Pith. sign in

REVIEW 4 major objections 4 minor 77 references

ProT-GFDM: A Generative Fractional Diffusion Model for Protein Generation

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read ProT-GFDM claims that swapping Brownian motion for a Markov approximation of fractional Brownian motion in a score-based diffusion model improves 32-residue protein backbone generation, raising density by 7.19% and coverage by 5.66%.

desk verdict A competent application of an existing fractional diffusion framework to protein fragment distance maps, but the headline 'outperforms' claim rests on single-run comparisons with no error bars. read the letter →

arxiv 2504.21092 v1 pith:2IAAUUD3 submitted 2025-04-29 q-bio.QM

Xiao Liang , Wentao Ma , Eric Paquet , Herna Lydia Viktor , Wojtek Michalowski This is my paper · ORCID
classification q-bio.QM MSC 60G2260H10
keywords fractionalBrownianmotionscore-basedgenerativemodelsproteingenerationalpha-carbondistancemapsMarkovapproximationoffBmHurstindexdiffusionSDEbackbonemodeling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the stochastic process driving a score-based diffusion model does not have to be Brownian motion. It substitutes a Markov approximation of fractional Brownian motion—noise with positively correlated increments when the Hurst index $H$ exceeds $1/2$—so the forward process can carry long-range dependencies through protein structures. Tested on 32-residue alpha-carbon distance maps, the model reports a 7.19% gain in density (fidelity), a 5.66% gain in coverage (diversity), and a 1.01% improvement in the Fréchet inception distance over a standard score-based baseline. If the comparison holds, fractional driving noise becomes a practical lever for structure generation rather than a mathematical curiosity.

What carries the argument

The central object is MA-fBm, the Markov approximation of fractional Brownian motion: a weighted sum of $K$ Ornstein–Uhlenbeck processes with geometrically spaced mean-reversion speeds, with weights chosen to minimize the $L^2$ approximation error to true fractional Brownian motion. It replaces the Brownian driver in the forward SDE, injecting long-range dependence controlled by the Hurst index $H$ while keeping the system finite-dimensional and Markovian, so the reverse-time SDE and probability-flow ODE remain tractable. The score is learned on the augmented state $(X, Y^1, \dots, Y^K)$ by augmented score matching.

What would settle it

Re-run the baseline and ProT-GFDM ($H=0.8$, $K=3$) on the same data split with multiple random seeds and report the distributions of density, coverage, and FID; the central claim fails if the 7.19% density and 5.66% coverage advantages collapse into overlapping error bars or reverse.

Watch

Extended reading notes

Core claim

The paper's central claim is that a fractional diffusion model built on a Markov approximation of fractional Brownian motion (MA-fBm) generates protein backbone structures better than a conventional Brownian-driven diffusion model. On 32-residue $\alpha$-carbon ($C_\alpha$) distance maps with $H=0.8$ and $K=3$ Ornstein–Uhlenbeck terms, ProT-GFDM reports density 1.118 versus 1.043 for the variance-preserving SDE baseline, coverage 0.934 versus 0.884, and Fréchet inception distance 74.614 versus 75.368. The paper also claims that the choice of noise schedule and solver changes the trade-off: the cosine schedule reaches its best FID (73.452) at low $H$ with $K=3$, the linear schedule gives the highest density and coverage at $H=0.8$, and among samplers the predictor-corrector SDE and the adaptive RK45 ODE give the best quality at 1,000 steps.

Load-bearing premise

The comparison rests on the assumption that the standard score-based baseline was run under equivalent conditions and that the reported metric gaps are not random run-to-run noise, since the paper reports no seeds, error bars, or baseline tuning details.

Editorial extensions

If this is right

  • With a linear noise schedule, $H=0.8$ and $K=3$ is the best configuration tested, so superdiffusive noise is the setting to copy for similar protein tasks.
  • The cosine schedule changes the picture: it reaches a lower FID at $H=0.2$ and $K=3$ than any linear-schedule run, so the best Hurst index depends on the noise schedule.
  • Solver choice matters as much as the driving noise: predictor-corrector sampling at 1,000 steps gives the best SDE results, and adaptive RK45 at 1,000 steps gives the best ODE results.
  • Raising $K$ from 2 to 3 and doubling solver steps from 1,000 to 2,000 produce only marginal or inconsistent gains, so the fractional model's advantage does not depend on extra compute.

Reading between the lines

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

  • If the reported gains reproduce across independent training runs, fractional driving noise should transfer to other structured outputs with long-range correlations, such as RNA backbones or small-molecule conformer ensembles, though the paper tests only 32-residue protein fragments.
  • The paper fixes $H$ at 0.2, 0.5, and 0.8, but a data-driven estimate of the Hurst index from each training set could outperform either preset and make the method adaptive.
  • The noise-schedule crossover suggests that $H$, $K$, the schedule, and the solver interact; a joint selection rule for these four choices may yield larger gains than any single best setting reported.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript applies the generative fractional diffusion model (GFDM) framework of [26] to generate 32-residue Cα distance maps. The forward dynamics replace Brownian motion with a Markov approximation of fractional Brownian motion governed by the Hurst index H and K Ornstein-Uhlenbeck processes; experiments vary H in {0.2, 0.5, 0.8}, K in {2, 3}, linear and cosine noise schedules, and several SDE/ODE solvers, comparing density, coverage, and FID against a single variance-preserving SDE (VP-SDE) baseline. The abstract claims a 7.19% density increase, a 5.66% coverage increase, and a 1.01% FID reduction relative to that baseline. Sections 2 through 4.3 restate the ScoreSDE and GFDM derivations from prior work; Section 5 contains the empirical study.

Significance. If the reported gains were reproducible and robust, the paper would demonstrate a useful application of fractional dynamics to protein backbone generation and would provide evidence that superdiffusive noise helps capture long-range dependencies in Cα distance maps. The theoretical framework is not new: Sections 4.1 through 4.3 closely follow [26], so the paper's own contribution is the empirical evaluation. No code, trained models, or seed-level results are provided, so the reproducibility of the headline claim cannot currently be assessed. The empirical comparison to a VP-SDE baseline is a reasonable first step, and the claims are falsifiable, but the evidence as reported is not yet sufficient to establish that ProT-GFDM 'outperforms conventional score-based models.'

major comments (4)
  1. [Section 5, Table 4] The headline comparison rests on single-run measurements without seeds or error bars. The chosen configuration H=0.8, K=3 is the best of the 12 FVP variants evaluated on the test metrics, and no baseline tuning history is given. Under selection among 12 configurations, the expected gap from a baseline can inflate even under a true null hypothesis, so the reported 7.19% density gain and 5.66% coverage gain are not distinguishable from run-to-run noise as presented.
  2. [Section 5, Tables 6 and 7] The claimed fractional-dynamics effect is not isolated from solver and schedule choices. Within the same fractional model at H=0.8, K=3, changing the solver from Euler-Maruyama to the PC sampler changes density from 1.118 to 1.224 (Table 6), which is a larger swing than the 7.19% gain attributed to fractional dynamics; RK45 at 1000 steps yields FID 73.8 (Table 7), below the headline 74.614. Additionally, Table 5 reports FID 73.452 for cosine H=0.2, K=3, contradicting the text following Table 4 that H=0.8, K=3 achieves the lowest FID. The causal attribution to H therefore requires re-running the VP baseline under the same solver, schedule, and selection protocol with repeated seeds.
  3. [Section 6, Conclusion] The conclusion that 'higher H generally improves density and coverage in both noise schedules' is contradicted by Table 5: for the cosine schedule, density at H=0.5 is lower than at H=0.2 for both K=2 (0.799 versus 0.960) and K=3 (0.832 versus 0.960). The statement that increasing K from 2 to 3 'does not significantly affect density' is also contradicted by Table 4 for the linear schedule at H=0.8 (density 1.0142 versus 1.118) and by Table 5 for the cosine schedule at H=0.5 (0.799 versus 0.832). The narrative should be revised to match the tabulated numbers.
  4. [Section 5, Evaluation metrics and dataset] The evaluation is limited to distributional metrics on 32x32 Cα distance maps with a single VP-SDE baseline; no comparison is made with other protein generative models, and no structural validity check (e.g., reconstruction of 3D coordinates, Ramachandran statistics, or designability) is reported. As a result, the title-level claim of 'protein generation' is supported only indirectly. At minimum, the paper should either add such validation or soften the claims accordingly.
minor comments (4)
  1. [Section 4.3] The notation 'Y[K] t := (Y1 1,..., YK t )' appears to contain typos; the stacked vector should likely be (Y^1_t, ..., Y^K_t). The weights written as 'ηk t,...,η k t' are also ambiguous and should be defined more carefully.
  2. [Section 5, Table 3 and surrounding text] The text says 'Coverage is not normalized' and then immediately says 'Coverage is bounded between 0 and 1'; the formula in Table 3 is a normalized average of indicators, so this contradiction should be resolved.
  3. [Section 5, Tables 6 and 7] The paper introduces NFEs as a measure of computational cost but never reports NFE values in the solver comparison tables; reporting NFEs alongside the iteration counts would make the efficiency comparison meaningful.
  4. [Section 3] The dataset description does not mention redundancy reduction or sequence-identity splitting between training and test sets; homologous chains across splits could inflate all reported metrics and should be addressed or documented.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: ProT-GFDM applies the external GFDM framework [26] to protein distance maps, and the reported performance gains are empirical test-set measurements, not quantities forced by construction; the only self-citation [25] is background and non-load-bearing.

full rationale

The paper's theoretical core is imported from the external GFDM work [26] and the Markov approximation of fractional Brownian motion from [27, 28], not derived from the paper's own outputs. Equations (9)-(19) restate the augmented forward/reverse SDE and PF-ODE framework of [26]; the paper does not define fBm, MA-fBm, or the Hurst index in terms of the protein metrics, and no fitted parameter is renamed as a prediction. The headline numbers in the abstract (7.19% density increase, 5.66% coverage improvement, 1.01% FID reduction) are arithmetic consequences of Table 4: the VP baseline row (density 1.043, coverage 0.884, FID 75.368) is compared with the best FVP run at H=0.8, K=3 (density 1.118, coverage 0.934, FID 74.614). These are test-set empirical measurements; the comparison is not forced by the equations. The H=0.5 FVP configurations do not reduce to the VP baseline by construction because the driving noise is a K-dimensional Markov approximation of fBm, and indeed Table 4 shows FVP H=0.5 differs from the VP baseline. The only self-citation is [25], a prior protein-generation paper by some of the current authors, cited in the introduction as related work ('Motivated by [24], the authors of [25] presented innovative Levy-Ito diffusion models...'); it is not used to justify the GFDM derivation, the score-matching loss, or the experimental claims. The absence of seeds and error bars and the post-hoc selection of H, K, schedule, and solver among twelve configurations are statistical robustness concerns, not circularity: those choices could inflate the apparent gain, but they do not make the reported numbers equivalent to the model's inputs by definition. The conclusion even notes that noise-schedule effects are inconsistent and that 'the interaction between the choice of noise schedule and the sampler remains unclear,' further indicating that the empirical claims are contingent measurements rather than definitional identities.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entity: fractional Brownian motion, the Markov approximation, and the score model all come from prior literature. The free parameters are configuration choices (H, K, noise schedule, nearest-neighbor order k) made after evaluating test-set metrics. The main axioms are the faithfulness of the Markov approximation, the validity of the truncated distance-map task, and the untested assumption that superdiffusive dynamics help protein generation.

free parameters (4)
  • Hurst index H = 0.8 for headline linear result; 0.2 for best cosine FID
    Chosen by hand from {0.2, 0.5, 0.8}. The paper states the true Hurst value is unknown and suggests data-driven estimation as future work (Section 6).
  • Number of OU processes K = 3 for headline result; 2 tested as alternative
    K controls the fidelity of the Markov approximation of fBm. K=3 is selected after seeing test metrics; higher K is described as more accurate but more expensive.
  • Noise schedule type = linear for best density and coverage; cosine for best FID
    Linear and cosine schedules are both tested and the better schedule depends on the metric. This is a configuration choice made after evaluating on the test set.
  • Nearest-neighbor order k in density and coverage metrics = not specified
    The density and coverage metrics depend on the kth nearest neighbor distance, but the value of k is never reported in the paper, so the metric values are not fully specified.
assumptions (5)
  • domain assumption The finite-dimensional Markov approximation with K=2 or 3 OU processes faithfully approximates fractional Brownian motion over the relevant time horizon.
    The paper relies on the MA-fBm construction from [26,27] but does not verify approximation error for its data or time horizon (Section 4.1).
  • domain assumption A 32 by 32 Cα distance map of the first 32 residues is a meaningful protein generation target.
    Distance maps are used because they are invariant to rotation and translation, but truncating to 32 residues and using fragment-level metrics is a modeling simplification (Section 3).
  • ad hoc to paper Superdiffusive dynamics with H=0.8 improve the capture of long-range dependencies in protein structures, which is beneficial for generation.
    This motivation is stated in the introduction and conclusion but never tested directly. The experimental results are mixed across noise schedules, and H=0.2 gives the best FID under the cosine schedule.
  • domain assumption Single-run evaluation on 12,000 samples is sufficient to rank model configurations.
    No repeated seeds or error bars are reported; all comparisons in Tables 4 through 7 are single-run numbers (Section 5).
  • standard math The reverse-time SDE and probability-flow ODE formulas for the augmented process are valid.
    The paper takes these from Anderson [30] and the GFDM paper [26] without re-deriving them (Section 4.2).

how reviews work

0 comments
Cite this review

Pith. "Pith review of ProT-GFDM: A Generative Fractional Diffusion Model for Protein Generation." pith.science (2026). https://pith.science/paper/2IAAUUD3

@misc{pith2026250421092,
  author       = {Pith},
  title        = {Pith review of: ProT-GFDM: A Generative Fractional Diffusion Model for Protein Generation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2IAAUUD3}},
  note         = {Machine review of arXiv:2504.21092}
}
read the original abstract

This work introduces the generative fractional diffusion model for protein generation (ProT-GFDM), a novel generative framework that employs fractional stochastic dynamics for protein backbone structure modeling. This approach builds on the continuous-time score-based generative diffusion modeling paradigm, where data are progressively transformed into noise via a stochastic differential equation and reversed to generate structured samples. Unlike classical methods that rely on standard Brownian motion, ProT-GFDM employs a fractional stochastic process with superdiffusive properties to improve the capture of long-range dependencies in protein structures. Trained on protein fragments from the Protein Data Bank, ProT-GFDM outperforms conventional score-based models, achieving a 7.19% increase in density, a 5.66% improvement in coverage, and a 1.01% reduction in the Frechet inception distance. By integrating fractional dynamics with computationally efficient sampling, the proposed framework advances generative modeling for structured biological data, with implications for protein design and computational drug discovery.

Figures

Figures reproduced from arXiv: 2504.21092 by the authors.

Figure 1
Figure 1. Protein structure representation and distance matrix. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Sample paths of fractional Brownian motion (fBm) by Hurst index [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Overview of score-based generative modeling through stochastic and ordinary [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Quantitative results for K = 2 H=0.2 H=0.5 H=0.8 0.8 1 1.2 0.93 1.03 1.12 0.84 0.89 0.93 Metric Value Performance for K = 3 Density Coverage [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]
Figure 6
Figure 6. Figure 6: Comparison of the Fr´echet inception distance (FID) performance [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]
Figure 7
Figure 7. Figure 7: Comparison of density, coverage, and the Fr´echet inception distance (FID) for [PITH_FULL_IMAGE:figures/full_fig_p026_7.png]
Figure 8
Figure 8. Figure 8: Comparison of density, coverage, and Fr´echet inception distance (FID) metrics [PITH_FULL_IMAGE:figures/full_fig_p027_8.png]
Figure 9
Figure 9. Figure 9: Comparison of density, coverage, and the Fr´echet inception distance (FID) [PITH_FULL_IMAGE:figures/full_fig_p028_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

77 extracted references · 66 canonical work pages

  1. [26]

    Generative fractional diffusion models

    Nobis G, Aversa M, Springenberg M, Detzel M, Ermon S, Nakajima S, Murray-Smith R, Lapuschkin S, Knochenhauer C, Oala L, et al. Generative fractional diffusion models. arXiv preprint. 2023;arXiv:2310.17638

    arXiv 2023

  2. [25]

    Annealed fractional L´ evy–It¯ o diffusion models for protein generation

    Paquet E, Soleymani F, Viktor HL, Michalowski W. Annealed fractional L´ evy–It¯ o diffusion models for protein generation. Comput Struct Biotechnol J. 2024

    work page 2024

  3. [1]

    Uncovering protein function: from classification to complexes

    Morris R, Black KA, Stollar EJ. Uncovering protein function: from classification to complexes. Essays Biochem. 2022;66:255–85

    work page 2022

  4. [2]

    Sensing the shape of functional proteins with topology

    Luo Y. Sensing the shape of functional proteins with topology. Nat Comput Sci. 2023;3(2):124–5

    work page 2023

  5. [3]

    The coming of age of de novo protein design

    Huang PS, Boyken SE, Baker D. The coming of age of de novo protein design. Nature. 2016;537(7620):320

    work page 2016

  6. [4]

    Recent advances in de novo protein design: principles, methods, and applications

    Pan X, Kortemme T. Recent advances in de novo protein design: principles, methods, and applications. J Biol Chem 2021;296:100558. https://doi.org/10.1016/j.jbc. 2021.100558

    arXiv 2021

  7. [5]

    Leveraging Deep Generative Model For Computational Protein Design And Optimization

    Lai B. Leveraging deep generative model for computational protein design and op- timization. arXiv preprint arXiv:2408.17241, 2024. https://doi.org/10.48550/ arXiv.2408.17241

    work page Pith review arXiv doi:10.48550/arxiv.2408.17241 2024

  8. [6]

    A comprehensive review and comparison of existing com- putational methods for protein function prediction

    Lin B, Luo X, Liu Y, Jin X. A comprehensive review and comparison of existing com- putational methods for protein function prediction. Brief Bioinform 2024;25:bbae289. https://doi.org/10.1093/bib/bbae289

    work page doi:10.1093/bib/bbae289 2024

Show all 77 references
  1. [7]

    Generative adversarial nets

    Goodfellow I, Pouget-Abadie J, Mirza M, et al. Generative adversarial nets. Adv Neural Inf Process Syst. 2014;27

    2014

  2. [8]

    Auto-encoding variational bayes

    Kingma DP, Welling M. Auto-encoding variational bayes. arXiv preprint. 2013;arXiv:1312.6114

    2013 arXiv

  3. [9]

    Variational inference with normalizing flows

    Rezende D, Mohamed S. Variational inference with normalizing flows. International Conference on Machine Learning. PMLR; 2015. p. 1530–8

    2015

  4. [10]

    Generative modeling for protein structures

    Anand N, Huang P. Generative modeling for protein structures. In: Bengio S, et al., editors. Advances in Neural Information Processing Systems. Vol. 31. Curran Associates; 2018

    2018

  5. [11]

    ProteinVAE: Variational autoencoder for trans- lational protein design

    Lyu S, Sowlati-Hashjin S, Garton M. ProteinVAE: Variational autoencoder for trans- lational protein design. bioRxiv. 2023

    2023

  6. [12]

    ProtTrans: Toward understanding the language of life through self-supervised learning

    Elnaggar A, Heinzinger M, Dallago C, et al. ProtTrans: Toward understanding the language of life through self-supervised learning. IEEE Trans Pattern Anal Mach Intell. 2021;44:7112–27

    2021

  7. [13]

    Prot-VAE: Protein transformer variational au- toencoder for functional protein design

    Sevgen E, Moller J, Lange A, et al. Prot-VAE: Protein transformer variational au- toencoder for functional protein design. bioRxiv. 2023

    2023

  8. [14]

    Expanding functional protein sequence spaces using generative adversarial networks

    Repecka D, Jauniskis V, Karpus L, et al. Expanding functional protein sequence spaces using generative adversarial networks. Nat Mach Intell. 2021;3:324–33.https: //doi.org/10.1038/s42256-021-00310-5 . 32

    2021 doi

  9. [15]

    Deep generative modeling for protein design

    Strokach A, Kim PM. Deep generative modeling for protein design. Curr Opin Struct Biol. 2022;72:226–36. https://doi.org/10.1016/j.sbi.2021.11.008

    2022 doi

  10. [16]

    Computational protein design with deep learning neural networks

    Wang J, Cao H, Zhang JZ, Qi Y. Computational protein design with deep learning neural networks. Sci Rep. 2018;8(1):1–9

    2018

  11. [17]

    DenseCPD: improving the accuracy of neural-network-based computational protein sequence design with DenseNet

    Qi Y, Zhang JZ. DenseCPD: improving the accuracy of neural-network-based computational protein sequence design with DenseNet. J Chem Inf Model. 2020;60(3):1245–52

    2020

  12. [18]

    De novo protein design by deep network hallucination

    Anishchenko I, et al. De novo protein design by deep network hallucination. Nature. 2021;600:547–52

    2021

  13. [19]

    Robust deep learning-based protein sequence design using Pro- teinMPNN

    Dauparas J, et al. Robust deep learning-based protein sequence design using Pro- teinMPNN. Science. 2022;378:49–56

    2022

  14. [20]

    ProtGPT2 is a deep unsupervised language model for protein design

    Ferruz N, Schmidt S, H¨ ocker B. ProtGPT2 is a deep unsupervised language model for protein design. Nat Commun. 2022;13:4348

    2022

  15. [21]

    Score-based gen- erative modeling through stochastic differential equations

    Song Y, Sohl-Dickstein J, Kingma DP, Kumar A, Ermon S, Poole B. Score-based gen- erative modeling through stochastic differential equations. Int Conf Learn Represent. 2020

    2020

  16. [22]

    Denoising diffusion probabilistic models

    Ho J, Jain A, Abbeel P. Denoising diffusion probabilistic models. NeurIPS. 2020

    2020

  17. [23]

    Generative modeling by estimating gradients of the data distribu- tion

    Song Y, Ermon S. Generative modeling by estimating gradients of the data distribu- tion. Adv Neural Inf Process Syst. 2019;32

    2019

  18. [24]

    Score-based generative models with L´ evy processes

    Yoon EB, Park K, Kim S, Lim S. Score-based generative models with L´ evy processes. Adv Neural Inf Process Syst. 2023;36:40694–707

    2023

  19. [27]

    Affine representations of fractional processes with appli- cations in mathematical finance

    Harms P, Stefanovits D. Affine representations of fractional processes with appli- cations in mathematical finance. Stoch Proc Appl. 2019;129(4):1185–2228. https: //doi.org/10.1016/j.spa.2018.04.010

    2019 doi

  20. [28]

    Variational inference for SDEs driven by fractional noise

    Daems R, Opper M, Crevecoeur G, Birdal T. Variational inference for SDEs driven by fractional noise. The Twelfth International Conference on Learning Representations

  21. [29]

    Improved denoising diffusion probabilistic models

    Nichol AQ, Dhariwal P. Improved denoising diffusion probabilistic models. Int Conf Mach Learn. 2021;8162–71. 33

    2021

  22. [30]

    Reverse-time diffusion equation models

    Anderson BD. Reverse-time diffusion equation models. Stochastic Process Appl. 1982;12(3):313–26

    1982

  23. [31]

    Numerical solution of stochastic differential equations

    Kloeden PE, Platen E. Numerical solution of stochastic differential equations. Springer; 1992

    1992

  24. [32]

    Neural ordinary differential equations

    Chen TQ, Rubanova Y, Bettencourt J, Duvenaud D. Neural ordinary differential equations. Adv Neural Inf Process Syst. 2018;31:6572–83

    2018

  25. [33]

    Basic local alignment search tool

    Altschul SF, Gish W, Miller W, et al. Basic local alignment search tool. J Mol Biol. 1990;215:403–10. https://doi.org/10.1016/S0022-2836(05)80360-2

    1990 doi

  26. [34]

    DeepRED: automated protein function prediction with multi-task feed-forward deep neural networks

    Rifaioglu AS, Do˘ gan T, Martin MJ, et al. DeepRED: automated protein function prediction with multi-task feed-forward deep neural networks. Sci Rep. 2019;9:7344

    2019

  27. [35]

    DeepGOPlus: improved protein function predic- tion from sequence

    Kulmanov M, Hoehndorf R. DeepGOPlus: improved protein function predic- tion from sequence. Bioinformatics. 2020;36:422–9. https://doi.org/10.1093/ bioinformatics/btz595

    2020

  28. [36]

    Structure-based protein function prediction using graph convolutional networks

    Gligorijevi´ c V, Renfrew PD, Kosciolek T, et al. Structure-based protein function prediction using graph convolutional networks. Nat Commun. 2021;12:3168. https: //doi.org/10.1038/s41467-021-23303-9

    2021 doi

  29. [37]

    Long short-term memory

    Hochreiter S, Schmidhuber J. Long short-term memory. Neural Comput. 1997;9:1735–80. https://doi.org/10.1162/neco.1997.9.8.1735

    1997 doi

  30. [38]

    Hierarchical graph transformer with contrastive learning for protein function prediction

    Zhonghui G, Luo X, Chen J, et al. Hierarchical graph transformer with contrastive learning for protein function prediction. Bioinformatics. 2023;39:btad410. https:// doi.org/10.1093/bioinformatics/btad410

    2023 doi

  31. [39]

    GeneMANIA: a real-time multiple as- sociation network integration algorithm for predicting gene function

    Mostafavi S, Ray D, Warde-Farley D, et al. GeneMANIA: a real-time multiple as- sociation network integration algorithm for predicting gene function. Genome Biol. 2008;9:1–15

    2008

  32. [40]

    DeepNF: deep network fusion for protein function prediction

    Gligorijevi´ c V, Barot M, Bonneau R. DeepNF: deep network fusion for protein function prediction. Bioinformatics. 2018;34:3873–81. https://doi.org/10.1093/ bioinformatics/bty440

    2018

  33. [41]

    The CAFA challenge reports improved protein function prediction and new functional annotations for hundreds of genes through experimental screens

    Zhou N, Jiang Y, Bergquist TR, et al. The CAFA challenge reports improved protein function prediction and new functional annotations for hundreds of genes through experimental screens. Genome Biol. 2019;20:1–23

    2019

  34. [42]

    A comprehensive review and comparison of ex- isting computational methods for protein function prediction

    Lin B, Luo X, Liu Y, Jin X. A comprehensive review and comparison of ex- isting computational methods for protein function prediction. Brief Bioinform. 2024;25(4):bbae289

    2024

  35. [43]

    Generative models for pro- tein sequence modeling: recent advances and future directions

    Mardikoraem M, Wang Z, Pascual N, Woldring D. Generative models for pro- tein sequence modeling: recent advances and future directions. Brief Bioinform. 2023;24:bbad358. 34

    2023

  36. [44]

    Scaffolding protein functional sites using deep learning

    Wang J, et al. Scaffolding protein functional sites using deep learning. Science. 2022;377:387–94

    2022

  37. [45]

    Score-based generative modeling for de novo protein design

    Lee JS, Kim J, Kim PM. Score-based generative modeling for de novo protein design. Nat Comput Sci. 2023;3:382–92

    2023

  38. [46]

    The Protein Data Bank: a computer-based archival file for macromolecular structures

    Bernstein FC, Koetzle TF, Williams GJB, Meyer EF, Brice MD, Rodgers JR, Kennard O, Shimanouchi T, Tasumi M. The Protein Data Bank: a computer-based archival file for macromolecular structures. Arch Biochem Biophys. 1978;185(2):584–91

    1978

  39. [47]

    Generative modeling for protein structures

    Anand N, Huang P. Generative modeling for protein structures. Adv Neural Inf Process Syst. 2018;31

    2018

  40. [48]

    Sampling realistic protein conformations using local structural bias

    Hamelryck T, Kent JT, Krogh A. Sampling realistic protein conformations using local structural bias. PLoS Comput Biol. 2006;2(9):e131

    2006

  41. [49]

    A generative, probabilistic model of local protein structure

    Boomsma W, Mardia KV, Taylor CC, Ferkinghoff-Borg J, Krogh A, Hamelryck T. A generative, probabilistic model of local protein structure. Proc Natl Acad Sci U S A. 2008;105(26):8932–7

    2008

  42. [50]

    Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling

    Wu J, Zhang C, Xue T, Freeman B, Tenenbaum J. Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling. Adv Neural Inf Pro- cess Syst. 2016;82–90

    2016

  43. [51]

    Protein structure prediction using Rosetta

    Rohl CA, Strauss CE, Misura KM, Baker D. Protein structure prediction using Rosetta. Methods Enzymol. 2004;383:66–93

    2004

  44. [52]

    Distributed optimization and statistical learning via the alternating direction method of multipliers

    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn. 2011;3(1):1–122

    2011

  45. [53]

    Fully differentiable full-atom protein backbone generation

    Anand N, Eguchi R, Huang PS. Fully differentiable full-atom protein backbone generation. ICLR 2019 Workshop DeepGenStruct. 2019. https://openreview.net/ forum?id=SJxnVL8YOV. Accessed 6 June 2024

    2019

  46. [54]

    Fractional Brownian motion in a nutshell

    Shevchenko G. Fractional Brownian motion in a nutshell. Int J Mod Phys Conf Ser. 2015;36. https://doi.org/10.1142/S2010194515600022

    2015 doi

  47. [55]

    Estimation of non-normalized statistical models by score matching

    Hyv¨ arinen A, Dayan P. Estimation of non-normalized statistical models by score matching. J Mach Learn Res. 2005;6(4)

    2005

  48. [56]

    Estimating the Hessian by backpropagating cur- vature

    Martens J, Sutskever I, Swersky K. Estimating the Hessian by backpropagating cur- vature. Proc 29th Int Conf Mach Learn. 2012;963–70

    2012

  49. [57]

    Sliced score matching: A scalable approach to density and score estimation

    Song Y, Garg S, Shi J, Ermon S. Sliced score matching: A scalable approach to density and score estimation. Conf Uncertainty Artif Intell. 2019;204

    2019

  50. [58]

    A connection between score matching and denoising autoencoders

    Vincent P. A connection between score matching and denoising autoencoders. Neural Comput. 2011;23(7):1661–74. 35

    2011

  51. [59]

    Generative modeling by estimating gradients of the data distribu- tion

    Song Y, Ermon S. Generative modeling by estimating gradients of the data distribu- tion. Adv Neural Inf Process Syst. 2019;11895–907

    2019

  52. [60]

    Improved techniques for training score-based generative models

    Song Y, Ermon S. Improved techniques for training score-based generative models. Adv Neural Inf Process Syst. 2020;33

    2020

  53. [61]

    Denoising diffusion implicit models

    Song J, Meng C, Ermon S. Denoising diffusion implicit models. Int Conf Learn Rep- resent. 2020

    2020

  54. [62]

    Numerical solution of stochastic differential equations

    Kloeden PE, Platen E. Numerical solution of stochastic differential equations. Vol

  55. [63]

    Approximate integration of stochastic differential equations

    Mil’shtein GN. Approximate integration of stochastic differential equations. Theory Probab Appl. 1975;19(3):557–000

    1975

  56. [64]

    Springer Science & Business Media; 2013

    2013

  57. [65]

    The probability flow ODE is provably fast

    Chen S, Chewi S, Lee H, Li Y, Lu J, Salim A. The probability flow ODE is provably fast. arXiv preprint. 2023;arXiv:2305.11798

    2023 arXiv

  58. [66]

    Numerical continuation methods: an introduction

    Allgower EL, Georg K. Numerical continuation methods: an introduction. Vol. 13. Springer Science & Business Media; 2012

    2012

  59. [67]

    Fast sampling of diffusion models with exponential integrator

    Zhang Q, Chen Y. Fast sampling of diffusion models with exponential integrator. arXiv preprint. 2022;arXiv:2204.13902

    2022 arXiv

  60. [68]

    DPM-solver: A fast ODE solver for diffusion probabilistic model sampling in around 10 steps

    Lu C, Zhou Y, Bao F, Chen J, Li C, Zhu J. DPM-solver: A fast ODE solver for diffusion probabilistic model sampling in around 10 steps. arXiv preprint. 2022;arXiv:2206.00927

    2022 arXiv

  61. [69]

    U-Net: convolutional networks for biomedical im- age segmentation

    Ronneberger O, Fischer P, Brox T. U-Net: convolutional networks for biomedical im- age segmentation. Int Conf Med Image Comput Comput Assist Interv. 2015;234–41

    2015

  62. [70]

    Variational diffusion models

    Kingma D, Salimans T, Poole B, Ho J. Variational diffusion models. Adv Neural Inf Process Syst. 2021;34:21696–707

    2021

  63. [71]

    Improved precision and recall metric for assessing generative models

    Kynk¨ a¨ anniemi T, Karras T, Laine S, Lehtinen J, Aila T. Improved precision and recall metric for assessing generative models. Adv Neural Inf Process Syst. 2019;3929–38

    2019

  64. [72]

    Assessing generative models via precision and recall

    Sajjadi MS, Bachem O, Lucic M, Bousquet O, Gelly S. Assessing generative models via precision and recall. Adv Neural Inf Process Syst. 2018;31

    2018

  65. [73]

    Is noise conditioning necessary for denoising generative models? arXiv preprint

    Sun Q, Jiang Z, Zhao H, He K. Is noise conditioning necessary for denoising generative models? arXiv preprint. 2025;arXiv:2502.13129

    2025

  66. [74]

    Reliable fidelity and diversity metrics for generative models

    Naeem MF, Oh SJ, Uh Y, Choi Y, Yoo J. Reliable fidelity and diversity metrics for generative models. Int Conf Mach Learn. 2020;7176–85

    2020

  67. [75]

    Score nor- malization for a faster diffusion exponential integrator sampler

    Xia G, Danier D, Das A, Fotiadis S, Nabiei F, Sengupta U, Bernacchia A. Score nor- malization for a faster diffusion exponential integrator sampler. NeurIPS Workshop Diffusion Models. 2023. 37

    2023

  68. [76]

    DPM-Solver++: fast solver for guided sampling of diffusion probabilistic models

    Lu C, Zhou Y, Bao F, Chen J, Li C, Zhu J. DPM-Solver++: fast solver for guided sampling of diffusion probabilistic models. arXiv preprint. 2022;arXiv:2211.01095. 36

    2022 arXiv

  69. [2024]

    https://openreview.net/forum?id=rtx8B94JMS

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.