# Tilted Schr"odinger Bridge Matching

arXiv: https://arxiv.org/abs/2609.34642 · HTML: https://mlsanity.com/paper/2609.34642/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 49 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Entropic Neural Optimal Transport via Diffusion Processes](https://mlsanity.com/paper/2211.01156/) (2022)
- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [Stochastic Optimal Control Matching](https://mlsanity.com/paper/2312.02027/) (2023)
- [Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models](https://mlsanity.com/paper/2605.10759/) (2026)

## Built on by (most cited first, 1 of 1)

- [Tangent Schr"odinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities](https://mlsanity.com/paper/2610.02906/) (2026)

## Abstract (arXiv)

Schr"odinger bridges provide an entropy-regularized framework and a principled solution for unpaired domain translation. In practice, a pretrained bridge may need to be adapted to human preferences or physical constraints through a reward a problem closely related to reward tilting in diffusion models but underexplored for Schr"odinger bridges. We introduce Tilted Schr"odinger Bridge Matching (TSBM), a post-training method for fine-tuning a learned bridge P between source p0 and target p1 toward a reward-tilted target p1rpropto p1er, while preserving source p0. We formulate this adaptation as alternating optimization initialized from P, provide theoretical justification, and derive a practical algorithm based on Adjoint Matching. We evaluate TSBM on unpaired image-to-image translation targeting digit properties in MNIST and facial attributes in CelebA.