Recent advances in conditional generative modeling have introduced Continuous conditional Generative Adversarial Network (CcGAN) and Continuous Conditional Diffusion Model (CCDM) for estimating high-dimensional data distributions conditioned on scalar, continuous regression labels (e.g., angles, ages, or temperatures). However, these approaches face fundamental limitations: CcGAN suffers from data imbalance due to fixed-size vicinity constraints, while CCDM requires computationally expensive iterative sampling. To address these issues, we propose CcGAN-AVAR, an enhanced CcGAN framework featuring (1) two novel components for handling data imbalance - an adaptive vicinity mechanism that dynamically adjusts vicinity size and a multi-task discriminator that enhances generator training through auxiliary regression and density ratio estimation - and (2) the GAN framework's native one-step generator, enable 30x-2000x faster inference than CCDM. Extensive experiments on four benchmark datasets (64x64 to 256x256 resolution) across eleven challenging settings demonstrate that CcGAN-AVAR achieves state-of-the-art generation quality while maintaining sampling efficiency.

Continuous Conditional Generative Modeling (CCGM) aims to estimate the distribution of high-dimensional data, typically images, conditioned on scalar continuous variables known as regression labels. While Continuous conditional Generative Adversarial Networks (CcGANs) were initially designed for this task, their adversarial training mechanism remains vulnerable to extremely sparse or imbalanced data, resulting in suboptimal outcomes. To enhance the quality of generated images, a promising alternative is to replace CcGANs with Conditional Diffusion Models (CDMs), renowned for their stable training process and ability to produce more realistic images. However, existing CDMs encounter challenges when applied to CCGM tasks due to several limitations such as inadequate U-Net architectures and deficient model fitting mechanisms for handling regression labels. In this paper, we introduce Continuous Conditional Diffusion Models (CCDMs), the first CDM designed specifically for the CCGM task. CCDMs address the limitations of existing CDMs by introducing specially designed conditional diffusion processes, a modified denoising U-Net with a custom-made conditioning mechanism, a novel hard vicinal loss for model fitting, and an efficient conditional sampling procedure. With comprehensive experiments on four datasets with varying resolutions ranging from 64x64 to 192x192, we demonstrate the superiority of the proposed CCDM over state-of-the-art CCGM models, establishing new benchmarks in CCGM. Extensive ablation studies validate the model design and implementation configuration of the proposed CCDM. Our code is publicly available at https://github.com/UBCDingXin/CCDM.

Continuous Conditional Generative Adversarial Networks (CcGANs) enable generative modeling conditional on continuous scalar variables (termed regression labels). However, they can produce subpar fake images due to limited training data. Although Negative Data Augmentation (NDA) effectively enhances unconditional and class-conditional GANs by introducing anomalies into real training images, guiding the GANs away from low-quality outputs, its impact on CcGANs is limited, as it fails to replicate negative samples that may occur during the CcGAN sampling. We present a novel NDA approach called Dual-NDA specifically tailored for CcGANs to address this problem. Dual-NDA employs two types of negative samples: visually unrealistic images generated from a pre-trained CcGAN and label-inconsistent images created by manipulating real images' labels. Leveraging these negative samples, we introduce a novel discriminator objective alongside a modified CcGAN training algorithm. Empirical analysis on UTKFace and Steering Angle reveals that Dual-NDA consistently enhances the visual fidelity and label consistency of fake images generated by CcGANs, exhibiting a substantial performance gain over the vanilla NDA. Moreover, by applying Dual-NDA, CcGANs demonstrate a remarkable advancement beyond the capabilities of state-of-the-art conditional GANs and diffusion models, establishing a new pinnacle of performance. Our codes can be found at https://github.com/UBCDingXin/Dual-NDA.

Subsampling unconditional generative adversarial networks (GANs) to improve the overall image quality has been studied recently. However, these methods often require high training costs (e.g., storage space, parameter tuning) and may be inefficient or even inapplicable for subsampling conditional GANs, such as class-conditional GANs and continuous conditional GANs (CcGANs), when the condition has many distinct values. In this paper, we propose an efficient method called conditional density ratio estimation in feature space with conditional Softplus loss (cDRE-F-cSP). With cDRE-F-cSP, we estimate an image's conditional density ratio based on a novel conditional Softplus (cSP) loss in the feature space learned by a specially designed ResNet-34 or sparse autoencoder. We then derive the error bound of a conditional density ratio model trained with the proposed cSP loss. Finally, we propose a rejection sampling scheme, termed cDRE-F-cSP+RS, which can subsample both class-conditional GANs and CcGANs efficiently. An extra filtering scheme is also developed for CcGANs to increase the label consistency. Experiments on CIFAR-10 and Tiny-ImageNet datasets show that cDRE-F-cSP+RS can substantially improve the Intra-FID and FID scores of BigGAN. Experiments on RC-49 and UTKFace datasets demonstrate that cDRE-F-cSP+RS also improves Intra-FID, Diversity, and Label Score of CcGANs. Moreover, to show the high efficiency of cDRE-F-cSP+RS, we compare it with the state-of-the-art unconditional subsampling method (i.e., DRE-F-SP+RS). With comparable or even better performance, cDRE-F-cSP+RS only requires about \textbf{10}\% and \textbf{1.7}\% of the training costs spent respectively on CIFAR-10 and UTKFace by DRE-F-SP+RS.

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 (e.g., 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 (a.k.a. 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 can 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.

Majority of state-of-the-art deep learning methods for vision applications are discriminative approaches, which model the conditional distribution. The success of such approaches heavily depends on high-quality labeled instances, which are not easy to obtain, especially as the number of candidate classes increases. In this paper, we study the complementary learning problem. Unlike ordinary labels, complementary labels are easy to obtain because an annotator only needs to provide a yes/no answer to a randomly chosen candidate class for each instance. We propose a generative-discriminative complementary learning method that estimates the ordinary labels by modeling both the conditional (discriminative) and instance (generative) distributions. Our method, we call Complementary Conditional GAN (CCGAN), improves the accuracy of predicting ordinary labels and is able to generate high quality instances in spite of weak supervision. In addition to the extensive empirical studies, we also theoretically show that our model can retrieve the true conditional distribution from the complementarily-labeled data.