Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusion-like transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, leading to a lateral drift in the network. An increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle lateral drift into an effective diffusion. We expect the drifting/diffusive regime transition to be generic for deformable particles.