Class-conditional extensions of generative adversarial networks (GANs), such as auxiliary classifier GAN (AC-GAN) and conditional GAN (cGAN), have garnered attention owing to their ability to decompose representations into class labels and other factors and to boost the training stability. However, a limitation is that they assume that each class is separable and ignore the relationship between classes even though class overlapping frequently occurs in a real-world scenario when data are collected on the basis of diverse or ambiguous criteria. To overcome this limitation, we address a novel problem called class-distinct and class-mutual image generation, in which the goal is to construct a generator that can capture between-class relationships and generate an image selectively conditioned on the class specificity. To solve this problem without additional supervision, we propose classifier's posterior GAN (CP-GAN), in which we redesign the generator input and the objective function of AC-GAN for class-overlapping data. Precisely, we incorporate the classifier's posterior into the generator input and optimize the generator so that the classifier's posterior of generated data corresponds with that of real data. We demonstrate the effectiveness of CP-GAN using both controlled and real-world class-overlapping data with a model configuration analysis and comparative study. Our code is available at https://github.com/takuhirok/CP-GAN/.