huggingface / huggingface/diffusers
Formulation of reverse diffusion process in DDPM ( 1 - alpha_prod_t = beta_prod_t assumption)
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Descrizione
### Describe the bug
I looked into sampling code of DDPM, and I believe there's a mistake:
#### I believe the code makes assumption that 1 - alpha_prod_t = beta_prod_t, which simply isn't true.
Original sampling algorithm:
[original paper](https://arxiv.org/pdf/2006.11239)

x_0 prediction from sample and predicted noise :
Eqn 15 from paper, as referenced in code snippet as well:

code implementation in diffusers:
https://github.com/huggingface/diffusers/blob/1e8cf2763d37fa66cfba2fb87acfe3443068ce43/src/diffusers/schedulers/scheduling_ddpm.py#L446-L449
### Here, it clearly seems like the 1 - alpha_prod_t = beta_prod_t is being used.
investigated from post by @AlejandroBaron in https://github.com/huggingface/diffusers/discussions/9431_
### Reproduction
I haven't tested out code, but this seems fundamental formulation issue.
### Logs
_No response_
### System Info
0.30.3
### Who can help?
@sayakpaul @DN6 @yiy
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