Diverse observations from the 2011 Mw 9.0 Tohoku-oki earthquake pointed to large coseismic fault slip proximal to the Japan Trench. This seismic failure prompted a reevaluation of the conventional view that the outer fore-arc is generally aseismic. However, the nature of near-trench fault slip during this event remains debated, without consensus on whether slip peaked at the trench or at greater depths. Here we develop a probabilistic approach to image the spatiotemporal evolution of coseismic seafloor displacement from near-field tsunami observations. In a Bayesian framework, we sample ensembles of nonlinear models parameterized to focus on near-trench features, incorporating the uncertainty in modeling dispersive tsunami waves in addition to nominal observational errors. Our models indicate that seafloor in the region of the earthquake was broadly uplifted and tilted seaward approaching the deep-ocean trench. Over length scales of 40 km, seafloor uplift peaks at 5 $pm$ 0.6 m near the inner-outer fore-arc transition and decreases to 2 m at the trench axis over a distance of 50 km, corresponding to a seafloor tilt of 0.06 $pm$ 0.02 m/km. Over length scales of 20 km, peak uplift reaches 7 $pm$ 2 m at the similar location, but uplift at the trench is less constrained. Elastic modeling that reproduces the observed tilt requires a coseismic slip deficit at the trench. Such a deficit is effectively consistent with a metastable frictional model for the shallowest megathrust. While large shallow earthquakes in the region cannot be completely ruled out, aseismic deformation is the most likely mode for satisfying the long-term slip budget.