Incremental adaptation techniques for speech recognition are aimed at adjusting acoustic models quickly and stably to time-variant acoustic characteristics due to temporal changes of speaker, speaking style, noise source, etc. Recently we proposed a novel incremental adaptation framework based on a macroscopic time evolution system, which models the time-variant characteristics by successively updating posterior distributions of acoustic model parameters. In this paper, we provide a unified interpretation of the proposal and the two major conventional approaches of indirect adaptation via transformation parameters (e.g. Maximum Likelihood Linear Regression (MLLR)) and direct adaptation of classifier parameters (e.g. Maximum A Posteriori (MAP)). We reveal analytically and experimentally that the proposed incremental adaptation involves both the conventional and their combinatorial approaches, and simultaneously possesses their quick and stable adaptation characteristics.