Title: Tree-Rings Watermarks: Invisible Fingerprints for Diffusion Images
Venue: NeurIPS 2023
Accepted: yes
Keywords: Diffusion Model

Watermark

Privacy and Security
Abstract: Watermarking the outputs of generative models is a crucial technique for tracing copyright and preventing potential harm from AI-generated content. In this paper, we introduce a novel technique called Tree-Ring Watermarking that robustly fingerprints diffusion model outputs.  Unlike existing methods that perform post-hoc modifications to images after sampling, Tree-Ring Watermarking subtly influences the entire sampling process, resulting in a model fingerprint that is invisible to humans. The watermark embeds a pattern into the initial noise vector used for sampling. These patterns are structured in Fourier space so that they are invariant to convolutions, crops, dilations, flips, and rotations.  After image generation, the watermark signal is detected by inverting the diffusion process to retrieve the noise vector, which is then checked for the embedded signal.  We demonstrate that this technique can be easily applied to arbitrary diffusion models, including text-conditioned Stable Diffusion, as a plug-in with negligible loss in FID. Our watermark is semantically hidden in the image space and is far more robust than watermarking alternatives that are currently deployed.

Tree-Rings Watermarks: Invisible Fingerprints for Diffusion Images

Abstract

Watermarking the outputs of generative models is a crucial technique for tracing copyright and preventing potential harm from AI-generated content. In this paper, we introduce a novel technique called Tree-Ring Watermarking that robustly fingerprints diffusion model outputs. Unlike existing methods that perform post-hoc modifications to images after sampling, Tree-Ring Watermarking subtly influences the entire sampling process, resulting in a model fingerprint that is invisible to humans. The watermark embeds a pattern into the initial noise vector used for sampling. These patterns are structured in Fourier space so that they are invariant to convolutions, crops, dilations, flips, and rotations. After image generation, the watermark signal is detected by inverting the diffusion process to retrieve the noise vector, which is then checked for the embedded signal. We demonstrate that this technique can be easily applied to arbitrary diffusion models, including text-conditioned Stable Diffusion, as a plug-in with negligible loss in FID. Our watermark is semantically hidden in the image space and is far more robust than watermarking alternatives that are currently deployed. Code is available at https://github.com/YuxinWenRick/tree-ring-watermark .

1 Introduction

The development of diffusion models has led to a surge in image generation quality. Modern textto-image diffusion models, like Stable Diffusion and Midjourney, are capable of generating a wide variety of novel images in an innumerable number of styles. These systems are general-purpose image generation tools, able to generate new art just as well as photo-realistic depictions of fake events for malicious purposes.

The potential abuse of text-to-image models motivates the development of watermarks for their outputs. A watermarked image is a generated image containing a signal that is invisible to humans and yet marks the image as machine-generated. Watermarks document the use of image generation systems, enabling social media, news organizations, and the diffusion platforms themselves to mitigate harms or cooperate with law enforcement by identifying the origin of an image [Bender et al., 2021, Grinbaum and Adomaitis, 2022].

Research and applications of watermarking for digital content have a long history, with many approaches being considered over the last decade [O'Ruanaidh and Pun, 1997, Langelaar et al., 2000]. However, so far research has always conceptualized the watermark as a minimal modification imprinted onto an existing image [Solachidis and Pitas, 2001, Chang et al., 2005, Liu et al., 2019, Fei et al., 2022]. For example, the watermark currently deployed in Stable Diffusion [Cox et al., 2007], works by modifying a specific Fourier frequency in the generated image.

The watermarking approach we propose in this work is conceptually different: This is the first watermark that is truly invisible, as no post-hoc modifications are made to the image. Instead,

Generation

Predict

FFT

x

T

Watermarked x

T

IFFT

DDIM

'A Teddy bear in

Washington DC'

Watermarked Image

Attack

Detection

DDIM Inversion

+ FFT

'' (empty prompt)

Distance to

<

Predefined Key:

Watermarking

Strong Perturbation

the distribution of generated images is imperceptibly modified and an image is drawn from this modified distribution. This way, the actual sample carries no watermark in the classical additive sense, however an algorithmic analysis of the image can detect the watermark with high accuracy. From a more practical perspective, the watermark materializes in minor changes in the potential layouts of generated scenes, that cannot be distinguished from other random samples by human inspection.

This new approach to watermarking, which we call Tree-Ring Watermarking based on the patterns imprinted into the Fourier space of the noise vector of the diffusion model, can be easily incorporated into existing diffusion model APIs and is invisible on a per-sample basis. Most importantly, Tree-Ring Watermarking is far more robust than existing methods against a large battery of common image transformations, such as crops, color jitter, dilation, flips, rotations, or noise. Tree-Ring Watermarking requires no additional training or finetuning to implement, and the watermark can only be detected by parties in control of the image generation model. We validate the watermark in a number of tests, measuring negligible impact on image quality scores, high robustness to transformations, the low false-positive rate in detection, and usability for arbitrary diffusion models both with and without text conditioning.

2 Related Work

Diffusion Models Diffusion Models, arising out of the score-based generative models of the formalism of Song and Ermon [2019, 2020], are the currently strongest models for image generation [Ho et al., 2020, Dhariwal and Nichol, 2021]. Diffusion models are capable of sampling new images at inference time by iteratively processing an initial noise map. The most prominent sampling algorithm in deployment is DDIM sampling [Nichol and Dhariwal, 2021] without additional noise, which can generate high-quality images in fewer steps than traditional DDPM sampling. Diffusion models are further accelerated for practical usage by optimizing images only in the latent space of a pre-trained VAE, such as in latent diffusion [Rombach et al., 2022].

Watermarking Digital Content Strategies to imprint watermarks onto digital content, especially images, have a long tradition in computer vision. Approaches such as Boland [1996], Cox et al. [1996], O'Ruanaidh and Pun [1997] describe traditional watermark casting strategies based on imprinting a watermark in a suitable frequency decomposition of the image, constructed through DCT, DWT, Fourier-Mellin, or complex wavelet transformations. These frequency transformations all share the beneficial property that simple image manipulations, such as translations, rotations, and resizing are easily understandable and watermarks can be constructed with robustness to these transformations in mind. A fair evaluation of watermarking approaches appears in Pitas [1998], Kutter and Petitcolas [1999], which highlight the importance of measurement of false-positive rates

for each strategy and ROC-curves under attack through various image manipulations. Work continues on imprinting watermarks, with strategies based on SVD decompositions [Chang et al., 2005], Radon transformations [Seo et al., 2004] and based on multiple decompositions [Al-Haj, 2007].

Fingerprinting and Watermarking Generative Models The development of modern deep neural networks opened up new possibilities for 'deep' watermarking. Hayes and Danezis [2017] and Zhu et al. [2018] propose strategies to learn watermarking end-to-end, where both the watermark encoder and the watermark decoder are learned models, optimized via adversarial objectives to maximize transmission and robustness [Zhang et al., 2019]. Notably these approaches still work like a traditional watermark in that the encoder imprints a post-hoc signal onto a given image - however the type of imprint is now learned. We refer to Wan et al. [2022] for an overview. A recent improvement is two-stage processes like Yu et al. [2022], where the trained encoder is used to imprint the watermark onto the training data for a generative model. This leads to a trained generative model where the watermark encoder is 'baked in' to the model, making it easier to generate watermarked data. The Stable Signature of Fernandez et al. [2023], applies this idea to latent diffusion models by finetuning the latent decoder based on a pre-trained watermark encoder. Zhao et al. [2023] similarly train on watermarked data for unconditional diffusion models.

Existing image watermarking approaches first learn a watermark signal and then learn to either embed it into generated data or the generating model. This pipeline stands in contrast to watermarking approaches for language models such as Kirchenbauer et al. [2023]. There, no training is necessary to generate watermarked data and the output distribution of the generative model is altered to encode a watermark into generated data in a distributional sense. In the same vein, we propose an approach to alter the output distribution of diffusion models to effectively watermark their outputs. As discussed, this has a number of advantages, in comparison to related work we especially highlight that no training is necessary, that the watermark works with existing models, and that this is the first watermark that does not rely on minor modification of generated images. In this sense, this is the first watermark that is really 'invisible', see Appendix Figure 6.

We note in passing that watermarking the output of generative models is not to be confused with the task of watermarking the weights of whole models, such as in Uchida et al. [2017], Zhang et al. [2018], Bansal et al. [2022], who are concerned with identifying and fingerprinting models for intellectual property reasons.

2.1 Diffusion Models and Diffusion Inversion

We first introduce the basic notation for diffusion models and DDIM sampling [Ho et al., 2020, Song and Ermon, 2020, Dhariwal and Nichol, 2021]. A forward diffusion process consists of T steps of the noise process a predefined amount of Gaussian noise vector to a real data point x 0 ∈ q ( x ) , where q ( x ) is the real data distribution, specifically:

where β t ∈ (0 , 1) is the scheduled variance at step t . The closed-form for this sampling is

For the reverse diffusion process, DDIM [Song and Ermon, 2020] is an efficient deterministic sampling strategy, mapping from a Gaussian vector x T ∼ N (0 , 1) to an image x 0 ∈ q ( x ) . For each denoising step, a learned noise-predictor ϵ θ estimates the noise ϵ θ ( x t ) added to x 0 . According to Equation (1), we can derive the estimation of x 0 as:

Then, we add the estimated noise to ˆ x 0 to find x t -1 :

We denote such a recursively denoising process from x T to x 0 as x 0 = D θ ( x T ) .

However, given the learned model ϵ θ ( x t ) , it is also possible to move in the opposite direction 1 . Starting from an image x 0 , Dhariwal and Nichol [2021] describes an inverse process that retrieves an initial noise vector x T which maps to an image ˆ x 0 close to x 0 through DDIM, where ˆ x 0 = D θ ( x T , 0) ≈ x 0 . This inverse process depends on the assumption that x t -1 -x t ≈ x t +1 -x t . Therefore, from x t → x t +1 , we follow:

We denote the whole inversion process from a starting real image x 0 to x T as x T = D † θ ( x 0 ) .

In this work, we re-purpose DDIM inversion D † θ for watermark detection. Given a generated image x 0 with a starting noise x T , we apply DDIM inversion to find ˆ x T . We empirically find DDIM's inversion performance to be quite strong, and ˆ x T ≈ x T . While it may not be surprising that inversion is accurate for unconditional diffusion models, inversion also succeeds well-enough for conditional diffusion models, even when the conditioning c is not provided. This property of inversion will be exploited heavily by our watermark below.

3 Method

In this section, we provide a detailed description of each layer of Tree-Ring Watermarking .

3.1 Overview of Tree-Ring Watermarking

Diffusion models convert an array of Gaussian noise into a clean image. Tree-Ring Watermarking chooses the initial noise array so that its Fourier transform contains a carefully constructed pattern near its center. This pattern is called the 'key.' This initial noise vector is then converted into an image using the standard diffusion pipeline with no modifications. To detect the watermark in an image, the diffusion model is inverted using the process described in Section 2.1 to retrieve the original noise array used for generation. This array is then checked to see whether the key is present.

Rather than imprint the key into the Gaussian array directly, which might cause noticeable patterns in the resulting image, we imprint the key into the Fourier transform of the starting noise vector. We choose a binary mask M , and sample the key k ∗ ∈ C | M | . As such, the initial noise vector x T ∈ R L can be described in Fourier space as

For reasons described below, we choose M as a circular mask with radius r centered on the lowfrequency modes.

At detection time, given an image x ′ 0 , the model owner can obtain an approximated initial noise vector x ′ T through the DDIM inversion process: x ′ T = D † θ ( x ′ 0 ) . The final metric is calculated as the L1 distance between the inverted noise vector and the key in the Fourier space of the watermarked area M , i.e.

and the watermark is detected if this falls below a tuned threshold τ . The process described above is straightforward. However, its success depends strongly on the construction of the 'key' pattern, which we discuss below.

3.2 Constructing a Tree-Ring Key

We watermark images by placing a 'key' pattern into the Fourier space of the original Gaussian noise array. Our patterns can exploit several classical properties of the Fourier transform for periodic signals that we informally state here.

A rotation in pixel space corresponds to a rotation in Fourier space.

A translation in pixel space multiplies all Fourier coefficients by a constant complex number.

A dilation/compression in pixel space corresponds to a compression/dilation in Fourier space.

Color jitter in pixel space (adding a constant to all pixels in a channel) corresponds to changing the magnitude of the zero-frequency Fourier mode.

A number of classical watermarking strategies rely on watermarking in Fourier space and exploit similar invariances [Pitas, 1998, Solachidis and Pitas, 2001]. Our watermark departs from classical methods by applying a Fourier watermark to a random noise array before diffusion takes place. Curiously, we will observe below that the invariant properties above are preserved in x T even when image manipulations are done in pixel space of x 0 .

In addition to exploiting the invariances above, the chosen key should also be statistically similar to Gaussian noise. Note that the Fourier transform of a Gaussian noise array is also distributed as Gaussian noise. For this reason, choosing a highly non-Gaussian key may cause a distribution shift that impacts the diffusion model.

We consider three different types of keys, with the respective benefits of each pattern being demonstrated in subsequent experimental sections. We believe there are numerous other interesting and practical types that can be explored in future work.

Tree-RingZeros : We choose the mask to be a circular region to preserve invariance to rotations in image space. The key is chosen to be an array of zeros, which creates invariance to shifts, crops, and dilations. This key is invariant to manipulations, but at the cost of departing severely from the Gaussian distribution. It also prevents multiple keys from being used to distinguish between models.

Tree-RingRand : We draw the a fixed key k ∗ from a Gaussian distribution. The key has the same iid Gaussian nature as the original Fourier modes of the noise array, and so we anticipate this strategy will have the least impact on generation quality. This method also offers the flexibility for the model owner to possess multiple keys. However, it is not invariant to make image manipulations.

Tree-RingRings : We introduce a pattern comprised of multiple rings , and constant value along each ring. This makes the watermark invariant to rotations. We choose the constant ring values from a Gaussian distribution. This provides some invariance to multiple types of image transforms, while also ensuring that the overall distribution is only minimally shifted from an isotropic Gaussian.

3.3 Deriving P-values for Watermark Detection

A key desideratum for a reliable watermark detector is that it provide an interpretable P-value that communicates to the user how likely it is that the observed watermark could have occurred in a natural image by random chance. In addition to making detection results interpretable, P-values can be used to set the threshold of detection, i.e., the watermark is 'detected' when p is below a chosen threshold α . By doing so, one can explicitly control the false positive rate α, making false accusations statistically unlikely.

To this end, we construct a statistical test for the presence of the watermark that produces a rigorous P-value. The forward diffusion process is designed to map images onto Gaussian noise, and so we assume a null hypothesis in which the entries in the array x ′ T obtained for a natural image are Gaussian. We find that this assumption holds quite well in practice, see Figure 7.

For any test image x ′ 0 , we compute the approximate initial vector x ′ T and then set y = F ( x ′ T ) . We then define the following null hypothesis

Here, σ 2 is an unknown variance, which we estimate for each image 2 using the formula σ 2 = 1 M ∑ i ∈ M | y i | 2 . To test this hypothesis, we define the score

No Watermark

Watermarked

Attacked

'Anime art of a dog in Shenandoah National Park'

P-value

= 0

.

27

3

.

73

e-

60

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.

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e-

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'Synthwave style artwork of a person is kayaking in Acadia National Park'

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'An astronaut riding a horse in Zion National Park'

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'A painting of Yosemite National Park in Van Gogh style'

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07

When H 0 is true, the distribution of η is exactly a noncentral χ 2 distribution [Patnaik, 1949], with | M | degrees of freedom and non-centrality parameter λ = 1 σ 2 ∑ i | k ∗ i | 2 .

We declare an image to be watermarked if the value of η is too small to occur by random chance.

The probability of observing a value as small as η is given by the cumulative distribution function Φ χ 2 of the noncentral χ 2 distribution:

Φ χ 2 is a standard statistical function [Glasserman, 2003], available in scipy and many other statistics libraries.

We show qualitative examples of the proposed watermarking scheme and accompanying P-values in Figure 2. For each prompt, we show the generated image with and without the watermark, and

also a watermarked image subjected to a transformation. For each image, we report a P-value. As expected, these values are large for non-watermarked images, and small (enabling rejection of the null hypothesis) when the watermark is present. Transformations reduce the watermark strength as reflected in the increased P-value.

4 Experiments

We perform experiments on two common diffusion models to measure the efficacy and reliability of the Tree-Ring Watermarking technique across diverse attack scenarios. Furthermore, we carry out ablation studies to provide an in-depth exploration of this technique.

4.1 Experimental Setting

We employ Stable Diffusion-v2 [Rombach et al., 2022], an open-source, state-of-the-art latent text-toimage diffusion model, along with a 256 × 256 ImageNet diffusion model 3 [Dhariwal and Nichol, 2021]. In the main experiment, we use 50 inference steps for generation and detection for both models. For Stable Diffusion, we use the default guidance scale of 7 . 5 , and we use an empty prompt for DDIM inversion, emulating that the image prompt would be unknown at detection time. The watermark radius r we use is 10 . Later, we conduct more ablation studies on these important hyperparameters. All experiments are conducted on a single NVIDIA RTX A4000.

In our comparative analysis, we consider four baselines: two training-free methods, DwtDct and DwtDctSvd [Cox et al., 2007]; a pre-trained GAN-based watermarking model, RivaGAN [Zhang et al., 2019, Goodfellow et al., 2014]; and a pre-trained watermarking V AE decoder, used exclusively for Stable Diffusion model experiments, named Stable Signature [Fernandez et al., 2023]. However, these baseline methods are designed for steganography, which conceals a target bit-string within an image. To ensure a fair comparison with our exclusively watermarking method, we employ the distance between the decoded bit-string and the target bit-string (Bit Accuracy) as the measurement metric. The approach of Cox et al. [2007] is currently deployed as a watermark mechanism in Stable Diffusion 4 .

4.2 Benchmarking Watermark Accuracy and Image Quality

To benchmark the effectiveness of the watermark, we primarily report the area under the curve ( AUC ) of the receiver operating characteristic (ROC) curve, and the True Positive Rate when the False Positive Rate is at 1% , denoted as TPR @1% FPR . To demonstrate the generation quality of the watermarked images, we assess the Frechet Inception Distance ( FID ) [Heusel et al., 2017] for both models. Additionally, for the Stable Diffusion model, we also evaluate the CLIP score [Radford et al., 2021] between the generated image and the prompt, as measured by OpenCLIP-ViT/G [Cherti et al., 2022]. For AUC and TPR @1% FPR, we create 1 , 000 watermarked and 1 , 000 unwatermarked images for each run. For FID, we generate 5 , 000 images for Stable Diffusion and 10 , 000 images for the ImageNet Model. The FID of Stable Diffusion is evaluated on the MS-COCO-2017 training dataset [Lin et al., 2014], and the FID of the ImageNet Model is gauged on the ImageNet-1k training dataset [Deng et al., 2009]. All reported metrics are averaged across 5 runs using different random seeds following this protocol.

In Table 1, we present the main experimental results for Stable Diffusion and the ImageNet model. In the clean setting, all baselines except DwtDct and all Tree-Ring Watermarking variants are strongly detectable. Tree-RingRand and Tree-RingRings show negligible impact on the FID and no impact on the CLIP score.

4.3 Benchmarking Watermark Robustness

To benchmark the robustness of our watermark, we focus on documenting its performance under 6 prevalent data augmentations utilized as attacks. These include 75 ◦ rotation, 25% JPEG compression, 75% random cropping and scaling, Gaussian blur with an 8 × 8 filter size, Gaussian noise with σ = 0 . 1 , and color jitter with a brightness factor of 6 . Additionally, we conduct ablation studies to

investigate the impact of varying intensities of these attacks. We report both AUC and TPR @1% FPR in the average case where we average the metrics over the clean setting and all attacks. In all ablation studies, we report the average case.

In Table 1, the baseline methods fail in the presence of adversaries. On the contrary, our methods demonstrate higher reliability in adversarial settings. Among them, Tree-RingRings performs the best under adversarial conditions, a result of our careful watermark pattern design.

Further, we show the AUC for each attack setting in Table 2. Notably, Tree-RingZeros demonstrates high robustness against most perturbations, except for Gaussian noise and color jitter. Similarly, Tree-RingRand is robust in most scenarios but performs poorly when faced with rotation, as expected. Overall, Tree-RingRings delivers the best average performance while offering the model owner the flexibility of multiple different random keys. It is worth noting that the baseline method RivaGan also demonstrates strong robustness in most scenarios, but it is important to highlight that our method is training-free and really 'invisible'.

4.4 Ablation Experiments

In this section, we undertake exhaustive ablation studies with the Ring pattern on several key hyperparameters to demonstrate the efficacy of Tree-Ring Watermarking . Except for the ablation on attacks, the reported numbers represent averages over all attack scenarios and clean images.

Number of Steps Used for Generation and Detection. A key unknown variable for the model owner at the detection time is the actual number of inference steps used during the generation time.

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This factor could potentially impact the precision of the DDIM inversion approximation of the initial noise vector. To scrutinize this, we systematically vary the number of steps for both the generation and detection time. Due to the computational demands of sampling with a high number of inference steps, we employ a total of 400 images for each run.

In Figure 3, we compare AUC across all step combinations. Surprisingly, even with a significant difference between the generation-time and detection-time # steps, the decrease in AUC is minimal when the model owner uses a reasonable number of inference steps for detection without knowledge of the true generation-time steps. This indicates that the DDIM inversion maintains its robustness in approximating the initial noise vector, and is effective for watermark detection irrespective of the exact number of steps employed. Interestingly, we notice a trend where the detection power appears to be slightly stronger with fewer inference steps at detection

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0.808 0.923 0.966 0.972 0.971 0.970 0.969 0.968 0.967

0.801 0.919 0.962 0.968 0.968 0.967 0.966 0.965 0.964

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time or a larger number of inference steps at generation time. This is an advantageous scenario as the model owner now does not actually need to carry out a large number of steps for DDIM inversion, while concurrently, the model owner (or the user) is free to choose the number of generation steps that achieve the best quality [Rombach et al., 2022].

Watermark radii. The radius of injected watermarking patterns is another critical hyperparameter affecting robustness and generation quality. The corresponding results are shown in Figure 4(a). As the watermarking radius increases, the watermark's robustness improves. Nevertheless, there is a trade-off with generation quality. We overall confirm a radius of 16 to provide reasonably low FID while maintaining strong detection power.

Guidance scales. Guidance scale is a hyperparameter that controls the significance of the text condition. Higher guidance scales mean the generation more strictly adheres to the text guidance, whereas lower guidance scales provide the model with greater creative freedom. Optimal guidance scales typically range between 5 and 15 for the Stable Diffusion model we employ. We explore this factor from 2 to 18 in Figure 4(b) and highlight that the strength of the guidance is always unknown during detection time. Although a higher guidance scale does increase the error for DDIM inversion due to the lack of this ground-truth guidance during detection, the watermark remains robust and reliable even at a guidance scale of 18 . This is again beneficial for practical purposes, allowing the model owner to keep guidance scale a tunable setting for their users.

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under each attack with various attack strengths. As shown in Figure 5, even with extreme perturbations like Gaussian blurring with kernel size 40 , Tree-Ring Watermarking can still be reliably detected.

5 Limitations and Future Work

Tree-Ring Watermarking requires the model owner to use DDIM during inference. Today, DDIM is still likely the most popular sampling method due to its economical use of GPU resources and high quality. However, the proposed watermark will need to be adapted to other sampling schemes should DDIM fall out of favor. Further, the proposed watermark is by design only verifiable by the model owner because model parameters are needed to perform the inversion process. This has advantages against adversaries, who cannot perform a white-box attack on the watermark or even verify whether an ensemble of manipulations broke the watermark. However, it also restricts third parties from detecting the watermark without relying on an API. Finally, it is currently not yet clear how large the capacity for multiple keys k ∗ would be. Would it be possible to assign a unique key to every user of the API?

The effectiveness of the proposed watermark is directly related to the accuracy of the inverse DDIM process. Future work that improves the accuracy of this inversion [Zhang et al., 2023], or utilizes invertible diffusion models as described in Wallace et al. [2022], would also improve watermarking power further.

6 Conclusion

We propose a new approach to watermarking generative diffusion models using minimal shifts of their output distribution. This leads to watermarks that are truly invisible on a per-sample basis. We describe how to optimally shift, so that the watermark remains detectable even under strong image manipulations that might be encountered in daily usage and handling of generated images.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method to add the watermark to the images generated by the diffusion model during the generation process. It subtly inﬂuences the entire sampling process, resulting in a model fingerprint that is invisible to humans. In terms of the specific approach, the watermark embeds a pattern into the initial noise vector used for sampling. These patterns are structured in Fourier space so that they are invariant to convolutions, crops, dilations, ﬂips, and rotations. After image generation, the watermark signal is detected by inverting the diffusion process (DDIM Inversion) to retrieve the noise vector, which is then checked for the embedded signal.\n\nSTRENGTHS:\n- Although not practical, I think the idea is interesting.\n- Good writing. This paper is well written and easy to follow.\n\nWEAKNESSES:\n- I consider the method proposed in this paper as image watermarking. My biggest concern is that the method is not practical. Image watermarking algorithms have been extensively studied, what are the advantages of this method over those methods? What's more, the method has some fatal flaws, such as the modified initial noise no longer satisfies the standard Gaussian noise, which will have an impact on the diversity and quality of the synthesis results, the necessity to use DDIM inversion to recover the watermark, etc.\n- Although three construction strategies are proposed in this paper, the resulting initialized noise does not satisfy the standard Gaussian distribution, which has an impact on the diversity and quality of the final synthesis results. However, there is no relevant experimental analysis in this paper. Please provide quantitative and qualitative experiments regarding the diversity and quality (CLIP Score, FID does not accurately reflect this, so user study is required) of the synthesis results.\n- The stable diffusion uses a classifier-free guidance in the synthesis process, and the guidance is generally set to 7.5. This paper uses empty text to recover the initial noise through DDIM inversion is not able to reconstruct accurately. The experiments in this paper also prove this, so there is a big vulnerability in the method presented in this paper.\n- For multiple key capacity, the experimental analysis needs to be provided.\n\nQUESTIONS:\nSee Weaknesses\n\nLIMITATIONS:\nThe negative impact of using this technique needs to be declared and discussed.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a watermarking scheme for image generative AI based on diffusion process. The watermark is embedded in the initial noise pattern before diffusion. Detection succeeds in reversing the diffusion to get an estimate of the initial noise pattern.\n\nSTRENGTHS:\nS1. The idea is simple and super original.\nS2. The watermarking technique seems to be very robust.\n\nWEAKNESSES:\nW1. Terminology. Being a watermarker for a long time, I am surprised by some atypical wordings. Mainly:\n- fingerprint / fingerprinting: Fingerprint usually denotes a passive forensics technique (like robust hash) whereas watermarking is an active technique (the content/model is modified). I found the title very confusing for instance.\n- to imprint: the correct term is 'to embed' in the watermarking literature.\n\nW2. Bold claims. I disagree with the following statements\n- Line 35: \"This is the first watermark that is truly invisible as no post-hoc are made to the image\". I strongly disagree. The difference between watermarked and non-watermarked generated images are super visible since their visual content are not the same (see Fig.~2). How can you pretend to be invisible. The thing is that nobody has access to the non-watermarked generated images therefore we do not care about the visibility. We only care about the generation quality (FID and CLIP score).\n- Line 47: \"the watermark can only be detected by parties in control of the image generation model\". This is a drawback, not an advantage.\n- Line 81: \"Stable Signature applies this idea\". If \"this idea\" relates to training a model with watermarked images (a la Yu et al. [2022]), then this statement is wrong.\n\nW3. No theoretical background.\n- Line 157: \"Curiously, we will observe that ...\" I understand that \"curiously\" as \"we do not know why but this happens to hold.\"\n- The threshold for a required FPR is *experimentally* set. First, over 1,000 unwatermarked images ONLY for a FPR=1%. A population size of 1,000 yields an accuracy above +/- 1% (95% confidence) in the estimation of a small probability. So, 1,000 is definitively not enough... and this is just FPR=1%. See https://en.wikipedia.org/wiki/Sample_size_determination\nBy the way, since the secret key is a Gaussian vector (even for the three-ring), there might be a way to set the threshold theoretically. At least, in watermarking literature, this is the case for Gaussian secret vector and cosine similarity thanks to the regularised beta incomplete function.\n- Some properties are outlined but they are not exactly put into practice:\nLine 149: Rotation - Done -> this explains the rings.\nLine 150: Translation - Not Done. The magnitude of the Fourier coefficients are invariant to translation but neither the embedding nor the detection works with magnitude. Therefore, the robustness to translation remains unexplained.\nLine 151: Dilation (ie. stretching) - Not Done. Same comment. I am surprised that Rand and Ring show some robustness since a stretching should desynchronise the watermark signal.\nLine 152: Color jitter - Done -> don't rely on the DC coefficient.\n\nW4: Flawed benchmark.\nFernandez et al. [2023] is cited but not included in the comparison. I do not see any reason. On the contrary, some old schemes called \"DwtDct\" and \"DwtDctSvd\" are included. The attached reference is the bible Cox et al. 2007. I do not remember that this book proposes these transformations. Dwt alone -> Yes. Dct alone -> Yes (But, it is well known that there are not robust to geometric attacks). However, DwtDct (ie. the concatenation of Dwt o Dct) -> Does not makes sense. DwtDctSvd  -> even worse. It would have been much better to compare to recent image watermarking like those cited in Lines 70-80 (especially HiddeN and followers).\n\nConclusion: the benchmark does not include key schemes but includes 2 non-sense techniques.     \n\nW5. I prefer A LOT the metric TPR@1%FPR because it makes sense from a practical point of view whereas AUC delivers poor information. For instance, Fig. 3 is hard to decipher: AUC = 0.948 is green lighted whereas such AUC corresponds to a TPR of 0.1 in some other plots. \nSame for Table 2.\n\nQUESTIONS:\nQ1. Why the detection score is the L1 distance? A watermarker would have use the cosine similarity.\n\nQ2. How do you explain the robustness to translation and crop/scaling? Is the crop random (ie. not a central crop)?\n\nLIMITATIONS:\nSome features are presented as advantages whereas these are limitations.\n\nL1. Line 192 \"However, these baselines methods are designed for steganography\". No, these are watermarking schemes. They offer multi-bit watermarking, whereas you only offer zero-bit watermarking.\n\nL2. The scheme is extremely sensitive to Gaussian noise. A jitter of 2 is ok, but a noise std = 0.1 (out of 255?) pulls down the watermark.\n\nL3. Line 285: \"Further, the proposed watermark is by design only verifiable by the model owner ... this has advantages\". I do not think so. For security reason, the model cannot be disclosed. Fernandez et al. does not have this drawback.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method for watermarking images created by diffusion models, a popular class of generative models. Whereas traditional watermarking methods operate directly on images (e.g. in pixel space or Fourier/wavelet representations), the proposed watermark is embedded in a Fourier representation of the diffusion model’s initial noise distribution. As a result the watermark does not introduce perceptible artifacts, is robust to common image transformations, and can be detected with knowledge of the model weights via a noise inversion process. This method is a promising step towards allowing the operators of generative models to identify synthetic media produced by their systems.\n\nSTRENGTHS:\nThe proposed method is novel and operates by intervening in the sampling process (akin to recent language-model watermarks [1]) rather than “post-hoc” on generated images. This kind of “distributional” watermarking of generative models is increasingly emerging as an attractive alternative to traditional methods.\n\nThe proposed method appears straightforward to implement and does not require re-training the diffusion model.\n\nSolid experimental evaluation against reasonable watermarking baselines, including ablations on key generation & detection parameters.\n\nThe authors provide code for reproducing their experiments.\n\n\n[1] Kirchenbauer, John and Geiping, Jonas and Wen, Yuxin and Katz, Jonathan and Miers, Ian and Goldstein, Tom. “A Watermark for Large Language Models”. https://arxiv.org/abs/2301.10226\n\nWEAKNESSES:\nIn line 157, the authors briefly mention a key result: “Curiously, we will observe below that the invariant properties above are preserved in xT even when image manipulations are done in pixel space of x0.” I think this could be discussed in more depth, as the success of the proposed approach essentially rests on this seemingly counterintuitive property. Do the authors have any theories as to why this property holds?\n\nWatermark capacity is barely touched on. It is common knowledge that watermark robustness, imperceptibility, and information-carrying capacity typically exist in a trade-off. The authors essentially propose a 1-bit watermark in the case of “Tree-Rings-Zeros,” while the actual capacity of the “Rand” and “Rings” variants is murkier (it is not clear how much two keys need to differ in order to be distinguishable, and how many simultaneous keys could operate in practice). While the authors’ main concern is differentiating between watermarked and un-watermarked content — for which capacity may not be essential — I think that at the very least, the difference in capacity between the proposed and baseline approaches should be mentioned. For instance, RivaGAN embeds 32-bit messages (which may be sufficient to “assign a unique key to every user of the API,” in the authors’ words). It is therefore reasonable to wonder whether RivaGAN might achieve better imperceptibility and robustness if trained with a lower capacity closer to that of the proposed method. I don’t think it is necessary for the authors to perform additional experiments along these lines, but a brief mention of the capacities of each method would better contextualize their existing results.\n\nRobustness of the proposed method to multiple simultaneous transformations looks low (Figure 7 in appendix) — it looks like even two simultaneous transformations can lower TPR@1%FPR to under 10%? It would be nice to see some discussion of this in the appendix (e.g. if any transformation combinations prove particularly effective at breaking the watermark without significantly degrading image quality). It would also be nice to see versions of Figure 7 for both baseline watermarks in the appendix.\n\nWhile model weight watermarking approaches are addressed briefly in the related work section (lines 94-97), the authors do not state why such approaches are not viable for the task at hand. Naively, it seems reasonable that a watermark embedded within the model weights during training could be at least as strong as one embedded in the diffusion noise at sampling. An extra sentence or two explaining why such approaches are not considered would be good (e.g. training-free methods are more desirable, existing model weight watermarking methods lack robustness or produce characteristic outputs for only a few \"trigger\" inputs, etc.).\n\nQUESTIONS:\n(These are more comments than questions, and aren't critical to my review/score of the paper)\n\nFrom Tables 1-4, it looks like RivaGAN is actually very competitive with the proposed method on robustness aside from the rotation transform, on which it is not trained. Given that RivaGAN’s attention mechanism supposedly encourages it to hide image modifications in textures, it is possible that a RivaGAN trained on rotation transformations might achieve robustness results on par with the proposed method while allowing for 32-bit watermark capacity. I don’t think this necessarily merits a mention in the paper, but it seems worth pointing out.\n\nOne class of adversaries against which the proposed method might fare substantially better than post-hoc methods like RivaGAN is “generative autoencoder” attacks that use off-the-shelf pretrained image models [2]. An experiment with this kind of transformation probably falls into the realm of future work, but could potentially present a very strong argument for the kind of distributional watermarking approach proposed in the paper over post-hoc image modification.\n\n[2] Zhao, Xuandong and Zhang, Kexun and Wang, Yu-Xiang and Li, Lei. “Generative Autoencoders as Watermark Attackers: Analyses of Vulnerabilities and Threats”. https://arxiv.org/abs/2306.01953\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes watermarking the generated image from diffusion models by watermarking the initial noise and the reverse DDIM process is directly used as the watermark extraction. Experiments show the influence on the visual quality and robustness of the proposed method against various distortions.\n\nSTRENGTHS:\n1) This paper is easy to read.\n2) Watermarking the AIGC is an interesting problem.\n\nWEAKNESSES:\n1) The threat model shall be clarified. For example, who conducts the watermarking process and executes the verification stage? If the user’s ability/behavior (generation process) is unknown as mentioned in L236, why does the user like to use the tree-rings as his initial noise rather than a clean initial noise? \n\n2) As shown in Fig2, compared with other post-processing watermarking, the generated image by the proposed method is charged by a large margin, although the objective FID score is better.\n\n3) What is the influence on the editability of the watermarked noise? In other words, given different prompts, it would be better to show some visual examples of generated images by clean and tree-rings noise, respectively.\n\n4) Section 2.1 shall be reorganized. For example, in L100, a forward diffusion process is from clean data $X_0$ to noise.\n\n5) Some related work is missing. [1] focuses on watermarking the generative models, which also tries to watermark the internal noise.\n\n[1] Ong, Ding Sheng, et al. \"Protecting intellectual property of generative adversarial networks from ambiguity attacks.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021.\n\nQUESTIONS:\n1) What is the influence on the editability of the watermarked noise?\n\n2) If there are two different tree rings embedded into two initial noises, will it affect the integrity of the proposed method? This may be related to the capacity mentioned in Limitations.\n\nLIMITATIONS:\nMentioned in the manuscript.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}