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Robust Physics-Guided Diffusion for Full-Waveform Inversion

Jishen Peng, Enze Jiang, Zheng Ma, Xiongbin Yan

Abstract

We develop a robust physics-guided diffusion framework for full-waveform inversion that combines a score-based generative prior with likelihood guidance computed through wave-equation simulations. We adopt a transport-based data-consistency potential (Wasserstein-2), incorporating wavefield enhancement via bounded weighting and observation-dependent normalization, thereby improving robustness to amplitude imbalance and time/phase misalignment. On the inference side, we introduce a preconditioned guided reverse-diffusion scheme that adapts the guidance strength and spatial scaling throughout the reverse-time dynamics, yielding a more stable and effective data-consistency guidance step than standard diffusion posterior sampling (DPS). Numerical experiments on OpenFWI datasets demonstrate improved reconstruction quality over deterministic optimization baselines and standard DPS under comparable computational budgets.

Robust Physics-Guided Diffusion for Full-Waveform Inversion

Abstract

We develop a robust physics-guided diffusion framework for full-waveform inversion that combines a score-based generative prior with likelihood guidance computed through wave-equation simulations. We adopt a transport-based data-consistency potential (Wasserstein-2), incorporating wavefield enhancement via bounded weighting and observation-dependent normalization, thereby improving robustness to amplitude imbalance and time/phase misalignment. On the inference side, we introduce a preconditioned guided reverse-diffusion scheme that adapts the guidance strength and spatial scaling throughout the reverse-time dynamics, yielding a more stable and effective data-consistency guidance step than standard diffusion posterior sampling (DPS). Numerical experiments on OpenFWI datasets demonstrate improved reconstruction quality over deterministic optimization baselines and standard DPS under comparable computational budgets.
Paper Structure (32 sections, 66 equations, 10 figures, 8 tables, 2 algorithms)

This paper contains 32 sections, 66 equations, 10 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Full-waveform inversion (FWI)
  4. Bayesian formulation of FWI
  5. Score-Based Generative Model
  6. Setup and notation
  7. Forward diffusion process
  8. Variance-preserving diffusion and transition kernel
  9. Reverse-time dynamics and score learning
  10. Conditional Diffusion for Bayesian Inversion
  11. Diffusion-based posterior solver
  12. Baseline DPS discretization for FWI
  13. Limitations of $\ell_2$-guided DPS in FWI
  14. Our method: OT-guided preconditioned DPS for FWI
  15. OT-based data-consistency potential
  16. ...and 17 more sections

Figures (10)

  • Figure 1: Comparison of the original and weighted wavefield traces at Receiver 1 for the first three source--receiver pairs. The original recordings are dominated by early large-amplitude arrivals, whereas the proposed bounded weighting compresses the dynamic range and renders later weak-amplitude events more comparable in scale.
  • Figure 2: Inversion results across different datasets. The first row displays the true velocity field $v_\mathrm{true}$. Rows 2 to 5 show the inverted velocity fields $v_\mathrm{rec}$ obtained using different algorithms. Rows 6 to 9 present the difference between the true and inverted velocity fields, $v_\mathrm{rec}-v_\mathrm{true}$. The observed wavefield has been perturbed with additive noise of intensity $\sigma = 0.05$.
  • Figure 3: Relative $l_2$-error of the reconstructed velocity field $v$ versus the TV regularization parameter $\alpha$ for the two deterministic methods: (a) $W_2+\mathrm{TV}$ and (b) OT-WE$+\mathrm{TV}$.
  • Figure 4: Relative $l_2$-error of the reconstructed velocity field $v$ versus the iteration number for the two deterministic methods with their optimal TV regularization parameters $\alpha$: (a) $W_2+\mathrm{TV}$ and (b) OT-WE$+\mathrm{TV}$.
  • Figure 5: Ablation study on CurveVel-B. The top panel shows the ground-truth velocity model. The second and third panels report reconstructions obtained with $W_2$-based and MSE-based guidance, respectively. From left to right, the columns correspond to Only (baseline DPS), Step (preconditioned guidance update $P_i=\rho_iD_i$), Enh (wavefield enhancement: amplitude-adaptive weighting and misfit-scale normalization), and All (Step+Enh). The bottom two panels show the corresponding error maps (reconstruction minus ground truth).
  • ...and 5 more figures