What does this PR do?

Dealing with #8728

In the original issue, I observed that using BrownianInterval could provide a slight speedup in the diffusion loop. However, the performance gain was primarily due to not setting halfway_tree=True in the arguments, which caused the results to differ from the original implementation.

To maintain deterministic results before and after using BrownianInterval, it’s not feasible to accelerate the implementation in this way. Nonetheless, I still believe it’s worthwhile to migrate from BrownianTree to BrownianInterval since BrownianTree is noted as a legacy class in the torchsde documentation.

Test Settings

I test the numeric and image output using following script on an A100 GPU device with OS 20.04.1-Ubuntu

import torch
from diffusers.pipelines.stable_diffusion_xl import StableDiffusionXLPipeline
from diffusers.schedulers.scheduling_dpmsolver_sde import DPMSolverSDEScheduler
from PIL import Image

pipe = StableDiffusionXLPipeline.from_pretrained("stabilityai/stable-diffusion-xl-base-1.0")
scheduler = DPMSolverSDEScheduler()
pipe.scheduler = scheduler
pipe = pipe.to("cuda")

generator = torch.manual_seed(1996)
prompt = "A cat"
out = pipe(prompt, generator=generator)  # Run the model for 10 timesteps
out.images[0].save("output_tree.png")

Test Output

Using BrownianTree

Using BrownianInterval

SHA result

sha256sum output_tree.png output_interval.png
55215252f7488ee788ce2932a9f305aa9880cf6e42ed9251e0f81eeaf1ea3879  output_tree.png
55215252f7488ee788ce2932a9f305aa9880cf6e42ed9251e0f81eeaf1ea3879  output_interval.png

Before submitting

• This PR fixes a typo or improves the docs (you can dismiss the other checks if that's the case).
• Did you read the contributor guideline?
• Did you read our philosophy doc (important for complex PRs)?
• Was this discussed/approved via a GitHub issue or the forum? issue Using torchsde.BrownianInterval instead of torchsde.BrownianTree in class BatchedBrownianTree #8728
• Did you make sure to update the documentation with your changes? Here are the
  documentation guidelines, and
  here are tips on formatting docstrings.
• Did you write any new necessary tests?

Who can review?

@yiyixuxu