Background: In cell differentiation, a less specialized cell differentiates into a more specialized one, even though all cells in one organism have (almost) the same genome. Epigenetic factors such as histone modifications are known to play a significant role in cell differentiation. We previously introduce cell-type trees to represent the differentiation of cells into more specialized types, a representation that partakes of both ontogeny and phylogeny. Results: We propose a maximum-likelihood (ML) approach to build cell-type trees and show that this ML approach outperforms our earlier distance-based and parsimony-based approaches. We then study the reconstruction of ancestral cell types; since both ancestral and derived cell types can coexist in adult organisms, we propose a lifting algorithm to infer internal nodes. We present results on our lifting algorithm obtained both through simulations and on real datasets. Conclusions: We show that our ML-based approach outperforms previously proposed techniques such as distance-based and parsimony-based methods. We show our lifting-based approach works well on both simulated and real data.