School of AIA, Huazhong University of Science and Technology（华中科技大学AIA学院）；Department of Computer Science and Engineering, Shanghai Jiao Tong University（上海交通大学计算机科学与工程系）；Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学应用统计中心及统计学院）；School of EIC, Huazhong University of Science and Technology（华中科技大学EIC学院）
Hao Yang, Zhanbo Feng, Feng Zhou, Robert C Qiu, Zenan Ling
Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability arising from their inherent stochasticity. In this paper, we revisit time series diffusion models and present a comprehensive framework that encompasses most existing diffusion-based methods. Building on this theoretical foundation, we propose a novel diffusion-based time series forecasting model, the Series-to-Series Diffusion Bridge Model ($\mathrm{S^2DBM}$), which leverages the Brownian Bridge process to reduce randomness in reverse estimations and improves accuracy by incorporating informative priors and conditions derived from historical time series data. Experimental results demonstrate that $\mathrm{S^2DBM}$ delivers superior performance in point-to-point forecasting and competes effectively with other diffusion-based models in probabilistic forecasting.
Technical University Munich, Chair of Robotics, Artificial Intelligence and Embedded Systems（慕尼黑技术大学机器人、人工智能与嵌入式系统教研室）；ELLIS Unit Linz, LIT AI Lab, Johannes Kepler University Linz, Austria（林茨ELLIS单位，LIT人工智能实验室，林茨约翰内斯·开普勒大学，奥地利）；NXAI Lab & NXAI GmbH, Linz, Austria（NXAI实验室及NXAI GmbH，林茨，奥地利）
ADBM: Adversarial diffusion bridge model for reliable adversarial purification
Tsinghua University（清华大学）；Peking University（北京大学）；Beijing Institute of Technology（北京理工大学）；Aalborg University（奥尔堡大学）；Harbin Institute of Technology, Weihai（哈尔滨工业大学（威海））；Huawei Technologies（华为技术有限公司）
Aided design of bridge aesthetics based on Stable Diffusion fine-tuning
Jiangsu College of Finance & Accounting（江苏财会职业学院）；Lianyungang Open University（连云港开放大学）；Wanshi Antecedence Digital Intelligence Traffic Technology Co., Ltd（万事先行数字智能交通技术有限公司）
Latent Schr{ö}dinger Bridge Diffusion Model for Generative Learning
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；Center of Statistical Research and School of Statistics, Southwestern University of Finance and Economics（西南财经大学统计研究中心与统计学院）
Fraunhofer HHI（弗劳恩霍夫研究所）；Ghent University–imec FlandersMake–MIRO（根特大学–imec 荷兰弗拉芒Make–MIRO）；Technical University of Munich（慕尼黑技术大学）；Technical University of Berlin（柏林技术大学）；University of Potsdam（波茨坦大学）；University of Birmingham（伯明翰大学）；Imperial College London（伦敦帝国理工学院）
Underdamped Diffusion Bridges with Applications to Sampling
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；NVIDIA（NVIDIA公司）；Zuse Institute Berlin（柏林泽尼克研究所）；dida Datenschmiede GmbH（dida数据安全公司）；FZI Research Center for Information Technology（信息技术研究中心）
Dequantified Diffusion-Schr{ö}dinger Bridge for Density Ratio Estimation
The School of Mathematics, South China University of Technology, Guangzhou 510006, China（华南理工大学数学学院）；The School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510006, China（华南理工大学电子与信息工程学院）；The Department of Electrical Engineering, Columbia University, New York, NY 10027, USA（哥伦比亚大学电气工程系）
Dept. of Comp. Sci. & Tech., Institute for AI, BNRist Center（计算机科学与技术系，人工智能研究所，BNRist中心）；Tsinghua-Bosch Joint ML Center, Tsinghua University（清华大学-博世联合机器学习中心，清华大学）；Shengshu Technology（盛舒科技）；Pazhou Lab (Huangpu), Guangzhou, China（黄埔实验室（广州），中国）
Spherical Brownian Bridge Diffusion Models for Conditional Cortical Thickness Forecasting
Lab for AI in Medical Imaging, Technical University of Munich, Munich, Germany（人工智能医学影像实验室，慕尼黑技术大学，慕尼黑，德国）；Munich Center for Machine Learning, Munich, Germany（慕尼黑机器学习中心，慕尼黑，德国）
