Measurement-Aligned Sampling for Inverse Problem
Shaorong Zhang, Rob Brekelmans, Yunshu Wu, Greg Ver Steeg
TL;DR
This paper introduces Measurement-Aligned Sampling (MAS), a new framework for solving inverse problems with diffusion models that effectively balances prior knowledge and measurement data, handling various noise types.
Contribution
MAS unifies and extends existing diffusion-based inverse problem methods, generalizing to unknown and non-Gaussian noise, and improves performance across multiple tasks.
Findings
MAS outperforms state-of-the-art methods in various inverse tasks.
MAS effectively handles both known Gaussian and unknown/non-Gaussian noise.
The framework maintains low computational cost while improving accuracy.
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, and often failed to maximizing the consistency to the measurement, especially in the challenging setting of non-Gaussian or unknown noise. To address these issues, we propose Measurement-Aligned Sampling (MAS), a novel framework for linear inverse problem solving that flexibly balances prior and measurement information. MAS unifies and extends existing approaches such as DDNM, TMPD, while generalizing to handle both known Gaussian noise and unknown or non-Gaussian noise types. Extensive experiments demonstrate that MAS consistently outperforms state-of-the-art methods across a variety of tasks, while maintaining relatively low computational cost.
Peer Reviews
Decision·Submitted to ICLR 2026
1. The paper provides both probabilistic (Bayesian linear regression) and optimization perspectives for a single weighted objective balancing prior and measurement fidelity, with efficient closed-form solutions via SVD decomposition. 2. MAS outperforms baselines in several tasks, while maintaining efficiency comparable to DDNM. 3. The adaptive parameterization enables effective restoration on real-world degradations like JPEG and quantization without requiring exact noise specifications, thou
1. The k parameter in lacks principled selection criteria. Table 4 shows different values (k = 1.0, 3.0, 0.5) without rationale, which might require expensive grid searches for new tasks. This contradicts the claimed relatively low computational cost. 2. The probabilistic foundation defines η₁ ≥ 0, yet optimal results (Figure 4) use negative η₁ = -0.45. While numerical stability is addressed, the paper lacks justification for why violating this constraint improves performance. 3. While Table
1. The paper introduces effective techniques for handling both Gaussian noise and unknown noise sources. 2. The proposed method enhances the robustness of diffusion models in inverse problems.
1. This paper proposes an adaptive parameter scheme with $\eta_2 = ka_t / c_t$ to generalize approaches for linear inverse problems with diffusion models. This scheme seems to be heuristic. According to Appendix B.3, this scheme is obtained based on informal principles such as "hoping $\epsilon_{intro} + \epsilon_{new}$ is as close to $\mathcal{N}(0, c_t^2 \mathbb{I})$ as possible". There is no rigorous theoretical justification on the reason why $\eta_2$ must be proportional to $a_t/c_t$. 2. T
- The framework of optimization problem with weighted matrix that reflects the geometry of the forward operator generalize existing method and eventually provide a better choice that improves the performance. - The proposed method extends the ability of solving inverse problem with diffusion models to unknown measurement noise. - The paper provides extensive comparison on various linear inverse problems and baselines.
- The writing can be improved. Especially, it is quite hard to figure out the most important factor among a lot of parameters such as $\eta_1, \eta_2, c_t, r_t, \sigma_y, \sigma_\epsilon$. - Discussion on negative $\eta_1$ does not explain the reason why "overshoot" is better than other cases. Appendix B.2 provides a discussion about why "overshoot" does not cause a crucial problem with non-invertible W.
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Taxonomy
TopicsFlow Measurement and Analysis