This paper describes the development of a Volterra series model for predicting transient soot emissions from a diesel engine with fuel flow rate and engine speed as the two inputs to the model. These two signals are usually available as outputs of the power management controller in diesel hybrids. Therefore, an accurate offline estimation of the transient soot emissions using these signals is instrumental in optimizing the control strategy for both fuel economy and emissions. In order to develop the model, transient soot data are first collected by Engine-in-the-loop experiments of conventional and hybrid vehicles. The data are then used to construct a third-order multiple-input single-output (MISO) Volterra series to successfully model this system. Parametric complexity of the model is reduced using proper orthogonal decomposition (POD), and the model is validated on various datasets. It is shown that the prediction accuracy of transient soot, both qualitatively and quantitatively, significantly improves over the steady-state maps, while the model still remains computationally efficient for systems level work.