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arxiv: 2605.01479 · v1 · submitted 2026-05-02 · 💻 cs.CV

Recognition: unknown

CSGuard: Toward Forgery-Resistant Watermarking in Diffusion Models via Compressed Sensing Constraint

Chen Tang, Hui Jin, Jiewei Lai, Lan Zhang, Pengcheng Sun, Yunhao Wang, Zhaopeng Zhang

Pith reviewed 2026-05-09 14:40 UTC · model grok-4.3

classification 💻 cs.CV
keywords watermarkingdiffusion modelsforgery resistancecompressed sensinglatent spacedigital forensicsimage attribution
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The pith

A secret matrix tied to compressed sensing makes diffusion model watermarks forgery-resistant by blocking inversion-regeneration attacks.

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

Existing latent watermarking for diffusion models lets attackers invert a watermarked image and regenerate it with any prompt to create false attribution on new content. CSGuard adds a compressed sensing constraint that requires the watermarked latent to obey a linear measurement defined by a secret matrix. Only the matrix owner can embed or verify correctly because regeneration without the matrix violates the constraint. The approach keeps image quality and legitimate detection rates intact while cutting forgery success sharply. If the binding holds, it supplies a practical way to attribute AI-generated images reliably for IP protection and forensics.

Core claim

CSGuard is the first forgery-resistant watermarking schema that leverages compressed sensing to bind the watermarked image generation and verification to a secret matrix. This ensures that only users possessing the secret matrix can correctly embed or verify the image watermark, prevents the illegal users from forgery without compromising generation quality and watermark integrity.

What carries the argument

The compressed sensing constraint, a linear measurement equation that the watermarked latent representation must satisfy using the secret matrix, which makes successful verification impossible unless the matrix is known during both embedding and checking.

If this is right

  • Forgery attack success rate falls from 100 percent to 28.12 percent.
  • All benign watermarked images continue to be detected correctly.
  • Generated image quality and original watermark strength remain unchanged.
  • Embedding and verification are possible only for holders of the secret matrix.

Where Pith is reading between the lines

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

  • The same matrix-binding idea could be tested on other latent generative models such as GANs or autoregressive image generators.
  • Periodic rotation of the secret matrix would limit damage if one instance is ever compromised.
  • Real-time platforms could adopt the check to flag unattributable or falsely attributed images before they spread.

Load-bearing premise

An attacker cannot recover or approximate the secret matrix from watermarked images or queries, so the constraint stays binding when the image is inverted and regenerated.

What would settle it

An attacker recovers a usable approximation of the secret matrix from several watermarked images and then forges new content that passes verification at a rate well above 28 percent.

Figures

Figures reproduced from arXiv: 2605.01479 by Chen Tang, Hui Jin, Jiewei Lai, Lan Zhang, Pengcheng Sun, Yunhao Wang, Zhaopeng Zhang.

Figure 1
Figure 1. Figure 1: Overview of CSGuard. By enforcing CS consistency on intermediate latents, CSGuard view at source ↗
Figure 2
Figure 2. Figure 2: Watermark performance under varying image distortions of different intensities. view at source ↗
Figure 3
Figure 3. Figure 3: Ablation study on the impact of observa view at source ↗
Figure 4
Figure 4. Figure 4: Watermark performance under varying CS recovery ratios and projection ratios. Top: Projection ratio fixed at 0.4, CS ratio varied. Bottom: CS ratio fixed at 0.8, projection ratio varied. Analysis on Projection Ratio. We an￾alyze the effect of the projection ratio (proj_ratio), which governs the Tproj , with results shown in view at source ↗
Figure 5
Figure 5. Figure 5: Comparative visualization of watermarking results. For each prompt (bottom), the left view at source ↗
Figure 6
Figure 6. Figure 6: TPR/ASR for benign and forged images under varying false positive rate (FPR) thresholds. view at source ↗
Figure 7
Figure 7. Figure 7: TPR/ASR for benign and forged images under varying matries. view at source ↗
read the original abstract

Latent-based diffusion model watermarking embeds watermarks into generated images' latent space to enable content attribution, offering a training-free solution for intellectual property protection and digital forensics. However, these methods exhibit a critical vulnerability to the forgery attack, attackers can extract the watermark by inverting the watermarked image and re-generating it with an arbitrary prompt, thereby enabling false attribution on malicious content. In this paper, we propose the CSGuard, the first forgery-resistant watermarking schema that leverages compressed sensing to bind the watermarked image generation and verification to a secret matrix. This ensures that only users possessing the secret matrix can correctly embed or verify the image watermark, prevents the illegal users from forgery without compromising generation quality and watermark integrity. Experimental results demonstrate that CSGuard achieves strong forgery resistance, reduces the attack success rate from 100.0\% to 28.12\%, and achieve 100\% detection rate on benign watermarked images without compromising watermarking effectiveness.

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

3 major / 2 minor

Summary. The paper proposes CSGuard, a training-free watermarking scheme for latent diffusion models that embeds watermarks in latent space while adding a compressed-sensing constraint tied to a secret sensing matrix. This binding is intended to prevent forgery attacks in which an adversary inverts a watermarked image and regenerates it under an arbitrary prompt. The central empirical claim is that the scheme reduces attack success rate from 100% to 28.12% while achieving 100% detection on benign watermarked images and preserving generation quality.

Significance. If the forgery-resistance property holds under realistic key-recovery attacks, the work would address a documented vulnerability in existing latent-space watermarking methods and provide a concrete mechanism for content attribution in generative AI. The compressed-sensing formulation offers a principled way to tie embedding and verification to a secret without retraining the diffusion model.

major comments (3)
  1. [§3] §3 (method): The forgery-resistance argument rests on the assumption that an attacker cannot recover or sufficiently approximate the secret matrix A from watermarked outputs or multiple queries. No security reduction, key-recovery analysis, or bound on the number of samples needed for matrix estimation (e.g., via least-squares on observed latents) is provided, leaving the central claim dependent on an unverified assumption.
  2. [§4] §4 (experiments): The reported attack-success rate of 28.12% and 100% benign detection rate are presented without experimental protocol details such as dataset sizes, number of trials, attack prompt distributions, or statistical confidence intervals. This absence prevents independent verification of the quantitative claims.
  3. [§4.2] §4.2 (attack evaluation): No experiments evaluate the scheme against matrix-estimation attacks (e.g., compressed-sensing recovery or linear regression on multiple watermarked latents). Such tests are load-bearing for the claim that the compressed-sensing constraint remains binding after inversion-plus-regeneration.
minor comments (2)
  1. [§3] Notation for the compressed-sensing constraint (presumably ||y - A x||) should be stated explicitly with dimensions of A and the precise embedding/verification equations.
  2. [Abstract] The abstract uses 'schema' where 'scheme' is the conventional term; this should be corrected for clarity.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below and indicate the revisions we intend to make.

read point-by-point responses

  1. Referee: [§3] §3 (method): The forgery-resistance argument rests on the assumption that an attacker cannot recover or sufficiently approximate the secret matrix A from watermarked outputs or multiple queries. No security reduction, key-recovery analysis, or bound on the number of samples needed for matrix estimation (e.g., via least-squares on observed latents) is provided, leaving the central claim dependent on an unverified assumption.

    Authors: We agree that the current manuscript lacks a formal security reduction or explicit key-recovery analysis. The CSGuard approach binds the watermark via the compressed-sensing constraint tied to the secret matrix A, so that verification and correct embedding require knowledge of A. In the revised version we will add a dedicated discussion subsection in §3 that references standard compressed-sensing recovery bounds (e.g., the number of measurements required for stable recovery of sparse signals) and explains why accurate estimation of A from a modest number of watermarked latents is computationally prohibitive in the high-dimensional latent space of diffusion models. We will also explicitly state the assumption and its limitations. revision: partial

  2. Referee: [§4] §4 (experiments): The reported attack-success rate of 28.12% and 100% benign detection rate are presented without experimental protocol details such as dataset sizes, number of trials, attack prompt distributions, or statistical confidence intervals. This absence prevents independent verification of the quantitative claims.

    Authors: We acknowledge the omission of detailed experimental protocols. In the revised manuscript we will expand §4 to report the exact dataset sizes and sources, the number of independent trials performed for each metric, the distribution and examples of attack prompts used, and statistical confidence intervals (or standard deviations) for the 28.12% attack-success rate and 100% benign-detection rate. revision: yes

  3. Referee: [§4.2] §4.2 (attack evaluation): No experiments evaluate the scheme against matrix-estimation attacks (e.g., compressed-sensing recovery or linear regression on multiple watermarked latents). Such tests are load-bearing for the claim that the compressed-sensing constraint remains binding after inversion-plus-regeneration.

    Authors: We agree that evaluating resilience to matrix-estimation attacks is important for substantiating the forgery-resistance claim. The current experiments focus on the practical inversion-plus-regeneration attack. In the revision we will add new experiments in §4.2 that simulate an attacker collecting multiple watermarked latents and attempting to recover or approximate A via least-squares regression or standard compressed-sensing recovery algorithms; we will then measure the resulting forgery success rate when the approximated matrix is used for regeneration. revision: yes

standing simulated objections not resolved
  • A complete cryptographic security reduction proving resistance to all possible adaptive key-recovery attacks; such a reduction would require substantial additional theoretical development beyond the scope of the present empirical study.

Circularity Check

0 steps flagged

No significant circularity; central construction is externally grounded and empirically evaluated.

full rationale

The paper introduces CSGuard by binding watermark embedding/verification to a secret sensing matrix A via a compressed-sensing constraint in the latent space of diffusion models. This construction is presented as a design choice that makes forgery (inversion + regeneration) fail without A, with experimental results showing attack success dropping to 28.12% while preserving 100% benign detection. No equations, derivations, or self-citations reduce the claimed resistance to a fitted parameter defined by the result itself, nor do they rename a known pattern or smuggle an ansatz. The secret-matrix premise is treated as an independent input (standard in keyed watermarking), and the forgery-resistance claim rests on empirical measurement rather than a tautological reduction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the unstated premise that the secret matrix cannot be recovered by an attacker who only sees watermarked outputs and that the compressed-sensing step survives the inversion attack; no free parameters or new physical entities are introduced beyond the matrix itself.

axioms (1)
  • domain assumption Latent inversion of a watermarked diffusion image followed by re-generation with an arbitrary prompt is a feasible and effective forgery attack.
    Invoked in the problem statement to motivate the need for forgery resistance.
invented entities (1)
  • Secret matrix used inside the compressed-sensing constraint no independent evidence
    purpose: To bind watermark embedding and verification so that only holders of the matrix succeed
    Introduced as the core mechanism; no independent evidence or external validation supplied in the abstract.

pith-pipeline@v0.9.0 · 5481 in / 1263 out tokens · 31599 ms · 2026-05-09T14:40:09.200656+00:00 · methodology

discussion (0)

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Reference graph

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