Models to describe the transport of particles in suspension flows have progressed considerably during the last decade. In one class of models, designated as suspension balance models, the stress in the particle phase is described by a constitutive equation, and particle transport is driven by gradients in this stress. In another class of models, designated as diffusive flux models, the motion of particles within the suspension is described through a diffusion equation based on shear rate and effective viscosity gradients. Original implementations of both classes of models lacked a complete description of the anisotropy of the particle interactions. Because of this, the prediction of particle concentration in torsional flows in parallel plate and cone-and-plate geometries did not match experimental data for either class of models. In this work, the normal stress differences for the suspension balance formulation are modeled using a frame-invariant flow-aligned tensor. By analogy, the diffusive flux model is reformulated using the same flow-aligned tensor, which allows separate scaling arguments for the magnitude of the diffusive flux to be implemented in the three principal directions of flow, Using these flow-aligned tensor formulations, the main shortcomings of the original models are eliminated in a unified manner. Steady-state and transient simulations are performed on various one-dimensional and two-dimensional flows for which experimental data are available, using finite-difference and finite-element schemes, respectively. The results obtained are in good agreement with experimental data for consistent sets of empirical constants, without the need for ad hoe additional terms.