---
title: "基于DDIM的可证明扩散后验采样方法用于线性逆问题"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.19333v1"
permalink: "https://feed.astralor.com/items/itm_7749e751c32ff2bc851a72a2"
published: "2026-07-21T17:53:36.000Z"
score: 79
channel: "ai"
tags: ["DDIM","PDDIM","后验采样","图像恢复","扩散模型","线性逆问题"]
---

# 基于DDIM的可证明扩散后验采样方法用于线性逆问题

## AI 点评

> 这篇论文将扩散后验采样简化为坐标级DDIM更新，理论证明简洁有力，是扩散模型求解逆问题的重要一步。对从事图像修复、压缩感知的研究者尤其值得关注，它提供了一个既高效又有保证的实用工具。

## 速览

本文提出一种简单高效的PDDIM算法，通过DDIM型采样器解决线性逆问题。该方法仅需对标准DDIM更新进行轻量级坐标修正，并显式融入测量模型。关键思想是在测量算子的每个奇异方向上分别进行后验采样：当观测信噪比低于扩散信噪比时，遵循学习到的扩散先验；否则切换到校准的基于测量的预测。理论证明该采样器收敛到以测量为条件的贝叶斯后验。实验表明，在图像恢复任务中，该方法在多数评估指标上优于现有扩散后验采样器。

## 关键点

- 提出PDDIM算法，仅需对DDIM进行坐标级修正即可实现后验采样。
- 理论证明PDDIM采样器收敛到条件后验分布。
- 在图像恢复任务中，PDDIM在多数指标上达到最优。

## 全文

Diffusion-based methods have achieved remarkable empirical success in solving inverse problems. However, many existing posterior samplers either lack rigorous theoretical guarantees or incur substantial computational overhead. We propose a simple and efficient algorithm, called \pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler. Our method requires only lightweight, coordinate-wise modifications to the standard DDIM update, while explicitly incorporating the measurement model. The key idea is to perform posterior sampling separately along each singular direction of the measurement operator: for each direction, the sampler follows the learned diffusion prior when the observation signal-to-noise ratio (SNR) is below the corresponding diffusion SNR, and switches to a calibrated measurement-based predictor otherwise. We prove that the proposed sampler converges to the Bayesian posterior conditioned on the measurements. Empirical results show that the proposed sampler performs favorably against existing diffusion-based posterior samplers across a range of image restoration tasks, achieving the best performance on the majority of evaluation metrics considered. Overall, our results convert posterior sampling for noisy linear inverse problems to simple coordinate-wise DDIM updates, yielding an efficient, easy-to-implement algorithm with provable posterior consistency.

---

引用前请核对原文;本文由星际流动整理:https://feed.astralor.com/items/itm_7749e751c32ff2bc851a72a2