Given \(f\) a weight \(2\) newform on \(\Gamma_0(N)\) (with \(N\) square-free for simplicity), the celebrated paper by B. Gross et al. [Math. Ann. 278, 497–562 (1987; Zbl 0641.14013)], proves that the \(f\)-component of Heegner points attached to quadratic imaginary fields of discriminant \(D\) such that all primes dividing \(N\) are split in \(K\) on the Jacobian of \(X_0(N)\) all lie in the same line (as \(D\) varies) and their position in this line gives the coefficients of a modular form \(g\) of weight \(3/2\), which is in Shimura-Shintani correspondence with \(f\). Subsequently, R. E. Borcherds [Duke Math. J. 97, No. 2, 219–233 (1999; Zbl 0967.11022); correction ibid. 105, No. 1, 183–184 (2000)] generalized this result using his notion of singular theta lifting. The aim of this paper is to generalize these type of results to higher weight modular forms, replacing Heegner points with CM Heegner cycles on Kuga-Sato varieties of Shimura curves. More precisely, the author shows that Heegner cycles of codimension \(m+1\) inside Kuga-Sato type varieties of dimension \(2m+1\) are coefficients of modular forms of weight \(3/2+m\) in the appropriate quotient group (for \(m=0\), recovering the known results of Gross-Kohnen-Zagier and Borcherds). The approach taken is similar to that of Borcherds, and the results obtained are complete, clear and perfectly analogous to those by Gross-Kohnen-Zagier and Borcherds. Complementary to this work, we shall notice that for CM Heegner cycles over modular curves, H. Xue proved a similar result following the original approach of Gross-Kohnen-Zagier: see [Math. Res. Lett. 17, No. 3, 573–586 (2010; Zbl 1227.11064)].