arxiv: 2605.08640 · v1 · submitted 2026-05-09 · 💻 cs.CV

Recognition: 2 theorem links

· Lean Theorem

FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors

Hendrik Sommerhoff , Michael Moeller

Authors on Pith no claims yet

Pith reviewed 2026-05-12 00:50 UTC · model grok-4.3

classification 💻 cs.CV

keywords plug-and-play methodsADMMflow-based priorsinverse problemsconvergence analysisrenoise-denoise operatorimage restoration

0 comments

The pith

Flow-based plug-and-play methods gain convergence guarantees by replacing stochastic steps with a deterministic expectation operator inside ADMM.

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

The paper formalizes the deterministic renoise-denoise operator that underlies flow-based plug-and-play priors as the expectation of the denoiser over the latent noise distribution. It then embeds this operator into the classical ADMM framework to produce FlowADMM and proves convergence when the flow network meets weak Lipschitz conditions, with the analysis holding for non-stationary time schedules. Experiments show the method reaches state-of-the-art results among flow-based PnP approaches on denoising, deblurring, super-resolution, and inpainting while using fewer data consistency evaluations. A sympathetic reader cares because inverse problems appear throughout imaging and signal processing, and this approach combines the power of generative flow models with reliable optimization that is easier to analyze and run efficiently.

Core claim

The central claim is that flow-based PnP methods implicitly rely on a deterministic operator given by the expectation of the denoiser over latent noise. FlowADMM integrates this operator into ADMM, establishing convergence under weak Lipschitz conditions on the flow network and extending the guarantees to non-stationary schedules. The resulting algorithm outperforms prior flow-based PnP methods on standard inverse problems while requiring fewer data consistency evaluations.

What carries the argument

the deterministic renoise-denoise operator, defined as the expectation of the flow denoiser with respect to the distribution of added latent noise, which replaces the stochastic step as the plug-and-play prior inside ADMM iterations

If this is right

The sequence of FlowADMM iterates converges to a solution of the inverse problem whenever the weak Lipschitz conditions hold.
The method requires fewer evaluations of the data consistency term than earlier flow-based plug-and-play approaches.
State-of-the-art performance among flow-based PnP methods is obtained on denoising, deblurring, super-resolution, and inpainting.
The convergence analysis continues to apply when the time schedule changes during execution.

Where Pith is reading between the lines

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

If the weak Lipschitz property can be verified or enforced for networks trained in practice, FlowADMM could replace stochastic variants in production image restoration pipelines.
The same deterministic expectation perspective might be applied to diffusion-model priors to obtain analogous convergence results for other iterative solvers.
The formalization suggests that proximal splitting methods beyond ADMM could incorporate the same renoise-denoise operator to gain similar guarantees.

Load-bearing premise

The flow network must satisfy weak Lipschitz conditions so that the renoise-denoise operator is well-defined and the ADMM iterates converge.

What would settle it

Construct or select a flow network that violates the weak Lipschitz condition and run FlowADMM on a simple denoising task to check whether the iterates diverge or fail to produce a stable restored image.

Figures

Figures reproduced from arXiv: 2605.08640 by Hendrik Sommerhoff, Michael Moeller.

**Figure 1.** Figure 1: Effect of the time parameter t on the mean renoise-denoise operator. For small t, interpolated points remain closer to noise and naturally spread out farther, producing diverse trajectories that recover coarse structure but average fine details. For large t, interpolated points stay closer to x, producing trajectories that resolve the fine detail and place the mean operator on the local bump. Flow matchin… view at source ↗

**Figure 2.** Figure 2: Example reconstructions for each task. We report the PSNR above each image. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Distribution of the Jacobian norm Lipschitz estimates along the late-stage FlowADMM [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

**Figure 4.** Figure 4: Trajectory visualization of a deblurring experiment [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗

**Figure 5.** Figure 5: Trajectory visualization of a super-resolution experiment [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗

**Figure 6.** Figure 6: Trajectory visualization of a random inpainting experiment [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗

**Figure 7.** Figure 7: Trajectory visualization of a box inpainting experiment. [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗

**Figure 8.** Figure 8: Results for CS MRI [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗

**Figure 9.** Figure 9: Results for motion deblurring 21 [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗

read the original abstract

Plug-and-play (PnP) methods for solving inverse problems have recently achieved strong performance by leveraging denoising priors based on powerful generative diffusion and flow models. However, existing diffusion- and flow-based PnP methods typically rely on stochastic renoise-denoise operations, which complicate the analysis of their convergence behavior. In this work, we identify and formalize the deterministic renoise-denoise operator underlying flow-based plug-and-play methods. This perspective reveals that these methods implicitly define a deterministic operator given by the expectation of a denoiser over the latent noise distribution. Building on this insight, we propose FlowADMM, a PnP algorithm that integrates the renoise-denoise operator into the classical alternating direction method of multiplier (ADMM) framework. We establish convergence guarantees for FlowADMM under weak Lipschitz conditions on the underlying flow network, and extend the analysis to non-stationary time schedules. Empirically, FlowADMM achieves state-of-the-art performance among flow-based PnP methods on a range of inverse problems, including denoising, deblurring, super-resolution, and inpainting, while requiring fewer data consistency evaluations than prior approaches.

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

FlowADMM formalizes the deterministic expectation of the renoise-denoise step for flow-based PnP, plugs it into ADMM, and states convergence under weak Lipschitz conditions on the flow net, but never checks whether the trained networks satisfy those conditions.

read the letter

The paper's main contribution is to pull the stochastic renoise-denoise operation out of flow-based plug-and-play and replace it with its deterministic expectation over the latent noise. They then embed that operator inside classical ADMM and give convergence statements that also cover non-stationary time schedules. This is more than a routine re-packaging; the explicit deterministic operator and the ADMM analysis do not appear in the earlier stochastic flow PnP literature the abstract cites. The practical claim is that the resulting FlowADMM needs fewer data-consistency steps while matching or beating other flow-based PnP methods on denoising, deblurring, super-resolution, and inpainting. That efficiency angle is worth noticing if you already run ADMM-style solvers on imaging tasks. The formalization itself is clean and could be reused even if the full convergence proof needs work. The soft spot is exactly where the stress-test note points: the convergence theorem requires the flow network to obey weak Lipschitz conditions so the operator stays well-defined and sufficiently contractive. The paper invokes this but supplies neither an analytic bound nor a numerical check on the specific trained networks used in the experiments. Without that link, the theory does not yet underwrite the reported results. Minor gaps in the abstract, such as missing error-bar details or statistical tests on the gains, are secondary but add to the same picture. This is for people who work on plug-and-play priors for inverse problems and want a version that is easier to analyze than the usual stochastic flow approaches. A reader who needs to implement or compare generative PnP methods will get concrete value from the operator view. The work is coherent on its own terms and shows honest engagement with the literature, so it deserves a serious referee. I would send it to peer review; the core algorithmic step is real and the theory can be tightened with the missing verification.

Referee Report

2 major / 1 minor

Summary. The paper formalizes the deterministic renoise-denoise operator underlying flow-based PnP methods as the expectation of the denoiser over the latent noise distribution, proposes FlowADMM by embedding this operator into the classical ADMM framework, establishes convergence guarantees under weak Lipschitz conditions on the flow network (with extension to non-stationary time schedules), and reports state-of-the-art empirical performance among flow-based PnP methods on denoising, deblurring, super-resolution, and inpainting while using fewer data consistency evaluations.

Significance. If the convergence result holds and the empirical gains prove robust, the work would strengthen the theoretical foundation of flow-based PnP algorithms by replacing stochastic renoise-denoise steps with a deterministic operator amenable to ADMM analysis, potentially improving reliability and efficiency in inverse-problem solvers.

major comments (2)

[Abstract / theory section] The convergence theorem (invoked in the abstract and presumably detailed in the theory section) rests on the assumption that the trained flow network satisfies a weak Lipschitz condition sufficient to make the deterministic renoise-denoise operator well-defined and contractive; however, the manuscript supplies neither an analytic verification for the specific architectures nor a numerical bound on the operator norm evaluated on the networks used in the experiments.
[Experiments section] The empirical claims of state-of-the-art performance and reduced data-consistency evaluations lack reported error bars, number of independent runs, or statistical significance tests, which weakens the ability to assess whether the observed gains are reliable or could be explained by variance.

minor comments (1)

[Section introducing the operator] Notation for the deterministic operator (expectation over latent noise) should be introduced with an explicit equation number in the main text to aid readability.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the thoughtful and constructive review. The comments highlight important aspects of the theoretical assumptions and empirical reporting that we will address in the revision. Below we respond point by point to the major comments.

read point-by-point responses

Referee: [Abstract / theory section] The convergence theorem (invoked in the abstract and presumably detailed in the theory section) rests on the assumption that the trained flow network satisfies a weak Lipschitz condition sufficient to make the deterministic renoise-denoise operator well-defined and contractive; however, the manuscript supplies neither an analytic verification for the specific architectures nor a numerical bound on the operator norm evaluated on the networks used in the experiments.

Authors: We agree that the manuscript would be strengthened by explicit verification of the weak Lipschitz condition. Analytic verification for general trained flow architectures is intractable because the networks are highly non-linear and the condition depends on the specific weights and architecture. However, numerical estimation of the operator norm of the deterministic renoise-denoise operator is feasible for the concrete models used in the experiments. We will add these numerical bounds (computed via finite differences or power iteration on representative batches) to an appendix in the revised manuscript, confirming that the condition holds with a comfortable margin for the networks and time schedules considered. revision: yes
Referee: [Experiments section] The empirical claims of state-of-the-art performance and reduced data-consistency evaluations lack reported error bars, number of independent runs, or statistical significance tests, which weakens the ability to assess whether the observed gains are reliable or could be explained by variance.

Authors: We acknowledge that the current experimental results are presented without statistical measures. In the revised manuscript we will rerun all experiments over at least five independent trials using different random seeds for initialization and sampling, report mean performance together with standard deviations, and include paired statistical significance tests (e.g., Wilcoxon signed-rank or t-tests) against the strongest baselines. These additions will be placed in the main experimental section and the corresponding tables. revision: yes

standing simulated objections not resolved

Analytic verification of the weak Lipschitz condition for arbitrary trained flow networks, which cannot be provided in closed form without architecture-specific assumptions beyond the scope of the paper.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper defines the deterministic renoise-denoise operator explicitly as the expectation of the denoiser over the latent noise distribution of the given flow model. Convergence guarantees are derived conditionally under an external weak Lipschitz assumption on the flow network itself, without any parameter fitting to the target inverse-problem data or reduction of the theorem to the reported performance numbers. No load-bearing step equates a derived quantity to its own inputs by construction, and the empirical results are presented as separate validation rather than as justification for the theory. The derivation remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claims rest on the existence of a deterministic expectation operator derived from the flow model and on the flow network obeying a weak Lipschitz condition; no additional free parameters are introduced beyond those already present in the pretrained flow network.

axioms (1)

domain assumption The flow network satisfies weak Lipschitz conditions that guarantee the renoise-denoise operator is well-defined and contractive.
Invoked to obtain convergence guarantees for FlowADMM and its non-stationary extension.

invented entities (1)

deterministic renoise-denoise operator no independent evidence
purpose: Replaces stochastic sampling with its expectation to enable deterministic ADMM analysis.
Defined as the expectation of the denoiser over the latent noise distribution; no independent falsifiable prediction is supplied beyond the convergence statement itself.

pith-pipeline@v0.9.0 · 5504 in / 1308 out tokens · 40134 ms · 2026-05-12T00:50:26.367589+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We establish convergence guarantees for FlowADMM under weak Lipschitz conditions on the underlying flow network... the operator Tt representing the fixed-t FlowADMM iteration... is averaged.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Lemma 1. Let the flow network vθt be Lipschitz with constant Lv(t). Then the residual operator Rt=(¯St−I) is Lipschitz continuous with constant (1−t)(1+tLv(t)).

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

38 extracted references · 38 canonical work pages · 1 internal anchor

[1]

Bauschke and Patrick L

Heinz H. Bauschke and Patrick L. Combettes.Fejér Monotonicity and Fixed Point Iterations, pages 91–109. Springer International Publishing, Cham, 2017. ISBN 978-3-319-48311-5. doi: 10.1007/978-3-319-48311-5_5. URL https://doi.org/10.1007/978-3-319-48311-5_ 5

work page doi:10.1007/978-3-319-48311-5_5 2017
[2]

D-Flow: Differen- tiating through Flows for Controlled Generation, July 2024

Heli Ben-Hamu, Omri Puny, Itai Gat, Brian Karrer, Uriel Singer, and Yaron Lipman. D-flow: Differentiating through flows for controlled generation.arXiv preprint arXiv:2402.14017, 2024

work page arXiv 2024
[3]

The perception-distortion tradeoff

Yochai Blau and Tomer Michaeli. The perception-distortion tradeoff. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 6228–6237, 2018

work page 2018
[4]

Distributed optimization and statistical learning via the alternating direction method of multipliers.Machine Learning, 3(1):1–122, 2010

Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers.Machine Learning, 3(1):1–122, 2010

work page 2010
[5]

Plug-and-play admm for image restoration: Fixed-point convergence and applications.IEEE Transactions on Computational Imaging, 3(1): 84–98, 2016

Stanley H Chan, Xiran Wang, and Omar A Elgendy. Plug-and-play admm for image restoration: Fixed-point convergence and applications.IEEE Transactions on Computational Imaging, 3(1): 84–98, 2016

work page 2016
[6]

Neural ordinary differential equations.Advances in neural information processing systems, 31, 2018

Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations.Advances in neural information processing systems, 31, 2018

work page 2018
[7]

StarGAN v2: Diverse image synthesis for multiple domains

Yunjey Choi, Youngjung Uh, Jaejun Yoo, and Jung-Woo Ha. StarGAN v2: Diverse image synthesis for multiple domains. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2020

work page 2020
[8]

Diffusion posterior sampling for general noisy inverse problems

Hyungjin Chung, Jeongsol Kim, Michael Thompson Mccann, Marc Louis Klasky, and Jong Chul Ye. Diffusion posterior sampling for general noisy inverse problems. InThe Eleventh Inter- national Conference on Learning Representations, 2023. URL https://openreview.net/ forum?id=OnD9zGAGT0k

work page 2023
[9]

A Survey on Diffusion Models for Inverse Problems

Giannis Daras, Hyungjin Chung, Chieh-Hsin Lai, Yuki Mitsufuji, Jong Chul Ye, Peyman Milanfar, Alexandros G Dimakis, and Mauricio Delbracio. A survey on diffusion models for inverse problems.arXiv preprint arXiv:2410.00083, 2024

work page internal anchor Pith review arXiv 2024
[10]

Regularising inverse problems with generative machine learning models.Journal of Mathematical Imaging and Vision, 66(1): 37–56, 2024

Margaret AG Duff, Neill DF Campbell, and Matthias J Ehrhardt. Regularising inverse problems with generative machine learning models.Journal of Mathematical Imaging and Vision, 66(1): 37–56, 2024

work page 2024
[11]

Solving inverse problems with FLAIR

Julius Erbach, Dominik Narnhofer, Andreas Robert Dombos, Bernt Schiele, Jan Eric Lenssen, and Konrad Schindler. Solving inverse problems with FLAIR. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2026. URL https://openreview. net/forum?id=w9xETx7HT1

work page 2026
[12]

Solv- ing inverse problems by joint posterior maximization with a vae prior.arXiv preprint arXiv:1911.06379, 2019

Mario Gonzalez, Andrés Almansa, Mauricio Delbracio, Pablo Musé, and Pauline Tan. Solv- ing inverse problems by joint posterior maximization with a vae prior.arXiv preprint arXiv:1911.06379, 2019

work page arXiv 1911
[13]

Diffusion models as plug-and-play priors.Advances in Neural Information Processing Systems, 35:14715–14728, 2022

Alexandros Graikos, Nikolay Malkin, Nebojsa Jojic, and Dimitris Samaras. Diffusion models as plug-and-play priors.Advances in Neural Information Processing Systems, 35:14715–14728, 2022

work page 2022
[14]

Flexisp: A flexible camera image processing framework.ACM Transactions on Graphics (ToG), 33(6):1–13, 2014

Felix Heide, Markus Steinberger, Yun-Ta Tsai, Mushfiqur Rouf, Dawid Paj ˛ ak, Dikpal Reddy, Orazio Gallo, Jing Liu, Wolfgang Heidrich, Karen Egiazarian, et al. Flexisp: A flexible camera image processing framework.ACM Transactions on Graphics (ToG), 33(6):1–13, 2014

work page 2014
[15]

Combettes Heinz H

Patrick L. Combettes Heinz H. Bauschke.Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, 2017

work page 2017
[16]

Gradient step denoiser for convergent plug-and-play.arXiv preprint arXiv:2110.03220, 2021

Samuel Hurault, Arthur Leclaire, and Nicolas Papadakis. Gradient step denoiser for convergent plug-and-play.arXiv preprint arXiv:2110.03220, 2021. 10

work page arXiv 2021
[17]

Proximal denoiser for convergent plug-and-play optimization with nonconvex regularization

Samuel Hurault, Arthur Leclaire, and Nicolas Papadakis. Proximal denoiser for convergent plug-and-play optimization with nonconvex regularization. InInternational Conference on Machine Learning, pages 9483–9505. PMLR, 2022

work page 2022
[18]

Denoising diffusion restoration models.Advances in neural information processing systems, 35:23593–23606, 2022

Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffusion restoration models.Advances in neural information processing systems, 35:23593–23606, 2022

work page 2022
[19]

Flowdps: Flow-driven posterior sampling for inverse problems

Jeongsol Kim, Bryan Sangwoo Kim, and Jong Chul Ye. Flowdps: Flow-driven posterior sampling for inverse problems. InProceedings of the IEEE/CVF International Conference on Computer Vision, pages 12328–12337, 2025

work page 2025
[20]

Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le. Flow matching for generative modeling. InThe Eleventh International Conference on Learning Representations, 2023. URLhttps://openreview.net/forum?id=PqvMRDCJT9t

work page 2023
[21]

Flow straight and fast: Learning to generate and transfer data with rectified flow

Xingchao Liu, Chengyue Gong, and qiang liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. InThe Eleventh International Conference on Learning Representations, 2023. URLhttps://openreview.net/forum?id=XVjTT1nw5z

work page 2023
[22]

Deep learning face attributes in the wild

Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. InProceedings of International Conference on Computer Vision (ICCV), December 2015

work page 2015
[23]

Pnp-flow: Plug-and-play image restoration with flow matching

Ségolène Martin, Anne Gagneux, Paul Hagemann, and Gabriele Steidl. Pnp-flow: Plug-and-play image restoration with flow matching. InInternational Conference on Learning Representations, 2025

work page 2025
[24]

Learning proximal operators: Using denoising networks for regularizing inverse imaging problems

Tim Meinhardt, Michael Moller, Caner Hazirbas, and Daniel Cremers. Learning proximal operators: Using denoising networks for regularizing inverse imaging problems. InProceedings of the IEEE international conference on computer vision, pages 1781–1790, 2017

work page 2017
[25]

Proximal algorithms.Foundations and Trends in optimization, 1(3):127–239, 2014

Neal Parikh and Stephen Boyd. Proximal algorithms.Foundations and Trends in optimization, 1(3):127–239, 2014

work page 2014
[26]

Training-free linear image inverses via flows.arXiv preprint arXiv:2310.04432, 2023

Ashwini Pokle, Matthew J Muckley, Ricky TQ Chen, and Brian Karrer. Training-free linear image inverses via flows.arXiv preprint arXiv:2310.04432, 2023

work page arXiv 2023
[27]

Flower: A flow-matching solver for inverse problems

Mehrsa Pourya, Bassam El Rawas, and Michael Unser. Flower: A flow-matching solver for inverse problems. InInternational Conference on Learning Representations, 2026

work page 2026
[28]

Plug-and-play image restoration with stochastic denoising regularization

Marien Renaud, Jean Prost, Arthur Leclaire, and Nicolas Papadakis. Plug-and-play image restoration with stochastic denoising regularization. InForty-first International Conference on Machine Learning, 2024

work page 2024
[29]

One network to solve them all–solving linear inverse problems using deep projection models

JH Rick Chang, Chun-Liang Li, Barnabas Poczos, BVK Vijaya Kumar, and Aswin C Sankara- narayanan. One network to solve them all–solving linear inverse problems using deep projection models. InProceedings of the IEEE International Conference on Computer Vision, pages 5888–5897, 2017

work page 2017
[30]

The little engine that could: Regularization by denoising (red).SIAM journal on imaging sciences, 10(4):1804–1844, 2017

Yaniv Romano, Michael Elad, and Peyman Milanfar. The little engine that could: Regularization by denoising (red).SIAM journal on imaging sciences, 10(4):1804–1844, 2017

work page 2017
[31]

Plug-and-play methods provably converge with properly trained denoisers

Ernest Ryu, Jialin Liu, Sicheng Wang, Xiaohan Chen, Zhangyang Wang, and Wotao Yin. Plug-and-play methods provably converge with properly trained denoisers. InInternational Conference on Machine Learning, pages 5546–5557. PMLR, 2019

work page 2019
[32]

Improving and generalizing flow-based genera- tive models with minibatch optimal transport.Transactions on Machine Learning Research,

Alexander Tong, Kilian FATRAS, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based genera- tive models with minibatch optimal transport.Transactions on Machine Learning Research,

work page
[33]

URLhttps://openreview.net/forum?id=CD9Snc73AW

ISSN 2835-8856. URLhttps://openreview.net/forum?id=CD9Snc73AW

work page
[34]

Plug-and-play priors for model based reconstruction

Singanallur V Venkatakrishnan, Charles A Bouman, and Brendt Wohlberg. Plug-and-play priors for model based reconstruction. In2013 IEEE global conference on signal and information processing, pages 945–948. IEEE, 2013. 11

work page 2013
[35]

Lipschitz regularity of deep neural networks: analysis and efficient estimation.Advances in neural information processing systems, 31, 2018

Aladin Virmaux and Kevin Scaman. Lipschitz regularity of deep neural networks: analysis and efficient estimation.Advances in neural information processing systems, 31, 2018

work page 2018
[36]

Learning deep cnn denoiser prior for image restoration

Kai Zhang, Wangmeng Zuo, Shuhang Gu, and Lei Zhang. Learning deep cnn denoiser prior for image restoration. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 3929–3938, 2017

work page 2017
[37]

Flow priors for linear inverse problems via iterative corrupted trajectory matching.Advances in Neural Information Processing Systems, 37:57389–57417, 2024

Yasi Zhang, Peiyu Yu, Yaxuan Zhu, Yingshan Chang, Feng Gao, Ying N Wu, and Oscar Leong. Flow priors for linear inverse problems via iterative corrupted trajectory matching.Advances in Neural Information Processing Systems, 37:57389–57417, 2024

work page 2024
[38]

Denoising diffusion models for plug-and-play image restoration

Yuanzhi Zhu, Kai Zhang, Jingyun Liang, Jiezhang Cao, Bihan Wen, Radu Timofte, and Luc Van Gool. Denoising diffusion models for plug-and-play image restoration. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1219–1229, 2023. A Proofs Proof of Remark 1.Forx 1 =xwe havex t =tx+ (1−t)x 0. By the law of total expecta...

work page 2023