Attal and Joye (J. Funct. Anal. 247, 2007) studied a repeated-interactions model driven by particles in a faithful normal state. As they observed, the limit dynamics obey a Langevin equation driven by quantum noises which satisfy the commutation relations for a quasifree state. Inspired by this example, we describe a general framework to handle such quasifree random walks. The theory of quasifree quantum stochastic integration required to describe the limit cocycles builds on early work of Hudson and Lindsay, together with more recent work of Lindsay, Margetts and Weatherall.