Unsupervised Region-Based Image Editing of Denoising Diffusion Models

Renshuai Tao; Wei Wang; Xiaohong Jia; Yao Zhao; Yue Song; Zixiang Li

REVIEW 4 major objections 4 minor 49 references

Unsupervised Region-Based Image Editing of Denoising Diffusion Models

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that a coarse mask alone can steer semantic edits in a pretrained diffusion model by projecting the masked region's Jacobian orthogonal to the unmasked region's Jacobian, achieving local editing without labels or training.

desk verdict The core projection (Eq. 14) is a rank-one Gram-Schmidt step while the Jacobians are matrices, so the derivation does not support the paper's central claim of suppressing all outside-region changes. read the letter →

arxiv 2412.12912 v1 pith:ATV7OWSQ submitted 2024-12-17 cs.CV cs.AI

Zixiang Li , Yue Song , Renshuai Tao , Xiaohong Jia , Yao Zhao , Wei Wang This is my paper · ORCID

classification cs.CVcs.AI

keywords region-basedimageeditingdiffusionmodelsunsupervisedsemanticdiscoveryJacobianprojectionh-spacemask-guidedfaceattributetraining-free

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to make local semantic editing of pretrained diffusion models work without any labels, extra training, or fine segmentation masks. Its idea is to find a direction in the model's internal h-space that changes pixels inside a user-specified region while leaving the complement almost untouched. The direction comes from the Jacobian of the masked noise-prediction output, projected orthogonal to the Jacobian of the unmasked output. The authors report that on smile editing this unsupervised procedure beats supervised baselines on image quality, identity preservation, and perceptual distance, while keeping changes outside the mask smaller than the closest unsupervised competitor. If correct, it turns a rough bounding box into a sufficient interface for precise attribute editing in pretrained U-Net diffusion models.

What carries the argument

The object carrying the argument is the Jacobian of the masked noise-prediction network with respect to the h-space latent, where h-space is the semantic latent space formed by the U-Net bottleneck skip connections. The load-bearing step is a single Gram-Schmidt-style orthogonal projection: the masked Jacobian is projected onto the unmasked Jacobian and the projection is subtracted, so the retained direction is the part of the masked sensitivity that is orthogonal to the non-masked sensitivity. Singular vectors of this projected Jacobian are approximated by power iteration, and the leading vector is applied as the edit direction during DDIM sampling.

What would settle it

For a fixed image and timestep, compute the masked and unmasked Jacobians, then compare the paper's projected direction with the direction that actually maximizes $\|J_m h\|/\|J_u h\|$, for instance the leading generalized eigenvector of $J_m^T J_m$ relative to $J_u^T J_u$. If the projected direction is not among the optimizers, the core equivalence fails; the test can be run on one CelebA-HQ image or on a small synthetic linear map.

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Extended reading notes

Core claim

The paper's central claim is that a local semantic edit direction can be computed from two Jacobians of the denoising network. With $f(h_t)=\epsilon^\theta_t(x_t,h_t)$ the noise prediction, the masked Jacobian $J_m=\partial(\epsilon^\theta_t\odot M)/\partial h_t$ encodes the sensitivity of the region of interest, and $J_u$ encodes the sensitivity of the complement. The paper proposes $J = J_m - \frac{J_m\cdot J_u}{J_u\cdot J_u}J_u$, a single orthogonal projection of the masked direction onto the subspace orthogonal to the unmasked direction, and claims this solves the objective of maximizing masked-region change while minimizing change elsewhere. The resulting vector is used as an edit direction in h-space across selected denoising time steps. Because changes in h-space propagate to x-space through the noise prediction network, suppressing the unmasked Jacobian component is claimed to suppress unwanted global changes.

Load-bearing premise

The whole method rests on the assumption that one orthogonal projection of the masked Jacobian onto the unmasked Jacobian is equivalent to maximizing masked-region change while minimizing unmasked-region change, and the paper does not prove this equivalence.

Editorial extensions

If this is right

A user can edit a local attribute with only a rough bounding box; no attribute labels, text prompt, or fine-tuning are needed.
The same mask can yield multiple distinct semantic edits, such as smile, left-slant, and right-slant for a mouth region.
Outside-mask preservation should transfer across datasets and U-Net diffusion architectures, since the method relies only on h-space Jacobians.
On smile editing, the unsupervised result can beat supervised edits on FID, identity similarity, and LPIPS, so supervision is not a prerequisite for high-quality local edits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper leaves implicit that the projection is only one Gram-Schmidt step against a single unmasked Jacobian; iterating it over several regional Jacobians or using a generalized eigenvector of $J_m^T J_m$ relative to $J_u^T J_u$ could satisfy the stated max/min objective more faithfully.
A testable extension is that because only a coarse mask is required, the interface should transfer to region-constrained editing outside faces, such as object-level or medical-image editing, wherever a U-Net diffusion model is available.
The paper also leaves implicit that h-space locality implies a family of timestep-dependent edit directions; checking whether a single direction stays optimal across all timesteps would clarify the robustness of the mask-only interface.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

The paper proposes RBE, a training-free method for local editing in diffusion models by using the Jacobian of the noise-prediction network with respect to h-space. The new ingredient is Eq. (14): an orthogonal projection of the masked Jacobian J_m against the unmasked Jacobian J_u, intended to suppress changes outside the edit region. That is a plausible idea, and the qualitative results indeed show better outside-region preservation than Semdiff. However, the central derivation is not there. In Eq. (14), J_m and J_u are treated as vectors, but they were defined as matrices (Eq. 6). The dot product is undefined as written. More importantly, the projection is a single rank-one subtraction, which only removes the component of J_m along one direction of J_u. If J_u has rank > 1—which it generally will, since it maps a multi-dimensional h-space to many pixels—this does not minimize unmasked changes. The correct projection would be J_m - J_u (J_u^T J_u)^+ J_u^T, i.e., removing the full row space. The authors give no argument that J_u is effectively rank-one, so the headline mechanism is unsupported.

What the paper does well: the motivation is clear, the method is simple, and the experiments cover multiple datasets and architectures. The comparison against Semdiff on local vs. non-local MSE is a useful direct test. The authors honestly acknowledge limits for very small masks and global attributes.

Soft spots beyond the theory: the connection between the optimization objective (Eq. 13) and the projection is asserted, not proven; the selection of the right singular vector for a desired attribute is not specified; and the quantitative comparison against supervised baselines uses only the smile attribute, with no error bars, and the paper's "state-of-the-art" claim overreaches. The appendix, where implementation details are promised, is missing from the arXiv version.

This is a likeable paper with a good idea, but the key equation does not do the advertised work. A referee should ask for a proper derivation (or a clear explanation of why a rank-one approximation suffices) and a more complete comparison. I would send it to review, but with the expectation of major revision.

Best, [Your name]

Referee Report

4 major / 4 minor

Summary. The paper proposes Region-Based Editing (RBE), a training-free method for local semantic editing in the h-space of pretrained U-Net diffusion models. The user provides a mask, the method computes Jacobians of the masked and unmasked regions of the noise-prediction network, applies an orthogonal projection to suppress unmasked-region sensitivity, and injects the resulting semantic direction during DDIM reverse sampling. The authors report qualitative results on CelebA-HQ, LSUN-church, and LSUN-bedroom and compare quantitatively with Asyrp, Boundary Diffusion, and Semdiff on the smile attribute, claiming state-of-the-art performance and even superiority over supervised baselines.

Significance. The paper addresses a relevant and timely problem: training-free, mask-only semantic editing with preservation of the unmasked image content. If the projection step were rigorously justified, the method would be a useful and practical contribution, and the qualitative examples do suggest that outside-mask preservation is better than in the compared baselines. The paper also gives a clear statement of limitations in the Discussion. However, the central mathematical claim connecting the optimization objective to the projection is not established, and the quantitative evaluation is too narrow to support the headline claim of surpassing supervised methods. The potential is real, but the manuscript needs substantial revision before the contribution can be assessed reliably.

major comments (4)

[Methodology, Eq. (13)-(14)] Equation (13) is not a well-defined optimization objective. It is written as 'arg max ... min ...' without specifying a norm, a scalarization, or the admissible set for h_t. Even if it is interpreted as 'maximize masked-region change while minimizing unmasked-region change,' the paper gives no derivation showing that the orthogonal projection in Eq. (14) optimizes this criterion. Because the entire method rests on this equivalence, the authors must either provide a rigorous proof under explicit assumptions or reformulate the objective and the projection as a heuristic and validate that heuristic experimentally.
[Methodology, Eq. (14)] As written, Eq. (14) uses single-vector dot products, but J_t in Eq. (6) and J_masked in Eq. (12) are matrices, and J_m and J_u have different numbers of rows because they correspond to masked and unmasked pixel sets. If the intended operation is a Gram-Schmidt projection of one Jacobian vector against another, the formula cancels only one direction of unmasked sensitivity. For a Jacobian J_u of rank greater than one, the orthogonal complement of the unmasked subspace is not obtained by a single rank-one subtraction; the correct form is J_m - J_u (J_u^T J_u)^+ J_u^T J_m (or an equivalent basis projection). The authors should either use the full projection or explicitly state and empirically justify a rank-one approximation.
[Experiments, Figure 3 and 'Unsupervised Editing through Jacobian'] The method can discover many right singular vectors for a masked region, but the paper never specifies how the vector corresponding to a desired attribute (e.g., 'smile' versus 'slanted mouth') is selected. Figure 3 shows that the same mouth mask yields different attributes, which suggests manual selection after the fact. Without a selection criterion, the method is not fully unsupervised, and the reported per-attribute results are not reproducible from the algorithmic description in the paper.
[Experiments, Table 2] The headline claim of surpassing supervised methods is based on a single attribute ('smile') and a single dataset, with no standard deviations, no number of runs, and no significance test. In addition, the MSE values in Table 2 are not decomposed into in-mask and out-of-mask components, even though outside-mask preservation is the central contribution of the paper; that decomposition is only shown in Figure 7 for one comparison against Semdiff. The comparison needs more attributes, more datasets, and statistical support to justify the strength of the claim.

minor comments (4)

[Background] There is a typo in 'Diffusion autuencoders'; it should be 'Diffusion autoencoders'.
[Experiments, Figure 7] The paragraph preceding Figure 7 says 'The qualitative results in Figure 7 also prove this point,' but Figure 7 is a quantitative bar-chart comparison of pixel changes; the wording should say 'quantitative results.'
[Experiments, Figure 3 caption] The caption states that the mask is used 'during training and do not need to add it during testing,' but the method is training-free; this should be rephrased as 'during editing' or the distinction should be clarified.
[Experimental Setup] The acronym 'Asyrp' is used without being defined or cited; please provide the full method name and a reference.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the method is evaluated on held-out images with fixed pretrained models; the only minor issue is a non-load-bearing self-citation, while the unproven Eq. 14 projection is a correctness risk rather than a circular step.

full rationale

The paper's derivation chain is not circular in the problematic sense. The proposed direction is constructed from Jacobians of a fixed pretrained diffusion model with a user-supplied mask (Eqs. 11-14); no parameter is fitted to the reported FID, ID, MSE, or LPIPS values, and the evaluation uses held-out CelebA-HQ images and independently trained baseline checkpoints. The claim that Eq. 14 'solves' Eq. 13 is an unproven mathematical assertion: if the unmasked Jacobian J_u has rank greater than one, the single-vector Gram-Schmidt projection in Eq. 14 does not generally minimize unmasked changes. This is a substantive correctness concern, but it is not circularity because Eq. 14 is not equivalent to Eq. 13 by construction and the empirical comparisons are not forced by the construction. The paper also relies on the assumption that h-space is locally Euclidean and that directions transfer across timesteps, but these are stated assumptions, not renamings of the target result. The only self-citation identified is the related-work reference to 'Song et al. 2024' (Flow Factorized Representation Learning), which is likely a co-author citation but is not load-bearing: it is mentioned as one example of representation learning and does not support the paper's central claims. The unspecified choice of which discovered direction corresponds to 'smile' or 'slanted mouth' is a reporting and selection concern, and it could weaken the strength of the semantic-discovery claim, but it does not reduce the derivation to its inputs. Overall, the central contribution has independent empirical content, so no significant circularity is found; the score of 2 reflects only the minor, non-load-bearing self-citation and the mild selection-loop concern noted by the reader.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several unproven assumptions: the local Euclidean structure of h-space, the linearization of the network, the optimality of the Gram-Schmidt projection, and the user's manual choice among discovered directions. The method itself introduces no new physical or model entities, but the projection-based optimization is an ad hoc design choice with no formal justification.

free parameters (4)

Edit strength (step size) α for semantic vector injection
Chosen by hand for each edit; no value specified in the main text. Governs the magnitude of the semantic change and is not derived.
Edit timestep range in the reverse process
Semantic vectors are applied over a selected set of timesteps; the range is chosen by hand and not reported in the main text.
Power iteration count for Jacobian approximation
The paper states power iteration is used to approximate eigenvectors of Jt^T Jt, but the number of iterations is not specified.
Mask region (bounding box or segmentation)
The user provides a coarse mask; the discovered semantic depends on mask placement and size, and the paper reports different attributes from the same facial region.

assumptions (4)

domain assumption h-space has local Euclidean properties and consistency across timesteps.
Assumed in Section 'Region-Based Semantic Discovery' and inherited from Kwon et al. (Asyrp); supports the use of vector addition in h-space for editing.
standard math The direction of maximum image change is given by the top right singular vector of the Jacobian Jt.
Standard linear-algebra fact, but applied here to a nonlinear network; the paper treats the network as locally linear without quantifying the approximation error.
ad hoc to paper The orthogonal projection in Eq. 14 solves the optimization objective in Eq. 13.
No proof is given; the projection is a single Gram-Schmidt step and its optimality for the max/min objective is not established.
domain assumption Masking the noise prediction with a Hadamard product and differentiating yields Jacobians whose top directions correspond to local semantic changes.
Assumed in Eq. 11-12; the paper provides no analysis of how masking interacts with the network's receptive field to confine semantic directions to the mask.

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Cite this review

Pith. "Pith review of Unsupervised Region-Based Image Editing of Denoising Diffusion Models." pith.science (2026). https://pith.science/paper/ATV7OWSQ

@misc{pith2026241212912,
  author       = {Pith},
  title        = {Pith review of: Unsupervised Region-Based Image Editing of Denoising Diffusion Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ATV7OWSQ}},
  note         = {Machine review of arXiv:2412.12912}
}

read the original abstract

Although diffusion models have achieved remarkable success in the field of image generation, their latent space remains under-explored. Current methods for identifying semantics within latent space often rely on external supervision, such as textual information and segmentation masks. In this paper, we propose a method to identify semantic attributes in the latent space of pre-trained diffusion models without any further training. By projecting the Jacobian of the targeted semantic region into a low-dimensional subspace which is orthogonal to the non-masked regions, our approach facilitates precise semantic discovery and control over local masked areas, eliminating the need for annotations. We conducted extensive experiments across multiple datasets and various architectures of diffusion models, achieving state-of-the-art performance. In particular, for some specific face attributes, the performance of our proposed method even surpasses that of supervised approaches, demonstrating its superior ability in editing local image properties.

Figures

Figures reproduced from arXiv: 2412.12912 by the authors.

**Figure 1.** Motivation of our proposed method. In this figure, mouth editing is used as an example. Direct editing often results in significant changes to areas beyond the mouth. By using Jacobian matrix projection, we can suppress these unwanted changes, allowing for more precise editing. demonstrated unexpected versatility across various domains, it becomes imperative to explore and leverage their intrinsic capabilities to … view at source ↗

**Figure 2.** Overview of our semantic discovery method and editing method. Firstly, we define mask M and function f, which can be found in our method section. We also use DDIM inversion to precompute xt and ht for later use. We use the power iteration method to calculate the Jacobian matrix Jt, and use Jt to calculate the required Vt. Finally, we set the modified timesteps, edit intensity and other parameters, and use DDIM to ge… view at source ↗

**Figure 3.** Qualitative results of our method. We experimented with the pre-trained DDPM model on the CelebA-HQ dataset with a resolution of 256*256. The leftmost image is the original image. The green box corresponds to the area where we use the mask. The area of the image mask in each column is the same. Please note that we only use the mask during training and do not need to add it during testing. In our experiment, the mask… view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Qualitative results. Our method has the best results on the overall structure and details. Our results show that while achieving good editing results, the image quality indicators FID, MSE, LPIPS, and the identity change ID of the person have achieved extremely high …

**Figure 4.** Figure 4: More semantic editing results Main Results of Attribute Editing In this subsection, we present the overall performance of our approach. Our specific experimental process is as follows: First, add a mask to a specific area on the image according to the Equation 11. Then…

**Figure 6.** Figure 6: Exemplary comparison of Semdiff and our RBE. We compare the remaining parts after editing the mask of the region. Our method has a clear advantage in image preservation outside the region. postures, it will bring more serious distortion results. Boundary Diffusion is …

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

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