Well, the "risk-neutral black-scholes framework", unfortunately, means different things to different people. If you mean the framework discussed in Black and Scholes' seminal paper, then the pdf associated to that is a log-normal density. True volatility in that framework is a constant parameter and your realized volatility pdf represents the true volatility + sampling noise (under that framework).
Hi Alan, true. Black-scholes assumes a constant (and log-normal) volatility. However, the industry has worked around this assumption, mainly either by generating the volatility itself as a stochastic variable, or creating a parametric form for the vol such that there is a one-to-one mapping between implied vol versus observed market (European Vanilla Price).
What I am merely trying to do (and feel for), is that if
a) I take the realized volatility pdf as the assumed distribution of the volatility
b) is there a way to map this assumed distribution of the volatility into the underlying variable pdf