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* Support training SD V2 with Flax

Mostly involves supporting a v_prediction scheduler.

The implementation in #1777 doesn't take into account a recent refactor of `scheduling_utils_flax`, so this should be used instead.

* Add to other top-level files.

* [Flax] Stateless schedulers, fixes and refactors

* Remove scheduling_common_flax and some renames

* Update src/diffusers/schedulers/scheduling_pndm_flax.py
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>

[FLAX] Fix loading scheduler from subfolder

* add conversion script for vae

* uP

* uP

* more changes

* push

* up

* finish again

* up

* up

* up

* up

* finish

* up

* uP

* up

* Apply suggestions from code review
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>
Co-authored-by: Anton Lozhkov <anton@huggingface.co>
Co-authored-by: Suraj Patil <surajp815@gmail.com>

* up

* up
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>
Co-authored-by: Anton Lozhkov <anton@huggingface.co>
Co-authored-by: Suraj Patil <surajp815@gmail.com>

* added broadcast_to_shape_from_left helper

* initial tests

* fixed pndm tests

* shape required for pndm

* added require_flax

* fix style

* fix more imports
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* Don't use `load_state_dict` if torch is not installed.

* Define `SchedulerOutput` to use torch or flax arrays.

* Don't import LMSDiscreteScheduler without torch.

* Create distinct FlaxSchedulerOutput.

* Additional changes required for FlaxSchedulerMixin

* Do not import torch pipelines in Flax.

* Revert "Define `SchedulerOutput` to use torch or flax arrays."

This reverts commit f653140134b74d9ffec46d970eb46925fe3a409d.

* Prefix Flax scheduler outputs for consistency.

* make style

* FlaxSchedulerOutput is now a dataclass.

* Don't use f-string without placeholders.

* Add blank line.

* Style (docstrings)

* add dep. warning for schedulers

* fix format

* pytorch only schedulers

* fix style

* remove match_shape

* pytorch only ddpm

* remove SchedulerMixin

* remove numpy from karras_ve

* fix types

* remove numpy from lms_discrete

* remove numpy from pndm

* fix typo

* remove mixin and numpy from sde_vp and ve

* remove remaining tensor_format

* fix style

* sigmas has to be torch tensor

* removed set_format in readme

* remove set format from docs

* remove set_format from pipelines

* update tests

* fix typo

* continue to use mixin

* fix imports

* removed unsed imports

* match shape instead of assuming image shapes

* remove import typo

* update call to add_noise

* use math instead of numpy

* fix t_index

* removed commented out numpy tests

* timesteps needs to be discrete

* cast timesteps to int in flax scheduler too

* fix device mismatch issue

* small fix

* Update src/diffusers/schedulers/scheduling_pndm.py
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* init schedulers docs

* add some docstrings, fix sidebar formatting

* add docstrings

* [Type hint] PNDM schedulers (#335)

* [Type hint] PNDM Schedulers

* ran make style

* updated timesteps type hint

* apply suggestions from code review

* ran make style

* removed unused import

* [Type hint] scheduling ddim (#343)

* [Type hint] scheduling ddim

* apply suggestions from code review

apply suggestions to also return the return type
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* make style

* update class docstrings

* add docstrings

* missed merge edit

* add general docs page

* modify headings for right sidebar
Co-authored-by: Partho <parthodas6176@gmail.com>
Co-authored-by: Santiago Víquez <santi.viquez@gmail.com>
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* add outputs for models

* add for pipelines

* finish schedulers

* better naming

* adapt tests as well

* replace dict access with . access

* make schedulers works

* finish

* correct readme

* make  bcp compatible

* up

* small fix

* finish

* more fixes

* more fixes

* Apply suggestions from code review
Co-authored-by: Suraj Patil <surajp815@gmail.com>
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>

* Update src/diffusers/models/vae.py
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>

* Adapt model outputs

* Apply more suggestions

* finish examples

* correct
Co-authored-by: Suraj Patil <surajp815@gmail.com>
Co-authored-by: Pedro Cuenca <pedro@huggingface.co>

* work in progress, fixing tests for numpy and make deterministic

* make tests pass via pytorch

* make pytorch == numpy test cleaner

* change default tensor format pndm --> pt

* Add a decorator for register_to_config

* All models and test

* clean ddpm api to match ddim

* correct ve sde class

* update pipeline API for ve sde

* make style

* Apply suggestions from code review
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

* improve comments for sde_ve scheduler, init tests

* more comments, tweaking pipelines

* timesteps --> num_training_timesteps, some comments

* merge cpu test, add m1 data

* fix scheduler tests with num_train_timesteps

* make np compatible, add tests for sde ve

* minor default variable fixes

* make style and fix-copies
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>