arxiv: 2605.09477 · v1 · submitted 2026-05-10 · 💻 cs.CV · cs.AI

Recognition: no theorem link

Outlier-Robust Diffusion Solvers for Inverse Problems

Jiahua Liu, Tongyao Pang, Wen Li, Yang Zheng, Zhaoqiang Liu

Pith reviewed 2026-05-12 04:22 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords diffusion modelsinverse problemsoutlier robustnessHuber lossiteratively reweighted least squaresnoise estimationimage reconstruction

0 comments

The pith

Diffusion models for inverse problems become robust to outliers by explicitly estimating noise and using Huber-loss reweighted least squares.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method to solve inverse problems with diffusion models when real-world measurements include outliers that break standard approaches. It first refines the input by estimating and subtracting noise explicitly, then casts the recovery as an iteratively reweighted least squares problem that uses the Huber loss to downweight outlier effects. The resulting optimization is solved approximately either by gradient descent or by a conjugate-gradient procedure that removes the need to tune step sizes. Experiments across image datasets and both linear and nonlinear tasks show the approach maintains performance where prior diffusion solvers degrade.

Core claim

By first estimating noise to clean the measurements and then optimizing a Huber-loss-based iteratively reweighted least squares objective that incorporates the diffusion prior, the method produces solutions that remain accurate even when outliers are present in the data.

What carries the argument

Huber-loss iteratively reweighted least squares objective applied after explicit noise estimation, solved by gradient or conjugate gradient steps while respecting the diffusion prior.

If this is right

The approach applies to both linear and nonlinear inverse problems.
Conjugate gradient solving removes the need for careful learning-rate tuning required by plain gradient descent.
Extensive tests on multiple image datasets show outperformance over recent diffusion-model methods in most outlier conditions.
Robustness holds under varying outlier strengths and task types.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same noise-estimation plus reweighting pattern could be tried with other generative priors besides diffusion models.
In applications such as medical or astronomical imaging the method may reduce the amount of manual data cleaning needed before inversion.
If the diffusion prior itself is weak on the target domain, the robustness gains may shrink even when the reweighting works as intended.

Load-bearing premise

The explicit noise estimation step must separate outliers and noise from the true signal without introducing new distortions that the diffusion model cannot correct.

What would settle it

A test set of synthetic inverse problems with precisely known outlier locations and magnitudes where the method's reconstructions show higher error or visible artifacts than a non-robust diffusion baseline.

Figures

Figures reproduced from arXiv: 2605.09477 by Jiahua Liu, Tongyao Pang, Wen Li, Yang Zheng, Zhaoqiang Liu.

**Figure 2.** Figure 2: Visualization results of our methods and other DM [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Visualization results of our methods and other DM [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 5.** Figure 5: Visualization results of our methods and other DM-based [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 4.** Figure 4: Visualization results of our methods and other DM-based [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 6.** Figure 6: Visualization of the relationship between the distortion metric PSNR and computational cost for the CelebA Gaussian deblurring [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: Visualization of the experimental results for the super-resolution ( [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: Visualization of the experimental results for the inpainting (random [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗

**Figure 9.** Figure 9: Visualization of the experimental results for the Gaussian deblurring task with a contamination factor of [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: Visualization of the experimental results for the motion deblurring task with a contamination factor of [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

**Figure 11.** Figure 11: Visualization of the experimental results for the nonlinear deblurring task with a contamination factor of [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

read the original abstract

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a practical pipeline for adding outlier robustness to diffusion inverse problem solvers by cleaning measurements with explicit noise estimation then applying Huber-loss IRLS solved by conjugate gradient.

read the letter

The core idea is straightforward: start with a diffusion model solver for inverse problems, add an upfront noise estimation step to reduce outlier effects in the measurements, then switch to a Huber loss inside an iteratively reweighted least squares objective. They solve that with either gradient descent or conjugate gradient to sidestep learning-rate tuning. This combination is presented as new for the diffusion-IP setting and the experiments claim it beats recent DM-based methods on linear and nonlinear tasks across image datasets under various outlier conditions.

Referee Report

0 major / 3 minor

Summary. The paper proposes outlier-robust diffusion-model solvers for inverse problems. It first applies explicit noise estimation to refine measurements and mitigate noise effects, then formulates an iteratively reweighted least squares (IRLS) objective using the Huber loss to handle outliers. The resulting optimization is solved approximately via gradient descent or, to avoid learning-rate tuning, via conjugate gradient with an efficient update strategy. Extensive experiments across multiple image datasets, covering linear and nonlinear tasks under varied conditions, are reported to show improved robustness to outliers and outperformance over recent DM-based methods in most cases.

Significance. If the noise-estimation step isolates outliers without distorting the signal recovered by the diffusion prior and the Huber-loss IRLS remains compatible with the diffusion model, the approach offers a practical, parameter-light extension of existing DM-IP frameworks. The dual solver options (GD and CG) and the breadth of experiments on linear/nonlinear tasks across datasets constitute a useful empirical contribution for real-world inverse problems with contaminated measurements.

minor comments (3)

[Abstract] The abstract states that the methods 'outperform recent DM-based methods in most cases' but provides no quantitative metrics, specific baselines, or outlier-level details; a summary table or explicit comparison metrics should appear in the experimental section.
[Methods] The 'efficient strategy for updating' the conjugate-gradient solver is mentioned but not specified; pseudocode or the exact update rule (e.g., how the weighting matrix is refreshed inside the CG loop) should be provided in the methods section to ensure reproducibility.
[Experiments] The Huber-loss threshold is listed as a free parameter; its selection procedure, sensitivity analysis, or default value across experiments should be stated explicitly.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, the assessment of its significance, and the recommendation for minor revision. No specific major comments were raised.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a direct integration of standard robust statistics tools (explicit noise estimation followed by Huber-loss-based IRLS solved via gradient descent or conjugate gradient) into an existing diffusion-model inverse-problem solver. No equations or steps reduce the claimed robustness or performance gains to a fitted parameter, self-citation chain, or definitional tautology. The method is described as an application of known techniques rather than a self-derived result, and the central claims rest on experimental validation across datasets rather than internal construction from the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The approach rests on standard diffusion-model assumptions for inverse problems and on the known properties of Huber loss and conjugate gradient; no new entities are introduced.

free parameters (1)

Huber loss threshold
Controls the point at which the loss switches from quadratic to linear; must be chosen or tuned for the outlier level.

axioms (2)

domain assumption Diffusion models provide a useful prior for solving linear and nonlinear inverse problems via guidance or sampling.
Invoked implicitly when the authors state that DM-based methods are the baseline being improved.
standard math Conjugate gradient converges reliably on the quadratic subproblems arising from IRLS.
Standard result in numerical linear algebra; no proof supplied in abstract.

pith-pipeline@v0.9.0 · 5447 in / 1355 out tokens · 37360 ms · 2026-05-12T04:22:45.866345+00:00 · methodology

discussion (0)

Reference graph

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2, 3, 5, 6 Outlier-Robust Diffusion Solvers for Inverse Problems Supplementary Material A. Comparison with IRLS-PnPDP Both our methods and the recent work, IRLS-PnPDP [32], employ the well-established iteratively reweighted least squares (IRLS) strategy to address outlier problems in IPs. Our methods leverage this strategy to mitigate outliers within the ...

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