# Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance

Source: [Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance](<https://www.sota2.com/research/paper/68fa7a371e209131cea81db2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-05T05:00:04.460Z

Authors: Saeed Mohseni-Sehdeh, Walid Saad, Kei Sakaguchi, Tao Yu

Published: 2025-07-22T19:35:14.000Z

## Abstract

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also generate samples from conditional distributions. In this paper, a novel diffusion-based framework is introduced for solving inverse problems using a piecewise guidance scheme. The guidance term is defined as a piecewise function of the diffusion timestep, facilitating the use of different approximations during high-noise and low-noise phases. This design is shown to effectively balance computational efficiency with the accuracy of the guidance term. Unlike task-specific approaches that require retraining for each problem, the proposed method is problem-agnostic and readily adaptable to a variety of inverse problems. Additionally, it explicitly incorporates measurement noise into the reconstruction process. The effectiveness of the proposed framework is demonstrated through extensive experiments on image restoration tasks, specifically image inpainting and super-resolution. Using a class conditional diffusion model for recovery, compared to the \\blue{pseudoinverse-guided diffusion model (\\textrm{\\(\\Pi\\)}GDM) baseline}, the proposed framework achieves a reduction in inference time of \\(25\\%\\) for inpainting with both random and center masks, and \\(23\\%\\) and \\(24\\%\\) for \\(4\\times\\) and \\(8\\times\\) super-resolution tasks, respectively, while incurring only negligible loss in PSNR and SSIM.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Inpainting on ImageNet center mask](<https://www.sota2.com/research/sota/image-inpainting-on-imagenet-center-mask.md>): Image Inpainting; ImageNet center mask; PSNR: 18.45.

- [Image Inpainting on ImageNet random mask](<https://www.sota2.com/research/sota/image-inpainting-on-imagenet-random-mask.md>): Image Inpainting; ImageNet random mask; PSNR: 26.57.

- [Super-resolution on ImageNet x4 scaling](<https://www.sota2.com/research/sota/super-resolution-on-imagenet-x4-scaling.md>): Super-Resolution; ImageNet x4 scaling; PSNR: 23.07.

- [Super-resolution on ImageNet x8 scaling](<https://www.sota2.com/research/sota/super-resolution-on-imagenet-x8-scaling.md>): Super-Resolution; ImageNet x8 scaling; PSNR: 20.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2507.18654>)

[PDF](<https://arxiv.org/pdf/2507.18654.pdf>)