Thanks.I have not used non-differentiable functions.Here is the code:
solver.py
class Solver(nn.Module):
    def __init__(self, args):
        super().__init__()
        self.args = args
        self.device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

        self.nets, self.nets_ema = build_model(args)
        # below setattrs are to make networks be children of Solver, e.g., for self.to(self.device)
        for name, module in self.nets.items():
            utils.print_network(module, name)
            setattr(self, name, module)
        for name, module in self.nets_ema.items():
            setattr(self, name + '_ema', module)

        if args.mode == 'train':
            self.optims = Munch()
            for net in self.nets.keys():
                if net == 'fan':
                    continue
                self.optims[net] = torch.optim.Adam(
                    params=self.nets[net].parameters(),
                    lr=args.f_lr if net == 'mapping_network' else args.lr,
                    betas=[args.beta1, args.beta2],
                    weight_decay=args.weight_decay)

            self.ckptios = [
                CheckpointIO(ospj(args.checkpoint_dir, '{:06d}_nets.ckpt'), **self.nets),
                CheckpointIO(ospj(args.checkpoint_dir, '{:06d}_nets_ema.ckpt'), **self.nets_ema),
                CheckpointIO(ospj(args.checkpoint_dir, '{:06d}_optims.ckpt'), **self.optims)]
        else:
            self.ckptios = [CheckpointIO(ospj(args.checkpoint_dir, '{:06d}_nets_ema.ckpt'), **self.nets_ema)]

        self.to(self.device)
        for name, network in self.named_children():
            # Do not initialize the FAN parameters
            if ('ema' not in name) and ('fan' not in name):
                print('Initializing %s...' % name)
                network.apply(utils.he_init)

    def _save_checkpoint(self, step):
        for ckptio in self.ckptios:
            ckptio.save(step)

    def _load_checkpoint(self, step):
        for ckptio in self.ckptios:
            ckptio.load(step)

    def _reset_grad(self):
        for optim in self.optims.values():
            optim.zero_grad()

    def train(self, loaders):
        args = self.args
        nets = self.nets
        nets_ema = self.nets_ema
        optims = self.optims

        # fetch random validation images for debugging
        fetcher = InputFetcher(loaders.src, loaders.ref, args.latent_dim, 'train')
        fetcher_val = InputFetcher(loaders.val, None, args.latent_dim, 'val')
        inputs_val = next(fetcher_val)

        # resume training if necessary
        if args.resume_iter > 0:
            self._load_checkpoint(args.resume_iter)

        # remember the initial value of ds weight
        initial_lambda_ds = args.lambda_ds

        print('Start training...')
        start_time = time.time()
        for i in range(args.resume_iter, args.total_iters):
            # fetch images and labels
            inputs = next(fetcher)
            x_real, y_org = inputs.x_src, inputs.y_src
            x_ref, x_ref2, y_trg = inputs.x_ref, inputs.x_ref2, inputs.y_ref
            z_trg, z_trg2 = inputs.z_trg, inputs.z_trg2

            masks = nets.fan.get_heatmap(x_real) if args.w_hpf > 0 else None

            # train the discriminator
            d_loss, d_losses_latent = compute_d_loss(
                nets, args, x_real, y_org, y_trg, z_trg=z_trg, masks=masks)
            self._reset_grad()
            d_loss.backward()
            optims.discriminator.step()

            d_loss, d_losses_ref = compute_d_loss(
                nets, args, x_real, y_org, y_trg, x_ref=x_ref, masks=masks)
            self._reset_grad()
            d_loss.backward()
            optims.discriminator.step()

            # train the generator
            g_loss, g_losses_latent = compute_g_loss(
                nets, args, x_real, y_org, y_trg, z_trgs=[z_trg, z_trg2], masks=masks)
            self._reset_grad()
            g_loss.backward()
            optims.generator.step()
            optims.mapping_network.step()
            optims.style_encoder.step()

            g_loss, g_losses_ref = compute_g_loss(
                nets, args, x_real, y_org, y_trg, x_refs=[x_ref, x_ref2], masks=masks)
            self._reset_grad()
            g_loss.backward()
            optims.generator.step()

            # compute moving average of network parameters
            moving_average(nets.generator, nets_ema.generator, beta=0.999)
            moving_average(nets.mapping_network, nets_ema.mapping_network, beta=0.999)
            moving_average(nets.style_encoder, nets_ema.style_encoder, beta=0.999)

            # decay weight for diversity sensitive loss
            if args.lambda_ds > 0:
                args.lambda_ds -= (initial_lambda_ds / args.ds_iter)

            # print out log info
            if (i+1) % args.print_every == 0:
                elapsed = time.time() - start_time
                elapsed = str(datetime.timedelta(seconds=elapsed))[:-7]
                log = "Elapsed time [%s], Iteration [%i/%i], " % (elapsed, i+1, args.total_iters)
                all_losses = dict()
                for loss, prefix in zip([d_losses_latent, d_losses_ref, g_losses_latent, g_losses_ref],
                                        ['D/latent_', 'D/ref_', 'G/latent_', 'G/ref_']):
                    for key, value in loss.items():
                        all_losses[prefix + key] = value
                all_losses['G/lambda_ds'] = args.lambda_ds
                log += ' '.join(['%s: [%.4f]' % (key, value) for key, value in all_losses.items()])
                print(log)

            # generate images for debugging
            if (i+1) % args.sample_every == 0:
                os.makedirs(args.sample_dir, exist_ok=True)
                utils.debug_image(nets_ema, args, inputs=inputs_val, step=i+1)

            # save model checkpoints
            if (i+1) % args.save_every == 0:
                self._save_checkpoint(step=i+1)

            # compute FID and LPIPS if necessary
            if (i+1) % args.eval_every == 0:
                calculate_metrics(nets_ema, args, i+1, mode='latent')
                calculate_metrics(nets_ema, args, i+1, mode='reference')

    @torch.no_grad()
    def sample(self, loaders):
        args = self.args
        nets_ema = self.nets_ema
        os.makedirs(args.result_dir, exist_ok=True)
        self._load_checkpoint(args.resume_iter)

        src = next(InputFetcher(loaders.src, None, args.latent_dim, 'test'))
        ref = next(InputFetcher(loaders.ref, None, args.latent_dim, 'test'))

        fname = ospj(args.result_dir, 'reference.jpg')
        print('Working on {}...'.format(fname))
        utils.translate_using_reference(nets_ema, args, src.x, ref.x, ref.y, fname)

        fname = ospj(args.result_dir, 'video_ref.mp4')
        print('Working on {}...'.format(fname))
        utils.video_ref(nets_ema, args, src.x, ref.x, ref.y, fname)

    @torch.no_grad()
    def evaluate(self):
        args = self.args
        nets_ema = self.nets_ema
        resume_iter = args.resume_iter
        self._load_checkpoint(args.resume_iter)
        calculate_metrics(nets_ema, args, step=resume_iter, mode='latent')
        calculate_metrics(nets_ema, args, step=resume_iter, mode='reference')


def compute_d_loss(nets, args, x_real, y_org, y_trg, z_trg=None, x_ref=None, masks=None):
    assert (z_trg is None) != (x_ref is None)
    # with real images
    x_real.requires_grad_()
    out = nets.discriminator(x_real, y_org)
    print(out.grad_fn)
    loss_real = adv_loss(out, 1)
    loss_reg = r1_reg(out, x_real)

    # with fake images
    with torch.no_grad():
        if z_trg is not None:
            s_trg = nets.mapping_network(z_trg, y_trg)
        else:  # x_ref is not None
            s_trg = nets.style_encoder(x_ref, y_trg)

        x_fake = nets.generator(x_real, s_trg, masks=masks)
    out = nets.discriminator(x_fake, y_trg)
    loss_fake = adv_loss(out, 0)

    loss = loss_real + loss_fake + args.lambda_reg * loss_reg
    return loss, Munch(real=loss_real.item(),
                       fake=loss_fake.item(),
                       reg=loss_reg.item())


def compute_g_loss(nets, args, x_real, y_org, y_trg, z_trgs=None, x_refs=None, masks=None):
    assert (z_trgs is None) != (x_refs is None)
    if z_trgs is not None:
        z_trg, z_trg2 = z_trgs
    if x_refs is not None:
        x_ref, x_ref2 = x_refs

    x_real.requires_grad_()
    # adversarial loss
    if z_trgs is not None:
        s_trg = nets.mapping_network(z_trg, y_trg)
    else:
        s_trg = nets.style_encoder(x_ref, y_trg)

    x_fake = nets.generator(x_real, s_trg, masks=masks)
    out = nets.discriminator(x_fake, y_trg)
    loss_adv = adv_loss(out, 1)

    # style reconstruction loss
    s_pred = nets.style_encoder(x_fake, y_trg)
    loss_sty = torch.mean(torch.abs(s_pred - s_trg))

    # diversity sensitive loss
    if z_trgs is not None:
        s_trg2 = nets.mapping_network(z_trg2, y_trg)
    else:
        s_trg2 = nets.style_encoder(x_ref2, y_trg)
    x_fake2 = nets.generator(x_real, s_trg2, masks=masks)
    x_fake2 = x_fake2
    #x_fake2 = x_fake2.detach()
    loss_ds = torch.mean(torch.abs(x_fake - x_fake2))

    # cycle-consistency loss
    masks = nets.fan.get_heatmap(x_fake) if args.w_hpf > 0 else None
    s_org = nets.style_encoder(x_real, y_org)
    x_rec = nets.generator(x_fake, s_org, masks=masks)
    loss_cyc = torch.mean(torch.abs(x_rec - x_real))

    loss = loss_adv + args.lambda_sty * loss_sty \
        - args.lambda_ds * loss_ds + args.lambda_cyc * loss_cyc
    return loss, Munch(adv=loss_adv.item(),
                       sty=loss_sty.item(),
                       ds=loss_ds.item(),
                       cyc=loss_cyc.item())


def moving_average(model, model_test, beta=0.999):
    for param, param_test in zip(model.parameters(), model_test.parameters()):
        param_test.data = torch.lerp(param.data, param_test.data, beta)


def adv_loss(logits, target):
    assert target in [1, 0]
    targets = torch.full_like(logits, fill_value=target)
    loss = F.binary_cross_entropy_with_logits(logits, targets)
    return loss


def r1_reg(d_out, x_in):
    # zero-centered gradient penalty for real images
    batch_size = x_in.size(0)
    grad_dout = torch.autograd.grad(
        outputs=d_out.sum(), inputs=x_in,
        create_graph=True, retain_graph=True, only_inputs=True
    )[0]
    grad_dout2 = grad_dout.pow(2)
    assert(grad_dout2.size() == x_in.size())
    reg = 0.5 * grad_dout2.view(batch_size, -1).sum(1).mean(0)
    return reg

model.py
class ResBlk(nn.Module):
    def __init__(self, dim_in, dim_out, actv=nn.LeakyReLU(0.2),
                 normalize=False, downsample=False):
        super().__init__()
        self.actv = actv
        self.normalize = normalize
        self.downsample = downsample
        self.learned_sc = dim_in != dim_out
        self._build_weights(dim_in, dim_out)

    def _build_weights(self, dim_in, dim_out):
        self.conv1 = nn.Conv2d(dim_in, dim_in, 3, 1, 1)
        self.conv2 = nn.Conv2d(dim_in, dim_out, 3, 1, 1)
        if self.normalize:
            self.norm1 = nn.InstanceNorm2d(dim_in, affine=True)
            self.norm2 = nn.InstanceNorm2d(dim_in, affine=True)
        if self.learned_sc:
            self.conv1x1 = nn.Conv2d(dim_in, dim_out, 1, 1, 0, bias=False)

    def _shortcut(self, x):
        if self.learned_sc:
            x = self.conv1x1(x)
        if self.downsample:
            x = F.avg_pool2d(x, 2)
        return x

    def _residual(self, x):
        if self.normalize:
            x = self.norm1(x)
        x = self.actv(x)
        x = self.conv1(x)
        if self.downsample:
            x = F.avg_pool2d(x, 2)
        if self.normalize:
            x = self.norm2(x)
        x = self.actv(x)
        x = self.conv2(x)
        return x

    def forward(self, x):
        x = self._shortcut(x) + self._residual(x)
        return x / math.sqrt(2)  # unit variance


class AdaIN(nn.Module):
    def __init__(self, style_dim, num_features):
        super().__init__()
        self.norm = nn.InstanceNorm2d(num_features, affine=False)
        self.fc = nn.Linear(style_dim, num_features*2)

    def forward(self, x, s):
        h = self.fc(s)
        h = h.view(h.size(0), h.size(1), 1, 1)
        gamma, beta = torch.chunk(h, chunks=2, dim=1)
        return (1 + gamma) * self.norm(x) + beta


class AdainResBlk(nn.Module):
    def __init__(self, dim_in, dim_out, style_dim=64, w_hpf=0,
                 actv=nn.LeakyReLU(0.2), upsample=False):
        super().__init__()
        self.w_hpf = w_hpf
        self.actv = actv
        self.upsample = upsample
        self.learned_sc = dim_in != dim_out
        self._build_weights(dim_in, dim_out, style_dim)

    def _build_weights(self, dim_in, dim_out, style_dim=64):
        self.conv1 = nn.Conv2d(dim_in, dim_out, 3, 1, 1)
        self.conv2 = nn.Conv2d(dim_out, dim_out, 3, 1, 1)
        self.norm1 = AdaIN(style_dim, dim_in)
        self.norm2 = AdaIN(style_dim, dim_out)
        if self.learned_sc:
            self.conv1x1 = nn.Conv2d(dim_in, dim_out, 1, 1, 0, bias=False)

    def _shortcut(self, x):
        if self.upsample:
            x = F.interpolate(x, scale_factor=2, mode='nearest')
        if self.learned_sc:
            x = self.conv1x1(x)
        return x

    def _residual(self, x, s):
        x = self.norm1(x, s)
        x = self.actv(x)
        if self.upsample:
            x = F.interpolate(x, scale_factor=2, mode='nearest')
        x = self.conv1(x)
        x = self.norm2(x, s)
        x = self.actv(x)
        x = self.conv2(x)
        return x

    def forward(self, x, s):
        out = self._residual(x, s)
        if self.w_hpf == 0:
            out = (out + self._shortcut(x)) / math.sqrt(2)
        return out


class HighPass(nn.Module):
    def __init__(self, w_hpf, device):
        super(HighPass, self).__init__()
        self.filter = torch.tensor([[-1, -1, -1],
                                    [-1, 8., -1],
                                    [-1, -1, -1]]).to(device) / w_hpf

    def forward(self, x):
        filter = self.filter.unsqueeze(0).unsqueeze(1).repeat(x.size(1), 1, 1, 1)
        return F.conv2d(x, filter, padding=1, groups=x.size(1))


class Generator(nn.Module):
    def __init__(self, img_size=256, style_dim=64, max_conv_dim=512, w_hpf=1):
        super().__init__()
        dim_in = 2**14 // img_size
        self.img_size = img_size
        self.from_rgb = nn.Conv2d(3, dim_in, 3, 1, 1)
        self.encode = nn.ModuleList()
        self.decode = nn.ModuleList()
        self.to_rgb = nn.Sequential(
            nn.InstanceNorm2d(dim_in, affine=True),
            nn.LeakyReLU(0.2),
            nn.Conv2d(dim_in, 3, 1, 1, 0))

        # down/up-sampling blocks
        repeat_num = int(np.log2(img_size)) - 4
        if w_hpf > 0:
            repeat_num += 1
        for _ in range(repeat_num):
            dim_out = min(dim_in*2, max_conv_dim)
            self.encode.append(
                ResBlk(dim_in, dim_out, normalize=True, downsample=True))
            self.decode.insert(
                0, AdainResBlk(dim_out, dim_in, style_dim,
                               w_hpf=w_hpf, upsample=True))  # stack-like
            dim_in = dim_out

        # bottleneck blocks
        for _ in range(2):
            self.encode.append(
                ResBlk(dim_out, dim_out, normalize=True))
            self.decode.insert(
                0, AdainResBlk(dim_out, dim_out, style_dim, w_hpf=w_hpf))

        if w_hpf > 0:
            device = torch.device(
                'cuda' if torch.cuda.is_available() else 'cpu')
            self.hpf = HighPass(w_hpf, device)

    def forward(self, x, s, masks=None):
        x = self.from_rgb(x)
        cache = {}
        for block in self.encode:
            if (masks is not None) and (x.size(2) in [32, 64, 128]):
                cache[x.size(2)] = x
            x = block(x)
        for block in self.decode:
            x = block(x, s)
            if (masks is not None) and (x.size(2) in [32, 64, 128]):
                mask = masks[0] if x.size(2) in [32] else masks[1]
                mask = F.interpolate(mask, size=x.size(2), mode='bilinear')
                x = x + self.hpf(mask * cache[x.size(2)])
        return self.to_rgb(x)


class MappingNetwork(nn.Module):
    def __init__(self, latent_dim=16, style_dim=64, num_domains=2):
        super().__init__()
        layers = []
        layers += [nn.Linear(latent_dim, 512)]
        layers += [nn.ReLU()]
        for _ in range(3):
            layers += [nn.Linear(512, 512)]
            layers += [nn.ReLU()]
        self.shared = nn.Sequential(*layers)

        self.unshared = nn.ModuleList()
        for _ in range(num_domains):
            self.unshared += [nn.Sequential(nn.Linear(512, 512),
                                            nn.ReLU(),
                                            nn.Linear(512, 512),
                                            nn.ReLU(),
                                            nn.Linear(512, 512),
                                            nn.ReLU(),
                                            nn.Linear(512, style_dim))]

    def forward(self, z, y):
        h = self.shared(z)
        out = []
        for layer in self.unshared:
            out += [layer(h)]
        out = torch.stack(out, dim=1)  # (batch, num_domains, style_dim)
        idx = torch.LongTensor(range(y.size(0))).to(y.device)
        s = out[idx, y]  # (batch, style_dim)
        return s


class StyleEncoder(nn.Module):
    def __init__(self, img_size=256, style_dim=64, num_domains=2, max_conv_dim=512):
        super().__init__()
        dim_in = 2**14 // img_size
        blocks = []
        blocks += [nn.Conv2d(3, dim_in, 3, 1, 1)]

        repeat_num = int(np.log2(img_size)) - 2
        for _ in range(repeat_num):
            dim_out = min(dim_in*2, max_conv_dim)
            blocks += [ResBlk(dim_in, dim_out, downsample=True)]
            dim_in = dim_out

        blocks += [nn.LeakyReLU(0.2)]
        blocks += [nn.Conv2d(dim_out, dim_out, 4, 1, 0)]
        blocks += [nn.LeakyReLU(0.2)]
        self.shared = nn.Sequential(*blocks)

        self.unshared = nn.ModuleList()
        for _ in range(num_domains):
            self.unshared += [nn.Linear(dim_out, style_dim)]

    def forward(self, x, y):
        h = self.shared(x)
        h = h.view(h.size(0), -1)
        out = []
        for layer in self.unshared:
            out += [layer(h)]
        out = torch.stack(out, dim=1)  # (batch, num_domains, style_dim)
        idx = torch.LongTensor(range(y.size(0))).to(y.device)
        s = out[idx, y]  # (batch, style_dim)
        return s


class Discriminator(nn.Module):
    def __init__(self, img_size=256, num_domains=2, max_conv_dim=512):
        super().__init__()
        dim_in = 2**14 // img_size
        blocks = []
        blocks += [nn.Conv2d(3, dim_in, 3, 1, 1)]

        repeat_num = int(np.log2(img_size)) - 2
        for _ in range(repeat_num):
            dim_out = min(dim_in*2, max_conv_dim)
            blocks += [ResBlk(dim_in, dim_out, downsample=True)]
            dim_in = dim_out

        blocks += [nn.LeakyReLU(0.2)]
        blocks += [nn.Conv2d(dim_out, dim_out, 4, 1, 0)]
        blocks += [nn.LeakyReLU(0.2)]
        blocks += [nn.Conv2d(dim_out, num_domains, 1, 1, 0)]
        self.main = nn.Sequential(*blocks)

    def forward(self, x, y):
        out = self.main(x)
        out = out.view(out.size(0), -1)  # (batch, num_domains)
        idx = torch.LongTensor(range(y.size(0))).to(y.device)
        out = out[idx, y]  # (batch)
        return out


def build_model(args):
    generator = Generator(args.img_size, args.style_dim, w_hpf=args.w_hpf)
    mapping_network = MappingNetwork(args.latent_dim, args.style_dim, args.num_domains)
    style_encoder = StyleEncoder(args.img_size, args.style_dim, args.num_domains)
    discriminator = Discriminator(args.img_size, args.num_domains)
    generator_ema = copy.deepcopy(generator)
    mapping_network_ema = copy.deepcopy(mapping_network)
    style_encoder_ema = copy.deepcopy(style_encoder)

    nets = Munch(generator=generator,
                 mapping_network=mapping_network,
                 style_encoder=style_encoder,
                 discriminator=discriminator)
    nets_ema = Munch(generator=generator_ema,
                     mapping_network=mapping_network_ema,
                     style_encoder=style_encoder_ema)

    if args.w_hpf > 0:
        fan = FAN(fname_pretrained=args.wing_path).eval()
        nets.fan = fan
        nets_ema.fan = fan

    return nets, nets_ema