After I saw your next video "Cross Attention | method and math explained", I would like to see ControlNet's openpose in PyTorch Implementation which control posing on image of a dogs. Or if it is too complicate, you may simplify it to control 2 - 3 branches shape of a tree.
This videos is crazy! I don't get tired of recommend it to anyone interesting in diffusion models. I have recently started to research with these type of models and I think your video as huge source of information and guidance in this topic. I find myself recurrently re-watching your video to revise some information. Incredible work, we need more people like you!
We chose Diffusion Model as part of our course project, and your videos do save much of my time to understand the concepts and have more focus on implementing the main part. I am really grateful for your contribution.
Hey! I am start my CompSci Masters program in the Fall, and just wanted to say that I love this video. I've never really had time to sit down and learn PyTorch, so the brevity of this video is greatly appreciated! It gives me a fantastic starting point that I can tinker around with, and I have an idea on how I can apply this in a non-conventional way that I haven't seen much research on... Thanks again!
thank you so much for your detailed explaination of the code. It helped me a lot on my way of learning diffusion model. Wish there are more youtubers like you!
Hi, @Outlier , thank you for the awesome explanation ! Just one observation, I believe in line 50 of your code (at 19:10) it should be: uncond_predicted_noise = model(x,t,None) 😁
This is my first few days of trying to understand diffusion models. Coding was kinda fun on this one. I will take a break for 1-2 months and study something related like GANs or VAE, or even energy-based models. Then comeback with more general understanding :) Thanks !
Hello, thanks for your a lot contribution ! But a bit confused, At 06:04, just sampling from N(0, 1) totally randomly would not have any "trace" of an image. How come the model infer the image from the totally random noise ?
Hey there, that is sort of the "magic" of diffusion models which is hard to grasp your mind around. But since the model is trained to always see noise between 0% and 100% it sees full noise during training for which it is then trained to denoise it. And usually when you provide conditioning to the model such as class labels or text information, the model has more information than just random noise. But still, unconditional training still works.
Great video I faced a question at 19:10 line 50 of the code. why do we call ```model(x,label,None)``` what happened to t? shouldn't we instead call it like ```model(x,t,None)``` ?? also line 17 in ema (20:31) ```retrun old * self.beta +(1+self.beta) * new``` why 1+self.beta? shouldnt it be 1-self.beta?
Wonderful video! I notice that at 18:50, the equation for the new noise seems to differ from Eq. 6 in the CFG paper, as if the unconditioned and conditioned epsilons are reversed. Can you comment on that?
great walkthrough. but where would i implement dynamic or static thresholding as described in the imagen paper? the static thresholding clips all values larger then 1 but my model regularly outputs numbers as high as 5. but it creates images and loss decreases to 0.016 with SmoothL1Loss.
Sorry if I am misunderstanding, but at 19:10, shouldn't the code be: "uncond_predicted_noise = model(x, t, None)" instead of "uncond_predicted_noise = model(x, labels, None)" Also, according to the CFG paper's formula, shouldn't the next line be: "predicted_noise = torch.lerp(predicted_noise, uncond_predicted_noise, -cfg_scale)" under the definition of lerp? One last question: have you tried using L1Loss instead of MSELoss? On my implementation, L1 Loss performs much better (although my implementation is different than yours). I know the ELBO term expands to essentially an MSE term wrt predicted noise, so I am confused as to why L1 Loss performs better for my model. Thank you for your time.
8:38 in the UNet section, how do you decide on the number of channels to set in both input and output to the Down and Up classes. Why just 64,128, etc. ?
@@outliier oh okay got it. Thank you so much for clearing that and for the video! I had seen so many videos / read articles for diffusion but yours were the best and explained every thing which others considered prerequisites!! Separating the paper explanation and implementation was really helpful.
Could you please explain the paper "High Resolution Image Synthesis With Latent Diffusion Models" and its implementations? Your explanations are exceptionally crystal.
Roughly how long does an Epoch take for you? I am using rtx3060 mobile and achieving an epoch every 24 minutes. Also i cannot work with a batch size greater than 8 and a img size greater than 64 because it overfills my GPUs 6gb memory. I thought this was excessive for such small batch and img size?
Thank you so much for this amazing video! In mention that the first DDPM paper show no necessary of lower bound formulation, could you tell me the specific place in the paper? thanks!
With this training method, wouldn't there be a possibility of some timesteps not being trained in an epoch? wouldn't it be better to shuffle the whole list of timesteps and then sample sequentially with every batch?
having hard time to understand the mathematical and code aspect of diffusion model although i have a good high level understanding...any good resource i can go through? id appreciate it
` x = torch.randn((n, 3, self.img_size, self.img_size)).to(self.device) predicted_noise = model(x, t) ` in the deffusion class why you create an noise and pass that noise into the model to predict noise ... please explain
Which paper are you referring to? In the first paper, you would just set the variance to beta and since you add the std * noise you take the sqrt(beta)
People in Earth Observation know that images from Synthetic Aperture Radar have random speckles. People have tried removing the speckles using wavelets. I wonder how Denoising Diffusion would fare. The difficulty that I see is the need for x0 the un-noised image. What do you think?
Really nice video! I also enjoyed your explanation video - great work in general :) However, I noticed at around 5:38, you are defining sample_timesteps with low=1. I am pretty sure that this is wrong, as Python indexes at 0 meaning you skip the first noising step every time you access alpha, alpha_cumprod etc. Correct me if I am wrong but all the other implementations also utilise zero-indexing.
Random person 6 months later, but you could try decreasing the batch size during training. Your results may not look like what he got in the video though!
Thank you very much for this very easy-to-understand implementation. I have one question: I don't understand the function def noise_images. Assume that we have img_{0}, img_{1}, ..., img_{T}, which are obtained from adding the noise iteratively. I understand that img{t} is given by the formula "sqrt_alpha_hat * img_{0} + sqrt_one_minus_alpha_hat * Ɛ". However, I don't understand the function "def noise_images(self, x, t)" in [ddpm.py]. It return Ɛ, where Ɛ = torch.randn_like(x). So, this is just a noise signal draw directly from the normal distribution. I suppose this random noise is not related to the input image? It is becasue randn_like() returns a tensor with the same size as input x that is filled with random numbers from a normal distribution with mean 0 and variance 1 In training, the predicted noise is compared to this Ɛ (line 80 in [ddpm.py]). Why we are predicting this random noise? Shouldn't we predict the noise added at time t, i.e. "img_{t} - img_{t-1}"?
I had the same misconception before. It was actually explained by "AI Coffee Break with Letitia" channel in a video titled "How does Stable Diffusion work? - Latent Diffusion Models EXPLAINED". Basically, the model tries to predict the WHOLE noise added to the image to go from noised image to a fully denoised image in ONE STEP. Because it's a hard task to do, the model does not excel at that so at inference we denoise it iteratively, each time subtracting only a small fraction of the noise predicted by the model. In this way, the model produces much better quality samples. At least that's how I understood it :P
@@Laszer271 While I understand it predicts the "whole noise", this "whole noise" is newly generated and I suppose the ground truth is (img_{t} - img_{0)).. still can't wrap my head around it.
Thank you so much for this amazing video! You mention that changing the original DDPM to a conditional model should be as simple as adding in the condition at some point during training. I was just wondering if you had any experience with using DDPM to denoise images? I was planning on conditioning the model on the input noisy data by concatenating it to yt during training. I am going to try and play around with your github code and see if I can get something to work with denoising. Wish me luck!
There are from Yannick Kilcher (on the right side), the one in the lower left is from AICoffeeBreak, the one in the top right corner is the first video that comes when you google „diffusion models explained“ and I forgot the middle one sorry. But shouldnt be hard to find
You do not use any LR scheduler. Is this intentional? My understanding is that EMA is a functional equivalent of LR scheduler, but then I do not see any comparison between EMA vs e.g. cosine LR scheduler. Can you elaborate more on that?
Great videos on diffusion models, very understandable explanations! For how many hours did you train it? I tried adjusting your conditional model and train with a different dataset, but it seems to take forever :D
Hi Sir, Good afternoon. i wanna run the ddpm_conditional for my ultrasound images dataset having 5 classes and all the images have equal sizes 256*256 and also images are greyscale images. but i am encountering this error. " RuntimeError: Given groups=1, weight of size [256, 1, 3, 3], expected input[4, 3, 256, 256] to have 1 channels, but got 3 channels instead". i already had a changing regarding the channel and the size
I think you would just sample 10-50k images from the trained model and then take 10-50k images from the original dataset and then calculate the FID and IS
Your videos are a blessing. Thank you very much!!! Have you tried using DDIM to accelerate predictions? Or any other idea to decrease the number of steps needed?
I have not tried any speedups in any way. But feel free to try it out and tell me / us what works best. In the repo I do linked a fork which implements a couple additions which make the training etc. faster. You can check that out too here: github.com/tcapelle/Diffusion-Models-pytorch
Great video, thanks for making it. I started working with diffusion models very recently and I used you implementation as base for my model. I am currently facing a problem that the MSE loss starts very close to 1 and continues like that but varying between 1.0002 and 1.0004, for this reason the model is not training properly. Did you face any issue like this one? I am using the MNIST dataset to train the network, I wanted to first test it with some less complex dataset.
I am facing similar problems. I did the experiment on CIFAR10 dataset. The mse loss starts descresing normally but at some points the loss increse to 1 and never descrese again.
Hey, I am getting an error when i try to use one channel "RuntimeError: Given groups=1, weight of size [64, 1, 3, 3], expected input[4, 3, 64, 64] to have 1 channels, but got 3 channels instead" What can I do?
@@outliier There are Diffusion implementations out there that are a lot longer but it also makes it harder to understand what is happening. You removing all the unnecessary parts and just focusing on the absolute minimum is much better in my opinion. Well done.
Link to the code: github.com/dome272/Diffusion-Models-pytorch
21:56 The way you starred your own repo makes my day bro 🤣🤣 really appreciate your work, just keep going!!
@@bao-dai xd
@@outliier Thanks for sharing but how do you not get bored or tired of doing the same thing for so long and deal with all the math?
@@leif1075 I love to do it. I don’t get bored
After I saw your next video "Cross Attention | method and math explained", I would like to see ControlNet's openpose in PyTorch Implementation which control posing on image of a dogs. Or if it is too complicate, you may simplify it to control 2 - 3 branches shape of a tree.
Hello, this has become a great video once again. We didn't understand much, but it's still nice to watch. Greetings from home say Mam & Dad. ;-))))
This videos is crazy! I don't get tired of recommend it to anyone interesting in diffusion models. I have recently started to research with these type of models and I think your video as huge source of information and guidance in this topic. I find myself recurrently re-watching your video to revise some information. Incredible work, we need more people like you!
Thank you so much for the kind words!
Great, this video is finally out! Awesome coding explanation! 👏
These implementation videos are marvelous. You really should do more of them. Big fan of your channel!
We chose Diffusion Model as part of our course project, and your videos do save much of my time to understand the concepts and have more focus on implementing the main part. I am really grateful for your contribution.
Hey! I am start my CompSci Masters program in the Fall, and just wanted to say that I love this video.
I've never really had time to sit down and learn PyTorch, so the brevity of this video is greatly appreciated! It gives me a fantastic starting point that I can tinker around with, and I have an idea on how I can apply this in a non-conventional way that I haven't seen much research on...
Thanks again!
Love to hear that
Good luck on your journey!
After my midterm week i wanna study diffusion models with your videos im so exited .thanks a lot for good explanation
this is the most underrated channel i've ever seen, amazing explanation !
thank you so much!
I was wating for so long i learnd about condicional difusion models
Incredible. Very thorough and clear. Very, very well done.
thank you so much for your detailed explaination of the code. It helped me a lot on my way of learning diffusion model. Wish there are more youtubers like you!
Hi, @Outlier , thank you for the awesome explanation !
Just one observation, I believe in line 50 of your code (at 19:10) it should be:
uncond_predicted_noise = model(x,t,None)
😁
good catch thank you. (It's correct in the github code tho :))
most informative and easy to understand video on diffusion models on youtube, Thanks Man
This channel seems to be growing very fast. Thanks for this amazing tutorial.🤩
Sincere gratitude for this tutorial, this has really helped me with my project. Please continue with such videos.
The best video for diffusion! Very Clear
This is my first few days of trying to understand diffusion models. Coding was kinda fun on this one. I will take a break for 1-2 months and study something related like GANs or VAE, or even energy-based models. Then comeback with more general understanding :) Thanks !
And transformers for the attention mechanisms + positional encoding
I got that snatched in the past 2 months. Gotta learn the math, what is actually a distribution etc.@@zenchiassassin283
Congrats, This is a great channel!! hope to see more of these videos in the future.
This video is really timely and needed. Thanks for the implementation and keep up the good work!
Dude, you're amazing! Thanks for uploading this!
The Under rated OG channel
Thank you for sharing the implementation since authentic resources are rare
great tutorial! looking to seeing more of this! keep it up!
Hello, thanks for your a lot contribution ! But a bit confused, At 06:04, just sampling from N(0, 1) totally randomly would not have any "trace" of an image. How come the model infer the image from the totally random noise ?
Hey there, that is sort of the "magic" of diffusion models which is hard to grasp your mind around. But since the model is trained to always see noise between 0% and 100% it sees full noise during training for which it is then trained to denoise it. And usually when you provide conditioning to the model such as class labels or text information, the model has more information than just random noise. But still, unconditional training still works.
Great video
I faced a question at 19:10 line 50 of the code. why do we call
```model(x,label,None)```
what happened to t? shouldn't we instead call it like ```model(x,t,None)``` ??
also line 17 in ema (20:31) ```retrun old * self.beta +(1+self.beta) * new``` why 1+self.beta? shouldnt it be 1-self.beta?
Amazing tutorial, very informative and clear, nice work!
Very well done! Keep the great content!!
Wonderful video! I notice that at 18:50, the equation for the new noise seems to differ from Eq. 6 in the CFG paper, as if the unconditioned and conditioned epsilons are reversed. Can you comment on that?
Thank you. Best explanation with good DNN models
Very helpful walk-through. Thank you!
Thank you so much for this sharing, that was perfect!
great walkthrough. but where would i implement dynamic or static thresholding as described in the imagen paper? the static thresholding clips all values larger then 1 but my model regularly outputs numbers as high as 5. but it creates images and loss decreases to 0.016 with SmoothL1Loss.
Thanks, this implementation really helped clear things up.
nice demonstration, thanks for sharing
Incredible explanation, thanks a lot!
Sorry if I am misunderstanding, but at 19:10, shouldn't the code be:
"uncond_predicted_noise = model(x, t, None)" instead of "uncond_predicted_noise = model(x, labels, None)"
Also, according to the CFG paper's formula, shouldn't the next line be: "predicted_noise = torch.lerp(predicted_noise, uncond_predicted_noise, -cfg_scale)" under the definition of lerp?
One last question: have you tried using L1Loss instead of MSELoss? On my implementation, L1 Loss performs much better (although my implementation is different than yours). I know the ELBO term expands to essentially an MSE term wrt predicted noise, so I am confused as to why L1 Loss performs better for my model.
Thank you for your time.
Great videos by the way
Ah, I see you already fixed the first question in the codebase
8:38 in the UNet section, how do you decide on the number of channels to set in both input and output to the Down and Up classes. Why just 64,128, etc. ?
People just go with powers of 2 usually. And usually you go to more channels in the deeper layers of the network.
@@outliier oh okay got it. Thank you so much for clearing that and for the video! I had seen so many videos / read articles for diffusion but yours were the best and explained every thing which others considered prerequisites!! Separating the paper explanation and implementation was really helpful.
Could you please explain the paper "High Resolution Image Synthesis With Latent Diffusion Models" and its implementations? Your explanations are exceptionally crystal.
Roughly how long does an Epoch take for you? I am using rtx3060 mobile and achieving an epoch every 24 minutes. Also i cannot work with a batch size greater than 8 and a img size greater than 64 because it overfills my GPUs 6gb memory. I thought this was excessive for such small batch and img size?
Looking forward for some video on Classifier Guidance as well. Thanks.
Thank you so much for this amazing video! In mention that the first DDPM paper show no necessary of lower bound formulation, could you tell me the specific place in the paper? thanks!
Fantastic video!
With this training method, wouldn't there be a possibility of some timesteps not being trained in an epoch? wouldn't it be better to shuffle the whole list of timesteps and then sample sequentially with every batch?
Can you please explain how to use Woodfisher technique to approximate second-order gradients? Thanks
Thank you very much, it has solved my urgent need
Thank you for the review. So, what is the key to make a step from text description to image? Can you please pinpoint where it is explained?
It's definitely cool and helpful! Thanks!!!
Could you also make a video on how to implement DDIM? Or make a GitHub repository about it?
having hard time to understand the mathematical and code aspect of diffusion model although i have a good high level understanding...any good resource i can go through? id appreciate it
`
x = torch.randn((n, 3, self.img_size, self.img_size)).to(self.device)
predicted_noise = model(x, t)
`
in the deffusion class why you create an noise and pass that noise into the model to predict noise ... please explain
Very cool. How would DDIM models be different? Do they use a deterministic denoising sampler?
yes indeed
Very nicely explained. Thanks.
Why is the bias off in the initial convolutional block?
awesome implementation!
Awesome video.
Hi , I want to use a single underwater image dataset what changes do i have to implement on the code?
6:57 Why the formula is ... + torch.sqrt(beta) instead of calculated posterior variance like in paper?
Which paper are you referring to? In the first paper, you would just set the variance to beta and since you add the std * noise you take the sqrt(beta)
Great video!! You make coding seem like playing super mario 😂😂
last self attention layer (64, 64) changes my training type from 5 minutes to hours per epoch, do you know why?
training on a single rtx 3060 TI gpu
best diffusion youtube
People in Earth Observation know that images from Synthetic Aperture Radar have random speckles. People have tried removing the speckles using wavelets. I wonder how Denoising Diffusion would fare. The difficulty that I see is the need for x0 the un-noised image.
What do you think?
thanks for your amazing efforts!
it is very helpful!! You are a genius.. :) thank you!!
Really nice video! I also enjoyed your explanation video - great work in general :)
However, I noticed at around 5:38, you are defining sample_timesteps with low=1. I am pretty sure that this is wrong, as Python indexes at 0 meaning you skip the first noising step every time you access alpha, alpha_cumprod etc. Correct me if I am wrong but all the other implementations also utilise zero-indexing.
this function sample the timesteps of the denoising step. selecting time=0 is the original image itself. there is no point in taking 0 timestep.
Awesome! How did you type Ɛ in code?
@outliier Do you think there is a way to run the code with a 3060 GPU on personal desktop? I get the error message: CUDA out of memory.
Random person 6 months later, but you could try decreasing the batch size during training. Your results may not look like what he got in the video though!
There is a slight bug at 19:11
it should be
uncond_predicted_noise = model(x, t, None)
and not
uncond_predicted_noise = model(x, labels, None)
Yes correct. Good catch
Hi! Can you please explain why the output is getting two stitched images?
What do you mean with two stitched images?
Thank you very much for this very easy-to-understand implementation. I have one question: I don't understand the function def noise_images.
Assume that we have img_{0}, img_{1}, ..., img_{T}, which are obtained from adding the noise iteratively. I understand that img{t} is given by the formula "sqrt_alpha_hat * img_{0} + sqrt_one_minus_alpha_hat * Ɛ".
However, I don't understand the function "def noise_images(self, x, t)" in [ddpm.py].
It return Ɛ, where Ɛ = torch.randn_like(x). So, this is just a noise signal draw directly from the normal distribution. I suppose this random noise is not related to the input image? It is becasue randn_like() returns a tensor with the same size as input x that is filled with random numbers from a normal distribution with mean 0 and variance 1
In training, the predicted noise is compared to this Ɛ (line 80 in [ddpm.py]).
Why we are predicting this random noise? Shouldn't we predict the noise added at time t, i.e. "img_{t} - img_{t-1}"?
I had the same misconception before. It was actually explained by "AI Coffee Break with Letitia" channel in a video titled "How does Stable Diffusion work? - Latent Diffusion Models EXPLAINED".
Basically, the model tries to predict the WHOLE noise added to the image to go from noised image to a fully denoised image in ONE STEP. Because it's a hard task to do, the model does not excel at that so at inference we denoise it iteratively, each time subtracting only a small fraction of the noise predicted by the model. In this way, the model produces much better quality samples. At least that's how I understood it :P
@@Laszer271 While I understand it predicts the "whole noise", this "whole noise" is newly generated and I suppose the ground truth is (img_{t} - img_{0)).. still can't wrap my head around it.
So the process of adding noise and removing it happens in a loop
Thank you so much for this amazing video! You mention that changing the original DDPM to a conditional model should be as simple as adding in the condition at some point during training. I was just wondering if you had any experience with using DDPM to denoise images? I was planning on conditioning the model on the input noisy data by concatenating it to yt during training. I am going to try and play around with your github code and see if I can get something to work with denoising. Wish me luck!
one CRAZY thing to take from this code (and video)
GREEK LETTERS ARE CAN BE USED AS VARIABLE NAME IN PYTHON
Amazing stuff!
great video. please can you list the creators of the other helpful videos at 00:52? thanks
There are from Yannick Kilcher (on the right side), the one in the lower left is from AICoffeeBreak, the one in the top right corner is the first video that comes when you google „diffusion models explained“ and I forgot the middle one sorry. But shouldnt be hard to find
I think your code bugs when adjust image_size?
Thank you for the video.
How can we use diffusion model for inpainting?
This is GOLD
Great video!
Can you please tell me how much time was need to train this 3000 image for 500 Epoch?
You do not use any LR scheduler. Is this intentional? My understanding is that EMA is a functional equivalent of LR scheduler, but then I do not see any comparison between EMA vs e.g. cosine LR scheduler. Can you elaborate more on that?
Great videos on diffusion models, very understandable explanations! For how many hours did you train it? I tried adjusting your conditional model and train with a different dataset, but it seems to take forever :D
Yea it took quite long. On the 3090 it trained a couple days (2-4 days I believe)
@@outliier Thanks for the feedback. Ok seems like I didn't do a mistake, but only need more patience!
@@maybritt-sch Yea. Let me know how it goes or if you need help
How can i increase the size of the generated image here?
Hi Sir, Good afternoon. i wanna run the ddpm_conditional for my ultrasound images dataset having 5 classes and all the images have equal sizes 256*256 and also images are greyscale images. but i am encountering this error. " RuntimeError: Given groups=1, weight of size [256, 1, 3, 3], expected input[4, 3, 256, 256] to have 1 channels, but got 3 channels instead". i already had a changing regarding the channel and the size
Hey, can you post your code on github and give the error?
How can i increase the img size to 128 pixels square?
thanks for the easiest implementation. could you plz tell us how to find FID and IS score for these images?
I think you would just sample 10-50k images from the trained model and then take 10-50k images from the original dataset and then calculate the FID and IS
@@outliier thanks
Your videos are a blessing. Thank you very much!!! Have you tried using DDIM to accelerate predictions? Or any other idea to decrease the number of steps needed?
I have not tried any speedups in any way. But feel free to try it out and tell me / us what works best. In the repo I do linked a fork which implements a couple additions which make the training etc. faster. You can check that out too here: github.com/tcapelle/Diffusion-Models-pytorch
@@outliier Thank you! I will try it for sure.
hey can we use an image as a condition
Great video, thanks for making it. I started working with diffusion models very recently and I used you implementation as base for my model. I am currently facing a problem that the MSE loss starts very close to 1 and continues like that but varying between 1.0002 and 1.0004, for this reason the model is not training properly. Did you face any issue like this one? I am using the MNIST dataset to train the network, I wanted to first test it with some less complex dataset.
I am facing similar problems. I did the experiment on CIFAR10 dataset. The mse loss starts descresing normally but at some points the loss increse to 1 and never descrese again.
Can you do one for tensorflow too btw very good explaination
How did you learn do much?
I read a lot of papers and watched a lot of tutorials
Great Video,
On what Data did you train your model again?
great video, you got one new subscriber
This video is priceless.
Great video! How long did it take to train the models?
About 3-4 days on an rtx 3090.
Thank you for sharing!
Hey, I am getting an error when i try to use one channel
"RuntimeError: Given groups=1, weight of size [64, 1, 3, 3], expected input[4, 3, 64, 64] to have 1 channels, but got 3 channels instead"
What can I do?
You need to change the input and output channels in the unet code
Can we use diffusion to a neural architecture for classification
I think people have done that to. But I don’t remember the papers. But maybe just look for „diffusion models for classification“
@@outliier thanks, I figured it out myself.
Where is the link to the code?
sorry I totally forgot to put the link in the description. I updated it now, but here is the link too: github.com/dome272/Diffusion-Models-pytorch
@@outliier There are Diffusion implementations out there that are a lot longer but it also makes it harder to understand what is happening. You removing all the unnecessary parts and just focusing on the absolute minimum is much better in my opinion. Well done.
is anyone find the DDPM Unet architecture figure, I can't find it