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arXiv · 2609.34642

Tilted Schrödinger Bridge Matching

Sergei Kholkin·Evgeny Burnaev·Alexander Korotin
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Abstract

Schrödinger 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 Schrödinger bridges. We introduce Tilted Schrödinger Bridge Matching (TSBM), a post-training method for fine-tuning a learned bridge $P$ between source $p_0$ and target $p_1$ toward a reward-tilted target $p_1^r\propto p_1e^r$, while preserving source $p_0$. 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.

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Sergei Kholkin, Evgeny Burnaev, Alexander Korotin. 2026-09-28. Tilted Schrödinger Bridge Matching. https://arxiv.org/abs/2609.34642

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