发表机构
Nanyang Technological University; University of Helsinki（南洋理工大学; 赫尔辛基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出源空间广义贝叶斯推断框架，利用少步iMF传输映射表示隐式先验，在高斯源空间采样，并给出误差界，实验验证其准确高效及文本引导能力。
AI 中文摘要
贝叶斯推断越来越多地使用信息丰富但隐式的先验，这些先验仅通过样本表示，如历史集成、模拟器输出和预训练生成模型。同样的计算问题出现在测试时引导任务（广义贝叶斯）中，其中显式的正权重（例如，指数化的奖励）倾斜隐式先验。我们开发了一个源空间广义贝叶斯推断框架，该框架结合了廉价的少步先验传输与后验稳定性保证。具体来说，我们使用一步或几步改进的MeanFlow（iMF）映射表示先验，并在其高斯源空间中执行后验采样。我们建立了精确后验与学习后验之间的Wasserstein误差界，该界以联合总体iMF和辅助速度损失表示，分解为训练次优性和模型类逼近误差。在iMF源空间中，我们采用带有预条件Crank-Nicolson更新的并行退火，并引入一种混合变体，该变体结合了分裂哈密尔顿蒙特卡洛以提高采样效率。合成实验表明，所提出的框架能够准确且高效地逼近后验分布，而CLIP引导的ImageNet实验展示了其将预训练iMF图像先验引导至文本指定偏好的能力。
英文摘要
Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models. The same computational problem appears in the test-time guidance task (generalized Bayes), where an explicit positive weight, e.g., an exponentiated reward, tilts an implicit prior. We develop a framework for source-space generalized Bayesian inference that combines inexpensive few-step prior transports with posterior stability guarantees. Specifically, we represent the prior using a one- or few-step improved MeanFlow (iMF) map and perform posterior sampling in its Gaussian source space. We establish Wasserstein error bounds between the exact and learned posteriors in terms of the joint population iMF and auxiliary-velocity loss, decomposed into training suboptimality and model-class approximation error. In the iMF source space, we adopt parallel tempering with preconditioned Crank-Nicolson updates and introduce a hybrid variant that incorporates split Hamiltonian Monte Carlo to improve sampling efficiency. Synthetic experiments show that the proposed framework can approximate posterior distributions accurately and efficiently, while CLIP-guided ImageNet experiments demonstrate its ability to steer a pretrained iMF image prior toward text-specified preferences.
