Can the Scheduler and Model be paired without any constraints?

Hello everyone,
I’ve experimented with several diffusion pipelines by replacing their schedulers with different ones. In some cases, the pipeline continues to perform well, but in others, it doesn’t. This leads me to a few questions:

  1. Is there a specific relationship between the Model and the Scheduler?
  2. Does the design of the Model impose constraints on the choice of the Scheduler?
  3. Are there any research papers or resources that discuss this topic or provide insights into understanding Schedulers better?

Thank you in advance for your time and suggestions. I greatly appreciate any guidance or references that could help clarify these questions!