# Power-scaled Bayesian Inference with Score-based Generative Models

arXiv: https://arxiv.org/abs/2504.10807 · HTML: https://mlsanity.com/paper/2504.10807/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 13 of 13)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Controllable seismic velocity synthesis using generative diffusion models](https://mlsanity.com/paper/2402.06277/) (2024)
- [ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems](https://mlsanity.com/paper/2405.05398/) (2024)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [Detecting and diagnosing prior and likelihood sensitivity with power-scaling](https://mlsanity.com/paper/2107.14054/) (2021)
- [WISER: multimodal variational inference for full-waveform inversion without dimensionality reduction](https://mlsanity.com/paper/2405.10327/) (2024)
- [An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring](https://mlsanity.com/paper/2410.01218/) (2024)
- [Machine learning-enabled velocity model building with uncertainty quantification](https://mlsanity.com/paper/2411.06651/) (2024)
- [Variational Prior Replacement in Bayesian Inference and Inversion](https://mlsanity.com/paper/2406.04072/) (2024)

## Built on by (most cited first, 1 of 1)

- [SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior](https://mlsanity.com/paper/2604.00307/) (2026)

## Abstract (arXiv)

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.