Answers.Body: <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>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-07T02:54:48.970Z
Answers.Text: Can you explain why we need to use exponential and what is the reason behiind it ? I
Answers.UserDisplayName: mat
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-07T08:50:49.937Z
Answers.Text: @mat it's literally the gaussian PDF, it's not a "reason", it's its definition
Answers.UserDisplayName: Alberto
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2023-08-06T10:13:22.227Z
Answers.LastActivityDate: 2023-08-06T10:13:22.227Z
Answers.UserDisplayName: Alberto
Body: <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>
  
Tags: <generative-adversarial-networks><diffusion-models>
Title: Math behind Diffusion models explanation?
UserDisplayName: mat
ThreadText: # 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 math behind the diffusion models ,
  
  As i dont have a math 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 math 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
  
  ---
  
  ## 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**: @mat it's literally the gaussian PDF, it's not a "reason", it's its definition  
  
  ---
  
  