Calibrated Test-Time Guidance for Bayesian Inference

2026-02-25

AI Summary

This work addresses a fundamental limitation in existing test-time guidance methods for diffusion models, which fail to correctly sample from the Bayesian posterior due to structural approximation errors, thereby introducing inference bias. The paper is the first to identify and rectify this structural bias by proposing a theoretically consistent alternative estimator that enables calibrated posterior sampling. Built upon the test-time guidance framework of diffusion models, the method introduces a consistency-aware estimator designed to preserve the fidelity of Bayesian inference. Experimental results demonstrate that the proposed approach significantly outperforms current methods across multiple Bayesian inference tasks and achieves state-of-the-art performance in black hole image reconstruction.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Bayesian inference
• test-time guidance
• posterior calibration
• diffusion models
• miscalibrated inference

Innovation

• test-time guidance
• Bayesian inference
• posterior calibration
• diffusion models
• consistent estimators