An important class of psychological models of decision making assumes that evidence is accumulated by a diffusion process to a response criterion. These models have successfully accounted for reaction time (RT) distributions and choice probabilities from a wide variety of experimental tasks. An outstanding theoretical problem is how the integration process that underlies diffusive evidence accumulation can be realized neurally. Wang (2001, 2002) has suggested that long timescale neural integration may be implemented by persistent activity in reverberation loops. We analyze a simple recurrent decision making architecture and show that it leads to a diffusive accumulation process. The process has the form of a time-inhomogeneous Ornstein-Uhlenbeck velocity process with linearly increasing drift and diffusion coefficients. The resulting model predicts RT distributions and choice probabilities that closely approximate those found in behavioral data.