If one had to extract the implied volatility smile from a local volatility model, one can simply use the relationship:
$\sigma^2_{imp}(t, x)T = \int_t^T \sigma^2_{loc}(s, x)ds$
with $\sigma_{loc}$ the dupire formula for local volatility for a given time $t$ and moneyness $x$.
With the same formula, one can extract the model forcast for the forward smile by replacing $t$ with a future date $S$, $t<S<T$.
Now suppose we have a mixture model that consists in a weighted sum of two local volatilities and the price is given by:
$\text{Price}_{\text{mixture}} = p \cdot \text{Price}_{\text{LocVol1}} + (1-p)\cdot \text{Price}_{\text{LocVol2}}$
How can I extract the smile from the mixture model ?