DPM++ leaves residual noise in SDXL images, which is unexpected

[nhnt11]

Describe the bug

When using DPM++ with SDXL, there is residual noise in the result.

Upon investigation, my colleague @CodeCorrupt and I found that the final sigma was non-zero which we empirically deemed to be the culprit - i.e. when we set the final sigma to 0 artificially, the images were clean.

Reproduction

import torch
from diffusers import StableDiffusionXLPipeline
from typing import cast
from diffusers import DPMSolverMultistepScheduler, StableDiffusionPipeline, 

sdxl_model = cast(StableDiffusionXLPipeline, StableDiffusionXLPipeline.from_pretrained(
    'stabilityai/stable-diffusion-xl-base-1.0',
    torch_dtype=torch.float16,
    use_safetensors=True,
    variant="fp16",
    revision="76d28af79639c28a79fa5c6c6468febd3490a37e",
)).to('cuda')
common_config = {'beta_start': 0.00085, 'beta_end': 0.012, 'beta_schedule': 'scaled_linear'}
scheduler =  DPMSolverMultistepScheduler(**common_config)

generator = torch.Generator(device='cuda')
sdxl_model.scheduler = scheduler
generator.manual_seed(96404382)
params = {
    'prompt': ['clorful abstract background, glowing gradient waves on black background'],
    'negative_prompt': [''],
    "num_inference_steps": 40,
    "guidance_scale": 8,
    "width": 1024,
    "height": 1024
}
sdxl_res = sdxl_model(**params, generator=generator, output_type='pil')
sdxl_img = sdxl_res.images[0]
display(sdxl_img)

Output with diffusers main:

Output with a hack to set the last sigma to 0:

Logs

No response

System Info

• diffusers version: 0.22.1
• Platform: Linux-5.4.0-166-generic-x86_64-with-glibc2.31
• Python version: 3.11.5
• PyTorch version (GPU?): 2.1.0+cu121 (True)
• Huggingface_hub version: 0.17.1
• Transformers version: 4.34.0
• Accelerate version: 0.22.0
• xFormers version: not installed
• Using GPU in script?: yes
• Using distributed or parallel set-up in script?: no

Who can help?

@yiyixuxu @patrickvonplaten

[nhnt11]

Here is the code where we manually set the last sigma to 0: playgroundai@3b4a2fd

[bghira]

well that wouldn't be DPM++ then, now would it? :D it's a different scheduler you made. you probably want to rescale the betas.

[nhnt11]

@bghira Wouldn't the DPM++ implementation already technically not be DPM++ by that definition if you use the euler_at_final flag? I think there are several approximations in place to increase numerical stability of these schedulers that admittedly compromise the theory.

Note that for many other samplers, diffusers explicitly appends a 0 sigma. My understanding is that this is necessary due to the way the diffusion loop is implemented: for every loop iteration, the unet pass happens before stepping the scheduler, and so the final iteration will step the scheduler before returning the result. If the scheduler adds noise in that final step, you get a noisy result.

Opinion: I think it's a valid tradeoff to compromise the theory a bit when implementing math in finite precision computing environments :)

Disclaimer: very new at all this so just thinking out loud and learning :)

[yiyixuxu]

as discussed here you can use use_lu_lambdas and euler_at_final to avoid this issue
#5541

thanks :)

[nhnt11]

Hey @yiyixuxu, thanks for the pointer - but we're already using those. For clarity - we needed to add this hack to zero out the last sigma ON TOP of the euler_at_final option (or with Lu lambdas, or with Karras sigmas).

[spezialspezial]

It brings a bit of relief but using lu_lambdas and euler_at_final does not solve this issue. Thanks to @nhnt11 for the investigation!

[mar-muel]

@nhnt11 Interesting! But is this issue maybe not related to poor performance of DPM++ for SDXL in general?

For example, in Automatic1111 (based on the k-diffusion repo) I'm seeing similar artefacting for the DPM++ 2M scheduler:

"colorful abstract background, glowing gradient waves on black background"
Steps: 20, Sampler: DPM++ 2M, CFG scale: 7.5, Seed: 42, Size: 1024x1024, Model hash: 31e35c80fc, Model: sd_xl_base_1.0, Version: v1.7.0

But then using DPM++ 2M Karras gives

"colorful abstract background, glowing gradient waves on black background"
Steps: 20, Sampler: DPM++ 2M Karras, CFG scale: 7.5, Seed: 42, Size: 1024x1024, Model hash: 31e35c80fc, Model: sd_xl_base_1.0, Version: v1.7.0

Similar improvements can be obtained by setting use_karras_sigmas=True in diffusers.

I agree with you that use_lu_lambdas/euler_at_final are more of an extension to DPM++ and not really a "fix" for it.

EDIT: I tried this again today, and it indeed improves results!

[github-actions]

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[patrickvonplaten]

This PR should have also improved the quality: #6477