Optimal transport meets speech: a tutorial review

2026-09-24

AI Summary

This study addresses the severe distribution mismatch in speech signals caused by dynamic variations, noise interference, and cross-modal discrepancies. To tackle this challenge, it presents the first systematic review of optimal transport (OT) applied to speech processing. By integrating entropy regularization with deep neural network frameworks, the proposed approach achieves effective cross-domain distribution alignment and transformation while establishing theoretical connections to generative models. The work comprehensively surveys foundational OT theory and deep learning algorithms, validating their efficacy across tasks including speech enhancement, recognition, and spoofing detection. Experimental results demonstrate that OT significantly mitigates distributional shifts in complex acoustic scenarios, thereby advancing the practical engineering deployment of OT theory within the speech processing domain.

Abstract

Optimal Transport (OT) provides a principled framework for comparing and transforming probability distributions while preserving geometric structure. Recently, OT has gained significant attention in machine learning due to its ability to measure discrepancies between distributions, even when their supports do not overlap, making it effective for tasks such as generative modeling, domain adaptation, and transfer learning. Despite its success in fields such as computer vision and natural language processing, OT remains relatively underexplored in speech research. Speech signals present unique challenges, including temporal dynamics, speaker variability, noise, reverberation, and heterogeneous multimodal representations involving audio, text, and visual information. These factors often lead to distribution mismatches, where OT offers a natural framework for alignment and interpretation. This work aims to promote broader adoption of OT in speech processing by: (1) reviewing OT foundations through intuitive physical interpretations and highlighting connections to modern generative models; (2) presenting computational algorithms suitable for deep learning frameworks; and (3) demonstrating OT applications in cross-domain and cross-modal speech tasks, including speech enhancement, automatic speech recognition, language and speaker recognition, and audio spoof detection. We highlight OT's strong potential for addressing distributional variations in real-world speech applications.

Problem

• Optimal Transport
• Speech Processing
• Distribution Mismatch
• Multimodal Representations
• Domain Adaptation

Innovation

• Optimal Transport
• Speech Processing
• Generative Models
• Cross-modal Alignment
• Domain Adaptation