Adaptive Multimodal Protein Plug-and-Play with Diffusion-Based Priors

Amartya Banerjee; Caroline Moosm\"uller; Harlin Lee; Xingyu Xu

REVIEW 4 major objections 4 minor 1 cited by

Adaptive Multimodal Protein Plug-and-Play with Diffusion-Based Priors

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Adam-PnP fuses noisy experimental data into a pretrained protein diffusion model on the fly, reaching sub-ångström backbone reconstruction from partial coordinates plus distances.

desk verdict A sensible practical idea for multimodal protein PnP, but the central claim that adaptive weighting causes the sub-angstrom accuracy is unsupported by the experiments. read the letter →

arxiv 2507.21260 v1 pith:5XI5SAUO submitted 2025-07-28 cs.LG cs.AIq-bio.QM

Amartya Banerjee , Xingyu Xu , Caroline Moosmüller , Harlin Lee This is my paper · ORCID

classification cs.LGcs.AIq-bio.QM

keywords diffusionmodelsplug-and-playpriorsproteinbackbonereconstructionmultimodalinverseproblemsadaptivenoiseestimationdynamicmodalityweightingmaximumaposteriori

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

Adam-PnP is a way to push a pretrained protein diffusion model toward a structure that fits several noisy experimental measurements at once. The paper's claim is that its two added ingredients, an online estimate of each modality's noise level and a weighting that trusts low-noise measurements more, remove the need to hand-tune modality weights and improve reconstruction. On a 127-residue test protein, fusing partial Cα coordinates with pairwise distances reaches a backbone RMSD of 0.65±0.18 Å, better than any single modality, while a low-resolution density map is automatically down-weighted when it hurts. If correct, this makes diffusion-based protein structure determination more practical for scarce or mixed-quality experimental data.

What carries the argument

The load-bearing machinery is the bias-corrected online variance estimator in Eq. (9) paired with the inverse-variance weighting of Eq. (10). Given a denoised structure estimate, the residual of each modality is decomposed into measurement noise minus the denoiser's prediction error; the estimator takes the median of squared residuals, subtracts an annealed Lipschitz-based bias term that shrinks as the diffusion time goes to zero, and smooths the result with an exponential moving average. The resulting inverse-variance weights turn the multimodal maximum-a-posteriori objective into a weighted gradient sum whose per-modality scale is set at runtime, with a momentum update added for stability. It is this estimator-weighting pair, not the diffusion backbone itself, that the paper claims makes the fusion adaptive.

What would settle it

Run the partial-coordinates-plus-distances experiment with γ set to 0 in Eq. (9), keeping everything else unchanged. If the 0.65±0.18 Å RMSD persists, the bias-corrected noise estimator is not what produces the sub-angstrom result; if it degrades, the estimator is doing the claimed work. Repeating with a range of γ values would show how sensitive the headline number is to this free parameter.

Watch

Extended reading notes

Core claim

The central claim is that multimodal posterior sampling in protein space can be run as an alternating Plug-and-Play loop, denoise with a pretrained diffusion model, then take a weighted gradient step toward the measurements, and that the loop's free knobs can be set from the data instead of by hand. For each modality, the noise estimate is the median squared residual between measurement and the forward model applied to the current denoised structure, corrected by an annealed bias term meant to subtract the denoiser's remaining error, and smoothed with an exponential moving average. Each modality is then weighted by inverse variance, so precise sources dominate automatically. The paper reports that this recipe reconstructs the test protein to 0.65±0.18 Å from partial coordinates plus distances, that combining modalities beats any single one, and that the learned noise level tracks the true noise.

Load-bearing premise

The adaptive noise estimator works only if the hand-tuned annealed bias term γ(1−t)(L_i τ_t)², with γ free and τ_t never defined, is a good model of the denoiser's remaining error; if that bias correction is wrong, the reported accuracy gains cannot be attributed to the adaptive mechanism.

Editorial extensions

If this is right

Fusing partial Cα coordinates and Cα-Cα distances yields backbone reconstructions at 0.65±0.18 Å, better than either modality alone on the same protein.
A low-resolution density map by itself fails to fold the protein, and adding it to a high-resolution pairing slightly hurts; the dynamic weighting is what prevents the low-quality modality from corrupting the result.
Accuracy degrades gracefully under data scarcity: with half the coordinates and 2,000 distances the method still lands at roughly 0.7-0.9 Å, and with 70% of coordinates it drops to about 0.1-0.35 Å.
Because only differentiability of the forward model is assumed, the same adaptive loop extends to other experimental observables, such as SAXS, NMR restraints, or crosslinks, without re-tuning the fusion weights.

Reading between the lines

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

One testable extension is to replace the hand-annealed bias term in Eq. (9) with an empirical calibration of the denoiser error; if the reconstruction accuracy does not change, the bias model is not the mechanism driving the gains.
The inverse-variance weighting is effectively adaptive precision weighting, so the estimator-weighting pair could plausibly be ported to other diffusion-based inverse solvers beyond protein backbones, since it only needs residuals and a Lipschitz bound for each forward model.
The headline 0.65 Å result comes from one 127-residue protein over three random seeds, so the same protocol should be run across diverse folds, lengths, and flexibility regimes before treating sub-angstrom accuracy as the expected operating point.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper adds an online noise-variance estimator and precision-based weighting to a plug-and-play diffusion loop for protein backbone reconstruction. That's a sensible practical idea, and the writing is clear. The experiments show plausible behavior—more data helps, and low-res density guidance hurts—and the noise-estimation table (Table 3) provides a sanity check that the estimator roughly tracks true noise.

The problem is that the main claim—that the adaptive mechanism is what delivers the 0.65 Å RMSD—is not actually tested. There is no ablation with fixed noise levels or fixed weights, so the reported gains over P alone could come from the guidance in general, not from the adaptation. The improvement of P+D over P (0.65±0.18 vs 0.74±0.26 Å) is well within error bars, and the 'state-of-the-art' label is not backed by any comparison to the cited inverse-protein methods [8,10]. There is also an undefined τ_t in Eq. (9) and Algorithm 1; without it the bias correction cannot be instantiated, and the bound on the mean residual is applied to a median estimator, which is a hole. These are not minor issues—they hit the central causal claim.

That said, the paper is not incoherent. The method is a reasonable heuristic and the experimental gaps are fixable: add a fixed-weight control, compare to at least one prior method, and define the notation. As it stands, the submission reads like a workshop paper with a strong abstract.

Who gets value from this? People working on integrative structural biology who want a quick baseline to compare against; the idea of self-adapting noise levels could be useful even if the paper doesn't prove it. A serious referee should see it, not because the current version is acceptable, but because the problem is relevant and the authors are onto something. I'd send it out but expect major revision before acceptance.

Referee Report

4 major / 4 minor

Summary. Adam-PnP is a plug-and-play reconstruction method that uses a pretrained Chroma diffusion model as a prior and steers reverse diffusion by gradients from multimodal experimental data. The proposed contributions are an online noise-variance estimator (Eqs. 8-9) with a bias-correction term, precision-based dynamic weighting (Eq. 10), and a momentum update (Eqs. 13-14). Experiments reconstruct PDB 7r5b from combinations of partial Cα coordinates (P), pairwise distances (D), and simulated density maps (E). Table 1 reports a best RMSD of 0.65±0.18 Å for P+D and 0.67±0.19 Å for P+D+E; Table 2 shows improved reconstruction with more high-resolution data; Table 3 compares estimated vs true noise for D. The paper concludes that adaptive noise estimation and dynamic weighting are responsible for the improved accuracy.

Significance. The problem is practically important, because experimental structure determination often combines noisy, heterogeneous measurements with unknown noise levels. The paper's modularity with respect to forward models and its use of a pretrained protein diffusion prior are appealing. The evaluation uses an external crystal structure for RMSD, and error bars over three seeds are reported. If the causal claims were established, the framework could be a useful toolbox for integrative modeling. However, the current manuscript does not yet substantiate the core attribution of the performance to the adaptive mechanism, and it omits comparisons that would support the state-of-the-art claim.

major comments (4)

[Section 3.2, Eq. (9); Algorithm 1, line 12] The key estimator \hat\sigma^2_{i,t} is not fully specified because \tau_t (and \tau_{t-1|t} in Algorithm 1, line 12) is never defined and c_t is left as an unspecified constant. The bias term \gamma(1-t)(L_i \tau_t)^2 is motivated only by a loose bound and can absorb arbitrary bias through the free constants \gamma and c_t. As written, the method cannot be instantiated, checked, or reproduced. Please define \tau_t and c_t precisely, or give a fully specified alternative bias model with a justification.
[Section 4, Tables 1-3] There is no ablation that isolates the adaptive noise estimation and dynamic weighting. The manuscript compares modality combinations but never runs the same PnP procedure with fixed (oracle or grid-selected) noise levels and fixed weights, so the observed RMSD improvements cannot be attributed to adaptation. Add control experiments with (i) true noise variances and fixed weights, (ii) adaptive estimation disabled, and (iii) manually tuned constant weights, and report the resulting RMSDs and whether any differences are statistically significant. Also report the learned weights w_{i,t} over time to support the claim that E is down-weighted.
[Section 4, Table 1 and Introduction] The phrase 'state-of-the-art' is not backed by any comparison to the cited inverse-protein methods [8] (Levy et al., 2024) and [10] (Maddipatla et al., 2025), or to other baselines such as Chroma with no guidance. Without shared benchmarks and baseline numbers, the 0.65 Å RMSD cannot be interpreted as SOTA. Please provide direct comparisons on 7r5b under the same conditions, or clearly state that no comparison was performed and temper the claim accordingly.
[Section 4, experimental protocol] The reported RMSD uses 'the lowest-energy sampled structure' (Section 4). This selection rule is potentially optimistic: if many reverse-diffusion samples are drawn per seed and the lowest-energy one is chosen, the reported values may reflect an oracle over samples rather than typical performance. Please state how many samples are generated, what energy is used for selection, and also report the mean RMSD over samples or the RMSD of the final sample. In addition, Table 3 provides noise estimates only for the distance modality D; to support the multimodal claim, show estimates for P and especially E, whose down-weighting is invoked in the discussion of Table 1.

minor comments (4)

[Section 4.2, Table 2 caption] There is a typo in the Table 2 caption: '0,2' should be '0.2'.
[Section 4.2.1 and Table 3] The text says the learned noise 'closely tracked' the true noise, but for \sigma_D=0.05 the estimate is 0.086±0.009, a relative error of about 72%. The claim should be softened or the discrepancy explained.
[Section 3.2] The values of the hyperparameters \gamma, \epsilon, EMA decay, \rho, and \eta are not reported. Since the method is introduced as reducing manual tuning, please provide the chosen values and a short sensitivity analysis, especially for \gamma, which appears to be hand-tuned.
[Section 2.3 and Algorithm 1] The notation is inconsistent between \tilde z_0, \hat z_0, and z_t, and line 12 introduces \alpha_{t-1|t} and \tau_{t-1|t} without definition. Please clarify the discretization of Eq. (5) that Algorithm 1 implements, and align the notation with the text.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the headline RMSD is measured against an external crystal structure and the adaptive noise estimator is not fitted to that target.

full rationale

The central result, a backbone RMSD of 0.65±0.18 Å for P+D, is evaluated against the deposited ground-truth crystal structure of PDB 7r5b using RMSD(ˆx,x*) = min_T ||Tˆx−x*||, which is an external benchmark. The adaptive noise estimator in Eq. (9) is derived from a residual decomposition and is not fitted to this target, so the prediction is not forced by construction. The only self-citation is [14] (Xu and Chi), cited in a list of PnP frameworks alongside [12,13]; the paper does not invoke a uniqueness theorem or ansatz from that work, and no load-bearing argument reduces to it. The skeptics' concerns about Eq. (9) center on the undefined τ_t and free constants γ, c_t, which make the estimator uninstantiable from the text; this is a reproducibility or correctness gap, not circularity. Similarly, the absence of a fixed-weight control means the causal attribution to adaptive weighting is not demonstrated, but this is an evidentiary weakness rather than a reduction of the prediction to its inputs. No fitted parameter is renamed as a prediction, and no known result is repackaged under new coordinates. The paper is therefore self-contained against external benchmarks, with only a minor and non-load-bearing self-citation.

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

The central claim rests on several hand-picked hyperparameters and unproven convergence assumptions; the adaptive estimator is a heuristic, not a derived result.

free parameters (6)

γ = not reported
Scale of the bias subtraction in Eq. (9); no sensitivity analysis.
ε = not reported
Floor in Eqs. (9) and (10); hand-chosen.
EMA decay factor = not reported
Smoothing of noise estimates over timesteps; value not specified.
ρ (momentum decay) = not reported
Momentum parameter in Eq. (13).
η (guidance step size) = not reported
Learning rate in Eq. (14); critical for convergence.
τt (noise scale in reverse process) = undefined
Appears in Eq. (9) and in Algorithm 1's noise injection, but is never defined in the paper.

assumptions (5)

domain assumption The pre-trained Chroma score sθ(xt,t) approximates the true score of protein structures and provides a valid prior for posterior sampling.
Section 2.2 treats Dθ as a plug-in for the prior in Eq. (6); this assumes the learned prior generalizes to the experimental-conditioned setting.
ad hoc to paper The reverse-time SDE (Eq. 5) with inserted likelihood gradients converges to samples from the posterior p(x|Y).
Algorithm 1 interleaves denoising and gradient ascent steps; no proof of convergence to the MAP mode is given, and the non-convex multimodal objective makes this nontrivial.
domain assumption Each forward model Fi is known, differentiable, and has a known Lipschitz constant Li.
Eq. (9) uses Li in the bias correction, but the paper never provides Li values for the masking, distance, or density operators.
ad hoc to paper The denoising-error bias E[||Fi(Rz0)-Fi(Rz*)||²] satisfies the bound ct(Li τt)² and is well approximated by γ(1−t)(Li τt)².
The estimator in Eq. (9) requires this approximation; τt and ct are undefined, and the annealing in t is assumed without justification.
domain assumption The plug-and-play iteration is equivalent to MAP optimization in Eq. (6).
Section 2.3 frames PnP as MAP estimation, but alternating projection onto a learned prior and likelihood is only heuristic for general forward models.

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Cite this review

Pith. "Pith review of Adaptive Multimodal Protein Plug-and-Play with Diffusion-Based Priors." pith.science (2026). https://pith.science/paper/5XI5SAUO

@misc{pith2026250721260,
  author       = {Pith},
  title        = {Pith review of: Adaptive Multimodal Protein Plug-and-Play with Diffusion-Based Priors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5XI5SAUO}},
  note         = {Machine review of arXiv:2507.21260}
}

read the original abstract

In an inverse problem, the goal is to recover an unknown parameter (e.g., an image) that has typically undergone some lossy or noisy transformation during measurement. Recently, deep generative models, particularly diffusion models, have emerged as powerful priors for protein structure generation. However, integrating noisy experimental data from multiple sources to guide these models remains a significant challenge. Existing methods often require precise knowledge of experimental noise levels and manually tuned weights for each data modality. In this work, we introduce Adam-PnP, a Plug-and-Play framework that guides a pre-trained protein diffusion model using gradients from multiple, heterogeneous experimental sources. Our framework features an adaptive noise estimation scheme and a dynamic modality weighting mechanism integrated into the diffusion process, which reduce the need for manual hyperparameter tuning. Experiments on complex reconstruction tasks demonstrate significantly improved accuracy using Adam-PnP.

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

22 extracted references · 17 canonical work pages · cited by 1 Pith paper

[8]

Visualization of membrane protein domains by cryo-electron microscopy of dengue virus,

Wei Zhang, Paul R Chipman, Jeroen Corver, Peter R Johnson, Ying Zhang, Suchetana Mukhopadhyay, Tim- othy S Baker, James H Strauss, Michael G Rossmann, and Richard J Kuhn, “Visualization of membrane protein domains by cryo-electron microscopy of dengue virus,” Nature Structural & Molecular Biology, vol. 10, no. 11, pp. 907–912, 2003

work page 2003
[10]

Denoising diffusion probabilistic models,

Jonathan Ho, Ajay Jain, and Pieter Abbeel, “Denoising diffusion probabilistic models,” inAdvances in Neural Information Processing Systems. 2020, vol. 33, pp. 6840– 6851, Curran Associates, Inc

work page 2020
[1]

While experimental techniques like X- ray crystallography [1], cryo-electron microscopy (cryo-EM) [2], and nuclear magnetic resonance (NMR) spectroscopy

INTRODUCTION The determination of three-dimensional protein structures is fundamental for understanding biological function and for novel drug design. While experimental techniques like X- ray crystallography [1], cryo-electron microscopy (cryo-EM) [2], and nuclear magnetic resonance (NMR) spectroscopy

work page
[2]

whitened

PRELIMINARIES 2.1. Problem Formulation We represent a protein backbone by its 3-dimensional coor- dinates x∈R 4N×3 , where N is the number of amino acid residues. Fori= 1, . . . , M, we observe noisy measurements yi =F i(x∗) +ηi, ηi ∼ N(0;σ2 i I),(1) where noise level σi is unknown, but the forward model Fi is known and differentiable. ηi is independent o...

arXiv 2025
[3]

Data from these methods can be sparse, noisy, ambiguous, and often incomplete

provide invaluable structural information, they each have limitations. Data from these methods can be sparse, noisy, ambiguous, and often incomplete. Computational methods are crucial for integrating these diverse data streams to pro- duce high-resolution structural models. Recently, deep gen- erative models, especially denoising diffusion probabilistic m...

work page 2024
[4]

It uniquely integrates multimodal likelihoods with a novel adaptive engine for noise estimation and weighting

METHODOLOGY Algorithm 1 implements this PnP strategy as an iterative re- finement process within the diffusion model’s reverse SDE in (5). It uniquely integrates multimodal likelihoods with a novel adaptive engine for noise estimation and weighting. We emphasize that Adam-PnP is modular and can accommodate any differentiable forward model Fi(x) that maps ...

work page
[5]

• Pairwise Cα distances (D): FD(x) computes a vector of pairwise Cα-Cα distances

EXPERIMENTAL RESULTS We evaluated Adam-PnP on the task of reconstructing the 127-residue protein with PDB ID: 7r5b from various com- binations of three data modalities [8, 10]: • Partial Cα coordinates (P): FP (x) =Px is a masking operator that selects a known subset of coordinates. • Pairwise Cα distances (D): FD(x) computes a vector of pairwise Cα-Cα di...

work page
[6]

Our results demonstrate that by fusing comple- mentary high-resolution data, our method can achieve sub- Angstrom accuracy

CONCLUSION In this work, we have presented a framework for protein struc- ture determination that effectively integrates a powerful dif- fusion prior with multiple, heterogeneous experimental data modalities. Our results demonstrate that by fusing comple- mentary high-resolution data, our method can achieve sub- Angstrom accuracy. Furthermore, we have sho...

work page

Show all 22 references

[7]

Jan Drenth,Principles of protein X-ray crystallography, Springer Science & Business Media, 2007

2007
[9]

Protein structure determination in solu- tion by nuclear magnetic resonance spectroscopy,

Kurt Wuthrich, “Protein structure determination in solu- tion by nuclear magnetic resonance spectroscopy,”Sci- ence, vol. 243, no. 4887, pp. 45, 1989

1989
[11]

Illuminating protein space with a programmable generative model,

John B Ingraham, Max Baranov, Zak Costello, Karl W Barber, Wujie Wang, Ahmed Ismail, Vincent Frappier, Dana M Lord, Christopher Ng-Thow-Hing, Erik R Van Vlack, et al., “Illuminating protein space with a programmable generative model,”Nature, vol. 623, no. 7989, pp. 1070–1078, 2023

2023
[12]

De novo design of protein structure and function with rfdiffusion,

Joseph L Watson, David Juergens, Nathaniel R Bennett, Brian L Trippe, Jason Yim, Helen E Eisenach, Woody Ahern, Andrew J Borst, Robert J Ragotte, Lukas F Milles, et al., “De novo design of protein structure and function with rfdiffusion,”Nature, vol. 620, no. 7976, pp. 1089– 1...

2023
[13]

Proteina: Scaling flow-based protein structure generative models,

Tomas Geffner, Kieran Didi, Zuobai Zhang, Danny Rei- denbach, Zhonglin Cao, Jason Yim, Mario Geiger, Chris- tian Dallago, Emine Kucukbenli, Arash Vahdat, et al., “Proteina: Scaling flow-based protein structure generative models,”arXiv preprint arXiv:2503.00710, 2025

2025 arXiv
[14]

Inverse problems with experiment-guided alphafold,

Advaith Maddipatla, Nadav Bojan Sellam, Meital Bojan, Sanketh Vedula, Paul Schanda, Ailie Marx, and Alex M Bronstein, “Inverse problems with experiment-guided alphafold,”arXiv preprint arXiv:2502.09372, 2025

2025 arXiv
[15]

Gen- erative modeling of protein ensembles guided by crystallographic electron densities,

Sai Advaith Maddipatla, Nadav Bojan Sellam, San- keth Vedula, Ailie Marx, and Alex Bronstein, “Gen- erative modeling of protein ensembles guided by crystallographic electron densities,”arXiv preprint arXiv:2412.13223, 2024

2024 arXiv
[16]

Solv- ing inverse problems in protein space using diffusion- based priors,

Axel Levy, Eric R Chan, Sara Fridovich-Keil, Fr´ed´eric Poitevin, Ellen D Zhong, and Gordon Wetzstein, “Solv- ing inverse problems in protein space using diffusion- based priors,”arXiv preprint arXiv:2406.04239, 2024

2024 arXiv
[17]

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,” inInternational Conference on Learning Representations, 2021

2021
[18]

Plug-and-play priors for model based reconstruction,

Singanallur V Venkatakrishnan, Charles A Bouman, and Brendt Wohlberg, “Plug-and-play priors for model based reconstruction,” in2013 IEEE global conference on signal and information processing. IEEE, 2013, pp. 945– 948

2013
[19]

Diffusion models as plug-and-play priors,

Alexandros Graikos, Nikolay Malkin, Nebojsa Jojic, and Dimitris Samaras, “Diffusion models as plug-and-play priors,”Advances in Neural Information Processing Systems, vol. 35, pp. 14715–14728, 2022

2022
[20]

Provably robust score-based diffusion posterior sampling for plug-and-play image re- construction,

Xingyu Xu and Yuejie Chi, “Provably robust score-based diffusion posterior sampling for plug-and-play image re- construction,” inAdvances in Neural Information Pro- cessing Systems. 2024, vol. 37, pp. 36148–36184, Curran Associates, Inc

2024
[21]

Some methods of speeding up the convergence of iteration methods,

Boris T Polyak, “Some methods of speeding up the convergence of iteration methods,”Ussr computational mathematics and mathematical physics, vol. 4, no. 5, pp. 1–17, 1964

1964
[22]

Using quaternions to calculate rmsd,

Evangelos A Coutsias, Chaok Seok, and Ken A Dill, “Using quaternions to calculate rmsd,”Journal of com- putational chemistry, vol. 25, no. 15, pp. 1849–1857, 2004

2004

Pith tools

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

[1] [8]

Visualization of membrane protein domains by cryo-electron microscopy of dengue virus,

Wei Zhang, Paul R Chipman, Jeroen Corver, Peter R Johnson, Ying Zhang, Suchetana Mukhopadhyay, Tim- othy S Baker, James H Strauss, Michael G Rossmann, and Richard J Kuhn, “Visualization of membrane protein domains by cryo-electron microscopy of dengue virus,” Nature Structural & Molecular Biology, vol. 10, no. 11, pp. 907–912, 2003

work page 2003

[2] [10]

Denoising diffusion probabilistic models,

Jonathan Ho, Ajay Jain, and Pieter Abbeel, “Denoising diffusion probabilistic models,” inAdvances in Neural Information Processing Systems. 2020, vol. 33, pp. 6840– 6851, Curran Associates, Inc

work page 2020

[3] [1]

While experimental techniques like X- ray crystallography [1], cryo-electron microscopy (cryo-EM) [2], and nuclear magnetic resonance (NMR) spectroscopy

INTRODUCTION The determination of three-dimensional protein structures is fundamental for understanding biological function and for novel drug design. While experimental techniques like X- ray crystallography [1], cryo-electron microscopy (cryo-EM) [2], and nuclear magnetic resonance (NMR) spectroscopy

work page

[4] [2]

whitened

PRELIMINARIES 2.1. Problem Formulation We represent a protein backbone by its 3-dimensional coor- dinates x∈R 4N×3 , where N is the number of amino acid residues. Fori= 1, . . . , M, we observe noisy measurements yi =F i(x∗) +ηi, ηi ∼ N(0;σ2 i I),(1) where noise level σi is unknown, but the forward model Fi is known and differentiable. ηi is independent o...

arXiv 2025

[5] [3]

Data from these methods can be sparse, noisy, ambiguous, and often incomplete

provide invaluable structural information, they each have limitations. Data from these methods can be sparse, noisy, ambiguous, and often incomplete. Computational methods are crucial for integrating these diverse data streams to pro- duce high-resolution structural models. Recently, deep gen- erative models, especially denoising diffusion probabilistic m...

work page 2024

[6] [4]

It uniquely integrates multimodal likelihoods with a novel adaptive engine for noise estimation and weighting

METHODOLOGY Algorithm 1 implements this PnP strategy as an iterative re- finement process within the diffusion model’s reverse SDE in (5). It uniquely integrates multimodal likelihoods with a novel adaptive engine for noise estimation and weighting. We emphasize that Adam-PnP is modular and can accommodate any differentiable forward model Fi(x) that maps ...

work page

[7] [5]

• Pairwise Cα distances (D): FD(x) computes a vector of pairwise Cα-Cα distances

EXPERIMENTAL RESULTS We evaluated Adam-PnP on the task of reconstructing the 127-residue protein with PDB ID: 7r5b from various com- binations of three data modalities [8, 10]: • Partial Cα coordinates (P): FP (x) =Px is a masking operator that selects a known subset of coordinates. • Pairwise Cα distances (D): FD(x) computes a vector of pairwise Cα-Cα di...

work page

[8] [6]

Our results demonstrate that by fusing comple- mentary high-resolution data, our method can achieve sub- Angstrom accuracy

CONCLUSION In this work, we have presented a framework for protein struc- ture determination that effectively integrates a powerful dif- fusion prior with multiple, heterogeneous experimental data modalities. Our results demonstrate that by fusing comple- mentary high-resolution data, our method can achieve sub- Angstrom accuracy. Furthermore, we have sho...

work page