  We present $\nu$-Flows, a novel method for restricting the likelihood space
of neutrino kinematics in high energy collider experiments using conditional
normalizing flows and deep invertible neural networks. This method allows the
recovery of the full neutrino momentum which is usually left as a free
parameter and permits one to sample neutrino values under a learned conditional
likelihood given event observations. We demonstrate the success of $\nu$-Flows
in a case study by applying it to simulated semileptonic $t\bar{t}$ events and
show that it can lead to more accurate momentum reconstruction, particularly of
the longitudinal coordinate. We also show that this has direct benefits in a
downstream task of jet association, leading to an improvement of up to a factor
of 1.41 compared to conventional methods.
