diffusers/docs/source/api/schedulers.mdx

<!--Copyright 2022 The HuggingFace Team. All rights reserved.

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with
the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on
an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the
specific language governing permissions and limitations under the License.
-->

# Schedulers

Diffusers contains multiple pre-built schedule functions for the diffusion process.

## What is a schduler?
The schedule functions, denoted *Schedulers* in the library take in the output of a trained model, a sample which the diffusion process is iterating on, and a timestep to return a denoised sample.

- Schedulers define the methodology for iteratively adding noise to an image or for updating a sample based on model outputs.
    - adding noise in different manners represent the algorithmic processes to train a diffusion model by adding noise to images.
    - for inference, the scheduler defines how to update a sample based on an output from a pretrained model.
- Schedulers are often defined by a *noise schedule* and an *update rule* to solve the differential equation solution.

### Discrete versus continuous schedulers
All schedulers take in a timestep to predict the updated version of the sample being diffused.
The timesteps dictate where in the diffusion process the step is, where data is generated by iterating forward in time and inference is executed by propagating backwards through timesteps.
Different algorithms use timesteps that both discrete (accepting `int` inputs), such as the [`DDPMScheduler`] or [`PNDMScheduler`], and continuous (accepting 'float` inputs), such as the score-based schedulers [`ScoreSdeVeScheduler`] or [`ScoreSdeVpScheduler`].

## Designing Re-usable schedulers
The core design principle between the schedule functions is to be model, system, and framework independent.
This allows for rapid experimentation and cleaner abstractions in the code, where the model prediction is separated from the sample update.
To this end, the design of schedulers is such that:
- Schedulers can be used interchangeably between diffusion models in inference to find the preferred trade-off between speed and generation quality.
- Schedulers are currently by default in PyTorch, but are designed to be framework independent (partial Numpy support currently exists).


## API
The core API for any new scheduler must follow a limited structure.
- Schedulers should provide one or more `def step(...)` functions that should be called to update the generated sample iteratively.
- Schedulers should provide a `set_timesteps(...)` method that configures the parameters of a schedule function for a specific inference task.
- Schedulers should be framework-agonstic, but provide a simple functionality to convert the scheduler into a specific framework, such as PyTorch
with a `set_format(...)` method.

### Core
The base class [`SchedulerMixin`] implements low level utilities used by multiple schedulers.

#### SchedulerMixin
[[autodoc]] SchedulerMixin

#### SchedulerOutput
The class [`SchedulerOutput`] contains the ouputs from any schedulers `step(...)` call.
[[autodoc]] schedulers.scheduling_utils.SchedulerOutput

### Existing Schedulers

#### Denoising diffusion implicit models (DDIM)

Original paper can be found here.

[[autodoc]] schedulers.scheduling_ddim.DDIMScheduler

#### Denoising diffusion probabilistic models (DDPM)

Original paper can be found [here](https://arxiv.org/abs/2010.02502).

[[autodoc]] schedulers.scheduling_ddpm.DDPMScheduler

#### Varience exploding, stochastic sampling from Karras et. al

Original paper can be found [here](https://arxiv.org/abs/2006.11239).

[[autodoc]] schedulers.scheduling_karras_ve.KarrasVeScheduler

#### Linear multistep scheduler for discrete beta schedules

Original implementation can be found [here](https://arxiv.org/abs/2206.00364).


[[autodoc]] schedulers.scheduling_lms_discrete.LMSDiscreteScheduler

#### Pseudo numerical methods for diffusion models (PNDM)

Original implementation can be found [here](https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L181).

[[autodoc]] schedulers.scheduling_pndm.PNDMScheduler

#### variance exploding stochastic differential equation (SDE) scheduler

Original paper can be found [here](https://arxiv.org/abs/2011.13456).

[[autodoc]] schedulers.scheduling_sde_ve.ScoreSdeVeScheduler

#### variance preserving stochastic differential equation (SDE) scheduler

Original paper can be found [here](https://arxiv.org/abs/2011.13456).

<Tip warning={true}>

Score SDE-VP is under construction.

</Tip>

[[autodoc]] schedulers.scheduling_sde_vp.ScoreSdeVpScheduler