The information filter has evolved into a key tool for distributed and decentralized multisensor estimation and control. Essentially, it is an algebraical reformulation of the Kalman filter and provides estimates on the information about an uncertain state rather than on a state itself. Whereas many practicable Kalman filtering techniques for nonlinear system and sensor models have been developed, approaches towards nonlinear information filtering are still scarce and limited. In order to deal with nonlinear systems and sensors, this paper derives an approximation technique for arbitrary probability densities that provides the same distributable fusion structure as the linear information filter. The presented approach not only constitutes a nonlinear version of the information filter, but it also points the direction to a Hilbert space structure on probability densities, whose vector space operations correspond to the fusion and weighting of information.