Algorithm 1.

Training of SADI

Input: distribution $q_k\left({\mathbf{x}}_0\right)$ and the corresponding weight $c_k$ for $k\in \left[K\right]$, target selection strategy, training epochs $N$, maximum number of diffusion steps $S$, noise level ${\left\{{\beta }_s\right\}}_{s=1}^S$
Output: Trained denoising function ${\mathit{ϵ}}_{\theta }$
1:	for $i\in \{1,\dots ,N\}$ do
2:	Sample $k\sim 𝒞\left\{c_1,c_2,\dots ,c_K\right\}$
3:	Sample $s\sim \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\{1,\dots ,S\}$, and ${\mathbf{x}}_0\sim q_k\left({\mathbf{x}}_0\right)$
4:	Separate observed values ${\mathbf{x}}_0$ into target part ${\mathbf{x}}_0^{ta}$ and conditional part ${\mathbf{x}}_0^{co}$ by the target selection strategy
5:	Sample $\mathit{ϵ}\sim 𝒩(0,\mathbf{I})$ where the dimension of $\mathit{ϵ}$ corresponds to ${\mathbf{x}}_0^{ta}$
6:	Calculate noisy targets ${\mathbf{x}}_s^{ta}=\sqrt{{\bar{\alpha }}_s}{\mathbf{x}}_0^{ta}+\sqrt{1-{\bar{\alpha }}_s}\mathit{ϵ}$
7:	Take gradient step on $\nabla {∥\mathit{ϵ}-{\mathit{ϵ}}_{\theta }\left({\mathbf{x}}_s^{ta},s\mid {\mathbf{x}}_0^{co}\right)∥}_2^2$
8:	end for