Algorithm 1. Mitigating inappropriate concepts in image generation.

1: Input: text prompt embedding ${\mathcal{P}}_{text}$, inappropriate words embedding ${\mathcal{P}}_{inappr}$, unconditional embedding $\mathrm{\varnothing }$

2: Output: Image without inappropriateness $\mathcal{I}$

3: Initial randomized latent $z_T\sim \mathcal{N}(0,1)$

4: for $t\leftarrow T,\dots ,1$ do

5:  if $t<T-\tau$ then

6:    $z_{t-1}\leftarrow$ DM( $z_t,{\mathcal{P}}_{text},{\mathcal{P}}_{inappr},\mathrm{\varnothing },t$) $\{$

7:    Mtext, $M_{inappr}\leftarrow at{t}_{\epsilon }({\mathcal{P}}_{text},{\mathcal{P}}_{inappr},\mathrm{\varnothing })$

8:     $M_r\leftarrow M_{inappr}-M_{text}$

9:     $M_r\leftarrow \mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}(M_r)$

10:      $M_t\leftarrow M_{text}-\lambda M_r$

11:    $\}$

12:  else

13:    $z_{t-1}\leftarrow$ DM( $z_t,{\mathcal{P}}_{text},\mathrm{\varnothing },t$)

14:  end if

15: end for

16: return $\mathcal{I}\leftarrow Generate(z_0)$