arXiv · 2026 · Preprint (accepted at AAAI 2026)
Dai et al. (Institute of Acoustics, Chinese Academy of Sciences) · → Paper · Demo: ? · Code: ?
Reformulates the signal-to-noise ratio (SNR) metric with a corrected phase-distance term to produce GOMPSNR, an objective metric that correlates far more strongly with perceptual audio quality, and derives a family of loss functions from the same formulation that improve neural vocoder and codec training.
Problem
SNR and its variants (segSNR, SI-SNR) have long served as simple, reference-based objective metrics for audio generation tasks, but repeated studies have shown they correlate poorly with human perception and are being displaced by metrics such as MCD and M-STFT. The paper investigates why SNR fails and whether a corrected formulation can restore its usefulness, since a mathematically simple, interpretable, frame-wise metric is otherwise attractive as a training signal and evaluation tool for neural vocoders and codecs.
Method
The authors decompose SNR from the time domain into the time-frequency domain, where it separates into a magnitude term and a phase-dependent correlation term. Visualizing the magnitude and phase residuals between vocoder outputs and references shows that the phase component of SNR is measured unreliably: magnitude residuals are structurally informative, but phase residuals computed the conventional way are not, because raw instantaneous phase (IP) has an irregular, wrapped structure.
Building on an existing omnidirectional phase (OP) representation that computes phase derivatives (instantaneous frequency and group delay) across eight adjacent time-frequency bins plus the center bin, the paper substitutes these omnidirectional phase derivatives for IP inside the SNR formula to obtain OMPSNR. It then identifies a further instability: the sign of SNR’s correlation component changes around ±π/2 phase error, amplifying sensitivity to phase perturbations. Correcting this term to be non-positive and replacing the nonlinear mapping with a strictly linear one yields the final metric, GOMPSNR (Generalized Omnidirectional Phase-oriented SNR) (§Generalized Omnidirectional Phase-oriented SNR, Table 1).
The same omnidirectional phase-derivative formulation is then extended into three loss functions: OP loss (phase-only, using the anti-wrapping function to unwrap phase derivatives), a magnitude-weighted variant (WOP) that scales the OP loss by the relative magnitude at each time-frequency bin, and two magnitude-phase joint losses derived from the classic RI (real-imaginary) loss: OmniRI (ORI), which substitutes omnidirectional phase derivatives for IP inside the RI formulation, and Coupled OmniRI (CORI), which multiplies a point-wise magnitude distance by the unwrapped omnidirectional phase-derivative distance (§Coupling Magnitude and Phase in Loss Functions). All losses are evaluated as drop-in replacements for the loss terms of four state-of-the-art vocoders (Vocos, APNet, APNet2, and RNDVoc), each retrained under its original GAN adversarial training pipeline (multi-period and multi-resolution spectrogram discriminators, hinge GAN loss, feature matching, mel-spectrogram loss) for 2 million steps, with only the phase/magnitude reconstruction term swapped.
Key Results
On officially pretrained Vocos evaluated on LibriTTS, SNR shows essentially no correlation with perceptual metrics (PCC and SRCC both below 0.1 against PESQ, UTMOS, VQScore, NISQA, and DistillMOS), while GOMPSNR shows a comparatively strong correlation with the same metrics, and clearly outperforms the intermediate OMPSNR variant (§Validation on GOMPSNR, Figure 4).
For loss functions, on Vocos trained on LJSpeech, the vanilla phase loss and OP loss provide no improvement over the baseline training recipe, but the magnitude-weighted WOP loss improves every objective metric reported (PESQ 3.749→3.928, UTMOS 4.128→4.168, MCD 2.451→2.256, GOMPSNR 4.299→5.232) (§Phase-oriented Loss Functions, Table 2). The vanilla RI loss slightly degrades performance, while OmniRI and Coupled OmniRI (L1) improve it; the best combination on Vocos/LJSpeech (linear magnitude loss + WOP + CORI) reaches PESQ 4.035 and UTMOS 4.19, versus 3.749/4.128 for the unmodified baseline (§Joint Magnitude and Phase Optimization, Table 2). Applying the same well-chosen loss combination across four vocoders on both LJSpeech and LibriTTS consistently outperforms each vocoder’s original loss configuration, including RNDVoc, the strongest baseline in the comparison (§Comprehensive Evaluation on Loss Functions, Tables 3–4). The loss combination also improves two neural audio codecs (WavTokenizer and Vocos-as-codec) across bandwidths on LibriTTS, with larger gains at lower bandwidths (§Evaluation on Neural Audio Codecs, Figure 5).
Novelty Assessment
The core contribution is a targeted mathematical correction to a well-known but distrusted metric (SNR): identifying the phase-distance term as the source of its unreliability and replacing it with an already-published omnidirectional phase-derivative representation, then further stabilizing the correlation term’s sign behavior. This is an incremental but precise formulation change rather than a new measurement paradigm. The loss-function contributions (WOP, ORI, CORI) follow directly from the same phase-derivative substitution applied to training objectives rather than to the metric itself, so the paper’s architectural surface is entirely borrowed (existing vocoders, existing discriminators, existing GAN training recipe); the novelty is confined to the metric and loss reformulation and the systematic empirical validation of both across several vocoders, two datasets, and two codec models.
Field Significance
moderate — This paper provides a mathematically grounded diagnosis of why SNR fails as a perceptual proxy and offers a drop-in replacement metric plus a family of loss functions validated across multiple independent vocoder architectures and two datasets. It is directly useful to anyone training or evaluating neural vocoders and codecs, which are components of most TTS pipelines, though its scope is narrowly the waveform-reconstruction stage rather than the generative TTS/VC/spoken-conversational-agent systems themselves.
Claims
- supports: A metric’s mathematical decomposition into magnitude and phase components can reveal which component is responsible for its poor correlation with human perception, enabling a targeted rather than wholesale replacement.
Evidence: Visualizing magnitude and phase residuals separately shows the magnitude residual is structurally informative while the raw phase residual is not, isolating inaccurate phase-distance measurement as the cause of SNR’s weak perceptual correlation. (§Generalized Omnidirectional Phase-oriented SNR)
- supports: Replacing raw instantaneous phase with omnidirectional phase derivatives in a reference-based audio metric substantially improves its correlation with perceptual quality metrics.
Evidence: On Vocos/LibriTTS, SNR shows PCC/SRCC below 0.1 against five perceptual metrics (PESQ, UTMOS, VQScore, NISQA, DistillMOS), while GOMPSNR (built on the same omnidirectional phase-derivative substitution) shows comparatively strong correlation with the same metrics. (§Validation on GOMPSNR, Figure 4)
- supports: Magnitude-weighting a phase-only reconstruction loss can unlock the perceptual benefit of phase supervision that an unweighted phase loss fails to provide.
Evidence: On Vocos/LJSpeech, the unweighted OP phase loss gives no improvement over the baseline, but the magnitude-weighted WOP loss improves PESQ, UTMOS, MCD, M-STFT, V/UV F1, periodicity RMSE, and pitch RMSE simultaneously. (§Phase-oriented Loss Functions, Table 2)
- complicates: The choice between logarithmic and linear magnitude weighting in a reconstruction loss trades off dataset-dependent overfitting against perceptual quality, so no single weighting is uniformly best.
Evidence: Linear-magnitude weighting degrades MCD, M-STFT, and GOMPSNR on the smaller LJSpeech dataset relative to logarithmic weighting, attributed to overfitting on speech energy, even though it improves perceptual quality metrics. (§Comprehensive Evaluation on Loss Functions)
- refines: A vocoder-training loss reformulation validated on waveform vocoders can transfer to neural audio codec training with larger relative gains at lower bitrates.
Evidence: Applying the same well-chosen loss combination (linear magnitude + WOP + CORI) to WavTokenizer and Vocos-as-codec on LibriTTS improves objective quality at all tested bandwidths, with more pronounced improvement at lower bandwidths where compression is more aggressive. (§Evaluation on Neural Audio Codecs, Figure 5)
Limitations and Open Questions
The paper validates GOMPSNR and its derived losses only as an intrusive (reference-based) metric requiring a time-aligned ground-truth waveform, so its applicability to non-parallel or streaming evaluation settings is untested. All experiments use GAN-based vocoders and two codec systems (WavTokenizer, Vocos); no autoregressive, diffusion, or flow-matching generative TTS system is evaluated, so transfer of the metric or losses to those paradigms is not demonstrated. The correlation analysis in Figure 4 is reported for a single pretrained Vocos checkpoint on LibriTTS rather than aggregated across all four vocoders and both datasets, leaving the generality of the correlation improvement only partially quantified. The paper also acknowledges that its own best loss combination still involves a dataset-dependent choice between linear and logarithmic magnitude weighting, meaning practitioners must still tune this choice rather than adopting one fixed recipe.
Wiki Connections
- Evaluation Metrics — proposes GOMPSNR, a reformulated reference-based objective metric intended to replace SNR for audio generation quality assessment, validated by its correlation with existing perceptual metrics.
- GAN Vocoder — retrains four GAN-based vocoders (Vocos, APNet, APNet2, RNDVoc) under their original adversarial training pipelines with only the reconstruction loss term swapped, showing the proposed loss functions consistently outperform each vocoder’s original loss configuration.
- Neural Audio Codec — extends the same loss functions to two neural audio codecs (WavTokenizer and Vocos operating as a codec), showing consistent gains across bandwidths, with larger relative improvement at lower bitrates.
- Vocos — used as the primary vocoder for the metric-correlation analysis and as one of the four vocoders retrained with the proposed loss functions; also evaluated as a neural audio codec.
- HiFi-GAN — its multi-period discriminator and adversarial training recipe are adopted unchanged as the GAN training backbone for all retrained vocoders.
- BigVGAN — cited as a large-scale universal neural vocoder representative of the class of GAN vocoders this paper’s loss functions are designed to improve.
- WavTokenizer — one of two neural audio codecs on which the proposed loss combination is evaluated, with decoder-only fine-tuning under a frozen encoder and codebook.
- RNDVoc — used as the strongest baseline vocoder in the comprehensive loss-function comparison, and still improved further by the paper’s proposed loss combination despite already achieving the best baseline results.