Tracking algorithms are traditionally based on either a variational approach or a Bayesian one. In the variational case, a cost function is established between two consecutive frames and minimized by standard optimization algorithms. In the Bayesian case, a stochastic motion model is used to maintain temporal consistency. Among the Bayesian methods we focus on the particle filter, which is especially suited for handling multimodal distributions. In this paper, we present a novel approach to fuse both methodologies in a single tracker where the importance sampling of the particle filter is given implicitly by the optimization algorithm of the variational method. Our technique is capable of outlying nuclei and tracking the lineage of biological cells using different motion models for mitotic and non-mitotic stages of the life of a cell. We validate its ability to track the lineage of HeLa cells in fluorescence microscopy.