Wall slip is ubiquitous in molten polymer flows, yet its role in polymer diffusive instability (PDI)—a unique viscoelastic instability driven by polymer stress diffusion at vanishing Reynolds numbers—remains uncharacterized. Here, we combine linear stability analysis and direct numerical simulations (DNS) to investigate PDI in viscoelastic plane Poiseuille flow under Navier slip conditions ($u=b{\tau }_{xy}$). Four distinct PDI modes are identified: PDI-1 (negative phase velocity, including antisymmetric PDI-1a and symmetric PDI-1s) and PDI-2 (positive phase velocity, including PDI-2a and PDI-2s). Wall slip exerts differential regulatory effects: it stabilizes PDI-1 (PDI-1s fully stabilizes at $b=0.003$) but triggers PDI-2 instability under small $b$. Energy balance analysis reveals PDI-1 is dominated by base-state conformation tensor contributions, while PDI-2 is driven by base-state velocity gradients. DNS validates these linear predictions, showing consistent nonlinear evolution for symmetric/antisymmetric perturbations. Our findings provide a quantitative basis for PDI control in polymer processing.

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• Flow instability
• Shear flows
• Slip boundary effects
• Transition to turbulence
• Polymers