Power-scaled Bayesian inference for velocity-model estimation

Score-based generative models have emerged as powerful tools for conditional generation in Bayesian inference. While promising, a common criticism of these methods is their reliance on strong, structured priors, which can dominate the inference process and limit the network’s dependence on observed data. To address this issue, we propose a modification to the generative sampling algorithm that incorporates power scaling of both priors and likelihoods. Our approach enables flexible control over the relative influence of the prior and likelihood without requiring retraining for different scaling configurations. We demonstrate this in the context of synthesizing seismic velocity models conditioned on imaged seismic data. By sampling from intermediate power posteriors, our method naturally supports sensitivity analysis and allows us to assess how varying prior and likelihood weights determines the behavior of the posterior. Through a comprehensive set of experiments, we examine the impact of the power parameters in three scenarios: scaling only the prior, scaling only the likelihood, and scaling both simultaneously. The results show that increasing the likelihood power up to a certain threshold improves the fidelity of posterior samples to the conditioning data, while reducing prior power increases structural diversity in the generated models. Furthermore, moderate likelihood scaling leads to reduced shot data residuals, demonstrating its effectiveness for posterior refinement.