\begin{equation}
\begin{aligned}
    & \mathbb{E}_{X \sim p_{\text{data}}, Z \sim p_{\gamma}(\cdot|X)} \left[ \sum_{y} p_m(y|X) \log  p_\theta(y|X \cdot Z) \right]  \\
    & = \mathbb{E}_{X \sim p_{\text{data}}, Y \sim p_m, Z \sim p_{\gamma}(\cdot|X), \Tilde{X} \sim p_{\iota}(\cdot|X,Z)} [\log p_\theta(Y|\Tilde{X})] \\
    & \leq  \mathbb{E}_{X \sim p_{\text{data}}, Y \sim p_m} [\log \mathbb{E}_{Z \sim p_{\gamma}(\cdot|X), \Tilde{X} \sim p_{\iota}(\cdot|X,Z)} \log p_\theta(Y|\Tilde{X})]
    \, ,
\end{aligned}
\end{equation}
