Model Watermarking: Methods & Challenges

• Model watermarking is a method that embeds secret identifiers into neural networks’ parameters, activations, or outputs to establish ownership and verify integrity.
• It incorporates robust schemes to survive modifications, fragile approaches for tamper detection, and generative techniques for artifact provenance.
• Researchers assess watermarking by evaluating fidelity, robustness, capacity, and response to attacks, addressing key challenges in practical deployment.

Model watermarking is the practice of embedding identification information into a trained neural network, or associating a secret, verifiable signal with its behavior or outputs, so that later one can test ownership, provenance, or integrity. In robust watermarking the target property is typically copyright attribution; in fragile watermarking it is tamper detection. The watermark may reside in parameters, intermediate activations, outputs, or the sampling process of a generative model, and verification may require white-box access, black-box query access, or, in generative settings, only access to generated artifacts (Boenisch, 2020, Gao et al., 2024).

1. Objectives, threat models, and conceptual scope

Model watermarking is fundamentally an intellectual-property technology. The motivating premise, stated repeatedly across the literature, is that modern models require substantial data, computation, and expertise, and therefore constitute valuable assets whose theft, redistribution, or unauthorized reuse must be detectable after deployment (Boenisch, 2020). In API settings, the central black-box threat is model extraction: an adversary queries a deployed model, records outputs, and trains a surrogate model to reproduce its functionality. In image processing networks this takes the form of paired input-output imitation; in MLaaS classification services it is standard knowledge distillation; in generative systems it extends to provenance and ownership claims over synthesized content (Zhang et al., 2020, Xu et al., 16 Jan 2025, Fang et al., 30 May 2025).

The field distinguishes two principal security objectives. Robust watermarking seeks a signal that survives pruning, compression, quantization, fine-tuning, transfer learning, distillation, or light post-processing, because the owner wants attribution to remain possible even after substantial model modification (Boenisch, 2020). Fragile watermarking reverses that design goal: the watermark should break under unauthorized modification, thereby functioning as an integrity alarm rather than a copyright mark. In this view, a successful fragile watermark has fidelity, retrievability before attack, and fragility after attack (Gao et al., 2024, Robinette et al., 2024).

Generative-model watermarking adds a provenance dimension. In diffusion, language, and tabular generators, the owner often wants to prove that a suspicious artifact or dataset originated from a particular model instance or keyed deployment. This moves the verification problem from parameter inspection toward statistical detection over outputs, prompt-triggered behavior, or keyed sampling traces (Liu et al., 2023, Chen et al., 12 Feb 2025, Fang et al., 30 May 2025).

2. Taxonomies of model watermarking

The most widely used taxonomy organizes model watermarking along five axes: embedding method, verification access, capacity, authentication, and uniqueness (Boenisch, 2020). The first axis separates parameter-based schemes, which encode the watermark in model weights or new architectural components, from trigger-based or behavioral schemes, which assign special behavior to selected inputs. Related work also treats model fingerprinting as adjacent but conceptually distinct, because it often exploits pre-existing distinctive behavior rather than explicitly embedding new information (Boenisch, 2020).

Verification access induces the classic white-box/black-box distinction. White-box schemes require access to parameters or internal activations for extraction; black-box schemes require only query access; some generative and output-watermarking approaches approach a no-box regime in which only generated artifacts are available for statistical testing (Boenisch, 2020). Fragile watermarking introduces an additional orthogonal classification by generation and detection access: Gen W–Det W, Gen W–Det B, Gen B–Det B, with the survey noting no established Gen B–Det W line of work (Gao et al., 2024).

Capacity distinguishes zero-bit ownership tests from multi-bit schemes that encode signatures, serial numbers, or user identifiers. Authentication asks whether the watermark is cryptographically tied to an owner, such as through a digital signature or serial-number construction. Uniqueness asks whether all recipients share one watermark or whether each receives a distinct mark for traitor tracing or leak attribution (Boenisch, 2020).

A second major conceptual divide is robust versus fragile watermarking. Robust schemes prioritize survival under attack; fragile schemes prioritize sensitivity to tampering such as backdoors, poisoning, compression, pruning, bit flips, or parameter manipulation. The fragile-watermarking literature therefore borrows many ideas from adversarial-example generation and multimedia fragile watermarking, but repurposes them toward integrity verification of models rather than attribution alone (Gao et al., 2024).

3. Embedding mechanisms and verification protocols

A generic parameter-based formulation augments the task objective with a watermark regularizer,

$$L(\theta) = L_O(\theta) + \lambda L_R(\theta; w, k),$$

where $L_O$ is the original task loss and $L_R$ enforces a watermark $w$ under secret material $k$ (Boenisch, 2020). Uchida-style regularization biases selected weights so that their projection recovers a bit string; later variants use spread-transform dither modulation, anti-collusion coding, or discriminator-guided training to reduce statistical detectability of watermarked parameters (Boenisch, 2020). Passport-style methods instead insert new parameters or layers whose correct values are required for normal operation.

Behavioral watermarks typically define a trigger set and train the model so that special inputs induce secret outputs. In classification this is usually a backdoor-like trigger-to-label mapping. DeepSigns and related schemes extend the idea to output-activation statistics or intermediate-feature distributions, while BlackMarks turns specially crafted inputs into multi-bit output codes recoverable by black-box querying (Boenisch, 2020). Such approaches are operationally attractive because verification does not require weight access, but they inherit the fragility, ambiguity, and attack surface of backdoor methods.

Image-to-image models motivated a distinct output-space formulation. “Model Watermarking for Image Processing Networks” embeds a unified invisible watermark into every output through a task-agnostic barrier after the target model, so that any surrogate trained on those outputs learns the watermark as part of the public behavior (Zhang et al., 2020). “Deep Model Intellectual Property Protection via Deep Watermarking” develops the same idea with an embedding network, extractor, discriminator, and a self-watermarked variant in which the barrier is absorbed into the task network itself (Zhang et al., 2021). “Exploring Structure Consistency for Deep Model Watermarking” then replaces whole-image consistency with structure consistency, aligning the watermark to edges or semantic regions so that it survives surrogate training with geometric data augmentation (Zhang et al., 2021). HVS-guided schemes further refine perceptual placement by embedding watermark information in less visually sensitive channels, such as $R/B$ or $U/V$, while retaining black-box extractability from outputs (Zhang et al., 2022).

A different black-box construction is the branch backdoor protocol of “Performance-lossless Black-box Model Watermarking.” It wraps the deployed API with a parallel branch that is activated only by cryptographic triggers derived from a message authentication code. Because ordinary inputs almost never activate the branch, the paper proves lossless performance of the protocol by reduction while preserving black-box verifiability through trigger generation and response verification (Zhao et al., 2023).

4. Generative-model watermarking across modalities

Generative model watermarking extends the problem from decision behavior to sampling behavior and artifact provenance. In diffusion-based image generation, one line of work fine-tunes the generator so that trigger prompts produce a secret image. “Watermarking Diffusion Model” introduces NAIVEWM and FIXEDWM for latent diffusion models: the former activates on a special token appearing anywhere in the prompt, while the latter activates only when the trigger appears in a fixed position, which is more stealthy because the trigger token alone is insufficient (Liu et al., 2023). A complementary line embeds the watermark into the model itself rather than prompt semantics. “Image Watermarking of Generative Diffusion Models” trains a diffusion model jointly with a watermark autoencoder so that all generated images carry a decodable watermark image, enabling both watermark presence detection and watermark-type classification for attribution across models (Chen et al., 12 Feb 2025).

Tabular generative models expose a different constraint set. Early tabular watermarking either edited cells post hoc or ported latent-noise watermarking from diffusion images. “MUSE: Model-Agnostic Tabular Watermarking via Multi-Sample Selection” argues that tabular diffusion pipelines are poorly suited to inversion because quantile normalization, VAEs, and DDIM inversion collectively make latent recovery fragile and expensive. MUSE instead samples multiple candidate rows and selects one using a keyed scoring function, avoiding inversion altogether and remaining compatible with any tabular generative model that supports repeated sampling. Its detection statistic is the mean watermark score

$S(T) = \frac{1}{N}\sum_{i=1}^N s_k(\mathbf{x}_i),$

and the paper derives explicit relationships among detectability, candidate count, and dataset size (Fang et al., 30 May 2025).

Language-model watermarking has developed along both statistical and triggerable lines. WaterPool introduces a key-centered decomposition into a key module and a mark module, showing that many trade-offs between imperceptibility, efficacy, and robustness arise from the key module rather than the mark itself. WaterPool preserves a complete key sampling space while using semantics-based search to improve key restoration, and functions as a plug-in for existing statistical watermarks such as KGW, EXP, and ITS (Huang et al., 2024). Neural Honeytrace addresses MLaaS extraction with a training-free wrapper that encodes similarity information into output distributions and label frequencies; it reports that the average number of samples required for a worst-case t-Test-based copyright claim is reduced from 193,252 to 1,857 with zero training cost (Xu et al., 16 Jan 2025).

5. Evaluation criteria, attacks, and recurring disputes

The standard evaluation vocabulary comprises fidelity, robustness, reliability, integrity, capacity, secrecy, efficiency, and generality (Boenisch, 2020). Fidelity measures degradation on the original task; robustness measures survival under attacks such as fine-tuning, pruning, quantization, compression, distillation, transfer learning, or output post-processing; reliability and integrity are the low-false-negative and low-false-positive sides of verification; capacity, secrecy, and efficiency capture message size, detectability of the watermark itself, and operational overhead (Boenisch, 2020). In practice, the metrics vary strongly by modality: accuracy or downstream task loss for discriminative models, PSNR and SSIM for image-processing outputs, IS and FID for watermarked diffusion models, BER or NC for explicit watermark recovery, and AUC or TPR@FPR for black-box detection (Zhang et al., 2020, Zhang et al., 2022, Liu et al., 2023, Fang et al., 30 May 2025).

Attack taxonomies in the review literature distinguish watermark detection, suppression, forging, overwriting, and removal (Boenisch, 2020). Detection attacks attempt to determine whether watermarking is present; suppression hides the watermark at verification time; forging and overwriting create ownership ambiguity; removal tries to erase the watermark while preserving utility. For output-watermarked image-processing models, data augmentation during surrogate training is particularly destructive to fixed-pattern watermarks, which is why structure consistency becomes necessary (Zhang et al., 2021). For triggerable black-box schemes, adaptive label recovery and hard-label channels sharply reduce transmitted watermark information, motivating the information-theoretic analysis and multi-step distributional encoding of Neural Honeytrace (Xu et al., 16 Jan 2025).

Ensemble distillation exposes another recurrent weakness of trigger-set methods. CosWM addresses this by embedding a weak periodic signal into output probabilities rather than relying on conflicting label-level backdoors, then verifying it via Lomb–Scargle spectral analysis. The method is explicitly designed for black-box ownership verification against ensemble distillation, where averaging teacher outputs can erase ordinary triggers (Charette et al., 2022).

Evaluation itself has become a research problem. For diffusion-image watermarking, WMVLM argues that existing assessments are fragmented across residual and semantic schemes, often lack interpretability, and neglect important security considerations. It therefore proposes a unified VLM-based framework that scores residual watermarks by artifact strength and erasure resistance, and semantic watermarks by latent distribution shifts, while also generating natural-language explanations of the underlying evidence (Yang et al., 29 Jan 2026).

6. Limitations, open problems, and research directions

Despite rapid diversification, formal security remains limited in much of the literature. Many schemes are evaluated empirically under selected attacks rather than under comprehensive adaptive adversaries. Trigger-based approaches remain vulnerable to trigger recovery, ambiguity, and removal techniques inherited from backdoor research; output-space watermarks for image-processing models can be fragile to spatial transforms unless the watermark is explicitly structure-aligned; and some diffusion and generative schemes rely on assumptions about invertibility, prompt secrecy, or private decoders that do not automatically yield public verifiability (Boenisch, 2020, Zhang et al., 2021, Liu et al., 2023, Chen et al., 12 Feb 2025).

A second limitation is benchmarking heterogeneity. Classification, image processing, language generation, diffusion synthesis, and tabular synthesis all use different notions of watermark strength, distortion, and attack success. This suggests that comparisons across paradigms remain difficult unless evaluation frameworks become more standardized. The emergence of modality-specific theory—such as WaterPool’s key-centered analysis for LLMs and MUSE’s detectability calibration for tabular generators—indicates that watermark design is increasingly conditioned on the computational and statistical peculiarities of each model class (Huang et al., 2024, Fang et al., 30 May 2025).

A third open issue is deployment practicality. Training-based watermarks can be expensive and inflexible; training-free or plug-and-play methods are attractive but must still resist adaptive attacks. Branch-based protocols and inference-time wrappers address the retraining burden in API settings, while model-agnostic sampling-based methods show that watermarking can sometimes avoid direct modification of model internals altogether (Zhao et al., 2023, Xu et al., 16 Jan 2025, Fang et al., 30 May 2025).

The field is therefore moving along several fronts at once: toward performance-lossless black-box protocols, toward architecture-agnostic watermarking for generative models, toward integrity-oriented fragile schemes, and toward better evaluation and interpretability. A plausible implication is that future systems will combine multiple layers—parameter or branch signatures for ownership, output-space or statistical marks for provenance, and fragile probes for integrity—rather than relying on any single watermarking primitive.