CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshots

• URL: http://arxiv.org/abs/2505.17354v1
• Date: Fri, 23 May 2025 00:12:49 GMT
• Title: CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshots
• Authors: Keisuke Kawano, Takuro Kutsuna, Naoki Hayashi, Yasushi Esaki, Hidenori Tanaka,
• Abstract summary: We propose Continuous-Time Optimal Transport Flow (CT-OT Flow), which infers high-resolution time labels via partial optimal transport and reconstructs a continuous-time data distribution through a temporal kernel smoothing.<n>CT-OT Flow consistently outperforms state-of-the-art methods on synthetic benchmarks and achieves lower reconstruction errors on real scRNA-seq and typhoon-track datasets.
• Score: 8.656560659184303
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In many real-world scenarios, such as single-cell RNA sequencing, data are observed only as discrete-time snapshots spanning finite time intervals and subject to noisy timestamps, with no continuous trajectories available. Recovering the underlying continuous-time dynamics from these snapshots with coarse and noisy observation times is a critical and challenging task. We propose Continuous-Time Optimal Transport Flow (CT-OT Flow), which first infers high-resolution time labels via partial optimal transport and then reconstructs a continuous-time data distribution through a temporal kernel smoothing. This reconstruction enables accurate training of dynamics models such as ODEs and SDEs. CT-OT Flow consistently outperforms state-of-the-art methods on synthetic benchmarks and achieves lower reconstruction errors on real scRNA-seq and typhoon-track datasets. Our results highlight the benefits of explicitly modeling temporal discretization and timestamp uncertainty, offering an accurate and general framework for bridging discrete snapshots and continuous-time processes.

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