The fundamental question of how cells maintain their characteristic size remains open. Cell size measurements made through microscopic time-lapse imaging of microfluidic single cell cultivations have posed serious challenges to classical cell growth models and are supporting the development of newer, nuanced models that explain empirical findings better. Yet current models are limited, either to specific types of cells and/or to cell growth under specific microenvironmental conditions. Together with the fact that tools for robust analysis of said time-lapse images are not widely available as yet, the above-mentioned point presents an opportunity to progress the cell growth and size homeostasis discourse through generative, probabilistic modeling and analysis of the utility of different statistical estimation and inference techniques in recovering the parameters of the same. In this thesis, I present a novel Model Framework for simulating microfluidic single-cell cultivations with 36 different simulation modalities, each integrating dominant cell growth theories and generative modelling techniques. I also present a comparative analysis of how different Frequentist and Bayesian probabilistic inference techniques such as Nuisance Variable Elimination and Variational Inference work in the context of a case study of the estimation of a single model describing a microfluidic cell cultivation.