  Single-dish far-infrared (far-IR) and sub-millimetre (sub-mm) point source
catalogues and their connections with catalogues at other wavelengths are of
paramount importance. However, due to the large mismatch in spatial resolution,
cross-matching galaxies at different wavelengths is challenging. This work aims
to develop the next-generation deblended far-IR and sub-mm catalogues and
present the first application in the COSMOS field. Our progressive deblending
used the Bayesian probabilistic framework known as XID+. The deblending started
from the Spitzer/MIPS 24 micron data, using an initial prior list composed of
sources selected from the COSMOS2020 catalogue and radio catalogues from the
VLA and the MeerKAT surveys, based on spectral energy distribution modelling
which predicts fluxes of the known sources at the deblending wavelength. To
speed up flux prediction, we made use of a neural network-based emulator. After
deblending the 24 micron data, we proceeded to the Herschel PACS (100 & 160
micron) and SPIRE wavebands (250, 350 & 500 micron). Each time we constructed a
tailor-made prior list based on the predicted fluxes of the known sources.
Using simulated far-IR and sub-mm sky, we detailed the performance of our
deblending pipeline. After validation with simulations, we then deblended the
real observations from 24 to 500 micron and compared with blindly extracted
catalogues and previous versions of deblended catalogues. As an additional
test, we deblended the SCUBA-2 850 micron map and compared our deblended fluxes
with ALMA measurements, which demonstrates a higher level of flux accuracy
compared to previous results.We publicly release our XID+ deblended point
source catalogues. These deblended long-wavelength data are crucial for studies
such as deriving the fraction of dust-obscured star formation and better
separation of quiescent galaxies from dusty star-forming galaxies.
