Power-scaled Bayesian Inference with Score-based Generative Models

Huseyin Tuna Erdinc, Yunlin Zeng, Abhinav Gahlot, Felix Johan Herrmann

Abstract:

We propose a score-based generative algorithm for sampling from
power-scaled priors and likelihoods within the Bayesian inference
framework. Our algorithm enables flexible control over prior--likelihood
influence without requiring retraining for different power-scaling
configurations. Specifically, we focus on synthesizing seismic velocity
models conditioned on imaged seismic. Our method enables sensitivity
analysis by sampling from intermediate power posteriors, allowing us to
assess the relative influence of the prior and likelihood on samples of
the posterior distribution. Through a comprehensive set of experiments,
we evaluate the effects of varying the power parameter in different
settings: applying it solely to the prior, to the likelihood of a
Bayesian formulation, and to both simultaneously. The results show that
increasing the power of the likelihood up to a certain threshold
improves the fidelity of posterior samples to the conditioning data
(e.g., seismic images), while decreasing the prior power promotes
greater structural diversity among samples. Moreover, we find that
moderate scaling of the likelihood leads to a reduced shot data
residual, confirming its utility in posterior refinement.