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SleekEagle OP t1_itxpvth wrote

Reply to comment by Serverside in [D] Poisson Flow Generative Models - new physics inspired generative model by SleekEagle

My pleasure! I'm not sure I understand exactly what you're asking, could you try to rephrase it? In particular, I'm not sure what you mean by preservation of the data distribution.

Maybe this will help answer: Given an exact Poisson field generated by a continuous data distribution, PFGMs provide an exact deterministic mapping to/from a uniform hemisphere. While we do not know this Poisson field exactly, we can estimate given many data points sampled from the distribution. PFGMs therefore provide a deterministic mapping between the uniform hemisphere and the distribution that corresponds to the learned empirical field, but not exactly to the data distribution itself. Given a lot of data, though, we expect this approximate distribution to be very close to the true distribution (universal to all generative models)

Thanks for reading! I did have a little trouble getting the repo working on my local machine, so I might expect some trouble if I were you. I reached out to the authors while writing this article and I believe they are planning on continuing research into PFGMs, so don't forget to keep an eye out for future developments!

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Serverside t1_itxsq3p wrote

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!

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SleekEagle OP t1_itzjvvo wrote

Got it! Yeah the ultimate crux of it is the proof that any continuous compact distribution has a field that approaches uniform flux density at infinity

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