## 2 Methodology
### Architectural Appearance Generation Module
The feature map \(\mathbf{F}_{z,i}\) is then multiplied by \(\mathbf{w}_{i}\) and \(\mathbf{b}_{i}\), respectively, and the two results are added together to yield the output \(\mathbf{F}_{\mathbf{T},i}\in\mathbb{R}^{H_{i}\times W_{i}\times C_{i}}\). Finally, the resulting feature map \(\mathbf{F}_{i}\in\mathbb{R}^{H_{i}\times W_{i}\times C_{i}}\) of the \(i\)-th STF block is obtained after applying a ReLU activation function. This block is formulated as follows:  
\[\mathbf{w}_{i}=f_{i,1}^{T}(\mathbf{T}) \tag{15}\]  
\[\mathbf{b}_{i}=LeakyReLU\big{(}g_{i}^{T}\big{(}f_{reshape}\Big{(}f_{i,2}^{T}(T) \Big{)}\big{)}\big{)} \tag{16}\]  
\[F_{\mathbf{T},i}^{j,k,l}=w_{i}^{l}\times F_{z,i}^{j,k,l}+b_{i}^{l}\times F_{z,i}^{ j,k,l} \tag{17}\]  
Figure 3:0  
Figure 3:1 Architectures of the sparse and text fusion blocks. The detailed network architecture is shown in Table A2 in Appendix A. MLPs, Conv, DeConv, ReLU, and LeakyReLU denote the multi-layer perceptron, Conv, DeConv, rectified linear unit activation function, and LeakyReLU activation function, respectively. where \(LeakyReLU\) denotes the LeakyReLU activation function; \(f_{i,1}^{T}\) and \(f_{i,2}^{T}\) both denote a single MLP; \(g_{i}^{T}\) is a convolutional layer; and \(f_{reshape}\) denotes the reshaping operation, as shown in Figure 5b. The discriminator is inspired by the Target-Aware discriminator in the DF-GAN [24], demonstrating its ability to ascertain the consistency between input image semantics and text. To ensure a balanced and symmetrical structure with the generator, as well as semantic consistency between the conceptual sketches and input text, a simplified version of the target-aware discriminator is adopted, as shown in Figure 4b. The discriminator converts a sketch into feature maps, denoted as \(\textbf{F}_{6}^{\prime}\in\mathbb{R}^{4\times 4\times 128}\), using a convolutional layer and six DownBlock modules. Subsequently, the feature map \(\textbf{F}_{6}^{\prime}\) with the reshaped text feature \(\textbf{T}^{\prime}\in\mathbb{R}^{4\times 4\times 512}\) along the channels is concatenated. The output of the discriminator determines whether the sketch is semantically consistent with the textual description. To ensure the stability of the adversarial training process, the hinge loss [32] is used as the objective function of the DSTF-GAN. Additionally, the Matching-Aware zero-centered Gradient Penalty (MA-GP) of the DF-GAN [24] is incorporated into the objective function of the discriminator to reinforce the text-image's semantic consistency. The complete loss of the DSTF-GAN is expressed as follows:  
\[ \begin{array}{ll}\mathcal{L}_{D}=&-\mathbb{E}_{\textbf{x}\sim\mathbb{P}_{z }}[\min(0,-1+D(\textbf{x},\textbf{T}))]\\ &-(1/2)\mathbb{E}_{\textbf{z}\sim\mathbb{P}_{z}}[min(0,-1-D(G(\textbf{z}, \textbf{T}),\textbf{T}))]\\ &-(1/2)\mathbb{E}_{\textbf{x}\sim\mathbb{P}_{mis}}[min(0,-1-D(\textbf{x}, \textbf{T}))]\\ &+\mathbb{E}_{\textbf{x}\sim\mathbb{P}_{r}}[(\|\
abla_{\textbf{x}}D(\textbf{x },\textbf{T})\|+\|\
abla_{\textbf{T}}D(\textbf{x},\textbf{T})\|)^{p}]\end{array}  \tag{19}\]  
\[\mathcal{L}_{G}=-\mathbb{E}_{\textbf{z}\sim\mathbb{P}_{z}}[D(G(\textbf{z}, \textbf{T}),\textbf{T})] \tag{20}\]  
where \(z\) is the noise vector; \(\textbf{T}\) is the text feature; \(\mathbb{P}_{r},\mathbb{P}_{z},\text{and}\)\(\mathbb{P}_{mis}\) denote the real data, Gaussian, and mismatched data distributions, respectively; and \(k\) and \(p\) are two hyperparameters to balance the effectiveness of the gradient penalty. The DSTF-GAN is trained using Algorithm 2.