Calibrated Test-Time Guidance for Bayesian Inference

TL;DR

This paper identifies the miscalibration issues in existing test-time guidance methods for diffusion models and proposes new estimators that enable accurate Bayesian posterior sampling, improving performance on inference and image reconstruction tasks.

Contribution

The authors introduce consistent estimators for test-time guidance that achieve calibrated Bayesian inference, addressing the limitations of existing reward-maximizing approaches.

Findings

Outperforms previous methods on Bayesian inference tasks

Achieves state-of-the-art results in black hole image reconstruction

Enables calibrated sampling from the Bayesian posterior

Abstract

Test-time guidance is a widely used mechanism for steering pretrained diffusion models toward outcomes specified by a reward function. Existing approaches, however, focus on maximizing reward rather than sampling from the true Bayesian posterior, leading to miscalibrated inference. In this work, we show that common test-time guidance methods do not recover the correct posterior distribution and identify the structural approximations responsible for this failure. We then propose consistent alternative estimators that enable calibrated sampling from the Bayesian posterior. We significantly outperform previous methods on a set of Bayesian inference tasks, and match state-of-the-art in black hole image reconstruction.