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Cosmic rays that escape their acceleration site interact with the ambientmedium and produce gamma rays as the result of inelastic proton-protoncollisions. The detection of such diffuse emission may reveal the presence ofan accelerator of cosmic rays, and also constrain the cosmic ray diffusioncoefficient in its vicinity. Preliminary results in this direction have beenobtained in the last years from studies of the gamma-ray emission frommolecular clouds located in the vicinity of supernova remnants, which are theprime candidate for cosmic ray production. Hints have been found for asignificant suppression of the diffusion coefficient with respect to theaverage one in the Galaxy. However, most of these studies rely on theassumption of isotropic diffusion, which may not be very well justified. Here,we extend this study to the case in which cosmic rays that escape anaccelerator diffuse preferentially along the magnetic field lines. As a firstapproximation, we further assume that particles are strongly magnetized andthat their transport perpendicular to the magnetic field is mainly due to thewandering of the field lines. The resulting spatial distribution of runawaycosmic rays around the accelerator is, in this case, strongly anisotropic. Anapplication of the model to the case of the supernova remnant W28 demonstrateshow the estimates of the diffusion coefficient from gamma-ray observationsstrongly depend on the assumptions made on the isotropy (or anisotropy) ofdiffusion. For higher levels of anisotropy of the diffusion, larger values ofthe diffusion coefficient are found to provide a good fit to data. Thus,detailed models for the propagation of cosmic rays are needed in order tointerpret in a correct way the gamma-ray observations.

Anisotropic CR diffusion and gamma-ray production close to supernova remnants, with an application to W28