Brian Karrer, Ricky TQ Chen, and Yaron Lipman. Generator matching: Generative modeling with arbitrary markov processes. arXiv preprint arXiv:2410.20587, 2024

    arXiv

  34. [42]

    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

    2022

  35. [43]

    Matplotlib: A 2d graphics environment

    John D Hunter. Matplotlib: A 2d graphics environment. Computing in science & engineering, 9 0 (03): 0 90--95, 2007

    2007

  36. [44]

    A lagrangian approach to extremal curves on stiefel manifolds

    Knut H \"u per, Irina Markina, and F \'a tima Silva Leite. A lagrangian approach to extremal curves on stiefel manifolds. AIMS, 2021

    2021

  37. [45]

    Crystal structure prediction by joint equivariant diffusion

    Rui Jiao, Wenbing Huang, Peijia Lin, Jiaqi Han, Pin Chen, Yutong Lu, and Yang Liu. Crystal structure prediction by joint equivariant diffusion. Advances in Neural Information Processing Systems, 36, 2024

    2024

  38. [46]

    Torsional diffusion for molecular conformer generation

    Bowen Jing, Gabriele Corso, Jeffrey Chang, Regina Barzilay, and Tommi Jaakkola. Torsional diffusion for molecular conformer generation. Advances in Neural Information Processing Systems, 35: 0 24240--24253, 2022

    2022

  39. [47]

    Generative modeling on manifolds through mixture of riemannian diffusion processes

    Jaehyeong Jo and Sung Ju Hwang. Generative modeling on manifolds through mixture of riemannian diffusion processes. arXiv preprint arXiv:2310.07216, 2023

    2023 arXiv

  40. [48]

    Maximum likelihood estimators for the matrix von mises-fisher and bingham distributions

    Peter E Jupp and Kanti V Mardia. Maximum likelihood estimators for the matrix von mises-fisher and bingham distributions. The Annals of Statistics, 7 0 (3): 0 599--606, 1979

    1979

  41. [49]

    Universal structure conversion method for organic molecules: from atomic connectivity to three-dimensional geometry

    Yeonjoon Kim and Woo Youn Kim. Universal structure conversion method for organic molecules: from atomic connectivity to three-dimensional geometry. Bulletin of the Korean Chemical Society, 36 0 (7): 0 1769--1777, 2015

    2015

  42. [50]

    Equivariant flow matching

    Leon Klein, Andreas Kr \"a mer, and Frank Noe. Equivariant flow matching. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=eLH2NFOO1B

    2023

  43. [51]

    Jupyter notebooks-a publishing format for reproducible computational workflows

    Thomas Kluyver, Benjamin Ragan-Kelley, Fernando P \'e rez, Brian E Granger, Matthias Bussonnier, Jonathan Frederic, Kyle Kelley, Jessica B Hamrick, Jason Grout, Sylvain Corlay, et al. Jupyter notebooks-a publishing format for reproducible computational workflows. Elpub, 2016: ...

    2016

  44. [52]

    Momentum stiefel optimizer, with applications to suitably-orthogonal attention, and optimal transport

    Lingkai Kong, Yuqing Wang, and Molei Tao. Momentum stiefel optimizer, with applications to suitably-orthogonal attention, and optimal transport. arXiv preprint arXiv:2205.14173, 2022

    2022 arXiv

  45. [53]

    Determination of molecular structure from microwave spectroscopic data

    J Kraitchman. Determination of molecular structure from microwave spectroscopic data. American Journal of Physics, 21 0 (1): 0 17--24, 1953

    1953

  46. [54]

    End-to-end crystal structure prediction from powder x-ray diffraction

    Qingsi Lai, Lin Yao, Zhifeng Gao, Siyuan Liu, Hongshuai Wang, Shuqi Lu, Di He, Liwei Wang, Cheng Wang, and Guolin Ke. End-to-end crystal structure prediction from powder x-ray diffraction. arXiv preprint arXiv:2401.03862, 2024

    2024 arXiv

  47. [55]

    Rdkit documentation

    Greg Landrum. Rdkit documentation. Release, 1 0 (1-79): 0 4, 2013

    2013

  48. [56]

    Scalfani, Daniel Probst, Kazuya Ujihara, guillaume godin, Axel Pahl, Rachel Walker, Juuso Lehtivarjo, Francois Berenger, strets123, and jasondbiggs

    Greg Landrum, Paolo Tosco, Brian Kelley, Ric, David Cosgrove, sriniker, Riccardo Vianello, gedeck, NadineSchneider, Gareth Jones, Eisuke Kawashima, Dan N, Andrew Dalke, Brian Cole, Matt Swain, Samo Turk, Aleksandr Savelev, Alain Vaucher, Maciej Wójcikowski, Ichiru Take, Vincen...

    2024

  49. [57]

    John M. Lee. Smooth Manifolds, pp.\ 1--29. Springer New York, New York, NY, 2003. ISBN 978-0-387-21752-9. doi:10.1007/978-0-387-21752-9_1. URL https://doi.org/10.1007/978-0-387-21752-9_1

    2003 doi

  50. [58]

    Study of Benzene Fragmentation , Isomerization , and Growth Using Microwave Spectroscopy

    Kin Long Kelvin Lee and Michael McCarthy. Study of Benzene Fragmentation , Isomerization , and Growth Using Microwave Spectroscopy . The Journal of Physical Chemistry Letters, 10 0 (10): 0 2408--2413, April 2019. ISSN 1948-7185. doi:10.1021/acs.jpclett.9b00586

    2019 doi

  51. [59]

    Bayesian Analysis of Theoretical Rotational Constants from Low-Cost Electronic Structure Methods

    Kin Long Kelvin Lee and Michael McCarthy. Bayesian Analysis of Theoretical Rotational Constants from Low-Cost Electronic Structure Methods . The Journal of Physical Chemistry A, 124 0 (5): 0 898--910, February 2020. ISSN 1089-5639. doi:10.1021/acs.jpca.9b09982

    2020 doi

  52. [60]

    Solving inverse problems in protein space using diffusion-based priors

    Axel Levy, Eric R Chan, Sara Fridovich-Keil, Fr \'e d \'e ric Poitevin, Ellen D Zhong, and Gordon Wetzstein. Solving inverse problems in protein space using diffusion-based priors. arXiv preprint arXiv:2406.04239, 2024

    2024 arXiv

  53. [61]

    Expressive sign equivariant networks for spectral geometric learning

    Derek Lim, Joshua Robinson, Stefanie Jegelka, and Haggai Maron. Expressive sign equivariant networks for spectral geometric learning. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=UWd4ysACo4

    2023

  54. [62]

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

    2023

  55. [63]

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

    Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003, 2022

    2022 arXiv

  56. [64]

    Scaling riemannian diffusion models

    Aaron Lou, Minkai Xu, Adam Farris, and Stefano Ermon. Scaling riemannian diffusion models. Advances in Neural Information Processing Systems, 36, 2024

    2024

  57. [65]

    A variational perspective on solving inverse problems with diffusion models

    Morteza Mardani, Jiaming Song, Jan Kautz, and Arash Vahdat. A variational perspective on solving inverse problems with diffusion models. arXiv preprint arXiv:2305.04391, 2023

    2023 arXiv

  58. [66]

    High-resolution mass spectrometers

    Alan G Marshall and Christopher L Hendrickson. High-resolution mass spectrometers. Annu. Rev. Anal. Chem., 1: 0 579--599, 2008

    2008

  59. [67]

    An efficient algorithm for the riemannian logarithm on the stiefel manifold for a family of riemannian metrics

    Simon Mataigne, Ralf Zimmermann, and Nina Miolane. An efficient algorithm for the riemannian logarithm on the stiefel manifold for a family of riemannian metrics. arXiv preprint arXiv:2403.11730, 2024

    2024 arXiv

  60. [68]

    Molecule Identification with Rotational Spectroscopy and Probabilistic Deep Learning

    Michael McCarthy and Kin Long Kelvin Lee. Molecule Identification with Rotational Spectroscopy and Probabilistic Deep Learning . The Journal of Physical Chemistry A, 124 0 (15): 0 3002--3017, April 2020. ISSN 1089-5639, 1520-5215. doi:10.1021/acs.jpca.0c01376

    2020 doi

  61. [69]

    McCarthy, Kin Long Kelvin Lee, P

    Michael C. McCarthy, Kin Long Kelvin Lee, P. Brandon Carroll, Jessica P. Porterfield, P. Bryan Changala, James H. Thorpe, and John F. Stanton. Exhaustive Product Analysis of Three Benzene Discharges by Microwave Spectroscopy . The Journal of Physical Chemistry A, 124 0 (25): 0...

    2020 doi

  62. [70]

    2018 census of interstellar, circumstellar, extragalactic, protoplanetary disk, and exoplanetary molecules

    Brett A McGuire. 2018 census of interstellar, circumstellar, extragalactic, protoplanetary disk, and exoplanetary molecules. The Astrophysical Journal Supplement Series, 239 0 (2): 0 17, 2018

    2018

  63. [71]

    McGuire, P

    Brett A. McGuire, P. Brandon Carroll, Ryan A. Loomis, Ian A. Finneran, Philip R. Jewell, Anthony J. Remijan, and Geoffrey A. Blake. Discovery of the interstellar chiral molecule propylene oxide ( CH3CHCH2O ). Science, 352 0 (6292): 0 1449--1452, June 2016. doi:10.1126/science.aae0328

    2016 doi

  64. [72]

    Geomstats: A python package for riemannian geometry in machine learning

    Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susa...

    2020

  65. [73]

    Nina Miolane, Luís F. Pereira, Saiteja Utpala, Nicolas Guigui, Alice Le Brigant, Hzaatiti, Yann Cabanes, Johan Mathe, Niklas Koep, elodiemaignant, ythanwerdas, xpennec, tgeral68, Christian, Tra My Nguyen, Olivier Peltre, John Harvey, pchauchat, julesdeschamps, Quentin Barthéle...

    2024

  66. [74]

    Untargeted analysis of environmental contaminants in surface snow samples of svalbard islands by liquid chromatography-high resolution mass spectrometry

    Benedetta Giannelli Moneta, Sara Elsa Aita, Elena Barbaro, Anna Laura Capriotti, Andrea Cerrato, Aldo Lagan \`a , Carmela Maria Montone, Susy Piovesana, Federico Scoto, Carlo Barbante, et al. Untargeted analysis of environmental contaminants in surface snow samples of svalbard...

    2023

  67. [75]

    A diagonalization-free optimization algorithm for solving kohn--sham equations of closed-shell molecules

    Martin Mrovec and JA Berger. A diagonalization-free optimization algorithm for solving kohn--sham equations of closed-shell molecules. Journal of Computational Chemistry, 42 0 (7): 0 492--504, 2021

    2021

  68. [76]

    Estimating noise correlations across continuous conditions with wishart processes

    Amin Nejatbakhsh, Isabel Garon, and Alex Williams. Estimating noise correlations across continuous conditions with wishart processes. Advances in Neural Information Processing Systems, 36, 2024

    2024

  69. [77]

    Star-shaped denoising diffusion probabilistic models

    Andrey Okhotin, Dmitry Molchanov, Arkhipkin Vladimir, Grigory Bartosh, Viktor Ohanesian, Aibek Alanov, and Dmitry P Vetrov. Star-shaped denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 36, 2024

    2024

  70. [78]

    Python for scientific computing

    Travis E Oliphant. Python for scientific computing. Computing in science & engineering, 9 0 (3): 0 10--20, 2007

    2007

  71. [79]

    Conjugate priors and posterior inference for the matrix langevin distribution on the stiefel manifold

    Subhadip Pal, Subhajit Sengupta, Riten Mitra, and Arunava Banerjee. Conjugate priors and posterior inference for the matrix langevin distribution on the stiefel manifold. 2020

    2020

  72. [80]

    Py T orch: An imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Py T orch: An imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems, 32, 2019

    2019

  73. [81]

    Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, and Ricky T. Q. Chen. Multisample flow matching: Straightening flows with minibatch couplings. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jo...

    2023

  74. [82]

    Smith, Ishan Misra, Aditya Grover, Heli Ben-Hamu, and Yaron Lipman

    Omri Puny, Matan Atzmon, Edward J. Smith, Ishan Misra, Aditya Grover, Heli Ben-Hamu, and Yaron Lipman. Frame averaging for invariant and equivariant network design. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=zIUyj55nXR

    2022

  75. [83]

    Connections between the accuracy of rotational constants and equilibrium molecular structures

    Cristina Puzzarini and John F Stanton. Connections between the accuracy of rotational constants and equilibrium molecular structures. Physical Chemistry Chemical Physics, 25 0 (3): 0 1421--1429, 2023

    2023

  76. [84]

    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 0 (1): 0 1--7, 2014

    2014

  77. [85]

    3Dmol .js: Molecular visualization with WebGL

    Nicholas Rego and David Koes. 3Dmol .js: Molecular visualization with WebGL . Bioinformatics, 31 0 (8): 0 1322--1324, 2015

    2015

  78. [86]

    Crystal structure determination from powder diffraction patterns with generative machine learning

    Eric A Riesel, Tsach Mackey, Hamed Nilforoshan, Minkai Xu, Catherine K Badding, Alison B Altman, Jure Leskovec, and Danna E Freedman. Crystal structure determination from powder diffraction patterns with generative machine learning. Journal of the American Chemical Society, 2024

    2024

  79. [87]

    Einops: Clear and reliable tensor manipulations with einstein-like notation

    Alex Rogozhnikov. Einops: Clear and reliable tensor manipulations with einstein-like notation. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=oapKSVM2bcj

    2022

  80. [88]

    Relaxation of conformers and isomers in seeded supersonic jets of inert gases

    RS Ruoff, TD Klots, T Emilsson, and HS Gutowsky. Relaxation of conformers and isomers in seeded supersonic jets of inert gases. The Journal of chemical physics, 93 0 (5): 0 3142--3150, 1990

    1990

  81. [89]

    Seifert, Michael J

    Marcus Schwarting, Nathan A. Seifert, Michael J. Davis, Ben Blaiszik, Ian Foster, and Kirill Prozument. Twins in rotational spectroscopy: Does a rotational spectrum uniquely identify a molecule?, April 2024

    2024

  82. [90]

    Structure determination of strawberry aldehyde by broadband microwave spectroscopy: Conformational stabilization by dispersive interactions

    Steven T Shipman, Justin L Neill, Richard D Suenram, Matt T Muckle, and Brooks H Pate. Structure determination of strawberry aldehyde by broadband microwave spectroscopy: Conformational stabilization by dispersive interactions. The Journal of Physical Chemistry Letters, 2 0 (5...

    2011

  83. [91]

    Pseudoinverse-guided diffusion models for inverse problems

    Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guided diffusion models for inverse problems. In International Conference on Learning Representations, 2023 a . URL https://openreview.net/forum?id=9_gsMA8MRKQ

    2023

  84. [92]

    Loss-guided diffusion models for plug-and-play controllable generation

    Jiaming Song, Qinsheng Zhang, Hongxu Yin, Morteza Mardani, Ming-Yu Liu, Jan Kautz, Yongxin Chen, and Arash Vahdat. Loss-guided diffusion models for plug-and-play controllable generation. In International Conference on Machine Learning, pp.\ 32483--32498. PMLR, 2023 b

    2023

  85. [93]

    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. arXiv preprint arXiv:2011.13456, 2020

    2011 arXiv

  86. [94]

    Solving inverse problems in medical imaging with score-based generative models

    Yang Song, Liyue Shen, Lei Xing, and Stefano Ermon. Solving inverse problems in medical imaging with score-based generative models. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=vaRCHVj0uGI

    2022

  87. [95]

    Equivariant flow matching with hybrid probability transport for 3d molecule generation

    Yuxuan Song, Jingjing Gong, Minkai Xu, Ziyao Cao, Yanyan Lan, Stefano Ermon, Hao Zhou, and Wei-Ying Ma. Equivariant flow matching with hybrid probability transport for 3d molecule generation. In Thirty-seventh Conference on Neural Information Processing Systems, 2023 c

    2023

  88. [96]

    Sonstrom, Zoua Pa Vang, Haley N

    Reilly E. Sonstrom, Zoua Pa Vang, Haley N. Scolati, Justin L. Neill, Brooks H. Pate, and Joseph R. Clark. Rapid Enantiomeric Excess Measurements of Enantioisotopomers by Molecular Rotational Resonance Spectroscopy . Organic Process Research & Development, 27 0 (7): 0 1185--119...

    2023 doi

  89. [97]

    A rotational investigation of the three isomeric forms of cyanoethynylbenzene ( HCC-C 6 H 4 - CN ): Benchmarking experiments and calculations using the `` Lego brick'' approach

    Jean-Thibaut Spaniol, Kin Long Kelvin Lee, Olivier Pirali, Cristina Puzzarini, and Marie-Aline Martin-Drumel . A rotational investigation of the three isomeric forms of cyanoethynylbenzene ( HCC-C 6 H 4 - CN ): Benchmarking experiments and calculations using the `` Lego brick'...

    2023 doi

  90. [98]

    Dirichlet flow matching with applications to dna sequence design

    Hannes Stark, Bowen Jing, Chenyu Wang, Gabriele Corso, Bonnie Berger, Regina Barzilay, and Tommi Jaakkola. Dirichlet flow matching with applications to dna sequence design. arXiv preprint arXiv:2402.05841, 2024

    2024 arXiv

  91. [99]

    pandas-dev/pandas: Pandas

    The pandas development team . pandas-dev/pandas: Pandas . URL https://github.com/pandas-dev/pandas

  92. [100]

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

    Alexander Tong, Kilian FATRAS, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based generative models with minibatch optimal transport. Transactions on Machine Learning Research, 2024. ISSN 283...

    2024

  93. [101]

    Python reference manual, volume 111

    Guido Van Rossum, Fred L Drake, et al. Python reference manual, volume 111. Centrum voor Wiskunde en Informatica Amsterdam, 1995

    1995

  94. [102]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (eds.), Advances in Neural Info...

    2017

  95. [103]

    Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St \'e fan J

    Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St \'e fan J. van der Walt , Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nels...

    2020

  96. [104]

    Accuracy of the rotational constants

    Natalaja Vogt, J \"u rgen Vogt, and Jean Demaison. Accuracy of the rotational constants. Journal of molecular structure, 988 0 (1-3): 0 119--127, 2011

    2011

  97. [105]

    Jakob, J

    W. Jakob, J. Rhinelander, D. Moldovan and others https://github.com/pybind/pybind11/graphs/contributors . pybind11 -- Seamless operability between C++11 and Python https://github.com/pybind/pybind11 , 2017

    2017

  98. [106]

    Particle filtering on the stiefel manifold with optimal transport

    Zhichao Wang and Victor Solo. Particle filtering on the stiefel manifold with optimal transport. In 2020 59th IEEE Conference on Decision and Control (CDC), pp.\ 4111--4116. IEEE, 2020

    2020

  99. [107]

    Seaborn: statistical data visualization

    Michael L Waskom. Seaborn: statistical data visualization. Journal of Open Source Software, 6 0 (60): 0 3021, 2021

    2021

  100. [108]

    Observation of the simplest criegee intermediate ch2oo in the gas-phase ozonolysis of ethylene

    Caroline C Womack, Marie-Aline Martin-Drumel, Gordon G Brown, Robert W Field, and Michael C McCarthy. Observation of the simplest criegee intermediate ch2oo in the gas-phase ozonolysis of ethylene. Science advances, 1 0 (2): 0 e1400105, 2015

    2015

  101. [109]

    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. arXiv preprint arXiv:2203.02923, 2022

    2022 arXiv

  102. [110]

    Grassmann manifold flows for stable shape generation

    Ryoma Yataka, Kazuki Hirashima, and Masashi Shiraishi. Grassmann manifold flows for stable shape generation. Advances in Neural Information Processing Systems, 36: 0 72377--72411, 2023

    2023

  103. [111]

    Automated, context-free assignment of asymmetric rotor microwave spectra

    Lia Yeh, Lincoln Satterthwaite, and David Patterson. Automated, context-free assignment of asymmetric rotor microwave spectra. The Journal of chemical physics, 150 0 (20), 2019

    2019

  104. [112]

    Se (3) diffusion model with application to protein backbone generation

    Jason Yim, Brian L Trippe, Valentin De Bortoli, Emile Mathieu, Arnaud Doucet, Regina Barzilay, and Tommi Jaakkola. Se (3) diffusion model with application to protein backbone generation. arXiv preprint arXiv:2302.02277, 2023

    2023 arXiv

  105. [113]

    Zaleski and Kirill Prozument

    Daniel P. Zaleski and Kirill Prozument. Automated assignment of rotational spectra using artificial neural networks. The Journal of Chemical Physics, 149 0 (10): 0 104106, September 2018. ISSN 0021-9606. doi:10.1063/1.5037715

    2018 doi

  106. [114]

    Trivialized momentum facilitates diffusion generative modeling on lie groups

    Yuchen Zhu, Tianrong Chen, Lingkai Kong, Evangelos A Theodorou, and Molei Tao. Trivialized momentum facilitates diffusion generative modeling on lie groups. arXiv preprint arXiv:2405.16381, 2024

    2024 arXiv

  107. [115]

    Computing the riemannian logarithm on the stiefel manifold: Metrics, methods, and performance

    Ralf Zimmermann and Knut H \"u per. Computing the riemannian logarithm on the stiefel manifold: Metrics, methods, and performance. SIAM Journal on Matrix Analysis and Applications, 43 0 (2): 0 953--980, 2022

    2022

  108. [116]

    @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 ...

  109. [117]

    \@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@firs...

  110. [118]

    fingerprint

    @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 \@bibset...

    2022 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.