This paper examines the importance of particle diffusion relative to advection in bed load transport. Particle diffusion is not included in existing approaches to bedload transport. Based on recent advances in the probabilistic theory of sediment transport, this paper emphasizes the part played by particle diffusion in bedload transport. The proposed model consists of the classic Saint-Venant-Exner equations supplemented by an advection-diffusion equation for particle activity (solid volume of particles in motion per unit streambed area). The model is solved numerically using standard finite-volume techniques. Our numerical simulations consider two case studies: (i) bed degradation under subcritical flow conditions and (ii) anti-dune development in supercritical flows on sloping gravel beds. These simulations show that particle diffusion plays a key role in bedload transport under non-uniform flow conditions. The diffusive sediment transport rate may be as large as the advective transport rate. When anti-dunes develop and migrate upstream, particle diffusion can create fluctuations in the sediment transport rate, whose amplitude compares with the capacity transport rate. Non-uniform flows can be characterized by a typical length, referred to as the adaptation length, which represents the distance that a particle dislodged from the bed travels before it reaches steady-state velocity. We show that the adaptation length is controlled by the particle advection velocity, particle diffusivity, and entrainment/deposition rates, but is independent of the bedform wavelength (contrary to common belief). For simulating bed degradation and anti-dune migration in gravel-bed rivers, a benchmark analysis of different bedload transport models provides evidence that those including particle diffusion perform better than classic models. (C) 2016 Elsevier Inc. All rights reserved.