arXiv:2512.04044v2 Announce Type: replace-cross Abstract: Language model watermarking schemes fall into two broad categories: inference-time methods, which modify the decoding process at generation time, and model-embedded methods, which encode a secret signal directly into the model weights. Inference-time watermarking methods incur additional inference overhead and are not applicable in the increasingly prevalent open-weight model settings. In contrast, model-embedded watermarks introduce no additional inference latency-generation uses the standard sampling pipeline-and are particularly well-suited to open-weight settings. However, existing model-embedded approaches such as GaussMark face a fundamental quality-detectability trade-off: achieving strong detection power typically requires weight perturbations that noticeably degrade generation quality. Our key insight is that regularizing toward a high-quality reference distribution decouples quality preservation from proximity to the base model, enabling a better quality-detectability trade-off. Building on this insight, we introduce MarkTune, a theoretically grounded on-policy fine-tuning framework that uses the GaussMark detection statistic as a reward while preserving generation quality through cross-entropy on high-quality human text or KL divergence to a stronger oracle model. Empirically, MarkTune substantially improves the quality-detectability frontier of GaussMark, approaching the detectability of strong inference-time schemes while preserving generation quality and downstream task performance. Marktune also remains robust under the evaluated text-editing and open-weight attacks and generalizes across datasets, retaining substantial detection power on corpora unseen during training. Code is available at https://github.com/zhyzmath/MarkTune-LLM-Watermarking.