https://yiwen-cai.github.io/tags/flow-matching/Recent content in Flow Matching on Yiwen CaiHugo -- gohugo.iozh-cncaiyiwen.cs@foxmail.com (Yiwen Cai)caiyiwen.cs@foxmail.com (Yiwen Cai)© 2026 Yiwen CaiFri, 11 Sep 2026 17:20:09 +0800https://yiwen-cai.github.io/notes/diffusion/score-based-diffusion/Fri, 11 Sep 2026 00:00:00 +0000caiyiwen.cs@foxmail.com (Yiwen Cai)https://yiwen-cai.github.io/notes/diffusion/score-based-diffusion/从条件 score 的后验平均出发，推导高斯路径下 score、去噪器与速度场的转换，用 Fokker–Planck 方程解释如何给 ODE 加噪而保持边缘分布，并将 score matching 化为噪声回归。https://yiwen-cai.github.io/notes/diffusion/flow-matching/Wed, 02 Sep 2026 00:00:00 +0000caiyiwen.cs@foxmail.com (Yiwen Cai)https://yiwen-cai.github.io/notes/diffusion/flow-matching/Flow Matching 通过回归可解析的条件向量场，间接学到边缘向量场，实现 simulation-free 训练。涵盖条件概率路径、边缘化技巧、连续性方程与 Gaussian CondOT 的完整推导。https://yiwen-cai.github.io/notes/diffusion/generative-modeling/Tue, 01 Sep 2026 00:00:00 +0000caiyiwen.cs@foxmail.com (Yiwen Cai)https://yiwen-cai.github.io/notes/diffusion/generative-modeling/生成建模的核心任务不是寻找唯一的「最佳答案」，而是学习一个未知的数据分布并从中采样：把图像、视频、分子统一表示为向量，用有限数据集逼近 p_data，并区分无条件生成与条件生成。https://yiwen-cai.github.io/notes/diffusion/flow-and-diffusion-models/Tue, 01 Sep 2026 00:00:00 +0000caiyiwen.cs@foxmail.com (Yiwen Cai)https://yiwen-cai.github.io/notes/diffusion/flow-and-diffusion-models/深入解析连续时间生成模型的基础范式：从向量场定义、ODE 与 Flow 映射，到布朗运动、SDE 随机动力学及数值模拟（Euler 与 Euler-Maruyama 方法），建立确定性流与随机扩散的统一视角。