Implementation error of v_prediction in eulara and eular

[yelanyelan]

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?

[yiyixuxu]

hi! thanks for the issue
note that sample is scaled with 1/ ((sigma**2 + 1) ** 0.5) for euler scheduler

self.scheduler.scale_model_input() is always called inside pipeline at each step

diffusers/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py

Line 1047 in e4b8f17

latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)

here is how scale_model_input is implemented for euler scheduler

diffusers/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py

Line 255 in e4b8f17

def scale_model_input(

for ddim we do not scale sample

diffusers/src/diffusers/schedulers/scheduling_ddim.py

Line 238 in e4b8f17

def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:

[yelanyelan]

Thx u. I did not notice the features of the Euler scheduler. Now I fully understand. YiYi Xu ***@***.***> 于2024年2月22日周四 16:20写道：

…

hi! thanks for the issue note that sample is scaled with 1/ ((sigma**2 + 1) ** 0.5) for euler scheduler self.scheduler.scale_model_input() is always called inside pipeline at each step https://github.com/huggingface/diffusers/blob/e4b8f173b97731686e290b2eb98e7f5df2b1b322/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py#L1047 here is how scale_model_input is implemented for euler scheduler https://github.com/huggingface/diffusers/blob/e4b8f173b97731686e290b2eb98e7f5df2b1b322/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py#L255 for ddim we do not scale sample https://github.com/huggingface/diffusers/blob/e4b8f173b97731686e290b2eb98e7f5df2b1b322/src/diffusers/schedulers/scheduling_ddim.py#L238 — Reply to this email directly, view it on GitHub <#7046 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACXEPNYW4ZTBR7ZQTJ4EZK3YU35TVAVCNFSM6AAAAABDS5AZEKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMYTSNJYHEZDMOBQGI> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[luocfprime]

hi! thanks for the issue note that sample is scaled with 1/ ((sigma**2 + 1) ** 0.5) for euler scheduler

self.scheduler.scale_model_input() is always called inside pipeline at each step

diffusers/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py

Line 1047 in e4b8f17

latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)

here is how scale_model_input is implemented for euler scheduler

diffusers/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py

Line 255 in e4b8f17

def scale_model_input(

for ddim we do not scale sample

diffusers/src/diffusers/schedulers/scheduling_ddim.py

Line 238 in e4b8f17

def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:

Hi, may I ask what exactly does scale_model_input do in the EulerDiscreteScheduler?

I've checked the original EDM paper and k-diffusion implementation, the scaling coefficient $s(t)$ is 1 in the paper, and the model input of k-diffusion sample_euler does not require extra scaling.

    for i in trange(len(sigmas) - 1, disable=disable):
        gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
        eps = torch.randn_like(x) * s_noise
        sigma_hat = sigmas[i] * (gamma + 1)
        if gamma > 0:
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        denoised = model(x, sigma_hat * s_in, **extra_args) # no extra scaling for x

But in diffusers implementation, the input latent is scaled by 1 / ((sigma**2 + 1) ** 0.5), may I ask the rationale behind this?

Thanks!

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[yifanlu0227]

@luocfprime Do you understand this scaling now? I am also confused.

[luocfprime]

No. Not yet.

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---- Replied Message ---- | From | Yifan ***@***.***> | | Date | 07/21/2025 00:41 | | To | ***@***.***> | | Cc | Chaofan ***@***.***>, Mention ***@***.***> | | Subject | Re: [huggingface/diffusers] Implementation error of v_prediction in eulara and eular (Issue #7046) | yifanlu0227 left a comment (huggingface/diffusers#7046) @luocfprime Do you understand this scaling now? I am also confused. — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you were mentioned.Message ID: ***@***.***>

[yifanlu0227]

I think it's the preconditioning of VP / iDDPM + DDIM