def forward_mas(self, outputs, z_p, m_p, logs_p, x, x_mask, y_mask, g, lang_emb, noise_scale=0.01):
        # find the alignment path
        attn_mask = torch.unsqueeze(x_mask, -1) * torch.unsqueeze(y_mask, 2)
        with torch.no_grad():
            o_scale = torch.exp(-2 * logs_p)
            logp1 = torch.sum(-0.5 * math.log(2 * math.pi) - logs_p, [1]).unsqueeze(-1)  # [b, t, 1]
            logp2 = torch.einsum("klm, kln -> kmn", [o_scale, -0.5 * (z_p**2)])
            logp3 = torch.einsum("klm, kln -> kmn", [m_p * o_scale, z_p])
            logp4 = torch.sum(-0.5 * (m_p**2) * o_scale, [1]).unsqueeze(-1)  # [b, t, 1]
            logp = logp2 + logp3 + logp1 + logp4
            
            # Adding Gaussian noise to the log probabilities
            epsilon = torch.randn_like(logp) * torch.std(logp) * noise_scale
            logp += epsilon
            
            attn = maximum_path(logp, attn_mask.squeeze(1)).unsqueeze(1).detach()  # [b, 1, t, t']

        # duration predictor
        attn_durations = attn.sum(3)
        if self.args.use_sdp:
            loss_duration = self.duration_predictor(
                x.detach() if self.args.detach_dp_input else x,
                x_mask,
                attn_durations,
                g=g.detach() if self.args.detach_dp_input and g is not None else g,
                lang_emb=lang_emb.detach() if self.args.detach_dp_input and lang_emb is not None else lang_emb,
            )
            loss_duration = loss_duration / torch.sum(x_mask)
        else:
            attn_log_durations = torch.log(attn_durations + 1e-6) * x_mask
            log_durations = self.duration_predictor(
                x.detach() if self.args.detach_dp_input else x,
                x_mask,
                g=g.detach() if self.args.detach_dp_input and g is not None else g,
                lang_emb=lang_emb.detach() if self.args.detach_dp_input and lang_emb is not None else lang_emb,
            )
            loss_duration = torch.sum((log_durations - attn_log_durations) ** 2, [1, 2]) / torch.sum(x_mask)
        outputs["loss_duration"] = loss_duration
        
        return outputs, attn