LUHmWDydue/LUHmWDydue.md

Generative Models Are Self-Watermarked: Declaring Model Authentication Through Re-Generation

Anonymous authors Paper under double-blind review

Abstract

As machine- and AI-generated content proliferates, protecting the intellectual property of generative models has become imperative, yet verifying data ownership poses formidable challenges, particularly in cases of unauthorized reuse of generated data. Confirming the ownership of the data is challenging, as the data generation process is opaque to those verifying the authenticity. Our work is dedicated to detecting data reuse from a single sample.

While watermarking has been the traditional method to detect AI-generated content by embedding specific information within models or their outputs, which could compromise the quality of outputs, our approach instead identifies inherent fingerprints in the outputs without altering models. The verification is achieved by requiring the (authentic) models to re-generate the data. Furthermore, we propose a method that iteratively re-generates the data to enhance these fingerprints in the generation stage. The strategy is both theoretically sound and empirically proven effective with recent advanced text and image generative models. Our approach is significant because it avoids extra operations or measures, such as (1) modifying model parameters, (2) altering the generated outputs, or (3) employing additional classification models for verification. This enhancement broadens the applicability of authorship verification (1) to track the IP violation in generative models published without explicitly designed watermark mechanisms and (2) to produce outputs without compromising their quality.

1 Introduction

In recent years, the emergence of Artificial Intelligence Generated Content (AIGC), including tools like ChatGPT, Claude, DALL-E, Stable Diffusion, Copilot, has marked a significant advancement in the quality of machine-generated content. These generative models are increasingly being offered by companies as part of pay-as-you-use services on cloud platforms. While such development has undeniably accelerated the advancement and dissemination of AI technology, it has simultaneously raised substantial concerns regarding the misuse of these models. A key challenge lies in authenticating the author (or source) of the content generated by these models, which encompasses two primary aspects: (1) protecting the Intellectual Property (IP) of the authentic generator when content is misused, and (2) tracing the responsibility of the information source to ensure accountability. Traditionally, the primary approach for safeguarding IP of the contents generated by AI generator has involved embedding subtle but verifiable watermarks into their outputs, such as text (He et al., 2022a;b; Kirchenbauer et al., 2023a), images (Zear et al., 2018; Zhao et al., 2023b) and code (Lee et al., 2023). These watermarking techniques typically involve adding supplementary information to the deep learning model's parameters and architectures or direct post-processing alterations to the generated outputs. However, these alterations could potentially degrade the quality of the generated content. An alternative strategy has been the classification of data produced by a specific model to distinguish it from content generated by other models or humans (Solaiman et al., 2019b; Ippolito et al., 2020). Nonetheless, this often requires training additional classifiers to verify authorship, raising concern about their ability to generalize and maintain robustness across evolving generative models, especially with few training samples.

Figure 1: The two-stage framework leveraging fingerprints in generative models. In (I) Generation Stage, models generate output in traditional ways and optionally re-generate the output k ∈ [1..K] times to enhance the fingerprints. In (II) Verification Stage, the authentication of data ownership is established by assessing the distance between the suspected data (left) and its re-generated version (right). There exists a distinguishable margin between the distances by authentic generator (Ga, at the bottom) and contrasting benign generator (Gc, at the top), exemplified by models from OpenAI and Stability AI respectively. In response to the challenges of authorship authentication and IP protection, our approach is strategically designed to exploit the inherent characteristics of generative models. Firstly, we recognize that generative models possess unique attributes - akin to model fingerprints - such as specific styles and embedded knowledge. In the Verification Stage in our framework, we utilize these implicit fingerprints by measuring the distance D between the genuine data samples with content re-generated by the authentic and contrasting models. Secondly, to enhance the distinctive nature of these fingerprints, our approach in the Generation Stage involves using the original model to iteratively re-generate outputs from previous iterations. This process is grounded in fixed-point theory (Granas & Dugundji, 2003) and its practical applications. Through this iterative re-generation, the model's inherent fingerprints become more pronounced, enhancing the effectiveness of our verification process.

In Figure 1, we present a conceptual framework for authorship verification through re-generation.

Stage I: Generation The authentic generator targets producing outputs that involve stealthy but significant signatures that are distinguishable from other generative models or humans. We consider two distinct approaches: (i) 'Traditional Generation' produces the authentic outputs xa from a given text input as a prompt, i.e., xa = Ga(xp), where xp = "Storm on Sea of Galilee"; and (ii) 'Iterative Re-Generation' enhances the model's unique signature by re-generating the data multiple times using a 're-painting' or 'paraphrasing' mode, i.e., x ⟨k+1⟩ a = Ga(x ⟨k⟩ a ). Here Ga is the authentic generative model which is DALL·E (Ramesh et al., 2021) in this example.

Stage II: Verification In this stage, authentic model Ga verifies the origin of its artefact xa by comparing the 'distance' D between xa and its re-generation by the authentic model Ga(xa) or other contrasting models Gc(xa). Intuitively, the one-step regeneration distance of an image originally generated by the authentic model, such as DALL·E by OpenAI, is expected to be smaller when compared to itself than to a contrasting model not involved in its initial generation, i.e., D(xa, Ga(xa)) < D(xa, Gc(xa)). Furthermore, the more re-generations an image undergoes during the *Generation Stage*, the lower its one-step regeneration distance of the authentic model becomes at the Verification Stage, *i.e.,* D(x ⟨i⟩ a , Ga(x ⟨i⟩ a )) < D(x ⟨j⟩ a , Ga(x ⟨j⟩ a )), when i > j. We summarize the key advantages and contributions of our work as follows:

• We validate the effectiveness of using re-generated data as a key indicator for authorship verification.

This approach is designed to be functional in black-box settings and applies across various generative applications, such as Natural Language Generation (NLG) and Image Generation (IG).

• We introduce an iterative re-generation technique to enhance the inherent fingerprints of generative models. We use fixed-point theory to demonstrate that modifications achieved through re-generation converge to minimal edit distances. This ensures a distinct separation between the outputs of authentic models and those generated by other models.

• We have developed a practical verification protocol that streamlines the process of data ownership validation in generative models. This protocol is especially useful in legal settings, as it eliminates the need for generators to disclose their model parameters or watermarking strategies, thereby preserving confidentiality and proprietary integrity.

• A notable advantage of our approach is its reliance solely on the standard generative models, without resorting to additional interventions, including (1) manipulating or fine-tuning generative model parameters, (2) post-editing the outputs, or (3) additional independent classification models for verification. This simplicity in design not only preserves the original quality of the generated content but also enhances the feasibility and accessibility of our verification method.

2 Related Work

Recent advancements in the field of generative modeling, exemplified by innovations like DALL·E (Ramesh et al.), Stable Diffusion (Rombach et al., 2022), ChatGPT, Claude, Gemini, and others. However, this proliferation of synthetic media has simultaneously raised ethical concerns. These concerns include the potential for misuse in impersonation (Hernandez, 2023; Verma, 2023), dissemination of misinformation (Pantserev, 2020; Hazell, 2023; Mozes et al., 2023; Sjouwerman, 2023), academic dishonesty (Lund et al., 2023), and copyright infringement (Brundage et al., 2018; Rostamzadeh et al., 2021; He et al., 2022a; Xu & He, 2023).

In response, there is an increasing focus on the need to trace and authenticate the origins of such content to prevent its illegitimate use in Artificial Intelligence-Generated Content (AIGC). Considering the distinct nature of image and text, we will review the authorship identification in image and text generation models separately.

Authorship Identification For Image Generation Models

Image watermarking, recognized as a standard approach to verify ownership and safeguard the copyright of a model, involves imprinting a unique watermark onto generated images. Conventional methods encompass direct alterations to pixel values, for instance, in the spatial domain, or the incorporation of watermarks into altered image forms, such as in the frequency domain (Cox et al., 2008).

With the advancements of deep learning techniques, multiple works have suggested leveraging neural networks to seamlessly encode concealed information within images in a fully trainable manner (Zhu et al., 2018; Yang et al., 2019; Ahmadi et al., 2020; You et al., 2020). Inspired by this idea, Fernandez et al. (2022) incorporate watermarks into the latent space formulated by a self-supervised network such as DINO (Caron et al., 2021). This approach modulates the features of the image within a specific region of the latent space, ensuring that subsequent transformations applied to watermarked images preserve the integrity of the embedded information. Subsequently, watermark detection can be conducted based on this same latent space.

Similarly, Fernandez et al. (2023) introduce a binary signature directly into the decoder of a diffusion model, resulting in images that contain an imperceptibly embedded binary signature. This binary signature can be accurately extracted using a pre-trained watermark extractor during verification.

Given the escalating concerns regarding the misuse of deep fakes, as highlighted in the literature (Brundage et al., 2018; Harris, 2019), several studies have proposed methodologies for attributing the origin of an image, specifically discerning between machine-generated and authentic images. This task is rendered feasible through the identification of subtle, yet machine-detectable, patterns unique to images generated by Generative Adversarial Networks (GANs), as evidenced in recent research (Marra et al., 2019; Afchar et al., 2018; Güera & Delp, 2018; Yu et al., 2019). Furthermore, the detection of deep fakes is enhanced by analyzing inconsistencies in the frequency domain or texture representation between authentic and fabricated images, as indicated in recent studies (Zhang et al., 2019; Durall et al., 2020; Liu et al., 2020).

Authorship Identification For Natural Language Generation Models

Likewise, content generated by text generation models is increasingly vulnerable to various forms of misuse, including the spread of misinformation and the training of surrogate models (Wallace et al., 2020; Xu et al., 2022). Consequently, a growing interest has been in protecting the authorship (or IP) of text generation models or detecting machine-generated text.

A straightforward solution is to incorporate watermarks into the generated text. However, unlike images, textual information is composed of discrete tokens, making the watermarking process for text a difficult endeavor due to the potential for inadvertent alternation that can change its semantic meaning (Katzenbeisser & Petitolas, 2000). One solution to preserve semantic integrity during watermarking involves synonym substitution (Topkara et al., 2006; Chang & Clark, 2014; He et al., 2022a). Nevertheless, the simplistic approach to synonym substitution is vulnerable to detection through statistical analyses. In response, He et al. (2022b) have proposed a conditional synonym substitution method to enhance both stealthiness and robustness of substitution-based watermarks. Moreover, Venugopal et al. (2011) adopted bit representation to encode semantically similar sentences, enabling the selection of watermarked sentences through bit manipulation.

The previously discussed methods have been centered on applying watermarks through post-editing. However, with the emergence of LLMs, there has been a significant shift towards developing watermarks tailored for LLMs to identify machine-generated text. A notable approach in this area employs biased sampling strategies to alter token distribution at each generation step, favoring tokens from specific pre-defined categories (Kirchenbauer et al., 2023a;b; Zhao et al., 2023a). Despite their innovation, these methods face vulnerabilities to "rewriting" attacks, where watermarked sentences are paraphrased either automatically or manually, thus challenging the identification of original authorship (Christ et al., 2023). To address this issue, Kuditipudi et al. (2023) propose a robust approach that maps a sequence of random numbers generated from a randomized watermark key to the outputs of a language model. This technique maintains the watermark's detectability, notwithstanding text alterations such as substitutions, insertions, or deletions.

Interest in post-hoc detection has surged as a complementary measure to watermarking. This trend is driven by the fact that developers often keep the details of their watermarking algorithms confidential to prevent them from being compromised if leaked. Depending on whether machine-generated or human-authored text samples are available, one can utilize either zero-shot or training-based detection methods. Zero-shot detection relies on the premise that language model-generated texts inherently contain detectable markers, identifiable through analysis techniques such as perplexity (Idnay et al., 2022; Tian, 2023) or average pertoken log probability (Solaiman et al., 2019a; Mitchell et al., 2023). The training-based approaches leverage features from pre-trained language models to distinguish between machine-generated and human-authored texts (Solaiman et al., 2019a; Bakhtin et al., 2019; Jawahar et al., 2020; Chen et al., 2023). However, these approaches yield a binary outcome, classifying texts as machine-generated or human-generated. Instead, our approach can determine the origin of text generated by any LLMs, moving beyond binary outcomes.

3 Background

The most recent advanced large generative models usually support two modes for generating outputs: Prompt-based Generation: The authentic generator G produces outputs xa conditioned on the given prompts xp, expressed as xa = G(xp). (1) The selection of prompt inputs xp varies widely, ranging from textual descriptions to images.

Paraphrasing Content: The generators can also "paraphrase" the intended outputs, including texts or images, by reconstructing the content $${\mathit{x}}_a^{⟨\mathrm{n}\mathrm{e}\mathrm{w}⟩}=\mathcal{G}({\mathit{x}}_a^{⟨\mathrm{o}\mathrm{l}\mathrm{d}⟩})\mathrm{.}\{\backslash boldsymbol\{x\}\}\_\{a\}^\{\backslash langle\backslash mathrm\{new\}\backslash rangle\}=\{\backslash mathcal\{G\}\}(\{\backslash boldsymbol\{x\}\}\_\{a\}^\{\backslash langle\backslash mathrm\{old\}\backslash rangle\}).$$ a). (2) As a Natural Language Generation (NLG) example, we can use round-trip translation (Gaspari, 2006) or prompt the Large Language Model (LLM) to "paraphrase" a sentence. As an image generation (IG) example, given a generated image xa, the "paraphrasing" process will be (1) rebuilding partial images of the randomly masked region M[t] in the original image x ⟨old⟩ a , i.e., x ⟨new⟩ a [t] = G(x ⟨old⟩ a , M[t]) (von Platen et al., 2022), and (2) merge these rebuilt portions as a whole image as the "paraphrased" output,

$${\mathbf{x}}_a=\mathcal{G}({\mathbf{x}}_p)\mathrm{.}\backslash mathbf\{x\}\_\{a\}=\{\backslash mathcal\{G\}\}(\backslash mathbf\{x\}\_\{p\}).$$ $$(1)(1)$$ $$\left(2\right)\backslash left(2\backslash right)$$

$$\begin{array}{cccc}& {\mathbf{x}}_a^{(\mathrm{n}\mathrm{e}\mathrm{w})}=\mathrm{M}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{e}(\{{\mathbf{x}}_a^{(\mathrm{n}\mathrm{e}\mathrm{w})}[t]{\}}_{t=1}^T)\mathrm{.}& & \text{(1)}\end{array}\backslash mathbf\{x\}\_\{a\}^\{(\backslash mathrm\{new\})\}=\backslash mathrm\{Merge\}(\backslash \{\backslash mathbf\{x\}\_\{a\}^\{(\backslash mathrm\{new\})\}[t]\backslash \}\_\{t=1\}^\{T\}).\backslash tag\{1\}$$ $$\left(3\right)\backslash left(\{\backslash mathrm\{3\}\}\backslash right)$$

t=1). (3) This iterative re-generation uses prior outputs as inputs, where x ⟨0⟩ a is the initial output from the promptbased conditional generation. Our method will use Prompt-based Generation mode for initial output generation and Paraphrasing Content mode for both (1) iteratively polishing the generated contents and (2) authorship verification.

4 Methodology

Our research primarily focuses on the threat posed by malicious users who misuse generated content without authorization. Specifically, we delve into cases where the owner of authentic generative models, referred to as Ga, allows access to their models in a black-box fashion, permitting external queries to their APIs for content generation. This black-box setting is consistent with the current application practices of Large Foundation Models. Hereby, unscrupulous users could take advantage of the generated content, xa, while disregarding the legitimate creator's license for their own profits. To address this issue, API providers can actively monitor the characteristics of publicly available data to identify potential cases of plagiarism or misuse. This can be accomplished by applying the re-generation and measuring the corresponding edit distance in the verification stage, as described in Section 4.2. To enhance verification accuracy, the authentic model Ga can employ an iterative re-generation approach to bolster the fingerprinting signal, as introduced and proved in Section 4.3.

If there are suspicions of plagiarism, the company can initiate legal proceedings against the alleged plagiarist through a third-party arbitration, following the verification protocol (see Algorithm 2) on the output with iterative re-generation (see Algorithm 1), as demonstrated in Section 4.1. The motivation and intuition of the approach proposed in Section 4.1 are explained in Sections 4.2 and 4.3.

4.1 Data Generation And Verification Protocol

Hereby, the defense framework is comprised of two key components, responding to the Generation and Verification Stages in Figure 1: (1) Iterative Generation (Algorithm 1), which progressively enhances the fingerprint signal in the generated outputs; and (2) Verification (Algorithm 2) is responsible for confirming the authorship of the data sample through a one-step re-generation process using both authentic model Ga and suspected contrasting model Gc, with a confidence margin δ > 0.

Our verification protocol takes inspiration from human artists' capability to reproduce their work that closely resembles the original. Similarly, our process of iterative re-generation mirrors the way artists refine their unique writing or painting styles. Moreover, the distinctive 'style' of the generative model becomes increasingly pronounced with each re-generation cycle, as it converges to a more 'stable' output. This process is formulated by the iterative functions and their tendency to converge to fixed points is proved in Theorem 2. Algorithm 1 Generation Algorithm for Stage I.

Input: Prompt input xp for generation and number of iterations K.

Output: Image, Text, etc. content with implicit fingerprints.

1: x ⟨0⟩ a ← G(xp) ▷ Initial generation from prompts.

2: for k ← 1 to K do ▷ Iterate K steps.

3: x ⟨k⟩ a ← G(x ⟨k−1⟩ a ) ▷ Re-generation using "paraphrasing".

4: end for 5: return x ⟨K⟩ a Algorithm 2 Verification Algorithm for Stage II.

Input: Data sample x ⟨K⟩ a generated by Ga and misused by Gc.

The threshold δ for confident authentication.

Output: Unauthorized usage according to a contrasting generator.

1: ya ← Ga(x ⟨K⟩ a ) ▷ Regenerate data by model Ga.

2: yc ← Gc(x ⟨K⟩ a ) ▷ Regenerate data by model Gc.

3: r ← D(yc, x ⟨K⟩ a )/D(ya, x ⟨K⟩ a ) ▷ Calculate the exceeding distance ratio.

4: return r > 1 + δ

4.2 Authorship Verification Through Re-Generation Distance

An authentic generative model Ga that aims to distinguish between the data samples it generated, denoted as xa, with the benign samples xc generated by other models Gc for contrast. To verify the data, the authentic model (1) re-generates the data Ga(x) and (2) evaluates the distance between the original sample and the re-generated sample, defined as d(x, G) ≜ D(G(x), x). In essence, samples produced by the authentic model are expected to exhibit lower 'self-edit' distance, as they share the same generative model Ga, which uses identical internal knowledge, such as writing or painting styles, effectively serving as model fingerprints. In mathematical terms, we have

i.e., $d(\mathbf{x}{a},\mathcal{G}{a})<d(\mathbf{x}{c},\mathcal{G}{a})$. $$\left(4\right)\backslash left(\{4\}\backslash right)$$ $\left(5\right)$. D(Ga(xa), xa) < D(Ga(xc), xc), (4) i.e., d(xa, Ga) < d(xc, Ga). (5) Consequently, models can identify the authentic samples generated by themselves by evaluating the 'selfedit' distance, which can be viewed as a specialized form of a classification function for discriminating the authentic and contrasting models. Additionally, the re-generation process and corresponding 'edit' distances can serve as explainable and comprehensible evidence to human judges.

4.3 Enhancing Fingerprint Through Iterative Re-Generation

While we have claimed that the data samples generated through the vanilla generative process can be verified, there is no theoretical guarantee regarding the 'self-edit' distance for certifying these samples using the authentic model. To address this limitation, we introduce an iterative re-generation method that improves the fingerprinting capability of the authentic generative model, as it manages to reduce the 'self-edit' distances.

This property will be utilized in verification, as the re-generation step in Verification Stage serves as the (K + 1)-th re-generation step after K steps in the Generation Stage regarding the authentic model. This section provides a theoretical foundation for examining the characteristics of re-generated samples by exploring the convergence behavior of the fixed points by iterative functions.

Definition 1 (The Fixed Points of a Lipschitz Continuous Function) Given a multi-variable function f : R m → R m is L*-Lipschitz continuous,* i.e., ∥f(x) − f(y)∥ ≤ L · ∥x − y∥, where L ∈ (0, 1). For any initial point x ⟨0⟩*, the sequence* {x ⟨k⟩}∞ k=0 is acquired by the recursion x ⟨k+1⟩ = f(x ⟨k⟩). The sequence converges to a fixed point x ∗*, where* x ∗ = f(x ∗).

Theorem 2 (The Convergence of Step Distance for k**-th Re-generation)** The distance between the input and output of the k*-th iteration is bounded by*

$$\mathrm{\parallel }{\mathbf{x}}^{⟨K+1⟩}-{\mathbf{x}}^{⟨K⟩}\mathrm{\parallel }\le L^K\cdot \mathrm{\parallel }{\mathbf{x}}^{⟨1⟩}-{\mathbf{x}}^{⟨0⟩}\mathrm{\parallel },\backslash |\backslash mathbf\{x\}^\{\backslash langle\; K+1\backslash rangle\}-\backslash mathbf\{x\}^\{\backslash langle\; K\backslash rangle\}\backslash |\backslash leq\; L^\{K\}\backslash cdot\backslash |\backslash mathbf\{x\}^\{\backslash langle1\backslash rangle\}-\backslash mathbf\{x\}^\{\backslash langle0\backslash rangle\}\backslash |,$$ $$\left(6\right)\backslash left(6\backslash right)$$ ⟨0⟩∥, (6) and the distance converges to 0 given L ∈ (0, 1).

$1).\overline{1}$ Proof We apply L-Lipschitz continuous property recursively,

$$\mathrm{\parallel }{\mathbf{x}}^{(K+1)}-{\mathbf{x}}^{(K)}\mathrm{\parallel }=\mathrm{\parallel }f({\mathbf{x}}^{(K)})-f({\mathbf{x}}^{(K-1)})\mathrm{\parallel }\backslash |\backslash mathbf\{x\}^\{(K+1)\}-\backslash mathbf\{x\}^\{(K)\}\backslash |=\backslash |f(\backslash mathbf\{x\}^\{(K)\})-f(\backslash mathbf\{x\}^\{(K-1)\})\backslash |$$ $$\leq L\cdot|\mathbf{x}^{(K)}-\mathbf{x}^{(K-1)}|=L\cdot|f(\mathbf{x}^{(K-1)})-f(\mathbf{x}^{(K-2)})|$$ $$\leq L^{2}\cdot|\mathbf{x}^{(K-1)}-\mathbf{x}^{(K-2)}|\leq\cdots$$ $$\leq L^{k}\cdot|\mathbf{x}^{(1)}-\mathbf{x}^{(0)}|.$$ ⟨0⟩∥. (7) The theory can be extended to distance metrics in Banach space.

Theorem 3 (Banach Fixed-Point Theorem) (Banach, 1922; Ciesielski, 2007) Let (X , D) be a complete metric space, and f : X → X is a contraction mapping, if there exists L ∈ (0, 1) such that for all x, y ∈ X

$\downarrow$ . $$\mathbb{D}(f(\mathbf{x}),f(\mathbf{y}))\le L\cdot \mathbb{D}(\mathbf{x},\mathbf{y})\mathrm{.}\backslash mathbb\{D\}(f(\backslash mathbf\{x\}),f(\backslash mathbf\{y\}))\backslash leq\; L\backslash cdot\backslash mathbb\{D\}(\backslash mathbf\{x\},\backslash mathbf\{y\}).$$ $\downarrow$ . $2\cdot T b$ . $$m2,m\backslash \; 2,$$ $$\mathbf{\Sigma }\backslash mathbf\{\backslash Sigma\}$$

D(f(x), f(y)) ≤ L · D(x, y). (8) Then, we have the following convergence of the distance sequence similar to Theorem 2,

$$\mathbb{D}({\mathbf{x}}^{⟨K+1⟩}-{\mathbf{x}}^{⟨K⟩})\le L^K\cdot \mathbb{D}({\mathbf{x}}^{⟨1⟩}-{\mathbf{x}}^{⟨0⟩})\mathrm{.}\backslash mathbb\{D\}(\backslash mathbf\{x\}^\{\backslash langle\; K+1\backslash rangle\}-\backslash mathbf\{x\}^\{\backslash langle\; K\backslash rangle\})\backslash leq\; L^\{K\}\backslash cdot\backslash mathbb\{D\}(\backslash mathbf\{x\}^\{\backslash langle1\backslash rangle\}-\backslash mathbf\{x\}^\{\backslash langle0\backslash rangle\}).$$ ⟨0⟩). (9)

5 Experiments

This section aims to demonstrate the efficacy of our re-generation framework of authorship authentication on generated text and image separately. For both Natural Language Generation (NLG) and Image Generation (IG) scenarios, in Sections 5.2 and 5.3, we first generate the initial intended data samples followed by several steps of 'paraphrasing' (for NLG) or 'inpainting' (for IG) as re-generation, detailed in Algorithm 1. Then, we test the properties of these samples by three series of experiments.

1. Distance Convergence: We verify the convergence of the distance between all one-step regenerations k ∈ [1..K].

2. Discrepancy: We illustrate the discrepancy between the distances by the authentic generative models and the 'suspected' other models for contrast.

3. Verification: We report the verification performance using precision and recall of the identified samples by the authentic models vs those from other contrasting models.

5.1 Experimental Setup

Despite falling under the same framework for authorship verification, Natural Language Generation (NLG) and Image Generation (IG) use distinct generative models and varying metrics for measuring distance.

Generative Models. For text generation, we consider four generative models: 1) M2M (Fan et al., 2021): a multilingual encoder-decoder model trained for many-to-many multilingual translation; 2) mBART-large50 (Tang et al., 2021): a model fine-tuned on mBART for multilingual machine translation between any pair of 50 languages; Cohere: a large language model developed by Cohere; 4) GPT3.5-turbo (version: 0613): a chat-based GPT3.5 model developed by OpenAI.2 1We estimated L for Stable Diffusion models with results presented in Appendix B.3. 2We have also studied GPT4 and present its corresponding results in the Appendix C.2.

For image generation, we examine five primary generative models based on the Stable Diffusion (SD) architecture (Rombach et al., 2022). All models are trained on a subset of the LAION-2B dataset (Schuhmann et al., 2022) consisting of CLIP-filtered image-text pairs. These models are: 1) SDv2.1; 2) SDv2; 3) SDv2.1 Base; 4) SDXLv1.0 (Podell et al., 2023), which distinguishes itself by employing an ensemble of experts pipeline for latent diffusion, where the base model first generates noisy latent that is refined using a specialized denoising model 5) SDXL Base0.9 (Podell et al., 2023).3 More information on model architecture and training, and the quality of re-generated images is demonstrated in Appendix B.1. Distance Metrics. To gauge the similarity between generated outputs, we employ three popular similarity metrics for NLG experiments, 1) BLEU calculates the precision of the overlap of various n-grams (usually 1 to 4) between the candidate and the reference sentences (Papineni et al., 2002); 2) ROUGE-L calculates the F-1 score of longest common subsequence between the candidate and reference sentences (Lin, 2004) and 3) BERTScore computes the similarity between candidate and reference tokens using cosine similarity on their embeddings. Then, the token-level scores are aggregated to produce a single score for the whole text (Zhang et al., 2020). For IG experiments, we consider the following distance metrics: 1) CLIP Cosine Distance measures the semantic similarity of two images using pre-trained CLIP image-text models (Radford et al., 2021); 2) LPIPS compares perceptual style differences between two images (Zhang et al., 2018); 3) Mean Squared Error (MSE) serves as a pixel-level metric that compares all raw pixel values in the image pair; 4) Structural Similarity Index (SSIM) assesses image degradation based on luminance, contrast, and structure (Wang et al., 2004). We transform all similarity scores s ∈ [0, 1] to distances d by d = 1 − s.

Note that we gauge the success of our approach based on the satisfactory performance of any of these metrics when applied to the verification of generative models.

5.2 Natural Language Generation Experiments

In the study of text generation, the primary objective is to produce sentences that fulfill specific requirements, including translation, paraphrasing, summarization, etc.. Then, one can re-generate intended output sentences via 'paraphrasing' them. This study focuses on machine translation (specifically from French to English) as the primary generation task.4 Considering that M2M and mBART are restricted to machine translation tasks, we utilize round-trip translation as a way for paraphrasing. Specifically, for each roundtrip translation step, an English input sentence is first translated into French and then translated back to English. We repeat this process multiple times to observe the change of the 'edit' distances. To reproduce the primary experiment, i.e., Fr-En translation, using GPT3.5-turbo and Cohere, we perform a zero-shot prompting using the following prompts:

• Translate to English: You are a professional translator. You should translate the following sentence to English and output the final result only: {INPUT}
• Translate to French: You are a professional translator. You should translate the following sentence to French and output the final result only: {INPUT} Text generative models have been known to exhibit superior performance when test data inadvertently overlaps with pre-training data, a phenomenon referred to as data contamination (Magar & Schwartz, 2022).

To address this potential issue, we sample 200 sentences from the in-house data as the starting point for each model. To mitigate biases arising from varied sampling strategies, we set the temperature and top p to 0.7 and 0.95 for all NLG experiments. Distance Convergence. The dynamics of the distance change across three metrics and various generative models are depicted in Figure 2. We observe a remarkable distance reduction between the first and second iterations in all settings. Subsequently, the changes in distance between consecutive iterations exhibit a

3Additionally, we explored other variants, including SDv1.5, SDv1.4, and Nota-AI's BK-SDM Base. The corresponding experiments and results are provided in Appendix B.1.

4In addition to machine translation, we examine paraphrasing and summarization as the generation tasks in Section 5.4

Figure 2: The convergence analysis of the distances in iterations based on various metrics on the re-generated text of 200 samples from in-house datasets.

Figure 3: Density distribution of one-step re-generation among four text generation models, where the input to the one-step re-generation is the k-th iteration from the authentic models. The authentic models from left to right are: 1) M2M, 2) mBART, 3) GPT3.5-turbo, and 4) Cohere. diminishing pattern, tending to converge after approximately 5-7 rounds of re-generation. These observed trends are consistent with the Fixed-Point Theorem as elaborated in Section 4.3. Discrepancy. In our previous study of iterative re-generation using the same model, we observe the convergence of 'edit' distances which can be utilized to distinguish the authentic model from its counterparts. As delineated in Section 4.2, for each French sentence x from the corpus, we apply the prompt-mode of authentic model to yield xa via a translation. Both authentic and contrasting models are considered to perform a one-step re-generation of xa to obtain y for verification. We measure the distance between xa and y (including ya and yc). As illustrated in Figure 3, the density distribution associated with the authentic model demonstrates a noticeable divergence from those of models for contrast, thus affirming the hypothesis discussed in Section 4.2. This pattern also holds when using ROUGE-L and BERTScore for distance measures, as evidenced by their respective density distributions in Appendix C.1.

Table 1: The precision of differentiating contrast models (Gc, mBART, Cohere, and GPT3.5-turbo) from the authentic model (Ga, M2M) using various δ ∈ {0.05, 0.1, 0.2, 0.4}, based on BLUE, ROUGE-L, and BERTScore, respectively.

δ	mBART	Cohere	GPT3.5-turbo
BLEU	ROUGE	BERT	BLEU	ROUGE	BERT	BLEU	ROUGE	BERT
0.05	94.0	92.0	91.0	99.0	99.0	99.0	93.0	89.0	92.0
0.10	91.0	92.0	90.0	98.0	99.0	99.0	92.0	88.0	92.0
0.20	91.0	92.0	90.0	98.0	99.0	99.0	91.0	87.0	90.0
0.40	88.0	88.0	85.0	95.0	97.0	99.0	87.0	85.0	85.0

Gc	M2M	mBART	Cohere	GPT3.5-turbo
Ga	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑
	(a) k = 1
M2M	-	-	94.0	98.0	99.0	99.0	93.0	95.0
mBART	85.0	89.0	-	-	100.0	100.0	89.0	92.0
Cohere	60.0	64.0	63.0	57.0	-	-	65.0	51.0
GPT3.5-turbo	87.0	92.0	90.0	92.0	99.0	99.0	-	-
	(b) k = 3
M2M	-	-	94.0	99.0	100.0	100.0	95.0	97.0
mBART	85.0	93.0	-	-	100.0	100.0	90.0	96.0
Cohere	75.0	83.0	73.0	76.0	-	-	63.0	69.0
GPT3.5-turbo	89.0	92.0	93.0	95.0	97.0	98.0	-	-
	(c) k = 5
M2M	-	-	94.0	98.0	98.0	99.0	95.0	99.0
mBART	91.0	96.0	-	-	100.0	100.0	88.0	94.0
Cohere	71.0	81.0	83.0	87.0	-	-	69.0	73.0
GPT3.5-turbo	90.0	94.0	94.0	98.0	95.0	97.0	-	-

Table 2: The precision and recall of verifying the authentic models (Ga) using different contrasting models (Gc).

We observe the difficulty of distinguishing Cohere from other models merely based on the outputs from the first iteration, i.e., without re-generation. We attribute the distinctive behavior of Cohere to its relatively slower convergence than other models.5 However, as depicted in Figure 2, the distances observed in subsequent iterations of the same model experience a substantial reduction. This implies the re-generated outputs in the Generation Stage possess enhanced fingerprints. In particular, we can derive x ⟨k⟩ a from 5 iterations of Ga(·). Figure 3 shows that increasing k enhances the differentiation of the authentic model's density distribution compared to other models. This distinction becomes evident even in the case of Cohere, which remains indistinguishable at k = 1. This enhancement for Cohere is also corroborated in the verification experiments in the next paragraph.

Verification. We employ Algorithm 2 to ascertain if a given sentence originates from the authentic models.

The determination hinges on the threshold parameter, δ. Thus, we designate M2M as the authentic model, while using mBART, Cohere, and GPT3.5-turbo as contrasting models to determine the optimal value of δ.

As indicated in Table 1, a threshold of 0.05 certifies that the three contrasting models can validate that more than 93% of the samples are derived from M2M. As anticipated, an increase in the value of δ augments the stringency criteria, resulting in a reduction in verification precision. Therefore, we fix δ at 0.05 for ensuing evaluations unless stated otherwise.

As indicated in Table 2, our approach undertakes the validation of authorship, yielding a precision exceeding 85% and a recall rate surpassing 88% across M2M, mBART, and GPT3.5-turbo. Moreover, both precision and recall metrics improve with additional re-generation iterations. Although with a slower convergence

5The underlying reason behind the slow convergence for Cohere is investigated in Appendix C.3.1. speed on Cohere, the verification performance on its samples improved significantly given more re-generation iterations, see Cohere lines in Table 2.

5.3 Image Generation Experiments

The main objective of the image generation task is to produce an image given a text prompt using a generative model, a.k.a prompt-mode. To generate the initial proposal of images, we sample 200 captions as prompts each from MS-COCO dataset (COCO) (Lin et al., 2014) and Polo Club Diffusion DB dataset (POLO) (Wang et al., 2022), then we generate initial images x ⟨0⟩corresponding to the prompts using all assigned models. For re-generation, we consider two settings: (1) watermarking images through inpainting a pre-defined sub-regions and (2) fingerprinting enhancement through full image re-generation. The subsequent two paragraphs detail the methodologies for each setting.

Watermarking through Sub-Region Inpainting When re-generating authentic image xa, we first mask a sub-region, i.e., 1/N (N = 10 in our experiments) of its pixels with fixed positions as the watermark pattern. Then, all pixels in the masked regions are re-generated by inpainting using a generative model. Similar to text generation, the inpainting step is iterated multiple times, following Algorithm 1. The comprehensive description of the watermarking procedure is provided in Appendix A.1. Fingerprinting through Full-Image Re-generation In the re-generation setting, we first split all possible mask positions into N (N = 8 in our experiments) non-overlapped sets, coined segments, each with 1/N pixel positions. We parallelly reconstruct each segment based on the rest (N −1)/N pixels of the image as the context in generation. Then, we reassemble these N independent segments into a new full image y.

When analyzing reconstructions of ya = Ga(xa) by contrasting models yc = Gc(xa), there is an expectation that models may exhibit variations in painting masked regions due to their inherent biases.

In this study, to generate the samples from the authentic models, each model first generates 200 initial images x ⟨0⟩ given the captions, which are then re-generated over one to five iterations using 'inpainting' approaches. In the verification stage, by comparing ya and yc to the original xa, we aim to identify subtle model fingerprints based on the 'edit-distance' from the original data to re-generated content. We use LPIPS and CLIP similarity between image pairs to estimate their difference.6 Additionally, the consistency of the image quality during re-generated is demonstrated in Figure 4 and a detailed discussion is provided in Appendix C.3.2.

Distance Convergence. Similar to text re-generation experiments, the re-generation distance converges for both watermarking and fingerprinting settings, as illustrated in Figures 5 and 11, indicated by consistent downward trends across datasets and distance metrics. This implies that the re-generation process converges, with subsequent iterations yielding images that more closely resemble their predecessors. While our methodology proves efficacious in both scenarios, subsequent sections will prioritize the full-image regeneration setting as it is independent of the masks, which are considered confidential to the generative model.

Details about the watermarking setting can be found in Appendix A.1.1. Discrepancy. In our study, we focus on the setting of iterative re-generation through inpainting and observe convergence that can reveal differences between models. Like the NLG section, for verification, both authentic and contrasting models perform an additional one-step re-generation of xa to obtain y and the CLIP distance is measured between the outputs. As illustrated in Figure 6, the one-step re-generation density distribution of the authentic model predominantly peaks at lower values across all generative models.

This indicates that authentic models can effectively distinguish their outputs from those of non-authentic models. Then, we examine the effectiveness of 'inpainting' as re-generation for Generation Stage. As illustrated in Figure 7, re-generation can successfully enhance their fingerprints by k = 5 iterations. While most models, on average, may require fewer rounds of re-generation to deeply impart their fingerprints, with more rounds of re-generation, even older models' fingerprints can be successfully enhanced. Overall, the quality of the

6The results based on MSE and SSIM are also reported in Appendix A.2.1.

Figure 4: The quality of fingerprinted images over multiple iterations of full-image re-generation using SDXL 0.9B.

Figure 5: The convergence analysis of the distances in iterations based on CLIPS and LPIPS metrics on re-generated images of 200 samples on Coco and Polo datasets. images is retained during re-generation, as showcased in Figure 4. At the same time, the strength of the fingerprints embedded in model outputs is reinforced over iterations, as illustrated in Figure 7.

Verification. In accordance with the text generation framework, we utilize Algorithm 2 to evaluate verification performance, selecting optimal parameters k = 5 and δ = 0.05 based on the results of the text generation experiment. As demonstrated in Table 3, models reliably identify images from the authentic model, with precision often exceeding 80% and recall around 85%.

5.4 Generalization And Robustness Evaluation

Task Generalization To demonstrate the generalization of our approach, we further examine two popular text generation tasks, paraphrasing and summarization, as the target generation tasks. The prompts for the prompt mode are:

• Paraphrasing: You are a professional language facilitator. You should paraphrase the following sentence and output the final result only: {INPUT}

Figure 6: Density distribution of one-step re-generation among four image generation models on Polo Dataset. The authentic models from left to right are: 1) SD 2.1, 2) SDXL 1.0, 3) SD 2, 4) SDXL Base 0.9.

Figure 7: Verifying data generated by authentic Ga SDv2.1 and SDv 2.1 Base on Coco Dataset at various iterations using CLIP distance.

• Summarization: You are a professional language facilitator. You should summarize the following

Document Using One Sentence: {Input}

We consider prompt-based paraphrasing for one-step re-generation (i.e., paraphrasing mode), opting for a k value of 5 due to its superior performance. As for backbone models for text generation tasks, we consider GPT3.5-turbo, Llama2-chat-7B (Touvron et al., 2023), and Mistral (Jiang et al., 2023a). Table 4 demonstrates that while paraphrasing and summarization tasks exhibit performance degradation compared to machine translation, our approach effectively distinguishes IPs among various models. This supports the overall effectiveness of our approach across a wide range of text-generation tasks.

Table 4: The precision of verifying the authentic models (Ga) using different contrasting models (Gc).

The target tasks are paraphrasing and summarization.

Gc	GPT3.5-turbo	Zephyr	Mistral
Ga	Precision ↑	Precision ↑	Precision ↑
Paraphrasing
GPT3.5-turbo	-	75.0	69.0
Zephyr	84.0	-	69.0
Mistral	74.0	76.0	-
Summarization
GPT3.5-turbo	-	92.0	68.0
Zephyr	88.0	-	67.0
Mistral	86.0	86.0	-

Until now, we assumed that malicious users employed the authentic model to generate text and images, subsequently utilizing and disseminating them directly.

Nevertheless, in order to circumvent potential IP infringements, malicious users may choose to modify the generated content prior to its public dissemination.

Gc	SD v2.1	SD v2	SD v2.1B	SDXL 0.9	SDXL 1.0
Ga	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑
SD v2.1	-	-	80.0	86.0	99.5	99.5	98.5	99.5	99.0	100.0
SD v2	77.5	81.5	-	-	99.0	100.0	96.5	97.0	95.5	97.5
SD v2.1B	81.5	83.5	82.5	86.5	-	-	88.5	92.0	89.5	91.0
SDXL 0.9	97.5	97.5	96.5	98.0	99.5	99.5	-	-	92.0	93.5
SDXL 1.0	95.5	96.0	92.5	95.5	100.0	100.0	94.5	96.0	-	-

Table 3: The precision and recall of verifying the authentic models Ga using different contrasting models Gc on Polo Dataset, given k = 5 and δ = 0.05. This situation poses a challenge to the effectiveness of our approach in protecting the IP claims associated with the altered content. Robustness Evaluation To examine the robustness of our verification process, we corrupt the generated outputs using paraphrasing and perturbation attacks. Our robustness assessment commenced with a paraphrasing attack targeting image generation. This experiment was designed to test the efficacy of our verification process in identifying plagiarized images. Specifically, we consider images that are originally generated by one authentic model (Model A) and then regenerated or paraphrased by another attack model (Model B), coined as A_B. We experiment with SD v2.1 as the authentic model A and SDXL 1.0 as the paraphrasing model B.

In verification, we re-generate these paraphrased A_B images using both the authentic and paraphrasing models to analyze the distance density distribution variations. Furthermore, we assess this paraphrasing attack at different rounds of generation x ⟨K⟩ a where K is 1, 3, and 5 by the authentic model.

The results, represented in Figure 8, show comparisons between D(A_B, GA(A_B)) and D(A_B, GB(A_B)), indicating the distance between the paraphrased image (created by A then paraphrased by B) and re-generated images.

Figure 8: The variations in the distance density distribution of paraphrasing images through the authentic model and contrasting model. The paraphrased images are initially generated by SDv2.1 (authentic model) and then paraphrased by models SDXL 1.0 at different iterations K (1, 3 & 5) by the authentic model. Additionally, SDv2 acts as a contrasting model for the set of images which is produced by SDv2.1 and then paraphrased by SDXL 1.0.

We observe a significant challenge in attributing authorship to the original creator model once the image is plagiarized (even at higher values of re-generation iteration K in Algorithm 1). The distance between the paraphrased image to the authentic model and the paraphrasing model cannot be differentiated making it increasingly difficult to distinguish whether the SDv2.1 model or another paraphrasing model generated the image. This overlap in the density distributions is a limitation in our methodology, which relies on discerning the nuances in these distances for authorship attribution. This is a common weakness of any fingerprinting or watermarking methods where there is no provable robustness guarantee (Jiang et al., 2023b).

Table 5: The evaluation of robustness evaluation for text generation with perturbed substitution when k = 5 using precision.

Table 6: The precision of robustness evaluation for image generation with Brightness Perturbation when k = 5.

Perturbation rates	M2M	mBART	Cohere	Perturbation rate	SD v2	SD v2.1B	SDXL 1.0
0%	90.0	94.0	95.0
10%	91.0	91.0	97.0
20%	84.0	84.0	95.0
30%	84.0	74.0	94.0
40%	79.0	75.0	93.0
50%	69.0	65.0	92.0	0.00	76.0	97.5	94.0
	1.01	35.0	97.0	85.0
	1.02	41.5	91.0	87.0
	1.05	34.5	94.0	59.5
	1.10	35.0	93.0	44.0
	1.50	23.5	91.5	41.5

However, the results also reveal a noteworthy strength in the methodology. There is a discernible and consistently large distance when comparing paraphrased images to those generated by a contrast model (i.e., an unrelated model, one which was neither the authentic nor the paraphrasing model). This finding is crucial as it suggests that despite the challenges in direct attribution, our approach can reliably detect when an external model, not involved in the image's original creation or its paraphrasing, is falsely claimed as the author. Therefore, this method could potentially be leveraged to establish joint authorship in scenarios where the paraphrased image is claimed by a third party, ensuring proper credit is given to the authentic and paraphrasing models involved in the image's creation.

We investigate perturbation attacks in both text and image generation tasks. For our NLP experiments, we randomly perturb X% of the words preceding the one-step re-generation procedure by substituting them with random words. The value of X ranges from 10% to 50%. We designate GPT3.5-turbo as the authentic model. We set k = 5, due to its outperforming performance. As depicted in Table 5, as the perturbation rate increases, we observe a gradual decline in the verification performance of our method. In general, the efficacy of watermark verification remains reasonably positive. Nevertheless, we argue that perturbations in the range of 30% to 50% have a notable adverse impact on the quality of the generated texts, rendering them significantly less valuable for potential attackers.

Regarding image generation, we introduce two types of perturbations: Brightness alterations and Gaussian Noise. For brightness alterations, we modify the brightness of 10% of randomly chosen pixels. As the intensity of this perturbation increases, we observe a corresponding decrease in verification precision. Notably, as detailed in Table 6, the precision for the SDXL 1.0 model declines sharply but stabilizes when the perturbation rate reaches 1.02. Beyond this point, the model's robustness significantly deteriorated. In our second experiment, we applied Gaussian noise with a mean (µ = 0) and standard deviation (σ = 4) to a random selection of image pixels. This process has a negligible effect on verification accuracy across different models, as shown in Table 7. Even with noise affecting up to 50% of the pixels, the models demonstrated a high precision range of 89-99%, underscoring their robustness to substantial random noise.

Table 7: The precision of robustness evaluation for image generation with Gaussian Noise Perturbation with Gaussian Noise µ = 0, σ = 4 when k = 5.

Perturbation rates SD v2 SD v2.1B SDXL 1.0 0.00 76.0 97.5 94.0 0.01 82.0 94.5 82.0 0.05 100.0 98.5 91.0 0.10 97.0 99.0 95.0 0.20 99.5 100.0 93.5 0.50 99.0 99.0 89.5 1.00 99.5 99.0 66.5 Distance Differentiation between Natural and AI-Generated Images In order to assess the viability of our framework to detect plagiarism on naturally made images (i.e., shot on camera), we re-generate natural images from the MS COCO 2017 Evaluation set (Lin et al., 2014) with previously used image generation models for one iteration. We compare the Clip distances between these natural images and their respective re-generations to the distance between the AI-generated images and their re-generation for one

Figure 9: Comparison of Density Distribution of Re-generation Distances in Verification Stage, acquired by Natural and AI Image Re-generations. iteration by the corresponding models as presented in Figure 9. There is a clear distinction in the distance density distribution when AI-generated images are re-generated using AI our Generation Algorithm 1, the distance remains low whereas using a natural image for re-generation results in further distances even with the most advanced AI models.

6 Conclusion

In this work, we observe the intrinsic fingerprint in both text and vision generative models, which can be identified and verified by contrasting the re-generation of the suspicious data samples by authentic models and contrasting models. Furthermore, we propose iterative re-generation in the Generation Stage to enhance the fingerprints and provide a theoretical framework to ground the convergence of one-step re-generation distance by the authentic model. Our research paves the way towards a generalized authorship authentication for deep generative models without (1) modifying the original generative model, (2) post-processing to the generated outputs, or (3) an additional model for identity classification.

References

Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. In 2018 IEEE international workshop on information forensics and security (WIFS), pp. 1–7. IEEE, 2018.

Mahdi Ahmadi, Alireza Norouzi, Nader Karimi, Shadrokh Samavi, and Ali Emami. Redmark: Framework for residual diffusion watermarking based on deep networks. Expert Systems with Applications, 146:113157, 2020.

Anton Bakhtin, Sam Gross, Myle Ott, Yuntian Deng, Marc'Aurelio Ranzato, and Arthur Szlam. Real or fake? learning to discriminate machine from human generated text. arXiv preprint arXiv:1906.03351, 2019.

Stefan Banach. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales.

Fundamenta mathematicae, 3(1):133–181, 1922.

Miles Brundage, Shahar Avin, Jack Clark, Helen Toner, Peter Eckersley, Ben Garfinkel, Allan Dafoe, Paul Scharre, Thomas Zeitzoff, Bobby Filar, et al. The malicious use of artificial intelligence: Forecasting, prevention, and mitigation. arXiv preprint arXiv:1802.07228, 2018.

Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 9650–9660, 2021.

Ching-Yun Chang and Stephen Clark. Practical Linguistic Steganography using Contextual Synonym Substitution and a Novel Vertex Coding Method. Computational Linguistics, 40(2):403–448, 06 2014. ISSN 0891-2017. doi: 10.1162/COLI_a_00176. URL https://doi.org/10.1162/COLI_a_00176.

Yutian Chen, Hao Kang, Vivian Zhai, Liangze Li, Rita Singh, and Bhiksha Ramakrishnan. Gpt-sentinel: Distinguishing human and chatgpt generated content. arXiv preprint arXiv:2305.07969, 2023.

Miranda Christ, Sam Gunn, and Or Zamir. Undetectable watermarks for language models. arXiv preprint arXiv:2306.09194, 2023.

Krzysztof Ciesielski. On stefan banach and some of his results. Banach Journal of Mathematical Analysis, 1(1):1–10, 2007.

Ingemar J. Cox, Matthew L. Miller, Jeffrey A. Bloom, Jessica Fridrich, and Ton Kalker. Digital Watermarking and Steganography. The Morgan Kaufmann Series in Multimedia Information and Systems, 2 edition, 2008.

Ricard Durall, Margret Keuper, and Janis Keuper. Watch your up-convolution: Cnn based generative deep neural networks are failing to reproduce spectral distributions. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 7890–7899, 2020.

Angela Fan, Shruti Bhosale, Holger Schwenk, Zhiyi Ma, Ahmed El-Kishky, Siddharth Goyal, Mandeep Baines, Onur Celebi, Guillaume Wenzek, Vishrav Chaudhary, et al. Beyond english-centric multilingual machine translation. The Journal of Machine Learning Research, 22(1):4839–4886, 2021.

Pierre Fernandez, Alexandre Sablayrolles, Teddy Furon, Hervé Jégou, and Matthijs Douze. Watermarking images in self-supervised latent spaces. In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3054–3058, 2022. doi: 10.1109/ICASSP43922. 2022.9746058.

Pierre Fernandez, Guillaume Couairon, Hervé Jégou, Matthijs Douze, and Teddy Furon. The stable signature: Rooting watermarks in latent diffusion models. arXiv preprint arXiv:2303.15435, 2023.

Federico Gaspari. Look who's translating. impersonations, Chinese whispers and fun with machine translation on the Internet. In Viggo Hansen and Bente Maegaard (eds.), Proceedings of the 11th Annual Conference of the European Association for Machine Translation, Oslo, Norway, June 19–20 2006. European Association for Machine Translation. URL https://aclanthology.org/2006.eamt-1.19.

Andrzej Granas and James Dugundji. Fixed Point Theory, volume 14. Springer, 2003. David Güera and Edward J. Delp. Deepfake video detection using recurrent neural networks. In 2018 15th IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), pp. 1–6, 2018.

doi: 10.1109/AVSS.2018.8639163.

Douglas A. Harris. Deepfakes: False pornography is here and the law cannot protect you. Duke law and technology review, 17:99–127, 2019. URL https://api.semanticscholar.org/CorpusID:158596286.

Julian Hazell. Large language models can be used to effectively scale spear phishing campaigns. arXiv preprint arXiv:2305.06972, 2023.

Xuanli He, Qiongkai Xu, Lingjuan Lyu, Fangzhao Wu, and Chenguang Wang. Protecting intellectual property of language generation apis with lexical watermark. Proceedings of the AAAI Conference on Artificial Intelligence, 36(10):10758–10766, Jun. 2022a. doi: 10.1609/aaai.v36i10.21321. URL https://ojs.aaai.org/index.php/AAAI/article/view/21321.

Xuanli He, Qiongkai Xu, Yi Zeng, Lingjuan Lyu, Fangzhao Wu, Jiwei Li, and Ruoxi Jia. CATER: Intellectual property protection on text generation APIs via conditional watermarks. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho (eds.), Advances in Neural Information Processing Systems, 2022b.

URL https://openreview.net/forum?id=L7P3IvsoUXY.

Joe Hernandez. That panicky call from a relative? it could be a thief using a voice clone, ftc warns. NPR, 2023. URL https://www.npr.org/2023/03/22/1165448073/voice-clones-ai-scams-ftc.

Alain Hore and Djemel Ziou. Image quality metrics: Psnr vs. ssim. In 2010 20th international conference on pattern recognition, pp. 2366–2369. IEEE, 2010.

Betina Idnay, Caitlin Dreisbach, Chunhua Weng, and Rebecca Schnall. A systematic review on natural language processing systems for eligibility prescreening in clinical research. Journal of the American Medical Informatics Association, 29(1):197–206, 2022.

Daphne Ippolito, Daniel Duckworth, Chris Callison-Burch, and Douglas Eck. Automatic detection of generated text is easiest when humans are fooled. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pp. 1808–1822, Online, July 2020. Association for Computational Linguistics. doi: 10.18653/v1/2020.acl-main.164. URL https://aclanthology.org/2020.acl-main.164.

Ganesh Jawahar, Muhammad Abdul Mageed, and VS Laks Lakshmanan. Automatic detection of machine generated text: A critical survey. In Proceedings of the 28th International Conference on Computational Linguistics, pp. 2296–2309, 2020.

Albert Q Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, et al. Mistral 7b. arXiv preprint arXiv:2310.06825, 2023a.

Zhengyuan Jiang, Jinghuai Zhang, and Neil Zhenqiang Gong. Evading watermark based detection of aigenerated content. In Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications Security, CCS '23, pp. 1168–1181, New York, NY, USA, 2023b. Association for Computing Machinery. ISBN 9798400700507. doi: 10.1145/3576915.3623189. URL https://doi.org/10.1145/3576915.

Stephan Katzenbeisser and Fabien Petitolas. Information hiding techniques for steganography and digital watermaking. EDPACS, 28(6):1–2, 2000. doi: 10.1201/1079/43263.28.6.20001201/30373.5. URL https: //doi.org/10.1201/1079/43263.28.6.20001201/30373.5.

Bo-Kyeong Kim, Hyoung-Kyu Song, Thibault Castells, and Shinkook Choi. On architectural compression of text-to-image diffusion models. arXiv preprint arXiv:2305.15798, 2023.

John Kirchenbauer, Jonas Geiping, Yuxin Wen, Jonathan Katz, Ian Miers, and Tom Goldstein. A watermark for large language models. International Conference on Machine Learning, 2023a.

John Kirchenbauer, Jonas Geiping, Yuxin Wen, Manli Shu, Khalid Saifullah, Kezhi Kong, Kasun Fernando, Aniruddha Saha, Micah Goldblum, and Tom Goldstein. On the reliability of watermarks for large language models. In The Twelfth International Conference on Learning Representations, 2023b.

Rohith Kuditipudi, John Thickstun, Tatsunori Hashimoto, and Percy Liang. Robust distortion-free watermarks for language models. arXiv preprint arXiv:2307.15593, 2023.

Taehyun Lee, Seokhee Hong, Jaewoo Ahn, Ilgee Hong, Hwaran Lee, Sangdoo Yun, Jamin Shin, and Gunhee Kim. Who wrote this code? watermarking for code generation. arXiv preprint arXiv:2305.15060, 2023.

Chin-Yew Lin. ROUGE: A package for automatic evaluation of summaries. In Text Summarization Branches Out, pp. 74–81, Barcelona, Spain, July 2004. Association for Computational Linguistics. URL https: //aclanthology.org/W04-1013.

Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13, pp. 740–755. Springer, 2014.

Zhengzhe Liu, Xiaojuan Qi, and Philip HS Torr. Global texture enhancement for fake face detection in the wild. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 8060–8069, 2020.

Brady D Lund, Ting Wang, Nishith Reddy Mannuru, Bing Nie, Somipam Shimray, and Ziang Wang. Chatgpt and a new academic reality: Artificial intelligence-written research papers and the ethics of the large language models in scholarly publishing. Journal of the Association for Information Science and Technology, 74(5):570–581, 2023.

Inbal Magar and Roy Schwartz. Data contamination: From memorization to exploitation. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pp.

157–165, 2022.

Francesco Marra, Diego Gragnaniello, Luisa Verdoliva, and Giovanni Poggi. Do gans leave artificial fingerprints? In 2019 IEEE Conference on Multimedia Information Processing and Retrieval (MIPR), pp.

506–511, 2019. doi: 10.1109/MIPR.2019.00103.

Eric Mitchell, Yoonho Lee, Alexander Khazatsky, Christopher D Manning, and Chelsea Finn. Detectgpt: Zero-shot machine-generated text detection using probability curvature. In International Conference on Machine Learning, pp. 24950–24962. PMLR, 2023.

Maximilian Mozes, Xuanli He, Bennett Kleinberg, and Lewis D Griffin. Use of llms for illicit purposes: Threats, prevention measures, and vulnerabilities. arXiv preprint arXiv:2308.12833, 2023.

Konstantin A. Pantserev. The Malicious Use of AI-Based Deepfake Technology as the New Threat to Psychological Security and Political Stability, pp. 37–55. Springer International Publishing, Cham, 2020. ISBN 978-3-030-35746-7. doi: 10.1007/978-3-030-35746-7_3. URL https://doi.org/10.1007/ 978-3-030-35746-7_3.

Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. Bleu: a method for automatic evaluation of machine translation. In Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics, pp. 311–318, Philadelphia, Pennsylvania, USA, July 2002. Association for Computational Linguistics. doi: 10.3115/1073083.1073135. URL https://aclanthology.org/P02-1040.

Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952, 2023.

Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pp. 8748–8763. PMLR, 2021.

Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents.

Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation. In International Conference on Machine Learning, pp. 8821–8831. PMLR, 2021.

Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10684–10695, June 2022.

Negar Rostamzadeh, Emily Denton, and Linda Petrini. Ethics and creativity in computer vision. arXiv preprint arXiv:2112.03111, 2021.

Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. Laion-5b: An open largescale dataset for training next generation image-text models. Advances in Neural Information Processing Systems, 35:25278–25294, 2022.

Stu Sjouwerman. How ai is changing social engineering forever. Forbes, 2023. URL https://www.forbes.

com/sites/forbestechcouncil/2023/05/26/how-ai-is-changing-social-engineering-forever/ ?sh=2031e2c0321b.

Irene Solaiman, Miles Brundage, Jack Clark, Amanda Askell, Ariel Herbert-Voss, Jeff Wu, Alec Radford, Gretchen Krueger, Jong Wook Kim, Sarah Kreps, et al. Release strategies and the social impacts of language models. arXiv preprint arXiv:1908.09203, 2019a.

Irene Solaiman, Miles Brundage, Jack Clark, Amanda Askell, Ariel Herbert-Voss, Jeff Wu, Alec Radford, and Jasmine Wang. Release strategies and the social impacts of language models. CoRR, abs/1908.09203, 2019b. URL http://arxiv.org/abs/1908.09203.

Yuqing Tang, Chau Tran, Xian Li, Peng-Jen Chen, Naman Goyal, Vishrav Chaudhary, Jiatao Gu, and Angela Fan. Multilingual translation from denoising pre-training. In Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021, pp. 3450–3466, Online, August 2021. Association for Computational Linguistics. doi: 10.18653/v1/2021.findings-acl.304. URL https://aclanthology.org/ 2021.findings-acl.304.

Edward Tian. Gptzero, 2023. URL https://gptzero.me/.

Umut Topkara, Mercan Topkara, and Mikhail J. Atallah. The hiding virtues of ambiguity: Quantifiably resilient watermarking of natural language text through synonym substitutions. In Proceedings of the 8th Workshop on Multimedia and Security, MM&Sec '06, pp. 164–174, New York, NY, USA, 2006. Association for Computing Machinery. ISBN 1595934936. doi: 10.1145/1161366.1161397. URL https://doi.org/ 10.1145/1161366.1161397.

Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023.

Ashish Venugopal, Jakob Uszkoreit, David Talbot, Franz Och, and Juri Ganitkevitch. Watermarking the outputs of structured prediction with an application in statistical machine translation. In Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, pp. 1363–1372, Edinburgh, Scotland, UK., July 2011. Association for Computational Linguistics. URL https://aclanthology.org/ D11-1126.

Pranshu Verma. They thought loved ones were calling for help. it was an ai scam. The Washington Post, 2023. URL https://www.washingtonpost.com/technology/2023/03/05/ai-voice-scam/.

Patrick von Platen, Suraj Patil, Anton Lozhkov, Pedro Cuenca, Nathan Lambert, Kashif Rasul, Mishig Davaadorj, and Thomas Wolf. Diffusers: State-of-the-art diffusion models. https://github.com/ huggingface/diffusers, 2022.

Eric Wallace, Mitchell Stern, and Dawn Song. Imitation attacks and defenses for black-box machine translation systems. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 5531–5546, Online, November 2020. Association for Computational Linguistics. doi: 10.18653/v1/2020.emnlp-main.446. URL https://aclanthology.org/2020.emnlp-main.446.

Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004.

Zijie J Wang, Evan Montoya, David Munechika, Haoyang Yang, Benjamin Hoover, and Duen Horng Chau.

Diffusiondb: A large-scale prompt gallery dataset for text-to-image generative models. arXiv preprint arXiv:2210.14896, 2022.

Qiongkai Xu and Xuanli He. Security challenges in natural language processing models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing: Tutorial Abstracts, pp. 7–12, 2023.

Qiongkai Xu, Xuanli He, Lingjuan Lyu, Lizhen Qu, and Gholamreza Haffari. Student surpasses teacher: Imitation attack for black-box NLP APIs. In Proceedings of the 29th International Conference on Computational Linguistics, pp. 2849–2860, Gyeongju, Republic of Korea, October 2022. International Committee on Computational Linguistics. URL https://aclanthology.org/2022.coling-1.251.

Kuan Yang, Kejiang Chen, Weiming Zhang, and Nenghai Yu. Provably secure generative steganography based on autoregressive model. In Chang D. Yoo, Yun-Qing Shi, Hyoung Joong Kim, Alessandro Piva, and Gwangsu Kim (eds.), Digital Forensics and Watermarking, pp. 55–68, Cham, 2019. Springer International Publishing. ISBN 978-3-030-11389-6.

Weike You, Hong Zhang, and Xianfeng Zhao. A siamese cnn for image steganalysis. IEEE Transactions on Information Forensics and Security, 16:291–306, 2020.

Ning Yu, Larry S Davis, and Mario Fritz. Attributing fake images to gans: Learning and analyzing gan fingerprints. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 7556–7566, 2019.

Aditi Zear, Amit Kumar Singh, and Pardeep Kumar. A proposed secure multiple watermarking technique based on dwt, dct and svd for application in medicine. Multimedia tools and applications, 77:4863–4882, 2018.

Richard Zhang. richzhang/perceptualsimilarity, Sep 2023. URL https://github.com/richzhang/ PerceptualSimilarity.

Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 586–595, 2018.

Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q. Weinberger, and Yoav Artzi. Bertscore: Evaluating text generation with bert. In International Conference on Learning Representations, 2020. URL https: //openreview.net/forum?id=SkeHuCVFDr.

Xu Zhang, Svebor Karaman, and Shih-Fu Chang. Detecting and simulating artifacts in gan fake images. In 2019 IEEE International Workshop on Information Forensics and Security (WIFS), pp. 1–6, 2019. doi: 10.1109/WIFS47025.2019.9035107.

Xuandong Zhao, Yu-Xiang Wang, and Lei Li. Protecting language generation models via invisible watermarking. In International Conference on Machine Learning, pp. 42187–42199. PMLR, 2023a.

Yunqing Zhao, Tianyu Pang, Chao Du, Xiao Yang, Ngai-Man Cheung, and Min Lin. A recipe for watermarking diffusion models. arXiv preprint arXiv:2303.10137, 2023b.

Jiren Zhu, Russell Kaplan, Justin Johnson, and Li Fei-Fei. Hidden: Hiding data with deep networks. In Proceedings of the European conference on computer vision (ECCV), pp. 657–672, 2018.

A Experimental Setup For Image Generation A.1 Embedding Watermark Through Inpainting

To analyze the stability and convergence properties of inpainting models, we perform an iterative masked image infilling procedure. Given an input image x from model G, we iteratively inpaint with mask M:

$${\mathbf{x}}^{⟨k+1⟩}=\mathcal{G}({\mathbf{x}}^{⟨k⟩},M)\backslash mathbf\{x\}^\{\backslash langle\; k+1\backslash rangle\}=\{\backslash mathcal\{G\}\}(\backslash mathbf\{x\}^\{\backslash langle\; k\backslash rangle\},M)$$ $$(10)(10)$$ ⟨k⟩, M) (10) Here, the mask M not only guides the inpainting but also functions as the medium to embed our watermark. As we iteratively inpaint using a mask M, the watermark becomes more deeply embedded, serving as a distinctive signature to identify the authentic model Ga.

A.1.1 Convergence Of Watermarked Images

The iterative masked inpainting procedure displays consistent convergence behavior across models. With a fixed binary mask covering 1/10th of the image, the distance between successive image generations decreases rapidly over the first few iterations before stabilizing. This is evidenced by the declining trend in metrics like MSE, LPIPS, and CLIP similarity as iterations increase.

The early convergence suggests the generative models are effectively reconstructing the masked regions in a coherent manner. While perfect reconstruction is infeasible over many passes, the models appear to reach reasonable stability within 5 iterations as shown in Figure 10 and 11.

Convergence to a stable equilibrium highlights latent fingerprints in the model behavior. The consistent selfreconstruction statistics form the basis for distinguishing authentic sources in the subsequent fingerprinting experiments. The watermarking convergence analysis highlights model stability and confirms that iterative inpainting effectively removes embedded watermarks without degrading image quality (see Figures in C.3.2).

BK-SDM SDv2.1 Base SDXL Base0.9

0 1 2 3 4

Figure 10: The convergence analysis of the distances in iteration based on various metrics on the watermarked images of 200 samples from Polo datasets.

Figure 11: The convergence analysis of the distances in iterations based on various metrics on the watermarked images of 200 samples from Coco dataset

A.2 Enhancing And Verifying Fingerprint Through Re-Generation

We divide an image into non-overlapping segments and have models reconstruct masked regions to expose inherent fingerprints. Given an image x, we generate segment masks M1*, ..., M*T covering x and apply G to reconstruct each part:

$$y[t]=\mathcal{G}(x,M[t])y[t]=\{\backslash mathcal\{G\}\}(x,M[t])$$ $$(11)(11)$$ y[t] = G(x, M[t]) (11) By analyzing reconstructed segments y[t] and the composited image y, model-specific artifacts can be quantified without additional pattern information. The non-overlapping reconstructed segments are merged to form the composite image y, we can obtain this by using the corresponding mask and extracting the reconstructed portion. A salient feature of our proposed re-generation paradigm is its independence from any additional information about the image partitioning pattern. The model's unique fingerprint emerges naturally during re-generation, regardless of how the image is divided or the components are merged. We experiment on 5 latest SD models - SDv 2.1, SD v2.1B, SD v2, SDXL 1.0, and SDXL0.9B using 8 segmented masks each covering 1/8th of the image thereby totaling full image coverage. Model fingerprints are identified through LPIPS, and CLIP similarities between original xa and reconstructed y.

A.2.1 Convergence Of Re-Generated Images

Enhancing fingerprint re-generation shows consistent convergence in perceptual metrics like CLIP and LPIPS within four iterations (see Figure 12 and 13). However, traditional metrics such as MSE and SSIM lack clear convergence, suggesting inpainting effectively captures visual content but not at the pixel level. The models converge to unique stable points, revealing inherent fingerprints based on their biases and training data. This divergence is important for model attribution. Overall, re-generation effectively exposes these fingerprints while maintaining visual integrity, underscoring perceptual superiority over pixel-based metrics in evaluating generative model fingerprints.

Figure 12: The convergence analysis of the distances in iteration based on various metrics on the re-generated images of 200 samples from Polo dataset.

Figure 13: The convergence analysis of the distances in iteration based on various metrics on the re-generated images of 200 samples from Coco dataset. 23

B Computer Vision Supplementary Experiments And Details B.1 Image Generation Models

We consider eight models based on the Stable Diffusion architecture (Rombach et al., 2022). These models leverage the architecture and differ primarily in their training schemes. The models are selected to span a range of architectures, training schemes, and dataset sizes. This diversity allows us to explore model-specific behaviors for attribution and stability analysis.

Table 8: Summary of models based on the Stable Diffusion architecture for IG experiments. The bold models are used in our primary experiments.

Model	Description
Model1	Stable Diffusion 1.5: Fine-tuned from SD1.4 for 595k steps (Rombach et al., 2022)
Model2	Stable Diffusion 2.1 (SDv 2.1):	Fine-tuned from SDvTwo for 210k steps (Rombach et al.,
2022)
Model3	Stable Diffusion 1.4 (SD v1.4) : Initialized from SDv1.2 weights (Rombach et al., 2022)
Model4	Stable Diffusion XL 1.0 (SDXL 1.0): Larger backbone, trained on LAION-5B (Podell et al., 2023)
Model5	Block-removed Knowledge-distilled Stable Diffusion Model (Kim et al., 2023)
Model6	Stable Diffusion 2 (SD v2) (Rombach et al., 2022)
Model7	Stable Diffusion v 2.1 Base (SD v2.1B) (Rombach et al., 2022)
Model8	Stable Diffusion XL 0.9 (SDXL0.9B) (Podell et al., 2023)

All models support inpainting, allowing images to be edited given a mask and image. We utilize the inpainting pipeline - StableDiffussion and StableDiffusionXL - provided by HuggingFace (von Platen et al., 2022).7 Both SD v1.4 and SD v2 checkpoints were initialized with the weights of the SD v1.4 checkpoints and subsequently fine-tuned on "laion-aesthetics v2 5+". SDXL 1.0 employs a larger UNet backbone and a more potent text encoder (Podell et al., 2023). BKSDM is designed for efficient text-to-image synthesis, removing blocks from the U-Net and undergoing distillation pre-training on 0.22M LAION text-image pairs (Kim et al., 2023).

Image Inpainting: Image inpainting refers to filling in missing or masked regions of an image to reconstruct the original intact image. A fixed binary mask is applied to cover certain areas of the image. The binary masks are generated as blank images filled with random white pixels. To reconstruct images, the binary mask and original image are passed to the generative model's inpainting pipeline, where the values of the pixels in the masked areas are predicted based on the unmasked context. After inpainting, the reconstructed masked regions are merged back into the re-generated image for future iteration. We utilize the inpainting pipeline8- StableDiffussion and StableDiffusionXL - provided by HuggingFace (von Platen et al., 2022) that enables us to regenerate a given image multiple times by masking different parts of the image.

B.2 Distance Metrics For Images

Contrastive Language-Image Pretraining (CLIP) Cosine Distance The CLIP model encodes images into high-dimensional feature representations that capture semantic content and meaning (Radford et al., 2021). With pre-trained image-text models, we can easily capture the semantic similarity of two images, which is their shared meaning and content, regardless of their visual appearance.

CLIP uses a vision transformer model as the image encoder. The output of the final transformer block can be interpreted as a semantic feature vector describing the content of the image. Images with similar content will have feature vectors close together or aligned in the embedding space.

7https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion/inpaint 8https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion/inpaint To compare two images I1 and I2 using CLIP, we can encode them into feature vectors f1 and f2. The cosine distance between these semantic feature vectors indicates the degree of semantic alignment.

$$\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{\_}\mathrm{s}\mathrm{i}\mathrm{m}(f_1,f_2)=\frac{f_1\cdot f_2}{\mathrm{\parallel }{f}_1\mathrm{\parallel }\mathrm{\parallel }{f}_2\mathrm{\parallel }}\{\backslash mathrm\{cosine\backslash \_sim\}\}(f\_\{1\},f\_\{2\})=\{\backslash frac\{f\_\{1\}\backslash cdot\; f\_\{2\}\}\{\backslash |f\_\{1\}\backslash |\backslash |f\_\{2\}\backslash |\}\}$$

$$\left(12\right)\backslash left(12\backslash right)$$ $$(13)(13)$$ ∥f1∥∥f2∥(12) $$\mathrm{cosine\_dist}(f_1,f_2)=1-\mathrm{cosine\_sim}(f_1,f_2)\backslash operatorname\{cosine\backslash \_dist\}(f\_\{1\},f\_\{2\})=1-\backslash operatorname\{cosine\backslash \_sim\}(f\_\{1\},f\_\{2\})$$ cosine_dist(f1, f2) = 1 − cosine_sim(f1, f2) (13) Where · denotes the dot product and ∥ · ∥ denotes the L2 norm. The cosine distance ranges from 0 to 1, with 0 indicating perfectly aligned features. A lower distance between images implies more similar highlevel content and meaning in the images as captured by the CLIP feature embeddings. We specifically use OpenClip with a ConvNext-XXLarge encoder pretrained on laion2b dataset.

Learned Perceptual Image Patch Similarity (LPIPS) LPIPS metric focuses on perceptual and stylistic similarities by using a convolutional neural network pre-trained on human judgments of image patch similarities. The distance is measured between the CNN's intermediate feature representations of two images (Zhang et al., 2018).

$$\begin{array}{cccc}& d(x,x^{\mathrm{\prime }})=\sum _l\frac{1}{H_l{W}_l}\sum _{h,w}{\parallel w_l\odot ({\widehat{y}}_l^{hw}-{\widehat{y}}_l^{hw})\parallel }_2^2& & \text{(1)}\end{array}d(x,x^\{\backslash prime\})=\backslash sum\_\{l\}\backslash frac\{1\}\{H\_\{l\}W\_\{l\}\}\backslash sum\_\{h,w\}\backslash left\backslash |w\_\{l\}\backslash odot(\backslash hat\{y\}\_\{l\}^\{hw\}-\backslash hat\{y\}\_\{l\}^\{hw\})\backslash right\backslash |\_\{2\}^\{2\}\backslash tag\{1\}$$ $$(14)(14)$$

By comparing features across corresponding layers of the CNN, LPIPS can provide a fine-grained distance measuring subtle perceptual differences imperceptible in pixel space (Zhang et al., 2018). For example, changes to color scheme or artistic style that maintain semantic content will have a low CLIP distance but a higher LPIPS distance. We use the original implementation of Zhang (2023) Mean Squared Error (MSE) The mean squared error (MSE) between two images x and x ′is calculated as:

$$MSE(x,x^{\mathrm{\prime }})=\frac{1}{mn}\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}[x(i,j)-x^{\mathrm{\prime }}(i,j){]}^{2}M\; S\; E(x,x^\{\backslash prime\})=\{\backslash frac\{1\}\{m\; n\}\}\backslash sum\_\{i=0\}^\{m-1\}\backslash sum\_\{j=0\}^\{n-1\}[x(i,j)-x^\{\backslash prime\}(i,j)]^\{2\}$$

Where x and x ′ are m×n images represented as matrices of pixel intensities. The MSE measures the average of the squared intensity differences between corresponding pixels in x and x ′.

It provides a simple pixel-level similarity metric sensitive to distortions like noise, blurring, and coloring errors. However, MSE lacks perceptual relevance and is not robust to geometric/structural changes in the image.

Structural Similarity Index (SSIM) The structural similarity index (SSIM) (Hore & Ziou, 2010) compares corresponding 8 × 8 windows in the images across three terms - luminance, contrast, and structure:

$$SSIM(x,x^{\mathrm{\prime }})=\frac{(2{\mu }_x{\mu }_{x^{\mathrm{\prime }}}+c_1)(2{\sigma }_{x{x}^{\mathrm{\prime }}}+c_2)}{({\mu }_x^2+{\mu }_{x^{\mathrm{\prime }}}^2+c_1)({\sigma }_x^2+{\sigma }_{x^{\mathrm{\prime }}}^2+c_2)}S\; S\; I\; M(x,x^\{\backslash prime\})=\backslash frac\{(2\backslash mu\_\{x\}\backslash mu\_\{x^\{\backslash prime\}\}+c\_\{1\})(2\backslash sigma\_\{x\; x^\{\backslash prime\}\}+c\_\{2\})\}\{(\backslash mu\_\{x\}^\{2\}+\backslash mu\_\{x^\{\backslash prime\}\}^\{2\}+c\_\{1\})(\backslash sigma\_\{x\}^\{2\}+\backslash sigma\_\{x^\{\backslash prime\}\}^\{2\}+c\_\{2\})\}$$

Where µx, µx′ are mean intensities, σ 2 x , σ 2 x′ are variances, and σxx′ is covariance for windows in x and x ′.

c1, c2 stabilize division.

This decomposes similarity into comparative measurements of structure, luminance, and contrast. As a result, SSIM better matches human perceptual judgments compared to MSE. Values range from -1 to 1, with 1 being identical local structure.

As research rapidly improves generation quality, we expect future use cases to leverage such advanced generators. Analyzing these models is thus more indicative of real-world conditions going forward compared to earlier versions. Furthermore, the marked quality improvements in recent SD models present greater challenges for attribution and fingerprinting. Subtle inter-model differences become more difficult to quantify amidst high-fidelity outputs. Distance metrics like MSE and LPIPS are sensitive to quality, so lower baseline distortion is a more rigorous test scenario. By evaluating cutting-edge models without inpainting specialization, we aim to benchmark model fingerprinting efficacy on contemporary quality levels. Our experiments on the latest SD variants at scale also assess generalization across diverse high-fidelity generators. Successful attribution and stability analysis under these conditions will highlight the viability of our proposed techniques in real-world deployment.

B.3 Empirical Estimation Of The Lipschitz Constant L

For the empirical estimation of L We use all pairs of images (x and y) from Polo dataset, representing them as inputs and applying the re-generation function f(·). We measure their distances using D, i.e. Euclidean and LPIPS. The ratio below is the transformation of Equation 8:

$$L\le \frac{\mathbb{D}(x,y)}{\mathbb{D}(f(x),f(y))}L\backslash leq\{\backslash frac\{\backslash mathbb\{D\}(x,y)\}\{\backslash mathbb\{D\}(f(x),f(y))\}\}$$ $$\left(15\right)\backslash left(15\backslash right)$$ D(f(x), f(y)) (15)

Model	L_LPIPS Mean	L_LPIPS Std	L_Euclidean Mean	L_Euclidean Std
SD v2.1	0.976	0.015	1.000	0.001
SDXL 1.0	0.943	0.21	1.000	0.004
SD v2	0.975	0.016	1.000	0.001
SD v2.1B	0.970	0.023	1.000	0.002
SDXL 0.9	0.946	0.020	0.999	0.005

Table 9: Lipschitz Constant Estimation From Table 9, we csn observe LPIPS as a distance metric consistently produced lower L values compared to Euclidean distance. This demonstrates LPIPS as a superior metric for our framework, explaining why Euclidean distance fails for verification. Additionally, more advanced models exhibited improved L values, indicating better pertubation resilience and verification capacity. Our approach focuses on leveraging inherent model properties for verification rather than enforcing universal viability. For models currently unsupported, we suggest targeting enhancements to model robustness in line with these observations. Overall, the experiment validated LPIPS as an optimal distance function and revealed a correlation between model advancement and verifiability via intrinsic fingerprints.

B.4 Sample Prompts And Images Reproduced

In our computer vision experiments, we sample prompts from the MS-COCO 2017 Evaluation (Lin et al., 2014) and POLOCLUB (POLO) Diffusion Dataset (Wang et al., 2022) for image generation. We present a few example prompts and images produced for different models in the section below.

B.4.1 Coco Dataset Prompts

• A motorcycle with its brake extended standing outside.

• Off white toilet with a faucet and controls.

• A group of scooters rides down a street.

B.4.2 Polo Dataset Prompts

• A renaissance portrait of Dwayne Johnson, art in the style of Rembrandt!! Intricate. Ultra detailed, oil on canvas, wet-on-wet technique, pay attention to facial details, highly realistic, cinematic lightning, intricate textures, illusionistic detail.

Table 10: The precision and recall of verifying the authentic models Ga using different contrast models Gc on Coco Dataset.

Gc	SD v2.1	SD v2.	SD v2.1B	SDXL 0.9	SDXL 1.0
Ga	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑
	(a) k = 1
SD v2.1	-	-	87.5	90.5	97.5	97.5	96.5	98.0	97.0	97.5
SD v2.	89.0	91.5	-	-	97.0	98.0	96.0	97.0	95.5	97.5
SD v2.1B	14.5	19.0	2.0	3.0	-	-	47.5	53.0	48.5	56.0
SDXL 0.9	85.5	88.5	88.0	91.5	99.5	100.0	-	-	90.5	95.0
SDXL 1.0	92.5	96.0	89.5	93.0	98.0	98.5	95.5	97.0	-	-
	(b) k = 3
SD v2.1	-	-	73.0	77.0	97.5	98.5	94.5	96.5	95.5	96.5
SD v2.	72.0	79.0	-	-	97.0	99.0	95.0	96.0	94.5	95.5
SD v2.1B	74.0	79.0	74.5	79.5	-	-	82.0	86.0	81.5	85.5
SDXL 0.9	88.5	90.0	90.0	91.5	98.0	98.5	-	-	86.5	88.0
SDXL 1.0	91.5	94.5	92.5	95.0	100.0	100.0	89.0	91.0	-	-
	(c) k = 5
SD v2.1	-	-	66.0	73.0	99.5	99.5	94.5	97.0	93.0	96.0
SD v2.	72.5	81.5	-	-	96.0	96.5	91.0	92.5	94.0	95.0
SD v2.1B	78.5	83.5	77.0	82.5	-	-	82.5	87.0	85.5	89.5
SDXL 0.9	97.0	98.0	97.5	98.0	100.0	100.0	-	-	92.0	95.0
SDXL 1.0	93.0	96.0	92.5	93.0	99.0	99.5	88.0	90.5	-	-

• Epic 3D, become legend shiji! GPU mecha controlled by telepathic hackers, made of liquid, bubbles, crystals, and mangroves, Houdini SideFX, perfect render, ArtStation trending, by Jeremy Mann, Tsutomu Nihei and Ilya Kuvshinov.

• An airbrush painting of a cyber war machine scene in area 5 1 by Destiny Womack, Gregoire Boonzaier, Harrison Fisher, Richard Dadd.

B.5 Density Distribution Of A One-Step Re-Generation

The one-step re-generation density distributions reveal distinct model-specific characteristics, enabling discrimination as seen in Figure 14 and 15, Most models exhibit distinction, with each distribution showing unique traits. A notable exception in this behavior is observed for the SD v2.1B (see Figures 14 and 15). which initially demonstrates less discrimination. However, over extended iterations, SD v2.1B shows marked improvement, highlighting the capacity for iterative refinement. By the 5th iteration, there is a noticiable improvement in the discriminative nature of its one-step re-generation. This improvement is crucial as it highlights the model's capacity to refine and enhance its re-generative characteristics over time.

While LPIPS is not immediately effective in pinpointing the authentic model at the very first step, it still offers a powerful mechanism to distinguish between models. LPIPS is effective at differentiating between families of models, such as the Stable Diffusion models and the Stable Diffusion XL models, as visualized in Figure 16 for the Polo dataset and Figure 17 for the Coco dataset. The lack of effectiveness of LPIPS in identifying the authentic model is a primary reason why it was not chosen for verification. Further insights into the models' discriminative capabilities can be derived from Table 10 and 11, while SDv2.1B starts with lower accuracy in distinguishing itself, a significant improvement in accuracy is seen across iterations. The initially anomalous behavior transitions into more discriminating re-generation.

Table 11: The precision and recall of verifying the authentic models Ga using different contrast models Gc on Polo Dataset.

Gc	SD v2.1	SD v2.	SD v2.1B	SDXL 0.9	SDXL 1.0
Ga	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑
	(a) k = 1
SD v2.1	-	-	76.0	78.5	97.5	99.0	93.5	97.0	94.0	95.0
SD v2.	79.0	84.0	-	-	98.0	98.5	92.0	95.5	94.0	95.5
SD v2.1B	40.5	51.0	39.0	46.0	-	-	72.5	80.0	73.5	80.5
SDXL 0.9	86.0	88.5	85.0	89.5	99.5	99.5	-	-	91.5	95.5
SDXL 1.0	89.0	92.0	89.5	93.0	98.0	99.0	91.5	95.5	-	-
	(b) k = 3
SD v2.1	-	-	77.0	83.0	99.5	100.0	95.5	98.0	96.5	97.5
SD v2.	75.5	82.0	-	-	98.0	98.0	96.5	98.0	97.5	97.5
SD v2.1B	70.0	76.5	71.5	78.5	-	-	84.0	90.5	84.5	89.5
SDXL 0.9	92.5	95.0	91.0	94.0	100.0	100.0	-	-	91.0	94.0
SDXL 1.0	90.0	92.5	89.5	91.5	100.0	100.0	90.0	93.0	-	-
	(c) k = 5
SD v2.1	-	-	80.0	86.0	99.5	99.5	98.5	99.5	99.0	100.0
SD v2.	77.5	81.5	-	-	99.0	100.0	96.5	97.0	95.5	97.5
SD v2.1B	81.5	83.5	82.5	86.5	-	-	88.5	92.0	89.5	91.0
SDXL 0.9	97.5	97.5	96.5	98.0	99.5	99.5	-	-	92.0	93.5
SDXL 1.0	95.5	96.0	92.5	95.5	100.0	0.0	94.5	96.0	-	-

Figure 14: One Step Re-generation for various authentic models on the Polo Dataset using the CLIP metric at different iterations. The authentic models from top to bottom are: 1) SDv 2.1, 2) SD v2, 3) SD v2.1B,4) SDXL 1.0, 5) SDXL0.9B.

Figure 15: One Step Re-generation for various Authentic Models on the Coco Dataset using the CLIP metric at different iterations. The authentic models from top to bottom are: 1) SDv 2.1, 2) SD v2, 3) SD v2.1B, 4) SDXL 1.0, 5) SDXL0.9B.

0.02 0.04 0.06 0

0.02 0.04 0.06 0

0.02 0.04 0.06 0

0.02 0.04 0.06 0

0.02 0.04 0.06 0

Figure 16: One Step Re-generation for various Authentic Models on the Polo Dataset using the LPIPS metric at different iterations. The authentic models from top to bottom are: 1) SDv 2.1, 2) SD v2, 3) SD v2.1B, 4) SDXL 1.0, 5) SDXL0.9B.

0.02 0.04 0.06 0.0

0.00 0.02 0.04 0.06 0.0

0.02 0.04 0.06 0

0.02 0.04 0.06 0

0.02 0.04 0.06 0 Figure 17: One Step Re-generation for various Authentic Models on the Coco Dataset using the LPIPS metric at different iterations. The authentic models from top to bottom are: 1) SDv 2.1, 2) SD v2, 3) SD v2.1B, 4) SDXL 1.0, 5) SDXL0.9B.

C Supplementary Experiments For Text Generation Models C.1 Density Distribution Of A One-Step Re-Generation

In Figure 18, we illustrate the density distribution of one-step re-generation for four text generation models, using the first iteration from the authentic models as input. Excluding Cohere, the density distributions of the authentic models are discernible from those of the contrast models across BLEU, ROUGE-L, and BERTScore metrics.

Figure 18: Density distribution of one-step re-generation among four text generation models, where the input to the one-step re-generation is the first iteration from the authentic models. The authentic models from left to right are: 1) M2M, 2) mBART, 3) GPT3.5-turbo, and 4) Cohere. Figure 19 illustrates the density distribution when the input is the kth iteration from the authentic models. As k increases, the distinction between the authentic model's distribution and that of the contrast models becomes more pronounced.

Figure 19: Density distribution of one-step re-generation among four text generation models, where the input to the one-step re-generation is the kth iteration from the authentic models. The authentic models from left to right are: 1) M2M, 2) mBART, 3) GPT3.5-turbo, and 4) Cohere.

C.2 Experiments For Gpt4

In this section, we analyze the characteristics of GPT4. We first present the density distribution when the input is the kth iteration from the authentic models in Figure 20. Similarly, as k increases, the difference between the authentic model's distribution and the contrast models intensifies. Nonetheless, distinguishing between GPT3.5-turbo and GPT4 proves difficult, particularly when GPT3.5-turbo serves as the authentic model, even for larger values of k. Detailed examination reveals that GPT4's one-step re-generation bears resemblance to the k-th iteration of GPT3.5-turbo. This might stem from GPT3.5-turbo and GPT4 originating from the same institution, suggesting potential similarities in architecture and pre-training data. Thus, we contend that models stemming from the same institution inherently share identical intellectual property, thus obviating the possibility of intellectual property conflicts. Interestingly, when GPT4 is the authentic model, our methodology can differentiate it from GPT3.5-turbo, attributed to the marked difference between GPT3.5-turbo's one-step re-generation and GPT4's k-th iteration. This distinction, we surmise, is due to GPT4's superior advancement over GPT3.5-turbo.

Figure 20: Density distribution of one-step re-generation among four text generation models, where the input to the one-step re-generation is the kth iteration from the authentic models. The authentic models from left to right are: 1) M2M, 2) mBART, 3) GPT3.5-turbo, and 4) GPT4. In evaluating the verification of authentic models, our methodology, as depicted in Table 12, consistently confirms the authorship of all models with an accuracy exceeding 85%. Furthermore, the misclassification rate remains below 10%.

C.3 Quality Of Re-Generated Sentences And Images C.3.1 Text Re-Generations

In this section, we examine the quality of re-generated sentences. As illustrated in Figure 21, the re-generated sentences display high quality across most evaluation metrics, except for Cohere. The slower convergence observed for Cohere can be attributed to its subpar re-generation quality, which significantly deviates from that of other models. For further illustration, refer to the samples and their re-generations in Table 13-16.

Gc	M2M	mBART	GPT3.5-turbo	GPT4
Ga	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑	Precision ↑	Recall ↑
(a) k = 1
M2M	-	-	94.0	98.0	93.0	95.0	87.0	92.0
mBART	85.0	89.0	-	-	89.0	92.0	80.0	85.0
GPT3.5-turbo	87.0	92.0	90.0	92.0	-	-	51.0	69.0
GPT4	92.0	98.0	94.0	98.0	77.0	90.0	-	-
(b) k = 3
M2M	-	-	94.0	99.0	95.0	97.0	94.0	95.0
mBART	85.0	93.0	-	-	90.0	96.0	89.0	95.0
GPT3.5-turbo	89.0	92.0	93.0	95.0	-	-	51.0	72.0
GPT4	96.0	97.0	92.0	94.0	79.0	91.0	-	-
(c) k = 5
M2M	-	-	94.0	98.0	95.0	99.0	94.0	96.0
mBART	91.0	96.0	-	-	88.0	94.0	89.0	94.0
GPT3.5-turbo	90.0	94.0	94.0	98.0	-	-	55.0	83.0
GPT4	97.0	98.0	94.0	97.0	83.0	95.0	-	-

Table 12: The precision and recall of verifying the authentic models (Ga) using different contrast models (Gc).

BERTScore.

C.3.2 Image Re-Generations

An integral part of our evaluation process involves understanding the reproducibility of the images generated by different models across iterations. To this end, we present image re-generations for various authentic models in Figure 22-26. These re-generations provide insights into the consistency and stability of each model when tasked with reproducing the same visual content over multiple iterations.

Sample 1: Original input: Working in groups of 2 or 4 (even numbers may work better later on), suggest a heuristic to evaluate the utility of a given board configuration. Iteration 1: Working in groups of 2 or 4 (even numbers can work better later), suggests a heurist to evaluate the usefulness of a given table configuration.

Iteration 2: Working in groups of 2 or 4 (even numbers can work better later), suggests a heurist to evaluate the usefulness of a given table configuration.

Iteration 3: Working in groups of 2 or 4 (even numbers can work better later), suggests a heurist to evaluate the usefulness of a given table configuration.

Iteration 4: Working in groups of 2 or 4 (even numbers can work better later), suggests a heurist to evaluate the usefulness of a given table configuration.

Iteration 5: Working in groups of 2 or 4 (even numbers can work better later), suggests a heurist to evaluate the usefulness of a given table configuration.

Sample 2: Original input: Therefore, to improve the ethical coping ability of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethics knowledge base and KEPTMs for ethics domain are researched Iteration 1: Therefore, in order to improve the ethical treatment capacity of Chinese NLP techniques and their effectiveness of application in the field of ethics, the knowledge base of Chinese ethics and the KEPTMs for the field of ethics are studied.

Iteration 2: Therefore, in order to improve the ethical treatment capacity of Chinese NLP techniques and their effectiveness of application in the field of ethics, the knowledge base of Chinese ethics and KEPTMs for the field of ethics are studied. Iteration 3: Therefore, in order to improve the ethical treatment capacity of Chinese NLP techniques and their effectiveness of application in the field of ethics, the knowledge base of Chinese ethics and KEPTMs for the field of ethics are studied.

Iteration 4: Therefore, in order to improve the ethical treatment capacity of Chinese NLP techniques and their effectiveness of application in the field of ethics, the knowledge base of Chinese ethics and KEPTMs for the field of ethics are studied.

Iteration 5: Therefore, in order to improve the ethical treatment capacity of Chinese NLP techniques and their effectiveness of application in the field of ethics, the knowledge base of Chinese ethics and KEPTMs for the field of ethics are studied.

Sample 3: Original input: I kindly request a modification to the due date for my assignment. According to the previous thread, I was informed that I would receive an extension of 33 hours for this assignment. However, as of now, my Moodle account still indicates the original due date Iteration 1: I slowly ask for a change to the appropriate date for my task. According to the previous topic, I was informed that I would receive an extension of 33 hours for this task. However, from now on, my Moodle account still indicates the appropriate original date.

Iteration 2: I slowly ask for a change to the appropriate date for my task. According to the previous subject, I was informed that I would receive a 33-hour extension for this task. However, from now on, my Moodle account still indicates the appropriate original date.

Iteration 3: I slowly ask for a change to the appropriate date for my task. According to the previous topic, I was informed that I would receive a 33-hour extension for this task. However, from now on, my Moodle account still indicates the appropriate original date.

Iteration 4: I slowly ask for a change to the appropriate date for my task. According to the previous topic, I was informed that I would receive a 33-hour extension for this task. However, from now on, my Moodle account still indicates the appropriate original date. Iteration 5: I slowly ask for a change to the appropriate date for my task. According to the previous topic, I was informed that I would receive an extension of 33 hours for this task. However, from now on, my Moodle account still indicates the appropriate original date.

Sample 1: Original input: Working in groups of 2 or 4 (even numbers may work better later on), suggest a heuristic to evaluate the utility of a given board configuration. Iteration 1: If you work in groups of 2 or 4 (even numbers can work better later), suggest a mouse kit to evaluate the usefulness of a given configuration of the table.

Iteration 2: If you work in groups of 2 or 4 (even numbers can work better later), suggest a mouse kit to evaluate the usefulness of a particular table configuration.

Iteration 3: If you work in groups of 2 or 4 (even numbers can work better later), suggest a mouse kit to evaluate the usefulness of a particular table configuration.

Iteration 4: If you work in groups of 2 or 4 (even numbers can work better later), suggest a mouse kit to evaluate the usefulness of a given table configuration.

Iteration 5: If you work in groups of 2 or 4 (even numbers can work better later), suggest a mouse kit to evaluate the usefulness of a given table configuration.

Sample 2: Original input: Therefore, to improve the ethical coping ability of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethics knowledge base and KEPTMs for ethics domain are researched Iteration 1: For this reason, to improve the ethical adaptation capacity of Chinese NLP techniques and their effective application in the ethics field, the Chinese Ethics Knowledge Base and the KEPTMs for the ethics field are being studied.

Iteration 2: Therefore, to improve the ethical adaptation capacity of Chinese NLP techniques and their effective application in the field of ethics, the Chinese ethics knowledge base and the ECEs for the field of ethics are being studied.

Iteration 3: Consequently, in order to improve the ethical adaptation capacity of Chinese PLN techniques and their effective application in the field of ethics, the Chinese ethics knowledge base and ECE for the field of ethics are being studied.

Iteration 4: Consequently, in order to improve the ethical adaptation capacity of Chinese PLN techniques and their effective application in the field of ethics, the Chinese ethics knowledge base and UNECE for the field of ethics are being studied.

Iteration 5: Consequently, in order to improve the ethical adaptation capacity of Chinese PLN techniques and their effective application in the field of ethics, the Chinese ethics knowledge base and UNECE for the field of ethics are being studied.

Sample 3: Original input: I kindly request a modification to the due date for my assignment. According to the previous thread, I was informed that I would receive an extension of 33 hours for this assignment. However, as of now, my Moodle account still indicates the original due date.

Iteration 1: I am requesting a change to the due date of my assignment, and according to the previous thread, I have been informed that I will receive a 33-hour extension for this assignment, but at the moment my Moodle account still indicates the original due date.

Iteration 2: I am requesting a change to my assignment due date and, according to the previous thread, I have been informed that I have received a 33-hour extension for this assignment, but at the moment, my Moodle account still indicates the original due date.

Iteration 3: I am requesting a change to my assignment due date and, according to the previous thread, I have been informed that I have received a 33-hour extension for this assignment, but for the time being, my Moodle account still indicates the original due date.

Iteration 4: I am requesting a change to the due date of my assignment and, according to the previous thread, I have been informed that I have received a 33-hour extension for this assignment, but for the time being, my Moodle account still indicates the original due date. Iteration 5: I am requesting a change to the due date of my assignment and, according to the previous thread, I was informed that I have received a 33-hour extension for this assignment, but for the time being, my Moodle account still indicates the original due date.

Table 15: Three Original Samples And Their Corresponding K-Iteration From Gpt3.5-Turbo.

Sample 1: Original input: Working in groups of 2 or 4 (even numbers may work better later on), suggest a heuristic to evaluate the utility of a given board configuration. Iteration 1: Working in groups of 2 or 4 (even numbers might work better later on), propose a heuristic to evaluate the usefulness of a given board configuration.

Iteration 2: Working in groups of 2 or 4 (even numbers might work better in the future), propose a heuristic to evaluate the usefulness of a given board configuration.

Iteration 3: Working in groups of 2 or 4 (even numbers might work better in the future), propose a heuristic to evaluate the utility of a given board configuration.

Iteration 4: Working in groups of 2 or 4 (even numbers might work better in the future), propose a heuristic to evaluate the usefulness of a given board configuration. Iteration 5: Working in groups of 2 or 4 (even numbers might work better in the future), propose a heuristic to evaluate the usefulness of a given board configuration. Sample 2: Original input: Therefore, to improve the ethical coping ability of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethics knowledge base and KEPTMs for ethics domain are researched Iteration 1: Therefore, in order to improve the ethical adaptability of Chinese NLP techniques and their application efficiency in the field of ethics, the Chinese ethics knowledge base and KEPTMs for the field of ethics are studied.

Iteration 2: Therefore, in order to improve the ethical adaptability of Chinese natural language processing techniques and their effectiveness in the field of ethics, Chinese ethical knowledge base and KEPTMs for the field of ethics are studied.

Iteration 3: Therefore, in order to improve the ethical adaptability of Chinese natural language processing techniques and their effectiveness in the field of ethics, Chinese ethical knowledge base and KEPTMs for the field of ethics are studied.

Iteration 4: Therefore, in order to improve the ethical adaptability of Chinese natural language processing techniques and their effectiveness in the field of ethics, Chinese ethical knowledge base and KEPTMs for the field of ethics are being studied. Iteration 5: Therefore, in order to improve the ethical adaptability of Chinese natural language processing techniques and their effectiveness in the field of ethics, Chinese ethical knowledge base and KEPTMs for the field of ethics are being studied. Sample 3: Original input: I kindly request a modification to the due date for my assignment. According to the previous thread, I was informed that I would receive an extension of 33 hours for this assignment. However, as of now, my Moodle account still indicates the original due date. Iteration 1: I politely request a modification of the due date for my assignment. According to the previous thread, I was informed that I would be granted a 33-hour extension for this assignment. However, at the moment, my Moodle account still shows the original due date. Iteration 2: I politely request a modification of the deadline for my assignment. According to the previous thread, I was informed that I would be granted an additional 33 hours for this assignment. However, at the moment, my Moodle account still displays the original deadline.

Iteration 3: I politely request a change in the deadline for my assignment. According to the previous thread, I was informed that I would have an additional 33 hours for this assignment. However, currently, my Moodle account still displays the original deadline.

Iteration 4: I politely request a change in deadline for my assignment. According to the previous thread, I was informed that I would have an additional 33 hours for this assignment. However, currently, my Moodle account still displays the original deadline.

Iteration 5: I kindly request a change of deadline for my assignment. According to the previous thread, I was informed that I would have an additional 33 hours for this assignment. However, currently, my Moodle account still displays the original deadline.

Sample 1: Original input: Working in groups of 2 or 4 (even numbers may work better later on), suggest a heuristic to evaluate
the utility of a given board configuration. Iteration 1: Working in groups of 2 or 4 (odd numbers may work better later), suggests a heuristic to evaluate the
utility of a seating chart configuration. Iteration 2: Working in groups of 2 or 4 (odd numbers may work better later), suggests a heuristic for evaluating the
utility of a configuration of the seating plan. Iteration 3: Working in groups of 2 or 4 (odd numbers can work better later), suggests an algorithm for evaluating
the utility of a assistance plan configuration. Iteration 4: Working in groups of 2 or 4 (odd numbers can work better later), suggests an algorithm to evaluate the
utility of a plan of assistance configuration. Iteration 5: Working in groups of 2 or 4 (odd numbers may work better later), suggests an algorithm to evaluate the
utility of a configuration of assistance plans. Sample 2: Original input: Therefore, to improve the ethical coping ability of Chinese NLP techniques and their application
effectiveness in the field of ethics, the Chinese ethics knowledge base and KEPTMs for ethics domain are researched Iteration 1: Therefore, to improve the ethical sweeping capacity of Chinese NLP techniques and their effectiveness in
the ethical domain, Chinese knowledge bases on ethics and KEPTMs for the ethical domain are sought. Iteration 2: Therefore, to improve the ethical brushing capacity of Chinese NLP techniques and their effectiveness in
the ethical domain, Chinese knowledge bases on ethics and KEPTMs for the ethical domain are sought. Iteration 3: Therefore, to improve the brushing capacity of Chinese NLP methods and their effectiveness in the ethical
domain, Chinese knowledge bases on ethics and KEPTMs for the ethical domain are sought. Iteration 4: Therefore, to improve the brushing capacity of Chinese NLP methods and their effectiveness in the ethical
domain, Chinese knowledge bases on ethics and KEPTMs for the ethical domain are sought. Iteration 5: Therefore, to improve the brushing capacity of Chinese NLP methods and their effectiveness in the ethical
domain, Chinese knowledge bases on ethics and KEPTMs for the ethical domain are sought. Sample 3: Original input: I kindly request a modification to the due date for my assignment. According to the previous thread,
I was informed that I would receive an extension of 33 hours for this assignment. However, as of now, my Moodle
account still indicates the original due date. Iteration 1: Please extend the deadline for my assignment. I was informed that I will receive a 33 hour extension for
this assignment, however, it still shows the initial date on my Moodle account. Iteration 2: Please extend the deadline for my assignment. I was informed that I will receive a 33 hour extension for

Sample 1: Original input: Working in groups of 2 or 4 (even numbers may work better later on), suggest a heuristic to evaluate the utility of a given board configuration. Iteration 1: Working in groups of 2 or 4 (even numbers may work better later), propose a heuristic to evaluate the usefulness of a given board configuration.

Iteration 2: Working in groups of 2 or 4 (even numbers may work better later), propose a heuristic to evaluate the usefulness of a given board configuration.

Iteration 3: Working in groups of 2 or 4 (even numbers may work better later), propose a heuristic to evaluate the usefulness of a given board configuration.

Iteration 4: Working in groups of 2 or 4 (even numbers may work better later), propose a heuristic to assess the usefulness of a given board configuration.

Iteration 5: Working in groups of 2 or 4 (even numbers may work better later), propose a heuristic to evaluate the usefulness of a given board configuration.

Sample 2: Original input: Therefore, to improve the ethical coping ability of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethics knowledge base and KEPTMs for ethics domain are researched Iteration 1: Therefore, to improve the ethical management capacity of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethical knowledge base and KEPTMs for the field of ethics are being studied.

Iteration 2: Therefore, to improve the ethical management capacity of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethical knowledge base and KEPTMs for the field of ethics are under study.

Iteration 3: Therefore, to improve the ethical management capacity of Chinese NLP techniques and their application effectiveness in the field of ethics, the Chinese ethical knowledge base and KEPTMs for the field of ethics are currently under study.

Iteration 4: Therefore, to improve the ethical management capacity of Chinese NLP techniques and their application efficiency in the field of ethics, the Chinese ethical knowledge base and KEPTMs for the field of ethics are currently under study.

Iteration 5: Therefore, to improve the ethical management capacity of Chinese NLP techniques and their application efficiency in the field of ethics, the Chinese ethical knowledge base and KEPTMs for the field of ethics are currently under study.

Sample 3: Original input: I kindly request a modification to the due date for my assignment. According to the previous thread, I was informed that I would receive an extension of 33 hours for this assignment. However, as of now, my Moodle account still indicates the original due date.

Iteration 1: I kindly request a modification of the due date for my assignment. According to the previous thread, I was informed that I would receive a 33-hour extension for this assignment. However, at the present time, my Moodle account still shows the initial due date.

Iteration 2: I kindly request a change in the due date for my assignment. According to the previous thread, I was informed that I would receive a 33-hour extension for this assignment. However, at present, my Moodle account still displays the initial due date.

Iteration 3: I kindly request a change of the due date for my assignment. According to the previous thread, I was informed that I would receive a 33-hour extension for this assignment. However, at present, my Moodle account still displays the initial due date.

Iteration 4: I am kindly requesting a change in the due date for my assignment. According to the previous thread, I was informed that I would receive a 33-hour extension for this task. However, at the present time, my Moodle account still displays the initial due date. Iteration 5: I kindly request a change of the due date for my assignment. According to the previous thread, I was informed that I would receive a 33-hour extension for this task. However, at the present time, my Moodle account still displays the initial due date.

Figure 22: Initial image generation and subsequent re-generations by the SDv2.1 model on Coco and Polo datasets.

Figure 23: Initial image generation and subsequent re-generations by the SDv2 model on Coco and Polo datasets.

Figure 24: Initial image generation and subsequent re-generations by the SDv2.1B model on Coco and Polo datasets.

Figure 25: Initial image generation and subsequent re-generations by the SDXL1 model on Coco and Polo datasets.

Figure 26: Initial image generation and subsequent re-generations by the SDXL0.9 model on Coco and Polo datasets.