You're absolutely right - sorry, somehow I managed to miss the explicit time parameter in your equation two, and didn't read carefully enough to see that you were restricting the discussion to resnets and normalising flows.

You might be able to make a better connection to RNNs by having the input data as a 'forcing' function in your ODE. But you probably need some regularity conditions on the input data to make sure the result is nicely behaved.