EulerDiscreteScheduler is not complete and sign of c_out is wrong

[cameronalonso2]

Describe the bug

Hi, the implementation of EDM method here https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_euler_discrete.py misses the second-order correction step implemented here in the original paper https://arxiv.org/pdf/2206.00364.pdf: please see https://github.com/NVlabs/edm/blob/b2a26c921c5776cb52f7498248761d60649007a8/example.py#L65

        # Apply 2nd order correction.
        if i < num_steps - 1:
            denoised = net(x_next, t_next, class_labels).to(torch.float64)
            d_prime = (x_next - denoised) / t_next
            x_next = x_hat + (t_next - t_hat) * (0.5 * d_cur + 0.5 * d_prime)

without this step algorithm 2 in the paper is not complete. Also on this line: https://github.com/huggingface/diffusers/blob/0b7225e91852df668ce85a7f7a670c00272c9ed0/src/diffusers/schedulers/scheduling_euler_discrete.py#L238 the sign for c_out ((sigma / (sigma**2 + 1) ** 0.5) ) is not correct, from:

 pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))

this should be converted to:

 pred_original_sample = model_output * (sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))

It would be great if this could be corrected. Thank you.

Reproduction

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Logs

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System Info

Last version of diffusers in the github.

[patrickvonplaten]

Hey @cameronalonso2,

I think we should add a new scheduler "Euler2" for this. We should have finished this by the end of this week

[cameronalonso2]

Hi @patrickvonplaten thank you. It would be awesome. May I ask which method is the one implemented? and in which paper this is proposed? When I was testing it, I was not able to get the generation to work with this sampler, and I wanted to check the details in your know the original paper. thanks.

[patrickvonplaten]

Sure the current method comes from: https://github.com/crowsonkb/k-diffusion/blob/5b3af030dd83e0297272d861c19477735d0317ec/k_diffusion/sampling.py#L118

[cameronalonso2]

Thank you

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