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.
Conditional generative models have emerged as powerful tools for sampling from target conditional distributions, driving substantial advances across a wide range of scientific and applied domains. As these models proliferate, practitioners often face multiple plausible generators whose performance can vary with the task, data, or input condition. We propose an optimal model averaging framework for conditional generative models, allowing candidate generators to be combined even when they are accessible only through conditional samples without tractable densities. Specifically, we use a sample-based maximum mean discrepancy between conditional distributions, which first leads to a static model averaging method, StaticMA, assigning fixed weights to different candidates. In addition, we develop MoEMA (mixture-of-experts model averaging), an input-adaptive method that parameterizes covariate-dependent weights through a softmax neural-network gate. We establish in-sample and out-of-sample asymptotic optimality for the proposed methods, together with consistency of the estimated adaptive weight function under regularity conditions. The framework applies directly to Euclidean responses and extends to unstructured data by combining our formulation with fixed representation maps. Across a broad set of simulations and real-data studies spanning tabular, image, and text modalities, MoEMA generally improves over competing baselines, demonstrating the effectiveness of our proposed methods.
Conditional generative models are increasingly used as scenario generators for stochastic optimization, but standard training objectives emphasize uniform distributional fit rather than the downstream decisions induced by generated scenarios. This creates an objective mismatch: errors in statistically common regions may have little effect on decision regret, whereas errors in decision-sensitive regions can substantially change the optimal action. We propose Decision-Weighted Flow Matching (DW-FM), a regret-aligned training framework that preserves the simplicity of standard flow matching while reweighting its velocity-regression objective using decision-sensitive endpoint information. Theoretically, we connect downstream regret to pathwise velocity mismatch through a loss-induced decision discrepancy and an adjoint transport argument, yielding an ideal regret-aligned surrogate and practical endpoint-weighted objectives with regret guarantees. Empirically, we demonstrate the effectiveness of DW-FM on three CVaR-based contextual stochastic optimization benchmarks spanning synthetic portfolio, semi-real financial, and traffic-CVaR tasks, where DW-FM improves downstream regret over standard baselines.