Multiscale Wavelet Score-based Posterior Approximations for Seismic Inversion

We present a cascaded conditional wavelet score–based posterior surrogate (CWSGM) for seismic inversion that generates samples of subsurface velocity fields conditioned on physics-derived summaries (e.g., RTM images). Through multi-scale wavelet-based whitening, we specifically address ill-conditioning of the velocity model’s covariance (due to its fractal-like 1/f power spectrum), whose long range correlations hamper training neural networks to approximate the score function. This strategy improves the conditioning of the score-learning problem and accelerates both training and sampling. Experiments on the North Sea BG Model demonstrate that CWSGM accurately captures long-range geological correlations while reducing GPU memory usage by approximately 50% and sampling time by 73% compared to a single-scale vanilla score model. Overall, our approach enables efficient multi-scale generation of subsurface velocities at lower computational cost and provides a foundation for exploring alternative multiscale transforms that are more optimally aligned with seismic observations.