Denoising Diffusion Implicit Models（去噪隐式模型）

DDPM有一个很麻烦的问题，就是需要迭代很多步，十分耗时。有人提出了一些方法，比如one-step dm等等。较著名、也比较早的是DDIM。

原文：https://arxiv.org/pdf/2010.02502

参考博文：https://zhuanlan.zhihu.com/p/666552214?utm_id=0

训练过程与ddpm一致，推理过程发生变化，加速了扩散过程，结果也变得稳定一些。

 DDIM假设

 DM假设

ddim给出了一个新的扩散假设，结合ddpm的原假设，直接往新假设代入xt得到：

 根据原假设，联系上式：

得到：

 DDIM假设被变形为：

 x0可以根据扩散模型假设消去，得到：

 当然你可以隔着很多步，所以有：

 

DDIM代码如下：

#ddpm 
def sample_backward_step(self, x_t, t, net, simple_var=True,isUnsqueeze=True):

        n = x_t.shape[0]
        if isUnsqueeze:
            t_tensor = torch.tensor([t] * n,
                                dtype=torch.long).to(x_t.device).unsqueeze(1)
        else:
            t_tensor = torch.tensor([t] * n,
                                    dtype=torch.long).to(x_t.device)
        eps = net(x_t, t_tensor)


        if simple_var:
            var = self.betas[t]
        else:
            var = (1 - self.alpha_bars[t - 1]) / (
                1 - self.alpha_bars[t]) * self.betas[t]
        noise = torch.randn_like(x_t)
        noise *= torch.sqrt(var)

        mean = (x_t -
                (1 - self.alphas[t]) / torch.sqrt(1 - self.alpha_bars[t]) *
                eps) / torch.sqrt(self.alphas[t])
        x_t = mean + noise

        return x_t

#ddim
def time_backward_step(self, x_t, t, net, sample_step=5,isUnsqueeze=True):
        n = x_t.shape[0]
        if isUnsqueeze:
            t_tensor = torch.tensor([t] * n,
                                    dtype=torch.long).to(x_t.device).unsqueeze(1)
        else:
            t_tensor = torch.tensor([t] * n,
                                    dtype=torch.long).to(x_t.device)
        eps = net(x_t, t_tensor)

        xstar=torch.sqrt(1./self.alpha_bars[t])*x_t-torch.sqrt(1./self.alpha_bars[t]-1)*eps
        xstar=torch.clamp(xstar,-1,1)

        prev_t=t-sample_step if t-sample_step>0 else 0
        pred_xt=torch.sqrt(1-self.alpha_bars[prev_t])*eps
        x_prev=torch.sqrt(self.alpha_bars[prev_t])*xstar+pred_xt

        return x_prev

 DDIM结果图

 DDPM结果图

 

ddim inverse：

 Null-text Inversion for Editing Real Images using Guided Diffusion Models

    def ddim_inverse(self, x_t, t, net, label,sample_step=5,w=10,isUnsqueeze=True):

        n = x_t.shape[0]
        if isUnsqueeze:
            t_tensor = torch.tensor([t] * n,
                                    dtype=torch.long).to(x_t.device).unsqueeze(1)
        else:
            t_tensor = torch.tensor([t] * n,
                                    dtype=torch.long).to(x_t.device)
       
        cat = net(x_t, t_tensor, y=torch.ones_like(label) * 1)
       
       
        eps = (w + 1) * (cat) - w * un

        next_t = t + sample_step if t + sample_step < self.n_steps-1 else self.n_steps-1
        xstar=torch.sqrt(self.alpha_bars[next_t]/self.alpha_bars[t])*(x_t-torch.sqrt(1-self.alpha_bars[t])*eps)

        pred_xt=torch.sqrt(1-self.alpha_bars[next_t])*eps
        x_next=xstar+pred_xt

        return x_next