The use of liquid biopsies in the detection, diagnosis and treatment monitoring of different types of cancers and other diseases often requires identifying and enumerating instances of analytes that are rare. Most current techniques that aim to computationally isolate these rare instances or events first learn the signature of the event, and then scan the appropriate biological assay for this signature. While such techniques have proven to be very useful, they are limited because they must first establish what signature to look for, and only then identify events that are consistent with this signature. In contrast to this, in this study, we present an automated approach that does not require the knowledge of the signature of the rare event. It works by breaking the assay into a sequence of components, learning the probability distribution of these components, and then isolating those that are rare. This is done with the help of deep generative algorithms in an unsupervised manner, meaning without a-priori knowledge of the rare event associated with an analyte. In this study, this approach is applied to immunofluorescence microscopy images of peripheral blood, where it is shown that it successfully isolates biologically relevant events in blood from normal donors spiked with cancer-related cells and in blood from patients with late-stage breast cancer.