Diffusion Models | Paper Explanation | Math Explained

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

[@outliier]

Here is the implementation video in PyTorch: kzbin.info/www/bejne/inOmg5-krK-nkLc

[@bootsncats1873]

Q

[@homataha5626]

Hello, How did you make the animations in your video?

[@ulamss5]

Explaining the notations is a game changer... more educational content channels should do this.

[@AICoffeeBreak]

This is incredible! Did not see a video with the math explanations of diffusion models yet. And you animated it in manim! Just great. 😎

[@outliier]

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....

[@leif1075]

@@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?

[@sauvage_pikachu]

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!

[@elisawarner7942]

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!

[@felixvgs.9840]

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 :)

[@christiandeverall5661]

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!

[@AdmMusicc]

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.

[@nikitadeshpande6643]

You are the Outlier we cannot miss! Real gem. Thanks for the explanation man!

[@user-sz1iw4zi4y]

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.

[@kumaranragunathan7602]

Explaining the mathematical reasoning and formulas behind the model in such detailed fashion is amazing , keep up your good work

[@SteveSperandeo]

Excellent presentation. Great balance between depth and succinctness. Thank you!

[@xiaohaolin6464]

Excellent video! Very clear derivation, and good animation. You are a good teacher with loads of patience, and guided us step by step!

[@JasimUsmani]

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!

[@akshayshrivastava97]

Very well explained! You made sure to include a lot of important points others either omit or simply skim over. Thank you very much.

[@StephenRayner]

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 🎉

[@vladi21k]

After going through 4 different YT videos, yours was the only one that was clear enough for me to understand. Thank you very much!

[@anujshah7949]

Absolute king! Your work is such an important part of this community

[@kateyurkova6384]

Brilliant approach of lining up equations into a story, great work, thanks!

[@ravindrabisram137]

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!

[@kartikeyabhardwaj3919]

this is by far the best video on diffusion models that explains the math clearly, great job!

[@yahuiz7877]

awesome explanations!! look forward to more brilliant tutorial/explanation vids!!

[@TheKkunte]

This is the best explanation I have found so far. Thank you.

[@user-os4tw9hl5w]

Easily the best video on Diffusion models. Great work!

[@FLLCI]

Absolutely brilliant coverage! Keep up the good work. You are helping a lot of people.

[@user-fj9bh7kt7t]

you're a GOAT for this man, bringing together intuition and math notation is drastically underrepresented in general, thanks so much for this video

[@JBoy340a]

Wow! Amazing job explaining diffusion models and why they use the math they do.

[@srinathkumar1452]

Wow this is such a fantastic explanation. I love how you describe the intuitions behind the authors' mathematical choices.

[@icejust9195]

I really like your math part! Please keep going amazing work!

[@NellyParsley]

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

[@mohammadpishbin]

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.

[@Steveineiter]

One of the best explanations here on KZbin - thank you very much! 🥳

[@timforcade1029]

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.

[@andyfeng6]

Thank u for the detailed explaination, looking forward for your pytorch implementation video!

[@NicholasRenotte]

Wow, this is absolutely brilliant. Massive kudos for making quite the complex topic significantly more digestible!

[@yuhonglin8898]

Thanks for the fantastic introduction!! Well made video!

[@InturnetHaetMachine]

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.

[@javiersolisgarcia]

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!

[@PakkaponPhongtawee]

Amazing! The visualization is great and easy to follow.

[@chiscoduran9517]

Just the video that I needed, thanks so much!!!

[@oriyonay8825]

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 :)

[@markpayton3895]

Best video on diffusion model right now because of the math derivation of everything. Thank you!

[@user-sc7nn9sz3r]

what a wonderful and thoughtful way to deliver the whole langscape of the diffusion model! Nice video! 👍

[@Wondaful-mr2dl]

Truly awesome! Looking forward to the upcoming Pytorch implementation video!

[@sergiomanuel2206]

The video is perfect! Thank you so much. You helped me to understand better all the formulation! Thanks again!!

[@riazzai9250]

The explaination about loss function, especially the part of KL divergence, is amazing! I love your video!

[@user-ri9lg7dh7c]

Awesome! Right what I was looking for. Thank you for the explanation !)

[@codingblaze4611]

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.

[@MK-yj7pn]

Fantastic video, man. Explained the stuff really really well. Thanks.

[@wdabrilvi]

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.

[@itsnotthattough7588]

Thanks for the simple but detailed explanation! I wouldn't be able to understand the topic without your video.

[@autkarsh8830]

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!

[@statixvfx1793]

Great explanation, thank you for sharing your knowledge! Subscribed!

[@Shashank-vv4ex]

Tons of thanks for this amazing explanation!!

[@sedi_rockstar7481]

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!

[@outliier]

thank you so much!

[@RezaSoumi]

Thank you. Your explanation has been profoundly enlightening and exceptionally lucid, providing me with a comprehensive understanding.

[@brianpulfer4159]

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!

[@TheSeamau5]

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 🙏

[@sanjaybhandari2487]

Hopping for more great contents .

[@frapbrab664]

You're the GOAT man, very great summary of diffusion

[@bayesianmonk]

You have a superpower of explaining math. Really enjoyed it.

[@ziyuwan4513]

Thanks for the great explanation!!! This video is amazing!

[@cutethanks]

The most clear explanation I’ve seen on YT. Much more clear than that from MIT lectures lol Many thanks

[@inakitodc6816]

just the best expanation by far I have seen in days of searching. congrats

[@deadbeat_genius_daydreamer]

Excellent video mate, keep up the good work ✌️✌️

[@shakibyazdani9276]

Well explained, Thanks for the great explanation man!

[@homataha5626]

that was really enjoyable!! Thank you very much!

[@pengxiaohan3371]

Nice explaination in Math. Rarely see a such detailed diffusion model explaination video. Good job and thanks

[@fahim78611]

Greatly explained the papers and it's depend topics 👏👏👏

[@CarloRobiati]

awesome content, thanks for sharing!

[@fizzarubab8959]

Thank you for the wonderful explanation!

[@ashok_learn]

I salute your hardwork on this video. Thank you from the bottom of my heart. 😃

[@IndrainKorea]

Thank you for the explanation, it's really well made, I can see you put a lot of efforts in it, well done! 👏👍

[@williamdevena8565]

Great Video! Hands down the best explanation of DDPM’s math

[@ruoyufeng6727]

Fantastic video, looking for your next video !

[@vikimazo]

Thanks! A great explanation!

[@yyq90]

So satisfied to know that we just need to predict the noise!!! After so many formulars...🙏🙏🙏

[@azmerawyotorawi684]

I'm grateful to you for all your help

[@Magnify.]

Great video, thank you for this!

[@stevemurch3245]

Very well done. Animations are super helpful and the math explanation is clear.

[@WWG1-WGA]

Men! you did awesome !. Subscribed and I'll keep learning

[@simonetruglia]

Keep going mate, this one is an amazing video about the subject

[@dockosow7187]

this is amazing how you explain the maths. thank you for sharing. Thank you a lot

[@checkout8352]

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

[@spyrosmarkesinis443]

Great content, cheers man!

[@rajatagrawal5339]

The detailed explanation is mindblowing. I learned a lot today. Thank You.❣

[@Larry-ko5mc]

Well done!

[@yogeshsingular]

Really great video. We need more videos like this. Helped me understand cryptic papers which can be very frustrating...

[@kelseywang7709]

really nice explanations!! thank you so much

[@ichdu1933]

Good Video. Thank you for your work!

[@aspiringmango1929]

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!

[@lukasaichberger3081]

You are right! To be precise, he should be talking about the expected value of the log ratio.

[@ruofengmusictech]

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

[@spiritual-Aatma]

Video is really well made. You did well to summarize to keep things simple and explanatory.

[@QuOUseTERSEa]

This helps me a lot! You are really a good presenter.

[@user-gq6hm8kn6t]

Wonderful video! This really helps me to better understand the threom behind ddpm, many thanks

[@kevon217]

Thanks for this great explanation!

[@Jianju69]

Viele danke for explaining all of this so clearly.

[@arpitpatel5814]

Thank you for your efforts. 🙏🏻

[@brunokemmer]

Awesome video! great work!

[@assafsinger6110]

absolutely incredible video

[@chemaguerra1635]

This breakdown is godsend!