  We address spectral tunneling of walking spatial solitons in photorefractive
media with nonlocal diffusion of the nonlinear response and an imprinted
shallow optical lattice. In contrast to materials with local nonlinearities,
where solitons travelling across the lattice close to the Bragg angle suffer
large radiative losses, in photorefractive media with diffusion nonlinearity
resulting in self-bending solitons survive when their propagation angle
approaches and even exceeds the Bragg angle. In the spatial frequency domain
this effect can be considered as tunneling through the band of spatial
frequencies centered around the Bragg frequency where the spatial group
velocity dispersion is positive.
