  We introduce a probabilistic technique for full-waveform inversion, employing
variational inference and conditional normalizing flows to quantify uncertainty
in migration-velocity models and its impact on imaging. Our approach integrates
generative artificial intelligence with physics-informed common-image gathers,
reducing reliance on accurate initial velocity models. Considered case studies
demonstrate its efficacy producing realizations of migration-velocity models
conditioned by the data. These models are used to quantify amplitude and
positioning effects during subsequent imaging.
