DDPM中建模的$q(\mathbf{x}_{t-1} \vert \mathbf{x}_t, \mathbf{x}_0)$满足正态分布， $$ q(\mathbf{x}_{t-1} \vert \mathbf{x}_t, \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_{t-1}; \tilde{\boldsymbol{\mu}}(\mathbf{x}_t, \mathbf{x}_0), \tilde{\beta}_t \mathbf{I}) \\ \tilde{\beta}_t = \frac{1 - \bar{\alpha}_{t-1}}{1 - \bar{\alpha}_t} \cdot \beta_t $$ DDIM中建模的$q_\sigma(\mathbf{x}_{t-1} \vert \mathbf{x}_t, \mathbf{x}_0)$如下，第一个等式二三步用到了重参数技巧和多个独立高斯分布的等价形式， $$ \begin{aligned} \mathbf{x}_{t-1} &= \sqrt{\bar{\alpha}_{t-1}
Axuanz
Updating as per fate.
