Confidence in judgments is a fundamental aspect of decision making, and tasks that collect confidence judgments are an instantiation of multiple-choice decision making. We present a model for confidence judgments in recognition memory tasks that uses a multiple-choice diffusion decision process with separate accumulators of evidence for the different confidence choices. The accumulator that first reaches its decision boundary determines which choice is made. Five algorithms for accumulating evidence were compared, and one of them produced proportions of responses for each of the choices and full response time distributions for each choice that closely matched empirical data. With this algorithm, an increase in the evidence in one accumulator is accompanied by a decrease in the others so that the total amount of evidence in the system is constant. Application of the model to the data from an earlier experiment (Ratcliff, McKoon, & Tindall, 1994) uncovered a relationship between the shapes of z-transformed receiver operating characteristics and the behavior of response time distributions. Both are explained in the model by the behavior of the decision boundaries. For generality, we also applied the decision model to a 3-choice motion discrimination task and found it accounted for data better than a competing class of models. The confidence model presents a coherent account of confidence judgments and response time that cannot be explained with currently popular signal detection theory analyses or dual-process models of recognition.