We study the effects of strong inter-particle interaction on diffraction of a Bose-Einstein condensate of ^6\mathrm{Li}_26Li2 molecules from a periodic potential created by pulses of a far detuned optical standing wave. For short pulses we observe the standard Kapitza-Dirac diffraction, with the contrast of the diffraction pattern strongly reduced for very large interactions due to interaction-dependent loss processes. For longer pulses diffraction shows the characteristic for matter waves

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... ging on an array of tubes and coherent channeling transport. We observe a slowing down of the time evolution governing the population of the momentum modes caused by the strong atom interaction. A simple physical explanation of that slowing down is the phase shift caused by the self-interaction of the forming matter wave patterns inside the standing light wave. Simple 1D mean field simulations qualitatively capture the phenomenon, however to quantitatively reproduce the experimental results the molecular scattering length has to be multiplied by factor of 4.2. In addition, two contributions to interaction-dependent degradation of the coherent diffraction patterns were identified: (i) in-trap loss of molecules during the lattice pulse, which involves dissociation of Feshbach molecules into free atoms, as confirmed by radio-frequency spectroscopy and (ii) collisions between different momentum modes during separation. This was confirmed by interferometrically recombining the diffracted momenta into the zero-momentum peak, which consequently removed the scattering background.