DenMark: Robust Semantic Watermarking for Diffusion Language Models

We introduce the first watermark tailored for diffusion language models (DLMs), an emergent LLM paradigm able to generate tokens in arbitrary order, in contrast to standard autoregressive language models (ARLMs) which generate tokens sequentially. While there has been much work in ARLM watermarking, a key challenge when attempting to apply these schemes directly to the DLM setting is that they rely on previously generated tokens, which are not always available with DLM generation. In this work we address this challenge by: (i) applying the watermark in expectation over the context even when some context tokens are yet to be determined, and (ii) promoting tokens which increase the watermark strength when used as context for other tokens. This is accomplished while keeping the watermark detector unchanged. Our experimental evaluation demonstrates that the DLM watermark leads to a >99% true positive rate with minimal quality impact and achieves similar robustness to existing ARLM watermarks, enabling for the first time reliable DLM watermarking.

This work presents Dual-Embedding Watermarking (DEW), a semantic watermarking scheme for large language models (LLMs) that leverages contextual and token-level embeddings to enhance robustness against paraphrasing and translation. DEW utilizes a signal-processing methodology, applying algebraic vector-space operations to token and context embeddings to derive a watermark signal that degrades gracefully under semantic shifts. The method obfuscates the watermark by projecting embedding vectors through pseudo-random matrices seeded with a secret key. Relevant distributions derived from the underlying algebra are evaluated and employed for statistical testing and benchmarking of DEW. Experimental results across multiple LLMs indicate that DEW improves post-paraphrase detection while maintaining competitive text quality, and remains detectable after translation, even when prior semantic watermarks degrade significantly. These findings position DEW as a practical and robust solution for safeguarding LLM-generated text and addressing critical issues in responsible AI deployment.

Statistical watermarking is a common approach for verifying whether text was written by a language model. Most existing schemes assume autoregressive generation, where tokens are produced left to right and contextual hashing is well defined. Diffusion language models generate text by denoising tokens in arbitrary order, so these schemes cannot be applied directly. A recent watermark by Gloaguen et al. addresses this gap for LLaDA 8B Instruct and reports true positive detection above 99%. This paper studies what happens when watermarked text is rewritten not once but several times. Using the same watermark configuration, 1,605 watermarked completions of about 300 tokens each are produced across five WaterBench domains. Each completion is rewritten by four open weight language models, from 1.5B to 8B parameters, none of which know the watermark key. Five rewrite styles are tested: paraphrase, humanize, simplify, academic, and summarize expand. Each style is chained for up to five hops, producing 160,500 rewritten texts in total. The watermark is detected on 87.9% of the original outputs at the standard significance threshold. After a single rewrite, detection falls to between 14% and 41% depending on the rewriter and style. After five chained rewrites, detection falls to 4.86%, meaning 94.76% of the originally detected texts are no longer flagged. After three rewrites, the detector score has dropped 86% of the way from its watermarked baseline toward the null distribution. Repeated rewriting is therefore a much stronger attack than a single rewrite, and the result holds across all four rewriters tested.