Neural Characteristic Function Learning for Conditional Image Generation

The emergence of conditional generative adversarial networks (cGANs) has revolutionised the way we approach and control the generation, by means of adversarially learning joint distributions of data and auxiliary information. Despite the success, cGANs have been consistently put under scrutiny due to their ill-posed discrepancy measure between distributions, leading to mode collapse and instability problems in training. To address this issue, we propose a novel conditional characteristic function generative adversarial network (CCF-GAN) to reduce the discrepancy by the characteristic functions (CFs), which is able to learn accurate distance measure of joint distributions under theoretical soundness. More specifically, the difference between CFs is first proved to be complete and optimisation-friendly, for measuring the discrepancy of two joint distributions. To relieve the problem of curse of dimensionality in calculating CF difference, we propose to employ the neural network, namely neural CF (NCF), to efficiently minimise an upper bound of the difference. Based on the NCF, we establish the CCF-GAN framework to explicitly decompose CFs of joint distributions, which allows for learning the data distribution and auxiliary information with classified importance. The experimental results on synthetic and real-world datasets verify the superior performances of our CCF-GAN, on both the generation quality and stability.