Power-scaled Bayesian Inference with Score-based Generative mModels

2025-04-15

AI Summary

This study addresses imaging-driven seismic velocity modeling by proposing a fractional Score-based Generative Model (SGM) framework embedded with a power-scaling mechanism to enable tunable Bayesian posterior inference. Methodologically, it introduces the power-posterior formalism into score matching and Denoising Diffusion Probabilistic Models (DDPMs) for the first time, allowing independent, continuous adjustment of prior and likelihood weights without retraining—thus enabling multi-scale posterior sampling. The key contributions are: (i) a physically interpretable Bayesian sensitivity analysis tool that quantifies how prior/likelihood strength governs sample fidelity and structural diversity; and (ii) empirical findings showing that moderately increasing likelihood weight substantially reduces data misfit, reducing prior weight enhances geological structural diversity, and intermediate power-posteriors yield robust uncertainty quantification.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Sampling from power-scaled priors and likelihoods in Bayesian inference
• Assessing prior-likelihood influence on posterior distribution samples
• Improving fidelity of posterior samples to conditioning data

Innovation

• Score-based generative algorithm for Bayesian inference
• Flexible control over prior-likelihood influence
• Sensitivity analysis via intermediate power posteriors