Abstract: This paper introduces a new particle-based approach to incompressible fluid simulation. We depart from previous Lagrangian methods by considering fluid particles no longer purely as material points, but also as volumetric parcels that partition the fluid domain. The fluid motion is described as a time series of well-shaped power diagrams (hence the name power particles), offering evenly spaced particles and accurate pressure computations. As a result, we circumvent the typical excess damping arising from kernel-based evaluations of internal forces or density without having recourse to auxiliary Eulerian grids. The versatility of our solver is demonstrated by the simulation of multiphase flows and free surfaces.