Algorithm 1 Training of ETDiffIR

Input:LR image $\mu =I_{LR}$, HR image $x_0=I_{HR}$, text caption c, total step T. 1: Initialization: Random sample ${ϵ}_t\sim \mathcal{N}(0,{\rho }^2)$, $t\in [0,T]$, $T=100$. 2: repeat 3:    $\tilde{t}=\mathrm{TIFB}(\mu ,c,t)$;                              ▷Enhance 4:    ${\widehat{ϵ}}_t={\widehat{f}}_{\varphi }(I_t,c,\tilde{t})$;                           ▷Predict noise 5:    $\mathrm{d}x=[{\alpha }_t(\mu -x)-{\beta }_t^2{\nabla }_{x}log{q}_t\left(x\right)]\mathrm{d}t+{\beta }_t\mathrm{d}\tilde{w}$;    ▷Substitute score into Equation (6) 6:    $\mathcal{L}\left(\varphi \right)={\Sigma }_{t=0}^T{\gamma }_t\mathbb{E}[\parallel \stackrel{\mathrm{reversed}{x}_{t-1}}{\overbrace{x_t-{\left(\mathrm{d}{x}_t\right)}_{{\widehat{f}}_{\varphi }}}}-x_{t-1}^{\ast }\parallel ]$;                    ▷Loss 7:    ${\nabla }_{\varphi }\mathcal{L}$;                               ▷Gradient descent 8:until converged