Generative models of cell dynamics: from Neural ODEs to flow matching

Neural Ordinary Differential Equations (Neural ODEs) have emerged as a prominent framework for modeling complex dynamical systems. Their ability to describe a system's underlying dynamical law has attracted attention to applications in life sciences. Single-cell data presents challenges due to noise, sparsity, and the inability to explicitly profile single cells across time. However, pioneering works have demonstrated how Neural ODE-based models can overcome these hurdles, aid mechanistic modeling of cellular development, and approximate population dynamics through the lens of Flow Matching. This article studies why Neural ODEs are suited for modeling the dynamic processes in single-cell data and broader computational health fields, from standard time-series parameterizations to generative models based on optimal transport. We first explore the mathematical properties of Neural ODEs and their application to modeling cellular dynamics. Successively, we zoom into how recent innovations in generative modeling enable efficient and expressive cell state transition modeling through the simulation-free Flow Matching approach. Finally, we present challenges in modeling single-cell dynamics that drive ongoing research in single-cell biology. This work shows that Neural ODEs, as a machine learning framework, are appropriate for modeling dynamic processes in cellular data and promises to advance our understanding of the dynamics in cellular systems.