1. A model-based distortion compensating noise reduction apparatus for speech recognition, the apparatus comprising: a speech absence probability calculator for calculating the probability distribution for absence and existence of a speech by using the sound absence and existence information for frames; a noise estimation updater for estimating a more accurate noise component by updating the variance of the clean speech and noise for each frame; a speech absence probability-based noise filter for outputting a first clean speech through the speech absence probability transmitted from the speech absence probability calculator and a first noise filter; a post probability calculator for calculating post probabilities for mixtures using a Gaussian mixture model (GMM) containing a clean speech in the first clean speech; and a final filter designer for forming a second noise filter and outputting an improved final clean speech signal using the second noise filter.