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REVIEW 5 major objections 5 minor 3 cited by

Velocity Model Building and Editing with Guided Denoising Diffusion Implicit Models

T0 review · 5 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read A pretrained diffusion model, guided by well-log and migrated-image constraints, can both locally edit and fully rebuild seismic velocity models, producing sharper structure than classical least-squares inversion.

desk verdict Plausible diffusion-based velocity editing framework, but the VME evaluation is confounded and the synthetic test has training leakage; deserves peer review after major revision. read the letter →

arxiv 2603.01231 v2 pith:4OK6S27D submitted 2026-03-01 physics.geo-ph

Francesco Brandolin , Tariq Alkhalifah This is my paper · ORCID
classification physics.geo-ph MSC 86A22
keywords velocitymodelbuildingdiffusionmodelsDDIMinversionseismicimagingwell-loginterpolationstructuralpreconditioninginverseproblemsVikingGraben
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 tries to establish that a single pretrained diffusion prior can serve as the engine for both velocity-model editing (localized updates to an existing model) and full velocity-model building (global updating), two tasks normally run as separate workflows. The trick is to project the starting velocity model into the latent space of a diffusion model trained on high-resolution synthetic velocity examples using DDIM inversion, then reverse-sample under guidance that enforces well-log measurements and image-derived structural information. The authors claim the resulting models recover sharper interfaces and more realistic fine-scale structure than Tikhonov-regularized least-squares inversion, while still honoring the well data and the large-scale background. They also show that an imaging-based regularization term propagates well information laterally away from the wells, and their ablation study identifies the accuracy of the estimated structural slope field as the main factor controlling reconstruction quality. If the framework holds, interpreters could inject new well or image information into a reservoir interval without rerunning a full inversion, and the same prior could build a full model when applied over the whole domain.

What carries the argument

Denoising Diffusion Implicit Model (DDIM) inversion: a deterministic reverse-time sampling schedule run forward, which maps a clean velocity model v0 into a latent trajectory that the same network can decode. The paper couples this with a structurally preconditioned Tikhonov inversion, reparameterizing the velocity update through a structural smoother S constructed from local slope estimates, and with an imaging-based sensitivity operator J(v)=D_z(q′(v)Δv) derived from a Born linearization of reverse-time migration. Together these yield a damped, Hessian-preconditioned update Δv_t that is injected into the last half of the DDIM reverse trajectory, so the diffusion prior supplies high-resolut

What would settle it

Run unguided DDIM inversion followed by deterministic reverse sampling on the same background model and measure the difference outside any intended edit mask; if the protected region's RMS error exceeds the velocity uncertainty accepted by the workflow, the global-consistency claim of VME fails. Equivalently, repeat the VME experiment with a background model far from the training distribution and check whether the masked region's output depends on the background in the protected region, which should be invariant if the mask is doing its job.

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Extended reading notes

Core claim

The paper's central claim is that DDIM inversion makes a pretrained diffusion model a workable prior for seismic velocity problems, provided the reverse sampling is steered by a structurally preconditioned well-matching inversion. A background model is deterministically mapped into latent noise; localized editing is performed by masking the latent trajectory and, during the final portion of the reverse pass, injecting a Gauss–Newton-style model update Δv_t computed from a structurally smoothed Tikhonov system with imaging-based regularization. The same update applied over the full domain gives velocity-model building as the unmasked limit of editing. The authors argue that this combination r

Load-bearing premise

The load-bearing premise is that the learned noise field is locally consistent along the DDIM trajectory—ϵθ(vt,t)≈ϵθ(v_{t+1},t+1)—so that inverting a background model and reverse-sampling it reproduces that background exactly outside the edit mask; the paper's own Fig. 2 shows the unguided reconstruction is already sharpened rather than identical, so if this mismatch is large the masked-protected background would be silently altered.

Editorial extensions

If this is right

  • Velocity-model editing and velocity-model building become the same operation: VMB is the unmasked, whole-domain limit of the masked editing procedure, so one pretrained prior and one guided sampler serve both tasks.
  • Because the prior is learned from high-resolution synthetic models, it can sharpen interfaces and suppress RTM artifacts even where well control is sparse, which classical Tikhonov regularization alone does not do.
  • The imaging-based sensitivity term extends well-log information laterally into unconstrained regions, improving not only the diffusion-guided result but also the classical least-squares baseline.
  • The ablation shows that the accuracy of structural slope estimates is the dominant factor in reconstruction quality; better slopes improve every method and let all of them recover subtle features such as a small fold that RTM-derived slopes miss.
  • The Viking Graben field experiments indicate the framework remains stable under short-offset, multiple-contaminated acquisition, so the method is not restricted to idealized synthetic settings.

Reading between the lines

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

  • Editorial: the DDIM local-consistency assumption (the same network evaluated one step apart returns nearly the same noise estimate) is already violated in the paper's own unguided reconstruction, so a production VME workflow should quantify how much masked editing silently alters the protected background before trusting the 'global consistency' claim.
  • The mask-and-guide mechanism transfers naturally to time-lapse monitoring, where only a reservoir interval changes between surveys and the background should stay fixed; that experiment is not in the paper but follows directly from the VME formulation.
  • Since the proposed method and DPS score nearly identically across experiments, the practical differentiator is controllability and the cost of the LSQR guidance step, which suggests a hybrid that keeps DPS's cheap gradient but adds structural preconditioning would be a worthwhile test.
  • The paper's own Discussion flags that a mismatched training prior can underperform least-squares; a practical deployment would need a prior-mismatch diagnostic, for instance measuring unguided reconstruction error on representative background models, before applying the method to a new basin.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes a unified framework for velocity-model editing (VME) and velocity-model building (VMB) that combines a learned diffusion prior with structurally preconditioned well-matching. A DDIM inversion is used to project a background velocity model into the diffusion latent space; localized editing is performed by reverse sampling with a mask that fixes the latent trajectory outside the edited region, while a Tikhonov-regularized structural update is injected as guidance. For VMB, the mask is removed and an imaging-based regularization term is added to propagate information away from wells. The method is compared with conventional Tikhonov least-squares and with Diffusion Posterior Sampling on the Volve synthetic model and on the Viking Graben field dataset, with an ablation study varying the source of the structural slope field. The paper claims that diffusion-based approaches recover sharper, more realistic velocity structures than classical inversion while preserving background consistency in editing.

Significance. If substantiated, the framework would be a useful bridge between learned generative priors and classical structurully preconditioned geophysical inversion, with practical relevance to well-constrained velocity updating. The paper is not circular in the sense of fitting the wells: the well-matching is an external constraint injected during sampling. It also includes a clear comparison against both a classical LSQR baseline and DPS, and an ablation that isolates the role of slope accuracy. However, the main comparative claims currently rest on a single synthetic test set with strong overlap between training and test geology, on a VME evaluation that may be confounded by global prior-driven changes, and on an imaging operator that is not a true migration operator. These issues are load-bearing for the paper's central claims, so the present evidence is insufficient for acceptance.

major comments (5)
  1. [§2.3, Eq. (11)] The symbol t is overloaded. In §2.3, t is introduced as the preconditioned model variable through v = S t, but the same letter is used for the diffusion time throughout the paper. Eq. (11) writes Δv_t = S (S^H M^H M S + λ^2 I)^{-1}[S^H M^H(w - M hat{v}_0(v_t)) - λ^2 t]; the t in the final term is not the diffusion time, yet no separate symbol or update rule is given. Since S is not shown to be invertible, it is also unclear how t is obtained from v = S t when v = hat{v}_0(v_t). As written, the guidance update is ambiguous and the algorithm is not fully reproducible. Please rename the preconditioned variable and state its initialization/recursion explicitly.
  2. [§2.4, Eqs. (13) and (17)] The quantity called the 'nonlinear imaging forward operator', R(v) = D_z(q(v) - q(v0)), is not an imaging operator in the RTM sense. It is a pointwise vertical derivative of the slowness-squared contrast: it contains no wavefield propagation, no source-receiver geometry, and no migration operation, and it vanishes at v = v0, whereas the migrated image I_RTM is generally nonzero. Eq. (17) then defines the image residual as I_RTM - R(v), which compares a migrated image with this derivative proxy. This matters because the imaging term is the mechanism claimed to propagate information away from the wells in VMB. Unless Eq. (13) is replaced by the actual linearized RTM operator, or at least validated against a modeled I_RTM, the 'imaging-based regularization' claim is not supported.
  3. [§2.2, Eq. (5); §3.1, Figs. 2 and 4] The mask projection in Eq. (5) preserves the DDIM-inverted latent trajectory v_inv_t outside the mask, not the original background v0. The paper's own Fig. 2 shows that unguided DDIM inversion followed by sampling produces a hat{v}_0 that differs from v0 and is sharpened by the prior. Therefore mask-constrained editing can alter the protected background, and the advertised 'global consistency' of VME is not guaranteed. The quantitative evaluation in Fig. 4 makes this worse: the Tikhonov-LS result is displayed and scored with the original background outside the editing region, while the diffusion result is shown as a full generated model. The reported SSIM advantage (0.569 vs 0.414) may thus reflect global prior sharpening rather than better localized editing. Please report mask-region-only metrics with identical background fill for both methods, and document the outside-mask residual rel
  4. [§3.1, training set and evaluation design] The diffusion prior is trained on 5000 models drawn from SEAM Arid, SEAM Arid Barrett, SEAM Phase I, Otway, and Volve, using augmented Volve-derived models; the synthetic test model is Volve. Although the exact true Volve model is excluded, the prior has seen Volve-like geology and statistics, so the synthetic experiments measure adaptation to the training family rather than generalization to a new geological setting. This weakens the abstract's claim of a broadly transferable learned prior and the field-data transfer argument. A held-out basin or geologically distinct synthetic test is needed for the generalization claim; the Viking Graben results are qualitative and do not by themselves resolve this issue.
  5. [§3.1 and §3.2, quantitative comparisons] The diffusion-sampling comparisons are based on a single synthetic realization with no error bars, despite the use of stochastic DDIM sampling (η = 0.5 for VME, η = 0.1 for VMB). The reported differences between the proposed method and DPS are small in several cases (VME SSIM 0.569 vs 0.569; VMB SSIM 0.623 vs 0.604), so without repeated seeds or uncertainty quantification the claims that the proposed method is 'slightly better' or more robust than DPS are not established. At minimum, report mean ± std over several noise realizations for the diffusion-based methods.
minor comments (5)
  1. [Abstract] The first sentence reads 'Velocity-model building is a fundamental components of seismic imaging workflows'; 'components' should be singular, and the sentence structure should be cleaned up.
  2. [§2.4] Typo: 'Tikhnov preconditioned inversion' should be 'Tikhonov'.
  3. [§3.3] The text says 'Figure 11 presents the velocity-model editing results' and then, in the following paragraph, 'Figure 11 presents the velocity-model building results'. The second reference should be to Fig. 12.
  4. [Fig. 3 and Fig. 8 captions] Some captions refer to 'the black dashed line marks the well position' while others refer to two dashed lines for well positions. Please make the notation consistent and clarify which lines are profile locations and which are wells.
  5. [§2.1] The notation hat{v}_0(v_t) is introduced but not explicitly named; since it is used throughout the guidance equations, a brief definition at first use would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the inversion is an explicit recursion with external well/image constraints; acknowledged approximations and evaluation asymmetries are correctness risks, not self-referential reductions.

full rationale

The derivation chain is not circular. DDIM inversion (Eq. 4) is an explicit forward recursion (v_{t+1} from v_t and εθ(vt,t)), and the paper specifically notes this avoids circular dependency; the only inversion assumption is the stated local consistency ϵθ(vt,t)≈ϵθ(v_{t+1},t+1), an approximation about the learned noise field, not a definition of the result. The VME guidance (Eqs. 8–12) and VMB guidance (Eqs. 19–21) solve a well-matching Tikhonov system with the external sampling operator M and the imaging residual I_RTM−R(v); these are data/physics constraints, independent of the output being claimed. The diffusion prior is trained on synthetic models, with augmented Volve-derived examples while withholding the exact test model; this raises generalization/leakage concerns but is not a reduction of the predicted velocity to its input. The ablation with slopes computed from the ground-truth model (Section 3.3) is openly labeled an idealized sensitivity study, not a blind prediction. Self-citations (Brandolin et al. 2024; Taufik and Alkhalifah 2024; Wang et al. 2024; Alfarhan et al. 2024) are related-work support and are not load-bearing. The skeptic's concern that LS is displayed/masked differently from the full diffusion outputs (Section 3.1) is a comparison-fairness issue, and the unguided DDIM reconstruction differing from v0 (Fig. 2) is a known approximation; neither is a circular step in the derivation. Under the required standard of exhibiting a specific equation-level reduction, there is no circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The framework rests on five load-bearing assumptions: DDIM inversion consistency, slope-based structural smoothing, the simplified imaging operator, the validity of the DDIM clean estimate for data residuals, and prior transfer from synthetic to field data. It introduces no invented physical entities, and its main free parameters are hand-set regularization and sampling weights.

free parameters (8)
  • Tikhonov damping λ = 0.01 (all guided experiments)
    Hand-set; controls strength of λ²||t+Δt||² regularization in Eqs. 8/19; no sensitivity study.
  • Imaging regularization weight κ = 0.001 (proposed diffusion VMB), 0.002 (LS comparison)
    Hand-set; balances image-domain residual against well residual in Eq. 19; different values used for compared methods.
  • Guidance update weight μ = 0.5
    Scales the injection of the model-space update into the DDIM step (Eqs. 12/21); hand-set.
  • DDIM stochasticity η = 0.5 (VME), 0.1 (VMB)
    Controls added noise during reverse sampling (Eq. 3); hand-set per task.
  • Warm-start diffusion time t_start/T = 0.1 (VME), 0.3 (VMB)
    Fraction of the diffusion trajectory that is executed; hand-set; affects how much of the prior is applied.
  • Guidance activation window and LSQR iterations = final 50% of steps; 2 LSQR iterations per step
    Hand-set; approximates the Hessian inverse in Eqs. 11/20; no convergence study.
  • Number of diffusion steps T = 600 (inversion/sampling), 1000 (training)
    Hand-set; smaller T accelerates sampling but may reduce fidelity.
  • Training dataset size and schedule = 5000 patches, 50 epochs, 24h9m on V100
    Data and training schedule chosen to build the prior; includes augmented Volve-derived models, creating evaluation overlap with the Volve test.
assumptions (5)
  • domain assumption DDIM inversion local consistency: ϵθ(vt,t) ≈ ϵθ(v_{t+1},t+1)
    Stated in Section 2.2; needed for latent-space editing and background preservation; Fig. 2 shows the prior-only reconstruction is not identical to v0, so the assumption is only approximate.
  • domain assumption The structural smoother S=P^H P built from plane-wave destruction slopes is a valid geological preconditioner
    Borrowed from Chen et al. (2016) and used in Eqs. 8/19; if slopes are unreliable, performance degrades (ablation, Section 3.3).
  • ad hoc to paper R(v)=D_z(q(v)-q(v0)) in Eq. 13 is an adequate imaging forward operator linking velocity to migrated image perturbations
    Introduced in Section 2.4 without derivation from RTM imaging; not validated against actual modeled images; used as the image-domain residual.
  • domain assumption The denoised estimate v_hat0(v_t) is close enough to the true clean velocity to compute well-log residuals during guided reverse sampling
    Used in Eqs. 11, 19, and 23; standard in DPS, but its validity at the early guided timesteps (t/T=0.1-0.5) is untested.
  • domain assumption A diffusion model trained on synthetic models is a representative prior for the field target Viking Graben
    Stated in Sections 3.1 and 4; field results are qualitative, so transferability is assumed rather than demonstrated.

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Cite this review

Pith. "Pith review of Velocity Model Building and Editing with Guided Denoising Diffusion Implicit Models." pith.science (2026). https://pith.science/paper/4OK6S27D

@misc{pith2026260301231,
  author       = {Pith},
  title        = {Pith review of: Velocity Model Building and Editing with Guided Denoising Diffusion Implicit Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4OK6S27D}},
  note         = {Machine review of arXiv:2603.01231}
}
read the original abstract

Velocity-model building is a fundamental component of seismic imaging, yet it remains a challenging inverse problem due to limited data coverage, nonlinearity, and the need to integrate heterogeneous information such as well logs. We introduce a unified framework for velocity-model editing and full velocity-model building that combines learned diffusion priors with structurally preconditioned inverse formulations. A diffusion model trained on high-resolution synthetic velocity examples provides a data-driven prior that is exploited through Denoising Diffusion Implicit Model (DDIM) inversion and guided sampling. For localized editing, the diffusion prior is coupled with a structurally preconditioned Tikhonov well-matching inversion, enabling controlled modification of selected regions while preserving global consistency. For full velocity-model building, we formulate a well-matching inverse problem augmented with imaging-based regularization and solve it using conventional least-squares, the proposed DDIM-guided method, and Diffusion Posterior Sampling (DPS). Synthetic experiments demonstrate that diffusion-based approaches recover sharper and more realistic velocity structures than classical inversion. Field-data applications on the Viking Graben dataset confirm robustness under realistic acquisition conditions. An ablation study highlights the critical role of structural slope guidance in inversion performance. Overall, the proposed framework bridges inverse problems and generative modeling, offering a flexible approach for practical seismic imaging workflows.

Figures

Figures reproduced from arXiv: 2603.01231 by the authors.

Figure 1
Figure 1. Overview of the DDIM-based inversion and guided editing workflow. Top row: DDIM inversion of the initial [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. (a) Background velocity model v0. (b) Corresponding latent representation vT obtained through DDIM inversion. (c) Reconstructed velocity model vˆ0 recovered by deterministic DDIM sampling [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Synthetic test setup and velocity-profile comparison. (a) Initial velocity model [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Results comparison for the VME synthetic test. (a) Ground-truth velocity model. (b) Conventional Tikhonov [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Velocity-model building (VMB) comparison for the synthetic test. (a) Original (ground-truth) velocity [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Viking Graben Dataset. (a) Initial migration velocity model [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: summarizes the effect of DDIM inversion and deterministic sampling on the field-data background velocity [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Velocity-model editing (VME) comparison for the Viking Graben Dataset. (a) Initial migration velocity [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Velocity-model building (VMB) comparison for the Viking Graben Dataset. (a) Original (ground-truth) [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: (a) Ground-truth velocity model. (b) Local slope field [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Velocity-model editing (VME) comparison for the synthetic test with slopes computed from the Ground Truth [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Velocity-model building (VMB) comparison for the synthetic test. (a) Original (ground-truth) velocity [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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    A joint velocity–slope diffusion prior plus plane-wave PDE regularization reconstructs more continuous, geologically plausible velocity models from sparse wells than structural preconditioning alone.

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.