  We analyse the radio-to-submillimetre spectral energy distribution (SED) for
the central pseudobulge of NGC~1365 using archival data from the Atacama Large
Millimeter/submillimeter Array (ALMA) and the Very Large Array (VLA). This
analysis shows that free-free emission dominates the continuum emission at
50--120~GHz and produces about 75 per cent of the 103~GHz continuum emission.
However, the fraction of 103~GHz continuum emission originating from free-free
emission varies significantly among different subregions in the pseudobulge,
particularly for an outflow from the AGN on the eastern pseudobulge where the
synchrotron emission produces half of the 103~GHz continuum emission. Free-free
emission also dominates at 103~GHz within the central 400 pc diameter region,
but this emission is associated with the AGN rather than star formation. The
star formation rate (SFR) within the pseudobulge derived from the ALMA
free-free emission is $8.9 \pm 1.1$~M$_\odot$~yr$^{-1}$. This is comparable to
the SFR from the mid-infrared emission but higher than the SFR from the
extinction-corrected H$\alpha$ line emission, mainly because the pseudobulge is
heavily dust obscured. The 1.5 GHz emission yields a comparable SFR for the
pseudobulge but may have lower SFRs within subregions of the pseudobulge
because of the diffusion outside of these regions of the electrons producing
the synchrotron radiation. We propose that applying a correction factor of 75
per cent to the 80--110~GHz continuum emission could provide valuable estimates
of the free-free emission without performing any SED decomposition, which could
derive extinction-free SFRs within 20 per cent accuracy.
