Pith. sign in

REVIEW 5 major objections 6 minor 1 cited by

Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions

T0 review · 5 major / 6 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 A two-stage surrogate that lets video diffusion refine only the residual of an S-DeepONet prior predicts spatio-temporal PDE solutions more accurately than either stage alone.

desk verdict A solid empirical extension of operator-plus-diffusion correctors to full space-time video prediction; the ranking claims need repeated-seed support before they are reliable. read the letter →

arxiv 2507.06133 v2 pith:HQHDWEOF submitted 2025-07-08 cs.CE

Jaewan Park , Farid Ahmed , Kazuma Kobayashi , Seid Koric , Syed Bahauddin Alam , Iwona Jasiuk , Diab Abueidda This is my paper
classification cs.CE
keywords GenerativeAIVideoDiffusionSequentialDeepOperatorNetworkResidualLearningTurbulencePlasticDeformationPDEsurrogatesNeuraloperators
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 argues that a two-stage surrogate predicts spatio-temporal PDE solutions far more accurately than either stage alone: a Sequential Deep Operator Network (S-DeepONet) first produces a coarse, physics-consistent field, and a video-diffusion model then learns only the pointwise residual between that prior and the true solution. On turbulent lid-driven cavity flow the hybrid cuts mean relative $L_2$ error from 4.57% to 0.83%, and on elasto-plastic dogbone tension from 4.42% to 2.94%. The design works by shifting the generative model's burden from the full solution to the smaller high-frequency correction, so diffusion sharpens vortices and stress hotspots without losing global coherence. The same architecture transfers across fluid and solid benchmarks with no problem-specific changes, suggesting a general recipe for nonlinear time-dependent PDE problems.

What carries the argument

The load-bearing mechanism is the residual decomposition $R = x_{\mathrm{GT}} - x_{\mathrm{prior}}$ feeding a conditional 3D U-Net video-diffusion backbone built on the Elucidated Diffusion Model (EDM) sampler. S-DeepONet, a branch-trunk operator network with a GRU branch and FNN trunk, maps the time-dependent boundary or loading function to a coarse video; that video and the original input function are injected into the denoiser through FiLM modulation and channel-wise concatenation, with a binary mask added for the dogbone geometry. Training targets the residual, linearly normalized to $[-1,1]$ with global training-set extrema, and at inference the output is unnormalized and added back to the prior. A time-wise focal loss reweights frames by relative per-frame error so sharp transients are not drowned out by easier frames.

What would settle it

Run the trained VD-PC-R model on a loading history that drives the prior into an extrapolation regime, so that the residual falls outside the training-set interval $[R_{\min}, R_{\max}]$; if the unnormalization in Eq. (21) saturates and the relative $L_2$ error grows well beyond the reported worst-case values, the in-range-residual assumption fails.

Watch

Extended reading notes

Core claim

The central discovery is that conditioning a video-diffusion corrector on a neural-operator prior and training it only on the residual field $R = x_{\mathrm{GT}} - x_{\mathrm{prior}}$ consistently beats both standalone baselines and the direct full-field diffusion variant. In the lid-driven cavity benchmark the residual variant VD-PC-R reaches 0.83% mean relative $L_2$ error versus 4.58% for S-DeepONet and 8.24% for unguided video diffusion; in the plasticity benchmark it reaches 2.94% versus 4.43% and 123%. The paper attributes this to the residual target being lower-entropy, to the prior providing a global low-frequency anchor at every diffusion step through channel-wise concatenation, and to a time-wise focal loss that concentrates training on transient frames that dominate physical fidelity.

Load-bearing premise

The whole approach rests on the assumption that the S-DeepONet prior is a globally coherent coarse approximation for every test input, so the difference the diffusion stage must learn stays small and inside the range of the examples seen during training.

Editorial extensions

If this is right

  • The hybrid cuts mean relative $L_2$ error to 0.83% for the flow benchmark and 2.94% for plasticity, and it also shrinks worst-case errors by roughly a factor of four to seven.
  • Because the diffusion stage learns only the residual, it can focus capacity on sharpening high-frequency structures, which shows up visually as recovered vortices, clean stress hotspots, and suppressed speckle artifacts.
  • The same architecture, with no per-problem changes, transfers from incompressible turbulent flow to nonlinear elasto-plasticity, indicating the recipe is general for nonlinear time-dependent fields.
  • Wall-clock measurements show the hybrid runs in seconds per simulation, two to three orders of magnitude faster than the CFD or FEA solvers that produced the training data.

Reading between the lines

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

  • The method only requires a globally coherent coarse prior, so any operator or low-resolution solver that supplies one could replace S-DeepONet; the residual-training assumption would still hold as long as the prior's errors resemble training residuals.
  • The fixed $R_{\min}/R_{\max}$ unnormalization implies the method should degrade on inputs whose residuals leave the training range; a per-sample or adaptive normalization scheme would be a natural hardening.
  • Because the prior anchors each timestep, the hybrid may also stabilize long autoregressive roll-outs, which the standalone diffusion baseline visibly struggles with at later frames.
  • A stronger test of the 'high-frequency recovery' claim would be to compare the energy spectrum of the corrected flow field against the true RANS spectrum; the paper reports visual and pointwise error improvements but does not quantify spectral content.
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

5 major / 6 minor

Summary. The paper proposes a two-stage surrogate for spatio-temporal PDE fields: a Sequential DeepONet (S-DeepONet) generates a coarse prior from a time-dependent input function, and a conditional video diffusion model is trained to predict either the full solution field (VD-PC-D) or the residual between the ground truth and the prior (VD-PC-R). The framework is evaluated on turbulent lid-driven cavity flow (stream function) and elasto-plastic dogbone tension (von Mises stress), with four ablations: S-DeepONet alone, diffusion alone (VD-NP), and the two conditioned variants. The authors report that the residual-based hybrid reduces mean relative L2 error from 4.58% to 0.83% on the flow problem and from 4.43% to 2.94% on the plasticity problem, and they argue that the approach accelerates convergence and transfers across problem classes.

Significance. The integration of an operator prior with a video-diffusion corrector is timely and practically motivated, and the two-benchmark evaluation spans fluid and solid mechanics. The ablation grid (prior vs. no prior, direct vs. residual target) carefully isolates the contribution of each design choice, and the percentile tables and qualitative residual maps convey useful information. The reported runtime advantage over CFD/FEA is meaningful for design loops. However, the evidence is weakened by the absence of uncertainty quantification and by several unverified claims, so the significance depends on whether the authors can substantiate the ranking with repeated runs and targeted analyses.

major comments (5)
  1. [Section 3, Tables 2-8] The central claim that VD-PC-R 'consistently outperforms' all baselines rests on single runs. No standard deviations, seed counts, or paired significance tests are reported. This is especially consequential for the plasticity benchmark, where the mean Rel.L2 gap between VD-PC-R (2.94%) and VD-PC-D (3.17%) is small, and the worst-case errors remain high (15.3%). The authors should report multi-seed results or otherwise establish that the ranking is stable.
  2. [Section 2.2.3, Eq. (21)] The residual target is linearly normalized using global Rmin/Rmax from the training set. If a test residual falls outside this range, the unnormalization step saturates and the reconstructed field is clipped. The paper does not report the range or distribution of test residuals, nor the frequency of saturation, so the robustness of the residual variant to prior failures is unquantified.
  3. [Section 2.2.3 and Conclusions] The abstract and conclusions claim residual learning 'accelerates convergence', but no training curves or convergence diagnostics are provided. If this claim is to be made, the paper must supply evidence (e.g., loss-vs-epoch curves for VD-PC-D vs VD-PC-R).
  4. [Section 2.2.2, Eq. (15)] The statement in the abstract that the framework transfers 'without problem-specific architectural modifications' is contradicted by the addition of the dogbone binary mask. This is a problem-specific modification to the input channels; please revise the claim or clarify that the mask is a minor domain-specific addition.
  5. [Sections 1-3] The prior is described as 'physics-consistent', but the paper never checks whether the final generated fields satisfy the governing PDEs (e.g., incompressibility or the RANS equations for the cavity flow; equilibrium and plastic consistency for the dogbone). Without a physics-residual check, the claim that the result is 'physics-aware' is only supported by the data-fitting error. Adding such residuals would test whether the diffusion refinement preserves physical constraints.
minor comments (6)
  1. [Section 2.2.1] The training details for S-DeepONet (optimizer, learning rate, epochs, batch size) and for the diffusion model (sampling steps, guidance scale) are not provided; please include them for reproducibility.
  2. [Section 2.2.2, Eqs. (16)-(20)] The diffusion training objective is not fully specified; the notation \hat{x} in Eq. (16) is undefined, and the reader cannot tell whether the model predicts noise, x0, or a score. Please clarify the loss.
  3. [Section 2.2.2] The time-wise focal loss (Eqs. (19)-(20)) is introduced as a contribution, but no ablation demonstrates its effect. Please add an ablation or temper the description.
  4. [Figures 18-19] The y-axis label 'SDON' is not introduced; use 'S-DeepONet' consistently in figures and text.
  5. [Abstract and Introduction] The abstract says 'incompressible turbulent flow' while the introduction says 'laminar to turbulent lid-driven cavity'; be consistent about the flow regime.
  6. [Replication of results] The replication section only promises code 'upon the paper's acceptance'; consider providing an anonymous, accessible code repository during review to enable verification.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the residual-refinement pipeline is an independent decomposition with training-set normalization, and the only self-citation (S-DeepONet) is used as an adoptable baseline rather than as proof of the headline result.

full rationale

The paper's derivation chain is not circular. The residual target is defined as R = x_GT - x_prior (Section 2.2.3), and inference reconstructs x_hat = R_hat_unnormed + x_prior via Eq. (21); this is an algebraic decomposition, but the learned quantity R_hat is the output of a diffusion network trained on training-set residuals, and R_min and R_max are global extrema measured on the training set, not on test targets. Error is then measured against held-out ground truth (Eq. 22), so the reported accuracy improvement is an empirical result rather than a consequence of the definition. The only self-citation is the S-DeepONet baseline [7], whose authors overlap with the present paper; however, the prior is trained and evaluated in this paper, and the headline comparison (Tables 2 and 5) is measured directly against solver-generated ground truth, so the citation is not load-bearing. Concerns about missing seed-level statistics, absent training curves, and the promise of future code release in the Replication section are reproducibility and evidence-strength issues, not circularity. No step reduces by construction to its own input.

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

The paper's empirical claims rest on solver-generated data and standard deep-learning frameworks. The only paper-specific adjustable parameters are architecture and loss hyperparameters; no physical constants were fitted and no new physical entities were introduced.

free parameters (5)
  • S-DeepONet hidden dimension HD = 200
    Section 2.2.1: architecture hyperparameter chosen by hand, not derived from data or theory.
  • Number of GRU layers in S-DeepONet branch = 4
    Section 2.2.1: fixed architecture choice.
  • Time-wise focal loss exponent xi = 2
    Section 2.2.2: 'xi = 2 was taken empirically'; controls reweighting of hard frames.
  • Residual normalization range [Rmin, Rmax] = not reported numerically
    Eq. (21): global min/max of residual over training set; if test residual exceeds range, reconstruction saturates.
  • 3D U-Net depth = 4
    Section 2.2.2: 'depth-4 encoder-decoder 3D U-Net'; no channel counts or block layout given.
assumptions (5)
  • standard math Universal approximation theorem for DeepONet and the EDM/score-matching framework
    Grounds the operator and diffusion stages; not proved in the paper, taken from Refs [5,20].
  • domain assumption RANS with eddy viscosity and TKE closure describes the lid-driven cavity flow
    Equations (1)-(2); the training data are generated with this closure in Fluent, so the surrogate learns the solver's physics.
  • domain assumption Small-strain J2 plasticity with linear isotropic hardening describes the dogbone response
    Equations (4)-(8); standard continuum modeling, but a modeling choice that limits the regime.
  • domain assumption The 80-20 random split gives i.i.d. train/test loading histories
    Section 3: no analysis of distribution shift or extrapolation to unseen loading regimes.
  • domain assumption Ground truth from Fluent and Abaqus is sufficiently accurate
    Section 2.1: the surrogate is trained and evaluated against these solver outputs, so any solver bias is inherited.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions." pith.science (2026). https://pith.science/paper/HQHDWEOF

@misc{pith2026250706133,
  author       = {Pith},
  title        = {Pith review of: Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HQHDWEOF}},
  note         = {Machine review of arXiv:2507.06133}
}
read the original abstract

Video-diffusion models have recently set the standard in video generation, inpainting, and domain translation thanks to their training stability and high perceptual fidelity. Building on these strengths, we repurpose conditional video diffusion as a physics surrogate for spatio-temporal fields governed by partial differential equations (PDEs). Our two-stage surrogate first applies a Sequential Deep Operator Network (S-DeepONet) to produce a coarse, physics-consistent prior from the prescribed boundary or loading conditions. The prior is then passed to a conditional video diffusion model that learns only the residual: the point-wise difference between the ground truth and the S-DeepONet prediction. By shifting the learning burden from the full solution to its much smaller residual space, diffusion can focus on sharpening high-frequency structures without sacrificing global coherence. The framework is assessed on two disparate benchmarks: (i) vortex-dominated lid-driven cavity flow and (ii) tensile plastic deformation of dogbone specimens. Across these data sets the hybrid surrogate consistently outperforms its single-stage counterpart, cutting the mean relative L2 error from 4.57% to 0.83% for the flow problem and from 4.42% to 2.94% for plasticity, a relative improvements of 81.8% and 33.5% respectively. The hybrid approach not only lowers quantitative errors but also improves visual quality, visibly recovering fine spatial details. These results show that (i) conditioning diffusion on a physics-aware prior enables faithful reconstruction of localized features, (ii) residual learning reduces the problem, accelerating convergence and enhancing accuracy, and (iii) the same architecture transfers seamlessly from incompressible flow to nonlinear elasto-plasticity without problem-specific architectural modifications, highlighting its broad applicability to nonlinear, time-dependent continua.

Figures

Figures reproduced from arXiv: 2507.06133 by the authors.

Figure 1
Figure 1. Geometry and representative lid velocity of fluid dynamics simulation. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Specimen geometry and representative applied boundary conditions. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. S-DeepONet architecture tailored for video data. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Video diffusion model architecture. We freeze the trained S-DeepONet model and obtain prior video ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Histogram of Rel. L2 error for lid driven cavity flow example. 0 2 4 6 8 10 RMAE (%) 50 100 150 200 250 300 Occurrence VD-PC-R VD-PC-D VD-NP S-DeepONet [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 7
Figure 7. Figure 7: Stream function predictions for each model with true data for one representative sample. Temporal evolution [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Best-performing S-DeepONet case on Rel. L2 error, qualitative comparison. Results are shown at a selected timestep that illustrates typical model performance. Residuals are computed as the difference between each model’s prediction and the ground truth (GT) solution. T…
Figure 9
Figure 9. Figure 9: Median S-DeepONet case on Rel. L2 error, qualitative comparison. Results are shown at a selected timestep that illustrates typical model performance. Residuals are computed as the difference between each model’s prediction and the ground truth (GT) solution. t=16 Groun…
Figure 10
Figure 10. Figure 10: Worst S-DeepONet case on Rel. L2 error, qualitative comparison. Residuals are computed as the difference between each model’s prediction and the ground truth (GT) solution. standalone S-DeepONet respectively. Each figure contains two panels: (a) the predicted stream-f…
Figure 11
Figure 11. Figure 11: Histogram of Rel. L2 error for plastic defor￾mation on dogbone example. 10 0 10 1 10 2 10 3 RMAE (%) 0 20 40 60 80 100 120 140 Occurrence VD-PC-R VD-PC-D VD-NP S-DeepONet [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 13
Figure 13. Figure 13: Histogram of the Mean absolute error for plastic deformation on dogbone example. [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Temporal evolution of von Mises stress field predictions across critical timesteps during transient loading. [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: Best pereforming S-DeepONet case on MAE, qualitative comparison. Residuals are computed as the [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]
Figure 16
Figure 16. Figure 16: Median S-DeepONet case on MAE, qualitative comparison. Residuals are computed as the difference [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]
Figure 17
Figure 17. Figure 17: Worst S-DeepONet case on MAE, qualitative comparison. Residuals are computed as the difference be [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]
Figure 18
Figure 18. Figure 18: Wall clock time per lid-driven-cavity case: [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators

    cs.LG 2025-07 conditional novelty 4.0 of 10

    CMCO attaches conformalized Monte Carlo dropout intervals to DeepONet field predictions, achieving high average coverage but severe undercoverage in some test samples.

Reference graph

Works this paper leans on

51 extracted references · 26 canonical work pages · cited by 1 Pith paper

  1. [1]

    Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

    Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

    2023

  2. [2]

    Brunton, Bernd R

    Steven L. Brunton, Bernd R. Noack, and Petros Koumoutsakos. Machine learning for fluid mechanics.Annual Review of Fluid Mechanics, 52:477–508, 2020

    2020

  3. [3]

    A physics-informed deep neural network for surrogate modeling in classical elasto- plasticity.Computers and Geotechnics, 2023

    Mahdad Eghbalian, Mehdi Pouragha, and Richard Wan. A physics-informed deep neural network for surrogate modeling in classical elasto- plasticity.Computers and Geotechnics, 2023

    work page 2023

  4. [4]

    Fourier neural operator for parametric partial differential equations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. InInternational Conference on Learning Representations, 2021

    2021

  5. [5]

    Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021

    Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021

    2021

  6. [6]

    Junyan He, Seid Koric, Shashank Kushwaha, Jaewan Park, Diab Abueidda, and Iwona Jasiuk. Novel deeponet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads.Computer Methods in Applied Mechanics and Engineering, 415:116277, 2023

    work page 2023

  7. [7]

    Sequential deep operator networks (s-deeponet) for predicting full-field solutions under time-dependent loads.Engineering Applications of Artificial Intelligence, 127:107258, 2024

    Junyan He, Shashank Kushwaha, Jaewan Park, Seid Koric, Diab Abueidda, and Iwona Jasiuk. Sequential deep operator networks (s-deeponet) for predicting full-field solutions under time-dependent loads.Engineering Applications of Artificial Intelligence, 127:107258, 2024

    work page 2024

  8. [8]

    Predictions of transient vector solution fields with sequential deep operator network.Acta Mechanica, 235(8):5257–5272, 2024

    Junyan He, Shashank Kushwaha, Jaewan Park, Seid Koric, Diab Abueidda, and Iwona Jasiuk. Predictions of transient vector solution fields with sequential deep operator network.Acta Mechanica, 235(8):5257–5272, 2024

    work page 2024

Show all 51 references
  1. [9]

    Advanced deep operator networks to predict multiphysics solution fields in materials processing and additive manufacturing.Additive Manufacturing, 88:104266, 2024

    Shashank Kushwaha, Jaewan Park, Seid Koric, Junyan He, Iwona Jasiuk, and Diab Abueidda. Advanced deep operator networks to predict multiphysics solution fields in materials processing and additive manufacturing.Additive Manufacturing, 88:104266, 2024

    2024

  2. [10]

    Learning structured output representation using deep conditional generative models.Advances in neural information processing systems, 28, 2015

    Kihyuk Sohn, Honglak Lee, and Xinchen Yan. Learning structured output representation using deep conditional generative models.Advances in neural information processing systems, 28, 2015

    2015

  3. [11]

    Auto-encoding variational bayes, 2013

    Diederik P Kingma, Max Welling, et al. Auto-encoding variational bayes, 2013

    2013

  4. [12]

    Generative adversarial nets.Advances in neural information processing systems, 27, 2014

    Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets.Advances in neural information processing systems, 27, 2014

    2014

  5. [13]

    Neural discrete representation learning.Advances in neural information processing systems, 30, 2017

    Aaron Van Den Oord, Oriol Vinyals, et al. Neural discrete representation learning.Advances in neural information processing systems, 30, 2017

    2017

  6. [14]

    Deep unsupervised learning using nonequilibrium thermody- namics

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermody- namics. InInternational conference on machine learning, pages 2256–2265. pmlr, 2015

    2015

  7. [15]

    Denoising diffusion probabilistic models.Advances in neural information processing systems, 33: 6840–6851, 2020

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

    2020

  8. [16]

    Cascaded diffusion models for high fidelity image generation.Journal of Machine Learning Research, 23(47):1–33, 2022

    Jonathan Ho, Chitwan Saharia, William Chan, David J Fleet, Mohammad Norouzi, and Tim Salimans. Cascaded diffusion models for high fidelity image generation.Journal of Machine Learning Research, 23(47):1–33, 2022

    2022

  9. [17]

    Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598, 2022

    Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598, 2022

    2022 arXiv

  10. [18]

    Diffusion models beat gans on image synthesis.Advances in neural information processing systems, 34:8780–8794, 2021

    Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis.Advances in neural information processing systems, 34:8780–8794, 2021

    2021

  11. [19]

    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

  12. [20]

    Elucidating the design space of diffusion-based generative models.Advances in neural information processing systems, 35:26565–26577, 2022

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models.Advances in neural information processing systems, 35:26565–26577, 2022

    2022

  13. [21]

    Mcvd-masked conditional video diffusion for prediction, generation, and interpo- lation.Advances in neural information processing systems, 35:23371–23385, 2022

    Vikram V oleti, Alexia Jolicoeur-Martineau, and Chris Pal. Mcvd-masked conditional video diffusion for prediction, generation, and interpo- lation.Advances in neural information processing systems, 35:23371–23385, 2022

    2022

  14. [22]

    Video diffusion models.Advances in Neural Information Processing Systems, 35:8633–8646, 2022

    Jonathan Ho, Tim Salimans, Alexey Gritsenko, William Chan, Mohammad Norouzi, and David J Fleet. Video diffusion models.Advances in Neural Information Processing Systems, 35:8633–8646, 2022

    2022

  15. [23]

    A survey on video diffusion models.ACM Computing Surveys, 57(2):1–42, 2024

    Zhen Xing, Qijun Feng, Haoran Chen, Qi Dai, Han Hu, Hang Xu, Zuxuan Wu, and Yu-Gang Jiang. A survey on video diffusion models.ACM Computing Surveys, 57(2):1–42, 2024

    2024

  16. [24]

    Kingma, Ben Poole, Mohammad Norouzi, David J

    Jonathan Ho, William Chan, Chitwan Saharia, Jay Whang, Ruiqi Gao, Alexey Gritsenko, Diederik P. Kingma, Ben Poole, Mohammad Norouzi, David J. Fleet, and Tim Salimans. Imagen video: High definition video generation with diffusion models, 2022

    2022

  17. [25]

    Diffusion schrödinger bridge with applications to score-based generative modeling.Advances in Neural Information Processing Systems, 34:17695–17709, 2021

    Valentin De Bortoli, James Thornton, Jeremy Heng, and Arnaud Doucet. Diffusion schrödinger bridge with applications to score-based generative modeling.Advances in Neural Information Processing Systems, 34:17695–17709, 2021

    2021

  18. [26]

    Hamprecht, Yoshua Bengio, and Aaron C

    Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred A. Hamprecht, Yoshua Bengio, and Aaron C. Courville. On the spectral bias of neural networks. InInternational Conference on Machine Learning, pages 5301–5310. PMLR, 2019

  19. [27]

    Generative downscaling of pde solvers with physics-guided diffusion models.Journal of Scientific Computing, 101(3):1–23, 2024

    Yulong Lu and Wuzhe Xu. Generative downscaling of pde solvers with physics-guided diffusion models.Journal of Scientific Computing, 101(3):1–23, 2024

    2024

  20. [28]

    Residual corrective diffusion modeling for km-scale atmospheric downscaling.Communications Earth & Environment, 6(1):124, 2025

    Morteza Mardani, Noah Brenowitz, Yair Cohen, Jaideep Pathak, Chieh-Yu Chen, Cheng-Chin Liu, Arash Vahdat, Mohammad Amin Nabian, Tao Ge, Akshay Subramaniam, et al. Residual corrective diffusion modeling for km-scale atmospheric downscaling.Communications Earth & Environment, 6(...

    2025

  21. [29]

    Latentpinns: Generative physics-informed neural networks via a latent representation learning

    Mohammad H Taufik and Tariq Alkhalifah. Latentpinns: Generative physics-informed neural networks via a latent representation learning. Artificial Intelligence in Geosciences, page 100115, 2025

    2025

  22. [30]

    Generative adversarial neural operators.Transactions on Machine Learning Research, 2022

    Md Ashiqur Rahman, Manuel A Florez, Anima Anandkumar, Zachary E Ross, and Kamyar Azizzadenesheli. Generative adversarial neural operators.Transactions on Machine Learning Research, 2022

    2022

  23. [31]

    Alex Glyn-Davies, Connor Duffin, O Deniz Akyildiz, and Mark Girolami.ϕ-dvae: Physics-informed dynamical variational autoencoders for unstructured data assimilation.Journal of Computational Physics, 515:113293, 2024

    2024

  24. [32]

    Physics-informed diffusion models.arXiv preprint arXiv:2403.14404, 2024

    Jan-Hendrik Bastek, WaiChing Sun, and Dennis M Kochmann. Physics-informed diffusion models.arXiv preprint arXiv:2403.14404, 2024

    2024 arXiv

  25. [33]

    Integrating neural operators with diffusion models improves spectral representation in turbulence modeling.arXiv preprint arXiv:2409.08477, 2024

    Vivek Oommen, Aniruddha Bora, Zhen Zhang, and George Em Karniadakis. Integrating neural operators with diffusion models improves spectral representation in turbulence modeling.arXiv preprint arXiv:2409.08477, 2024. 23

    2024 arXiv

  26. [34]

    Real-time inference and extrapolation via a diffusion-inspired temporal transformer operator (ditto).arXiv preprint arXiv:2307.09072, 2023

    Oded Ovadia, Vivek Oommen, Adar Kahana, Ahmad Peyvan, Eli Turkel, and George Em Karniadakis. Real-time inference and extrapolation via a diffusion-inspired temporal transformer operator (ditto).arXiv preprint arXiv:2307.09072, 2023

    2023 arXiv

  27. [35]

    Reynolds-averaged navier–stokes equations for turbulence modeling.Applied Mechanics Reviews, 62(4):040802, 06 2009

    Giancarlo Alfonsi. Reynolds-averaged navier–stokes equations for turbulence modeling.Applied Mechanics Reviews, 62(4):040802, 06 2009. ISSN 0003-6900. doi: 10.1115/1.3124648. URLhttps://doi.org/10.1115/1.3124648

    2009 doi

  28. [36]

    Abaqus/standard user’s manual version 2024, 2024

    SIMULIA Dassault Systèmes. Abaqus/standard user’s manual version 2024, 2024

    2024

  29. [37]

    Simo and Thomas J

    Juan C. Simo and Thomas J. R. Hughes.Computational Inelasticity, volume 7 ofInterdisciplinary Applied Mathematics. Springer, New York, 1998

    1998

  30. [38]

    Dover Publications, Mineola, NY , 2008

    Jacob Lubliner.Plasticity Theory. Dover Publications, Mineola, NY , 2008

    2008

  31. [39]

    Learning phrase representations using rnn encoder-decoder for statistical machine translation.arXiv preprint arXiv:1406.1078, 2014

    Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation.arXiv preprint arXiv:1406.1078, 2014

    2014 arXiv

  32. [40]

    Edict: Exact diffusion inversion via coupled transformations

    Bram Wallace, Akash Gokul, and Nikhil Naik. Edict: Exact diffusion inversion via coupled transformations. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22532–22541, 2023

    2023

  33. [41]

    Film: Visual reasoning with a general conditioning layer

    Ethan Perez, Florian Strub, Harm De Vries, Vincent Dumoulin, and Aaron Courville. Film: Visual reasoning with a general conditioning layer. InProceedings of the AAAI conference on artificial intelligence, volume 32, 2018

    2018

  34. [42]

    Focal loss for dense object detection

    Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dollar. Focal loss for dense object detection. InProceedings of the IEEE International Conference on Computer Vision (ICCV), pages 2980–2988, Oct 2017

    2017

  35. [43]

    Resshift: Efficient diffusion model for image super-resolution by residual shifting

    Zongsheng Yue, Jianyi Wang, and Chen Change Loy. Resshift: Efficient diffusion model for image super-resolution by residual shifting. Advances in Neural Information Processing Systems, 36:13294–13307, 2023

    2023

  36. [44]

    Residual denoising diffusion models

    Jiawei Liu, Qiang Wang, Huijie Fan, Yinong Wang, Yandong Tang, and Liangqiong Qu. Residual denoising diffusion models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2773–2783, 2024

    2024

  37. [45]

    Zehua Chen, Yihan Wu, Yichong Leng, Jiawei Chen, Haohe Liu, Xuejiao Tan, Yang Cui, Ke Wang, Lei He, Sheng Zhao, Jiang Bian, and Danilo P. Mandic. Resgrad: Residual denoising diffusion probabilistic models for text to speech. InInternational Conference on Machine Learning, 2023

    2023

  38. [46]

    Denoising diffusion error correction codes

    Yoni Choukroun and Lior Wolf. Denoising diffusion error correction codes. InAdvances in Neural Information Processing Systems, 2022

    2022

  39. [47]

    Ansys fluent user’s guide, release 2024 r1, 2024

    ANSYS Inc. Ansys fluent user’s guide, release 2024 r1, 2024

    2024

  40. [48]

    Progressive distillation for fast sampling of diffusion models

    Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. InInternational Conference on Learning Representations, 2022

    2022

  41. [49]

    Consistency models

    Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. InInternational Conference on Machine Learning, 2023

    2023

  42. [50]

    Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity

    William Fedus, Barret Zoph, and Noam Shazeer. Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity. Journal of Machine Learning Research, 23(120):1–39, 2022

    2022

  43. [51]

    Gnot: A general neural operator transformer for operator learning

    Zhongkai Hao, Zhengyi Wang, Hang Su, Chengyang Ying, Yinpeng Dong, Songming Liu, Ze Cheng, Jian Song, and Jun Zhu. Gnot: A general neural operator transformer for operator learning. InInternational Conference on Machine Learning, pages 12556–12569. PMLR, 2023. 24 Appendix Appe...

    2023

Pith tools

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