Algorithm 2 Inference of ETDiffIR

Input: LR image $\mu =I_{LR}$, text caption c, total step T. Output: The restored image $I_{HR}$.

1: Initialization: Random sample $x_T\sim \mathcal{N}(0,{\rho }^2)$, $f_{\varphi }$ is the pretrained ERUNet, T = 100. EM is Euler-Maruyama method. 2: for $t=T$ to 1 do 3:    $\tilde{t}=\mathrm{TIFB}(\mu ,c,t)$;                              ▷Enhance 4:    ${\widehat{ϵ}}_t={\widehat{f}}_{\varphi }(x_t,\mu ,c,\tilde{t})$                             ▷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:    $x_{t-1}=x_t-\mathrm{EM}\left(\mathrm{d}{x}_t\right)$;                            ▷Reverse SDE 7:  end for 8: $I_{HR}=x_0$;