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Trajectory Inference with Smooth Schr\"odinger Bridges

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arxiv 2503.00530 v1 pith:EUM3VDHZ submitted 2025-03-01 stat.ML cs.LG

Wanli Hong , Yuliang Shi , Jonathan Niles-Weed This is my paper · ORCID
classification stat.MLcs.LG
keywords smoothodingerproblemschrprocessapplicationsbridgebridges
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Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schr\"odinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though na\"ively smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Mat\'ern processes) for which the resulting Smooth Schr\"odinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. The code can be found at https://github.com/WanliHongC/Smooth_SB

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs

    math.PR 2025-07 conditional novelty 6.0 of 10

    When the m marginal constraints are the time-marginals of an SDE with time-dependent drift, the multi-marginal Schrödinger bridge converges to the SDE's law at KL rate O(m^{-1}).

  2. DICE: Discrete inverse continuity equation for learning population dynamics

    cs.LG 2025-07 conditional novelty 6.0 of 10

    DICE recovers the vector field driving population-level dynamics from unpaired time marginals through a discrete inverse continuity equation, with a unique minimizer and a first-order time-discretization error.

  3. Multi-marginal temporal Schr\"odinger Bridge Matching from unpaired data

    cs.LG 2025-10 reject novelty 5.0 of 10

    MMtSBM extends diffusion Schrödinger bridge matching to multiple time marginals via a factorized iterative Markovian fitting algorithm, claiming state-of-the-art trajectory inference and video generation from unpaired data.

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