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.
Keywords
Publication details
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Cite this article
APA 7
Kholkin, S., Burnaev, E., & Korotin, A. (2026). Tilted Schrödinger Bridge Matching. https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching
MLA 9
Kholkin, Sergei, et al. "Tilted Schrödinger Bridge Matching." https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching.
Chicago (author–date)
Kholkin, Sergei, Evgeny Burnaev, and Alexander Korotin. 2026. "Tilted Schrödinger Bridge Matching." https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching.
Harvard
Kholkin, S., Burnaev, E. and Korotin, A. (2026) 'Tilted Schrödinger Bridge Matching', Available at: https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching.
Vancouver
Kholkin S, Burnaev E, Korotin A. Tilted Schrödinger Bridge Matching. https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching
IEEE
S. Kholkin, E. Burnaev, and A. Korotin, "Tilted Schrödinger Bridge Matching," https://omanscience.com/en/articles/tilted-schr-dinger-bridge-matching.