# Optimal transport meets speech: a tutorial review

arXiv: https://arxiv.org/abs/2609.31787 · HTML: https://mlsanity.com/paper/2609.31787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 72 of its 135 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 30 of 72)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Joint CTC-Attention based End-to-End Speech Recognition using Multi-task Learning](https://mlsanity.com/paper/1609.06773/) (2016)
- [Sparse Sinkhorn Attention](https://mlsanity.com/paper/2002.11296/) (2020)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Recent Advances in End-to-End Automatic Speech Recognition](https://mlsanity.com/paper/2111.01690/) (2021)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)

## Abstract (arXiv)

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.