Dual Watermarking: Techniques & Applications

• Dual watermarking mechanism is a strategy that embeds two independent watermarks within a host medium to enable both copyright protection and content authentication.
• It employs diverse methods such as transform-domain embedding, layered payload partitioning, and deep learning architectures to improve imperceptibility and resistance to attacks.
• The approach optimizes trade-offs between robustness and fidelity, demonstrating practical applications across images, audio, text, and AI-generated content.

A dual watermarking mechanism is a strategy in digital watermarking that integrates two distinct watermark signals, components, or objectives within the same host medium—such as images, audio, text, or generated content. The dual approach can serve purposes such as simultaneous copyright protection and authentication, or enhance resilience against various attacks through redundancy, division of payloads, or specialized roles of each watermark. The practical implementations vary widely, spanning classical signal methods, deep learning, and adversarial settings. Below is a comprehensive, technically focused exposition of dual watermarking mechanisms across their algorithmic, mathematical, architectural, and applied dimensions.

1. Conceptual Principles of Dual Watermarking

Dual watermarking refers to embedding two independent or functionally complementary watermark signals into the same content. The two watermarks may serve different purposes—e.g., content authentication vs. copyright, detection vs. identification, or adversarial disruption vs. traceability. Their embedding may occur at different locations, sub-bands, latent spaces, or logical "channels" within the content.

Typical strategies observed include:

• Hierarchical or Layered Embedding: Partitioning watermark information into critical "base" and "^^^^2^^^^" layers for robustness (e.g., (Golestani et al., 2015)).
• Frequency/Spatial Separation: Placing watermarks in distinct frequency bands or regions (e.g., embedding in DWT HL and LH subbands (Joseph et al., 2013)) or in designated token subsets for detection/identification (Fu et al., 19 Jun 2025).
• Dual-functional Network Architectures: Using separate neural modules for imperceptibility and robustness (Ma et al., 2022, Sun et al., 13 Dec 2024) or adversarial defense and traceability (Zhang et al., 2023).
• Distributional or Latent-Space Assignment: Mapping watermarks onto specific intervals of the latent distribution (diffusion or VAE latent spaces) for dual purposes such as copyright tracing and tampering localization (Chen et al., 30 Jun 2025).

This dualization mitigates the inherent trade-offs present in single watermark designs, such as between imperceptibility, robustness, recovery performance, and adaptability to diverse application needs.

2. Major Algorithmic and Mathematical Frameworks

2.1 Dual Embedding and Distributional Strategies

• Multiple Transform Domain Embedding: Dual watermarking schemes employ DWT–SVD (Dhanalakshmi et al., 2010, Joseph et al., 2013) or DCT domain (Golestani et al., 2015) to embed different watermarks in distinct transform coefficients for improved imperceptibility and robustness.
• Sequential and Orthogonal Embedding: In STDM-based schemes (Li et al., 2016), multiple watermarks are embedded along orthogonal projections. Embedding equations:

$g = x + U K, \quad K = U_I^{-1}(QDMV - P),$

where each watermark bit modulates projections along a unique direction.

2.2 Deep Learning Architectures

• Dual-Decoders (Teacher–Student): The END$^2$ architecture (Sun et al., 13 Dec 2024) employs a clean (“teacher”) and a distorted (“student”) decoder. The teacher handles clean watermarked inputs for gradient flow, while the student handles non-differentiable distortions. Alignment loss is enforced by cosine similarity:

$$\mathcal{L}_{s,t} = 2 - 2\langle \bar{z}_s, sg[\bar{z}_t] \rangle$$

where $sg[\cdot]$ denotes stop-gradient.

• Invertible and Non-Invertible Hybrid: The CIN framework (Ma et al., 2022) integrates an invertible neural network for high-fidelity reversible embedding and an attention-based non-invertible decoder for robustness under strong, non-differentiable attacks. A noise discriminator dynamically selects the most reliable extraction branch.
• Adversarial–Traceable Duality: In Dual Defense (Zhang et al., 2023), adversarial features are synthesized to disrupt face-swapping models, while an embedded robust watermark remains extractable post perturbation.

2.3 Partitioning and Payload Management

• Partitioned and Layered Payloads: Embedding a "base" part in robust coefficients and an "enhancement" part in less robust regions increases both reliability and data payload (Golestani et al., 2015); mathematical partitioning is achieved via SVD truncation, wavelet decomposition, or scalable coding principles from video (such as H.264/SVC).
• Token-Subset Splitting in LLMs: In LLMs, the dual watermarking scheme designates a fraction $r_d$ of tokens for detection and the rest for identification. For each token, the indicator $d_i$ determines assignment:

$$d_i = 1 \text{ if } (h_i \bmod 100) < 100 \cdot r_d, \text{ else } 0$$

(Fu et al., 19 Jun 2025).

3. Robustness, Tamper Detection, and Extraction

3.1 Robustness via Redundancy and Adaptivity

• Embedding separate components at structurally distinct stages or locations (e.g., early-stage “structure” and late-stage “detail” watermarking in diffusion models (Xing et al., 29 Aug 2025)) ensures resilience to generative, geometric, and value-metric attacks. Loss functions combine message recovery, normalization, and higher-order statistical penalties to maintain visual and functional quality:

$$\mathcal{L} = \lambda_{msg} \mathcal{L}_{msg} + \lambda_{init} \mathcal{L}_{init} + \lambda_{low} \mathcal{L}_{low} + \lambda_{high} \mathcal{L}_{high}$$

3.2 Tamper-Aware Decoding

• TAG-WM (Chen et al., 30 Jun 2025) localizes tampering by comparing original and reconstructed localization watermarks using XOR-based masks and statistical thresholds. This mask guides selective (majority-vote) extraction of the copyright watermark, improving recovery even under high tampering or adversarial manipulations.

3.3 Efficient Locating and Extraction

• In neural audio watermarking (IDEAW (Li et al., 29 Sep 2024)), an initial lightweight locating code is extracted first; only upon successful localization is the main watermark message recovered, dramatically improving locating efficiency and reducing computational burden compared to exhaustive search.

4. Applications and Security Implications

Dual watermarking mechanisms are engineered for enhanced security and verifiability across diverse domains:

• Image and Multimedia: Robust copyright and authentication (Dhanalakshmi et al., 2010, Padhi et al., 21 Feb 2025), tamper localization (Chen et al., 30 Jun 2025), and proactive forensics in generated and edited content.
• LLMs: Simultaneous detection and user identification (Fu et al., 19 Jun 2025), quality-preserving watermarking via context-aware adjustment (Yang et al., 9 Jun 2025), or adaptive trade-offs between model distortion and detection ability (Cai et al., 19 Mar 2024).
• Audio: High-capacity, attack-resilient watermarking with efficient synchronization (Li et al., 29 Sep 2024).
• Source Code: Dual-channel embedding—natural (identifier-level) and formal (code structure)—ensuring robustness against both semantic-preserving attacks and syntax-focused transformations (Yang et al., 2023).

A summary of core dual watermarking design dimensions is provided below:

Domain	Dual Mechanism	Extraction Principle
Images	Visible + Invisible, or Robust + Fragile	Transform inversion, SVD, DWT, ML
LLMs/Text	Token set split for detection/identification	Score aggregation; thresholding
Audio	Message + Locating code (dual INN)	Two-stage INN, locating refinement
Diffusion Img	Structure mark (early) + Detail mark (late)	ODE/adjoint solver optimization
Source Code	Natural channel (naming) + Formal channel	Code rewrite; ML decoding

5. Theoretical Insights and Trade-offs

5.1 Trade-off Analysis

• Embedding two watermarks inevitably increases the risk of mutual distortion; architectural (e.g., separate channels, residual addition, non-interfering SVD subbands) and optimization-based strategies (dedicated loss terms, payload partitioning) are employed to minimize such interactions.
• Information-theoretic analysis for LLM watermarks reveals that naive joint encoding increases false positive rates exponentially with key capacity (Fu et al., 19 Jun 2025). Separating responsibilities to dedicated token subsets controls this risk, aligning theoretical upper bounds with practical detection rates.

5.2 Optimization and Capacity

• Adaptive algorithms such as online dual gradient ascent (Cai et al., 19 Mar 2024) or inference-time optimization with adjoint sensitivity (Xing et al., 29 Aug 2025) achieve Pareto/balanced optimality between robustness and imperceptibility.
• Capacity can be flexibly scaled by orthogonalizing projection vectors (Li et al., 2016), using layered payloads, or augmenting code channels, with trade-offs dictated by intrinsic channel limitations or practical attack resilience.

6. Open Challenges and Future Directions

• Coordinated Multi-Watermark Embedding: Maintaining minimal interference and maximal robustness for each channel remains a nuanced design problem, especially under complex or adversarial attack scenarios.
• Scalability: Efficient extraction and minimal run-time overhead are emphasized in recent work (e.g., multi-branch pre-generation in LLMs (Yang et al., 9 Jun 2025), efficient locating in audio (Li et al., 29 Sep 2024)).
• Generative and Regeneration Attacks: Future research may address improved robustness under ever-more sophisticated model inversion, data stealing, or surrogate model copying scenarios (Ma et al., 2023, Xing et al., 29 Aug 2025).
• Theoretical Boundaries: Continued paper of optimality, trade-off boundaries (e.g., KL-constrained detection (Cai et al., 19 Mar 2024)), and error rate scaling, especially in high-capacity or high-adversary settings.

Dual watermarking mechanisms—understood as the coordinated embedding of independent or complementary watermark signals—form a central axis for contemporary digital content protection, authentication, and forensic tracing. Their design synthesizes transform theory, statistical modeling, deep learning, and optimization, yielding systems that are robust, adaptive, and fit for the evolving threat landscape in digital media and AI-generated content.