Typo in noise level formula in Karras scheduler

[sgrigory]

Describe the bug

Comparing the formula for noise levels in KarrasVeScheduler

diffusers/src/diffusers/schedulers/scheduling_karras_ve.py

Lines 107 to 113 in a45dca0

	self.schedule = [
	(
	self.config.sigma_max
	* (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
	)
	for i in self.timesteps
	]

with Karras, Tero, et al. (VE column of Table 1), it seems to me that there is **2 missing, and the correct formula should be

self.schedule = [
            (
                self.config.sigma_max**2
                * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
            )
            for i in self.timesteps
        ]

This way the noise indeed ranges from sigma_min to sigma_max, as the docstring says.

Please let me know if I'm misunderstanding something here

This actually affects the generated images: they become less grainy and oversaturated after this is fixed

Reproduction

No response

Logs

No response

System Info

• diffusers version: 0.4.0.dev0
• Platform: Linux-5.10.133+-x86_64-with-Ubuntu-18.04-bionic
• Python version: 3.7.14
• PyTorch version (GPU?): 1.12.1+cu113 (True)
• Huggingface_hub version: 0.9.1
• Transformers version: 4.22.1
• Using GPU in script?: Yes
• Using distributed or parallel set-up in script?: No

[natolambert]

Hi @sgrigory - great catch! This scheduler isn't used in any big spaces / demos yet, so do you want to make a PR to change this? If not, I can easily do so (there may need to be a couple updated tests too) 🤗

[sgrigory]

@natolambert - thanks, sure, here is the PR: #627 . I've fixed one affected test I found, please let me know if you see any others which need adjustments