[Vuln3rat0r]

Summary

LMSDiscreteScheduler.step sets multistep order from step_index instead of the number of stored derivatives. When sampling starts at an offset index (begin_index > 0, such as img2img or inpainting with strength < 1), step_index evaluates to a high value while self.derivatives holds only the first sample. The scheduler calculates higher-order polynomial coefficients while missing derivatives are silently truncated by zip(), corrupting early denoising steps.

Bounding order by len(self.derivatives) ensures polynomial quadrature matches available history, executing order ramp-up correctly from the initial offset step.

Fixes #15108.

Testing

• Added test_step_order_with_begin_index in tests/schedulers/test_scheduler_lms.py verifying that step calculation at an offset index matches a 1st-order Euler update on step 1 and accumulates derivatives on step 2.
• Updated test_full_loop_with_noise pinned values to reflect corrected Adams-Bashforth integration when running truncated schedules.
• Verified exact reconstruction on StableDiffusionImg2ImgPipeline with an ideal predictor (relative error drops from 8.24% to 0.00%).
• Ran full test suite in tests/schedulers/test_scheduler_lms.py (33 passed).

Reviewers

@yiyixuxu @dg845