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arxiv: 2605.28711 · v2 · pith:U7DAL6M4new · submitted 2026-05-27 · 💻 cs.LG

Stage-wise Distortion-Perception Traversal in Zero-shot Inverse Problems with Diffusion Models

Jiawei Zhang , Ziyuan Liu , Leon Yan , Zhenyu Xiao , Yuantao Gu This is my paper

Pith reviewed 2026-06-29 13:27 UTC · model grok-4.3

classification 💻 cs.LG
keywords diffusion modelsinverse problemsdistortion-perception tradeoffMAP estimationposterior samplingzero-shotlatent diffusion
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The pith

A two-stage diffusion method achieves flexible distortion-perception traversal in zero-shot inverse problems.

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

The paper introduces MAP-RPS as a stage-wise framework that lets a single diffusion model navigate the distortion-perception tradeoff in Bayesian inverse problems. It first applies MAP estimation to approximate the MMSE solution and deliver a low-distortion starting point. A subsequent re-noised posterior sampling stage then progressively raises perceptual quality. Theoretical analyses back the validity of each stage, and the method extends to latent diffusion models for wider use. Experiments indicate stronger traversal performance across inverse tasks than prior approaches.

Core claim

The authors claim that the MAP-RPS method, consisting of an MAP estimation stage that approximates the MMSE solution followed by a re-noised posterior sampling stage that improves perceptual quality, enables effective stage-wise traversal of the distortion-perception tradeoff in zero-shot inverse problems with diffusion models, with theoretical support for both stages and an extension to latent space.

What carries the argument

The MAP-RPS framework, where an MAP estimation stage supplies low-distortion initialization and a re-noised posterior sampling stage raises perceptual quality.

If this is right

  • Users gain inference-time control over the distortion-perception balance without retraining the diffusion model.
  • The approach works as an efficient solver for real-world inverse problems.
  • Extension to latent space allows use of large pre-trained latent diffusion backbones.
  • Theoretical analyses establish validity for the two stages separately.

Where Pith is reading between the lines

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

  • Similar staged initialization followed by sampling might apply to other generative models for inverse problems.
  • Task-specific tuning of the switch point between stages could further optimize results for particular applications.
  • The method may reduce the need for multiple specialized models when perceptual preferences vary across users.

Load-bearing premise

The MAP estimation stage reliably approximates the MMSE solution and the re-noised posterior sampling stage improves perceptual quality without instability or new artifacts.

What would settle it

An experiment in which re-noised posterior sampling after the MAP stage fails to raise perceptual metrics or produces results no better than standard posterior sampling on the same tasks.

Figures

Figures reproduced from arXiv: 2605.28711 by Jiawei Zhang, Leon Yan, Yuantao Gu, Zhenyu Xiao, Ziyuan Liu.

Figure 1
Figure 1. Figure 1: Distortion–Perception tradeoff of different algorithms on FFHQ. 3.3. MAP-RPS in latent space In this section, we extend the proposed MAP-RPS frame￾work to latent diffusion models, referred to as LMAP-RPS. Latent diffusion models introduce an encoder E and a de￾coder D to establish a mapping between the original data space and a lower-dimensional latent space in which a diffu￾sion model is trained. We denot… view at source ↗
Figure 2
Figure 2. Figure 2: Visualizations of MAP-RPS and LMAP-RPS with varying t0 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The performance of LMAP-RPS on 8× super-resolution, 4× compressed sensing and 128 × 128 box inpainting on FFHQ (σy = 0.1). no longer covered by Theorem 3.2 or Theorem C.2. To further evaluate the proposed method under challenging settings, we consider inverse problems with substantially more severe degradations, which are expected to induce more complex posterior structures. The considered tasks include 8×… view at source ↗
Figure 4
Figure 4. Figure 4: D-P curve of LMAP-RPS on 128 × 128 box inpainting on ImageNet with σy = 0.1. x y t0 = 0 t0 = 200 t0 = 400 t0 = 600 t0 = 800 I n p a i n t i n g ( 1 2 8 £ 1 2 8 B o x ) LMAP-RPS [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison with different posterior samplers and initialization methods. asymptotically consistent posterior sampling methods (Xu & Chi, 2024). Since our Stage 2 is not restricted to a particular sampler, integrating these methods into MAP-RPS and developing a more refined theoretical understanding are promising directions for future work. E.4. Alternative Stage 1 estimators. The MAP solver proposed in Sta… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between CCDF and MAP-RPS under the same zero-shot setting on FFHQ. posterior sampling stage, while our analysis focuses on the perceptual error, measured by W2, in the RPS stage. One may note that CCDF also discusses different diffusion processes. These processes mainly correspond to different parameterizations of the drift and diffusion terms. Since such parameterizations are equivalent up to a… view at source ↗
Figure 8
Figure 8. Figure 8: The performance of MAP-RPS and LMAP-RPS on the denoising task (σy = 0.3) on FFHQ with varying t1. F. Ablation studies F.1. Influence of t1 on the MAP estimation In Theorem 3.3, we approximate the stochastic gradient of the prior term using a fixed diffusion time step t1. Note that Theorem 3.3 relies on the following assumption: pX0|Xt1 (x0|xt1 ) ∝ N E [X0|Xt1 = xt1 ] , r2 t1 I  . (83) This assumption is g… view at source ↗
Figure 9
Figure 9. Figure 9: The performance of MAP-RPS and LMAP-RPS on the inpainting task (σy = 0.1) on FFHQ with varying w. 0 200 400 600 800 1000 t0 0.056 0.058 0.060 0.062 0.064 R M S E # MAP-RPS 0 200 400 600 800 1000 t0 0.054 0.056 0.058 0.060 0.062 0.064 0.066 R M S E # LMAP-RPS 9.0 9.5 10.0 10.5 11.0 11.5 p FID # 9.0 9.5 10.0 10.5 11.0 11.5 12.0 p FID # RMSE p FID [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The performance of MAP-RPS and LMAP-RPS on the super-resolution task (σy = 0.1) on FFHQ with varying t0. while LMAP-RPS exhibits a much milder degradation. This behavior aligns with our expectations: the VAE latent space is typically well modeled as a mixture of Gaussians, and in many regions it is dominated by a single Gaussian mode. This property closely matches the approximate validity of the assumptio… view at source ↗
Figure 11
Figure 11. Figure 11: D-P curves of MAP-RPS and DPS with sample averaging. F.3. Performance with a full range of t0 Here we present a more comprehensive analysis of how RMSE and FID vary with respect to t0 for both MAP-RPS and LMAP-RPS. We consider t0 ∈ {0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000} on the 4× super-resolution task on FFHQ, and the results are shown in [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: D-P curves of MAP-RPS and DPS with reduced discretization steps. F.4. Combining with empirical strategies Here we investigate the possibility of combining MAP-RPS with empirical strategies discussed in Appendix A, namely sample averaging and reducing the number of discretization steps. We select the MAP-RPS with an appropriate t0 that achieves the best FID as the base algorithm and apply the two strategie… view at source ↗
Figure 13
Figure 13. Figure 13: The performance of MAP-RPS and LMAP-RPS on the inpainting task (σy = 0.1) on FFHQ with varying N [PITH_FULL_IMAGE:figures/full_fig_p030_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Samples obtained by LMAP-RPS with varying t0 on 8× super-resolution, 4× compressed sensing and 128 × 128 box inpainting on FFHQ (σy = 0.1). 32 [PITH_FULL_IMAGE:figures/full_fig_p032_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Visualizations of D-P traversal of MAP-RPS, LMAP-RPS, VSDPS, PSCGAN-A, and PSCGAN-z on the denoising task (σy = 0.3) on FFHQ. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Visualizations of D-P traversal of MAP-RPS, LMAP-RPS, VSDPS, PSCGAN-A, and PSCGAN-z on the inpainting task (σy = 0.1) on FFHQ. 34 [PITH_FULL_IMAGE:figures/full_fig_p034_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Visualizations of D-P traversal of MAP-RPS, LMAP-RPS, VSDPS, PSCGAN-A, and PSCGAN-z on the anisotropic deblurring task (σy = 0.0) on FFHQ. 35 [PITH_FULL_IMAGE:figures/full_fig_p035_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Visualizations of D-P traversal of MAP-RPS, LMAP-RPS, VSDPS, PSCGAN-A, and PSCGAN-z on the super-resolution task (σy = 0.1) on FFHQ. 36 [PITH_FULL_IMAGE:figures/full_fig_p036_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Qualitative comparison of eleven inverse algorithms on inpainting, super-resolution, and anisotropic deblurring on MS-COCO. 37 [PITH_FULL_IMAGE:figures/full_fig_p037_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Qualitative comparison of eleven inverse algorithms on compressed sensing, high dynamic range reconstruction, and nonlinear deblurring on MS-COCO. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_20.png] view at source ↗
read the original abstract

The distortion-perception (D-P) tradeoff is a fundamental phenomenon of Bayesian inverse problems, which characterizes the inherent tension between distortion performance and perceptual quality. Enabling flexible traversal of the D-P tradeoff at inference time is crucial for practical applications. Despite the recent success of diffusion models in zero-shot inverse problem solving, efficient and principled strategies for D-P traversal in diffusion-based inverse algorithms remain inadequately characterized. In this paper, we propose a stage-wise framework for realizing D-P traversal using a single diffusion model in zero-shot inverse problems. Our proposed method, termed MAP-RPS, starts with an MAP estimation stage that approximates the MMSE solution and provides a low-distortion initialization, followed by a re-noised posterior sampling stage that progressively improves perceptual quality. We provide theoretical analyses for both stages, establishing the validity and effectiveness of the proposed design. Furthermore, we extend MAP-RPS to the latent space, yielding LMAP-RPS, which enjoys broader applicability by leveraging large-scale pre-trained latent diffusion backbones. Extensive experiments demonstrate that MAP-RPS and LMAP-RPS enable more effective D-P traversal on various tasks, while also exhibiting strong performance as efficient solvers for real-world inverse problems.

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

1 major / 0 minor

Summary. The paper proposes MAP-RPS, a stage-wise framework for distortion-perception (D-P) traversal in zero-shot inverse problems using diffusion models. It begins with an MAP estimation stage that approximates the MMSE solution to provide a low-distortion initialization, followed by a re-noised posterior sampling (RPS) stage that progressively improves perceptual quality. Theoretical analyses are provided to establish the validity of both stages. The method is extended to latent space as LMAP-RPS for use with large-scale pre-trained latent diffusion models. Experiments on various tasks demonstrate effective D-P traversal and strong performance as inverse problem solvers.

Significance. If the theoretical analyses hold and the experiments are reproducible, the work provides a principled, single-model approach to flexibly traversing the D-P tradeoff at inference time in zero-shot settings. This addresses a practical gap in diffusion-based inverse algorithms and could enable better control in applications like image restoration, with the latent extension broadening applicability to large models.

major comments (1)
  1. [Theoretical analyses for MAP estimation stage] The theoretical analysis of the MAP stage (claimed to approximate the MMSE solution) does not appear to state explicit conditions under which the approximation holds for the non-Gaussian, multimodal posteriors that arise in diffusion models for image inverse problems. In general Bayesian settings the mode and mean diverge outside local Gaussianity or small-noise regimes; without this regime being specified, the low-distortion initialization premise and the subsequent RPS analysis rest on an unsecured step.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The theoretical analysis of the MAP stage (claimed to approximate the MMSE solution) does not appear to state explicit conditions under which the approximation holds for the non-Gaussian, multimodal posteriors that arise in diffusion models for image inverse problems. In general Bayesian settings the mode and mean diverge outside local Gaussianity or small-noise regimes; without this regime being specified, the low-distortion initialization premise and the subsequent RPS analysis rest on an unsecured step.

    Authors: We agree that the manuscript would benefit from explicitly stating the conditions under which the MAP approximation to the MMSE solution is valid. The current theoretical analysis relies on the diffusion model's posterior properties but does not delineate the regime (e.g., local Gaussianity or small-noise settings) for multimodal cases. In the revised manuscript, we will add a paragraph in the MAP stage analysis section to specify these assumptions and discuss their relevance to the D-P traversal framework, thereby strengthening the foundation for both the initialization and the RPS stage. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation rests on independent theoretical analyses

full rationale

The paper's central claims rest on an MAP estimation stage approximating MMSE followed by re-noised posterior sampling, with explicit statements that theoretical analyses establish validity for both stages. No equations or steps in the abstract reduce by construction to fitted inputs, self-definitions, or self-citation chains; the analyses are presented as external to the method itself. The derivation chain is therefore self-contained against the provided description.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No details on free parameters, axioms, or invented entities are provided in the abstract.

pith-pipeline@v0.9.1-grok · 5752 in / 1076 out tokens · 30891 ms · 2026-06-29T13:27:39.504323+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

3 extracted references · 1 canonical work pages

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    Song, J., Meng, C., and Ermon, S

    URL https://openreview.net/forum? id=j8hdRqOUhN. Song, J., Meng, C., and Ermon, S. Denoising diffu- sion implicit models. InInternational Conference on Learning Representations, 2021a. URL https:// openreview.net/forum?id=St1giarCHLP. Song, J., Vahdat, A., Mardani, M., and Kautz, J. Pseudoinverse-guided diffusion models for inverse prob- lems. InInternati...

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    UniRepLKNet: A Universal Perception Large -Kernel ConvNet for Audio, Video, Point Cloud, Time -Series and Image Recognition,

    URL https://openreview.net/forum? id=GcvLoqOoXL. 11 Stage-wise Distortion–Perception Traversal in Zero-shot Inverse Problems with Diffusion Models Xu, X. and Chi, Y . Provably robust score-based diffusion posterior sampling for plug-and-play image reconstruc- tion.Advances in Neural Information Processing Systems, 37:36148–36184, 2024. Xue, Z., Cai, P., Y...

    work page doi:10.1109/cvpr52733.2024.00663 2024

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    local MAP

    that characterizes a fundamental property of strongly log-concave densities. Lemma B.2.(Brascamp & Lieb, 1976) Suppose that −logp(x) is twice continuously differentiable and strongly convex. Then for any test functionh, the following inequality holds: E|h(x)−E(h(x))| 2 ≤E h ∇h(x)T ∇2(−logp(x)) −1 ∇h(x) i .(29) The next lemma establishes a differential equ...

    1976