An explanation of the quantum measurement process must do more than produce the Born Rule. Conventional quantum mechanics makes other specific predictions about intermediate states, which develop before the completion of a measurement. This paper’s measurement model addresses that more general problem. For a detector with efficiency less than one, the model predicts the conventional quantum results almost exactly: an initial superposed state develops into a well-defined mixture of eigenstate and altered superposition. The minor departures of the model from conventional quantum mechanics could be revealed, in principle, in an optical interference experiment that is also described here. The measurement model assumes that the conversion into an eigenstate is not instantaneous but results from a random sequence of unitary perturbations arising from conventional quantum interactions with the microscopic components of the measuring device. A random walk model describes how wave functions change. And the model’s success relies on small biases in transition probabilities which, however, could be expected of a device designed to measure a specific observable. The biases help to define a generalized Ornstein-Uhlenbeck equation for the distribution of quantum states, and it admits solutions that substantially replicate those of conventional quantum mechanics.