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GOMPSNR: Reflourish the Signal-to-Noise Ratio Metric for Audio Generation Tasks

Conference: AAAI2026
arXiv: 2601.13758
Code: lingling-dai/GOMPSNR
Area: Audio and Speech
Keywords: signal-to-noise ratio, phase derivatives, audio quality metric, loss function, neural vocoder

TL;DR

By replacing the instantaneous phase with omnidirectional phase derivatives to reconstruct the SNR metric, GOMPSNR is proposed as a more reliable audio quality evaluation metric, deriving a new family of loss functions that significantly improve neural vocoder performance.

Background & Motivation

Limitations of Prior Work

Limitations of Prior Work: Background: Signal-to-Noise Ratio (SNR) has long served as a fundamental objective metric for quality evaluation in audio generation tasks. However, an increasing number of studies have shown that SNR and its variants (e.g., segSNR, SI-SNR) exhibit extremely low correlation with perceptual metrics such as PESQ and UTMOS, leading to their gradual marginalization. Meanwhile, MCD and M-STFT, which share similar mathematical formulations, remain mainstream metrics. This contradiction motivates the authors to investigate two core questions:

  1. Why does SNR fail? By expanding SNR from the time domain to the time-frequency domain, the authors find that SNR implicitly couples the measurements of amplitude and phase. While the residuals of the amplitude spectra exhibit a clear structure, the residuals of the phase spectra show an uninformative noise-like pattern, revealing that traditional instantaneous phase (IP) distance metrics are inherently unreliable.
  2. How to fix SNR? Phase derivatives (instantaneous frequency IF and group delay GD) exhibit much clearer structures than the instantaneous phase and can thus be used to replace IP for computing phase distances.

Goal

Goal: - The inaccurate measurement of phase distance in SNR is the key factor causing its inconsistency with human perception. - Direct calculation of phase distance is unreliable due to the phase wrapping property (values restricted to \([-\pi, \pi)\)) and high sensitivity to waveform shifts. - The sign of the correlation term \(C\) in the SNR formula flips around \(\theta - \hat{\theta} \approx \pm\pi/2\), causing numerical oscillation and making SNR excessively sensitive to phase errors.

Method

1. Omnidirectional Phase Derivatives

Using nine \(3 \times 3\) convolutional kernels with fixed parameters, \(\mathcal{K} \in \mathbb{R}^{9 \times 3 \times 3}\), omnidirectional phase derivatives are extracted from eight adjacent directions on the time-frequency spectrogram plus the instantaneous phase itself:

\[\nabla\theta = \theta \circledast \mathcal{K}\]

This is combined with the anti-wrapping function \(f_{AW}(x) = |x - 2\pi \cdot \text{round}(x / 2\pi)|\) to resolve the phase wrapping issue.

2. GOMPSNR Metric

SNR is expanded in the time-frequency domain as:

\[SNR = 10\log_{10} \frac{\sum_{k,l} |Y|^2}{\sum_{k,l}(|Y|^2 + |\hat{Y}|^2 + C)}\]

where the correlation term \(C = -2|Y||\hat{Y}|\cos(\theta - \hat{\theta})\). The improvement process consists of two steps:

  • OMPSNR: Replaces IP with omnidirectional phase derivatives, yielding \(C = -\frac{2}{9}|Y||\hat{Y}|\sum_i \cos(\nabla_i\theta - \nabla_i\hat{\theta})\).
  • GOMPSNR: Further replaces the \(\cos\) term with a linear mapping of the anti-wrapping function, ensuring \(C\) remains non-positive and eliminating numerical oscillations from sign flipping: \(C = \frac{2}{9}|Y||\hat{Y}|\sum_i(\frac{1}{\pi}f_{AW}(\nabla_i\theta - \nabla_i\hat{\theta}) - 1)\).

3. New Family of Loss Functions

Based on the same phase derivative concept, three types of new loss functions are proposed:

  • WOP Loss (Amplitude-Weighted Omnidirectional Phase Loss): Weights the OP loss with the amplitude spectrum so that high-energy regions receive more focus.
  • OmniRI Loss: Replaces the IP in the traditional RI loss with omnidirectional phase derivatives, decoupling the joint optimization of phase and amplitude.
  • CORI Loss (Coupled OmniRI): Couples the amplitude distance and phase derivative distance in a multiplicative manner to optimize both simultaneously.

4. Optimal Loss Function Combination

By searching for the optimal combination across three dimensions—amplitude loss (Log/Lin), phase loss (WOP), and coupled optimization loss (CORI)—the combination of Lin + WOP + CORI(L1) is ultimately recommended.

Key Experimental Results

Metric Validation: PCC and SRCC are calculated using the official pre-trained Vocos on LibriTTS: - The correlation of SNR with perceptual metrics is under 0.1, proving to be practically ineffective. - GOMPSNR exhibits a strong correlation with PESQ, UTMOS, VQScore, NISQA, and DistillMOS.

Ablation Study of Loss Functions on Vocos (LJSpeech): - Original Configuration: PESQ 3.749, UTMOS 4.128, GOMPSNR 4.299 - +WOP: PESQ 3.928 (+0.18), GOMPSNR 5.232 (+0.93) - +WOP+CORI(L1): PESQ 4.001, MCD 2.238, GOMPSNR 5.674

Cross-Vocoder Validation (LJSpeech, Lin+WOP+CORI Combination vs. Original): - Vocos: PESQ 3.749 -> 4.035, GOMPSNR 4.299 -> 5.749 - APNet2: PESQ 3.643 -> 3.901, GOMPSNR 4.961 -> 5.533 - RNDVoc: PESQ 4.033 -> 4.121, GOMPSNR 5.655 -> 5.822

Neural Audio Codec: Both WavTokenizer and Vocos codec achieve improvements across all bandwidths, with more significant gains observed at lower bandwidths (higher compression ratios).

Highlights & Insights

  • In-depth Problem Analysis: The root cause of SNR failure is mathematically derived and visualized to reside within the phase distance metric, presenting a highly rigorous logical argument.
  • Dual-track Progress on Metrics and Loss Functions: Improves both evaluation metrics and training losses from the same core insight, providing a unified and practical methodology.
  • Extensive Experimental Coverage: Comprehensive validation across 4 vocoders (Vocos, APNet, APNet2, RNDVoc) \(\times\) 2 datasets (LJSpeech, LibriTTS) plus Neural Audio Codec.
  • Plug-and-Play: The proposed loss function requires no modification of the model architecture and can replace the original losses directly, making it highly engineering-friendly.

Limitations & Future Work

  • Experiments are limited to vocoders and audio codecs, without validation on upstream tasks such as speech enhancement and speech separation.
  • GOMPSNR relies on reference signals (intrusive metric) and cannot be applied in reference-free scenarios.
  • The omnidirectional phase derivatives utilize fixed \(3 \times 3\) convolutional kernels, leaving the effects of larger receptive fields or learnable kernels unexplored.
  • The search for loss function combinations still relies on manual enumeration, lacking an automated search strategy.
  • Direct comparisons with recent non-intrusive perceptual metrics (e.g., DNSMOS, SpeechLMScore) are absent.
Method Type Phase Processing Correlation with Perceptual Metrics
SNR/SI-SNR Metric Implicit (Instantaneous Phase) Extremely Low (PCC/SRCC < 0.1)
OP Loss Loss Function Omnidirectional Phase Derivatives —
GOMPSNR Metric + Loss Omnidirectional Phase Derivatives + Anti-wrapping + Linear Mapping Significant Gain
M-STFT Metric Amplitude Spectrum Distance (Ignoring Phase) Moderate
PESQ/UTMOS Perceptual Metric Based on Auditory Models As Reference Standard

Highly related to the OP representation used in concurrent work RNDVoc (IJCAI 2025), GOMPSNR can be viewed as its generalization at the metric level.

  • The unreliability of phase distance metrics may also affect other tasks dependent on time-frequency representation (e.g., music generation, sound event detection), which is worth migrating and validating.
  • The concept of "weighting phase loss with amplitude" in WOP loss can be generalized to joint optimization scenarios of other multi-component signals.
  • The design philosophy of GOMPSNR (identifying the mathematical root cause of traditional metric failure and applying targeted corrections) can serve as a reference for metric improvements in other domains.

Rating

  • Novelty: 7/10 — The core contribution lies in introducing omnidirectional phase derivatives to SNR reconstruction; the concept is simple yet effective.
  • Experimental Thoroughness: 9/10 — Systematic evaluation across multiple vocoders, datasets, and metrics.
  • Writing Quality: 8/10 — Clear mathematical derivation and well-explained motivation.
  • Value: 8/10 — Provides a new metric that can directly replace SNR and plug-and-play loss functions, offering practical value to the audio generation community.