# Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models

arXiv: https://arxiv.org/abs/2602.07715 · HTML: https://mlsanity.com/paper/2602.07715/

## 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 30 of its 42 references that are in the map.
- First posted on arXiv 7 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Accelerating Diffusion Sampling with Optimized Time Steps](https://mlsanity.com/paper/2402.17376/) (2024)
- [On the Trajectory Regularity of ODE-based Diffusion Sampling](https://mlsanity.com/paper/2405.11326/) (2024)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Learning to Discretize Denoising Diffusion ODEs](https://mlsanity.com/paper/2405.15506/) (2024)
- [PyTorch Image Quality: Metrics for Image Quality Assessment](https://mlsanity.com/paper/2208.14818/) (2022)
- [Score-Optimal Diffusion Schedules](https://mlsanity.com/paper/2412.07877/) (2024)
- [Spectral Analysis of Diffusion Models with Application to Schedule Design](https://mlsanity.com/paper/2502.00180/) (2025)
- [Traversing Distortion-Perception Tradeoff using a Single Score-Based Generative Model](https://mlsanity.com/paper/2503.20297/) (2025)
- [Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models](https://mlsanity.com/paper/2506.13614/) (2025)

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

- [Mixture-of-Gaussians-Guided Schedule Design for Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2607.03517/) (2026)

## Abstract (arXiv)

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 these 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 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 that jointly account 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.