Body: <p>From <a href="https://arxiv.org/abs/2006.11239" rel="nofollow noreferrer">the paper</a>:</p>
  <p><a href="https://i.sstatic.net/oOzej.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oOzej.png" alt="enter image description here" /></a></p>
  <p>But what's the point of <span class="math-container">$q(x_t\mid x_t, x_0)$</span>? Right before that, we already have:</p>
  <p><a href="https://i.sstatic.net/I1Oiw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/I1Oiw.png" alt="enter image description here" /></a></p>
  <p>So we already know what <span class="math-container">$q(x_t\mid x_0)$</span> is for any <span class="math-container">$t$</span>.</p>
  <p>My questions:</p>
  <ul>
  <li>What's the point of showing (6)? (It is used throughout rest of formulas, but it could just depend on <span class="math-container">$x_0$</span> everywhere, no? Even during sampling it could just use <span class="math-container">$\hat{x_0}$</span>)</li>
  <li>Are (6) and (4) equivalent somehow?</li>
  </ul>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-03-15T14:39:06.127Z
Comments.Text: Can you please include the name and link to the paper in your post?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-03-16T20:08:20.843Z
Comments.Text: @nbro Will do - it's just the original DDPM paper. https://arxiv.org/abs/2006.11239
Comments.UserDisplayName: xyzzyrz
Tags: <diffusion-models>
Title: In DDPM, why is "forward posterior" needed?
UserDisplayName: xyzzyrz
ThreadText: # In DDPM, why is "forward posterior" needed?
  
  (Asked by: username_0 on 2024-03-14)
  
  From [the paper](https://arxiv.org/abs/2006.11239):
  
  [![enter image description here](https://i.sstatic.net/oOzej.png)](https://i.sstatic.net/oOzej.png)
  
  But what's the point of $q(x\_t\mid x\_t, x\_0)$? Right before that, we already have:
  
  [![enter image description here](https://i.sstatic.net/I1Oiw.png)](https://i.sstatic.net/I1Oiw.png)
  
  So we already know what $q(x\_t\mid x\_0)$ is for any $t$.
  
  My questions:
  
  * What's the point of showing (6)? (It is used throughout rest of formulas, but it could just depend on $x\_0$ everywhere, no? Even during sampling it could just use $\hat{x\_0}$)
  * Are (6) and (4) equivalent somehow?
  
  **Tags:** diffusion-models
  > **Comments:**
  > **username_1**: Can you please include the name and link to the paper in your post?  
  > **username_0**: @nbro Will do - it's just the original DDPM paper. https://arxiv.org/abs/2006.11239  
  
  ---
  
  ## 0 answers
  
  