Algorithm 1: Unsupervised Virtual Try-on (UVIRT)

Require: The weight of latent $L_1$ loss ${\lambda }_{latent}$, the weight of pixel $L_1$ loss ${\lambda }_{pixel}$, the weight of whitening regularization loss ${\lambda }_w$, the weight of coloring regularization loss ${\lambda }_c$, the batchsize m, Adam hyperparameters $\alpha {\beta }_1,{\beta }_2$

Require: Initial style and content encoder parameters in domain $\mathcal{A}$ and $\mathcal{B}$ ${\varphi }_{s_{\mathcal{A}}},{\varphi }_{s_{\mathcal{B}}},{\varphi }_{c_{\mathcal{A}}},{\varphi }_{c_{\mathcal{B}}}$, initial decoder parameters in domain $\mathcal{A}$ and $\mathcal{B}$${\theta }_{\mathcal{A}},{\theta }_{\mathcal{B}}$, initial discriminator parameters in domain $\mathcal{A}$ and $\mathcal{B}$ ${\psi }_{\mathcal{A}},{\psi }_{\mathcal{B}}$

while$\varphi ,\theta$ has not converged do

for $i=1,\dots ,m$ do

Sample each domain real data $x_{\mathcal{A}}\sim p_{dat{a}_{\mathcal{A}}}\left(x\right),x_{\mathcal{B}}\sim p_{dat{a}_{\mathcal{B}}}\left(x\right)$

$s_{\mathcal{A}},s_{\mathcal{B}}={StyleEncoder}_{{\varphi }_{s_{\mathcal{A}}}}\left(x_{\mathcal{A}}\right),{StyleEncoder}_{{\varphi }_{s_{\mathcal{B}}}}\left(x_{\mathcal{B}}\right)$

$c_{\mathcal{A}},c_{\mathcal{B}}={ContentEncoder}_{{\varphi }_{c_{\mathcal{A}}}}\left(x_{\mathcal{A}}\right),{ContentEncoder}_{{\varphi }_{c_{\mathcal{B}}}}\left(x_{\mathcal{B}}\right)$

$c_{\mathcal{BA}},c_{\mathcal{AB}}={GDWCT}_{{\theta }_{\mathcal{A}}}(c_{\mathcal{B}},s_{\mathcal{A}}),{GDWCT}_{{\theta }_{\mathcal{B}}}(c_{\mathcal{A}},s_{\mathcal{B}})$

$x_{\mathcal{BA}},x_{\mathcal{AB}}={Decoder}_{{\theta }_{\mathcal{A}}}\left(c_{\mathcal{BA}}\right),{Decoder}_{{\theta }_{\mathcal{B}}}\left(c_{\mathcal{AB}}\right)$

${\mathcal{L}}_{D_{adv}}^{\mathcal{A}},{\mathcal{L}}_{G_{adv}}^{\mathcal{A}}\leftarrow \frac{1}{2}{\left(D_{{\psi }_{\mathcal{A}}}\left(x_{\mathcal{A}}\right)-1\right)}^2+\frac{1}{2}{\left(D_{{\psi }_{\mathcal{A}}}\left(x_{\mathcal{BA}}\right)\right)}^2,\frac{1}{2}{\left(D_{{\psi }_{\mathcal{A}}}\left(x_{\mathcal{BA}}\right)-1\right)}^2$

${\mathcal{L}}_{D_{adv}}^{\mathcal{B}},{\mathcal{L}}_{G_{adv}}^{\mathcal{B}}\leftarrow \frac{1}{2}{\left(D_{{\psi }_{\mathcal{B}}}\left(x_{\mathcal{B}}\right)-1\right)}^2+\frac{1}{2}{\left(D_{{\psi }_{\mathcal{B}}}\left(x_{\mathcal{AB}}\right)\right)}^2,\frac{1}{2}{\left(D_{{\psi }_{\mathcal{B}}}\left(x_{\mathcal{AB}}\right)-1\right)}^2$

$\psi \leftarrow Adam\left({\nabla }_{{\psi }_{\mathcal{A}},{\psi }_{\mathcal{B}}}\frac{1}{m}{\sum }_{i=1}^m{\mathcal{L}}_{D_{adv}}^{\mathcal{A}}+{\mathcal{L}}_{D_{adv}}^{\mathcal{B}},{\psi }_{\mathcal{A}}+{\psi }_{\mathcal{B}},\alpha ,{\beta }_1{\beta }_2\right)$

$s_{\mathcal{BA}},s_{\mathcal{AB}}={StyleEncoder}_{{\varphi }_{s_{\mathcal{A}}}}\left(x_{\mathcal{BA}}\right),{StyleEncoder}_{{\varphi }_{s_{\mathcal{B}}}}\left(x_{\mathcal{AB}}\right)$

$c_{\mathcal{BA}},c_{\mathcal{AB}}={ContentEncoder}_{{\varphi }_{c_{\mathcal{A}}}}\left(x_{\mathcal{BA}}\right),{ContentEncoder}_{{\varphi }_{c_{\mathcal{B}}}}\left(x_{\mathcal{AB}}\right)$

$c_{\mathcal{ABA}},c_{\mathcal{BAB}}={GDWCT}_{{\theta }_{\mathcal{A}}}(c_{\mathcal{AB}},s_{\mathcal{BA}}),{GDWCT}_{{\theta }_{\mathcal{B}}}(c_{\mathcal{BA}},s_{\mathcal{AB}})$

$x_{\mathcal{ABA}},x_{\mathcal{BAB}}={Decoder}_{{\theta }_{\mathcal{A}}}\left(c_{\mathcal{ABA}}\right),{Decoder}_{{\theta }_{\mathcal{B}}}\left(c_{\mathcal{BAB}}\right)$

$c_{\mathcal{AA}},c_{\mathcal{BB}}={GDWCT}_{{\theta }_{\mathcal{A}}}(c_{\mathcal{A}},s_{\mathcal{A}}),{GDWCT}_{{\theta }_{\mathcal{B}}}(c_{\mathcal{B}},s_{\mathcal{B}})$

$x_{\mathcal{AA}},x_{\mathcal{BB}}={Decoder}_{{\theta }_{\mathcal{A}}}\left(c_{\mathcal{AA}}\right),{Decoder}_{{\theta }_{\mathcal{B}}}\left(c_{\mathcal{BB}}\right)$

${\mathcal{L}}_s^{\mathcal{BA}},{\mathcal{L}}_s^{\mathcal{AB}}\leftarrow {∥s_{\mathcal{BA}}-s_{\mathcal{A}}∥}_1,{∥s_{\mathcal{AB}}-s_{\mathcal{B}}∥}_1$

${\mathcal{L}}_c^{\mathcal{BA}},{\mathcal{L}}_c^{\mathcal{AB}}\leftarrow {∥c_{\mathcal{BA}}-c_{\mathcal{B}}∥}_1,{∥c_{\mathcal{AB}}-c_{\mathcal{A}}∥}_1$

${\mathcal{L}}_{cyc}^{\mathcal{ABA}},{\mathcal{L}}_{cyc}^{\mathcal{BAB}}\leftarrow {∥x_{\mathcal{ABA}}-x_{\mathcal{A}}∥}_1,{∥x_{\mathcal{BAB}}-x_{\mathcal{B}}∥}_1$

${\mathcal{L}}_i^{\mathcal{AA}},{\mathcal{L}}_i^{\mathcal{BB}}\leftarrow {∥x_{\mathcal{AA}}-x_{\mathcal{A}}∥}_1,{∥x_{\mathcal{BB}}-x_{\mathcal{B}}∥}_1$

${\Sigma }_c^{\mathcal{B}},{\Sigma }_c^{\mathcal{A}}=ComputeCovariance\left(c_{\mathcal{B}}\right),ComputeCovariance\left(c_{\mathcal{A}}\right)$

${\mathcal{R}}_w^{\mathcal{B}},{\mathcal{R}}_w^{\mathcal{A}}\leftarrow {∥{\Sigma }_c^{\mathcal{B}}-I∥}_1,{∥{\Sigma }_c^{\mathcal{A}}-I∥}_1$

$U{D}^{\mathcal{A}},U{D}^{\mathcal{B}}=s_{\mathcal{A}}^{CT},s_{\mathcal{B}}^{CT}$

$D^{\mathcal{A}},D^{\mathcal{B}}=Compute{L}_{2}Norm\left(s_{\mathcal{A}}^{CT}\right),Compute{L}_{2}Norm\left(s_{\mathcal{B}}^{CT}\right)$

$U^{\mathcal{A}},U^{\mathcal{B}}=\frac{U{D}^{\mathcal{A}}}{D^{\mathcal{A}}},\frac{U{D}^{\mathcal{B}}}{D^{\mathcal{B}}}$

${\mathcal{R}}_c^{\mathcal{A}},{\mathcal{R}}_c^{\mathcal{B}}\leftarrow {∥U_{\mathcal{A}}^T{U}_{\mathcal{A}}-I∥}_1,{∥U_{\mathcal{B}}^T{U}_{\mathcal{B}}-I∥}_1$

$\varphi ,\theta \leftarrow Adam({\nabla }_{{\varphi }_{s_{\mathcal{A}}},{\varphi }_{s_{\mathcal{B}}},{\varphi }_{c_{\mathcal{A}}},{\varphi }_{c_{\mathcal{B}}},{\theta }_{\mathcal{A}},{\theta }_{\mathcal{B}}}\frac{1}{m}{\sum }_{i=1}^m{\lambda }_{lantent}\left({\mathcal{L}}_s^{\mathcal{BA}}+{\mathcal{L}}_s^{\mathcal{AB}}+{\mathcal{L}}_c^{\mathcal{BA}}+{\mathcal{L}}_c^{\mathcal{AB}}\right)+$

${\lambda }_{pixel}\left({\mathcal{L}}_{cyc}^{\mathcal{ABA}}+{\mathcal{L}}_{cyc}^{\mathcal{BAB}}+{\mathcal{L}}_i^{\mathcal{AA}}+{\mathcal{L}}_i^{\mathcal{BB}}\right)+{\lambda }_w\left({\mathcal{R}}_w^{\mathcal{B}}+{\mathcal{R}}_w^{\mathcal{A}}\right)+{\lambda }_c\left({\mathcal{R}}_c^{\mathcal{B}}+{\mathcal{R}}_c^{\mathcal{A}}\right)+{\mathcal{L}}_{D_{adv}}^{\mathcal{B}}+{\mathcal{L}}_{G_{adv}}^{\mathcal{B}},$

${\varphi }_{s_{\mathcal{A}}}+{\varphi }_{s_{\mathcal{B}}}+{\varphi }_{c_{\mathcal{A}}}+{\varphi }_{c_{\mathcal{B}}}+{\theta }_{\mathcal{A}}+{\theta }_{\mathcal{B}},\alpha ,{\beta }_1{\beta }_2)$

end for

end while