How is Consistency for Any Point on the ODE Path Achieved in the Consistency Model?

[2019211753]

I've been exploring the Consistency model and am intrigued by its approach to maintaining consistency across the ODE path. The objective function appears to ensure that two specific points along the ODE path are consistent after being processed by f(·), and it also constrains the outcome of the boundary ε samples through f(·). However, I'm curious about how the model ensures that the result of processing any point along the ODE path by f(·) matches the ε samples.

Could anyone provide insights or explain the underlying mechanism that guarantees this level of consistency across the entire ODE path? Any further clarification or pointers to additional resources would be greatly appreciated.