# Forward implied vol vs Instantaneous vol

In the Discrete Stochastic Implied Volatility Model which is from the standard Heston Model, the model shows the evolution of forward implied volatilities with time.

I thought forward implied volatility for each time step is not the same as the instantaneous volatility of each time step.

Am I right?

For your reference, I attached the paper below.

http://www1.maths.ox.ac.uk/system/files/legacy/12804/StochasticImpliedVolatility.pdf