For quantum symmetric pairs
$(\textbf {U}, \textbf {U}^\imath )$
of Kac–Moody type, we construct
$\imath$
-canonical bases for the highest weight integrable
$\textbf U$
-modules and their tensor products regarded as
$\textbf {U}^\imath$
-modules, as well as an
$\imath$
-canonical basis for the modified form of the
$\imath$
-quantum group
$\textbf {U}^\imath$
. A key new ingredient is a family of explicit elements called
$\imath$
-divided powers, which are shown to generate the integral form of
$\dot {\textbf {U}}^\imath$
. We prove a conjecture of Balagovic–Kolb, removing a major technical assumption in the theory of quantum symmetric pairs. Even for quantum symmetric pairs of finite type, our new approach simplifies and strengthens the integrality of quasi-
$K$
-matrix and the constructions of
$\imath$
-canonical bases, by avoiding a case-by-case rank-one analysis and removing the strong constraints on the parameters in a previous work.