VAE on Xu'Bloghttps://xuquant.com/tags/vae/Recent content in VAE on Xu'BlogXu'Bloghttps://xuquant.com/og-default.pnghttps://xuquant.com/og-default.pngHugo -- 0.152.2zhMon, 25 May 2026 20:00:00 +0800熵与信息论：从 -log p 到深度学习https://xuquant.com/posts/mathematics/probability/entropy-and-information/Mon, 25 May 2026 20:00:00 +0800https://xuquant.com/posts/mathematics/probability/entropy-and-information/从公理化角度推出 -log p 的必然性，依次过熵、互信息、KL 散度、最大熵原理，再回到深度学习里反复出现的几种形态——交叉熵损失、ELBO、信息瓶颈、最大熵强化学习。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。