With light weight, high strength, and high performance, metal bent tubes have attracted increasing applications in aeronautics. However, the growing demand for customized tubular parts has led to a significant increase in the cost of conventional tube-bending processes, as they can only process tubes of a specific diameter. To this end, this paper proposes a variable diameter die (VDD) scheme which can bend tubes with a specific range of diameters. To investigate the formability of VDD-processed tubes for practical VDD applications, an accurate and reliable prediction method of cross-sectional distortion is imperative. Hence, we pioneer a novel intelligent model based on quantum-behaved particle swarm optimization (QPSO)-optimized back-propagation neural network (BPNN) to predict a rational cross-sectional distortion characterization index: average distortion rate. The adaptive adjustment of coefficients and the Gaussian distributed random vector are introduced to QPSO, which balance the search and enhance the diversity of the population, respectively. For further improvement in optimization performance, the informed initialization strategy is applied to QPSO. The efficiency of the proposed reinforced QPSO (RQPSO)-optimized BPNN model is evaluated by comparing the results with those of the BPNN, BPNN with Xavier initialization, several different particle swarm optimization variants-optimized BPNN models, and variants of popular machine learning models. The results indicated the superiority of RQPSO over other methods in terms of the coefficient of determination (${R}^2$), variance account for, root mean square error (MSE), mean absolute error, and standard deviation of MSE. Thus, the proposed novel algorithm could be employed as a reliable and accurate technique to predict the cross-sectional distortion of VDD-processed tubes.