The runaway diffusion coefficient, Dr, for the TJ-I tokamak has been deduced using two different methods: in the first, Dr is obtained using a steady state approach for values of the runaway confinement time tau r deduced from hard X ray (HXR) bremsstrahlung spectra; in the second, Dr is deduced from sawtooth oscillations of HXR flux, and from the soft X ray intensity, recorded simultaneously. Data have been taken in a scan with the toroidal magnetic field BT. Averaged values obtained for Dr=5-10 m2 s-1, decreasing with BT, are in both cases consistent. Assuming that magnetic turbulence is responsible for their transport, from Dr an averaged value of b/BT, the magnetic fluctuations level, can be deduced. The thermal conductivity coefficient chi e obtained using other diagnostics in TJ-I, is compared with Dr. The results are in good agreement with those obtained in TJ-I using probes, spectroscopic methods, power balance analysis and a coupled analysis for temperature and density pulses