Efficient Covariance-Aware Vicinal Latent Diffusion for Continuous Conditional Image Generation

Recent advances in continuous conditional generative modeling, including Continuous conditional Generative Adversarial Network (CcGAN) and Continuous Conditional Diffusion Model (CCDM), estimate high-dimensional data distributions conditioned on scalar regression labels such as angles, ages, or temperatures. However, fixed-size vicinal training in CcGAN can be sensitive to non-uniform label densities, whereas CCDM relies on computationally expensive iterative sampling. To address these issues, we propose CcGAN-AVAR, an imbalance-aware extension of CcGAN that combines soft/hybrid adaptive vicinity with auxiliary discriminator-guided regularization. The adaptive vicinity constructs a label-dependent local radius according to the available samples around each target condition, and the multi-task discriminator supplies both a regression signal for label consistency and a density-ratio-estimation signal for distribution matching. We further provide a theoretical interpretation characterizing how adaptive vicinal weighting affects the local bias-variance behavior of the discriminator target, how hybrid truncation reduces objective-level cross-condition mixing, and how the density-ratio-based generator penalty approximates a Pearson Chi-square discrepancy up to the estimation error of the density-ratio branch. Extensive experiments on four datasets, including the newly constructed imbalanced RC-49-I, covering resolutions from 64x64 to 256x256 across eleven settings, demonstrate that CcGAN-AVAR obtains strong generation quality and label consistency while preserving the one-step sampling efficiency of GANs, achieving 300x--2000x faster inference than CCDM.

Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data. In practice, however, acquiring high-quality labels is costly and time-consuming, leaving large volumes of unlabeled data unused. To address this, we introduce label-augmented conditional diffusion (LACD), a simple and effective approach that incorporates unlabeled examples by assigning them a designated trivial label and performing joint denoising score matching over the augmented dataset. We provide sufficient conditions guaranteeing population-level identifiability of the target conditional distribution under this scheme. Moreover, we establish rigorous statistical guarantees: when sufficiently many unlabeled samples are available, the sampling distribution produced by LACD converges strictly faster than the purely supervised estimator in total variation distance, and at least as fast in Wasserstein-1 distance. Extensive experiments on synthetic, image, and tabular benchmarks corroborate our theory and show substantial gains in sample efficiency and generative performance compared with the purely supervised estimator.

Unsupervised conditional image generation (UCGen) aims to control generation without relying on manually annotated labels, yet remains challenging due to unstructured semantic representations across granularities. To address this, we propose a novel coarse-to-fine UCGen framework (CoFi-UCGen) that explicitly disentangles global semantics from fine-grained variations, which to the best of our knowledge, sets out the first successful attempt for both coarse- and fine-grained conditional generation without any labels. More specifically, we first propose the adversarial semantic reciprocal learning theory to ensure the semantic consistency and completeness between images and latent spaces. Based on the consistency, we propose the bit-codes to learn a structured coarse-grained latent space, and further prove distinct global semantics inherent from our bit-codes while preserving independent noise sampling for generation. Building upon these bit-codes, we establish a fine-grained semantic basis and introduce a hierarchical modulation mechanism in diffusion models, by enabling layer-wise injection from coarse conditions to progressively control fine-grained attributes during generation. Extensive experiments demonstrate that without any label priors or pre-trained feature extractors, our CoFi-UCGen consistently outperforms existing UCGen methods in terms of image quality, semantic consistency, and control accuracy, verifying the effectiveness of explicit coarse-to-fine semantic decomposition for the challenging UCGen task.