A short summary of the paper

[aSleepyTree]

Excellent work!
Here I write about my understanding of this paper, if there are any mistakes I hope you can point them out, thank you very much.

As shown in Figure 2, previous methods like RDDM and ResShift learn the path from $\hat X_0$ to $X_0$($X_t = X_0 + \bar \alpha_t X_{res} + \bar \beta_t \epsilon$, where $\bar \alpha_t$ donates addition). Formally, they don't follow DDPM($X_t =\sqrt{\bar \alpha_t} X_0 + \bar \beta_t \epsilon$, where $\bar \alpha_t$ donates multiplication).

This paper presents learning from $R$ to $X_0$($X_t =\sqrt{\bar \alpha_t} X_0 +(1-\sqrt{\bar \alpha_t})R + \bar \beta_t \epsilon$, where $\bar \alpha_t$ donates multiplication). Some difficulties exist, such as $X_0$ being unknown in the reverse process (solution: Smooth equivalence transformation).

The most important point is that $\textbf{the form is consistent with DDPM, and almost all the benefits of the method are derived from it.}$

[YukinoshitaLove]

@aSleepyTree Great summary! (*´∀`)~♥ It's also worth mentioning that our original motivation was to find a point where the prior distribution is equal to the posterior distribution (as shown in Figure 2). Geometrically, it is an intersection point in the hyperspace.