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arxiv: 2505.17353 · v2 · pith:Z5TXQKIBnew · submitted 2025-05-23 · 💻 cs.CV · cs.AI· cs.LG· eess.IV

Dual Ascent Diffusion for Inverse Problems

Minseo Kim , Axel Levy , Gordon Wetzstein This is my paper

Pith reviewed 2026-05-19 14:22 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LGeess.IV
keywords inverse problemsdiffusion modelsdual ascentimage restorationMAP estimationoptimizationgenerative priors
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The pith

A dual ascent optimization framework with diffusion priors solves inverse problems more accurately and robustly than prior MAP or sampling methods.

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

The paper introduces a dual ascent optimization framework to solve maximum-a-posteriori estimation problems that use diffusion model priors for ill-posed inverse problems such as image restoration. Existing methods depend on various computational approximations that produce inaccurate or suboptimal results, whereas this approach integrates the diffusion prior directly through dual ascent steps. A sympathetic reader would care because the method is reported to deliver higher image quality across metrics, greater robustness when measurements contain high noise, faster runtime, and reconstructions that align more closely with the actual observations. These gains matter for applications like medical imaging and astrophysics where limited or noisy data must be turned into reliable images.

Core claim

We introduce a new approach to solving MAP problems with diffusion model priors using a dual ascent optimization framework. Our framework achieves better image quality as measured by various metrics for image restoration problems, it is more robust to high levels of measurement noise, it is faster, and it estimates solutions that represent the observations more faithfully than the state of the art.

What carries the argument

Dual ascent optimization framework that incorporates diffusion model priors to solve MAP estimation in inverse problems without relying on common approximations.

If this is right

  • Better image quality as measured by standard metrics on image restoration tasks.
  • Greater robustness when the input measurements contain high levels of noise.
  • Faster runtime than existing state-of-the-art approaches.
  • Reconstructed solutions that match the given observations more closely.

Where Pith is reading between the lines

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

  • The same dual-ascent structure might be tested with other types of generative priors besides diffusion models.
  • It could be adapted to inverse problems outside imaging, such as signal recovery in physics or astronomy.
  • Real-time implementations could be explored for settings where noise levels vary during acquisition.

Load-bearing premise

The dual ascent optimization framework can be combined with diffusion model priors to solve MAP problems while avoiding the inaccurate or suboptimal approximations that affect existing MAP and posterior sampling methods.

What would settle it

A head-to-head test on standard image restoration benchmarks with high added noise that shows no gains in quality metrics or data fidelity compared with current best methods would falsify the central claim.

Figures

Figures reproduced from arXiv: 2505.17353 by Axel Levy, Gordon Wetzstein, Minseo Kim.

Figure 1
Figure 1. Figure 1: Overview of DDiff. This example illustrates the motion deblurring task. Our method alternates between three steps (x-update, z-update, dual update). On the right, we show the evolution of x, z, and u throughout optimization. u-update. The update of the dual variable is readily available in Eq. 5. z-update. Following Eq. 4, the z-update consists in denoising x + u for a certain noise level σ˜ 2 . However, i… view at source ↗
Figure 2
Figure 2. Figure 2: Qualitative results. DDiff demonstrates sharper and cleaner results compared to DPS and DAPS. All tasks are run with a noise of standard deviation σ = 0.05. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of measurement noise level. DDiff demonstrates greater robustness as noise increases. This evaluation uses 10 FFHQ validation images. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative results at high measurement noise level. We use 10 randomly-chosen validation images and show the results of phase retrieval at σ = 0.3, comparing our method to the state-of-the-art algorithm DAPS [39]. 4.3 Ablation Studies Evaluation of time efficiency and quality of samples. One of the most limiting factors of sampling speed for diffusion-based methods is the number of neural function evaluat… view at source ↗
Figure 5
Figure 5. Figure 5: Evaluation of time efficiency and quality of samples. The y-axis shows LPIPS value and the x-axis shows the time (in sec.) taken to generate one sample image on a GeForce RTX 2080 Ti 12GB GPU. The number after the method name (500, 2k, etc.) indicates the NFEs. This evaluation uses 100 FFHQ validation images. Effect of dual variable and noising step. To illustrate the importance of dual variable u and the … view at source ↗
read the original abstract

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior sampling approaches, however, rely on different computational approximations, leading to inaccurate or suboptimal samples. To address this issue, we introduce a new approach to solving MAP problems with diffusion model priors using a dual ascent optimization framework. Our framework achieves better image quality as measured by various metrics for image restoration problems, it is more robust to high levels of measurement noise, it is faster, and it estimates solutions that represent the observations more faithfully than the state of the art.

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.

Referee Report

2 major / 2 minor

Summary. The paper introduces a dual ascent optimization framework for solving maximum-a-posteriori (MAP) estimation problems in ill-posed inverse problems, using diffusion models as priors. It positions this approach as avoiding the inaccurate or suboptimal approximations common in existing MAP and posterior sampling methods, and reports superior performance on image restoration tasks in terms of image quality metrics, robustness to high measurement noise, computational speed, and fidelity to observations.

Significance. If the central claim holds—that dual ascent with diffusion priors yields more accurate MAP solutions without the gradient or sampling approximations of prior work—it would offer a principled and potentially more reliable optimization route for diffusion-based inverse problems. This could improve results in domains such as medical imaging and astrophysics where faithful reconstruction under noise is critical. The absence of free parameters or ad-hoc inventions in the core framework is a positive structural feature.

major comments (2)
  1. [§3] §3 (Method, dual ascent formulation): The claim that the framework solves the MAP problem while sidestepping suboptimal approximations rests on convergence of dual ascent under the non-convex objective induced by the diffusion score function. Standard dual ascent provides only local convergence guarantees in non-convex settings; the manuscript does not appear to supply a global optimality proof, error bound relative to exact MAP, or analysis of inexact gradient steps/early stopping. This is load-bearing for the central claim that reported gains stem from the framework rather than implementation choices.
  2. [§5] §5 (Experiments): The reported improvements in metrics, noise robustness, and speed are presented without accompanying details on the number of independent runs, standard deviations, hyperparameter sensitivity (e.g., dual ascent step sizes or penalty parameters), or statistical tests against baselines. This makes it difficult to determine whether the gains are reproducible and attributable to the proposed method.
minor comments (2)
  1. [§2] Notation for the dual variable and the diffusion prior score should be introduced with explicit definitions in the first use to improve readability.
  2. [§5] Figure captions for the qualitative restoration examples should include the specific noise levels and inverse problem type (e.g., deblurring vs. inpainting) for each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments, which help us clarify the theoretical foundations and strengthen the experimental validation of our dual ascent framework for diffusion-based MAP estimation. We address each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (Method, dual ascent formulation): The claim that the framework solves the MAP problem while sidestepping suboptimal approximations rests on convergence of dual ascent under the non-convex objective induced by the diffusion score function. Standard dual ascent provides only local convergence guarantees in non-convex settings; the manuscript does not appear to supply a global optimality proof, error bound relative to exact MAP, or analysis of inexact gradient steps/early stopping. This is load-bearing for the central claim that reported gains stem from the framework rather than implementation choices.

    Authors: We agree that dual ascent applied to the non-convex objective induced by a diffusion score function yields local rather than global convergence guarantees, and the manuscript does not provide a global optimality proof or explicit error bounds relative to the exact MAP solution. Such global results are generally intractable for this class of problems. Our central claim is instead that the dual ascent formulation directly targets the MAP objective without the specific gradient or sampling approximations employed by prior MAP and posterior sampling methods. In the revision we will expand the discussion in §3 to explicitly state the local convergence properties, reference relevant results from non-convex optimization literature, and add targeted experiments analyzing the effects of inexact gradient steps and early stopping on solution quality. revision: partial

  2. Referee: [§5] §5 (Experiments): The reported improvements in metrics, noise robustness, and speed are presented without accompanying details on the number of independent runs, standard deviations, hyperparameter sensitivity (e.g., dual ascent step sizes or penalty parameters), or statistical tests against baselines. This makes it difficult to determine whether the gains are reproducible and attributable to the proposed method.

    Authors: We acknowledge that the experimental section would benefit from greater statistical detail. In the revised manuscript we will report the number of independent runs performed, include standard deviations for all quantitative metrics, present sensitivity analysis with respect to key hyperparameters such as dual ascent step sizes and penalty parameters, and add statistical significance tests comparing our method against the baselines. These additions will be incorporated into §5 and the supplementary material. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents a dual ascent optimization framework to solve MAP estimation problems using diffusion model priors, claiming it avoids the approximations of prior MAP and sampling methods. The provided abstract and context describe the approach as combining standard dual ascent with diffusion priors without any equations or steps that reduce the central result to a fitted parameter renamed as prediction, a self-definitional loop, or a load-bearing self-citation chain. No quoted derivation shows the output being equivalent to the input by construction, and the framework builds on independent optimization techniques applied to existing diffusion models. This is the common case of a self-contained contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that the dual ascent procedure integrates cleanly with diffusion priors.

pith-pipeline@v0.9.0 · 5639 in / 1182 out tokens · 65081 ms · 2026-05-19T14:22:25.817928+00:00 · methodology

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