DPM++ third order fixes

[StAlKeR7779]

What does this PR do?

This pull request addresses two issues:

Incorrect output in DPMSolverSinglestepScheduler

Fixed the issue where using solver_order=3 and a step count of 3n-1 resulted in incorrect output. The problem was caused by improper handling of final_sigmas_type=zero, leading to a log(0) error in the singlestep_dpm_solver_second_order_update function. The handling has been implemented in the simplest possible way, and I welcome any suggestions how it can done better.

Support for sde-dpmsolver++ in third order

Added support for the sde-dpmsolver++ algorithm to both the DPMSolverSinglestepScheduler and DPMSolverMultistepScheduler. Previously, using solver_order=3 would throw an error:
UnboundLocalError: local variable 'x_t' referenced before assignment
This was due to the lack of a branch to handle the sde-dpmsolver++ algorithm in the singlestep_dpm_solver_third_order_update and multistep_dpm_solver_third_order_update functions. My implementation is based on how the sde is already integrated into first and second-order solvers, so please review carefully to ensure correctness.

Fixes # (issue)
#9007

Who can review?

@yiyixuxu
@LuChengTHU (sorry if wrongly tag you)

[github-actions]

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[yiyixuxu]

can you take a look here? @hlky

[HuggingFaceDocBuilderDev]

The docs for this PR live here. All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

[hlky]

Thanks @StAlKeR7779! 🤗

Test

from diffusers import DPMSolverSinglestepScheduler, DPMSolverMultistepScheduler, StableDiffusionXLPipeline
import torch

solver_order = 3
algorithm_type = "sde-dpmsolver++"

model = "stabilityai/stable-diffusion-xl-base-1.0"
dpm_single = DPMSolverSinglestepScheduler.from_pretrained(model, subfolder="scheduler", solver_order=solver_order, algorithm_type=algorithm_type)
dpm_multi = DPMSolverMultistepScheduler.from_pretrained(model, subfolder="scheduler", solver_order=solver_order, algorithm_type=algorithm_type)

pipeline = StableDiffusionXLPipeline.from_pretrained(model, variant="fp16", torch_dtype=torch.float16)
pipeline.enable_vae_tiling()
pipeline = pipeline.to("cuda")

prompt = "a photo of an astronaut riding a horse on mars"

pipeline.scheduler = dpm_single
num_inference_steps = 23

image = pipeline(prompt, num_inference_steps=num_inference_steps, generator=torch.Generator().manual_seed(0)).images[0]
image.save("dpm_single.png")

pipeline.scheduler = dpm_multi

image = pipeline(prompt, num_inference_steps=num_inference_steps, generator=torch.Generator().manual_seed(0)).images[0]
image.save("dpm_multi.png")

Outputs

DPMSolverMultistepScheduler

DPMSolverSinglestepScheduler