# Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

arXiv: https://arxiv.org/abs/2306.02568 · HTML: https://mlsanity.com/paper/2306.02568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions](https://mlsanity.com/paper/1712.05884/) (2017)
- [FastSpeech 2: Fast and High-Quality End-to-End Text to Speech](https://mlsanity.com/paper/2006.04558/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Tacotron: Towards End-to-End Speech Synthesis](https://mlsanity.com/paper/1703.10135/) (2017)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [Diff-TTS: A Denoising Diffusion Model for Text-to-Speech](https://mlsanity.com/paper/2104.01409/) (2021)
- [DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanism](https://mlsanity.com/paper/2105.02446/) (2021)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [DanceFormer: Music Conditioned 3D Dance Generation with Parametric Motion Transformer](https://mlsanity.com/paper/2103.10206/) (2021)
- [FlowSeq: Non-Autoregressive Conditional Sequence Generation with Generative Flow](https://mlsanity.com/paper/1909.02480/) (2019)
- [Monotonic Chunkwise Attention](https://mlsanity.com/paper/1712.05382/) (2017)
- [Differentiable Dynamic Programming for Structured Prediction and Attention](https://mlsanity.com/paper/1802.03676/) (2018)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [A Review of Deep Learning Techniques for Speech Processing](https://mlsanity.com/paper/2305.00359/) (2023)
- [Latent Alignment and Variational Attention](https://mlsanity.com/paper/1807.03756/) (2018)
- [V2C: Visual Voice Cloning](https://mlsanity.com/paper/2111.12890/) (2021)
- [The Neural Noisy Channel](https://mlsanity.com/paper/1611.02554/) (2016)
- [Online Segment to Segment Neural Transduction](https://mlsanity.com/paper/1609.08194/) (2016)
- [Neural Speech Synthesis with Transformer Network](https://mlsanity.com/paper/1809.08895/) (2018)
- [Dynamic Temporal Alignment of Speech to Lips](https://mlsanity.com/paper/1808.06250/) (2018)
- [RyanSpeech: A Corpus for Conversational Text-to-Speech Synthesis](https://mlsanity.com/paper/2106.08468/) (2021)
- [VAENAR-TTS: Variational Auto-Encoder based Non-AutoRegressive Text-to-Speech Synthesis](https://mlsanity.com/paper/2107.03298/) (2021)
- [Leveraging Recursive Gumbel-Max Trick for Approximate Inference in Combinatorial Spaces](https://mlsanity.com/paper/2110.15072/) (2021)

## Abstract (arXiv)

We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at urlhttps://github.com/XinleiNIU/LatentOptimalPathsBayesianDP.