WaveDiffusion: Joint Latent Diffusion for Physically Consistent Seismic and Velocity Generation

Abstract

Full Waveform Inversion (FWI) is a critical technique in subsurface imaging, aiming to reconstruct high-resolution subsurface properties from surface measurements. Acoustic FWI involves two physical modalities, seismic waveforms and velocity maps, which are governed by the acoustic wave equation. Prior works primarily focus on the inverse problem, modeling the relationship between seismic and velocity as an image-to-image translation task. In this work, we study their relationship from a generative perspective. Our aim is to explore and characterize the latent space structure, and identify latent vectors that generate seismic-velocity pairs consistent with the governing partial differential equation (PDE). Specifically, we model seismic and velocity data jointly from a shared latent space via a diffusion process. In experiments, we find that diffusion progressively refines arbitrary latent vectors into ones that yield approximately physics-consistent seismic-velocity pairs, even without explicit physics constraints. This provides empirical evidence of PDE-consistency in latent diffusion, where sampling is biased toward PDE-valid solutions. In latent space, satisfying the acoustic wave equation can be approximated through sampling and gradient descent. We formalize this physics-consistent latent modeling task and quantify it through extensive experiments. On large-scale OpenFWI benchmarks, our approach produces high-fidelity, diverse, and physically consistent seismic-velocity pairs, demonstrating the potential of a data-driven latent diffusion for physically consistent generation in a complex scientific domain.