  We derive a general resummation formula for transverse-momentum distributions
of hard processes at the leading logarithmic level in the high-energy limit, to
all orders in the strong coupling. Our result is based on a suitable
generalization of high-energy factorization theorems, whereby all-order
resummation is reduced to the determination of the Born-level process but with
incoming off-shell gluons. We validate our formula by applying it to Higgs
production in gluon fusion in the infinite top mass limit. We check our result
up to next-to-leading order by comparison to the high energy limit of the exact
expression and to next-to-next-to leading by comparison to NNLL order trasverse
momentum (Sudakov) resummation, and we predict the high-energy behaviour at
next$^3$-to-leading order. We also show that the structure of the result in the
small transverse momentum limit agrees to all orders with general constraints
from Sudakov resummation.
