<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>

CC BY-SA 4.0
2024-03-15T14:39:06.127Z
Can you please include the name and link to the paper in your post?
nbro
CC BY-SA 4.0
2024-03-16T20:08:20.843Z
@nbro Will do - it's just the original DDPM paper. https://arxiv.org/abs/2006.11239
xyzzyrz
<diffusion-models>
In DDPM, why is "forward posterior" needed?
xyzzyrz
# 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**: @username_1 Will do - it's just the original DDPM paper. https://arxiv.org/abs/2006.11239  

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## 0 answers

