fixed_large_log variance sampling returns NaNs

[Robertboy18]

Describe the finding

DDPMScheduler.step() and DDPMParallelScheduler.step() treat fixed_large_log like an ordinary variance and take its square root. _get_variance() returns log(current_beta_t) for this mode, though, so the square root is applied to a negative value and the sample becomes NaN.

The intended scale is exp(0.5 * log_variance), which is equivalent to the sqrt(variance) used by fixed_large.

I have a small fix ready for both scheduler implementations, along with CPU regression tests comparing fixed_large_log against the equivalent fixed_large sampling result. Happy to open the PR if this approach sounds right : )

Reproduction

import torch
from diffusers import DDPMScheduler, DDPMParallelScheduler

for scheduler_class in (DDPMScheduler, DDPMParallelScheduler):
    scheduler = scheduler_class(variance_type="fixed_large_log")
    sample = torch.zeros((1, 2, 2, 2))
    model_output = torch.zeros_like(sample)
    output = scheduler.step(
        model_output,
        500,
        sample,
        generator=torch.Generator().manual_seed(0),
    ).prev_sample
    print(scheduler_class.__name__, torch.isnan(output).sum().item())

Current output:

DDPMScheduler 8
DDPMParallelScheduler 8

Expected: both outputs are finite and match fixed_large when using the same generator.

System info

• Diffusers version: 0.40.0.dev0 (main at 58eb52c)
• Python: 3.12.13
• PyTorch: 2.13.0+cu130
• Platform: Linux
• GPU used by reproduction: No
• Distributed setup: No

@yiyixuxu

[lllakshit]

I reproduced this on current main for both DDPMScheduler and DDPMParallelScheduler. Opened #14571 with the exp(0.5 * log) conversion in step() plus regression tests that check samples are finite and match fixed_large at the same seed.