Question about Eq.7 and its detailed proofs in supplement

[Henry-Bi]

Thanks for your great works! In 'ExposureDiffusion: Learning to Expose for Low-light Image Enhancement Supplementary Material' 1. Detail of proofs, there might exist a error.

$$\mathbb{E}_{q\left(X_{r e f}\right)}\left[\mathbb{E}_{p_{\Theta}\left(X_{0: T}\right)}\left[\frac{p_{\Theta}\left(X_T\right)}{q\left(X_T \mid X_{r e f}\right)}+\sum_{t=1}^T \log \frac{p_{\Theta}\left(X_{t-1} \mid X_t\right)}{q\left(X_{t-1} \mid X_t, X_{r e f}\right)}\right]\right]$$

should be

$$\mathbb{E}_{q\left(X_{r e f}\right)}\left[\mathbb{E}_{p_{\Theta}\left(X_{0: T}\right)}\left[\log \frac{p_{\Theta}\left(X_T\right)}{q\left(X_T \mid X_{r e f}\right)}+\sum_{t=1}^T \log \frac{p_{\Theta}\left(X_{t-1} \mid X_t\right)}{q\left(X_{t-1} \mid X_t, X_{r e f}\right)}\right]\right]$$