Semi-Supervised Conditional Diffusion via Label Augmentation

Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

Robust medical image segmentation across modalities remains challenging due to severe domain shifts and the lack of target-domain labels. While diffusion models have been explored for cross-domain generation and augmentation, target-domain conditional diffusion training typically relies on highly noisy pseudo masks; naively conditioning on a single Arg-Max pseudo-label can corrupt diffusion training and downstream segmentation. We propose UPDiff-UDA, a unified UDA framework whose core is an uncertainty-guided training objective for target-domain conditional diffusion. Given an imperfect source-trained segmenter, we use its per-pixel softmax distribution to form ranked pseudo-label maps (Arg-Max, Arg-2nd, Arg-3rd, ...). Each map yields a conditional score estimate, and we aggregate them via pixel-wise confidence weighting to obtain an uncertainty-reweighted score for score matching, improving robustness to pseudo-label noise while leveraging alternative plausible labels in uncertain regions. We further provide a theoretical justification showing that confidence-weighted aggregation follows a minimum-MSE convex-combination principle under the segmenter-induced surrogate label distribution. To improve pseudo-condition quality, we also introduce a feature-guided, low-degree-of-freedom Bézier curve adaptation to reduce appearance gaps. Experiments on multiple public datasets and modality shifts show that UPDiff-UDA generates high-fidelity labeled target-style samples for augmentation and consistently outperforms strong UDA baselines. The code for this project is available at: https://github.com/superlc1995/Multi-Channel-Uncertainty-Diffusion-UDA