Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models

2026-02-07

AI Summary

This work addresses the reliance on manual tuning and heuristic strategies in posterior sampling for zero-shot diffusion models when solving inverse problems. Under a Gaussianity assumption on the prior, the authors derive closed-form solutions for both an ideal posterior sampler and a diffusion-based reconstruction algorithm in the spectral domain, establishing—for the first time—a rigorous theoretical framework for analyzing zero-shot posterior sampling. Building upon this foundation, they propose a method-agnostic, adaptive parameter selection mechanism that automatically adjusts parameters based on the prior, degradation operator, and diffusion dynamics. The recommended parameters vary adaptively across diffusion timesteps, achieving a stable trade-off between perceptual quality and signal fidelity, and significantly outperforming conventional heuristic tuning strategies.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based solution that leverages prior knowledge. Such algorithms incorporate the observations through inference, often leaning on manual tuning and heuristics. In this work we propose a rigorous analysis of such approximate posterior-samplers, relying on a Gaussianity assumption of the prior. Under this regime, we show that both the ideal posterior sampler and diffusion-based reconstruction algorithms can be expressed in closed-form, enabling their thorough analysis and comparisons in the spectral domain. Building on these representations, we also introduce a principled framework for parameter design, replacing heuristic selection strategies used to date. The proposed approach is method-agnostic and yields tailored parameter choices for each algorithm, jointly accounting for the characteristics of the prior, the degraded signal, and the diffusion dynamics. We show that our spectral recommendations differ structurally from standard heuristics and vary with the diffusion step size, resulting in a consistent balance between perceptual quality and signal fidelity.

Problem

• zero-shot
• posterior sampling
• diffusion models
• inverse problems
• signal recovery

Innovation

• zero-shot posterior sampling
• diffusion models
• spectral analysis
• parameter design
• inverse problems