# EDMEulerScheduler

The Karras formulation of the Euler scheduler (Algorithm 2) from the [Elucidating the Design Space of Diffusion-Based Generative Models](https://huggingface.co/papers/2206.00364) paper by Karras et al. This is a fast scheduler which can often generate good outputs in 20-30 steps. The scheduler is based on the original [k-diffusion](https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L51) implementation by [Katherine Crowson](https://github.com/crowsonkb/).

## EDMEulerScheduler[[diffusers.EDMEulerScheduler]]
#### diffusers.EDMEulerScheduler[[diffusers.EDMEulerScheduler]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L49)

Implements the Euler scheduler in EDM formulation as presented in Karras et al. 2022 [1].

[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
https://huggingface.co/papers/2206.00364

This model inherits from [SchedulerMixin](/docs/diffusers/main/en/api/schedulers/overview#diffusers.SchedulerMixin) and [ConfigMixin](/docs/diffusers/main/en/api/configuration#diffusers.ConfigMixin). Check the superclass documentation for the generic
methods the library implements for all schedulers such as loading and saving.

add_noisediffusers.EDMEulerScheduler.add_noisehttps://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L433[{"name": "original_samples", "val": ": Tensor"}, {"name": "noise", "val": ": Tensor"}, {"name": "timesteps", "val": ": Tensor"}]- **original_samples** (`torch.Tensor`) --
  The original samples to which noise will be added.
- **noise** (`torch.Tensor`) --
  The noise tensor to add to the original samples.
- **timesteps** (`torch.Tensor`) --
  The timesteps at which to add noise, determining the noise level from the schedule.0`torch.Tensor`The noisy samples with added noise scaled according to the timestep schedule.

Add noise to the original samples according to the noise schedule at the specified timesteps.

**Parameters:**

sigma_min (`float`, *optional*, defaults to 0.002) : Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the EDM paper [1]; a reasonable range is [0, 10].

sigma_max (`float`, *optional*, defaults to 80.0) : Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the EDM paper [1]; a reasonable range is [0.2, 80.0].

sigma_data (`float`, *optional*, defaults to 0.5) : The standard deviation of the data distribution. This is set to 0.5 in the EDM paper [1].

sigma_schedule (`str`, *optional*, defaults to `karras`) : Sigma schedule to compute the `sigmas`. By default, we the schedule introduced in the EDM paper (https://huggingface.co/papers/2206.00364). Other acceptable value is "exponential". The exponential schedule was incorporated in this model: https://huggingface.co/stabilityai/cosxl.

num_train_timesteps (`int`, defaults to 1000) : The number of diffusion steps to train the model.

prediction_type (`str`, defaults to `epsilon`, *optional*) : Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process), `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen Video](https://huggingface.co/papers/2210.02303) paper).

rho (`float`, *optional*, defaults to 7.0) : The rho parameter used for calculating the Karras sigma schedule, which is set to 7.0 in the EDM paper [1].

final_sigmas_type (`str`, defaults to `"zero"`) : The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.

**Returns:**

``torch.Tensor``

The noisy samples with added noise scaled according to the timestep schedule.
#### index_for_timestep[[diffusers.EDMEulerScheduler.index_for_timestep]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L287)

Find the index of a given timestep in the timestep schedule.

**Parameters:**

timestep (`float` or `torch.Tensor`) : The timestep value to find in the schedule.

schedule_timesteps (`torch.Tensor`, *optional*) : The timestep schedule to search in. If `None`, uses `self.timesteps`.

**Returns:**

``int``

The index of the timestep in the schedule. For the very first step, returns the second index if
multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
#### scale_model_input[[diffusers.EDMEulerScheduler.scale_model_input]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L191)

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.

**Parameters:**

sample (`torch.Tensor`) : The input sample.

timestep (`int`, *optional*) : The current timestep in the diffusion chain.

**Returns:**

``torch.Tensor``

A scaled input sample.
#### set_begin_index[[diffusers.EDMEulerScheduler.set_begin_index]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L153)

Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

**Parameters:**

begin_index (`int`, defaults to `0`) : The begin index for the scheduler.
#### set_timesteps[[diffusers.EDMEulerScheduler.set_timesteps]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L215)

Sets the discrete timesteps used for the diffusion chain (to be run before inference).

**Parameters:**

num_inference_steps (`int`) : The number of diffusion steps used when generating samples with a pre-trained model.

device (`str` or `torch.device`, *optional*) : The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.

sigmas (`Union[torch.Tensor, List[float]]`, *optional*) : Custom sigmas to use for the denoising process. If not defined, the default behavior when `num_inference_steps` is passed will be used.
#### step[[diffusers.EDMEulerScheduler.step]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L333)

Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
process from the learned model outputs (most often the predicted noise).

**Parameters:**

model_output (`torch.Tensor`) : The direct output from learned diffusion model.

timestep (`float`) : The current discrete timestep in the diffusion chain.

sample (`torch.Tensor`) : A current instance of a sample created by the diffusion process.

s_churn (`float`) --

s_tmin  (`float`) --

s_tmax  (`float`) --

s_noise (`float`, defaults to 1.0) : Scaling factor for noise added to the sample.

generator (`torch.Generator`, *optional*) : A random number generator.

return_dict (`bool`) : Whether or not to return a `~schedulers.scheduling_euler_discrete.EDMEulerSchedulerOutput` or tuple.

**Returns:**

``~schedulers.scheduling_euler_discrete.EDMEulerSchedulerOutput` or `tuple``

If return_dict is `True`, `~schedulers.scheduling_euler_discrete.EDMEulerSchedulerOutput` is
returned, otherwise a tuple is returned where the first element is the sample tensor.

## EDMEulerSchedulerOutput[[diffusers.schedulers.scheduling_edm_euler.EDMEulerSchedulerOutput]]
#### diffusers.schedulers.scheduling_edm_euler.EDMEulerSchedulerOutput[[diffusers.schedulers.scheduling_edm_euler.EDMEulerSchedulerOutput]]

[Source](https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_edm_euler.py#L32)

Output class for the scheduler's `step` function output.

**Parameters:**

prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images) : Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop.

pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images) : The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance.

