Score-Matching on Xu'Bloghttps://xuquant.com/tags/score-matching/Recent content in Score-Matching on Xu'BlogXu'Bloghttps://xuquant.com/og-default.pnghttps://xuquant.com/og-default.pngHugo -- 0.152.2zhMon, 11 May 2026 09:00:00 +0800得分匹配、GAN 与生成模型的统一https://xuquant.com/posts/mathematics/probability/score-matching-gan/Mon, 11 May 2026 09:00:00 +0800https://xuquant.com/posts/mathematics/probability/score-matching-gan/从 Hyvarinen 得分匹配到去噪得分匹配，从 GAN 的对抗训练到得分函数，建立 VAE、GAN、扩散模型在分布匹配框架下的统一理解。变分自编码器：从 ELBO 到重参数化https://xuquant.com/posts/mathematics/probability/vae-elbo/Sat, 02 May 2026 09:00:00 +0800https://xuquant.com/posts/mathematics/probability/vae-elbo/从生成模型的推断难题出发，推导 ELBO 的两种等价形式，解释重参数化技巧的必要性，分析 VAE 的信息瓶颈与后验坍塌问题。扩散模型的 SDE/ODE 统一：随机微分方程到确定性采样https://xuquant.com/posts/mathematics/diffusion/sde-ode-unified/Wed, 22 Apr 2026 09:00:00 +0800https://xuquant.com/posts/mathematics/diffusion/sde-ode-unified/从离散马尔可夫链推导连续 SDE 极限，建立概率流 ODE 的严格推导，解释得分函数的几何意义与朗之万动力学的等价性。扩散模型的变分基础：从 ELBO 到去噪https://xuquant.com/posts/mathematics/diffusion/ddpm-variational/Sat, 18 Apr 2026 09:00:00 +0800https://xuquant.com/posts/mathematics/diffusion/ddpm-variational/从 ELBO 推导 DDPM 的变分下界，解释三项分解的物理意义，证明预测噪声与预测数据的等价性，建立扩散训练的变分理解。扩散模型与自动驾驶规划：从去噪的数学到轨迹的生成https://xuquant.com/posts/autonomous-driving/diffusion-for-driving/Sat, 08 Nov 2025 10:00:00 +0800https://xuquant.com/posts/autonomous-driving/diffusion-for-driving/面向自动驾驶的扩散模型原理深度梳理：从 DDPM 的变分推断到 Flow Matching 的直线耦合，从 Classifier-Free Guidance 的条件控制到 Truncated Diffusion 的截断加速——理解每一步'为什么'而非仅仅是'怎么做'。