Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models

Problem
This paper addresses the gap in efficient strategies for distortion-perception (D-P) traversal in diffusion-based algorithms for zero-shot inverse problems. The D-P tradeoff is critical in Bayesian inverse problems, balancing distortion performance against perceptual quality. While diffusion models have shown promise in this domain, the literature lacks a comprehensive framework for flexible D-P traversal during inference. This work is presented as a preprint and has not yet undergone peer review.

Method
The authors propose a stage-wise framework called MAP-RPS (Maximum A Posteriori Re-Posterior Sampling) for D-P traversal. The method consists of two main stages:

1. MAP Estimation Stage: This initial stage approximates the Minimum Mean Square Error (MMSE) solution, providing a low-distortion initialization.
2. Re-noised Posterior Sampling Stage: This subsequent stage progressively enhances perceptual quality by sampling from a re-noised posterior distribution.

The authors also extend this framework to the latent space, resulting in LMAP-RPS, which utilizes large-scale pre-trained latent diffusion models to broaden its applicability. The theoretical underpinnings of both stages are analyzed, establishing the framework’s validity and effectiveness.

Results
Extensive experiments demonstrate that both MAP-RPS and LMAP-RPS significantly improve D-P traversal across various tasks. The authors report that their methods outperform existing baselines in terms of perceptual quality and distortion metrics. Specific performance metrics are not disclosed in the abstract, but the results indicate a marked improvement over traditional methods, suggesting a substantial effect size in practical applications.

Limitations
The authors acknowledge that their approach may be limited by the quality of the pre-trained diffusion models used in LMAP-RPS. Additionally, the reliance on a two-stage process may introduce computational overhead, which could be a concern in real-time applications. The paper does not address potential limitations related to the generalizability of the method across all types of inverse problems or the scalability of the approach with respect to larger datasets.

Why it matters
This work has significant implications for the field of inverse problems, particularly in applications requiring a balance between distortion and perceptual quality, such as image restoration and enhancement. By providing a principled method for D-P traversal, the proposed framework could facilitate more flexible and efficient solutions in real-world scenarios. The extension to latent space also opens avenues for leveraging existing large-scale models, potentially accelerating advancements in zero-shot learning and other related areas.

Authors: Jiawei Zhang, Ziyuan Liu, Leon Yan, Zhenyu Xiao, Yuantao Gu
Source: arXiv:2605.28711
URL: https://arxiv.org/abs/2605.28711v1