Drift-diffusion models have been widely used to study the neural mechanisms of decisions guided by noisy stimuli. In this framework, momentary evidence is integrated through a scalar decision variable, which has been found to correlate with spike rates in many brain areas. However, the relationship between the decision variable (i.e., accumulated evidence) and spike rate is widely assumed to be fixed over the course of a single trial, even though sensory and motor weights on spiking activity vary over time. Allowing the weight of the decision variable to be temporally inhomogeneous may capture the decision process more accurately. Therefore, we incorporated hidden-Markov generalized linear models of spike trains into a drift-diffusion model, resulting in two independent Markov chains, one of the decision variable and the other of a coupling variable controlling the weight of the decision variable. In the resulting factorial hidden Markov drift diffusion model (FHMDDM), the spike rate is a nonlinear output of the weighted sum of inputs including the decision variable, spike history, and timing of task events, with the weight of the decision variable dependent on the coupling variable. Fitting FHMDDM to Neuropixels recordings from dorsomedial frontal cortex (dmFC) of rats discriminating between auditory click trains and to their behavioral choices, we found that compared to a model with temporally fixed weights, FHMDDM captures both the spike trains and choices more accurately. The posterior estimate of the coupling variable reveals that the weights of the decision variable on dmFC spiking are strongest at the beginning of a decision and decrease over deliberation. These results suggest that decision formation can be more accurately characterized by a time-varying relationship between the decision variable and spike trains and that processes separate from decision formation such as motor preparation have sizable influence over late dmFC spiking.