Let \(T\) be a positive operator from a vector lattice \(E\) with sufficiently many band projections into a Dedekind complete vector lattice \(F\). The author calls \(T\) atomic if \(T\) lies in the band generated by the lattice homomorphisms in the space \(L_r(E,F)\) of all regular operators from \(E\) into \(F\). The author calls \(T\) diffuse if it is disjoint to all atomic operators. A characterization of diffuse operators (Theorem~1.1) is as follows: \(T\) is diffuse if and only if, for each \(x\in E^+\), \(\inf\{\bigvee^{n}_{k=1}T\sigma_kx: \sum^{n}_{k=1}\sigma_kx=x\), \(\sigma_k \in {\mathcal B}(E)\}=0\), where \({\mathcal B}(E)\) is the Boolean algebra of band projections of \(E\). Various formulas for computing the diffuse and atomic components of an operator are obtained by the author. This paper has some intersections with the paper by \textit{C.~B.~Huijsmans} and \textit{B.~de~Pagter} [Compos. Math. 79, No. 3, 351-374 (1991; Zbl 0757.47023)]. For instance, Theorem~1.1 is a partial case of Theorem~2.2 in the above-mentioned paper.