If it helps you to understand at all, assuming you have a CS background, any time you see the word "tensor" you can replace it with "array" and you'll be 95% of the way to understanding it. Or "matrix" if you have a mathematical background.

Whereas CS arrays tend to be 1 dimensional, and sometimes 2 dimensional, tensors can be as many dimensions as you need. A 256x256 photo with RGB channels would be stored as a [256 x 256 x 3] tensor/array. If you want to store a bunch of them? Add a dimension to store each image. Want rows and columns of images? Make the dimensions [width x height x channels x rows x columns].

One of my favorite moments in Geoffrey Hinton's otherwise pretty info-dense Coursera neural network class was when he said-

"To deal with a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it."

I think this post explains tensors fairly well: https://www.kdnuggets.com/2018/05/wtf-tensor.html

Quote: "A tensor is a container which can house data in N dimensions. Often and erroneously used interchangeably with the matrix (which is specifically a 2-dimensional tensor), tensors are generalizations of matrices to N-dimensional space."

I got lost at the word 'tensor' too, but then I just googled it and skilled up...

But simply put, a 'tensor' is a 3+-dimensional array of floats. Or a stack of matrices.

I should have added that the images/figures really help. I think I’m about there.

You’re talking like using jargon makes something a bad explanation, but maybe you just aren’t the audience? Why not use words like that if it’s a super basic concept to your intended audience?

In the reverse diffusion process, the reason we can't directly jump from a noisy image at step t to a clean image at step 0 is that each possible noisy image at step t may be visited by potentially many real images during the forward diffusion process. Thus, our model which inverts the diffusion process by minimizing least-squares prediction error of a clean image given a noisy image at step t will learn to predict the mean over potentially many real images, which is not a itself a real image.

To generate an image we start with a noise sample and take a step towards the _mean_ of the distribution of real images which would produce that noise sample when running the forward diffusion process. This step moves us towards the _mean_ of some distribution of real images and not towards a particular real image. But, as we take a bunch of small steps and gradually move back through the diffusion process, the effective distribution of real images over which this inverse diffusion prediction averages has lower and lower entropy, until it's effectively a specific real image, at which point we're done.

The problem is that predicting a pixel requires knowing what the pixels around it looks like. But if we start with lots of noise, then the neighboring pixels are all just noise and have no signal.

You could also think of this as: We start with a terrible signal to noise ratio. So we need to average over very large areas to get any reasonable signal. But as we increase the signal, we can average over a smaller area to get the same signal-to-ratio.

In the beginning, we're averaging over large areas, so all the fine detail is lost. We just get 'might be a dog? maybe??'. What the network is doing is saying "if this a dog, there should be a head somewhere over here. So let me make it more like a head". Which improves the signal to noise ratio a bit.

After a few more steps, the signal is strong enough that we can get sufficient signal from smaller areas, so it starts saying 'head of a dog' in places. So the network will then start doing "Well, if this is a dog's head, there should be some eyes. Maybe two, but probably not three. And they'll be kinda somewhere around here".

Why do it this way?

Doing it this ways means the network doesn't need to learn "Here are all the ways dogs can look". Instead, it can learn a factored representation: A dog has a head and a body. The network only needs to learn a very fuzzy representation at this level. Then a head has some eyes and maybe a nose. Again, it only needs to learn a very fuzzy representation and (very) rough relative locations.

So it only when it get right down into fine detail that it actually needs to learn pixel perfect representation. But this is _way_ easier, because in small areas images have surprisingly very low entropy.

The 'text-to-image' bit is a just a twist on the basic idea. At the start when the network is going "dog? or it might be a horse?", we fiddle with the probabilities a bit so that the network starts out convinced there's a dog in there somewhere. At which point it starts making the most likely places look a little more like a dog.

Research is still ongoing here, but it seems like diffusion models despite being named after the noise addition/removal process don't actually work because of it.

There's a paper (which I can't remember the name of) that shows the process still works with different information removal operators, including one with a circle wipe, and one where it blends the original picture with a cat photo.

Also, this article describes CLIP being trained on text-image pairs, but Google's Imagen uses an off the shelf text model so that part doesn't seem to be needed either.

If you removed all of the noise in a corrupted image in one step, you would have a denoising autoencoder, which has been around since the mid-aughts or perhaps earlier. Denoising diffusion models remove noise a little bit at a time. Think about an image which only has a slight amount of noise added to it. It’s generally easier to train a model to remove a tiny amount of noise than a large amount of noise. At the same time, we likely introduced a small amount of change to the actual contents of the image.

Typically, in generating the training data for diffusion models, we add noise incrementally to an image until it’s essentially all noise. Going backwards from almost all noise to the original images directly in one step is a pretty dubious proposition.

I was wondering the same and this video [1] helped me better understand how the prediction is used. The original paper isn't super clear about this either.

The diffusion process predicts the total noise that was added to the image. But that prediction isn't great and applying it immediately wouldn't result in a good output. So instead, the noise is multiplied by a small epsilon and then subtracted from the noisy image. That process is iterated to get to the final result.

[1]https://www.youtube.com/watch?v=J87hffSMB60

You can think of it like solving a differential equation numerically. The diffusion model encodes the relationships between values in sensible images (technically in the compressed representations of sensible images). You can try to jump directly to the solution but the result won't be very good compared to taking small steps.

I’m pretty sure it’s a stability issue. With small steps the noise is correlated between steps; if you tried it in one big jump then you would essentially just memorize the input data. The maximum noise would act as a “key” and the model would memorize the corresponding image as the “value”. But if we do it as a bunch of little steps then the nearby steps are correlated and in the training set you’ll find lots of groups of noise that are similar which allows the model to generalize instead of memorizing.

Two diffusion processes are involved:

1- Forward Diffusion (adding noise, and training the Unet to predict how much noise is added in each step)

2- Generating the image by denoising. This doesn't predict the final image, each step only predicts a small slice of noise (the removal of which leads to images similar to what the model encountered in step 1).

So it is indeed an iterative processes in that way, each step taking one step towards the final image.

Agreed. "Stable Diffusion with Diffusers" and "The Annotated Diffusion Model" were excellent and are linked in the article. The code in Diffusers was also a good reference.

Yes, I can read it perfectly fine. It relies on a lot of notation that AI researchers are familiar with.

It's as clear as wiring diagram for me. But I read a lot of ML literature.

If you're in AI research, that's a pretty standard diagram

> Google had: distill.pub

Wait I thought they were just taking a break. Don't tell me it's being killed

I also thought about this video while reading the HN post. The Computerphile video completely omits the latent space, right? But instead spends a lot of time on the iterative denoising. Even though I like Computerphile a lot, I don't think this was the best tradeoff.