[Community] Fix Scalings for Boundary Conditions for Consistency Training Script

[dg845]

What does this PR do?

This PR fixes a bug in examples/research_projects/consistency_training/train_cm_ct_unconditional.py where the scalings_for_boundary_conditions function does not take into account sigma_min ($= \epsilon$ in the original CM paper) when calculating c_skip and c_out and thus does not satisfy the consistency model boundary condition $c_{\mbox{skip}}(\epsilon) = 1$ and $c_{\mbox{out}}(\epsilon) = 0$. The implementation should now correctly follow the parameterization given in Appendix C of the original Consistency Models paper.

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@patrickvonplaten
@sayakpaul
@patil-suraj

[sayakpaul]

Are we defaulting to reasonable values for these args?

[dg845]

sigma_min defaults to 0.002, which is the value of $\sigma_{min}$/$\epsilon$ used in the original Consistency Models paper and the improved Consistency Training paper (see Table 1 in the latter paper), which I believe is a reasonable default value.

(Note that sigma_min should be a small positive value rather than 0 to avoid numerical issues when using ODE solvers.)

[sayakpaul]

Cool! Do you think it makes sense to add this info to the README as well?

[dg845]

I have added documentation on the consistency training-specific hyperparameters to the README.

[sayakpaul]

Thank you! Just left a question.

[HuggingFaceDocBuilderDev]

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