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Welcome back to another episode of decoded.
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Today, I'm sitting down with YC visiting partner Francois Chahbar to talk about one of the most important topics in AI today, diffusion.
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Francois has been doing computer vision since 2012 when he started in Feifei Li's lab.
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And after a decade running Focal Systems, he's currently back at Stanford finishing his PhD working on diffusion-based world models for AGI.
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We're going to break down what diffusion is, how it's evolved over the past decade, and how it's used today.
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>> [music] >> Francois, thanks for being here. Thank you for having me.
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Well, we just got back from NeurIPS.
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We just spent a lot of time talking to researchers and thinking about all the newest models out there.
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Um, I think we saw diffusion pop up over and over and newer versions of this type of uh approaches that are not autoregressive LLMs.
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And so, I wanted to talk to you about those today.
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So, first, why don't we start by defining um what is diffusion?
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Diffusion is a very fundamental machine learning framework that allows you to learn any P data, any probability of data for any domain as long as you have the data.
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So, you're trying to learn some data distribution. >> That's right.
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Now, in a sense, all LLMs or all machine learning models are about learning data distributions.
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How does diffusion in particular, what what stances it take or what approach does it take to being able to learn distribution?
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>> Yeah, I mean, I think you can use diffusion to to always do that.
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The thing where it stands out in particular is mapping from high dimensions to high dimensions, especially in low data uh regimes.
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So, say I only have 30 images of Gary, which I actually have some code that we're going to walk through. >> Okay.
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Um, I only have 30 images of Gary and again, we're in this 1,000 by 1,000 by three uh uh dimensional space and I want to map to another three three million dimensional space with only 30 training samples and I can still do it.
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And it's pretty pretty powerful in that way. Okay, cool.
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So, so you have this ability to use relatively small amounts of data compared to the dimensionality to learn a P data. >> That's right.
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Um, what's the what's the basic process by which diffusion works?
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Like, just walk through like at a very high level and we'll walk through the math a little bit later, but at a very high level, how does this process actually work?
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We take some sample of the data, an image of Ankit, an image of Gary, and we just hit it with noise.
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And then we just keep hitting it with noise and we create this train of of noised up images.
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It's very easy to create noisy images, right?
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It's hard to create get walk backwards and create from noise images of you or Gary.
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And so, then we flip it and then we try to have teach the model to reverse that process. And that's basically it. Okay, cool.
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So, it's basically a a noiser and a denoiser and the denoiser is the model that you end up training. >> Exactly. Yeah.
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You will uh you will basically teach your force and and give it uh noised up images and then have it learn intermediate representations to get to back to P data. >> Cool. Nice.
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And what kind of stuff is diffusion used for today?
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What are our some applications that it's widely deployed in?
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It's honestly surprising how uh uh applicable this process is.
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I think the the uh original 2015 Joshua Sohl Dickinson paper was on CIFAR-10, which is just images.
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Um, and I think it's got it has its roots in images, but it is far uh uh more sprawling than just images.
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As you've seen, we you know, uh uh DeepMind just won the Nobel Prize for doing this exact procedure on protein folding.
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Uh you can drive cars with this with the diffusion policy paper, which is like an insane result.
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Um, you can um uh predict the weather.
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Um, there's really no limit to the things that this can do.
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Yeah, it's pretty incredible to see.
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I mean, you have these image and video generation models that seem to be really advancing over the last few years.
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Stable Diffusion is the one I think many people have heard of and then newer versions of it seem to be using this as well.
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And then yeah, in the world of life sciences that um my company was in, too, I think we see this newest generation of life sciences AI companies are heavily investing in these set of technologies.
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There's a model called DiffDock that works really well for predicting uh small molecule binding to proteins.
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And then yeah, AlphaFold, especially the newest AlphaFold version, has used diffusion pretty heavily.
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It's really cool to see the same core piece of technology applied to so many different domains. >> Yeah, yeah.
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This class of models has evolved over the years and, you know, there's a whole slew of papers someone could read.
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So, you should probably go read the papers to learn all the details.
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But maybe at a high level we can try to trace out a few of the key innovations that happened starting with the paper you already mentioned that now led to the newest versions of these models.
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So, how would you map those out?
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Like, what was the the first kind of turn of the crank from this very high-level diffusion process you uh outlined?
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What was the first version of that that started to work? >> Yeah.
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So, I think the the 2015 original Joshua paper um is put up all the key pieces, all the key components of modern diffusion.
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And so, like now we're just playing with different things.
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So, the scheduler, how do we add noise, at what weight?
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Like, that's a whole part that we can discuss.
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What's the loss function?
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Should I predict Should the the deep learning model condition upon X of T predict uh the actual data X of T minus one or should it predict the error that was just added to it?
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Uh or should it predict the velocity, which is the error divided by the time?
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Uh should it predict the velocity of the the start and the end?
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That's called flow matching.
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There's so there's all these different plays on what the loss function is.
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So, in all of those, the idea is still to do denoising. >> Yes.
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Uh but the objective for each of them is somewhat different from each other.
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I mean, they're all pretty closely related, whether it's basically a delta between two things or the previous step or the first step.
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How do these all actually come together?
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But these are series of papers that happened one after another.
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Yeah, I think we just kind of hill climbed on this uh Fréchet inception distance metric.
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That's kind of a kooky weird um measure to see how good an image is.
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Um, but we just kept getting better and better and better on it by like doing these little tricks.
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And so, like it turns out that predicting the actual data itself is actually quite hard and like maybe predicting the error is actually easier.
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And then predicting the velocity was even easier than that.
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And then predicting the uh global error across the entire diffusion schedule is even easier than that.
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And like just kept finding easier and easier ways um to to basically uh sample from noise to data.
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And here, when you say easier, were was the ease largely driven by it was mathematically simpler or it was easier to implement and engineer or simpler to reason about or what >> What got easier, really?
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>> It actually is that, too, but I didn't mean it that way.
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What I actually meant was it's easier for the model to learn.
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Um, but it is also, and we'll go through some coding examples, the math actually got easier. >> Yeah.
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And like the the the code got smaller, which is actually opposite oppositely true in uh most of uh the case in most machine learning.
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You actually things get more complicated.
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I think we started with UNets and that was like the predominant architecture.
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We didn't really talk about architectures that much, but then we got into these uh diffusion transformers and like this cross attention mechanism and things like that.
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And so, um yeah, we just kept getting better and better at reducing uh FID. Hm, interesting.
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Should we dive into some code examples? >> Let's do it. Let's do it.
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I'll walk you through I made about uh 1 2 3 4 5 6 7 of these that I implemented um with varying levels of success.
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But uh the the all the structures are going to be the same.
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So, the the Joshua paper, the non-equilibrium uh thermodynamics paper, uh you can see here here are some nice images of Gary you can see here. Very nice.
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This is the what I could find online. Nice.
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Um and then >> are images of Gary that you've downsampled so that they're 1,000 by 1,000 or they're they're smaller, I think. >> by 64. 64 by 64.
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Yeah, they're really small.
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This is a very small example. Yeah.
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64 and then I randomly augment it to create more data. Great.
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>> Um cuz I was I was lazy and that was easier than uh downloading more images of Gary.
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>> [laughter] >> Didn't want to didn't want to get security called on you. Exactly.
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So, and then wait, I implemented this diffusion schedule and this is probably one of the most important like of all the parts of diffusion to that's difficult to comprehend, I would say that the noise schedule is actually the hardest part to understand and that I really like I struggled with myself.
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And so, if you can see here, the noise that's added from time step uh zero to T to 10 to 25 all the way to 100, uh it's clearly destroying the structure. Yes.
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And then we want to train the model.
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>> is basically random static. Exactly.
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And we want to basically reverse this and from here get to here and have the model get to that point, get to this point, get to my etc.
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And so, uh the interesting part, and this is Joshua really you know, uh implemented almost everything that we needed for diffusion.
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Um, and there was just a few little tweaks that were missing and he didn't he didn't scale it up.
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That's to me the the parts that um uh were were were missing.
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And if you see here the um the noise schedule, so it would make sense to me that I would have linear interpolation between uh the image and the noise.
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And I would start with like one and zero, one being the image and zero being the noise.
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>> And you gradually add it.
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But if you do that, it actually is massively unstable because the instantaneous amount of error that you're adding is very small in the beginning. >> Right.
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Like, on a relative basis. >> basis.
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And then at the end, you have to to destroy all that to get to complete noise, you need to add a lot of error.
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And so, like if you're a model and you're just looking at this little chunk of the noise schedule, then you have to handle a lot of error in one step.
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And on this side of of the schedule, you need to handle such small amounts of error.
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And what you actually want is constant rel- like relatively constant amount of error being introduced every single time step. >> Right.
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And that the the cumulative sum of all that error actually ends up looking like this uh like this curve here.
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That's the uh the pink curve. >> Yeah. Yeah.
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And so, they called this a beta schedule.
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Beta is the diffusion rate, the rate of diffusion that I'm I'm doing while I'm rolling this thing out from time zero to time T, capital T.
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And and so you can see here the the beta schedule.
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So we we have usually have some beta min to beta max.
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And then we one minus that is the alpha.
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And you can think about the beta as like how much noise I'm adding at every time step.
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And you think about the alpha as how much signal is being retained. Yeah, being retained.
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And then the term that really matters is the alpha bar and these are the weight weights that are used and it has this kind of like one minus sigmoid looking thing.
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But that's basically the noise schedule.
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And once you get that right, really this this this part here then everything kind of else just works.
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And then I trained some model and then we can actually So there what was the training objective again?
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So you were adding this noise and the training objective was to do what exactly?
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The train in this case it's to minimize the KL divergence between the distribution the real distribution and the distribution that I'm learning.
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And so I won't go through the code for this one cuz it's a little bit hairier but you can kind of see the result on these generated images after a 100 diffusion steps at inference time.
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And you can see that the Frechet inception distance is 222 which is like extremely high today.
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Like today modern modern day would be like maybe like eight or 10 or something.
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And what's interesting here is I mean you kind of scroll through it there but it's and you mentioned it there's quite a lot of code that it actually takes to do that KL divergence base loss.
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I suspect that in these later models you're going to show it it gets significantly simpler.
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So I'm just mentally noting that cuz I suspect there's going to be interesting contrast to draw between these two.
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Yeah, so the next one I would like to show is flow matching which is it's just so beautiful and simple.
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And this was out of meta Yarin Lipman where he basically said we don't need a lot of this stuff.
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What we need to do forget the if you think about the noising process as being this like I start from data.
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I randomly sample a vector of noise and I just go in this direction. And then I do it again. I go in this direction. I do it again. I go in that direction.
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I go in this direction that direction.
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And then I'm here at noise.
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And then you have to teach the thing to go in the exact opposite path.
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And you have to do this very circuitous path.
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And so at test time it's actually quite expensive.
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You have to do We've all waited for you know chat GPT or to or midjourney to like make an image and takes a while.
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What it's doing is like a thousand calls to the model again and again iterating through to get to that point of your data.
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Instead And like intuitively it's like okay we're doing the circuitous path but surely there's a shorter path between those two.
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And so that's what makes flow matching so cool to me at least is that they said forget all of that intermediary results.
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There is a a velocity a global velocity between the noise and the data and it's just this direction.
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It's just this straight line.
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And I don't care where you are go in that line.
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Wherever you are you're over here go in that line and teach it to go in that line.
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And that's what flow matching does.
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And so I'll show you the code and it's really quite simple.
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It really is quite simple. And so this pretty cool. So here you go.
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The you basically have like 10 15 lines of code that is the most powerful machine learning procedure ever.
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So I I have some data I an image of Gary.
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I have some noise that I I I some isotropic Gaussian noise that I sample from.
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There's some time that I'm I'm trying to index into in the diffusion schedule.
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And I'm and I create XT which is the image at the noised up image that's somewhere between extremely noisy and not noisy at all.
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And and that's basically just this sampling procedure.
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It's T times data plus one minus that times noise. That's right.
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And then I compute the velocity which is independent of the time.
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I don't care where you are it's just the global this global velocity which is this the noise minus the data and then it I return that back to my training loop which is the shortest amount of code training loop [laughter] I've ever written which it's five lines of code. I have my batch. I have some time.
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I sample from that function I just explained before.
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And then I have my prediction from the model.
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I feed it in this some element some noised up image somewhere between lots of noise and little noise is X of T let's call it.
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And I just want it to predict the velocity that I want to go.
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And this is also really powerful cuz here you know you have model abstracted but that model can be any model.
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So you can put in whatever the relevant model is for your distribution whether that's a protein model for proteins or if it's an LLM for text or an image based model for images that is a very clean abstraction as long as you can then predict this velocity and then move in that direction. That's right.
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This code here has nothing to do with images.
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It could be weather data.
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It could be you know stock market data.
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It could be trajectories from a robotics in a teleops setup. It could be proteins. It could be DNA.
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It doesn't really matter.
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It's all the exact same code.
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And so and then also we haven't talked about the architecture.
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So like this model here could be anything you want it to be. Like it could be a RNN.
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It could be a U-Net which is typically you know traditionally is.
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And and modernly they use these diffusion transformers doing this cross attention mechanism.
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And so it can be whatever you want.
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But it's all that is independent from whether or not you're doing flow matching or not.
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matching or not. I think this is like a really profoundly interesting result in that especially this I think we often assume as models have gotten more sophisticated that they become less accessible for people to
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understand but this is quite literally 10 lines of code >> [laughter] >> that explains essentially all of the most important kind of mathematical and fundamental foundations of the models that we all see as generating basically like magical AI results on our phones. Of course there's lots of engineering
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Of course there's lots of engineering how you scale them up you know that that model could be a 100 billion parameter transformer.
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Data centers you know GPUs. Yeah 100%.
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So it's the engineering that's the really hard part there but a lot of the basic machine learning math is actually quite straightforward. That's right.
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And so there's a bunch of these like tangent fields to diffusion that all have some different interpretation on what's actually happening but it's all the same exact math.
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And most people learning diffusion actually get quite confused because if you talk to some you know probabilistic graphical model people they'll say oh this is a probabilistic graphical model and what's actually this is a hidden Markov model and what we're doing is we're learning this like Markovian thing or whatever.
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It's like okay fine but like it's just noise minus data.
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>> [laughter] >> And like you should just show that first.
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And then like if you think about it from like a physics perspective and and there's all this stat mech people that have that interpretation.
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There's a whole bunch of these different interpretations.
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I think it's it gets a little bit confusing.
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And then the whole stochastic differential equation people like thinking about that this is an SDE.
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And I think that's all fine and it probably is helpful to think about but in terms of teaching it it's actually quite quite simple which is powerful.
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So if we go back to here you can see that this just literally predicting the velocity.
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Your goal is to have the model predict You're minimizing the loss between predicted velocity and velocity. >> velocity. That's it.
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And that's super stable and it's it's really clean.
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And then at test time for the physics people this is like a Euler step kind of thing that you're doing where you call the model a bunch of times and you iteratively refine.
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So back to the hill climbing that we were talking about I'll grab some random noise here X and I just do and I call basically reverse that that noising process to denoise denoise denoise and It's literally Euler's method.
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Like you're you're using the velocity to point in the direction you want to in the direction and just keep going keep going keep going until you've done the number of steps.
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The one thing that I really don't like about diffusion as it's done today is that I can't keep calling it beyond if I only trained on 100 diffusion steps in my diffusion schedule.
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If I change that at test time it doesn't work.
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And so you can't like oh I want to even better so I'll call it even more.
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That doesn't You can't I've tried it it doesn't work.
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There's various tricks people try there but yeah. Yeah.
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And so like the there's games played that is actually quite exciting.
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All the expense >> But what I was trying to be clear here here you're saying that's not relevant. It's not relevant.
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In this type of model you don't have this time dependency. Well so you do.
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So at this time if you change for example the number of steps if you double it.
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Let's say that and you expect to get even higher resolution images.
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It actually will just turn into like white.
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Like it actually just like doesn't work at all.
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So you can't step beyond number of steps that was trained.
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That's an important detail.
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There are tricks that people are doing to try to compress that representation.
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So like if at train time I train for 100 steps and at test time I want to do 10 steps.
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Then what you can do is you can do distillation into the model to try to have the 10 step model learn the 100 step models thing.
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But then you still got to train with 10 steps.
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And so like if you're training with with X steps you have to be using X steps at test time. I see. Interesting.
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You've talked about this concept of a squint test why don't you define the squint test for a second.
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Tell me a little about where this comes from and then I'd be curious to hear how you think about diffusion models in the context of general intelligence broadly.
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Yann LeCun has this like interesting lecture where he talks about our discovery of flight and that we didn't need flapping wings.
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We kept trying to mimic a bat and how that was a waste of time.
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And to that I say you're 100% right.
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However we did need two wings.
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Then you look at the Wright brothers' original plane and you squint and you look at a bird, you're just like, "Hmm, while we have helicopters and we have jets and things like that and rockets, like we we got there eventually."
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And so there's many elements in the set of things that can achieve flight and they have different pros and cons.
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And there are many elements in the set of things that can achieve intelligence.
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We are the only existence proof of it at all.
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And like I'm sure there will be more elements in the set and maybe LLMs, broadly speaking, can get there.
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But if I squint and I look at LLM setup, which I I see this, you know, monolithic stack transformers, the same thing, stack stack stack, and there's three stages of training.
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We do this pre-train, you know, SFT, you know, post-train, and then no learning at at all beyond that.
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And it produces exactly one token at a time.
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>> Right, so in order to token.
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In order to token at a time and it never goes backwards.
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And then you look at a brain, massively massive amounts of recursion.
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You have one learning procedure the whole time.
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You have these two lobes that with a corpus callosum that between them that's kind of going back and forth like this and we think and then I definitely don't think in one token at a time.
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When I write code, I don't write one little character at a time. I never go backwards.
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And I kind of like I'm going backwards, I'm recursively improving.
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I'm going backwards again and again.
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I'm I'm thinking in concepts.
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>> There's just like dynamic process that's emitting concepts and then higher-level higher-level concepts and then lower-level manifestations of them.
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>> I'm sure that may be happening inside the LLM, but it's like it's almost like stuck.
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It can't do more than in one step even though if it might want to cuz it has to is the way that we we trained it.
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>> Right, like it might have all that in the LLM, but then it's it's sort of bottleneck ultimately by all the emits.
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Action space is one is one >> token at a time.
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And so I think that that's where I think about diffusion, there's like a two main things that diffusion gives me.
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It doesn't get me all the way to to pass my squint test, but it gives me two things that I for sure the brain is doing.
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Number one, the entire all of biology and nature leverages randomness. Randomness is good.
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And what is diffusion doing?
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It's leveraging randomness.
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If you give me data and I noise it up and from that I can learn about the data.
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And like is the can the brain add noise to input data? Absolutely. Like absolutely.
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Neurons are massively random.
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This log-normal distributions, spike patterns, and things like that.
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And the other one is this emission of one thing at a time versus thinking in concepts and then decoding into a big chunk of text and thought and revisioning of the previous thoughts and things like that.
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And so I think diffusion gives me both of those things for sure.
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People probably heard of stable diffusion as a very common application of this.
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People it's an image generation model that was pretty widely available for the last few years.
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What people may not be so aware of is all the other ways that diffusion is used in the last few years in products that people are widely using.
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So what are some of the areas on which diffusion is most widely accessible?
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Yeah, it's really any mapping from very high-dimensional P data to very high-dimensional action spaces or P data that you may want to map to.
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And so I mean, yeah, of course everyone knows generating images cuz we've done Midjourney and things like that and even more modern versions of that with Sora and VEO and Flux and SD3 now and things like that.
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And we've generating videos which is just images stable together and and video gen and image gen and things like that.
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However, there's so many more applications that now we're seeing that's the most exciting part in my my view of all the new applications.
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And so whether or not you're now creating sentences, I mean diffusion LLMs was one of the biggest topics that we saw at NeurIPS.
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Whether it's continuous diffusion LLMs or discrete diffusion LLMs.
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That's it's writing code now. It's creating proteins.
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I mean DeepMind has won the Nobel Prize for that.
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There is robotic policies, this diffusion policy thing which I think might actually be one of the biggest uses of it and will result in like robots actually working and Rosie the robot actually working.
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There's weather forecasting for the GenCast.
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It's the most accurate weather forecasting system in the world. It's really anything.
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Even like I mentioned Harrison working on the diffs, diffusion for failure sampling.
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Just like sampling from for failures and like bad things that could happen. We can do that as well.
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So a lot of the the products where we see people actually using AI, especially for things other than just text-based chat, a lot of them are using diffusion, especially on images, videos, increasingly now things like code, the life sciences.
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So yeah, pretty pretty wide birth of things. >> Yeah.
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In fact, I would say the only two holdouts right now where state of the art is not diffusion, diffusion has eaten all of AI except two.
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AR LLMs still are outperforming and gameplay and things like AlphaGo.
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And so MCTS is still state of the art for those types of things.
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And so we haven't seen diffusion really take step in those two fold those two areas, but more research is needed.
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So to bring the conversation to a head now, how should people think about this research area?
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Either as researchers contributing to the field or as founders looking to build a new product?
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Yeah, I mean I would think about maybe this falls in two camps.
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If you're training models yourself or if you're using models and and you know, not in the business of training models.
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If you're in the business of training models, I would seriously look at diffusion.
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I don't care what your application is.
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You should be looking at this procedure even if it's just to get a latent space that you can then train off of.
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And so there's no application in machine learning that I I don't think you should be heavily looking at diffusion procedures as a fundamental piece of of your training loop.
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In the in the case of people who are are not training models, I would just like update your prior on how good these things are getting.
25:38
And if you just look at in the last 5 years on how good image generation got from Midjourney when it first came out to VEO and Sora and Flux and SD3 now, it's like it's like 1,000 times better, right?
25:52
The answer was just scale it up.
25:54
And that takes time and that takes money and all those things and data.
25:57
And now you apply that to proteins. You apply that to DNA.
25:59
You apply that to robotics policies. A self-driving car.
26:04
I mean it is skate to where the puck's going to go.
26:08
All these things are going to work and we're watching it happen.
26:09
It may cost money and time and you know, those kinds of things, but those are those are solvable things.
26:15
Those are tractable problems that we can go solve.
26:17
And also the core procedure of diffusion is getting better.
26:21
That's another major A lot simpler.
26:22
A lot simpler and it's getting like it's we're just working better.
26:26
And so skate to where the puck's going to go.
26:27
Bet that Rosie the robot will work in people's homes.
26:30
Bet that the the protein folding is only going to get better and now we're going to apply that to DNA and all these other metabolomics and things like that.
26:39
>> We we see founders develop new models for robotics or for text generation or for video using diffusion.
26:43
Um and we see founders who are using all of these methods coming from other places build companies on top of them.
26:49
And it seems like there's this whole new wave of companies that can be built on either end of this now. Right.
26:53
I think it's going to redefine the entire economy.
26:56
Thanks so much for joining us.
26:56
We're going to keep digging in on topics related to machine learning research like diffusion.
27:00
Can't wait to see you at the next one. >> [music]