TraceMark-LDM: Robust Watermarking in LDMs

• TraceMark-LDM is an authenticatable watermarking framework for latent diffusion models that embeds watermarks via binary-guided rearrangement of Gaussian random variables.
• It integrates encoder fine-tuning and structured partitioning of latent variables to embed a 256-bit identifier while preserving the natural Gaussian distribution.
• The framework achieves superior robustness with >95% bit accuracy under various attack scenarios, all without detectable degradation in image quality metrics.

TraceMark-LDM is an authenticatable watermarking framework for Latent Diffusion Models (LDMs) that integrates binary-guided rearrangement of Gaussian random variables to achieve forensic attribution of AI-generated images, while maintaining non-destructive image quality. By encoding multi-bit watermarks directly in the stochastic generation process and coupling this with fine-tuning of LDM encoders, TraceMark-LDM attains robust, high-capacity, and near-invisible watermarking superior to existing state-of-the-art methods, even under intensive content distortion or re-generation scenarios (Luo et al., 30 Mar 2025).

1. Latent Diffusion Models and the Watermarking Problem

LDMs, such as Stable Diffusion v2.1, utilize a VAE encoder $E$ to compress images $I$ into a low-dimensional latent $z_0$. A forward diffusion process transforms $z_0$ into $z_T\sim\mathcal{N}(0,I)$, and a reverse denoising chain (DDPM/DDIM) reconstructs $z_0$, which is then decoded by $D$ to output pixels. Conventional watermarking approaches—embedding identifiers into pixels or intermediate noise—perturb latent Gaussian priors, causing measurable declines in image fidelity (increased FID, decreased CLIP-Score) and vulnerability to post-processing. The central technical challenge is to invisibly encode a $k$-bit identifier within $z_T$'s sampling, preserving the marginal $\mathcal{N}(0,I)$ and thereby retaining image quality and reliable recovery post-attack.

2. TraceMark-LDM Embedding Pipeline

TraceMark-LDM encodes a $k$-bit watermark $m$ via structured rearrangement of latent variables during image generation, involving partitioning, rearrangement based on bit values, and postprocessing to conceal the watermark.

2.1 Sampling and Partitioning

The algorithm samples $z\sim\mathcal{N}(0,I)$ with latent dimension $r=c\cdot h\cdot w$, and partitions $z$ into negative ($N$) and non-negative ($P$) subsets.

2.2 Binary-Guided Rearrangement

Quartile partitions $N_1\subset N$, $P_1\subset P$ are extracted as the largest (absolute value) elements. For each watermark bit $b_j$, a “large-element” sequence $z_l$ is formed by cycling through bits and selecting an element from $N_1$ if $b_j=0$, $P_1$ if $b_j=1$, repeating $m$ until $z_l\in\mathbb{R}^{r/2}$ is assembled. The rearrangement operator $R_l(z, b_j)$ selects unused elements accordingly.

2.3 Group Rearrangement of Small Elements

Remaining elements $R$ are sorted; most negative/positive halves ($R_n$, $R_p$) are split into $k/2$ disjoint groups $G_n$ and $G_p$. Each group's sum signals the bit: $g_j$ chosen from $G_n$ encodes $b_j=0$ $(\sum g_j<0)$, from $G_p$ for $b_j=1$ $(\sum g_j>0)$. Concatenation yields $z_s\in\mathbb{R}^{r/2}$.

2.4 Interleaving, Permutation, and Generation

The sequences $z_l$ and $z_s$ are interleaved to yield $z_m$; a secret key-dependent permutation $\pi(m)$ is applied, producing $z_{wt}$. This watermarked noise then passes through the LDM denoising chain to reconstruct $z_0$, which is decoded to the final image $I_{wm}$.

2.5 Encoder Fine-Tuning

DDIM inversion and VAE encoding introduce extraction errors. Fine-tuning the encoder $E_\theta$ (decoder $D$ fixed) is performed: generating $I=D(z_0)$, applying random distortions $A$ to $I$, and optimizing

$$\mathcal{L}_{inv}(\theta) = \mathbb{E}[\|z_0 - E_\theta(I')\|^2],$$

$$\mathcal{L}_{sim}(\theta) = \mathbb{E}[LPIPS(D(z_0), D(E_\theta(I')))],$$

with $$\mathcal{L}(\theta) = \mathcal{L}_{inv} + \lambda \mathcal{L}_{sim}$$, $\lambda=1$, for 100 epochs ($\sim$200 images, distortions: median, JPEG, blur, noise, resize). This approach reduces bit-flip rates during extraction under attack.

3. Watermark Extraction and Authentication

Upon receiving a possibly attacked image $I^*$:

1. Encode $z_0'=E_{finetuned}(I^*)$;
2. Apply DDIM inversion to recover $z_{wt}'$;
3. Unshuffle via $\pi^{-1}$ to reconstruct $z_m'$;
4. De-interleave into $z_l'$ and $z_s'$;
5. Decode $z_l'$: $\hat b_j^{(l)}=0$ if $p<0$, $1$ otherwise;
6. Decode $z_s'$: $$\hat b_j^{(s)}=\text{sign}\left(\sum_{x\in g} x\right)$$;
7. Merge streams and repeat voting over repetitions to obtain final recovered $m'$;
8. Authenticate: compare $m'$ against user signatures. Attribution accepted if Hamming similarity $>\tau$ (threshold for FPR=$10^{-6}$).

4. Experimental Results and Benchmarking

The backbone is Stable Diffusion v2.1 ($512\times512$ images, latent $4\times64\times64$). Sampling uses DPM-Solver ($50$ steps, guidance $7.5$), inversion by DDIM ($50$ steps, null prompt, guidance $1$). Attacks simulated include median filter ($k=3$–$19$), JPEG ($Q=10$–$90$), Gaussian blur ($r=2$–$10$), Gaussian noise ($\sigma=0.05$–$0.25$), salt-&-pepper ($p=0.05$–$0.4$), resize ($0.1$–$0.9$), VAE regen (quality $1$–$5$), and diffusion regen ($300$–$700$ DDPM steps). Watermark length is $k=256$ bits, repeated $\approx r/(2k)$ times.

Metric	Baseline	TraceMark-LDM	Statistical Test
FID	24.90	24.96	$t=0.773$ ($<2.101$)
CLIP Score	0.3647	0.3649	$t=0.372$ ($<2.101$)
Attribution (benign)	—	100% bit acc.	TPR@$10^{-6}$ ≈ 1.0

TraceMark-LDM demonstrates no statistical degradation of image quality. Robustness is sustained at $\geq 96\%$ bit accuracy across distortions, $99.4\%$ accuracy under salt-and-pepper $p=0.4$, $96.7\%$ under VAE regen $q=5$, $74.1\%$ under diffusion regen with $700$ steps—the latter remains highest among compared methods.

5. Comparative Analysis with State-of-the-Art Methods

TraceMark-LDM is contrasted with prominent LDM watermarking approaches:

• Posterior-image methods (DwtDct, RivaGAN): degrade FID ($t\gg2.1$) and lack robustness to distortions beyond mild JPEG.
• In-generation methods (Stable Signature, Latent Watermark): require costly U-Net fine-tuning or suffer quality loss for high-capacity embedding ($>32$ bits).
• Initial-noise methods (Tree-Rings, Gaussian Shading): cause distributional distortions or operational inefficiency (e.g., slow ChaCha20 encryption).

TraceMark-LDM achieves performance-lossless watermark embedding (no observable FID/CLIP drop), supports multi-bit capacity ($256$ bits), maintains $\gtrsim 95\%$ bit accuracy under all attacks, exceeds $70\%$ under extreme re-generation, and entails only moderate overhead (100-epoch encoder fine-tune, no per-image encryption or U-Net retraining). These properties yield superior bit-accuracy versus robustness trade-off (cf. Table I, Table III in source).

6. Context and Implications

TraceMark-LDM addresses the forensic attribution requirement for AI-generated content—a concern of increasing societal and legal significance. By integrating watermarking into the generative sampling step and developing resilience to post-processing and re-generation, the framework suggests a paradigm wherein provenance can be guaranteed with minimal operational disruption and strong resistance to adversarial attacks. A plausible implication is that similar binary-guided rearrangement and encoder fine-tuning methodologies could be extended to other generative architectures reliant on latent Gaussian sampling, offering broad utility in AIGC attribution and copyright protection domains (Luo et al., 30 Mar 2025).