Full Waveform Inversion (FWI) is a powerful tool for subsurface velocity reconstruction but remains highly ill-posed, sensitive to acquisition limitations, often requiring some form of regularization to reduce artifacts and enhance resolution. While recent developments have shown that generative models can inject learned priors directly into the FWI optimization process, such approaches typically require additional, computationally expensive inversion iterations. In this study, we propose a post-FWI refinement strategy based on a Flow Matching (FM) generative model, which leverages learned geological priors without re-running FWI. The method guides the deterministic generative process using the FWI result, as well as well logs, if available. Synthetic and field data experiments demonstrate that we can inject well information and our geological expectations (prior) into the provided FWI result, and thus, we can effectively enhance its resolution and geological quality. In fact, the well prior even managed to alter the model depth to fit the well information, which is a form of correcting for depth misties.
Seismic wavefield simulation is fundamental to seismology, but conventional finite-difference (FD) methods remain limited by numerical dispersion and stability constraints, which often require dense spatial grids and small time steps and thereby severely limit the effectiveness of iterative inversion workflows. We introduce a conditional diffusion-based wavefield propagator that advances seismic wavefields recursively from one time step to the next. Instead of learning an unconditional data distribution of wavefield evolution, the model is conditioned by a short history of recent wavefield time steps (snapshots), the velocity model, and the wavefield time step index, allowing it to represent the conditional transition between adjacent physical states. By training the network to directly predict the clean next wavefield snapshot, this strong physical conditioning makes it possible to replace the iterative reverse diffusion process with a single network evaluation for each predicted snapshot. To improve stability over long recursive rollouts, we further introduce a causal time-weighted loss, in which adaptive weights, accumulated as exponential moving averages of per-snapshot training errors, emphasize training directions that are consistent with the forward propagation sequence and reduce the amplification of one-step prediction errors. Because the learned propagator is tied to the temporal spacing of the training snapshots rather than to the FD stability limit, it can advance the wavefield using a physical time step ten times larger than that required by the underlying solver. Experiments on the Overthrust, SEG/EAGE, and Marmousi models show that the proposed method accurately reproduces wavefield snapshots and shot gathers and achieves an end-to-end speedup of 2.17 x over a GPU-accelerated tenth-order staggered-grid FD implementation under matched hardware conditions.
