Watermarking Diffusion Language Models with Learned Foresight and Balanced Bands

Hyojun Kim, Hyeseon An, Yo-Sub Han

Green-red watermarks favor tokens from a green list that a secret key derives from the preceding tokens. Diffusion language models, however, often choose a token before its preceding tokens, and the token later shapes its neighbors' green lists. Prior work therefore tilts each choice to raise the expected number of green tokens at its own and its neighbors' positions. Building on this objective, we first learn two components that prior work keeps fixed: vocabulary bands that serve as green lists, separate competing candidates and keep the null distribution exact, and a foresight predictor that estimates how each candidate shifts its neighbors' predictions. Second, we count green tokens as the detector does, once per distinct context-token pair, so repetition earns nothing. On WaterBench with LLaDA-8B-Instruct, each learned component raises the z-score at equal distortion, and their gains are nearly additive. With a strong watermark, ours detects at least 96% of responses at a 1% false-positive rate while matching the LLM-judge score of unwatermarked text. Ours also detects more responses on Dream and as many or more on code and question answering without a significant loss in…