\begin{equation}
\begin{aligned}
    & \mathcal{L}_{\mathrm{R}}^{\mathrm{BCE}}  \\
    =&  E_{q_\phi\left(\boldsymbol{z} \mid \boldsymbol{x}\right)}\left[\log p_\theta\left(\boldsymbol{x} \mid \boldsymbol{z}\right)\right]\\
    =& E_{q_\phi\left(\boldsymbol{z} \mid \boldsymbol{x}\right)}\left[\sum_{d=1}^D \boldsymbol{x}_{d} \log \lambda_{\theta, d}\left(\boldsymbol{z}\right)+\left(1-\boldsymbol{x}_{d}\right) \log \left(1-\lambda_{\theta, d}\left(\boldsymbol{z}\right)\right)\right],
\end{aligned}
\end{equation}
