Generative modeling of single-cell RNA-seq data is crucial for tasks like trajectory inference, batch effect removal, and simulation of realistic cellular data. However, recent deep generative models simulating synthetic single cells from noise operate on pre-processed continuous gene expression approximations, overlooking the discrete nature of single-cell data, which limits their effectiveness and hinders the incorporation of robust noise models. Additionally, aspects like controllable multi-modal and multi-label generation of cellular data remain underexplored. This work introduces CellFlow for Generation (CFGen), a flow-based conditional generative model that preserves the inherent discreteness of single-cell data. CFGen reliably generates whole-genome, multi-modal, single-cell data, improving the recovery of crucial biological data characteristics while tackling relevant generative tasks such as rare cell type augmentation and batch correction. We also introduce a novel framework for compositional data generation using Flow Matching. By showcasing CFGen on a diverse set of biological datasets and settings, we provide evidence of its value to the fields of computational biology and deep generative models.

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the generalization properties of NODEs for dynamical systems beyond the observed data are underexplored. We systematically study the influence of weight and feature sparsity on forecasting as well as on identifying the underlying dynamical laws. Besides assessing existing methods, we propose a regularization technique to sparsify ``input-output connections'' and extract relevant features during training. Moreover, we curate real-world datasets including human motion capture and human hematopoiesis single-cell RNA-seq data to realistically analyze different levels of out-of-distribution (OOD) generalization in forecasting and dynamics identification respectively. Our extensive empirical evaluation on these challenging benchmarks suggests that weight sparsity improves generalization in the presence of noise or irregular sampling. However, it does not prevent learning spurious feature dependencies in the inferred dynamics, rendering them impractical for predictions under interventions, or for inferring the true underlying dynamics. Instead, feature sparsity can indeed help with recovering sparse ground-truth dynamics compared to unregularized NODEs.