As text-to-speech (TTS) systems continue to advance, provenance tracking and security verification of synthesized speech have become increasingly important. Audio watermarking provides active provenance by embedding imperceptible, machine-recoverable information into speech. However, existing post-hoc methods typically modify the waveform after synthesis, leaving the watermark vulnerable to compound perturbations. To address this limitation, we propose GAMW, a watermark injection framework integrated into the TTS generation process. Before waveform synthesis, GAMW embeds a content-adaptive multi-bit watermark residual into the generated representation, and its decoding objective combines focal modulation with dynamic per-bit weighting. We train and evaluate GAMW separately on two TTS backbones. With a 16-bit payload, GAMW improves decoding accuracy over the strongest baseline by 9.2 and 23.5 percentage points under individual and compound perturbations, respectively, while maintaining competitive speech quality. Reliable clean-speech decoding is also retained at higher payloads. Code is available at https://github.com/ZConJugaTe/GAMW.

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