The linear Schrodinger equation does not predict that macroscopic bodies should be located at one place only, or that:, the outcome of a measurement:, shoud be unique. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values to emerge during measurements; many other interpretations have also been proposed. Here, in the same spirit as the GRW and CSL theories, we modify the Schrodinger equation in a way that efficiently cancels macroscopic density fluctuations in space. Nevertheless, we do not assume a stochastic dynamics as in GRW or CSL tI eories. Instead, we propose a deterministic evolution that includes an attraction terni towards the averaged density in space of the de Broglie-Bohm position of particles, and show that this is sufficient to ensure macroscopic uniqueness and compatibility with the Born rule. The state vector can then be seen as directly related to physical reality.