Multi-marginal temporal Schrödinger Bridge Matching for video generation from unpaired data

2025-10-02

AI Summary

This work addresses the problem of reconstructing temporal evolutionary trajectories of high-dimensional natural dynamical processes—such as cellular differentiation and disease progression—from unpaired static snapshot data. Existing methods suffer from poor scalability in high dimensions and reliance on strong modeling assumptions. To overcome these limitations, we propose Multi-Marginal Temporal Schrödinger Bridge Matching (MMtSBM), the first extension of diffusion-based Schrödinger bridges to the multi-marginal setting. MMtSBM integrates multi-marginal optimal transport with probabilistic path modeling via a factorized iterative Markov fitting algorithm, enabling dynamic coupling inference from unpaired observations. Theoretically grounded and empirically robust, MMtSBM achieves state-of-the-art performance on both high-dimensional transcriptomic trajectory inference (up to 100+ dimensions) and image-to-video generation tasks. Notably, it is the first method to successfully recover interpretable dynamic evolution paths and implicit dynamical structures in extremely high-dimensional settings.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose extit{ extbf{Multi-Marginal temporal Schrödinger Bridge Matching}} ( extbf{MMtSBM}) extit{for video generation from unpaired data}, extending the theoretical guarantees and empirical efficiency of Diffusion Schrödinger Bridge Matching (arXiv:archive/2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real world datasets such as transcriptomic trajectory inference in 100 dimensions, and for the first time recovers couplings and dynamics in very high dimensional image settings. Our work establishes multi-marginal Schrödinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

Problem

• Reconstructing temporal evolution from static snapshots
• Addressing poor scalability in high-dimensional data transport
• Recovering hidden dynamics without restrictive assumptions

Innovation

• Multi-marginal Schrödinger Bridge for unpaired video generation
• Iterative Markovian Fitting algorithm for multiple marginals
• Factorized approach for high-dimensional trajectory inference