This work proposes the continuous conditional generative adversarial network (CcGAN), the first generative model for image generation conditional on continuous, scalar conditions (termed regression labels). Existing conditional GANs (cGANs) are mainly designed for categorical conditions (eg, class labels); conditioning on regression labels is mathematically distinct and raises two fundamental problems:(P1) Since there may be very few (even zero) real images for some regression labels, minimizing existing empirical versions of cGAN losses (aka empirical cGAN losses) often fails in practice;(P2) Since regression labels are scalar and infinitely many, conventional label input methods are not applicable. The proposed CcGAN solves the above problems, respectively, by (S1) reformulating existing empirical cGAN losses to be appropriate for the continuous scenario; and (S2) proposing a naive label input (NLI) method and an improved label input (ILI) method to incorporate regression labels into the generator and the discriminator. The reformulation in (S1) leads to two novel empirical discriminator losses, termed the hard vicinal discriminator loss (HVDL) and the soft vicinal discriminator loss (SVDL) respectively, and a novel empirical generator loss. The error bounds of a discriminator trained with HVDL and SVDL are derived under mild assumptions in this work. Two new benchmark datasets (RC-49 and Cell-200) and a novel evaluation metric (Sliding Fr\'echet Inception Distance) are also proposed for this continuous scenario. Our experiments on the Circular 2-D Gaussians, RC-49, UTKFace, Cell-200, and Steering Angle datasets show that CcGAN is able to generate diverse, high-quality samples from the image distribution conditional on a given regression label. Moreover, in these experiments, CcGAN substantially outperforms cGAN both visually and quantitatively.

翻译：这项工作提出了连续的有条件基因对抗网络(CcGAN),这是第一个以连续的卡路里条件为条件生成图像的基因模型(计算回归标签)。现有的有条件的GAN(cGAN)主要针对绝对条件设计(例如,类标签);对回归标签的调整在数学上是截然不同的,并提出了两个根本性问题:(P1) 由于某些回归标签可能很少(甚至为零)真实的图像,将现有的CGAN损失(aka 经验性cGAN损失)在实践上经常失败;(P2) 由于回归标签是卡路里和无限的,常规标签输入方法不适用。拟议的CCAN(cAN), CGAN(cAN), 常规标签输入方法(cGAN), 分别通过(S1) 修改现有的实证的 CGAN 损失, 和软性GL 数据库显示的CL 。