We propose an optimal silencer design method using the backpropagation of an artificial neural network (ANN) model and the generative design technique. The noise attenuation performance of a silencer is evaluated with its transmission loss (TL), which is a frequency-dependent quantity and strongly dependent on the partition layout inside the silencer. An ANN model is developed to predict the TL curve of the silencer with a given partition layout in the frequency domain. A partition layout generation algorithm is suggested, and a finite element analysis is conducted for training data generation. The backpropagation of a pre-trained ANN model is used for sensitivity analysis, which provides the sensitivity of a TL value with respect to design variables in a gradient-based optimization problem for silencer design. A candidate region is declared considering an existing partition layout, and only one design variable in the candidate region is updated for partition connectivity. The proposed method is successfully applied to single and multiple target frequency problems for optimal silencer design and yields various optimal partition layouts. In addition, we discuss the step-by-step characteristics and novelty of the proposed silencer design method in comparison with traditional silencer optimization methods. A comparison with the traditional shape and topology optimization methods for silencer design strongly supports the effectiveness of the proposed design method.