arXiv:2509.25507stat.MLcs.LG2025-09中稿 · ICML

无需训练即可生成条件样本,高效准确。

One-shot Conditional Sampling: MMD meets Nearest Neighbors

  • 基于MMD与最近邻,直接优化生成器实现单次采样。
  • 理论证明采样误差有界,分布收敛至真实条件分布。
  • 适合图像去噪、超分辨率等需快速条件生成场景。

如何从从未完全观测到的条件分布中生成样本?这一问题广泛存在于现代机器学习与经典统计中,涵盖计算机视觉中的图像后处理、基于模拟的推断中近似后验采样,以及复杂数据场景下的条件分布建模。相较于无条件采样,利用额外特征信息可实现更自适应、高效的采样。为此,我们提出条件生成器(CGMMD),一种新型条件采样框架。不同于多数现有方法,本方法将训练目标设定为无对抗性的直接最小化问题。其关键优势在于,生成器可在一次前向传播中输出条件样本,实现低测试时复杂度的一次性采样。我们建立了使用CGMMD采样时损失的严格理论界,并证明估计分布收敛至真实条件分布。过程中还推导出基于最近邻函数的统一浓度结果,可能具有独立研究价值。最后,实验表明,CGMMD在涉及复杂条件密度的合成任务,以及图像去噪和图像超分辨率等实际应用中均表现良好。

原文摘要 · Abstract (English)

How can we generate samples from a conditional distribution that we never fully observe? This question arises across a broad range of applications in both modern machine learning and classical statistics, including image post-processing in computer vision, approximate posterior sampling in simulation-based inference, and conditional distribution modeling in complex data settings. In such settings, compared with unconditional sampling, additional feature information can be leveraged to enable more adaptive and efficient sampling. Building on this, we introduce Conditional Generator using MMD (CGMMD), a novel framework for conditional sampling. Unlike many contemporary approaches, our method frames the training objective as a simple, adversary-free direct minimization problem. A key feature of CGMMD is its ability to produce conditional samples in a single forward pass of the generator, enabling practical one-shot sampling with low test-time complexity. We establish rigorous theoretical bounds on the loss incurred when sampling from the CGMMD sampler, and prove convergence of the estimated distribution to the true conditional distribution. In the process, we also develop a uniform concentration result for nearest-neighbor based functionals, which may be of independent interest. Finally, we show that CGMMD performs competitively on synthetic tasks involving complex conditional densities, as well as on practical applications such as image denoising and image super-resolution.

条件采样MMD生成模型图像修复

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