arxiv: 2512.18365 · v2 · submitted 2025-12-20 · 💻 cs.CV · cs.LG

Recognition: 2 theorem links

· Lean Theorem

Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidance

Badr Moufad , Navid Bagheri Shouraki , Alain Oliviero Durmus , Thomas Hirtz , Eric Moulines , Jimmy Olsson , Yazid Janati

Authors on Pith no claims yet

Pith reviewed 2026-05-16 20:18 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords zero-shot inpaintingdiffusion modelslikelihood surrogateimage reconstructionefficient samplingobservation consistencyGaussian posterior

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The pith

A new likelihood surrogate for diffusion inpainting produces Gaussian posterior samples directly, eliminating backpropagation through the denoiser and cutting inference costs.

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

Diffusion models act as priors for filling missing image regions in a way that stays consistent with the visible parts. Earlier zero-shot techniques used surrogate likelihood scores whose gradients had to be computed through the denoiser at every reverse step, creating heavy memory and time costs. The paper replaces those surrogates with one that directly supplies simple Gaussian posterior transitions. This change keeps strong consistency with observed pixels and produces coherent fillings while lowering the overall inference expense compared with fine-tuned baselines.

Core claim

The central claim is that a new likelihood surrogate can be chosen so that the ideal guidance score is approximated well enough to yield valid Gaussian posterior transitions at each reverse diffusion step. Sampling from these transitions requires no vector-Jacobian products through the denoiser network, removing the main computational overhead of prior zero-shot diffusion inpainting methods while still enforcing observation consistency and high-quality reconstructions.

What carries the argument

The decoupled likelihood surrogate that produces simple Gaussian posterior transitions for the reverse diffusion process.

Load-bearing premise

The proposed likelihood surrogate accurately approximates the ideal score and yields valid Gaussian posterior transitions without backpropagation through the denoiser network.

What would settle it

Running the method and a backpropagation-based zero-shot baseline on the same pretrained diffusion model and the same inpainting benchmarks, then checking whether the new reconstructions show visibly lower consistency with observed regions or higher error metrics, would settle the claim.

Figures

Figures reproduced from arXiv: 2512.18365 by Alain Oliviero Durmus, Badr Moufad, Eric Moulines, Jimmy Olsson, Navid Bagheri Shouraki, Thomas Hirtz, Yazid Janati.

**Figure 1.** Figure 1: Zero-shot inpainting edits generated by DING (50 NFEs) for different masking patterns using Stable Diffusion 3.5 (medium). Given masked inputs (left column), the model fills the missing regions according to diverse textual prompts. of inverse problems, from image restoration to scientific imaging, and has demonstrated strong editing performance without task-specific training. While current zero-shot method… view at source ↗

**Figure 2.** Figure 2: Examples of reconstructions on FFHQ and DIV2K with 50 NFEs. we include both training and validation splits (900 images in total), and generate captions for each image using BLIP-2 (Li et al., 2023); see Appendix B for details. All FFHQ and DIV2K images are resized to a resolution of 768 × 768. The PIE-Bench dataset contains 700 images of resolution 512 × 512, each paired with an inpainting mask and an edit… view at source ↗

**Figure 3.** Figure 3: Latent-space masking and its correspondence to pixel space using a central square mask. The encoder [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

**Figure 4.** Figure 4: Performance of DING on DIV2K under varying NFE budgets (20 to 500) across different masking [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗

**Figure 5.** Figure 5: Effect of prompt precision on inpainting quality. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗

**Figure 6.** Figure 6: Effect of prompt precision on inpainting quality. [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of DING and finetuned SD3 on PIE-Bench. Both methods have the same runtime of 2.2s. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗

**Figure 8.** Figure 8: Comparison of DING and zero-shot baselines on PIE-Bench. All methods use 50 NFEs. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗

**Figure 9.** Figure 9: Comparison of DING and zero-shot baselines on PIE-Bench. All methods use 50 NFEs. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗

**Figure 10.** Figure 10: Comparison of DING and zero-shot baselines on PIE-Bench. All methods use 50 NFEs. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗

**Figure 11.** Figure 11: Comparison of DING and zero-shot baselines on PIE-Bench. All methods use 50 NFEs. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗

read the original abstract

Diffusion models have emerged as powerful priors for image editing tasks such as inpainting and local modification, where the objective is to generate realistic content that remains consistent with observed regions. In particular, zero-shot approaches that leverage a pretrained diffusion model, without any retraining, have been shown to achieve highly effective reconstructions. However, state-of-the-art zero-shot methods typically rely on a sequence of surrogate likelihood functions, whose scores are used as proxies for the ideal score. This procedure however requires vector-Jacobian products through the denoiser at every reverse step, introducing significant memory and runtime overhead. To address this issue, we propose a new likelihood surrogate that yields simple and efficient to sample Gaussian posterior transitions, sidestepping the backpropagation through the denoiser network. Our extensive experiments show that our method achieves strong observation consistency compared with fine-tuned baselines and produces coherent, high-quality reconstructions, all while significantly reducing inference cost. Code is available at https://github.com/YazidJanati/ding.

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 decoupled surrogate gives a practical efficiency win for zero-shot inpainting if its Gaussian approximation holds up over the full trajectory.

read the letter

The paper's main contribution is a new likelihood surrogate that produces simple Gaussian posterior transitions for the reverse diffusion process. This sidesteps the vector-Jacobian products through the denoiser that earlier zero-shot methods required at every step. The result is lower memory and runtime while still using a pretrained diffusion prior. They release code, which helps with checking the implementation directly. Experiments report that the method keeps observation consistency and produces coherent outputs, competitive with fine-tuned baselines but at reduced cost. That efficiency angle is the clearest practical takeaway. The soft spot is the surrogate itself. The claim that it yields valid Gaussian transitions without drift in the masked regions rests on the derivation matching the true conditional score closely enough across hundreds of timesteps. Any systematic mismatch in mean or variance would accumulate and weaken the constraint, even if per-step error looks small. The abstract and stress-test note both flag this as the load-bearing assumption, and the provided details do not include an explicit error bound or ablation on approximation quality. If the full paper shows a clean derivation plus controls that rule out drift, the result strengthens; otherwise the efficiency gain could come at the price of subtle inconsistencies. This work is aimed at researchers and practitioners doing zero-shot image editing who care about inference speed. A reader already familiar with diffusion guidance methods would get the most out of it. It deserves peer review because the technical move is distinct and the efficiency claim is testable with the released code, even if the soundness of the surrogate needs closer scrutiny.

Referee Report

2 major / 2 minor

Summary. The paper introduces a decoupled diffusion guidance surrogate for zero-shot inpainting that produces simple Gaussian posterior transitions p(x_{t-1}|x_t, y) without requiring vector-Jacobian products through the pretrained denoiser at each reverse step. It claims this yields strong observation consistency with observed regions, coherent high-quality reconstructions, and substantially lower inference cost than fine-tuned baselines, all while using only standard pretrained diffusion priors.

Significance. If the surrogate derivation holds and the Gaussian transitions remain valid without drift, the work would meaningfully advance practical zero-shot editing by removing a key computational bottleneck in conditioned diffusion sampling, enabling faster inference on standard hardware while retaining the flexibility of pretrained models.

major comments (2)

[Method] The central efficiency and consistency claims rest on the new likelihood surrogate producing mean and variance that match (or sufficiently approximate) those induced by the true conditional score at every timestep. The manuscript must supply the explicit derivation of this surrogate (including how it decouples guidance to avoid backpropagation) and any supporting analysis showing absence of systematic mismatch in masked regions, as even small per-step errors can accumulate over hundreds of reverse steps and violate the observation constraint.
[Experiments] §4 (Experiments): the reported consistency and quality gains versus fine-tuned baselines must be supported by controls that isolate the effect of the surrogate approximation error; without per-timestep error metrics or trajectory-drift ablations on the masked regions, it is unclear whether the observed performance stems from the proposed surrogate or from other implementation details.

minor comments (2)

[Abstract] The abstract states 'strong observation consistency' without naming the quantitative metrics (e.g., PSNR, LPIPS, or masked-region L2) used to support this; these should be stated explicitly.
[Method] Notation for the surrogate (mean/variance schedules, decoupling operator) should be introduced with a clear table or equation block to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments highlight important points regarding the surrogate derivation and the need for stronger experimental controls. We address each major comment below and have revised the manuscript to incorporate additional details and analyses.

read point-by-point responses

Referee: [Method] The central efficiency and consistency claims rest on the new likelihood surrogate producing mean and variance that match (or sufficiently approximate) those induced by the true conditional score at every timestep. The manuscript must supply the explicit derivation of this surrogate (including how it decouples guidance to avoid backpropagation) and any supporting analysis showing absence of systematic mismatch in masked regions, as even small per-step errors can accumulate over hundreds of reverse steps and violate the observation constraint.

Authors: We agree that the derivation and error analysis deserve more explicit presentation. Section 3.2 now contains the full step-by-step derivation of the decoupled Gaussian posterior p(x_{t-1}|x_t, y) (Equations 5–9), showing how the surrogate likelihood is constructed to eliminate the vector-Jacobian product through the denoiser while preserving the conditional mean and variance structure. A new subsection 3.3 has been added that provides both a theoretical bound on the per-step approximation error in masked regions and empirical plots of the accumulated drift over the full reverse trajectory. These additions confirm that the surrogate remains sufficiently accurate for the observation constraint to hold. revision: yes
Referee: [Experiments] §4 (Experiments): the reported consistency and quality gains versus fine-tuned baselines must be supported by controls that isolate the effect of the surrogate approximation error; without per-timestep error metrics or trajectory-drift ablations on the masked regions, it is unclear whether the observed performance stems from the proposed surrogate or from other implementation details.

Authors: We have expanded §4 with two new controls. First, we report per-timestep masked-region MSE between the generated trajectory and the ground-truth observation at every reverse step, averaged over the test set. Second, we include an ablation that compares the full method against a version that replaces the surrogate with exact (but expensive) guidance at selected timesteps, quantifying trajectory drift. These results, now shown in Figure 4 and Table 3, demonstrate that the performance advantage is attributable to the surrogate rather than other implementation choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces an independent likelihood surrogate for decoupled diffusion guidance that approximates the conditional score to enable Gaussian posterior transitions without VJP through the denoiser. This surrogate is presented as a novel construction leveraging standard pretrained diffusion priors rather than being defined in terms of the target result or fitted to the paper's own outputs. No load-bearing step reduces by construction to self-citation, ansatz smuggling, or renaming of known results; the central efficiency and consistency claims rest on the surrogate's explicit form and experimental validation against external baselines. The derivation chain remains self-contained against the pretrained model and does not invoke uniqueness theorems or self-referential fits.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach relies on the standard assumption that pretrained diffusion models act as effective image priors and introduces one new conceptual entity (the decoupled surrogate) without additional free parameters beyond the pretrained model weights.

axioms (1)

domain assumption Pretrained diffusion models serve as strong priors for generating content consistent with observed image regions.
Invoked to justify zero-shot use without retraining.

invented entities (1)

Decoupled diffusion guidance surrogate no independent evidence
purpose: To produce Gaussian posterior transitions that avoid vector-Jacobian products through the denoiser.
New construct introduced to achieve efficiency; no independent falsifiable evidence outside the method itself is stated.

pith-pipeline@v0.9.0 · 5496 in / 1131 out tokens · 20515 ms · 2026-05-16T20:18:00.333692+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 washburn_uniqueness_aczel unclear

?

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

we propose a new likelihood surrogate that yields simple and efficient to sample Gaussian posterior transitions, sidestepping the backpropagation through the denoiser network
IndisputableMonolith.Foundation.BranchSelection branch_selection unclear

?

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

ˆπθ s|t(xs|zs, xt, y) = N(xs[m]; μθ s|t(xt;η)[m], η²s Id−dy) × N( xs[m]; (1−γs|t)μθ s|t(xt;η)[m] + γs|t (αs y + σs ˆxθ 1(zs,s)[m]), α²s σ²y γs|t Idy )

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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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.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors
cs.LG 2026-05 unverdicted novelty 7.0

Diffusion model priors enable training-free Bayesian sampling for more accurate rain field reconstruction from path-integrated commercial microwave link measurements than Gaussian process baselines.

Reference graph

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URL https://openreview.net/forum?id=bwJxUB0y46. 15 Preprint under review Figure 3: Latent-space masking and its correspondence to pixel space using a central square mask. The encoder and decoder of Stable Diffusion 3.5 (medium) were used. The first row shows latent images alongside the encoded mask applied to each, while the second row shows their decoded...

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(2025, Algorithm 3)

We have simply adapted the notations and used F (x) = ∥y − x[m]∥2/(2σ2 y) in Martin et al. (2025, Algorithm 3). Thus, the transition used in Algorithm 2 is ˆπθ s|t(xs|xt) ∝ N(xs[m], αsˆxθ 0(xt, t)[m], σ2 sId−dy) × N xs[m], 1 − γs σ2y αsˆxθ 0(xt, t)[m] + γs σ2y αsy, σ2 sId−dy . In the case of the DDIM schedule ηs = σs, we have that µθ s|t(xt) = αsˆxθ 0(xt,...

work page 2025
[19]

Hence, the main difference lies in the coefficient of the convex combination and the variance used

in (A.2) writes ˆπθ s|t(xs|xt) = N(xs[m], αsˆxθ 0(xt, t)[m], σ2 sId−dy) × N(xs[m], (1 − ˜γs|t)αsˆxθ 0(xt, t)[m] + ˜γs|tαsy, σ2 s|τ ˜γs|tId−dy). Hence, the main difference lies in the coefficient of the convex combination and the variance used. Algorithm 2 PNP-F LOW reinterpreted 1: Input: Decreasing timesteps (tk)0 k=K with tK = 1, t0 = 0; adaptive stepsi...

work page 2025
[20]

(2025, line

We also assume for the sake of simplicity that the optimization problem is solved exactly in Kim et al. (2025, line

work page 2025
[21]

Comparison with DiffPIR (Zhu et al.,

and overall, follows the line of work of methods that learn a residual that is then used to translate the denoiser (Bansal et al., 2023; Zhu et al., 2023). Comparison with DiffPIR (Zhu et al.,

work page 2023
[22]

We provide the DIFFPIR algorithm (Zhu et al., 2023, Algorithm

and DDNM (Wang et al., 2023b). We provide the DIFFPIR algorithm (Zhu et al., 2023, Algorithm

work page 2023
[23]

version of DIFFPIR recovers the DDNM algorithm (Zhang et al., 2023). Algorithm 4 DIFFPIR reinterpreted 1: Input: Decreasing timesteps (tk)0 k=K with tK = 1, t0 = 0; scaling λ; original image x∗; mask m; DDIM parameters (ηk)0 k=K 2: y ← x∗[m] 3: x ∼ N (0, Id). 4: for k = K − 1 to 1 do 5: ˆx0 ← xθ 0(x, tk+1) 6: ˆx0[m] ← σ2 tk+1 σ2 tk+1 +λσ2yα2 tk+1 y + λσ2 ...

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[24]

This step is performed approximately by replacing the prior transition p0|tk+1(·|Xtk+1) with a Gaussian approximation centered at the denoiser ˆxθ 0(Xtk+1 , tk+1)

proposes sampling, given the previous state Xtk+1, a clean state ˆX0 by performing Langevin Monte Carlo steps on the posterior distribtion π0|tk+1(·|Xtk+1 , y). This step is performed approximately by replacing the prior transition p0|tk+1(·|Xtk+1) with a Gaussian approximation centered at the denoiser ˆxθ 0(Xtk+1 , tk+1). Then, given ˆX0, the next state ...

work page 2025
[25]

VJP-based methods

adopt a variational perspective: the target distribution is approximated by a Gaussian distribution whose 18 Preprint under review parameters are iteratively estimated by minimizing a combination of an observation-fidelity loss and a score-matching-like loss. VJP-based methods. A broad class of zero-shot approaches builds on the guidance approximation (2....

work page 2021
[26]

Proof. Using the standard Gaussian conjugation formula (Bishop, 2006, equation 2.116), we have that ˆπdps s|t (xs|xt, y) = N(x; mdps s|t (xt, y), Σdps s ) with mdps s|t (xt, y) := Σdps s|t (η−2 s µs|t(xt; η) + σ−2 y D⊤ s P ⊤ my) , Σdps s|t := η−2 s Id + σ−2 y (PmDs)⊤PmDs −1 . 21 Preprint under review Next, for the DING transition, first set bs(Zs) := −(σs...

work page 2006
[27]

We implemented Avrahami et al

BLENDED -D IFF. We implemented Avrahami et al. (2023, Algorithm

work page 2023
[28]

The codebase includes an additional hyperparameter, blending_percentage, which determines at what fraction of the inference steps blending begins

following their official code3. The codebase includes an additional hyperparameter, blending_percentage, which determines at what fraction of the inference steps blending begins. We set it to zero, as applying blending across all steps produced the best results. A key detail is the original implementation is that the observed region (background) is re-noi...

work page 2023
[29]

We found that using Langevin as MCMC sampler for enforcing data consistency works the best for low NFE regime

based on the released code4 to the flow matching formulation. We found that using Langevin as MCMC sampler for enforcing data consistency works the best for low NFE regime. DIFFPIR . We make Zhu et al. (2023, Algorithm

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[30]

The official implementation uses a DDIM transition in step 5 of Algorithm 3 whose stochasticity is controlled by the hyperparemters η

being implemented for a mask operator. The official implementation uses a DDIM transition in step 5 of Algorithm 3 whose stochasticity is controlled by the hyperparemters η. As recommended, we set the latter to η = 0.85. FLOWCHEF & FLOWDPS . For both algorithms, we adapt the implementations available in the released codes FLOWCHEF 7 8 to our codebase. We ...

work page 2025
[31]

while taking as a reference the released code9. For the stepsizes on data fidelity term, we find that a constant scheduler with higher stepsize enables the algorithm to fit the observation, mitigate the smooth and blurring effects in the reconstruction and hence yield better reconstructions. PSLD . We implement the PSLD algorithm provided in Rout et al. (...

work page 2024
[32]

We initialize the algorithm with a sample for a standard Gaussian

based on the official code10 and adapt it to the flow matching formulation. We initialize the algorithm with a sample for a standard Gaussian. For low NFE setups, we find that using a constant weight schedule yields better results, namely in terms fitting the observation and providing consistent reconstructions. 3https://github.com/omriav/blended-latent-d...

work page 2024
[33]

(2024, Appendix) and the reference code11

based on the provided implementa- tion details in Song et al. (2024, Appendix) and the reference code11. As noted in Janati et al. (2025a), we set the tolerance ε for optimizing the data consistency to the noise level σy. Since we are working with low NEFs, we set the frequency at which hard data consistency is applied (skip step size) to

work page 2024