OptMark: Multi-Bit Watermarking for Diffusion Images

• OptMark is a multi-bit watermarking framework that integrates digital watermark embedding into the diffusion denoising process for robust copyright protection.
• It employs dual-stage watermark injection using inference-time optimization and adjoint sensitivity to achieve near-perfect bit accuracy and resilience to various attacks.
• The framework minimizes memory usage while maintaining image quality, proving effective against geometric, valuemetric, editing, and regeneration attacks.

OptMark refers to a robust multi-bit optimization-based watermarking framework for diffusion-generated images, designed to support digital copyright protection and large-scale user tracking while delivering high resilience to adversarial image transformations and attacks. Unlike traditional watermarking approaches that either offer zero-bit capacity or are vulnerable to geometric, valuemetric, editing, and regeneration attacks, OptMark strategically embeds watermarks throughout specific epochs of the diffusion denoising process using inference-time optimization, dual-stage watermark injection, and memory-efficient adjoint gradient computation (Xing et al., 29 Aug 2025).

1. Motivation and Technical Context

OptMark targets critical gaps in diffusion watermarking systems. Zero-bit watermarks lack scalability for tracking numerous users, while existing multi-bit schemes degrade under typical image perturbations and generative attacks inherent to large-scale AIGC (Artificial Intelligence Generated Content) platforms. Modern content provenance systems require both high watermark capacity (e.g., 48-bits per image) and robustness under arbitrary user actions that preserve copyright and usage accountability. OptMark situates its approach at the intersection of deep generative model security and scalable inference-time optimization.

2. Optimization-Based Embedding During Diffusion Denoising

OptMark’s embedding strategy modifies the latent representations $x_t$ during the iterative reverse denoising process (e.g., DDIM sampling). At designated time steps, structural and detail watermarks—learnable vectors $w_s$ and $w_d$—are injected into the latents via operators $F_s$ and $F_d$. The overall denoising at step $t$ applies:

• Early inference: $$\hat{\epsilon}_t = \epsilon_\theta(F_s(x_t, w_s), t, \psi(p))$$ at $t = t_s$
• Late inference: $$\hat{\epsilon}_t = \epsilon_\theta(F_d(x_t, w_d), t, \psi(p))$$ at $t = t_d$
• Elsewhere, standard denoising applies

$F_s$ and $F_d$ are parameterized to enforce both variance preservation and imperceptibility; for structural watermarking in the earliest steps ($t_s = T$, full noise), statistical normalization ensures that the modified latent matches the variance of $x_T$:

$$x_t^w = w_s + \sqrt{\frac{\mathrm{var}(x_T) - \mathrm{var}(w_s)}{\mathrm{var}(x_T)}} x_T$$

$$x_t^w = \sqrt{\frac{\mathrm{var}(x_T)}{\mathrm{var}(x_t^w)}} x_t^w$$

A dual-watermark mechanism is employed to maximize robustness: early-stage “structure” embedding counters generative attacks; late-stage “detail” embedding (e.g., $t_d$ in $[200,300]$, $t_d=251$ typical) enhances resistance to value-preserving and geometric transformations.

3. Regularization and Quality Constraints

The optimization objective integrates multiple regularization terms, resulting in a combined loss function:

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

where:

• $\mathcal{L}_{\text{msg}}$: hinge-margin decoding loss for reliable multi-bit watermark recovery
• $\mathcal{L}_{\text{init}}$: squared mean difference between watermarked and original latents
• $\mathcal{L}_{\text{low}}$: $L_2$ losses on mean/variance deviations for $w_s$ and $w_d$ (relative to $\mathcal{N}(0,0.01)$ initialization)
• $\mathcal{L}_{\text{high}}$: higher moment constraints including kurtosis and skewness for $w_s$, $w_d$ (to regularize tails and distribution symmetry)

These terms collectively enforce that the watermark remains imperceptible, well-dispersed, and robust to statistical anomaly detection.

4. Adjoint Sensitivity for Memory-Efficient Optimization

Standard inference-time optimization over $N$ diffusion steps incurs $O(N)$ memory due to forward and backward passes. OptMark implements the adjoint sensitivity method from neural ODEs, reducing this cost to $O(1)$ by treating the reverse denoising process as an ODE:

$\frac{dx_t}{dt} = f(x_t, t, c, w)$

$$\frac{da_t}{dt} = -a_t^T \left(\frac{\partial f(x_t, t, c, w)}{\partial x_t}\right)$$

$$\frac{\partial \mathcal{L}}{\partial w} = \int_0^T a_t^T \frac{\partial f(x_t, t, c, w)}{\partial w} dt$$

where $a_t = \frac{\partial \mathcal{L}}{\partial x_t}$ is propagated in reverse time. This enables scalable optimization of watermark parameters without memory bottlenecks, facilitating deep unrolling (high $N$) and robust watermark embedding.

5. Experimental Evaluation and Benchmarking

OptMark is benchmarked on Stable Diffusion v2.1 across 1,000 images with comparison to baseline pixel-level and semantic-level watermarking methods (e.g., DwtDct, SSL Watermark, Gaussian Shading, AquaLoRA). Metrics studied include bit accuracy, true positive rate (TPR), FID, and CLIP scores. Key findings:

• Bit accuracy and TPR $\approx 1.000$ in clean settings; high robustness under valuemetric, geometric, editing, and regeneration attacks across all attack types
• FID and CLIP: Watermarked images are visually and semantically indistinguishable from unmarked baselines
• Ablation studies confirm the necessity of both dual watermarks and composite regularizations
• Memory usage is minimized, enabling application-scale deployment

A plausible implication is that the integration of structure and detail watermarks yields a resilience profile superior to each technique individually.

6. Practical Implications and Future Research

OptMark provides an efficient, scalable framework for copyright protection and user-tracing in diffusion-generated content ecosystems. While its robustness against regeneration attacks is slightly lower than alternative semantic-level schemes, the system achieves strong performance across a comprehensive attack suite. Potential improvements include extending watermark extraction networks (using the denoising UNet instead of fixed encoders such as DINO), increasing efficiency, and generalizing the approach for alternative diffusion samplers.

7. Summary and Outlook

OptMark defines a robust multi-bit watermarking paradigm for diffusion models via inference-time optimization, dual-stage latent watermark injection, and memory-efficient adjoint gradient computation. Its design balances watermark capacity, imperceptibility, and attack resilience, facilitating its adoption for copyright and provenance tracking in next-generation AIGC platforms. Continued development of extraction architectures and expansion to diverse diffusion samplers may further improve performance and applicability in operational settings.