During this talk, I will discuss different Bayesian inference techniques we have developed in my group. The problem of Full-Waveform Inference is challenged by the large degrees of freedom, the expensive to evaluate forward operators, and the presence of parasitic local minima. In an effort to meet these challenges, we combine techniques from amortized simulation-based inference, generative models, and a hybrid of physics-based learned summary statistics. Our approach not only reduces dimensionality of the seismic data but it also simplifies the model-to-summarized data mapping while preserving information, so the posterior distribution remains informed.