Tokens Change, Structure Endures: Spectral Watermarking for Generated Speech

Kanghwi Lee; Kyeongseok Jeong; Jeongmin Liu

cs.SDSep 27, 2026

Tokens Change, Structure Endures: Spectral Watermarking for Generated Speech

Authors: Kanghwi Lee, Kyeongseok Jeong, Jeongmin Liu

Organizations: Institute of Neuroinformatics, University of Zurich and ETH Zurich, Switzerland · NAVER Cloud

Abstract

Watermarking is a promising tool for establishing the provenance of AI-generated speech. While many neural audio watermarking methods rely on a separately trained watermark generator, token-level watermarking is a training-free alternative that operates directly during generation. Its main weakness is retokenization: decoding generated speech to a waveform and encoding it again can change token identities and erode the watermark. To make the watermark robust to these changes, we propose Redwing, REtokenization-Durable Watermarking IN Generation. It builds a graph from the token substitutions observed under retokenization, whose Laplacian yields a basis that assigns similar values to tokens likely to substitute for one another. Over this basis, embedding and detection functions are jointly optimized to preserve watermark signal through retokenization while limiting embedding distortion and detector variability on unwatermarked speech. On the Moshi full-duplex system, after eight consecutive passes of Mimi resynthesis, Redwing achieves 80.7% TPR at a calibrated 1% FPR, compared with 8.3% for KGW and at most 7.3% for WMAR. It also has the highest TPR after eight passes through three other neural codecs (77.5-93.0%), and the gains generalize to TTS models at a speech-quality cost close to that of KGW. These results show that retokenization is not merely a source of noise: its transition structure can be exploited as a design principle for robust token-level watermarking.

Figures & tables

Method	Mimi (native)	EnCodec	SpeechTok.	SNAC	DAC16
Redwing	80.7 $\pm$ 3.2	85.0 $\pm$ 2.9	77.5 $\pm$ 3.3	93.0 $\pm$ 2.1	34.2 $\pm$ 3.8
KGW	8.3 $\pm$ 2.2	16.5 $\pm$ 3.0	5.3 $\pm$ 1.8	63.2 $\pm$ 3.8	12.5 $\pm$ 2.6
WMAR FT	5.5 $\pm$ 1.8	24.7 $\pm$ 3.4	2.2 $\pm$ 1.2	58.5 $\pm$ 3.9	10.3 $\pm$ 2.4
WMAR FT+Augs	7.3 $\pm$ 2.1	15.7 $\pm$ 2.9	2.0 $\pm$ 1.2	57.2 $\pm$ 3.9	20.7 $\pm$ 3.2
AudioSeal	22.5 ∗ $\pm$ 3.3	82.3 ∗ $\pm$ 3.0	1.5 $\pm$ 1.0	0.0 $\pm$ 0.3	0.2 $\pm$ 0.5
Timbre	0.0 $\pm$ 0.3	0.3 $\pm$ 0.6	0.0 $\pm$ 0.3	0.0 $\pm$ 0.3	0.0 $\pm$ 0.3

Table 1: Detection on Moshi after eight codec passes. Values are TPR (%) at the fixed threshold

\pm

the half-width of the 95 % interval. Post-hoc methods are below the line, and bold is as defined in Section 4 . ∗ The same attack also flags more than 5 % of unwatermarked answers (Table 14 ), so the cell is not bold. WavMark, which detects 0 % after every codec here, is omitted (Appendix C.1 ).

CosyVoice3
Method	Native	Mimi	EnCodec	SpeechTok.	SNAC	DAC16
Redwing	84.7 $\pm$ 2.9	68.8 $\pm$ 3.7	89.6 $\pm$ 2.5	61.2 $\pm$ 3.9	91.9 $\pm$ 2.2	94.0 $\pm$ 1.9
KGW	9.2 $\pm$ 2.3	1.2 $\pm$ 0.9	9.9 $\pm$ 2.4	2.8 $\pm$ 1.4	29.3 $\pm$ 3.6	21.9 $\pm$ 3.3
AudioSeal	15.1 ∗ $\pm$ 2.9	30.0 ∗ $\pm$ 3.7	56.4 ∗ $\pm$ 4.0	0.3 $\pm$ 0.6	0.0 $\pm$ 0.3	0.2 $\pm$ 0.5
Timbre	23.1 $\pm$ 3.4	0.3 $\pm$ 0.6	3.0 $\pm$ 1.4	0.0 $\pm$ 0.3	0.0 $\pm$ 0.3	0.2 $\pm$ 0.5
CRAW	5.7 $\pm$ 1.9	1.2 $\pm$ 0.9	61.5 $\pm$ 3.9	10.7 $\pm$ 2.5	11.7 $\pm$ 2.6	69.7 $\pm$ 3.7

Table 2: Detection on the TTS models after eight codec passes. The layout is as in Table 1 , with each model’s own resynthesis (Native) as the first codec.

Moshi (non-empty answers)
Method	UTMOSv2	DNSMOS Pro	NISQAv2	NISQA-TTS	KL/frame
Unwatermarked	3.15 $\pm$ 0.03	4.38 $\pm$ 0.04	4.64 $\pm$ 0.04	3.56 $\pm$ 0.05	0
Unwatermarked, FT decoder †	3.04 $\pm$ 0.03	4.33 $\pm$ 0.04	4.55 $\pm$ 0.04	3.40 $\pm$ 0.04	0
Unwatermarked, FT+Augs decoder †	3.16 $\pm$ 0.03	4.36 $\pm$ 0.04	4.61 $\pm$ 0.04	3.54 $\pm$ 0.05	0
Redwing	3.05 $\pm$ 0.03	4.47 $\pm$ 0.02	4.62 $\pm$ 0.03	3.52 $\pm$ 0.04	1.52
KGW	3.06 $\pm$ 0.04	4.35 $\pm$ 0.05	4.51 $\pm$ 0.06	3.44 $\pm$ 0.05	1.73

Table 3: Speech quality at the selected strengths. Mean

\pm

95 % CI (higher is better), for Moshi on non-empty answers. KL/frame is the cost. † Decoded with WMAR’s fine-tuned decoder, which changes quality even without a watermark. Bold (Section 4 ) covers only the watermarked rows.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Stream	1	2	3	4	5	6	7	8
Survival share	0.72	0.39	0.26	0.25	0.20	0.21	0.19	0.17
Participation, without	116	161	228	172	99	183	70	183
Participation, with	79	151	1.2	1.1	1.1	1.2	1.2	1.0
Single-token modes, with	0	2	15	14	15	11	14	15

Appendix

Table 4: Self-transitions and the basis on Moshi. The counts come from Moshi’s own Mimi channel, on the support of tokens with at least 50 occurrences. The survival share is the fraction of counted transitions that are self-transitions. Participation is the median participation ratio, the effective number of tokens covered, of the 16 leading nontrivial modes of the normalized adjacency, computed without and with self-transitions. The last row counts how many of these 16 modes put at least half of their mass on one token when self-transitions are kept.

Functions	$\delta$	KL (nats/frame)	UTMOSv2 difference	TPR (%)
Unbounded	0.05	0.05	$-0.04$	2
Unbounded	0.06	0.24	$-0.05$	7
Unbounded	0.07	0.94	$-0.48$	35
Unbounded	0.08	1.94	$-1.00$	68
Bounded ( $\kappa=5$ )	0.70	1.54	$+0.03$	97

Appendix

Table 5: Unbounded and bounded functions. All values are for Moshi’s streams 1–4 on the validation set (250 prompts). KL is the divergence per frame, summed over the four streams. The UTMOSv2 difference is paired against unwatermarked speech, and the TPR is at the fixed threshold without attack.

$\kappa$	1	2	3	4	5	6	7	8	Mean
	Stream
2	0.31	0.26	0.41	0.70	0.57	0.58	0.64	0.63	0.51
3	0.49	0.49	0.79	0.94	0.78	0.86	0.84	0.85	0.76
4	0.65	0.65	0.89	0.98	0.79	0.96	0.85	0.90	0.83
5	0.82	0.68	0.90	1.00	0.79	1.00	0.87	0.93	0.87
7	0.91	0.69	0.90	1.00	0.80	1.00	0.90	0.96	0.90

Appendix

Table 6: Objective retained under the bound

\kappa

. Each value is the attained objective divided by the unconstrained optimum

\sigma_{1}(M)

, for one Moshi stream.

Model	Clips	$\tau^{\star}=-2$	$-1$	$0$	$+1$	$+2$
Moshi	watermarked (600)	0.000	0.985	0.000	0.000	0.000
Moshi	unwatermarked (600)	0.055	0.073	0.047	0.058	0.070
CosyVoice3	watermarked (596)	0.002	0.000	0.988	0.002	0.002
CosyVoice3	unwatermarked (597)	0.055	0.047	0.062	0.049	0.060
MOSS-TTS	watermarked (593)	0.000	0.000	1.000	0.000	0.000
MOSS-TTS	unwatermarked (599)	0.048	0.047	0.078	0.053	0.060

Appendix

Table 7: Where the evidence peaks. Each value is the fraction of test clips whose maximizing offset

\tau^{\star}

takes the given value, when the search covers

\pm 8

frames and no attack is applied. An even spread would put 1/17, or 0.059, on each offset.

Set	Used for	Moshi	CosyVoice3	MOSS-TTS
Substitution counts	graph, basis and $P$	20 hours of LibriSpeech
Validation	strength $\delta$ and watermarked streams	250	250	250
Calibration	thresholds	1,200	1,000 (994)	1,000 (993)
Test	all reported results	600	600 (596–598)	600 (593–599)

Appendix

Table 8: Data sets. The numbers count prompts for Moshi and texts for the TTS models, and the calibration sets count unwatermarked answers. On the TTS models, a few generations failed or exceeded the tokenizer’s length limit and are excluded, and parentheses give the clips left.

Codec	Implementation	Setting
Mimi	Mimi of Moshi ( kyutai/moshiko-pytorch-bf16 )	8 quantizers
CosyVoice3 native	speech tokenizer, flow-matching decoder and HiFT vocoder	clip as its own prompt
MOSS-TTS native	MOSS audio tokenizer	32 quantizers
EnCodec	facebook/encodec_24khz	6 kbps
SpeechTokenizer	speechtokenizer_hubert_avg	all quantizers, 24 kHz input
SNAC	hubertsiuzdak/snac_24khz	all quantizers

Appendix

Table 9: Codecs. The table lists the checkpoint and the setting of each codec used in the attacks.

Set	Method	FPR	Identity	Mimi $\times 1$	Mimi $\times 8$	EnCodec $\times 8$
Test	Aligned-IS, $h=20$	1.7	4.7	3.3	2.0	0.5
Test	KGW	1.5	78.5	64.5	8.3	16.5
Validation	Aligned-IS, $h=20$	2.0	4.4	4.0	2.4	0.4
Validation	Aligned-IS, $h=50$	1.2	32.0	9.2	2.4	1.6
Validation	Aligned-IS, $h=100$	0.8	50.0	14.0	1.2	6.4
Validation	streams 1–4 only	1.2	3.2	2.0	2.0	0.4

Appendix

Table 10: Aligned-IS on Moshi. TPR (%) at the fixed threshold without attack (Identity), after one and eight Mimi passes, and after eight EnCodec passes. FPR is the rate on the unwatermarked answers of the same set without attack. The indented variants use

h=20

, and KGW is shown for reference.

Moshi
Method	DAC24	DAC44	Opus	MP3	AAC
Redwing	64.0 $\pm$ 3.8	94.8 $\pm$ 1.8	90.7 $\pm$ 2.3	93.5 $\pm$ 2.0	94.3 $\pm$ 1.9
KGW	36.3 $\pm$ 3.8	74.5 $\pm$ 3.5	57.8 $\pm$ 3.9	53.2 $\pm$ 4.0	73.8 $\pm$ 3.5
WMAR FT	30.0 $\pm$ 3.7	75.3 $\pm$ 3.4	61.0 $\pm$ 3.9	57.8 $\pm$ 3.9	76.7 $\pm$ 3.4
WMAR FT+Augs	57.2 $\pm$ 3.9	75.0 $\pm$ 3.5	52.7 $\pm$ 4.0	61.8 $\pm$ 3.9	76.3 $\pm$ 3.4
AudioSeal	100.0 $\pm$ 0.3	100.0 $\pm$ 0.3	76.3 $\pm$ 3.4	100.0 $\pm$ 0.3	100.0 $\pm$ 0.3

Appendix

Table 11: Detection after eight passes through high-fidelity codecs. TPR (%) on the test sets at the fixed threshold,

\pm

the half-width of the Wilson 95 % interval. DAC24 and DAC44 are the 24 and 44.1 kHz DAC models. Opus runs at 24 kbps, and MP3 and AAC at 64 kbps. Bold is as defined in Section 4 , within each model. None of these attacks flags more than 5 % of unwatermarked answers, so no cell is excluded from the bold as in Table 1 .

	Moshi								CosyVoice3						MOSS-TTS
Attack	Redwing	KGW	WMAR FT	WMAR FT+Augs	AudioSeal	WavMark	Timbre	CRAW	Redwing	KGW	AudioSeal	WavMark	Timbre	CRAW	Redwing	KGW	AudioSeal	WavMark	Timbre	CRAW
None	95	78	84	82	100	89	100	100	98	92	100	100	100	100	100	98	100	100	100	100
White noise (SNR)
40 dB	95	79	76	82	100	88	100	100	98	91	100	97	99	100	100	83	100	95	99	100
30 dB	95	78	45	81	100	75	89	100	98	89	100	61	86	100	100	53	100	66	85	100
20 dB	87	47	1	80	100	3	31	99	97	84	98	4	39	100	100	14	97	7	40	99

Appendix

Table 12: Detection after signal-processing attacks. TPR (%) on the test sets at the fixed threshold, rounded to whole percent. The Wilson 95 % interval of every value is at most 8 percentage points wide. Within each row and model, bold marks the highest TPR and every TPR whose interval overlaps it, and nothing when all overlap. ∗ The same attack also flags more than 5 % of unwatermarked answers, so the cell is excluded from the bold. WavMark does not embed into 67 of Moshi’s answers, which caps its TPR there at 89 %.

		After eight passes
Method	Identity	Mimi	EnCodec	SpeechTok.	SNAC	DAC16	DAC24	DAC44	Opus	MP3	AAC
Redwing	0.5	0.7	0.5	0.1	0.6	0.3	0.8	0.6	0.6	0.7	0.7
KGW	0.7	0.8	0.5	0.2	0.7	0.4	1.0	0.5	1.0	0.7	0.4
AudioSeal	4.3	42.2 ∗	79.1 ∗	2.0	2.7	4.5	3.5	4.3	7.0 ∗	4.4	3.4
WavMark	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Timbre	0.7	0.0	1.6	0.1	0.0	0.1	0.0	0.0	0.1	0.5	1.2

Appendix

Table 13: False positives on human speech. FPR (%) on the 1,000 WildVoice recordings that serve as Moshi’s prompts, at each method’s fixed threshold for Moshi, without attack (Identity) and after eight passes of each codec. ∗ Values above 5 %.

Moshi
		After eight passes
Method	Identity	Native	Mimi	EnCodec	SpeechTok.	SNAC	DAC16	DAC24	DAC44	Opus	MP3	AAC
Redwing	1.0	0.5	–	0.3	0.3	0.5	0.0	0.3	0.8	0.7	0.2	0.8
KGW	1.5	0.3	–	1.7	0.3	1.2	0.5	1.2	2.5	0.5	1.2	1.0
WMAR FT	1.3	0.0	–	0.5	0.3	0.3	0.2	0.5	0.5	0.3	0.2	0.3
WMAR FT+Augs	1.7	0.5	–	1.3	0.7	1.7	1.5	1.8	1.2	1.2	1.0	1.8

Appendix

Table 14: False positives after attack. FPR (%) on the unwatermarked test answers at each method’s fixed threshold, without attack (Identity) and after eight passes. Native is each model’s own codec, which is Mimi on Moshi. ∗ Values above 5 %.

No attack
Method	38–50	51–100	101–150	151–200	All
Redwing	75.6 $\pm$ 7.6	98.8 $\pm$ 2.0	100.0 $\pm$ 1.3	100.0 $\pm$ 1.1	94.8 $\pm$ 1.8
KGW	30.0 $\pm$ 6.8	93.6 $\pm$ 4.1	99.0 $\pm$ 2.5	100.0 $\pm$ 1.0	78.5 $\pm$ 3.3
After eight Mimi passes
Redwing	39.5 $\pm$ 8.7	75.8 $\pm$ 6.6	96.5 $\pm$ 3.3	100.0 $\pm$ 1.1	80.7 $\pm$ 3.2
KGW	1.8 $\pm$ 2.2	8.5 $\pm$ 4.7	9.6 $\pm$ 5.7	13.5 $\pm$ 4.9	8.3 $\pm$ 2.2

Appendix

Table 15: Detection on Moshi by answer length. TPR (%) at the fixed threshold on the test set

\pm

the 95 % Wilson half-width, by answer length in frames. Each bin covers 50 frames, or 4 s, and All is the TPR on all test answers.

Moshi (non-empty answers)
Method	UTMOSv2	DNSMOS Pro	NISQAv2	NISQA-TTS
Unwatermarked	3.15 $\pm$ 0.03	4.38 $\pm$ 0.04	4.64 $\pm$ 0.04	3.56 $\pm$ 0.05
AudioSeal	3.14 $\pm$ 0.03	4.37 $\pm$ 0.04	4.50 $\pm$ 0.04	3.32 $\pm$ 0.05
WavMark	2.88 $\pm$ 0.04	4.26 $\pm$ 0.04	4.54 $\pm$ 0.04	3.39 $\pm$ 0.04
Timbre	3.11 $\pm$ 0.03	4.31 $\pm$ 0.04	4.55 $\pm$ 0.05	3.30 $\pm$ 0.04
CRAW	2.92 $\pm$ 0.04	4.25 $\pm$ 0.05	3.96 $\pm$ 0.07	3.57 $\pm$ 0.05

Appendix

Table 16: Speech quality of the post-hoc methods. Mean

\pm

95 % CI on the test sets, as in Table 3 . Bold as in Table 3 .

Moshi (prompts non-empty for all)
Method	$\Delta$ UTMOSv2	$\Delta$ DNSMOS Pro	$\Delta$ NISQAv2	$\Delta$ NISQA-TTS
Redwing	$-0.09$ $\pm$ 0.04	$+0.10$ $\pm$ 0.05	$0.00$ $\pm$ 0.06	$-0.03$ $\pm$ 0.06
KGW	$-0.09$ $\pm$ 0.06	$-0.04$ $\pm$ 0.07	$-0.15$ $\pm$ 0.08	$-0.14$ $\pm$ 0.07
WMAR FT †	$-0.07$ $\pm$ 0.05	$-0.04$ $\pm$ 0.07	$-0.12$ $\pm$ 0.07	$-0.16$ $\pm$ 0.07
WMAR FT+Augs †	$-0.11$ $\pm$ 0.05	$-0.05$ $\pm$ 0.07	$-0.15$ $\pm$ 0.08	$-0.15$ $\pm$ 0.07
AudioSeal	$-0.01$ $\pm$ 0.02	$-0.01$ $\pm$ 0.01	$-0.15$ $\pm$ 0.01	$-0.24$ $\pm$ 0.02

Appendix

Table 17: Paired differences in speech quality. Mean difference from the unwatermarked answer to the same prompt

\pm

the 95 % CI on the test sets. On Moshi, only prompts with non-empty answers from the unwatermarked model, ours and KGW are used, and on the TTS models all clips. † Compared with the unwatermarked answers decoded by the same fine-tuned decoder.

Basis
					After eight passes
Variant	$\delta$	KL	UTMOSv2	Identity	Mimi	EnCodec	SpeechTok.	DAC16
Unwatermarked	–	0	3.15 $\pm$ 0.03	–	–	–	–	–
KGW	2	1.73	3.06 $\pm$ 0.04	78.5 $\pm$ 3.3	8.3 $\pm$ 2.2	16.5 $\pm$ 3.0	5.3 $\pm$ 1.8	12.5 $\pm$ 2.6
Redwing	0.7	1.52	3.05 $\pm$ 0.03	94.8 $\pm$ 1.8	80.7 $\pm$ 3.2	85.0 $\pm$ 2.9	77.5 $\pm$ 3.3	34.2 $\pm$ 3.8
Random basis	0.7	1.60	3.12 $\pm$ 0.03	92.0 $\pm$ 2.2	52.3 $\pm$ 4.0	36.0 $\pm$ 3.8	24.5 $\pm$ 3.4	45.5 $\pm$ 4.0

Appendix

Table 18: Ablations on Moshi. TPR (%) at the fixed threshold on the test set

\pm

the 95 % Wilson half-width, and UTMOSv2 on non-empty answers

\pm

the 95 % CI. Each variant removes one component and runs at its own budget-matched

\delta

, and KL is its cost per frame. The random basis uses 16 random orthonormal directions, and the transition basis the leading singular vectors of the transition matrix

P

. The random function is one fixed random

g=h

per stream, without basis or solve. ‡ The same watermarked answers as ours, but the detector scores them with the embedding function

g

in place of the solved detection function

h

, which tests whether a separate detection function is needed. Bold is as defined in Section 4 .

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CRAW: Codec Robust Audio Watermarking

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Multi-Bit Watermarking Watermarks Agentic Crawlers

Open paper AskPDF arXiv

Recent advances in generative speech models have made it increasingly difficult to distinguish authentic from synthetic audio, enabling new forms of fraud and misinformation. Audio watermarking offers a promising defense by embedding an imperceptible signal into generated speech that can later be detected to verify its provenance. However, recent studies have shown that existing post-hoc watermarking methods fail under neural codecs and denoisers, transformations routinely applied during real-world storage, transmission, and processing, severely limiting their practical utility. Here we introduce CRAW, a codec-robust audio watermarking framework that jointly improves robustness against neural re-synthesis while maintaining high perceptual quality. CRAW combines distortion-aware training with an attention-based pooling mechanism, inference-time perceptual mask- ing, and an error-correcting code to recover the fidelity lost during robust training. Experiments demonstrate that CRAW achieves state-of-the-art robustness against neural codecs, denoisers, and vocoders while maintaining perceptual quality comparable to existing post-hoc watermarking methods. The code is available at https://github.com/DavidC1212/craw.

Abstract

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