In this paper, we propose to apply diffusion model based posterior sampling to channel estimation (CE) problems. In the proposed solutions, we employ diffusion models to learn the score functions of the posterior channel data distribution and apply posterior sampling in the reverse process of denoising diffusion probabilistic models (DDPM) and denoising diffusion implicit models (DDIM) to recover the true channel response. We compare the performance of the proposed DDPM- and DDIM-based solutions with the linear minimum mean squared error (LMMSE) and a score matching and Langevin dynamics (SMLD)-based channel estimation solutions using clustered delay line (CDL)-C channel data. The results show that the proposed diffusion model based CE solutions are capable of achieving superior performance. In particular, compared with the DDPM-based solution, the DDIM-based solution can achieve an improved performance with a much reduced complexity.