Chemical reactions contain an inherent element of randomness, which presents itself as noise that interferes with cellular processes and communication. Here we discuss the ability of the spatial partitioning of molecular systems to filter and, thus, remove noise, while preserving regulated and predictable differences between single living cells. In contrast to active noise filtering by network motifs, cellular compartmentalization is highly effective and easily scales to numerous systems without requiring a substantial usage of cellular energy. We will use passive noise filtering by the eukaryotic cell nucleus as an example of how this increases predictability of transcriptional output, with possible implications for the evolution of complex multicellularity.