Calibrated Test-Time Guidance for Bayesian Inference
This addresses a calibration issue in Bayesian inference for diffusion models, which is incremental but important for improving reliability in applications like image reconstruction.
The paper tackled the problem of test-time guidance in diffusion models not sampling from the true Bayesian posterior, leading to miscalibrated inference, and proposed consistent estimators that enable calibrated sampling, significantly outperforming previous methods on Bayesian inference tasks and matching state-of-the-art in black hole image reconstruction.
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.