It seems that your real question is: is the PFP (Price Formation Process) diffusive from intraday to weekly sampling rate?
It is a very good question since on intraday, some academics found some multifractal features into intraday returns, meaning that the PFP is not a Geometric Brownian Motion at small scales (even considering stochastic volatility).
You have for instance successful modellings of the PFP using pint processes, and especially Hawkes ones (that are not diffusive and even not Markovian): Modeling microstructure noise with mutually exciting point processes by: E. Bacry, S. Delattre, M. Hoffmann, J. F. Muzy (forthcoming in Quant. Finance).
They obtained some formula to express characteristics of the diffusive limit of such processes with respect to ones of the underlying Hawkes process, like the large scale diffusive volatility:
(with $\phi$ the kernel of the Hawks process linking its stochastic intensity with its realizations and $\mu$ is the deterministic part of its intensity).
But also more "classical" multifractal approaches: Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
by: J. F. Muzy, J. Delour, E. Bacry in Euro. Phys. Journal B, Vol. 17 (2000), pp. 537-548.
In such cases, a classical "Hurst exponent" allows zooming in or out.