Santanu Subhash Rathod

Santanu Subhash Rathod, Pietro Liò, Xiao Zhang

Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths using linear interpolants that may not capture the underlying state evolution, especially when learning higher-order dynamics from irregular sampled observations. Constructing unified paths that satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across various deterministic and stochastic dynamical systems of varying complexity, as well as on cellular trajectory inference tasks, demonstrate the strong improvement of SplineFlow over existing baselines. Our code is available at: https://github.com/santanurathod/SplineFlow.

Santanu Subhash Rathod, Francesco Ceccarelli, Sean B. Holden et al.

Inferring trajectories from longitudinal spatially-resolved omics data is fundamental to understanding the dynamics of structural and functional tissue changes in development, regeneration and repair, disease progression, and response to treatment. We propose ContextFlow, a novel context-aware flow matching framework that incorporates prior knowledge to guide the inference of structural tissue dynamics from spatially resolved omics data. Specifically, ContextFlow integrates local tissue organization and ligand-receptor communication patterns into a transition plausibility matrix that regularizes the optimal transport objective. By embedding these contextual constraints, ContextFlow generates trajectories that are not only statistically consistent but also biologically meaningful, making it a generalizable framework for modeling spatiotemporal dynamics from longitudinal, spatially resolved omics data. Evaluated on three datasets, ContextFlow consistently outperforms state-of-the-art flow matching methods across multiple quantitative and qualitative metrics of inference accuracy and biological coherence. Our code is available at: \href{https://github.com/santanurathod/ContextFlow}{ContextFlow}