# QDSB: Quantized Diffusion Schr"odinger Bridges

arXiv: https://arxiv.org/abs/2605.11983 · HTML: https://mlsanity.com/paper/2605.11983/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [LAVIE: High-Quality Video Generation with Cascaded Latent Diffusion Models](https://mlsanity.com/paper/2309.15103/) (2023)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [Diffusion-4K: Ultra-High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2503.18352/) (2025)
- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Generalized Schr"odinger Bridge Matching](https://mlsanity.com/paper/2310.02233/) (2023)
- [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024)
- [Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm](https://mlsanity.com/paper/2110.06798/) (2021)
- [Making transport more robust and interpretable by moving data through a small number of anchor points](https://mlsanity.com/paper/2012.11589/) (2020)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [LightSBB-M: Bridging Schr"odinger and Bass for Generative Diffusion Modeling](https://mlsanity.com/paper/2601.19312/) (2026)

## Abstract (arXiv)

Learning generative models in settings where the source and target distributions are only specified through unpaired samples is gaining in importance. Here, one frequently-used model are Schr"odinger bridges (SB), which represent the most likely evolution between both endpoint distributions. To accelerate training, simulation-free SBs avoid the path simulation of the original SB models. However, learning simulation-free SBs requires paired data; a coupling of the source and target samples is obtained as the solution of the entropic optimal transport (OT) problem. As obtaining the optimal global coupling is infeasible in many practical cases, the entropic OT problem is iteratively solved on minibatches instead. Still, the repeated cost remains substantial and the locality can distort the global transport geometry. We propose quantized diffusion Schr"odinger bridges (QDSB), which compute the endpoint coupling on anchor-quantized endpoint distributions and lift the resulting plan back to original data points through cell-wise sampling. We show that the regularized optimal coupling is stable w.r.t. anchor quantization, with an error controlled by the quality of the anchor approximation. In real-world experiments, QDSB matches the sample quality of existing baselines, requiring substantially less time. Code and data are available at github.com/mathefuchs/qdsb.