Speech watermarking offers proactive traceability for synthetic speech, yet most existing models operate only after text-to-speech (TTS) synthesis by adding a watermark perturbation to the generated waveform. This post-hoc design leaves watermarking as an external step that can be omitted or bypassed and restricts the watermark to a shallow waveform representation. We propose NeuMark-Native, a TTS-native watermarking framework for neural codec-based synthesis. It embeds payload information into every generated codec-latent layer before waveform decoding, improving watermark persistence under downstream digital signal processing (DSP) and neural codec resynthesis. NeuMark-Native keeps the pretrained TTS model and the neural codec frozen, while optimizing only the watermark modules on generated codec tokens. Experiments on two corpora under 11 DSP attacks and 9 neural-codec attacks demonstrate robust watermark detection while preserving naturalness, intelligibility, and speech quality close to synthetic speech.

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