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Spherical Watermark: Encryption-Free, Lossless Watermarking for Diffusion Models

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.5Download Report PDF
AIGC Watermarking; Diffusion Models;
Abstract:

Diffusion models have revolutionized image synthesis but raise concerns around content provenance and authenticity. Digital watermarking offers a means of tracing generated media, yet traditional schemes often introduce distributional shifts and degrade visual quality. Recent lossless methods embed watermark bits directly into the latent Gaussian prior without modifying model weights, but still require per-image key storage or heavy cryptographic overhead. In this paper, we introduce Spherical Watermark, an encryption‐free and lossless watermarking framework that integrates seamlessly with diffusion architectures. First, our binary embedding module mixes repeated watermark bits with random padding to form a high-entropy code. Second, the spherical mapping module projects this code onto the unit sphere, applies an orthogonal rotation, and scales by a chi-square-distributed radius to recover exact multivariate Gaussian noise. We theoretically prove that the watermarked noise distribution preserves the target prior up to third-order moments, and empirically demonstrate that it is statistically indistinguishable from a standard multivariate normal distribution. Adopting Stable Diffusion, extensive experiments confirm that Spherical Watermark consistently preserves high visual fidelity while simultaneously improving traceability, computational efficiency, and robustness under attacks, thereby outperforming both lossy and lossless approaches.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
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Overview

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
17
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: lossless watermarking for diffusion models. The field addresses how to embed imperceptible ownership or provenance signals into images, videos, and other media generated by diffusion processes without degrading output quality. The taxonomy organizes research into four main branches. Watermark Embedding Mechanism explores how watermarks are injected—whether by manipulating latent noise distributions (e.g., Gaussian Shading[1], Tree Ring Watermarks[4]), conditioning the diffusion process itself (e.g., Watermark Conditioned Diffusion[16]), or modifying model weights and training procedures (e.g., Stable Signature[45]). Robustness and Security examines defenses against removal attacks and adversarial perturbations, with works like Attack Resilient Watermarking[3] and Groot[5] focusing on maintaining detectability under distortions. Domain-Specific Extensions adapt watermarking to specialized modalities such as video (Videomark[6], VideoShield[32]), 3D meshes (Robust Reversible 3D[43]), audio (Invisible Audio Watermarking[34]), and text-to-shape generation (T2SMark[39]). Application-Oriented Frameworks target practical deployment scenarios including federated learning (Federated Diffusion Watermarking[7]), black-box settings (Black Box Watermarking[9]), and copyright protection (DiffusionShield Copyright[22]). A particularly active line of work centers on latent noise manipulation, where methods preserve the statistical properties of the noise distribution to achieve losslessness while embedding detectable patterns. Spherical Watermark[0] sits within this cluster, emphasizing lossless noise distribution preservation through spherical coordinate transformations. This contrasts with approaches like Gaussian Shading[1], which also manipulates noise but may prioritize robustness trade-offs differently, and with training-based methods such as Stable Signature[45] that bake watermarks into model parameters rather than per-sample noise. Meanwhile, robustness-focused branches explore adversarial resilience (Attack Resilient Watermarking[3]) and adaptive attacks (Groot[5]), highlighting tensions between imperceptibility, capacity, and security. Open questions persist around balancing these competing objectives, scaling to diverse modalities, and ensuring watermark persistence across post-processing pipelines without sacrificing the core promise of lossless generation quality.

Claimed Contributions

Spherical Watermark framework for lossless, encryption-free watermarking

The authors propose a novel watermarking framework that embeds watermarks into diffusion models without requiring encryption or per-image key storage. The framework uses binary embedding and spherical mapping modules to transform watermark bits into Gaussian noise that is statistically indistinguishable from the original prior, enabling lossless watermarking with improved traceability and computational efficiency.

9 retrieved papers
Can Refute
Spherical mapping module with theoretical guarantees

The authors develop a spherical mapping technique that projects binary codes onto the unit sphere, applies orthogonal rotation, and scales by a chi-square-distributed radius. They theoretically prove that the resulting watermarked noise preserves the target Gaussian prior up to third-order moments and forms a spherical 3-design, ensuring statistical indistinguishability from standard Gaussian noise.

1 retrieved paper
Encryption-free design eliminating key storage overhead

The authors design a watermarking system that does not require per-image cryptographic keys or nonces, unlike prior lossless methods. This eliminates substantial storage and management overhead while maintaining strong traceability and robustness against attacks, offering improved computational efficiency compared to cryptography-based approaches.

7 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Spherical Watermark framework for lossless, encryption-free watermarking

The authors propose a novel watermarking framework that embeds watermarks into diffusion models without requiring encryption or per-image key storage. The framework uses binary embedding and spherical mapping modules to transform watermark bits into Gaussian noise that is statistically indistinguishable from the original prior, enabling lossless watermarking with improved traceability and computational efficiency.

Contribution

Spherical mapping module with theoretical guarantees

The authors develop a spherical mapping technique that projects binary codes onto the unit sphere, applies orthogonal rotation, and scales by a chi-square-distributed radius. They theoretically prove that the resulting watermarked noise preserves the target Gaussian prior up to third-order moments and forms a spherical 3-design, ensuring statistical indistinguishability from standard Gaussian noise.

Contribution

Encryption-free design eliminating key storage overhead

The authors design a watermarking system that does not require per-image cryptographic keys or nonces, unlike prior lossless methods. This eliminates substantial storage and management overhead while maintaining strong traceability and robustness against attacks, offering improved computational efficiency compared to cryptography-based approaches.

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