<p>That exponential comes from the PDF of the assumed distribution that you might have missed in the blogpost:</p>
<p><a href="https://i.sstatic.net/Wi58D.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Wi58D.png" alt="enter image description here" /></a></p>
<p>and</p>
<p><a href="https://i.sstatic.net/bPwae.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bPwae.png" alt="enter image description here" /></a></p>
<p>plug those PDF in that bayes formula and you will end up with those equations</p>

CC BY-SA 4.0
2023-08-07T02:54:48.970Z
Can you explain why we need to use exponential and what is the reason behiind it ? I
mat
CC BY-SA 4.0
2023-08-07T08:50:49.937Z
@mat it's literally the gaussian PDF, it's not a "reason", it's its definition
Alberto
CC BY-SA 4.0
2023-08-06T10:13:22.227Z
2023-08-06T10:13:22.227Z
Alberto
<p>I am recently reading this wonderful article <a href="https://lilianweng.github.io/posts/2021-07-11-diffusion-models/#what-are-diffusion-models" rel="nofollow noreferrer">https://lilianweng.github.io/posts/2021-07-11-diffusion-models/#what-are-diffusion-models</a> about the math behind the diffusion models ,</p>
<p>As i dont have a math background , i am stuck or not able to understand the below statement,</p>
<p><a href="https://i.sstatic.net/COVKR.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/COVKR.png" alt="enter image description here" /></a></p>
<p>I am able to get how the bayes rule is working, <strong>I dont understading what is the reason behind the exponential math below it.</strong></p>
<p>Kindly explain why it is used and what is the reason behind it or suggest any resources for getting an intuition.</p>

<generative-adversarial-networks><diffusion-models>
Math behind Diffusion models explanation?
mat
# Math behind Diffusion models explanation?

(Asked by: username_0 on 2023-08-05)

I am recently reading this wonderful article <https://lilianweng.github.io/posts/2021-07-11-diffusion-models/#what-are-diffusion-models> about the username_0h behind the diffusion models ,

As i dont have a username_0h background , i am stuck or not able to understand the below statement,

[![enter image description here](https://i.sstatic.net/COVKR.png)](https://i.sstatic.net/COVKR.png)

I am able to get how the bayes rule is working, **I dont understading what is the reason behind the exponential username_0h below it.**

Kindly explain why it is used and what is the reason behind it or suggest any resources for getting an intuition.

**Tags:** generative-adversarial-networks, diffusion-models


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## 1 answers

### Answer by username_1 on 2023-08-06. Score: 1

That exponential comes from the PDF of the assumed distribution that you might have missed in the blogpost:

[![enter image description here](https://i.sstatic.net/Wi58D.png)](https://i.sstatic.net/Wi58D.png)

and

[![enter image description here](https://i.sstatic.net/bPwae.png)](https://i.sstatic.net/bPwae.png)

plug those PDF in that bayes formula and you will end up with those equations

> **Comments:**
> **username_0**: Can you explain why we need to use exponential and what is the reason behiind it ? I  
> **username_1**: @username_0 it's literally the gaussian PDF, it's not a "reason", it's its definition  

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