Filtration via a porous medium is a ubiquitous process where high-fidelity physical models are needed. The classical cell model oversimplifies the filtration medium and results in biased and inaccurate predictions of the filter performance. This paper presents the discrete framework of a polydisperse cell model that can incorporate any measured pore size distribution. A new equation connecting the polydisperse cell efficiencies and the medium efficiency is derived from first principles. For ceramic filters, the discrete model demonstrates a generic prediction capability of the filtration efficiency with a root-mean-squared difference of 5.4%, while the counterpart of the classical cell model is 26.4%. In addition, the discrete model eliminates the biased predictions of the classical cell model on sub-100 nm particles.