Diffusion models (DMs) have recently achieved significant success in wireless communications systems due to their denoising capabilities. The broadcast nature of wireless signals makes them susceptible not only to Gaussian noise, but also to unaware interference. This raises the question of whether DMs can effectively mitigate interference in wireless semantic communication systems. In this paper, we model the interference cancellation problem as a maximum a posteriori (MAP) problem over the joint posterior probability of the signal and interference, and theoretically prove that the solution provides excellent estimates for the signal and interference. To solve this problem, we develop an interference cancellation diffusion model (ICDM), which decomposes the joint posterior into independent prior probabilities of the signal and interference, along with the channel transition probablity. The log-gradients of these distributions at each time step are learned separately by DMs and accurately estimated through deriving. ICDM further integrates these gradients with advanced numerical iteration method, achieving accurate and rapid interference cancellation. Extensive experiments demonstrate that ICDM significantly reduces the mean square error (MSE) and enhances perceptual quality compared to schemes without ICDM. For example, on the CelebA dataset under the Rayleigh fading channel with a signal-to-noise ratio (SNR) of $20$ dB and signal to interference plus noise ratio (SINR) of 0 dB, ICDM reduces the MSE by 4.54 dB and improves the learned perceptual image patch similarity (LPIPS) by 2.47 dB.