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This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Number 62403425, and was also supported by the China Postdoctoral Science Foundation under Grant Number 2025M781449. (Corresponding author: Xiaoyu Jiang and Zhichao Chen)Zehua Zou and Xiaoyu Jiang are with the Hangzhou International Innovation Institute, Beihang University, Hangzhou 311115, China (Email: 19076144g@connect.polyu.hk, jiangxiaoyu@buaa.edu.cn).Yiran Ma is with the State Key Laboratory of Industrial Control Technology, College of Control science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China (E-mail: mayiran@zju.edu.cn)Yulong Zhang is with the College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, China (E-mail: zhangyl@fzu.edu.cn).Zhengnan Li is with the School of Data Science, The Chinese University of Hong Kong, Shenzhen 518172, China (E-mail: 225040119@link.cuhk.edu.cn).Zeyu Yang is with the Zhejiang Key Laboratory of Industrial Solid Waste Thermal Hydrolysis Technology and Intelligent Equipment, Huzhou Key Laboratory of Intelligent Sensing and Optimal Control for Industrial Systems, School of Engineering, Huzhou University, Huzhou 313000, China (E-mail: yangzeyu@zjhu.edu.cn). Jinhao Xie is with MOE of the Key Laboratory of Bioinorganic and Synthetic Chemistry, the Key Lab of Low‐Carbon Chem & Energy Conservation of Guangdong Province, School of Chemistry, Sun Yat‐Sen University, Guangzhou 510275, China. (E-mail: xiejh25@mail2.sysu.edu.cn).Zhichao Chen is with the National Key Lab of General AI, School of Intelligence Science and Technology, Peking University, Beijing 100871, China (E-mail: 12032042@zju.edu.cn)
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By relaxing the objective function with a Wasserstein proximal operator, KProxNPLVM sidesteps the approximation errors that plague standard variational inference in Nonlinear Probabilistic Latent Variable Models.