xt−1=1αt(xt−βt1−αt‾z~)+1−αt−1‾1−αt‾βtzz~=UNet(xt,t)z∼N(0,I)σt≤1−αt−1‾1−αt‾βtx_{t-1}=\frac{1}{\sqrt{\alpha_t}}(x_t-\frac{\beta_t}{\sqrt{1-\overline{\alpha_t}}}\widetilde{z})+\sqrt{\frac{1-\overline{\alpha_{t-1}}}{1-\overline{\alpha_t}}\beta_t}z\\ \widetilde{z}=UNet(x_t,t) \qquad z \sim N(0,I)\\ \quad\\ \sigma_t\le\sqrt{\frac{1-\overline{\alpha_{t-1}}}{1-\overline{\alpha_t}}\beta_t}