Implementation error of v_prediction in eulara and eular

I came across a potential inconsistency in the implementation of v_prediction within the Euler scheduler when examining the source code. Specifically, in the computation of pred_original_sample, the formula is given as:
`pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))`
Where sigma is calculated as:
`sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)`
Substituting the definition of sigma into the equation for pred_original_sample, we arrive at:
`pred_original_sample = sample * alphas_cumprod - model_output * ((1-alphas_cumprod) ** 0.5)`
Here, it appears that `sample * alphas_cumprod` is missing a square root operation on `alphas_cumprod`. Shouldn't this be `sample * (alphas_cumprod**0.5)`? This seems to be an inconsistency, especially considering that in the DDIM scheduler as in
`(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output`.
Could this be an error?

Locate the Euler scheduler implementation and the computation of pred_original_sample. Check the reported substitution for sigma against the DDIM expression and the scheduler's prediction convention. Done means determining whether the square root is missing and documenting or correcting the implementation accordingly.

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