Coordinated patterns of precisely timed action potentials (spikes) emerge in a variety of neural circuits but their dynamical origin is still not well understood. One hypothesis states that synchronous activity propagating through feed-forward chains of groups of neurons (synfire chains) may dynamically generate such spike patterns. Additionally, synfire chains offer the possibility to enable reliable signal transmission. So far, mostly densely connected chains, often with all-to-all connectivity between groups, have been theoretically and computationally studied. Yet, such prominent feed-forward structures have not been observed experimentally. Here we analytically and numerically investigate under which conditions diluted feed-forward chains may exhibit synchrony propagation. In addition to conventional linear input summation, we study the impact of non-linear, non-additive summation accounting for the effect of fast dendritic spikes. The non-linearities promote synchronous inputs to generate precisely timed spikes. We identify how non-additive coupling relaxes the conditions on connectivity such that it enables synchrony propagation at connectivities substantially lower than required for linearly coupled chains. Although the analytical treatment is based on a simple leaky integrate-and-fire neuron model, we show how to generalize our methods to biologically more detailed neuron models and verify our results by numerical simulations with, e.g., Hodgkin Huxley type neurons.