Yeah you essentially answered what I was asking. I was basically asking if the output of a trained PFGM matched (or closely estimated) the empirical distribution of the training data. Since the end product of the “diffusion” was said to be a uniform distribution and the equations were ODEs not SDEs, I was having trouble wrapping my head around how the PFGM could be empirically matching the distribution. Thanks for answering all the questions!

I see. Thanks for the in depth response, and your answers make sense. The last follow up question I have is: Do PFGMs preserve the distribution of the data, or since it is transformed to a uniform distribution, is the original distribution of the data lost?

I know the other stochastic generative models usually try to match or preserve the distribution of data. Maybe you also somewhat answered this already in your second paragraph, but I just wanted to make sure I understood.

Again, your blog and code look neat. I look forward to toying with them on some data of my own.

Ok, I'll bite. It looks cool from what I see in the blog. How does the model being deterministic impact (or not impact) the generative capabilities? I would think that a deterministic mapping from original data to uniform angles would not perform as well when wanting to interpolate or extrapolate (for example, like VAEs vs normal autoencoders).

That's what cheaters say to cope with their terrible morals

Yeah I've read that paper you linked, but I have not really delved into trying to implement conditional SGM code myself (I've done work with conditional generative models in terms of GANs, VAEs, etc). I am also interested in lower dimensional data than images, so your code looked like a good starting point.

After some more reading, I'll give adding conditional capabilities to your code a shot.

Nice code! What would it take to make this conditional? I.e. for your circle example, produce a conditional distribution of points based on the arc-length (or some other label)?