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Full Waveform Inversion (FWI) reconstructs high-resolution subsurface velocity maps from seismic waveform data governed by partial differential equations (PDEs). Traditional machine learning approaches frame FWI as an image-to-image translation task, mapping seismic data to velocity maps via encoder-decoder architectures. In this paper, we revisit FWI from a new perspective: generating both modalities simultaneously. We found that both modalities can be jointly generated from a shared latent space using a diffusion process. Remarkably, our jointly generated seismic-velocity pairs inherently satisfy the governing PDE without requiring additional constraints. This reveals an interesting insight: the diffusion process inherently learns a scoring mechanism in the latent space, quantifying the deviation from the governing PDE. Specifically, the generated seismic-velocity pairs with higher scores are closer to the solutions of the governing PDEs. Our experiments on the OpenFWI dataset demonstrate that the generated seismic-velocity pairs not only yield high fidelity, diversity and physical consistency, but also can serve as effective augmentation for training data-driven FWI models.

The full paper can be found on arxiv:

WaveDiffusion: Exploring FullWaveform Inversion via Joint Diffusion in the Latent Space