# Learning the joint distribution of two sequences using little or no paired data

arXiv: https://arxiv.org/abs/2212.03232 · HTML: https://mlsanity.com/paper/2212.03232/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 60 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions](https://mlsanity.com/paper/1712.05884/) (2017)
- [Improving Neural Machine Translation Models with Monolingual Data](https://mlsanity.com/paper/1511.06709/) (2015)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [FastSpeech 2: Fast and High-Quality End-to-End Text to Speech](https://mlsanity.com/paper/2006.04558/) (2020)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [AudioLM: a Language Modeling Approach to Audio Generation](https://mlsanity.com/paper/2209.03143/) (2022)
- [Listen, Attend and Spell](https://mlsanity.com/paper/1508.01211/) (2015)
- [Tacotron: Towards End-to-End Speech Synthesis](https://mlsanity.com/paper/1703.10135/) (2017)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [W2v-BERT: Combining Contrastive Learning and Masked Language Modeling for Self-Supervised Speech Pre-Training](https://mlsanity.com/paper/2108.06209/) (2021)
- [vq-wav2vec: Self-Supervised Learning of Discrete Speech Representations](https://mlsanity.com/paper/1910.05453/) (2019)
- [Generative Spoken Language Modeling from Raw Audio](https://mlsanity.com/paper/2102.01192/) (2021)
- [SpeechT5: Unified-Modal Encoder-Decoder Pre-Training for Spoken Language Processing](https://mlsanity.com/paper/2110.07205/) (2021)
- [Unsupervised Speech Recognition](https://mlsanity.com/paper/2105.11084/) (2021)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [ContextNet: Improving Convolutional Neural Networks for Automatic Speech Recognition with Global Context](https://mlsanity.com/paper/2005.03191/) (2020)
- [SpeechStew: Simply Mix All Available Speech Recognition Data to Train One Large Neural Network](https://mlsanity.com/paper/2104.02133/) (2021)
- [MAESTRO: Matched Speech Text Representations through Modality Matching](https://mlsanity.com/paper/2204.03409/) (2022)
- [Large-scale Self-Supervised Speech Representation Learning for Automatic Speaker Verification](https://mlsanity.com/paper/2110.05777/) (2021)
- [SLAM: A Unified Encoder for Speech and Language Modeling via Speech-Text Joint Pre-Training](https://mlsanity.com/paper/2110.10329/) (2021)
- [Speech Recognition with Augmented Synthesized Speech](https://mlsanity.com/paper/1909.11699/) (2019)
- [PnG BERT: Augmented BERT on Phonemes and Graphemes for Neural TTS](https://mlsanity.com/paper/2103.15060/) (2021)
- [Listening while Speaking: Speech Chain by Deep Learning](https://mlsanity.com/paper/1707.04879/) (2017)
- [Towards End-to-end Unsupervised Speech Recognition](https://mlsanity.com/paper/2204.02492/) (2022)

## Built on by (most cited first, 3 of 3)

- [Fake it to make it: Using synthetic data to remedy the data shortage in joint multimodal speech-and-gesture synthesis](https://mlsanity.com/paper/2404.19622/) (2024)
- [Improving Joint Speech-Text Representations Without Alignment](https://mlsanity.com/paper/2308.06125/) (2023)
- [SequenceLayers: Sequence Processing and Streaming Neural Networks Made Easy](https://mlsanity.com/paper/2507.23292/) (2025)

## Abstract (arXiv)

We present a noisy channel generative model of two sequences, for example text and speech, which enables uncovering the association between the two modalities when limited paired data is available. To address the intractability of the exact model under a realistic data setup, we propose a variational inference approximation. To train this variational model with categorical data, we propose a KL encoder loss approach which has connections to the wake-sleep algorithm. Identifying the joint or conditional distributions by only observing unpaired samples from the marginals is only possible under certain conditions in the data distribution and we discuss under what type of conditional independence assumptions that might be achieved, which guides the architecture designs. Experimental results show that even tiny amount of paired data (5 minutes) is sufficient to learn to relate the two modalities (graphemes and phonemes here) when a massive amount of unpaired data is available, paving the path to adopting this principled approach for all seq2seq models in low data resource regimes.