This might be how they did inversion in the DDIM paper, but I couldn't find the exact method except a vague description of the inverse process "by running the sampler backwards" just like you described.

Edit to quote the paper: "...can encode from x0 to xT (reverse of Eq. (14)) and reconstruct x0 from the resulting xT (forward of Eq. (14))", page 9 section 5.4

Played around with this a bit more – if I do the noising with 1000 steps (i.e. the number of training steps, instead of 50 above), I get an output which actually "looks like" random noise (and has a standard deviation of 14.6 ~= sigma[0]) but which if used as starting noise for an image generation (without any prompt conditioning and with around 50 sampling steps) actually recreates the original image pretty well (and it's not blurry as when I used 50 steps in the noising)!

Not sure why it's so blurry when I use only 50 steps instead of 1000 to noise it, I'd expect the sampler to be able to approximate the noise using just a few dozen steps roughly as well as it's able to approximate the image when run in the "normal direction". The standard deviation of the noise is only around 12.5 or so when I use 50 steps instead of 1000, so maybe I have an off-by-one error or something somewhere that results in too little noise being added.

Great, that's exactly what the authors observed in the DDIM paper! If you don't mind, you are free to setup a quick demo with maybe one or two examples and push it to the github, that would be super cool for everyone to use!

Edit: And for the reason behind why 50 steps doesn't work as well, I guess maybe is that the forward process uses many tricks for acceleration while the inverse process was pretty much neglected and was not optimized (remember the first paper on diffusion models actually needed 1000 sampling steps too for good results), so you actually need to perform the diffusion correctly, for now (eg. 1000 steps).

Yeah, I'm generating a few examples now, and I'll post something in this subreddit and some code on Github later tonight. I didn't actually try your cross attention control code yet, I'll have to do that as well and see how all this fits together. :)

Wonder if the inversion code could be used to style transfer like in https://github.com/justinpinkney/stable-diffusion . Take clip1 embedding from image1, reconstruct the noise1, take image 2, find clip2, and recreate from noise1 to get a style2 result. Still only just read about it so haven't thought it through, but the reconstruction idea seemed very useful. I will think about it but i'm not sure i'm up to the task of coding it up/trying it out myself

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## u/bloc97 Sep 11 '22

This might be how they did inversion in the DDIM paper, but I couldn't find the exact method except a vague description of the inverse process "by running the sampler backwards" just like you described.

Edit to quote the paper: "...can encode from x0 to xT (reverse of Eq. (14)) and reconstruct x0 from the resulting xT (forward of Eq. (14))", page 9 section 5.4