  Given a graph $H$, a perfect $H$-factor in a graph $G$ is a collection of
vertex-disjoint copies of $H$ spanning $G$. K\"uhn and Osthus showed that the
minimum degree threshold for a graph $G$ to contain a perfect $H$-factor is
either given by $1-1/\chi(H)$ or by $1-1/\chi_{cr}(H)$ depending on certain
natural divisibility considerations. Given a graph $G$ of order $n$, a
$2$-edge-coloring of $G$ and a subgraph $G'$ of $G$, we say that $G'$ has high
discrepancy if it contains significantly (linear in $n$) more edges of one
color than the other. Balogh, Csaba, Pluh\'ar and Treglown asked for the
minimum degree threshold guaranteeing that every 2-edge-coloring of $G$ has an
$H$-factor with high discrepancy and they settled the case where $H$ is a
clique. Here we completely resolve this question by determining the minimum
degree threshold for high discrepancy of $H$-factors for every graph $H$.
