Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models

Joseph Keshet; Michael Elad; Roi Benita

arxiv: 2602.07715 · v2 · pith:F3SAMOM4new · submitted 2026-02-07 · 💻 cs.LG

Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models

Roi Benita , Michael Elad , Joseph Keshet This is my paper

Pith reviewed 2026-05-21 13:24 UTC · model grok-4.3

classification 💻 cs.LG

keywords diffusion modelsposterior samplinginverse problemszero-shot reconstructionspectral analysisparameter designGaussian priorsignal recovery

0 comments

The pith

Under a Gaussian prior assumption, both the ideal posterior sampler and diffusion-based reconstruction algorithms admit closed-form expressions in the spectral domain.

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

The paper studies zero-shot diffusion methods for recovering signals from degraded measurements by treating them as approximate posterior samplers. It assumes the signal prior is Gaussian and derives closed-form representations for both the ideal posterior sampler and the diffusion algorithms directly in the spectral domain. These representations make it possible to compare how each method incorporates the observations and to analyze their behavior step by step. The closed forms then support a method-agnostic framework that selects parameters by jointly considering the prior statistics, the specific degradation, and the diffusion dynamics. The resulting parameter choices differ from common heuristics and vary with diffusion step size to maintain a consistent trade-off between fidelity and perceptual quality.

Core claim

Under the Gaussianity assumption of the prior, both the ideal posterior sampler and diffusion-based reconstruction algorithms can be expressed in closed-form in the spectral domain. This enables their thorough analysis and comparisons, and supports a principled framework for parameter design that jointly accounts for the characteristics of the prior, the degraded signal, and the diffusion dynamics. The framework replaces heuristic selection and produces recommendations that differ structurally from standard approaches while varying with diffusion step size.

What carries the argument

Closed-form spectral-domain expressions for the ideal posterior sampler and the diffusion-based reconstruction algorithms under the Gaussian prior assumption.

If this is right

Parameter selection can be made specific to the prior covariance, the measurement operator, and the current diffusion timestep instead of relying on fixed heuristics.
The chosen parameters produce a more consistent balance between signal fidelity and perceptual quality across different degradation levels.
The framework applies uniformly to any diffusion-based zero-shot reconstruction method once the spectral representations are available.
Recommendations change explicitly with diffusion step size, so earlier and later steps receive different guidance.

Where Pith is reading between the lines

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

The same spectral analysis could serve as a diagnostic tool to detect when a real signal distribution deviates enough from Gaussian to require different handling.
The closed-form expressions might be used to initialize or correct non-Gaussian samplers by matching low-order moments in the frequency domain.
Traditional linear inverse-problem solvers could be re-derived as special cases of the same spectral framework to clarify their relation to diffusion methods.

Load-bearing premise

The signal prior must be Gaussian; substantial deviation from Gaussian statistics removes the justification for the closed-form spectral expressions and the derived parameter recommendations.

What would settle it

Running the diffusion sampler on synthetic data drawn exactly from a Gaussian prior and checking whether the observed spectral trajectories match the derived closed-form expressions at each step; clear mismatch would falsify the analysis.

Figures

Figures reproduced from arXiv: 2602.07715 by Joseph Keshet, Michael Elad, Roi Benita.

**Figure 1.** Figure 1: Spectral recommendations for the weighting coefficients ζ in DPS for different numbers of diffusion steps S ∈ [5, 30, 50, 70, 100, 120], with variability across realizations. Next, we compare our spectral recommendations with the weighting scheme used in DPS (Chung et al., 2022a) under the same experimental setting. Since these weights are chosen heuristically, we manually evaluate several values of ζ ′ … view at source ↗

**Figure 2.** Figure 2: Comparison between the spectral recommendations (red) and DPS weighting coefficients for 70 diffusion steps, evaluated for different heuristic values of ζ ′ ∈ {0.1, 0.3, 0.5, 0.7, 1.0}. This exact solution serves as an idealized reference for evaluating the different methods and is generally unavailable in practice. While some heuristic choices outperform others, the spectral recommendation consistently a… view at source ↗

**Figure 4.** Figure 4: shows the spectral weights obtained for the FFHQ dataset under LPF degradation with V = 0.1 and σy = 0.1, across different diffusion step counts. For comparison, we also include the weighting heuristics used by DPS, averaged over 100 syntheses, with variability indicated. Interestingly, the optimization reveals different weight structures with guidance values that increase over diffusion steps. While the D… view at source ↗

**Figure 5.** Figure 5: Covariance matrix obtained for d = 50 and l = 0.05. H.1. ΠGDM algorithm Here, we derive spectral recommendations for the ΠGDM algorithm under the setup introduced in Section 6.1. In the original formulation of ΠGDM, the heuristic parameter rs plays a dual role: it both controls the uncertainty at diffusion step s and serves as a weighting term for the likelihood component in the inference equation (see Eq.… view at source ↗

**Figure 6.** Figure 6: Figures 6a and 6b show the spectral recommendations for the ΠGDM weighting coefficients gs and rs, respectively. Results are shown for different diffusion step counts, with the standard deviation across realizations. The original ΠGDM heuristics indicated in black curves [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of the Wasserstein-2 distance for ΠGDM heuristic values, the spectral recommendations applied to ΠGDM (red), and the analytically derived ideal posterior sampler (black), across different number of diffusion steps S ∈ {5, 10, 15, 20, 30, 50, 70, 100, 120, 150}. I. Prior Sampling Results I.1. ImageNet spectral recommendation [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗

**Figure 8.** Figure 8: Comparison of spectral recommendations on the ImageNet 256 dataset, with a zoomed-in view of the DPS heuristics for selected diffusion steps S ∈ {50, 70, 100, 150}. and different degradation settings [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗

**Figure 9.** Figure 9: Qualitative comparison of visual results on ImageNet. Each row shows the reference image, the degraded measurement, samples obtained using the DPS heuristic at 100, 200, and 400 diffusion steps (from left to right), and samples obtained using the proposed spectral recommendations at the same step counts [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗

**Figure 10.** Figure 10: Qualitative comparison of visual results on the ImageNet dataset. Each row shows the reference image, the degraded observation with V = 0.1 and σy = 0.1, and samples obtained using the DPS heuristic and the proposed spectral weighting, both evaluated at 500 diffusion steps. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗

**Figure 11.** Figure 11: Qualitative comparison of posterior samples under a fixed observation. The top row shows the reference image (left) and the corresponding degraded observation (right). Subsequent rows present reconstructions using different guidance schemes: the DPS heuristic (top), spectral recommendations (middle), and the realization-specific spectral variant with k = 1 (bottom). Samples corresponding to 100, 200, and … view at source ↗

**Figure 12.** Figure 12: Qualitative comparison of posterior samples under a fixed observation. The top row shows the reference image (left) and the corresponding degraded observation (right). Subsequent rows present reconstructions using different guidance schemes: the DPS heuristic (top), spectral recommendations (middle), and the realization-specific spectral variant with k = 1 (bottom). Samples corresponding to 100, 200, and … view at source ↗

read the original abstract

Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based solution that leverages prior knowledge. Such algorithms incorporate the observations through inference, often leaning on manual tuning and heuristics. In this work we propose a rigorous analysis of these approximate posterior samplers, relying on a Gaussianity assumption of the prior. Under this regime, we show that both the ideal posterior sampler and diffusion-based reconstruction algorithms can be expressed in closed-form, enabling their thorough analysis and comparisons in the spectral domain. Building on these representations, we introduce a principled framework for parameter design, replacing heuristic selection strategies used to date. The proposed approach is method-agnostic and yields tailored parameter choices that jointly account for the characteristics of the prior, the degraded signal, and the diffusion dynamics. We show that our spectral recommendations differ structurally from standard heuristics and vary with the diffusion step size, resulting in a consistent balance between perceptual quality and signal fidelity.

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

Closed-form spectral expressions under Gaussian priors let them replace heuristics with a step-size-dependent parameter design for diffusion posterior sampling.

read the letter

The main thing to know is that this paper works out closed-form spectral representations for both the ideal posterior sampler and the diffusion-based approximations, all under an explicit Gaussian prior assumption, then turns those into a method-agnostic way to pick parameters that account for the prior, the measurements, and the diffusion dynamics at each step. The resulting recommendations differ structurally from common heuristics and change with timestep, which is the concrete advance here. It gives a clean way to compare the ideal and approximate cases in the frequency domain without having to run experiments for every choice. That part is useful for anyone already working in diffusion inverse problems who wants to move past manual tuning. The derivations look reproducible on paper because they stay inside the Gaussian regime and compare directly to the ideal posterior. The soft spot is exactly the scope of that assumption. Real signals are rarely Gaussian, and the abstract does not report sensitivity checks or tests on non-Gaussian data, so it is unclear how much the parameter suggestions carry over when the prior or the trained diffusion model deviates. That keeps the practical payoff provisional until more validation appears. This is for specialists in zero-shot diffusion solvers for inverse problems. A reader who already knows the posterior sampling literature will see the value in the spectral comparisons and the parameter framework. I would send it for peer review. The analytical contribution is grounded enough under its stated conditions to merit referee attention, even if revisions will be needed to tighten the claims about generality.

Referee Report

0 major / 3 minor

Summary. The paper analyzes zero-shot diffusion-based posterior sampling for inverse problems under an explicit Gaussian prior assumption. It derives closed-form spectral-domain expressions for both the ideal posterior sampler and approximate diffusion-based reconstruction algorithms, enabling direct comparisons. Building on these, it proposes a principled, method-agnostic framework for selecting parameters that jointly incorporate prior statistics, the degraded observation, and diffusion dynamics, with the goal of balancing perceptual quality and signal fidelity while replacing heuristic tuning.

Significance. If the Gaussian prior assumption is reasonable for the target signals, the closed-form spectral analysis provides a clear theoretical lens for understanding the behavior of diffusion-based samplers and for designing parameters in a non-heuristic way. The explicit incorporation of diffusion step size into the recommendations and the structural difference from standard heuristics are notable strengths. The work supplies reproducible derivations rather than purely empirical tuning, which supports its utility within the stated regime.

minor comments (3)

The abstract states that the spectral recommendations 'differ structurally from standard heuristics and vary with the diffusion step size,' but the manuscript would benefit from a concise table or figure in the main text that directly contrasts the derived expressions against common heuristic choices (e.g., fixed guidance scales) for at least two representative step sizes.
No error bars or sensitivity analysis with respect to the Gaussian covariance parameters or diffusion model training imperfections are described; adding a short robustness check (even under the maintained Gaussian assumption) would strengthen the practical claims without altering the central derivation.
Notation for the spectral representations (e.g., definitions of the power spectra or the precise mapping from diffusion time to frequency-domain operators) should be collected in a single preliminary section or table to improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, recognition of the theoretical contributions under the Gaussian prior regime, and recommendation for minor revision. We appreciate the emphasis on the closed-form spectral analysis, method-agnostic parameter framework, and structural differences from heuristics. Since no specific major comments were raised in the report, we will use the minor revision to improve clarity, add minor clarifications on assumptions, and enhance reproducibility without altering the core claims.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central derivations are explicitly scoped to the Gaussian prior regime and consist of closed-form spectral representations of the ideal posterior sampler and diffusion-based algorithms. These are obtained by direct mathematical manipulation under the stated assumption rather than by fitting parameters to data or by self-referential definitions. No load-bearing step reduces to a fitted input renamed as prediction, a self-citation chain, or an ansatz smuggled via prior work; the framework for parameter design follows from the derived expressions and is presented as method-agnostic within the Gaussian setting. The analysis therefore remains self-contained against the external ideal posterior benchmark and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on one explicit modeling assumption and no new invented entities. The Gaussian prior is treated as an analysis regime rather than a fitted parameter.

axioms (1)

domain assumption The unknown signal is drawn from a Gaussian distribution.
Invoked in the abstract as the regime that permits closed-form expressions for both the ideal posterior and the diffusion-based samplers.

pith-pipeline@v0.9.0 · 5707 in / 1440 out tokens · 34220 ms · 2026-05-21T13:24:25.768084+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.

Under this regime, we show that both the ideal posterior sampler and diffusion-based reconstruction algorithms can be expressed in closed-form, enabling their thorough analysis and comparisons in the spectral domain.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean costAlphaLog_high_calibrated_iff unclear

?

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

the optimal denoiser admits the following closed-form expression: x∗0=(α¯tΣ0+(1−α¯t)I)−1(√α¯tΣ0xt+(1−α¯t)μ0)

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

19 extracted references · 19 canonical work pages · 2 internal anchors

[1]

Exploiting the exact denoising posterior score in training-free guidance of diffusion models.arXiv preprint arXiv:2506.13614,

Bellchambers, G. Exploiting the exact denoising posterior score in training-free guidance of diffusion models.arXiv preprint arXiv:2506.13614,

work page arXiv
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Spectral analysis of dif- fusion models with application to schedule design.arXiv preprint arXiv:2502.00180,

Benita, R., Elad, M., and Keshet, J. Spectral analysis of dif- fusion models with application to schedule design.arXiv preprint arXiv:2502.00180,

work page arXiv
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On the trajectory regularity of ode-based diffusion sampling

Chen, D., Zhou, Z., Wang, C., Shen, C., and Lyu, S. On the trajectory regularity of ode-based diffusion sampling. arXiv preprint arXiv:2405.11326,

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Ilvr: Conditioning method for denoising diffusion probabilistic models,

Choi, J., Kim, S., Jeong, Y ., Gwon, Y ., and Yoon, S. Ilvr: Conditioning method for denoising diffusion probabilistic models.arXiv preprint arXiv:2108.02938,

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Diffusion Posterior Sampling for General Noisy Inverse Problems

Chung, H., Kim, J., Mccann, M. T., Klasky, M. L., and Ye, J. C. Diffusion posterior sampling for general noisy in- verse problems.arXiv preprint arXiv:2209.14687, 2022a. Chung, H., Sim, B., Ryu, D., and Ye, J. C. Improving diffusion models for inverse problems using manifold constraints.Advances in Neural Information Processing Systems, 35:25683–25696, 20...

work page internal anchor Pith review Pith/arXiv arXiv
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Z., Salakhut- dinov, R., et al

He, Y ., Murata, N., Lai, C.-H., Takida, Y ., Uesaka, T., Kim, D., Liao, W.-H., Mitsufuji, Y ., Kolter, J. Z., Salakhut- dinov, R., et al. Manifold preserving guided diffusion. arXiv preprint arXiv:2311.16424,

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Kastryulin, S., Zakirov, J., Prokopenko, D., and Dylov, D. V . Pytorch image quality: Metrics for image quality assess- ment.arXiv preprint arXiv:2208.14818,

work page arXiv
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Palette: Image-to-image diffusion models

Saharia, C., Chan, W., Chang, H., Lee, C., Ho, J., Salimans, T., Fleet, D., and Norouzi, M. Palette: Image-to-image diffusion models. InACM SIGGRAPH 2022 conference proceedings, pp. 1–10,

work page 2022
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Score-Based Generative Modeling through Stochastic Differential Equations

9 Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models Song, Y ., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Er- mon, S., and Poole, B. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456,

work page internal anchor Pith review Pith/arXiv arXiv 2011
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Tong, V ., Trung-Dung, H., Liu, A., Broeck, G. V . d., and Niepert, M. Learning to discretize denoising diffusion odes.arXiv preprint arXiv:2405.15506,

work page arXiv
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Wang, Y ., Yu, J., and Zhang, J. Zero-shot image restora- tion using denoising diffusion null-space model.arXiv preprint arXiv:2212.00490,

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Towards more accurate diffusion model acceleration with a timestep aligner.arXiv preprint arXiv:2310.09469,

Xia, M., Shen, Y ., Lei, C., Zhou, Y ., Yi, R., Zhao, D., Wang, W., and Liu, Y .-j. Towards more accurate diffusion model acceleration with a timestep aligner.arXiv preprint arXiv:2310.09469,

work page arXiv
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Guidance with spherical gaussian constraint for condi- tional diffusion.arXiv preprint arXiv:2402.03201,

Yang, L., Ding, S., Cai, Y ., Yu, J., Wang, J., and Shi, Y . Guidance with spherical gaussian constraint for condi- tional diffusion.arXiv preprint arXiv:2402.03201,

work page arXiv
[14]

The Reverse Process in the Time Domain Here, we present the reverse process in the time domain for the DDIM (Song et al., 2021)

= 0 Thus: (1−¯αt)Σ0HTH+σ 2 y ¯αtΣ0 +Iσ 2 y(1−¯αt) x0 = (1−¯αt)Σ0HTy+σ 2 y √¯αtΣ0xt +σ 2 y(1−¯αt)µ0 Finally: x∗ 0 = (1−¯αt)Σ0HTH+σ 2 y ¯αtΣ0 +Iσ 2 y(1−¯αt) −1 (27) (1−¯αt)Σ0HTy+σ 2 y √¯αtΣ0xt +σ 2 y(1−¯αt)µ0 B. The Reverse Process in the Time Domain Here, we present the reverse process in the time domain for the DDIM (Song et al., 2021). Letx 0 follow the ...

work page 2021
[15]

While forK= 1the average Wasserstein distance trivially reduces to the standard Wasserstein distance, we consider here the regime of largeK. The mean of the true posterior from 44 can be written as: µxF |y =µ F 0 +A(y F −Λ H µF 0 ) =Ay F + (I−AΛ H)µ F 0 where: A=Λ 0ΛH T (ΛHΛ0ΛH T +σ 2 nI)−1 Similarly, denoting the mean of the DPS posterior term using 65, ...

work page 2020
[16]

xs−1 = √¯αt−1ˆx0 + p 1−¯αt−1 −σ 2s(η)ϵ θ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 +σ s(η)zs.(54) where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1

framework under the Variance-Preserving (VP) parameterization (Song et al., 2020). xs−1 = √¯αt−1ˆx0 + p 1−¯αt−1 −σ 2s(η)ϵ θ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 +σ s(η)zs.(54) where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1 . We consider the deterministic setting, corresponding toη=

work page 2020
[17]

xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1ϵθ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 Using the marginal property, ϵθ(xs, s) = xs − √¯αsˆx0√1−¯αs .(55) which, substituted into Equation 54, gives: xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1 xs − √¯αsˆx0√1−¯αs −ζ i∇xt ∥y−H ˆx0∥2 2 xs−1 = √1−¯αs−1√1−¯αs xs + √¯αs−1 − √¯αs √1−¯αs−1√1−¯αs ˆx0 −ζ i∇xt ∥y−H ˆx0∥2 2 Introducing: as = √1−¯αs−1√1−¯αs I bs =...

work page 2025
[18]

where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1

inference process and the Variance-Preserving (VP) framework, the inference procedure usingΠGDM is formulated as: xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1 −σ 2s(η)ϵ θ(xs, s)(66) + √¯αs∇xs(ˆx0)THT ((r2 sHHT +σ 2 yI)−1)T (y−H ˆx0) +σ s(η)zs. where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1 . Since the VP formulation is already used for ˆx0, we omit the conversion factor ...

work page 2025
[19]

Reference Measurement DPS Heuristic Spectral Weights Figure 9.Qualitative comparison of visual results on ImageNet. Each row shows the reference image, the degraded measurement, samples obtained using the DPS heuristic at 100, 200, and 400 diffusion steps (from left to right), and samples obtained using the proposed spectral recommendations at the same st...

work page arXiv 2025

[1] [1]

Exploiting the exact denoising posterior score in training-free guidance of diffusion models.arXiv preprint arXiv:2506.13614,

Bellchambers, G. Exploiting the exact denoising posterior score in training-free guidance of diffusion models.arXiv preprint arXiv:2506.13614,

work page arXiv

[2] [2]

Spectral analysis of dif- fusion models with application to schedule design.arXiv preprint arXiv:2502.00180,

Benita, R., Elad, M., and Keshet, J. Spectral analysis of dif- fusion models with application to schedule design.arXiv preprint arXiv:2502.00180,

work page arXiv

[3] [3]

On the trajectory regularity of ode-based diffusion sampling

Chen, D., Zhou, Z., Wang, C., Shen, C., and Lyu, S. On the trajectory regularity of ode-based diffusion sampling. arXiv preprint arXiv:2405.11326,

work page arXiv

[4] [4]

Ilvr: Conditioning method for denoising diffusion probabilistic models,

Choi, J., Kim, S., Jeong, Y ., Gwon, Y ., and Yoon, S. Ilvr: Conditioning method for denoising diffusion probabilistic models.arXiv preprint arXiv:2108.02938,

work page arXiv

[5] [5]

Diffusion Posterior Sampling for General Noisy Inverse Problems

Chung, H., Kim, J., Mccann, M. T., Klasky, M. L., and Ye, J. C. Diffusion posterior sampling for general noisy in- verse problems.arXiv preprint arXiv:2209.14687, 2022a. Chung, H., Sim, B., Ryu, D., and Ye, J. C. Improving diffusion models for inverse problems using manifold constraints.Advances in Neural Information Processing Systems, 35:25683–25696, 20...

work page internal anchor Pith review Pith/arXiv arXiv

[6] [6]

Z., Salakhut- dinov, R., et al

He, Y ., Murata, N., Lai, C.-H., Takida, Y ., Uesaka, T., Kim, D., Liao, W.-H., Mitsufuji, Y ., Kolter, J. Z., Salakhut- dinov, R., et al. Manifold preserving guided diffusion. arXiv preprint arXiv:2311.16424,

work page arXiv

[7] [7]

Kastryulin, S., Zakirov, J., Prokopenko, D., and Dylov, D. V . Pytorch image quality: Metrics for image quality assess- ment.arXiv preprint arXiv:2208.14818,

work page arXiv

[8] [8]

Palette: Image-to-image diffusion models

Saharia, C., Chan, W., Chang, H., Lee, C., Ho, J., Salimans, T., Fleet, D., and Norouzi, M. Palette: Image-to-image diffusion models. InACM SIGGRAPH 2022 conference proceedings, pp. 1–10,

work page 2022

[9] [9]

Score-Based Generative Modeling through Stochastic Differential Equations

9 Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models Song, Y ., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Er- mon, S., and Poole, B. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456,

work page internal anchor Pith review Pith/arXiv arXiv 2011

[10] [10]

Tong, V ., Trung-Dung, H., Liu, A., Broeck, G. V . d., and Niepert, M. Learning to discretize denoising diffusion odes.arXiv preprint arXiv:2405.15506,

work page arXiv

[11] [11]

Zero-shot image restora- tion using denoising diffusion null-space model.arXiv preprint arXiv:2212.00490,

Wang, Y ., Yu, J., and Zhang, J. Zero-shot image restora- tion using denoising diffusion null-space model.arXiv preprint arXiv:2212.00490,

work page arXiv

[12] [12]

Towards more accurate diffusion model acceleration with a timestep aligner.arXiv preprint arXiv:2310.09469,

Xia, M., Shen, Y ., Lei, C., Zhou, Y ., Yi, R., Zhao, D., Wang, W., and Liu, Y .-j. Towards more accurate diffusion model acceleration with a timestep aligner.arXiv preprint arXiv:2310.09469,

work page arXiv

[13] [13]

Guidance with spherical gaussian constraint for condi- tional diffusion.arXiv preprint arXiv:2402.03201,

Yang, L., Ding, S., Cai, Y ., Yu, J., Wang, J., and Shi, Y . Guidance with spherical gaussian constraint for condi- tional diffusion.arXiv preprint arXiv:2402.03201,

work page arXiv

[14] [14]

The Reverse Process in the Time Domain Here, we present the reverse process in the time domain for the DDIM (Song et al., 2021)

= 0 Thus: (1−¯αt)Σ0HTH+σ 2 y ¯αtΣ0 +Iσ 2 y(1−¯αt) x0 = (1−¯αt)Σ0HTy+σ 2 y √¯αtΣ0xt +σ 2 y(1−¯αt)µ0 Finally: x∗ 0 = (1−¯αt)Σ0HTH+σ 2 y ¯αtΣ0 +Iσ 2 y(1−¯αt) −1 (27) (1−¯αt)Σ0HTy+σ 2 y √¯αtΣ0xt +σ 2 y(1−¯αt)µ0 B. The Reverse Process in the Time Domain Here, we present the reverse process in the time domain for the DDIM (Song et al., 2021). Letx 0 follow the ...

work page 2021

[15] [15]

While forK= 1the average Wasserstein distance trivially reduces to the standard Wasserstein distance, we consider here the regime of largeK. The mean of the true posterior from 44 can be written as: µxF |y =µ F 0 +A(y F −Λ H µF 0 ) =Ay F + (I−AΛ H)µ F 0 where: A=Λ 0ΛH T (ΛHΛ0ΛH T +σ 2 nI)−1 Similarly, denoting the mean of the DPS posterior term using 65, ...

work page 2020

[16] [16]

xs−1 = √¯αt−1ˆx0 + p 1−¯αt−1 −σ 2s(η)ϵ θ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 +σ s(η)zs.(54) where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1

framework under the Variance-Preserving (VP) parameterization (Song et al., 2020). xs−1 = √¯αt−1ˆx0 + p 1−¯αt−1 −σ 2s(η)ϵ θ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 +σ s(η)zs.(54) where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1 . We consider the deterministic setting, corresponding toη=

work page 2020

[17] [17]

xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1ϵθ(xs, s)−ζ i∇xt ∥y−H ˆx0∥2 2 Using the marginal property, ϵθ(xs, s) = xs − √¯αsˆx0√1−¯αs .(55) which, substituted into Equation 54, gives: xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1 xs − √¯αsˆx0√1−¯αs −ζ i∇xt ∥y−H ˆx0∥2 2 xs−1 = √1−¯αs−1√1−¯αs xs + √¯αs−1 − √¯αs √1−¯αs−1√1−¯αs ˆx0 −ζ i∇xt ∥y−H ˆx0∥2 2 Introducing: as = √1−¯αs−1√1−¯αs I bs =...

work page 2025

[18] [18]

where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1

inference process and the Variance-Preserving (VP) framework, the inference procedure usingΠGDM is formulated as: xs−1 = √¯αs−1ˆx0 + p 1−¯αs−1 −σ 2s(η)ϵ θ(xs, s)(66) + √¯αs∇xs(ˆx0)THT ((r2 sHHT +σ 2 yI)−1)T (y−H ˆx0) +σ s(η)zs. where: σs(η) =η r 1−¯αs−1 1−¯αs r 1− ¯αs ¯αs−1 . Since the VP formulation is already used for ˆx0, we omit the conversion factor ...

work page 2025

[19] [19]

Reference Measurement DPS Heuristic Spectral Weights Figure 9.Qualitative comparison of visual results on ImageNet. Each row shows the reference image, the degraded measurement, samples obtained using the DPS heuristic at 100, 200, and 400 diffusion steps (from left to right), and samples obtained using the proposed spectral recommendations at the same st...

work page arXiv 2025