Diffusion Models | Paper Explanation | Math Explained
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- Опубликовано: 9 июн 2024
- Diffusion Models are generative models just like GANs. In recent times many state-of-the-art works have been released that build on top of diffusion models such as #dalle or #imagen. In this video I give a detailed explanation of how they work. At first I explain the fundamental idea of these models and later we dive deep into the math part. I try to explain all of this on a really easy & intuitive level. After the math derivation, we look at the results from different papers and how they compare to other methods.
#diffusion #dalle2 #dalle #imagen
00:00 Introduction
02:48 Idea & Theory
07:06 Architecture
09:33 Math Derivation
26:59 Algorithms
28:22 Improvements
29:43 Results
31:34 Summary
Further Reading:
1. Paper: arxiv.org/pdf/1503.03585.pdf
2. Paper: arxiv.org/pdf/2006.11239.pdf
3. Paper: arxiv.org/pdf/2102.09672.pdf
4. Paper: arxiv.org/pdf/2105.05233.pdf
5. VAE & Reparam. Trick: lilianweng.github.io/posts/20...
6. Written Tutorial: lilianweng.github.io/posts/20...
PyTorch Implementation Video: • Diffusion Models | PyT...
Follow me on instagram lol: / dome271 
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Here is the implementation video in PyTorch: ruclips.net/video/TBCRlnwJtZU/видео.html
Q
Hello, How did you make the animations in your video?
Explaining the notations is a game changer... more educational content channels should do this.
For those who are confused about the recursive expansion at 13:13 (like I did), it's "a property of Gaussian distributions, where the variance of the sum of two independent Gaussian variables is the sum of their variances. "
I'm confused about the notation q(Xt|Xt-1) and p(Xt-1|Xt).
Never seen the result of a function presented as part of the argument before.
Not even sure I understood which is which from his prose.
Seems to follow from uncorrelated noise variables at different steps, using the formula var(X1+X2)=var(X1)+var(X2)+2cov(X1,X2) where cov(X1,X2)=0. We don't seem to need to use normality here
Hey, thanks very much for making this wonderful video! I just want to appreciate the fact that all notations are clearly explained before going into the math part. That helps a lot! Great work!
What an amazing video!! I looked everywhere for a comprehensible video about Diffusion Models and yours was simply the best… Please keep up the effort and the great content :)
This was the best ML paper review I have ever seen. You stopped making videos but I would really love to see you go through more of this for more research in the field man! Hatsoff to you.
This is incredible! Did not see a video with the math explanations of diffusion models yet. And you animated it in manim! Just great. 😎
thank you so much! actually it's not even animated with manim. It's all done in Premiere Pro haha. But I guess that I'll definitely do those things in manim in future videos....
@@outliier Thanks for sharing bit how do ppl.not get bored and frustrated during the math lart..even if you are a math genius..and if you don't think of the smweird step of taking out the first term of the sum..can't you still reach the same goal? So why do thst at all?
Amazing video; thanks a lot for going in depth on the math with simplified animations!
I've watched a bunch of videos trying to understand Diffusion (Ari Seff, Assembly AI etc) and this one taught me the most by far. Please keep making videos!
Wow, this is absolutely brilliant. Massive kudos for making quite the complex topic significantly more digestible!
After going through 4 different YT videos, yours was the only one that was clear enough for me to understand. Thank you very much!
This video is amazing. I think the format of your video was incredible, you went over the literature and told us how we got there, you went over the high-level explanation then got into the nitty-gritty detail and then just in case we miss something you gave an amazing recap. This is how all videos on deep learning should be. Especially as we're getting into more Niche topics.
Very well explained! You made sure to include a lot of important points others either omit or simply skim over. Thank you very much.
This is the first source I was able to find that explained the math behind diffusion models in a comprehensible way instead of glossing over it. Thanks a lot, you have earned my like and subscribe with just this video alone!
Excellent video! Very clear derivation, and good animation. You are a good teacher with loads of patience, and guided us step by step!
Thank you so much for making this video! It was very clear and I really appreciate how you walked through the math and the reasoning for how they went from the initial loss to writing it in terms of predicting the noise. Everything was well made. I look forward to watching your other videos!
You are the Outlier we cannot miss! Real gem. Thanks for the explanation man!
Excellent presentation. Great balance between depth and succinctness. Thank you!
Thank you for making such a high quality video explaining the math. Often, other channels do not emphasize on the math and this video is perfectly putting light on how exactly the math fits in diffusion models. Thank you for your amazing work. Please, make more such content!
Easily the best video on Diffusion models. Great work!
this is by far the best video on diffusion models that explains the math clearly, great job!
This is the best explanation I have found so far. Thank you.
you're a GOAT for this man, bringing together intuition and math notation is drastically underrepresented in general, thanks so much for this video
Absolutely brilliant coverage! Keep up the good work. You are helping a lot of people.
One of the best explanations here on RUclips - thank you very much! 🥳
Brilliant approach of lining up equations into a story, great work, thanks!
Absolute king! Your work is such an important part of this community
Explaining the mathematical reasoning and formulas behind the model in such detailed fashion is amazing , keep up your good work
U really liked that you showed the derivation in an understandable way
When the math part started I went to continue watching at the toilet
This is the first ever video of you that I get to see. Congrats, truly amazing. I believe you are among the first people on YT to dig into the math equations of ML papers like this, and I believe it's truly valuable. Keep it up!
what a wonderful and thoughtful way to deliver the whole langscape of the diffusion model! Nice video! 👍
Wow! Amazing job explaining diffusion models and why they use the math they do.
I really like your math part! Please keep going amazing work!
Nicely explained. Most of the people leave these derivatives thinking it would make the tutorial boring but without these derivativation we don't understand how was the methodology evolved. Great job reasearching and explaining.
Wow this is such a fantastic explanation. I love how you describe the intuitions behind the authors' mathematical choices.
this video is *by far* the best video on diffusion models i've seen on youtube. this was very pleasant to watch and you made everything really clear. brilliant!! i subscribed and turned on notifications :)
have an amazing day :)
You're the GOAT man, very great summary of diffusion
Amazing! The visualization is great and easy to follow.
Fantastic video, man. Explained the stuff really really well. Thanks.
Wow……. Haven’t read math in a while, this was explained excellently. I have a masters degree in physics but don’t do much math anymore since my degree in 2017.
I really like how much detail you went into with the derivations and the pausing to ground what we are doing with some intuition. Well done man 🎉
just the best expanation by far I have seen in days of searching. congrats
Thanks for the simple but detailed explanation! I wouldn't be able to understand the topic without your video.
I just watched your video on diffusion models, and I am incredibly impressed with the depth of information you provided. Your explanation was clear, concise, and immensely helpful. Thank you for sharing your knowledge on this topic. I learned a lot from your video and I truly appreciate your efforts in creating such valuable content.
Just want to say thank you. I believe this is one of the most high-quality videos I have ever seen given on diffusion models! Keep it going. I have subscribed!
thank you so much!
Best video on diffusion model right now because of the math derivation of everything. Thank you!
awesome explanations!! look forward to more brilliant tutorial/explanation vids!!
Thanks, the video was really helpful, it gave me such a great time in understanding diffusion models, kudos and keep on making such quality content!
Thank you. Your explanation has been profoundly enlightening and exceptionally lucid, providing me with a comprehensive understanding.
The video is perfect! Thank you so much. You helped me to understand better all the formulation! Thanks again!!
Man, this is incredible. When I saw these equations in the paper and other sources I was like "no way I am gonna understand that".. but with this video it all makes sense. Brilliantly done, thank you so much for your work. Instant subscribe and I am going to check other content on your channel :D
The explaination about loss function, especially the part of KL divergence, is amazing! I love your video!
Superb work.
1. Gone through the history of diffusion of models by explaining all the previous papers.
2. Giving an intuition of whole idea.
3. Explaining math behind it.
4. Also incorporating future prospects
Thanks for the fantastic introduction!! Well made video!
The most clear explanation I’ve seen on YT. Much more clear than that from MIT lectures lol
Many thanks
This is a really great video, thanks for your big effort explaining!
Thank u for the detailed explaination, looking forward for your pytorch implementation video!
You have a superpower of explaining math. Really enjoyed it.
Just the video that I needed, thanks so much!!!
Many thanks for this. I'm an artist with very limited math skills and though I can't say I understood the whole, your teaching gave me a solid basis and an understanding of this I've been wanting. You have another fan.
Appreciate the effort you put into this. You definitely can teach. If only I have a brain to understand math... still got some bits here and there. Thanks
Great Video! Hands down the best explanation of DDPM’s math
Thank you so much for delving deep into the math. I'm an engineer (not software) and self-learning AI. The papers are unfortunately not written in the most explainable way, and even though I've taken high level math courses for my degree, the notation and terminology in the papers make it pretty inaccessible and frustrating to follow. Thanks for going through this paper, I hope you continue to make more videos.
Awesome! Right what I was looking for. Thank you for the explanation !)
So satisfied to know that we just need to predict the noise!!! After so many formulars...🙏🙏🙏
I started reading articles and looking for learning content on diffusion modelling and the notation seemed a bit difficult. However, I am only half way through this video and I can assure you that this video is a must watch. Very clear explanation, I will recommend it to anyone interested in exploring this field, congratulations on your work!
I'm grateful to you for all your help
Tons of thanks for this amazing explanation!!
Very well done. Animations are super helpful and the math explanation is clear.
Thank you so much. I actually just recently worked out a lot of this math a couple weeks ago for a model I'm building and this video would've saved me so much time. Very clear. Thank you 🙏
Thanks for the great explanation!!! This video is amazing!
Video is really well made. You did well to summarize to keep things simple and explanatory.
Great explanation, thank you for sharing your knowledge! Subscribed!
16:24 I don't understand how you rewrote the KL divergence as the log ratio. Specifically, I don't understand how D_KL (q || p) = log(q / p). This is different from the definition of the KL divergence, which would suggest that D_KL (q || p) = integral q * log(q / p). Could someone please explain why D_KL (q || p) = log(q / p) in this case? Thank you! This was a fantastic video and your efforts are greatly appreciated!
You are right! To be precise, he should be talking about the expected value of the log ratio.
See the original paper arxiv.org/pdf/2006.11239.pdf page 2. The objective is to maximum the "expected" negative log likelihood. Since the expectation is calculated as integral over x_1...T rather than x_0, it'll be 1. You can think that everything the video talks about happen inside the E_q[ ... ] bracket
Really a life savior, thank you so much!!
Truly awesome! Looking forward to the upcoming Pytorch implementation video!
I was just using those tools to generate images but due to this video i got a lot more interested in understanding how they work. I hope you keep doing this kind of videos.
I salute your hardwork on this video. Thank you from the bottom of my heart. 😃
Thanks! A great explanation!
This helps me a lot! You are really a good presenter.
Greatly explained the papers and it's depend topics 👏👏👏
Wonderful video! This really helps me to better understand the threom behind ddpm, many thanks
Thank you for the explanation, it's really well made, I can see you put a lot of efforts in it, well done! 👏👍
Really great video. We need more videos like this. Helped me understand cryptic papers which can be very frustrating...
Nice explaination in Math. Rarely see a such detailed diffusion model explaination video. Good job and thanks
The detailed explanation is mindblowing. I learned a lot today. Thank You.❣
This breakdown is godsend!
that was really enjoyable!! Thank you very much!
Well explained, Thanks for the great explanation man!
Men! you did awesome !. Subscribed and I'll keep learning
this video is really get to the point and with good information and math
This video was a game changer. Thank you man, just earned a subscriber :)
Thank you so much!
Great video, thank you for this!
Thank you for the wonderful explanation!
Would have upvoted several times. Yours is the first video I found that actually goes into the math. Others just slap it onto the screen as fact, dazzling and confusing the viewer.
Fantastic video, looking for your next video !
this is amazing how you explain the maths. thank you for sharing. Thank you a lot
absolutely incredible video
Good Video. Thank you for your work!
I appreciate your effort
It will pay you back one day