Can Gas diffuse according to its partial pressure, not according to its concentration in gas mixture?
Strictly speaking, diffusion occurs due to gradients in chemical potential.
One implication of this is that sometimes diffusion can occur from lower to higher concentration.
See, for example, this nice class summary

If the total pressure is different, the transport will also occur by fast flow convection instead of diffusion until total (mechanical) pressures are equal (unless thermal transpiration effects are significant).