# Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis

arXiv: https://arxiv.org/abs/2312.03491 · HTML: https://mlsanity.com/paper/2312.03491/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 54 of its 65 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 30 of 54)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [FastSpeech 2: Fast and High-Quality End-to-End Text to Speech](https://mlsanity.com/paper/2006.04558/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech](https://mlsanity.com/paper/2106.06103/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [AudioLDM 2: Learning Holistic Audio Generation with Self-supervised Pretraining](https://mlsanity.com/paper/2308.05734/) (2023)
- [Make-An-Audio: Text-To-Audio Generation with Prompt-Enhanced Diffusion Models](https://mlsanity.com/paper/2301.12661/) (2023)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [NaturalSpeech 2: Latent Diffusion Models are Natural and Zero-Shot Speech and Singing Synthesizers](https://mlsanity.com/paper/2304.09116/) (2023)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale](https://mlsanity.com/paper/2303.06555/) (2023)
- [A Survey on Neural Speech Synthesis](https://mlsanity.com/paper/2106.15561/) (2021)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)

## Built on by (most cited first, 30 of 30)

- [Diffusion Bridge Implicit Models](https://mlsanity.com/paper/2405.15885/) (2024)
- [Self-Consistent Recursive Diffusion Bridge for Medical Image Translation](https://mlsanity.com/paper/2405.06789/) (2024)
- [Consistency Diffusion Bridge Models](https://mlsanity.com/paper/2410.22637/) (2024)
- [FrameBridge: Improving Image-to-Video Generation with Bridge Models](https://mlsanity.com/paper/2410.15371/) (2024)
- [SparseDM: Toward Sparse Efficient Diffusion Models](https://mlsanity.com/paper/2404.10445/) (2024)
- [Audio Super-Resolution with Latent Bridge Models](https://mlsanity.com/paper/2509.17609/) (2025)
- [Latent Schr"odinger Bridge Diffusion Model for Generative Learning](https://mlsanity.com/paper/2404.13309/) (2024)
- [Diffusion & Adversarial Schr"odinger Bridges via Iterative Proportional Markovian Fitting](https://mlsanity.com/paper/2410.02601/) (2024)
- [Diffusion-based Speech Enhancement with Schr"odinger Bridge and Symmetric Noise Schedule](https://mlsanity.com/paper/2409.05116/) (2024)
- [Finding Local Diffusion Schr"odinger Bridge using Kolmogorov-Arnold Network](https://mlsanity.com/paper/2502.19754/) (2025)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [DPBridge: Latent Diffusion Bridge for Dense Prediction](https://mlsanity.com/paper/2412.20506/) (2024)
- [Simplified Diffusion Schr"odinger Bridge](https://mlsanity.com/paper/2403.14623/) (2024)
- [VoiceBridge: General Speech Restoration with One-step Latent Bridge Models](https://mlsanity.com/paper/2509.25275/) (2025)
- [Series-to-Series Diffusion Bridge Model](https://mlsanity.com/paper/2411.04491/) (2024)
- [Schr"odinger Bridge Mamba for One-Step Speech Enhancement](https://mlsanity.com/paper/2510.16834/) (2025)
- [RefineBridge: Generative Bridge Models Improve Financial Forecasting by Foundation Models](https://mlsanity.com/paper/2512.21572/) (2025)
- [Recurrent Interpolants for Probabilistic Time Series Prediction](https://mlsanity.com/paper/2409.11684/) (2024)
- [A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2505.21528/) (2025)
- [GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance](https://mlsanity.com/paper/2606.03119/) (2026)
- [BridgeShape: Latent Diffusion Schr"odinger Bridge for 3D Shape Completion](https://mlsanity.com/paper/2506.23205/) (2025)
- [Incorporating Pre-trained Diffusion Models in Solving the Schr"odinger Bridge Problem](https://mlsanity.com/paper/2508.18095/) (2025)
- [Regularized Schr"odinger Bridge via Distortion-Perception Perturbation for High-Fidelity Speech Enhancement](https://mlsanity.com/paper/2511.11686/) (2025)
- [Learning Stochastic Bridges for Video Object Removal via Video-to-Video Translation](https://mlsanity.com/paper/2601.12066/) (2026)
- [Exploiting the Prior of Generative Time Series Imputation](https://mlsanity.com/paper/2512.23832/) (2025)
- [A Novel Automatic Framework for Speaker Drift Detection in Synthesized Speech](https://mlsanity.com/paper/2604.06327/) (2026)
- [DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation](https://mlsanity.com/paper/2605.05889/) (2026)
- [SB-RF: Schr"odinger Bridge Rectified Flow for One-Step Robust Speech Enhancement](https://mlsanity.com/paper/2606.05575/) (2026)
- [SR-Edit: Region-Aware Image Editing via Self-Refinement](https://mlsanity.com/paper/2609.02504/) (2026)
- [BridgeCodec: Mamba Enhanced Neural Audio Codec with Schr"odinger Bridge at Low Bitrate](https://mlsanity.com/paper/2610.15453/) (2026)

## Abstract (arXiv)

In text-to-speech (TTS) synthesis, diffusion models have achieved promising generation quality. However, because of the pre-defined data-to-noise diffusion process, their prior distribution is restricted to a noisy representation, which provides little information of the generation target. In this work, we present a novel TTS system, Bridge-TTS, making the first attempt to substitute the noisy Gaussian prior in established diffusion-based TTS methods with a clean and deterministic one, which provides strong structural information of the target. Specifically, we leverage the latent representation obtained from text input as our prior, and build a fully tractable Schrodinger bridge between it and the ground-truth mel-spectrogram, leading to a data-to-data process. Moreover, the tractability and flexibility of our formulation allow us to empirically study the design spaces such as noise schedules, as well as to develop stochastic and deterministic samplers. Experimental results on the LJ-Speech dataset illustrate the effectiveness of our method in terms of both synthesis quality and sampling efficiency, significantly outperforming our diffusion counterpart Grad-TTS in 50-step/1000-step synthesis and strong fast TTS models in few-step scenarios. Project page: https://bridge-tts.github.io/