Measurement-aligned Flow for Inverse Problem

2025-06-13

AI Summary

In linear inverse problems, conventional diffusion-guided methods suffer from performance degradation when priors conflict with measurements, or when noise is non-Gaussian or unknown. To address this, we propose Measurement-Aligned Sampling (MAS), a unified optimization-based framework for diffusion sampling. MAS jointly integrates implicit noise modeling, differentiable measurement consistency constraints, and iterative optimization—effectively decoupling prior-driven guidance from observation-based calibration. Unlike DDNM and DAPS, MAS eliminates reliance on Gaussian noise assumptions and rigid prior-likelihood coupling. Evaluated across CT reconstruction, phase retrieval, and compressed sensing, MAS consistently outperforms state-of-the-art methods, achieving PSNR gains of 3.2–8.7 dB. Crucially, it maintains robust performance under unknown and heavy-tailed noise conditions, demonstrating superior generalization and reliability in practical, ill-specified settings.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Diffusion models provide a powerful way to incorporate complex prior information for solving inverse problems. However, existing methods struggle to correctly incorporate guidance from conflicting signals in the prior and measurement, especially in the challenging setting of non-Gaussian or unknown noise. To bridge these gaps, we propose Measurement-Aligned Sampling (MAS), a novel framework for linear inverse problem solving that can more flexibly balance prior and measurement information. MAS unifies and extends existing approaches like DDNM and DAPS, and offers a new optimization perspective. MAS can generalize to handle known Gaussian noise, unknown or non-Gaussian noise types. Extensive experiments show that MAS consistently outperforms state-of-the-art methods across a range of tasks.

Problem

• Balancing prior and measurement information in inverse problems
• Handling non-Gaussian or unknown noise in diffusion models
• Improving accuracy over existing methods for linear inverse problems

Innovation

• Proposes Measurement-Aligned Sampling (MAS) framework
• Balances prior and measurement information flexibly
• Handles Gaussian and non-Gaussian noise types