Inverse lithography technology (ILT) can optimize the mask to gain the best process window and image quality when the design dimension shrinks. However, as a pixel level correction method, ILT is very time-consuming. In order to make the ILT method useful in real mask fabrication, the runtime of ILT-based optical proximity correction mask must evidently decrease while keeping the good lithographic metric performance. Our study proposes a framework to obtain the curvilinear ILT mask with generative adversarial network (GAN). It is subsequently refined with the traditional ILT to exclude unexpected outliers generated by the GAN method. We design conditional GAN, reverse GAN (RGAN), and high discretion GAN (HDGAN) to generate curvilinear ILT mask. Their runtime and the performance are compared. Compared with the CILT method, the speed of GAN type methods with the afterward refinement is increased by an order of magnitude. The RGAN has a better performance in edge placement error and process variation band evaluation, and HDGAN has a better performance in the mask error enhancement factor evaluation. The designed RGAN and HDGAN are promising in actual application to generate the curvilinear mask. They can evidently decrease the runtime and have better lithographic metric performance.